Finite Group Databasebeta

← C4×#72213266 #72269133

Subgroups — C4×#72213266 #72269133

Order 10368.

5238 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 5238 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×(C3⋊D3)⋊(C22⋊A4)C311yesmaximal, characteristic, complemented
2C22×C4×(C3⋊D3)⋊A4C312yesmaximal, complemented
3C4×C3⋊D3×C22⋊A4C311yesmaximal, characteristic, complemented
4C4×D3×A42—31nomaximal
5C4×A4×(C3⋊D3)⋊C3—42nomaximal
6#72242698C211yesmaximal, characteristic, complemented
7C4×(C22⋊A4)⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
8C2×#72213266C211yesmaximal, characteristic
9C2×(C22⋊A4)⋊H(3,𝔽3)C2211yescharacteristic
10#72213266C412yesdirect product factor
11C2×C3⋊D3×C22⋊A4C2×C311yescharacteristic
12C2×D3×A42—31no—
13C32×C4×C22⋊A4C2×C311yescharacteristic, complemented
14C3⋊Dic3×C22⋊A4C2×C311yescharacteristic, complemented
15C3×C4×A42—21no—
16C3×C4×A42D311yescharacteristic, complemented
17Dic3×A42—31no—
18C2×(C3⋊D3)⋊(C22⋊A4)C2×C311yescharacteristic
19C23×(C3⋊D3)⋊A4C2×C312yes—
20C4×C32⋊(C22⋊A4)C2×C311yescharacteristic, complemented
21C22×C4×C22⋊H(3,𝔽3)C2×C312yescomplemented
22(C3⋊Dic3)⋊(C22⋊A4)C2×C311yescharacteristic, complemented
23C22×(C3⋊Dic3)⋊A4C2×C312yescomplemented
24C2×C4×(C3⋊D3)⋊A4—32no—
25C2×C4×(C3⋊D3)⋊A4—32no—
26C2×C4×(C3⋊D3)⋊A4—32no—
27C2×C4×(C3⋊D3)⋊A4—32no—
28C4×(C3×A4)⋊A4—21no—
29C4×(C3×A4)⋊A4—22no—
30C2×A4×(C3⋊D3)⋊C3—42no—
31(C22⋊A4)⋊H(3,𝔽3)C2×C411yescharacteristic, complemented
32C4×A4×H(3,𝔽3)—42no—
33A4×(C3⋊Dic3)⋊C3—42no—
34C4×D3×C22⋊A4—31no—
35C4×D3×C22⋊A4—31no—
36C4×D3×C22⋊A4—91no—
37C22×C4×D3×A4—32no—
38C2×C4×A42—91no—
39C24×C4×C3⋊D3C3211yescharacteristic, complemented
40C2×C32×C22⋊A4C22×C311yescharacteristic
41C3⋊D3×C22⋊A4C3×C412yescomplemented
42C2×C3×A42—21no—
43C2×C3×A42C2×D311yescharacteristic
44D3×A42—32no—
45C4×A4×C3⋊D3—42no—
46C4×A4×C3⋊D3—121no—
47C3×C4×D3×A4—122no—
48C2×C32⋊(C22⋊A4)C22×C311yescharacteristic
49C23×C22⋊H(3,𝔽3)C22×C312yes—
50(C3⋊D3)⋊(C22⋊A4)C3×C412yescomplemented
51C22×(C3⋊D3)⋊A4—32no—
52C22×(C3⋊D3)⋊A4—32no—
53C22×(C3⋊D3)⋊A4—34no—
54C22×(C3⋊D3)⋊A4C3×C414yescomplemented
55C2×(C3×A4)⋊A4—21no—
56C2×(C3×A4)⋊A4—22no—
57C22×C4×(C3⋊D3)⋊C3—42no—
58C2×C4×C22⋊H(3,𝔽3)—32no—
59C2×C4×C22⋊H(3,𝔽3)—32no—
60C2×(C3⋊Dic3)⋊A4—32no—
61C2×(C3⋊Dic3)⋊A4—32no—
62C4×(C3⋊D3)⋊A4—34no—
63C4×(C3⋊D3)⋊A4—32no—
64C4×(C3⋊D3)⋊A4—32no—
65C4×(C3⋊D3)⋊A4—32no—
66C4×(C3⋊D3)⋊A4—42no—
67C4×(C3⋊D3)⋊A4—121no—
68C4×(C3⋊D3)⋊A4A412yescomplemented
69C2×A4×H(3,𝔽3)—42no—
70A4×(C3⋊D3)⋊C3—44no—
71C3×C4×(C3⋊D3)⋊C3—161no—
72C25×C3⋊D3C2×C3211yescharacteristic
73C2×D3×C22⋊A4—31no—
74C2×D3×C22⋊A4—31no—
75C2×D3×C22⋊A4—91no—
76C23×D3×A4—32no—
77C22×A42—91no—
78C24×C32×C4C2×C3211yescharacteristic, complemented
79C24×C3⋊Dic3C2×C3211yescharacteristic, complemented
80C23×C4×C3⋊D3—32no—
81C23×C4×C3⋊D3—32no—
82C23×C4×C3⋊D3—32no—
83C23×C4×C3⋊D3—32no—
84C23×C4×C3⋊D3—91no—
85C23×C4×C3⋊D3—91no—
86C23×C4×C3⋊D3—91no—
87C23×C4×C3⋊D3—91no—
88C3×C4×C22⋊A4—21no—
89C3×C4×C22⋊A4—21no—
90C3×C4×C22⋊A4—31no—
91C3×C4×C22⋊A4—61no—
92C3×C4×C22⋊A4C3×D311yescharacteristic
93C3×C4×C22⋊A4C3×D311yescharacteristic, complemented
94C22×C3×C4×A4—22no—
95C22×C3×C4×A4C3×D312yescomplemented
96Dic3×C22⋊A4—31no—
97Dic3×C22⋊A4—31no—
98Dic3×C22⋊A4—91no—
99C22×Dic3×A4—32no—
100C2×C4×D3×A4—92no—
101C2×C4×D3×A4—92no—
102C2×C4×D3×A4—92no—
103C2×C4×D3×A4—92no—
104C4×A42—31no—
105C4×A42—61no—
106C4×A42—62no—
107C4×A42—61no—
108C4×A42—91no—
109C32×C22⋊A4C2×C3×C411yescharacteristic, complemented
110C2×A4×C3⋊D3—42no—
111C2×A4×C3⋊D3—121no—
112C2×C3×D3×A4—122no—
113C3×A42—21no—
114C3×A42C4×D311yescharacteristic, complemented
115C32×C4×A4—42no—
116C32×C4×A4—42no—
117C32×C4×A4—82no—
118C32×C4×A4—121no—
119A4×C3⋊Dic3—42no—
120A4×C3⋊Dic3—121no—
121C3×Dic3×A4—122no—
122C23×(C3⋊D3)⋊C3—42no—
123C32⋊(C22⋊A4)C2×C3×C411yescharacteristic, complemented
124C22×C22⋊H(3,𝔽3)—32no—
125C22×C22⋊H(3,𝔽3)—32no—
126C22×C22⋊H(3,𝔽3)C2×C3×C412yescomplemented
127C2×(C3⋊D3)⋊A4—34no—
128C2×(C3⋊D3)⋊A4—32no—
129C2×(C3⋊D3)⋊A4—34no—
130C2×(C3⋊D3)⋊A4—34no—
131C2×(C3⋊D3)⋊A4—34no—
132C2×(C3⋊D3)⋊A4—42no—
133C2×(C3⋊D3)⋊A4—121no—
134C2×(C3⋊D3)⋊A4C2×A412yes—
135(C3×A4)⋊A4—21no—
136(C3×A4)⋊A4—22no—
137C22×C4×H(3,𝔽3)—42no—
138C22×(C3⋊Dic3)⋊C3—42no—
139C2×C4×(C3⋊D3)⋊C3—122no—
140C2×C4×(C3⋊D3)⋊C3—122no—
141C2×C4×(C3⋊D3)⋊C3—122no—
142C2×C4×(C3⋊D3)⋊C3—122no—
143C4×C22⋊H(3,𝔽3)—32no—
144C4×C22⋊H(3,𝔽3)—42no—
145C4×C22⋊H(3,𝔽3)—82no—
146C4×C22⋊H(3,𝔽3)—82no—
147C4×C22⋊H(3,𝔽3)—82no—
148C4×C22⋊H(3,𝔽3)—121no—
149C4×C22⋊H(3,𝔽3)C2×A412yescomplemented
150(C3⋊Dic3)⋊A4—32no—
151(C3⋊Dic3)⋊A4—42no—
152(C3⋊Dic3)⋊A4—121no—
153(C3⋊Dic3)⋊A4C2×A412yescomplemented
154C24×C4×D3—31no—
155C24×C4×D3—91no—
156C2×C4×C22⋊A4—91no—
157C2×C4×C22⋊A4—91no—
158C23×C4×A4—92no—
159C2×C3×(C3⋊D3)⋊C3—161no—
160A4×H(3,𝔽3)—42no—
161C3×C4×H(3,𝔽3)—161no—
162C3×(C3⋊Dic3)⋊C3—161no—
163C25×C32C22×C3211yescharacteristic
164C24×C3⋊D3—32no—
165C24×C3⋊D3—32no—
166C24×C3⋊D3—34no—
167C24×C3⋊D3—91no—
168C24×C3⋊D3—91no—
169C24×C3⋊D3—92no—
170C24×C3⋊D3C32×C412yescomplemented
171C2×C3×C22⋊A4—21no—
172C2×C3×C22⋊A4—21no—
173C2×C3×C22⋊A4—31no—
174C2×C3×C22⋊A4—61no—
175C2×C3×C22⋊A4C2×C3×D311yescharacteristic
176C2×C3×C22⋊A4C2×C3×D311yescharacteristic
177C23×C3×A4—22no—
178C23×C3×A4C2×C3×D312yes—
179D3×C22⋊A4—32no—
180D3×C22⋊A4—32no—
181D3×C22⋊A4—92no—
182C22×D3×A4—34no—
183C22×D3×A4—92no—
184C22×D3×A4—92no—
185C22×D3×A4—94no—
186C2×A42—31no—
187C2×A42—61no—
188C2×A42—62no—
189C2×A42—61no—
190C2×A42—92no—
191C23×C32×C4—32no—
192C23×C32×C4—32no—
193C23×C32×C4—91no—
194C23×C32×C4—91no—
195C23×C3⋊Dic3—32no—
196C23×C3⋊Dic3—32no—
197C23×C3⋊Dic3—91no—
198C23×C3⋊Dic3—91no—
199C22×C4×C3⋊D3—31no—
200C22×C4×C3⋊D3—34no—
201C22×C4×C3⋊D3—31no—
202C22×C4×C3⋊D3—32no—
203C22×C4×C3⋊D3—32no—
204C22×C4×C3⋊D3—32no—
205C22×C4×C3⋊D3—91no—
206C22×C4×C3⋊D3—91no—
207C22×C4×C3⋊D3—91no—
208C22×C4×C3⋊D3—92no—
209C22×C4×C3⋊D3—92no—
210C22×C4×C3⋊D3—92no—
211C22×C4×C3⋊D3—92no—
212C22×C4×C3⋊D3—92no—
213C22×C4×C3⋊D3—92no—
214C22×C4×C3⋊D3—92no—
215C22×C4×C3⋊D3—91no—
216C22×C4×C3⋊D3—91no—
217C22×C4×C3⋊D3—91no—
218C22×C4×C3⋊D3—91no—
219C22×C4×C3⋊D3—92no—
220C22×C4×C3⋊D3—92no—
221C22×C4×C3⋊D3—94no—
222C22×C4×C3⋊D3—94no—
223C22×C4×C3⋊D3—94no—
224C22×C4×C3⋊D3—94no—
225C22×C4×C3⋊D3—94no—
226C22×C4×C3⋊D3—94no—
227C22×C4×C3⋊D3—91no—
228C22×C4×C3⋊D3—92no—
229C22×C4×C3⋊D3—92no—
230C22×C4×C3⋊D3—92no—
231C22×C4×C3⋊D3—91no—
232C22×C4×C3⋊D3—91no—
233C22×C4×C3⋊D3C3×A412yescomplemented
234C22×C3×C4×D3—122no—
235C2×C3×C4×A4—32no—
236C2×C3×C4×A4—32no—
237C2×C3×C4×A4—62no—
238C2×C3×C4×A4—62no—
239C2×C3×C4×A4—362no—
240C2×Dic3×A4—92no—
241C2×Dic3×A4—92no—
242C4×D3×A4—32no—
243C4×D3×A4—92no—
244C4×D3×A4—92no—
245C4×D3×A4—94no—
246C4×D3×A4—92no—
247C4×D3×A4—122no—
248C4×D3×A4—122no—
249C4×D3×A4—361no—
250C4×D3×A4—361no—
251C4×D3×A4—362no—
252C4×D3×A4—363no—
253C2×C32×A4—42no—
254C2×C32×A4—42no—
255C2×C32×A4—82no—
256C2×C32×A4—121no—
257A4×C3⋊D3—44no—
258A4×C3⋊D3—122no—
259C3×D3×A4—124no—
260C3×C4×C3⋊D3—161no—
261C32×C4×D3—481no—
262C23×H(3,𝔽3)—42no—
263C22×(C3⋊D3)⋊C3—44no—
264C22×(C3⋊D3)⋊C3—122no—
265C22×(C3⋊D3)⋊C3—124no—
266C22×(C3⋊D3)⋊C3—122no—
267C2×C22⋊H(3,𝔽3)—32no—
268C2×C22⋊H(3,𝔽3)—32no—
269C2×C22⋊H(3,𝔽3)—42no—
270C2×C22⋊H(3,𝔽3)—82no—
271C2×C22⋊H(3,𝔽3)—82no—
272C2×C22⋊H(3,𝔽3)—82no—
273C2×C22⋊H(3,𝔽3)—121no—
274C2×C22⋊H(3,𝔽3)C22×A412yes—
275(C3⋊D3)⋊A4—34no—
276(C3⋊D3)⋊A4—44no—
277(C3⋊D3)⋊A4—122no—
278(C3⋊D3)⋊A4C4×A414yescomplemented
279C2×C4×H(3,𝔽3)—122no—
280C2×C4×H(3,𝔽3)—122no—
281C2×(C3⋊Dic3)⋊C3—122no—
282C2×(C3⋊Dic3)⋊C3—122no—
283C4×(C3⋊D3)⋊C3—42no—
284C4×(C3⋊D3)⋊C3—122no—
285C4×(C3⋊D3)⋊C3—122no—
286C4×(C3⋊D3)⋊C3—122no—
287C4×(C3⋊D3)⋊C3—124no—
288C4×(C3⋊D3)⋊C3—161no—
289C25×D3—31no—
290C25×D3—91no—
291C22×C22⋊A4—91no—
292C22×C22⋊A4—91no—
293C24×A4—92no—
294C24×C3×C4—31no—
295C24×C3×C4C32×D311yescharacteristic
296C24×Dic3—31no—
297C24×Dic3—91no—
298C23×C4×D3—92no—
299C23×C4×D3—92no—
300C23×C4×D3—92no—
301C23×C4×D3—92no—
302C23×C4×D3—272no—
303C23×C4×D3—272no—
304C23×C4×D3—272no—
305C23×C4×D3—272no—
306C23×C4×D3—271no—
307C23×C4×D3—273no—
308C23×C4×D3—273no—
309C23×C4×D3—273no—
310C23×C4×D3—273no—
311C23×C4×D3—271no—
312C23×C4×D3—271no—
313C23×C4×D3—271no—
314C4×C22⋊A4—21no—
315C4×C22⋊A4—31no—
316C4×C22⋊A4—61no—
317C4×C22⋊A4—61no—
318C4×C22⋊A4—91no—
319C4×C22⋊A4—91no—
320C4×C22⋊A4(C3⋊D3)⋊C311yescharacteristic, complemented
321C22×C4×A4—32no—
322C22×C4×A4—62no—
323C22×C4×A4—92no—
324C22×C4×A4—272no—
325C22×C4×A4—272no—
326C22×C4×A4—272no—
327C22×C4×A4—272no—
328C2×C3×H(3,𝔽3)—161no—
329C3×(C3⋊D3)⋊C3—162no—
330C24×C32—32no—
331C24×C32—32no—
332C24×C32—91no—
333C24×C32—91no—
334C24×C32C2×C32×C411yescharacteristic, complemented
335C23×C3⋊D3—31no—
336C23×C3⋊D3—34no—
337C23×C3⋊D3—31no—
338C23×C3⋊D3—32no—
339C23×C3⋊D3—34no—
340C23×C3⋊D3—34no—
341C23×C3⋊D3—34no—
342C23×C3⋊D3—91no—
343C23×C3⋊D3—92no—
344C23×C3⋊D3—92no—
345C23×C3⋊D3—92no—
346C23×C3⋊D3—92no—
347C23×C3⋊D3—92no—
348C23×C3⋊D3—92no—
349C23×C3⋊D3—94no—
350C23×C3⋊D3—94no—
351C23×C3⋊D3—91no—
352C23×C3⋊D3—91no—
353C23×C3⋊D3—92no—
354C23×C3⋊D3—92no—
355C23×C3⋊D3—94no—
356C23×C3⋊D3—98no—
357C23×C3⋊D3—98no—
358C23×C3⋊D3—94no—
359C23×C3⋊D3—91no—
360C23×C3⋊D3—92no—
361C23×C3⋊D3—92no—
362C23×C3⋊D3—94no—
363C23×C3⋊D3—92no—
364C23×C3⋊D3C2×C3×A412yes—
365C23×C3×D3—122no—
366C3×C22⋊A4—21no—
367C3×C22⋊A4—21no—
368C3×C22⋊A4—31no—
369C3×C22⋊A4—61no—
370C3×C22⋊A4C3×C4×D311yescharacteristic
371C3×C22⋊A4C3×C4×D311yescharacteristic, complemented
372C22×C3×A4—22no—
373C22×C3×A4—32no—
374C22×C3×A4—32no—
375C22×C3×A4—62no—
376C22×C3×A4—62no—
377C22×C3×A4—362no—
378C22×C3×A4C3×C4×D312yescomplemented
379C2×D3×A4—32no—
380C2×D3×A4—94no—
381C2×D3×A4—94no—
382C2×D3×A4—94no—
383C2×D3×A4—92no—
384C2×D3×A4—94no—
385C2×D3×A4—122no—
386C2×D3×A4—122no—
387C2×D3×A4—361no—
388C2×D3×A4—361no—
389C2×D3×A4—362no—
390C2×D3×A4—363no—
391A42—31no—
392A42—61no—
393A42—62no—
394A42—61no—
395C22×C32×C4—31no—
396C22×C32×C4—31no—
397C22×C32×C4—32no—
398C22×C32×C4—42no—
399C22×C32×C4—82no—
400C22×C32×C4—91no—
401C22×C32×C4—92no—
402C22×C32×C4—92no—
403C22×C32×C4—92no—
404C22×C32×C4—91no—
405C22×C32×C4—91no—
406C22×C32×C4—94no—
407C22×C32×C4—91no—
408C22×C32×C4C2×C3×A412yescomplemented
409C22×C3⋊Dic3—31no—
410C22×C3⋊Dic3—31no—
411C22×C3⋊Dic3—32no—
412C22×C3⋊Dic3—91no—
413C22×C3⋊Dic3—92no—
414C22×C3⋊Dic3—92no—
415C22×C3⋊Dic3—92no—
416C22×C3⋊Dic3—91no—
417C22×C3⋊Dic3—91no—
418C22×C3⋊Dic3—94no—
419C22×C3⋊Dic3—91no—
420C22×C3⋊Dic3C2×C3×A412yescomplemented
421C2×C4×C3⋊D3—32no—
422C2×C4×C3⋊D3—32no—
423C2×C4×C3⋊D3—32no—
424C2×C4×C3⋊D3—32no—
425C2×C4×C3⋊D3—91no—
426C2×C4×C3⋊D3—91no—
427C2×C4×C3⋊D3—91no—
428C2×C4×C3⋊D3—92no—
429C2×C4×C3⋊D3—92no—
430C2×C4×C3⋊D3—92no—
431C2×C4×C3⋊D3—94no—
432C2×C4×C3⋊D3—94no—
433C2×C4×C3⋊D3—94no—
434C2×C4×C3⋊D3—94no—
435C2×C4×C3⋊D3—94no—
436C2×C4×C3⋊D3—94no—
437C2×C4×C3⋊D3—94no—
438C2×C4×C3⋊D3—94no—
439C2×C4×C3⋊D3—94no—
440C2×C4×C3⋊D3—94no—
441C2×C4×C3⋊D3—94no—
442C2×C4×C3⋊D3—91no—
443C2×C4×C3⋊D3—91no—
444C2×C4×C3⋊D3—94no—
445C2×C4×C3⋊D3—94no—
446C2×C4×C3⋊D3—91no—
447C2×C4×C3⋊D3—91no—
448C2×C4×C3⋊D3—91no—
449C2×C4×C3⋊D3—91no—
450C2×C4×C3⋊D3—91no—
451C2×C4×C3⋊D3—92no—
452C2×C4×C3⋊D3—92no—
453C2×C4×C3⋊D3—92no—
454C2×C4×C3⋊D3—92no—
455C2×C4×C3⋊D3—92no—
456C2×C4×C3⋊D3—92no—
457C2×C4×C3⋊D3—92no—
458C2×C4×C3⋊D3—92no—
459C2×C4×C3⋊D3—92no—
460C2×C4×C3⋊D3—94no—
461C2×C4×C3⋊D3—94no—
462C2×C4×C3⋊D3—94no—
463C2×C4×C3⋊D3—91no—
464C2×C4×C3⋊D3—91no—
465C2×C4×C3⋊D3—91no—
466C2×C4×C3⋊D3—91no—
467C2×C4×C3⋊D3—91no—
468C2×C4×C3⋊D3—91no—
469C22×C3×Dic3—122no—
470C2×C3×C4×D3—362no—
471C2×C3×C4×D3—362no—
472C2×C3×C4×D3—362no—
473C2×C3×C4×D3—362no—
474C3×C4×A4—22no—
475C3×C4×A4—32no—
476C3×C4×A4—42no—
477C3×C4×A4—42no—
478C3×C4×A4—62no—
479C3×C4×A4—82no—
480C3×C4×A4—82no—
481C3×C4×A4—121no—
482C3×C4×A4—121no—
483C3×C4×A4—122no—
484C3×C4×A4—122no—
485C3×C4×A4—123no—
486C3×C4×A4—241no—
487C3×C4×A4—241no—
488C3×C4×A4—242no—
489C3×C4×A4—242no—
490C3×C4×A4—244no—
491C3×C4×A4—242no—
492C3×C4×A4—243no—
493C3×C4×A4—362no—
494C3×C4×A4D3×A412yescomplemented
495Dic3×A4—32no—
496Dic3×A4—92no—
497Dic3×A4—122no—
498Dic3×A4—122no—
499Dic3×A4—361no—
500Dic3×A4—361no—
501Dic3×A4—362no—
502Dic3×A4—363no—
503C25×C4—91noSylow
504C2×C3×C3⋊D3—161no—
505C2×C32×D3—481no—
506C32×A4—42no—
507C32×A4—42no—
508C32×A4—82no—
509C32×A4—121no—
510C33×C4—161no—
511C33×C4—161no—
512C33×C4—321no—
513C3×C3⋊Dic3—161no—
514C32×Dic3—481no—
515C22×H(3,𝔽3)—42no—
516C22×H(3,𝔽3)—122no—
517C22×H(3,𝔽3)—122no—
518C2×(C3⋊D3)⋊C3—42no—
519C2×(C3⋊D3)⋊C3—124no—
520C2×(C3⋊D3)⋊C3—124no—
521C2×(C3⋊D3)⋊C3—122no—
522C2×(C3⋊D3)⋊C3—124no—
523C2×(C3⋊D3)⋊C3—124no—
524C2×(C3⋊D3)⋊C3—161no—
525C22⋊H(3,𝔽3)—42no—
526C22⋊H(3,𝔽3)—82no—
527C22⋊H(3,𝔽3)—82no—
528C22⋊H(3,𝔽3)—82no—
529C22⋊H(3,𝔽3)—121no—
530C22⋊H(3,𝔽3)C2×C4×A412yescomplemented
531C4×H(3,𝔽3)—42no—
532C4×H(3,𝔽3)—122no—
533C4×H(3,𝔽3)—161no—
534C4×H(3,𝔽3)—322no—
535C4×H(3,𝔽3)—321no—
536(C3⋊Dic3)⋊C3—42no—
537(C3⋊Dic3)⋊C3—122no—
538(C3⋊Dic3)⋊C3—161no—
539C25×C3—31no—
540C25×C3C2×C32×D311yescharacteristic
541C24×D3—32no—
542C24×D3—92no—
543C24×D3—92no—
544C24×D3—92no—
545C24×D3—94no—
546C24×D3—272no—
547C24×D3—272no—
548C24×D3—274no—
549C24×D3—271no—
550C24×D3—273no—
551C24×D3—273no—
552C24×D3—276no—
553C24×D3—271no—
554C24×D3—272no—
555C2×C22⋊A4—21no—
556C2×C22⋊A4—31no—
557C2×C22⋊A4—61no—
558C2×C22⋊A4—61no—
559C2×C22⋊A4—92no—
560C2×C22⋊A4—92no—
561C2×C22⋊A4C2×(C3⋊D3)⋊C311yescharacteristic
562C23×A4—32no—
563C23×A4—62no—
564C23×A4—94no—
565C23×A4—272no—
566C23×A4—272no—
567C23×A4—274no—
568C23×C3×C4—32no—
569C23×C3×C4—32no—
570C23×C3×C4—92no—
571C23×C3×C4—92no—
572C23×C3×C4—91no—
573C23×C3×C4—93no—
574C23×C3×C4—93no—
575C23×C3×C4—91no—
576C23×C3×C4—362no—
577C23×Dic3—92no—
578C23×Dic3—92no—
579C23×Dic3—272no—
580C23×Dic3—272no—
581C23×Dic3—271no—
582C23×Dic3—273no—
583C23×Dic3—273no—
584C23×Dic3—271no—
585C22×C4×D3—32no—
586C22×C4×D3—92no—
587C22×C4×D3—92no—
588C22×C4×D3—92no—
589C22×C4×D3—94no—
590C22×C4×D3—91no—
591C22×C4×D3—93no—
592C22×C4×D3—91no—
593C22×C4×D3—92no—
594C22×C4×D3—272no—
595C22×C4×D3—272no—
596C22×C4×D3—272no—
597C22×C4×D3—274no—
598C22×C4×D3—271no—
599C22×C4×D3—271no—
600C22×C4×D3—272no—
601C22×C4×D3—272no—
602C22×C4×D3—272no—
603C22×C4×D3—272no—
604C22×C4×D3—272no—
605C22×C4×D3—272no—
606C22×C4×D3—272no—
607C22×C4×D3—271no—
608C22×C4×D3—271no—
609C22×C4×D3—273no—
610C22×C4×D3—271no—
611C22×C4×D3—271no—
612C22×C4×D3—273no—
613C22×C4×D3—271no—
614C22×C4×D3—271no—
615C22×C4×D3—273no—
616C22×C4×D3—273no—
617C22×C4×D3—273no—
618C22×C4×D3—273no—
619C22×C4×D3—276no—
620C22×C4×D3—276no—
621C22×C4×D3—276no—
622C22×C4×D3—276no—
623C22×C4×D3—276no—
624C22×C4×D3—276no—
625C22×C4×D3—276no—
626C22×C4×D3—273no—
627C22×C4×D3—272no—
628C22×C4×D3—272no—
629C22×C4×D3—276no—
630C22×C4×D3—276no—
631C22×C4×D3—2712no—
632C22×C4×D3—2712no—
633C22×C4×D3—2712no—
634C22×C4×D3—2712no—
635C22×C4×D3—2712no—
636C22×C4×D3—2712no—
637C22×C4×D3—276no—
638C22×C4×D3—276no—
639C22×C4×D3—276no—
640C22×C4×D3—273no—
641C22×C4×D3—273no—
642C22×C4×D3—273no—
643C22×C4×D3—274no—
644C22×C4×D3—274no—
645C22×C4×D3—274no—
646C22×C4×D3—274no—
647C22×C4×D3—274no—
648C22×C4×D3—274no—
649C22×C4×D3—272no—
650C22×C4×D3—272no—
651C22×C4×D3—272no—
652C22×C4×D3—271no—
653C22×C4×D3—271no—
654C22×C4×D3—271no—
655C2×C4×A4—92no—
656C2×C4×A4—92no—
657C2×C4×A4—92no—
658C2×C4×A4—182no—
659C2×C4×A4—182no—
660C2×C4×A4—272no—
661C2×C4×A4—272no—
662C2×C4×A4—272no—
663C2×C4×A4—272no—
664C2×C4×A4—274no—
665C2×C4×A4—272no—
666C2×C4×A4—362no—
667C2×C4×A4—362no—
668C2×C4×A4—1081no—
669C2×C4×A4—1081no—
670C3×H(3,𝔽3)—161noSylow
671C23×C32—31no—
672C23×C32—31no—
673C23×C32—32no—
674C23×C32—32no—
675C23×C32—42no—
676C23×C32—82no—
677C23×C32—91no—
678C23×C32—91no—
679C23×C32—92no—
680C23×C32—92no—
681C23×C32—92no—
682C23×C32—91no—
683C23×C32—91no—
684C23×C32—91no—
685C23×C32—94no—
686C23×C32C22×C3×A412yes—
687C22×C3⋊D3—32no—
688C22×C3⋊D3—32no—
689C22×C3⋊D3—34no—
690C22×C3⋊D3—32no—
691C22×C3⋊D3—32no—
692C22×C3⋊D3—34no—
693C22×C3⋊D3—92no—
694C22×C3⋊D3—94no—
695C22×C3⋊D3—92no—
696C22×C3⋊D3—91no—
697C22×C3⋊D3—92no—
698C22×C3⋊D3—94no—
699C22×C3⋊D3—98no—
700C22×C3⋊D3—94no—
701C22×C3⋊D3—98no—
702C22×C3⋊D3—94no—
703C22×C3⋊D3—94no—
704C22×C3⋊D3—94no—
705C22×C3⋊D3—94no—
706C22×C3⋊D3—94no—
707C22×C3⋊D3—94no—
708C22×C3⋊D3—94no—
709C22×C3⋊D3—92no—
710C22×C3⋊D3—92no—
711C22×C3⋊D3—94no—
712C22×C3⋊D3—94no—
713C22×C3⋊D3—92no—
714C22×C3⋊D3—92no—
715C22×C3⋊D3—98no—
716C22×C3⋊D3—98no—
717C22×C3⋊D3—92no—
718C22×C3⋊D3—91no—
719C22×C3⋊D3—94no—
720C22×C3⋊D3—92no—
721C22×C3⋊D3—98no—
722C22×C3⋊D3—98no—
723C22×C3⋊D3—94no—
724C22×C3⋊D3—92no—
725C22×C3⋊D3—92no—
726C22×C3⋊D3—91no—
727C22×C3⋊D3—91no—
728C22×C3⋊D3—92no—
729C22×C3⋊D3C3×C4×A414yescomplemented
730C22×C3×D3—124no—
731C22×C3×D3—362no—
732C22×C3×D3—364no—
733C22×C3×D3—362no—
734C2×C3×A4—22no—
735C2×C3×A4—32no—
736C2×C3×A4—32no—
737C2×C3×A4—42no—
738C2×C3×A4—42no—
739C2×C3×A4—62no—
740C2×C3×A4—62no—
741C2×C3×A4—82no—
742C2×C3×A4—82no—
743C2×C3×A4—121no—
744C2×C3×A4—121no—
745C2×C3×A4—122no—
746C2×C3×A4—122no—
747C2×C3×A4—123no—
748C2×C3×A4—241no—
749C2×C3×A4—241no—
750C2×C3×A4—242no—
751C2×C3×A4—242no—
752C2×C3×A4—244no—
753C2×C3×A4—242no—
754C2×C3×A4—243no—
755C2×C3×A4—364no—
756C2×C3×A4C2×D3×A412yes—
757D3×A4—34no—
758D3×A4—94no—
759D3×A4—124no—
760D3×A4—124no—
761D3×A4—362no—
762D3×A4—362no—
763D3×A4—364no—
764D3×A4—366no—
765C2×C32×C4—32no—
766C2×C32×C4—32no—
767C2×C32×C4—91no—
768C2×C32×C4—92no—
769C2×C32×C4—94no—
770C2×C32×C4—91no—
771C2×C32×C4—92no—
772C2×C32×C4—91no—
773C2×C32×C4—91no—
774C2×C32×C4—122no—
775C2×C32×C4—122no—
776C2×C32×C4—242no—
777C2×C32×C4—242no—
778C2×C32×C4—1441no—
779C2×C3⋊Dic3—32no—
780C2×C3⋊Dic3—32no—
781C2×C3⋊Dic3—91no—
782C2×C3⋊Dic3—92no—
783C2×C3⋊Dic3—94no—
784C2×C3⋊Dic3—91no—
785C2×C3⋊Dic3—92no—
786C2×C3⋊Dic3—91no—
787C2×C3⋊Dic3—91no—
788C4×C3⋊D3—34no—
789C4×C3⋊D3—32no—
790C4×C3⋊D3—32no—
791C4×C3⋊D3—32no—
792C4×C3⋊D3—92no—
793C4×C3⋊D3—92no—
794C4×C3⋊D3—94no—
795C4×C3⋊D3—92no—
796C4×C3⋊D3—94no—
797C4×C3⋊D3—94no—
798C4×C3⋊D3—92no—
799C4×C3⋊D3—92no—
800C4×C3⋊D3—91no—
801C4×C3⋊D3—91no—
802C4×C3⋊D3—91no—
803C4×C3⋊D3A4211yescharacteristic, complemented
804C2×C3×Dic3—362no—
805C2×C3×Dic3—362no—
806C3×C4×D3—122no—
807C3×C4×D3—362no—
808C3×C4×D3—362no—
809C3×C4×D3—362no—
810C3×C4×D3—364no—
811C3×C4×D3—481no—
812C3×C4×D3—481no—
813C3×C4×D3—1441no—
814C26—91no—
815C24×C4—91no—
816C24×C4—272no—
817C24×C4—272no—
818C24×C4—272no—
819C24×C4—272no—
820C24×C4—811no—
821C24×C4—811no—
822C24×C4—811no—
823C24×C4—811no—
824C24×C4C3×(C3⋊D3)⋊C311yescharacteristic, complemented
825C2×C33—161no—
826C2×C33—161no—
827C2×C33—321no—
828C3×C3⋊D3—162no—
829C32×D3—482no—
830C2×H(3,𝔽3)—42no—
831C2×H(3,𝔽3)—122no—
832C2×H(3,𝔽3)—122no—
833C2×H(3,𝔽3)—161no—
834C2×H(3,𝔽3)—322no—
835C2×H(3,𝔽3)—321no—
836(C3⋊D3)⋊C3—44no—
837(C3⋊D3)⋊C3—124no—
838(C3⋊D3)⋊C3—162no—
839C24×C3—32no—
840C24×C3—32no—
841C24×C3—31no—
842C24×C3—92no—
843C24×C3—92no—
844C24×C3—91no—
845C24×C3—93no—
846C24×C3—91no—
847C24×C3—93no—
848C24×C3—362no—
849C24×C3C32×C4×D311yescharacteristic
850C23×D3—32no—
851C23×D3—92no—
852C23×D3—94no—
853C23×D3—94no—
854C23×D3—94no—
855C23×D3—91no—
856C23×D3—93no—
857C23×D3—91no—
858C23×D3—92no—
859C23×D3—94no—
860C23×D3—274no—
861C23×D3—274no—
862C23×D3—272no—
863C23×D3—271no—
864C23×D3—274no—
865C23×D3—274no—
866C23×D3—271no—
867C23×D3—272no—
868C23×D3—276no—
869C23×D3—272no—
870C23×D3—272no—
871C23×D3—276no—
872C23×D3—272no—
873C23×D3—272no—
874C23×D3—272no—
875C23×D3—274no—
876C23×D3—274no—
877C23×D3—271no—
878C23×D3—271no—
879C23×D3—273no—
880C23×D3—273no—
881C23×D3—273no—
882C23×D3—276no—
883C23×D3—276no—
884C23×D3—276no—
885C23×D3—273no—
886C23×D3—2712no—
887C23×D3—2712no—
888C23×D3—2712no—
889C23×D3—276no—
890C23×D3—2712no—
891C23×D3—276no—
892C23×D3—276no—
893C23×D3—2712no—
894C23×D3—2724no—
895C23×D3—2724no—
896C23×D3—272no—
897C23×D3—272no—
898C23×D3—276no—
899C23×D3—276no—
900C23×D3—274no—
901C23×D3—276no—
902C23×D3—278no—
903C23×D3—278no—
904C23×D3—274no—
905C23×D3—271no—
906C23×D3—272no—
907C23×D3—272no—
908C23×D3—274no—
909C23×D3—272no—
910C22⋊A4—21no—
911C22⋊A4—31no—
912C22⋊A4—61no—
913C22⋊A4—61no—
914C22⋊A4C4×(C3⋊D3)⋊C311yescharacteristic, complemented
915C22×A4—32no—
916C22×A4—62no—
917C22×A4—92no—
918C22×A4—92no—
919C22×A4—92no—
920C22×A4—182no—
921C22×A4—182no—
922C22×A4—272no—
923C22×A4—274no—
924C22×A4—274no—
925C22×A4—274no—
926C22×A4—274no—
927C22×A4—362no—
928C22×A4—362no—
929C22×A4—1081no—
930C22×A4—1081no—
931C22×C3×C4—33no—
932C22×C3×C4—31no—
933C22×C3×C4—31no—
934C22×C3×C4—32no—
935C22×C3×C4—32no—
936C22×C3×C4—92no—
937C22×C3×C4—91no—
938C22×C3×C4—91no—
939C22×C3×C4—92no—
940C22×C3×C4—92no—
941C22×C3×C4—92no—
942C22×C3×C4—91no—
943C22×C3×C4—91no—
944C22×C3×C4—93no—
945C22×C3×C4—93no—
946C22×C3×C4—96no—
947C22×C3×C4—96no—
948C22×C3×C4—96no—
949C22×C3×C4—93no—
950C22×C3×C4—912no—
951C22×C3×C4—93no—
952C22×C3×C4—94no—
953C22×C3×C4—91no—
954C22×C3×C4—122no—
955C22×C3×C4—242no—
956C22×C3×C4—362no—
957C22×C3×C4—1082no—
958C22×C3×C4—1082no—
959C22×C3×C4—1082no—
960C22×C3×C4—1082no—
961C22×C3×C4C3×D3×A412yes—
962C22×Dic3—32no—
963C22×Dic3—92no—
964C22×Dic3—91no—
965C22×Dic3—93no—
966C22×Dic3—91no—
967C22×Dic3—92no—
968C22×Dic3—272no—
969C22×Dic3—271no—
970C22×Dic3—271no—
971C22×Dic3—272no—
972C22×Dic3—272no—
973C22×Dic3—272no—
974C22×Dic3—271no—
975C22×Dic3—271no—
976C22×Dic3—273no—
977C22×Dic3—273no—
978C22×Dic3—276no—
979C22×Dic3—276no—
980C22×Dic3—276no—
981C22×Dic3—273no—
982C22×Dic3—2712no—
983C22×Dic3—273no—
984C22×Dic3—274no—
985C22×Dic3—271no—
986C2×C4×D3—92no—
987C2×C4×D3—92no—
988C2×C4×D3—92no—
989C2×C4×D3—92no—
990C2×C4×D3—272no—
991C2×C4×D3—272no—
992C2×C4×D3—272no—
993C2×C4×D3—272no—
994C2×C4×D3—271no—
995C2×C4×D3—271no—
996C2×C4×D3—271no—
997C2×C4×D3—271no—
998C2×C4×D3—272no—
999C2×C4×D3—272no—
1000C2×C4×D3—272no—
1001C2×C4×D3—273no—
1002C2×C4×D3—274no—
1003C2×C4×D3—274no—
1004C2×C4×D3—274no—
1005C2×C4×D3—274no—
1006C2×C4×D3—274no—
1007C2×C4×D3—274no—
1008C2×C4×D3—274no—
1009C2×C4×D3—276no—
1010C2×C4×D3—276no—
1011C2×C4×D3—276no—
1012C2×C4×D3—276no—
1013C2×C4×D3—276no—
1014C2×C4×D3—273no—
1015C2×C4×D3—273no—
1016C2×C4×D3—273no—
1017C2×C4×D3—276no—
1018C2×C4×D3—2712no—
1019C2×C4×D3—2712no—
1020C2×C4×D3—2712no—
1021C2×C4×D3—2712no—
1022C2×C4×D3—2712no—
1023C2×C4×D3—2712no—
1024C2×C4×D3—2712no—
1025C2×C4×D3—276no—
1026C2×C4×D3—276no—
1027C2×C4×D3—276no—
1028C2×C4×D3—274no—
1029C2×C4×D3—274no—
1030C2×C4×D3—274no—
1031C2×C4×D3—274no—
1032C2×C4×D3—271no—
1033C2×C4×D3—271no—
1034C2×C4×D3—274no—
1035C2×C4×D3—274no—
1036C2×C4×D3—271no—
1037C2×C4×D3—271no—
1038C2×C4×D3—271no—
1039C2×C4×D3—271no—
1040C2×C4×D3—2712no—
1041C2×C4×D3—2712no—
1042C2×C4×D3—2712no—
1043C2×C4×D3—273no—
1044C2×C4×D3—2712no—
1045C2×C4×D3—273no—
1046C2×C4×D3—2712no—
1047C2×C4×D3—273no—
1048C2×C4×D3—273no—
1049C2×C4×D3—273no—
1050C2×C4×D3—2712no—
1051C2×C4×D3—273no—
1052C2×C4×D3—276no—
1053C2×C4×D3—276no—
1054C2×C4×D3—276no—
1055C2×C4×D3—273no—
1056C2×C4×D3—273no—
1057C2×C4×D3—273no—
1058C2×C4×D3—2712no—
1059C2×C4×D3—2712no—
1060C2×C4×D3—2712no—
1061C2×C4×D3—272no—
1062C2×C4×D3—272no—
1063C2×C4×D3—272no—
1064C2×C4×D3—272no—
1065C2×C4×D3—272no—
1066C2×C4×D3—272no—
1067C2×C4×D3—272no—
1068C2×C4×D3—272no—
1069C2×C4×D3—272no—
1070C2×C4×D3—271no—
1071C2×C4×D3—271no—
1072C2×C4×D3—274no—
1073C2×C4×D3—273no—
1074C2×C4×D3—274no—
1075C2×C4×D3—273no—
1076C2×C4×D3—271no—
1077C2×C4×D3—271no—
1078C2×C4×D3—274no—
1079C2×C4×D3—273no—
1080C2×C4×D3—271no—
1081C2×C4×D3—271no—
1082C4×A4—32no—
1083C4×A4—42no—
1084C4×A4—62no—
1085C4×A4—82no—
1086C4×A4—92no—
1087C4×A4—92no—
1088C4×A4—121no—
1089C4×A4—122no—
1090C4×A4—182no—
1091C4×A4—241no—
1092C4×A4—243no—
1093C4×A4—242no—
1094C4×A4—242no—
1095C4×A4—272no—
1096C4×A4—361no—
1097C4×A4—362no—
1098C4×A4—362no—
1099C4×A4—721no—
1100C4×A4—1081no—
1101C4×A4—1081no—
1102C22×C32—31no—
1103C22×C32—32no—
1104C22×C32—32no—
1105C22×C32—31no—
1106C22×C32—42no—
1107C22×C32—82no—
1108C22×C32—91no—
1109C22×C32—92no—
1110C22×C32—91no—
1111C22×C32—92no—
1112C22×C32—92no—
1113C22×C32—94no—
1114C22×C32—91no—
1115C22×C32—91no—
1116C22×C32—91no—
1117C22×C32—122no—
1118C22×C32—122no—
1119C22×C32—242no—
1120C22×C32—242no—
1121C22×C32—1441no—
1122C22×C32C2×C3×C4×A412yescomplemented
1123C2×C3⋊D3—34no—
1124C2×C3⋊D3—32no—
1125C2×C3⋊D3—34no—
1126C2×C3⋊D3—34no—
1127C2×C3⋊D3—34no—
1128C2×C3⋊D3—92no—
1129C2×C3⋊D3—92no—
1130C2×C3⋊D3—94no—
1131C2×C3⋊D3—94no—
1132C2×C3⋊D3—98no—
1133C2×C3⋊D3—98no—
1134C2×C3⋊D3—94no—
1135C2×C3⋊D3—92no—
1136C2×C3⋊D3—92no—
1137C2×C3⋊D3—91no—
1138C2×C3⋊D3—92no—
1139C2×C3⋊D3—92no—
1140C2×C3⋊D3—94no—
1141C2×C3⋊D3—92no—
1142C2×C3⋊D3—92no—
1143C2×C3⋊D3C2×A4211yescharacteristic
1144C2×C3×D3—122no—
1145C2×C3×D3—364no—
1146C2×C3×D3—364no—
1147C2×C3×D3—362no—
1148C2×C3×D3—364no—
1149C2×C3×D3—364no—
1150C2×C3×D3—481no—
1151C2×C3×D3—481no—
1152C2×C3×D3—1441no—
1153C3×A4—22no—
1154C3×A4—42no—
1155C3×A4—42no—
1156C3×A4—82no—
1157C3×A4—82no—
1158C3×A4—121no—
1159C3×A4—121no—
1160C3×A4—122no—
1161C3×A4—122no—
1162C3×A4—123no—
1163C3×A4—241no—
1164C3×A4—241no—
1165C3×A4—242no—
1166C3×A4—242no—
1167C3×A4—244no—
1168C3×A4—242no—
1169C3×A4—243no—
1170C3×A4C4×D3×A412yescomplemented
1171C32×C4—32no—
1172C32×C4—42no—
1173C32×C4—82no—
1174C32×C4—91no—
1175C32×C4—122no—
1176C32×C4—161no—
1177C32×C4—161no—
1178C32×C4—242no—
1179C32×C4—321no—
1180C32×C4—321no—
1181C32×C4—481no—
1182C32×C4—481no—
1183C32×C4—961no—
1184C32×C4—961no—
1185C32×C4—961no—
1186C32×C4—962no—
1187C32×C4—1441no—
1188C32×C4C2×A4211yescharacteristic, complemented
1189C3⋊Dic3—32no—
1190C3⋊Dic3—91no—
1191C3⋊Dic3C2×A4211yescharacteristic, complemented
1192C3×Dic3—122no—
1193C3×Dic3—362no—
1194C3×Dic3—481no—
1195C3×Dic3—481no—
1196C3×Dic3—1441no—
1197C25—92no—
1198C25—272no—
1199C25—272no—
1200C25—274no—
1201C25—811no—
1202C25—811no—
1203C25—812no—
1204C25C2×C3×(C3⋊D3)⋊C311yescharacteristic
1205C23×C4—32no—
1206C23×C4—32no—
1207C23×C4—91no—
1208C23×C4—91no—
1209C23×C4—92no—
1210C23×C4—272no—
1211C23×C4—272no—
1212C23×C4—274no—
1213C23×C4—271no—
1214C23×C4—271no—
1215C23×C4—272no—
1216C23×C4—272no—
1217C23×C4—272no—
1218C23×C4—811no—
1219C23×C4—811no—
1220C23×C4—811no—
1221C23×C4—811no—
1222C23×C4—811no—
1223C23×C4—812no—
1224C23×C4—812no—
1225C23×C4—812no—
1226C23×C4—812no—
1227C23×C4—812no—
1228C23×C4—812no—
1229C23×C4—812no—
1230C23×C4—811no—
1231C23×C4—811no—
1232C23×C4—812no—
1233C23×C4—812no—
1234C23×C4—814no—
1235C23×C4—814no—
1236C23×C4—814no—
1237C23×C4—814no—
1238C23×C4—814no—
1239C23×C4—814no—
1240C23×C4—811no—
1241C23×C4—812no—
1242C23×C4—812no—
1243C23×C4—811no—
1244C23×C4—812no—
1245C23×C4—811no—
1246C23×C4—811no—
1247C23×C4—811no—
1248C33—161no—
1249C33—161no—
1250C33—321no—
1251H(3,𝔽3)—42no—
1252H(3,𝔽3)—161no—
1253H(3,𝔽3)—322no—
1254H(3,𝔽3)—321no—
1255C23×C3—33no—
1256C23×C3—31no—
1257C23×C3—31no—
1258C23×C3—32no—
1259C23×C3—32no—
1260C23×C3—32no—
1261C23×C3—92no—
1262C23×C3—92no—
1263C23×C3—91no—
1264C23×C3—91no—
1265C23×C3—91no—
1266C23×C3—92no—
1267C23×C3—92no—
1268C23×C3—92no—
1269C23×C3—93no—
1270C23×C3—91no—
1271C23×C3—91no—
1272C23×C3—93no—
1273C23×C3—91no—
1274C23×C3—94no—
1275C23×C3—93no—
1276C23×C3—96no—
1277C23×C3—96no—
1278C23×C3—96no—
1279C23×C3—93no—
1280C23×C3—93no—
1281C23×C3—912no—
1282C23×C3—122no—
1283C23×C3—242no—
1284C23×C3—364no—
1285C23×C3—1082no—
1286C23×C3—1082no—
1287C23×C3—1084no—
1288C23×C3C2×C3×D3×A412yes—
1289C22×D3—34no—
1290C22×D3—94no—
1291C22×D3—92no—
1292C22×D3—92no—
1293C22×D3—94no—
1294C22×D3—92no—
1295C22×D3—96no—
1296C22×D3—92no—
1297C22×D3—94no—
1298C22×D3—272no—
1299C22×D3—274no—
1300C22×D3—272no—
1301C22×D3—272no—
1302C22×D3—274no—
1303C22×D3—271no—
1304C22×D3—271no—
1305C22×D3—272no—
1306C22×D3—274no—
1307C22×D3—272no—
1308C22×D3—272no—
1309C22×D3—273no—
1310C22×D3—274no—
1311C22×D3—274no—
1312C22×D3—278no—
1313C22×D3—278no—
1314C22×D3—274no—
1315C22×D3—274no—
1316C22×D3—274no—
1317C22×D3—274no—
1318C22×D3—274no—
1319C22×D3—274no—
1320C22×D3—274no—
1321C22×D3—272no—
1322C22×D3—272no—
1323C22×D3—276no—
1324C22×D3—276no—
1325C22×D3—276no—
1326C22×D3—273no—
1327C22×D3—2712no—
1328C22×D3—273no—
1329C22×D3—2712no—
1330C22×D3—276no—
1331C22×D3—276no—
1332C22×D3—2712no—
1333C22×D3—276no—
1334C22×D3—2712no—
1335C22×D3—2712no—
1336C22×D3—2712no—
1337C22×D3—2712no—
1338C22×D3—2712no—
1339C22×D3—2712no—
1340C22×D3—2712no—
1341C22×D3—2724no—
1342C22×D3—2712no—
1343C22×D3—2724no—
1344C22×D3—276no—
1345C22×D3—276no—
1346C22×D3—2712no—
1347C22×D3—2724no—
1348C22×D3—2724no—
1349C22×D3—274no—
1350C22×D3—274no—
1351C22×D3—272no—
1352C22×D3—272no—
1353C22×D3—278no—
1354C22×D3—278no—
1355C22×D3—272no—
1356C22×D3—276no—
1357C22×D3—2712no—
1358C22×D3—2724no—
1359C22×D3—2712no—
1360C22×D3—276no—
1361C22×D3—2724no—
1362C22×D3—276no—
1363C22×D3—272no—
1364C22×D3—274no—
1365C22×D3—273no—
1366C22×D3—271no—
1367C22×D3—271no—
1368C22×D3—272no—
1369C22×D3—272no—
1370C22×D3—278no—
1371C22×D3—278no—
1372C22×D3—276no—
1373C22×D3—274no—
1374C22×D3—272no—
1375C2×A4—32no—
1376C2×A4—42no—
1377C2×A4—62no—
1378C2×A4—82no—
1379C2×A4—92no—
1380C2×A4—92no—
1381C2×A4—94no—
1382C2×A4—121no—
1383C2×A4—122no—
1384C2×A4—182no—
1385C2×A4—182no—
1386C2×A4—241no—
1387C2×A4—243no—
1388C2×A4—242no—
1389C2×A4—242no—
1390C2×A4—274no—
1391C2×A4—361no—
1392C2×A4—364no—
1393C2×A4—364no—
1394C2×A4—721no—
1395C2×A4—1082no—
1396C2×A4—1082no—
1397C2×C3×C4—32no—
1398C2×C3×C4—32no—
1399C2×C3×C4—92no—
1400C2×C3×C4—92no—
1401C2×C3×C4—91no—
1402C2×C3×C4—92no—
1403C2×C3×C4—93no—
1404C2×C3×C4—94no—
1405C2×C3×C4—93no—
1406C2×C3×C4—96no—
1407C2×C3×C4—912no—
1408C2×C3×C4—96no—
1409C2×C3×C4—93no—
1410C2×C3×C4—91no—
1411C2×C3×C4—92no—
1412C2×C3×C4—93no—
1413C2×C3×C4—91no—
1414C2×C3×C4—91no—
1415C2×C3×C4—362no—
1416C2×C3×C4—362no—
1417C2×C3×C4—362no—
1418C2×C3×C4—722no—
1419C2×C3×C4—722no—
1420C2×C3×C4—1082no—
1421C2×C3×C4—1082no—
1422C2×C3×C4—1082no—
1423C2×C3×C4—1082no—
1424C2×C3×C4—1084no—
1425C2×C3×C4—1082no—
1426C2×C3×C4—1441no—
1427C2×C3×C4—1441no—
1428C2×Dic3—92no—
1429C2×Dic3—92no—
1430C2×Dic3—272no—
1431C2×Dic3—272no—
1432C2×Dic3—271no—
1433C2×Dic3—271no—
1434C2×Dic3—272no—
1435C2×Dic3—273no—
1436C2×Dic3—274no—
1437C2×Dic3—273no—
1438C2×Dic3—276no—
1439C2×Dic3—2712no—
1440C2×Dic3—276no—
1441C2×Dic3—273no—
1442C2×Dic3—272no—
1443C2×Dic3—273no—
1444C2×Dic3—271no—
1445C2×Dic3—271no—
1446C4×D3—31no—
1447C4×D3—91no—
1448C4×D3—92no—
1449C4×D3—92no—
1450C4×D3—94no—
1451C4×D3—92no—
1452C4×D3—272no—
1453C4×D3—272no—
1454C4×D3—272no—
1455C4×D3—274no—
1456C4×D3—271no—
1457C4×D3—272no—
1458C4×D3—272no—
1459C4×D3—273no—
1460C4×D3—274no—
1461C4×D3—272no—
1462C4×D3—274no—
1463C4×D3—273no—
1464C4×D3—271no—
1465C4×D3—273no—
1466C4×D3—274no—
1467C4×D3—276no—
1468C4×D3—276no—
1469C4×D3—2712no—
1470C4×D3—276no—
1471C4×D3—2712no—
1472C4×D3—2712no—
1473C4×D3—276no—
1474C4×D3—276no—
1475C4×D3—272no—
1476C4×D3—272no—
1477C4×D3—271no—
1478C2×C32—32no—
1479C2×C32—32no—
1480C2×C32—42no—
1481C2×C32—82no—
1482C2×C32—91no—
1483C2×C32—91no—
1484C2×C32—122no—
1485C2×C32—122no—
1486C2×C32—161no—
1487C2×C32—161no—
1488C2×C32—242no—
1489C2×C32—242no—
1490C2×C32—321no—
1491C2×C32—321no—
1492C2×C32—481no—
1493C2×C32—481no—
1494C2×C32—961no—
1495C2×C32—961no—
1496C2×C32—961no—
1497C2×C32—962no—
1498C2×C32—1442no—
1499C2×C32C22×A4211yescharacteristic
1500C3⋊D3—34no—
1501C3⋊D3—92no—
1502C3⋊D3C4×A4212yescomplemented
1503C3×D3—124no—
1504C3×D3—364no—
1505C3×D3—482no—
1506C3×D3—482no—
1507C3×D3—1442no—
1508C24—32no—
1509C24—32no—
1510C24—91no—
1511C24—91no—
1512C24—92no—
1513C24—274no—
1514C24—274no—
1515C24—271no—
1516C24—271no—
1517C24—274no—
1518C24—274no—
1519C24—272no—
1520C24—811no—
1521C24—811no—
1522C24—812no—
1523C24—811no—
1524C24—812no—
1525C24—812no—
1526C24—812no—
1527C24—814no—
1528C24—814no—
1529C24—812no—
1530C24—812no—
1531C24—812no—
1532C24—811no—
1533C24—814no—
1534C24—812no—
1535C24—812no—
1536C24—814no—
1537C24—814no—
1538C24—818no—
1539C24—818no—
1540C24—812no—
1541C24—812no—
1542C24C3×C4×(C3⋊D3)⋊C311yescharacteristic, complemented
1543C22×C4—31no—
1544C22×C4—31no—
1545C22×C4—32no—
1546C22×C4—91no—
1547C22×C4—92no—
1548C22×C4—92no—
1549C22×C4—92no—
1550C22×C4—91no—
1551C22×C4—91no—
1552C22×C4—94no—
1553C22×C4—91no—
1554C22×C4—92no—
1555C22×C4—272no—
1556C22×C4—272no—
1557C22×C4—272no—
1558C22×C4—272no—
1559C22×C4—271no—
1560C22×C4—271no—
1561C22×C4—272no—
1562C22×C4—812no—
1563C22×C4—812no—
1564C22×C4—812no—
1565C22×C4—812no—
1566C22×C4—811no—
1567C22×C4—812no—
1568C22×C4—811no—
1569C22×C4—811no—
1570C22×C4—811no—
1571C22×C4—812no—
1572C22×C4—814no—
1573C22×C4—814no—
1574C22×C4—814no—
1575C22×C4—814no—
1576C22×C4—814no—
1577C22×C4—814no—
1578C22×C4—814no—
1579C22×C4—812no—
1580C22×C4—812no—
1581C22×C4—812no—
1582C22×C4—811no—
1583C22×C4—811no—
1584C22×C4—814no—
1585C22×C4—814no—
1586C22×C4—814no—
1587C22×C4—814no—
1588C22×C4—814no—
1589C22×C4—814no—
1590C22×C4—811no—
1591C22×C4—811no—
1592C22×C4—811no—
1593C22×C4—811no—
1594C22×C4—812no—
1595C22×C4—812no—
1596C22×C4—812no—
1597C22×C4—814no—
1598C22×C4—811no—
1599C22×C4—811no—
1600C22×C4—814no—
1601C22×C4—814no—
1602C22×C4—811no—
1603C22×C4—811no—
1604C22×C4—811no—
1605C22×C4—811no—
1606C22×C4—811no—
1607C22×C4—812no—
1608C22×C4—812no—
1609C22×C4—812no—
1610C22×C4—811no—
1611C22×C4—811no—
1612C22×C4—814no—
1613C22×C4—811no—
1614C22×C4A4×(C3⋊D3)⋊C312yescomplemented
1615C22×C3—32no—
1616C22×C3—32no—
1617C22×C3—33no—
1618C22×C3—31no—
1619C22×C3—31no—
1620C22×C3—32no—
1621C22×C3—92no—
1622C22×C3—92no—
1623C22×C3—91no—
1624C22×C3—91no—
1625C22×C3—92no—
1626C22×C3—91no—
1627C22×C3—92no—
1628C22×C3—92no—
1629C22×C3—93no—
1630C22×C3—94no—
1631C22×C3—93no—
1632C22×C3—91no—
1633C22×C3—91no—
1634C22×C3—93no—
1635C22×C3—96no—
1636C22×C3—93no—
1637C22×C3—96no—
1638C22×C3—96no—
1639C22×C3—912no—
1640C22×C3—93no—
1641C22×C3—91no—
1642C22×C3—122no—
1643C22×C3—242no—
1644C22×C3—362no—
1645C22×C3—362no—
1646C22×C3—362no—
1647C22×C3—722no—
1648C22×C3—722no—
1649C22×C3—1082no—
1650C22×C3—1084no—
1651C22×C3—1084no—
1652C22×C3—1084no—
1653C22×C3—1084no—
1654C22×C3—1441no—
1655C22×C3—1441no—
1656C22×C3C3×C4×D3×A412yes—
1657C2×D3—31no—
1658C2×D3—91no—
1659C2×D3—94no—
1660C2×D3—94no—
1661C2×D3—94no—
1662C2×D3—92no—
1663C2×D3—94no—
1664C2×D3—274no—
1665C2×D3—274no—
1666C2×D3—272no—
1667C2×D3—274no—
1668C2×D3—274no—
1669C2×D3—272no—
1670C2×D3—272no—
1671C2×D3—272no—
1672C2×D3—272no—
1673C2×D3—274no—
1674C2×D3—274no—
1675C2×D3—276no—
1676C2×D3—276no—
1677C2×D3—278no—
1678C2×D3—278no—
1679C2×D3—273no—
1680C2×D3—274no—
1681C2×D3—2712no—
1682C2×D3—2712no—
1683C2×D3—2712no—
1684C2×D3—2712no—
1685C2×D3—276no—
1686C2×D3—276no—
1687C2×D3—2724no—
1688C2×D3—2724no—
1689C2×D3—276no—
1690C2×D3—276no—
1691C2×D3—276no—
1692C2×D3—272no—
1693C2×D3—272no—
1694C2×D3—271no—
1695C2×D3—274no—
1696C2×D3—276no—
1697C2×D3—272no—
1698C2×D3—272no—
1699A4—32no—
1700A4—42no—
1701A4—62no—
1702A4—82no—
1703A4—121no—
1704A4—122no—
1705A4—241no—
1706A4—243no—
1707A4—242no—
1708A4—242no—
1709A4—361no—
1710A4—721no—
1711C3×C4—32no—
1712C3×C4—31no—
1713C3×C4—92no—
1714C3×C4—93no—
1715C3×C4—91no—
1716C3×C4—122no—
1717C3×C4—161no—
1718C3×C4—242no—
1719C3×C4—321no—
1720C3×C4—362no—
1721C3×C4—362no—
1722C3×C4—481no—
1723C3×C4—722no—
1724C3×C4—961no—
1725C3×C4—961no—
1726C3×C4—1082no—
1727C3×C4—1441no—
1728C3×C4—1441no—
1729C3×C4D3×A4211yescharacteristic
1730Dic3—31no—
1731Dic3—91no—
1732Dic3—92no—
1733Dic3—272no—
1734Dic3—273no—
1735Dic3—271no—
1736C32—42no—
1737C32—82no—
1738C32—161no—
1739C32—161no—
1740C32—321no—
1741C32—321no—
1742C32—481no—
1743C32—481no—
1744C32—961no—
1745C32—961no—
1746C32—961no—
1747C32—962no—
1748C32C2×C4×A4211yescharacteristic, complemented
1749C23—31no—
1750C23—31no—
1751C23—32no—
1752C23—32no—
1753C23—91no—
1754C23—91no—
1755C23—92no—
1756C23—92no—
1757C23—92no—
1758C23—91no—
1759C23—91no—
1760C23—91no—
1761C23—94no—
1762C23—94no—
1763C23—272no—
1764C23—272no—
1765C23—274no—
1766C23—272no—
1767C23—272no—
1768C23—274no—
1769C23—812no—
1770C23—812no—
1771C23—814no—
1772C23—812no—
1773C23—812no—
1774C23—811no—
1775C23—811no—
1776C23—812no—
1777C23—814no—
1778C23—812no—
1779C23—814no—
1780C23—814no—
1781C23—814no—
1782C23—814no—
1783C23—814no—
1784C23—814no—
1785C23—814no—
1786C23—814no—
1787C23—814no—
1788C23—818no—
1789C23—818no—
1790C23—812no—
1791C23—811no—
1792C23—811no—
1793C23—814no—
1794C23—818no—
1795C23—818no—
1796C23—812no—
1797C23—812no—
1798C23—812no—
1799C23—818no—
1800C23—818no—
1801C23—812no—
1802C23—812no—
1803C23—814no—
1804C23—814no—
1805C23C2×A4×(C3⋊D3)⋊C312yes—
1806C2×C4—32no—
1807C2×C4—32no—
1808C2×C4—91no—
1809C2×C4—92no—
1810C2×C4—94no—
1811C2×C4—91no—
1812C2×C4—91no—
1813C2×C4—92no—
1814C2×C4—91no—
1815C2×C4—91no—
1816C2×C4—272no—
1817C2×C4—272no—
1818C2×C4—274no—
1819C2×C4—272no—
1820C2×C4—272no—
1821C2×C4—272no—
1822C2×C4—812no—
1823C2×C4—812no—
1824C2×C4—814no—
1825C2×C4—811no—
1826C2×C4—812no—
1827C2×C4—814no—
1828C2×C4—811no—
1829C2×C4—811no—
1830C2×C4—814no—
1831C2×C4—812no—
1832C2×C4—812no—
1833C2×C4—811no—
1834C2×C4—812no—
1835C2×C4—814no—
1836C2×C4—811no—
1837C2×C4—812no—
1838C2×C4—811no—
1839C2×C4—811no—
1840C2×C3—32no—
1841C2×C3—32no—
1842C2×C3—31no—
1843C2×C3—92no—
1844C2×C3—92no—
1845C2×C3—93no—
1846C2×C3—93no—
1847C2×C3—91no—
1848C2×C3—91no—
1849C2×C3—122no—
1850C2×C3—161no—
1851C2×C3—242no—
1852C2×C3—321no—
1853C2×C3—362no—
1854C2×C3—362no—
1855C2×C3—364no—
1856C2×C3—481no—
1857C2×C3—722no—
1858C2×C3—722no—
1859C2×C3—961no—
1860C2×C3—961no—
1861C2×C3—1084no—
1862C2×C3—1442no—
1863C2×C3—1442no—
1864C2×C3C2×D3×A4211yescharacteristic
1865D3—32no—
1866D3—92no—
1867D3—94no—
1868D3—274no—
1869D3—276no—
1870D3—272no—
1871C22—32no—
1872C22—32no—
1873C22—31no—
1874C22—31no—
1875C22—91no—
1876C22—92no—
1877C22—91no—
1878C22—92no—
1879C22—92no—
1880C22—94no—
1881C22—91no—
1882C22—91no—
1883C22—91no—
1884C22—91no—
1885C22—274no—
1886C22—274no—
1887C22—274no—
1888C22—274no—
1889C22—272no—
1890C22—814no—
1891C22—814no—
1892C22—814no—
1893C22—814no—
1894C22—812no—
1895C22—812no—
1896C22—812no—
1897C22—812no—
1898C22—818no—
1899C22—818no—
1900C22—812no—
1901C22—812no—
1902C22—812no—
1903C22—812no—
1904C22—811no—
1905C22C4×A4×(C3⋊D3)⋊C312yescomplemented
1906C4—32no—
1907C4—91no—
1908C4—91no—
1909C4—272no—
1910C4—811no—
1911C4#7221326611yescharacteristic, direct product factor
1912C3—31no—
1913C3—122no—
1914C3—161no—
1915C3—242no—
1916C3—321no—
1917C3—481no—
1918C3—961no—
1919C3—961no—
1920C3C4×D3×A4211yescharacteristic
1921C2—32no—
1922C2—32no—
1923C2—91no—
1924C2—91no—
1925C2—92no—
1926C2—274no—
1927C2—812no—
1928C2C2×#7221326611yescharacteristic
subgroupG/H
center, hypercenterC4#72213266
commutator, hypocenterC24×C32C2×C32×C4
FrattiniC2×C3C2×D3×A42
FittingC24×C32×C4C2×C32
socleC25×C3C2×C32×D3
prime radicalC2×#72213266C2
cosocleC25×C32C22×C32
LCSG ▷ C24×C32
UCSC1 ◁ C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C4×(C3⋊D3)⋊(C22⋊A4)C3semidirect
2. C22×C4×(C3⋊D3)⋊A4C3semidirect
3. C4×C3⋊D3×C22⋊A4C3semidirect
6. #72242698C2semidirect
7. C4×(C22⋊A4)⋊H(3,𝔽3)C2semidirect
10. #72213266C4direct (N × H)
13. C32×C4×C22⋊A4C2×C3semidirect
14. C3⋊Dic3×C22⋊A4C2×C3semidirect
16. C3×C4×A42D3semidirect
20. C4×C32⋊(C22⋊A4)C2×C3semidirect
21. C22×C4×C22⋊H(3,𝔽3)C2×C3semidirect
22. (C3⋊Dic3)⋊(C22⋊A4)C2×C3semidirect
23. C22×(C3⋊Dic3)⋊A4C2×C3semidirect
31. (C22⋊A4)⋊H(3,𝔽3)C2×C4semidirect
39. C24×C4×C3⋊D3C32semidirect
41. C3⋊D3×C22⋊A4C3×C4semidirect
50. (C3⋊D3)⋊(C22⋊A4)C3×C4semidirect
54. C22×(C3⋊D3)⋊A4C3×C4semidirect
68. C4×(C3⋊D3)⋊A4A4semidirect
78. C24×C32×C4C2×C32semidirect
79. C24×C3⋊Dic3C2×C32semidirect
93. C3×C4×C22⋊A4C3×D3semidirect
95. C22×C3×C4×A4C3×D3semidirect
109. C32×C22⋊A4C2×C3×C4semidirect
114. C3×A42C4×D3semidirect
123. C32⋊(C22⋊A4)C2×C3×C4semidirect
126. C22×C22⋊H(3,𝔽3)C2×C3×C4semidirect
149. C4×C22⋊H(3,𝔽3)C2×A4semidirect
153. (C3⋊Dic3)⋊A4C2×A4semidirect
170. C24×C3⋊D3C32×C4semidirect
233. C22×C4×C3⋊D3C3×A4semidirect
278. (C3⋊D3)⋊A4C4×A4semidirect
320. C4×C22⋊A4(C3⋊D3)⋊C3semidirect
334. C24×C32C2×C32×C4semidirect
371. C3×C22⋊A4C3×C4×D3semidirect
378. C22×C3×A4C3×C4×D3semidirect
408. C22×C32×C4C2×C3×A4semidirect
420. C22×C3⋊Dic3C2×C3×A4semidirect
494. C3×C4×A4D3×A4semidirect
530. C22⋊H(3,𝔽3)C2×C4×A4semidirect
729. C22×C3⋊D3C3×C4×A4semidirect
803. C4×C3⋊D3A42semidirect
824. C24×C4C3×(C3⋊D3)⋊C3semidirect
914. C22⋊A4C4×(C3⋊D3)⋊C3semidirect
1122. C22×C32C2×C3×C4×A4semidirect
1170. C3×A4C4×D3×A4semidirect
1188. C32×C4C2×A42semidirect
1191. C3⋊Dic3C2×A42semidirect
1502. C3⋊D3C4×A42semidirect
1542. C24C3×C4×(C3⋊D3)⋊C3semidirect
1614. C22×C4A4×(C3⋊D3)⋊C3semidirect
1748. C32C2×C4×A42semidirect
1905. C22C4×A4×(C3⋊D3)⋊C3semidirect
1911. C4#72213266direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×(C3⋊D3)⋊(C22⋊A4)3
C22×C4×(C3⋊D3)⋊A43
C4×C3⋊D3×C22⋊A43
C4×D3×A423
C4×A4×(C3⋊D3)⋊C34
#722426982
C4×(C22⋊A4)⋊H(3,𝔽3)2
C2×#722132662