Finite Group Databasebeta

← #67×C3⋊((C3⋊D3)⋊C3) #72260039

Subgroups — #67×C3⋊((C3⋊D3)⋊C3) #72260039

Order 3888.

2482 conjugacy classes of subgroups.

The subgroup lattice has 1589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C3⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
2C2×D3×C3⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
3#14518999C211yesmaximal, characteristic, complemented
4C3×#67×H(3,𝔽3)C211yesmaximal, characteristic, complemented
5#14518681C211yesmaximal, characteristic, complemented
6#14518676C211yesmaximal, characteristic, complemented
7Dic3×C3⋊((C3⋊D3)⋊C3)C211yesmaximal, characteristic, complemented
8#67×C3⋊(C3⋊D3)C311yesmaximal, characteristic, complemented
9C3×C3⋊D3×#67—31nomaximal
10D4×C3⋊((C3⋊D3)⋊C3)—31nomaximal
11#67×(C3⋊D3)⋊C3—33nomaximal
12C22×C32×H(3,𝔽3)C2211yescharacteristic, complemented
13C2×C3⋊(C3⋊((C3⋊D3)⋊C3))C2211yescharacteristic, complemented
14C2×C3×C3⋊((C3⋊D3)⋊C3)—22no—
15C2×C3×C3⋊((C3⋊D3)⋊C3)C2211yescharacteristic
16C2×C3×C3⋊((C3⋊D3)⋊C3)C2211yescharacteristic, complemented
17C2×C3×D3×H(3,𝔽3)C2211yescharacteristic, complemented
18D3×C3⋊((C3⋊D3)⋊C3)—22no—
19C3⋊(C3⋊((C3⋊Dic3)⋊C3))C2211yescharacteristic, complemented
20C3×Dic3×H(3,𝔽3)C2211yescharacteristic, complemented
21C22×C3×C3⋊(C3⋊D3)C2×C311yescharacteristic, complemented
22C22×C32×C3⋊D3—31no—
23C2×D3×C3⋊(C3⋊D3)C2×C311yescharacteristic, complemented
24C2×C3×D3×C3⋊D3—31no—
25#10620179C2×C311yescharacteristic, complemented
26C3×#6312—31no—
27C33×#67—21no—
28C33×#67D311yescharacteristic, complemented
29C33×#67C2×C311yescharacteristic, complemented
30#10620147C2×C311yescharacteristic, complemented
31#10620145C2×C311yescharacteristic, complemented
32Dic3×C3⋊(C3⋊D3)C2×C311yescharacteristic, complemented
33C3×#6292—31no—
34C3×#6290—31no—
35C3×Dic3×C3⋊D3—31no—
36C22×C3⋊((C3⋊D3)⋊C3)—21no—
37C22×C3⋊((C3⋊D3)⋊C3)—31no—
38C22×C3⋊((C3⋊D3)⋊C3)D311yescharacteristic, complemented
39C22×C3×(C3⋊D3)⋊C3—33no—
40C2×D3×(C3⋊D3)⋊C3—33no—
41C3×D4×H(3,𝔽3)—31no—
42#10619977—31no—
43#10619977—31no—
44#10619977—33no—
45#10619977—63no—
46#10619977—61no—
47C4⋊(C3⋊((C3⋊D3)⋊C3))—31no—
48C4×C3⋊((C3⋊D3)⋊C3)—31no—
49#67×H(3,𝔽3)—23no—
50#67×H(3,𝔽3)D313yescomplemented
51#6290⋊C3—33no—
52#6292⋊C3—33no—
53Dic3×(C3⋊D3)⋊C3—33no—
54C2×C32×H(3,𝔽3)—21no—
55C2×C32×H(3,𝔽3)C2311yescharacteristic
56C3⋊(C3⋊((C3⋊D3)⋊C3))—21no—
57C3×C3⋊((C3⋊D3)⋊C3)—21no—
58C3×C3⋊((C3⋊D3)⋊C3)D412yescomplemented
59C3×D3×H(3,𝔽3)—21no—
60D4×C3⋊(C3⋊D3)—31no—
61C3×D4×C3⋊D3—91no—
62C3⋊D3×#67—31no—
63C3⋊D3×#67—33no—
64C3⋊D3×#67—91no—
65C3⋊D3×#67—91no—
66C3⋊D3×#67—91no—
67C3×D3×#67—91no—
68C3×D3×#67—91no—
69C3×D3×#67—91no—
70C3×D3×#67—91no—
71D4×(C3⋊D3)⋊C3—93no—
72C22×C34—21no—
73C22×C34C2×D311yescharacteristic, complemented
74C22×C34C22×C311yescharacteristic, complemented
75C2×C3⋊(C3⋊(C3⋊D3))C22×C311yescharacteristic, complemented
76C2×C3×C3⋊(C3⋊D3)—22no—
77C2×C3×C3⋊(C3⋊D3)—31no—
78C2×C3×C3⋊(C3⋊D3)C22×C311yescharacteristic
79C2×C3×C3⋊(C3⋊D3)C22×C311yescharacteristic, complemented
80C2×C32×C3⋊D3—31no—
81C2×C32×C3⋊D3—31no—
82C2×C32×C3⋊D3—62no—
83C2×C33×D3—21no—
84C2×C33×D3C2×D311yescharacteristic, complemented
85C2×C33×D3C22×C311yescharacteristic, complemented
86D3×C3⋊(C3⋊D3)—22no—
87C3×D3×C3⋊D3—62no—
88C3⋊(C3⋊(C3⋊Dic3))C22×C311yescharacteristic, complemented
89C3×C3⋊(C3⋊Dic3)—31no—
90C33×Dic3—21no—
91C33×Dic3C2×D311yescharacteristic, complemented
92C33×Dic3C22×C311yescharacteristic, complemented
93C22×C3×H(3,𝔽3)—21no—
94C22×C3×H(3,𝔽3)—21no—
95C22×C3×H(3,𝔽3)—23no—
96C22×C3×H(3,𝔽3)—23no—
97C22×C3×H(3,𝔽3)—31no—
98C22×C3×H(3,𝔽3)—43no—
99C22×C3×H(3,𝔽3)—41no—
100C22×C3×H(3,𝔽3)C2×D311yescharacteristic, complemented
101C22×C3×H(3,𝔽3)C2×D313yescomplemented
102C2×C3⋊((C3⋊D3)⋊C3)—22no—
103C2×C3⋊((C3⋊D3)⋊C3)—22no—
104C2×C3⋊((C3⋊D3)⋊C3)—22no—
105C2×C3⋊((C3⋊D3)⋊C3)—21no—
106C2×C3⋊((C3⋊D3)⋊C3)—21no—
107C2×C3⋊((C3⋊D3)⋊C3)—31no—
108C2×C3⋊((C3⋊D3)⋊C3)—33no—
109C2×C3⋊((C3⋊D3)⋊C3)—63no—
110C2×C3⋊((C3⋊D3)⋊C3)—61no—
111C2×C3⋊((C3⋊D3)⋊C3)—62no—
112C2×C3⋊((C3⋊D3)⋊C3)C2×D311yescharacteristic
113C2×C3⋊((C3⋊D3)⋊C3)C2×D311yescharacteristic, complemented
114C2×D3×H(3,𝔽3)—23no—
115C2×D3×H(3,𝔽3)C2×D313yescomplemented
116C2×C3×(C3⋊D3)⋊C3—33no—
117C2×C3×(C3⋊D3)⋊C3—33no—
118C2×C3×(C3⋊D3)⋊C3—66no—
119D3×(C3⋊D3)⋊C3—66no—
120C3×C4×H(3,𝔽3)—31no—
121C3⋊((C3⋊Dic3)⋊C3)—31no—
122C3⋊((C3⋊Dic3)⋊C3)—33no—
123C3⋊((C3⋊Dic3)⋊C3)—63no—
124C3⋊((C3⋊Dic3)⋊C3)—61no—
125Dic3×H(3,𝔽3)—23no—
126Dic3×H(3,𝔽3)C2×D313yescomplemented
127C32×H(3,𝔽3)C2×D411yescharacteristic, complemented, Sylow
128C22×C3⋊(C3⋊D3)—31no—
129C22×C3⋊(C3⋊D3)C3×D311yescharacteristic, complemented
130C22×C3×C3⋊D3—31no—
131C22×C3×C3⋊D3—31no—
132C22×C3×C3⋊D3—33no—
133C22×C3×C3⋊D3—61no—
134C22×C3×C3⋊D3—91no—
135C22×C3×C3⋊D3—91no—
136C22×C3×C3⋊D3—91no—
137C22×C3×C3⋊D3—91no—
138C22×C32×D3—91no—
139C22×C32×D3—91no—
140C22×C32×D3—91no—
141C22×C32×D3—91no—
142C2×D3×C3⋊D3—31no—
143C2×D3×C3⋊D3—33no—
144C2×D3×C3⋊D3—91no—
145C2×D3×C3⋊D3—91no—
146C2×D3×C3⋊D3—91no—
147C2×C3×D32—91no—
148C2×C3×D32—91no—
149C2×C3×D32—91no—
150C2×C3×D32—91no—
151C33×D4—31no—
152C33×D4—31no—
153C33×D4—61no—
154#6312—31no—
155#6312—31no—
156#6312—33no—
157#6312—31no—
158#6312—61no—
159#6312—63no—
160#6312—91no—
161#6312—91no—
162#6312—91no—
163#6312—181no—
164#6312—181no—
165#6312—181no—
166C4⋊(C3⋊(C3⋊D3))—31no—
167C4×C3⋊(C3⋊D3)—31no—
168C3×#638—91no—
169C3×#638—91no—
170C3×#638—91no—
171C3×#638—91no—
172C3×#638—91no—
173C3×#638—91no—
174C3×#638—181no—
175C3×#638—181no—
176C3×#638—181no—
177C3×#638—181no—
178C3×C4⋊(C3⋊D3)—91no—
179C3×C4×C3⋊D3—91no—
180C32×#67—23no—
181C32×#67—21no—
182C32×#67—31no—
183C32×#67—31no—
184C32×#67—31no—
185C32×#67—31no—
186C32×#67—61no—
187C32×#67—61no—
188C32×#67—61no—
189C32×#67—61no—
190C32×#67—61no—
191C32×#67C3×D311yescharacteristic
192C32×#67C3×D313yescomplemented
193C32×#67C3⋊D311yescharacteristic, complemented
194#6292—31no—
195#6292—33no—
196#6292—91no—
197#6292—91no—
198#6292—91no—
199#6290—31no—
200#6290—33no—
201#6290—91no—
202#6290—91no—
203#6290—91no—
204Dic3×C3⋊D3—31no—
205Dic3×C3⋊D3—33no—
206Dic3×C3⋊D3—91no—
207Dic3×C3⋊D3—91no—
208Dic3×C3⋊D3—91no—
209C3×#626—91no—
210C3×#626—91no—
211C3×#626—91no—
212C3×#626—91no—
213C3×#625—91no—
214C3×#625—91no—
215C3×#625—91no—
216C3×#625—91no—
217C3×D3×Dic3—91no—
218C3×D3×Dic3—91no—
219C3×D3×Dic3—91no—
220C3×D3×Dic3—91no—
221C22×(C3⋊D3)⋊C3—33no—
222C22×(C3⋊D3)⋊C3—63no—
223C22×(C3⋊D3)⋊C3—93no—
224D4×H(3,𝔽3)—33no—
225D4×H(3,𝔽3)—63no—
226#638⋊C3—93no—
227#638⋊C3—93no—
228#638⋊C3—183no—
229C4⋊((C3⋊D3)⋊C3)—93no—
230C4×(C3⋊D3)⋊C3—93no—
231C2×C34—21no—
232C2×C34—21no—
233C2×C34—21no—
234C2×C34—41no—
235C2×C34C22×D311yescharacteristic
236C2×C34C23×C311yescharacteristic
237C3⋊(C3⋊(C3⋊D3))—21no—
238C3×C3⋊(C3⋊D3)—21no—
239C3×C3⋊(C3⋊D3)—61no—
240C3×C3⋊(C3⋊D3)C3×D412yescomplemented
241C32×C3⋊D3—32no—
242C32×C3⋊D3—61no—
243C33×D3—21no—
244C33×D3—21no—
245C33×D3—41no—
246C2×C3×H(3,𝔽3)—21no—
247C2×C3×H(3,𝔽3)—21no—
248C2×C3×H(3,𝔽3)—23no—
249C2×C3×H(3,𝔽3)—21no—
250C2×C3×H(3,𝔽3)—21no—
251C2×C3×H(3,𝔽3)—21no—
252C2×C3×H(3,𝔽3)—23no—
253C2×C3×H(3,𝔽3)—23no—
254C2×C3×H(3,𝔽3)—43no—
255C2×C3×H(3,𝔽3)—43no—
256C2×C3×H(3,𝔽3)—43no—
257C2×C3×H(3,𝔽3)—43no—
258C2×C3×H(3,𝔽3)—41no—
259C2×C3×H(3,𝔽3)—41no—
260C2×C3×H(3,𝔽3)—43no—
261C2×C3×H(3,𝔽3)—41no—
262C2×C3×H(3,𝔽3)—41no—
263C2×C3×H(3,𝔽3)—61no—
264C2×C3×H(3,𝔽3)C22×D311yescharacteristic
265C2×C3×H(3,𝔽3)C22×D313yes—
266C3⋊((C3⋊D3)⋊C3)—22no—
267C3⋊((C3⋊D3)⋊C3)—21no—
268C3⋊((C3⋊D3)⋊C3)—22no—
269C3⋊((C3⋊D3)⋊C3)—61no—
270C3⋊((C3⋊D3)⋊C3)—63no—
271C3⋊((C3⋊D3)⋊C3)—123no—
272C3⋊((C3⋊D3)⋊C3)—121no—
273C3⋊((C3⋊D3)⋊C3)#6712yesdirect product factor
274D3×H(3,𝔽3)—23no—
275D3×H(3,𝔽3)—43no—
276C3×(C3⋊D3)⋊C3—36no—
277C3×(C3⋊D3)⋊C3—63no—
278D4×C3⋊D3—91no—
279D4×C3⋊D3—93no—
280D4×C3⋊D3—271no—
281D4×C3⋊D3—271no—
282D4×C3⋊D3—271no—
283C2×C3×#67—271no—
284C3×D3×D4—271no—
285C3×D3×D4—271no—
286C3×D3×D4—271no—
287C3×D3×D4—271no—
288D3×#67—91no—
289D3×#67—91no—
290D3×#67—91no—
291D3×#67—91no—
292D3×#67—273no—
293C22×C33—21no—
294C22×C33—21no—
295C22×C33—21no—
296C22×C33—23no—
297C22×C33—21no—
298C22×C33—21no—
299C22×C33—23no—
300C22×C33—31no—
301C22×C33—31no—
302C22×C33—31no—
303C22×C33—31no—
304C22×C33—31no—
305C22×C33—31no—
306C22×C33—41no—
307C22×C33—43no—
308C22×C33—41no—
309C22×C33—61no—
310C22×C33—61no—
311C22×C33—61no—
312C22×C33—61no—
313C22×C33—61no—
314C22×C33—61no—
315C22×C33—61no—
316C22×C33—61no—
317C22×C33—61no—
318C22×C33—61no—
319C22×C33—121no—
320C22×C33—121no—
321C22×C33—121no—
322C22×C33—121no—
323C22×C33—121no—
324C22×C33D3211yescharacteristic, complemented
325C22×C33C2×C3×D311yescharacteristic
326C22×C33C2×C3×D313yescomplemented
327C22×C33C2×C3×D311yescharacteristic, complemented
328C22×C33C2×C3⋊D311yescharacteristic, complemented
329C2×C3⋊(C3⋊D3)—22no—
330C2×C3⋊(C3⋊D3)—31no—
331C2×C3⋊(C3⋊D3)—31no—
332C2×C3⋊(C3⋊D3)—33no—
333C2×C3⋊(C3⋊D3)—62no—
334C2×C3⋊(C3⋊D3)—61no—
335C2×C3⋊(C3⋊D3)—63no—
336C2×C3⋊(C3⋊D3)—91no—
337C2×C3⋊(C3⋊D3)—91no—
338C2×C3⋊(C3⋊D3)—91no—
339C2×C3⋊(C3⋊D3)—181no—
340C2×C3⋊(C3⋊D3)—181no—
341C2×C3⋊(C3⋊D3)—181no—
342C2×C3⋊(C3⋊D3)C2×C3×D311yescharacteristic
343C2×C3⋊(C3⋊D3)C2×C3×D311yescharacteristic, complemented
344C2×C3×C3⋊D3—31no—
345C2×C3×C3⋊D3—31no—
346C2×C3×C3⋊D3—33no—
347C2×C3×C3⋊D3—31no—
348C2×C3×C3⋊D3—31no—
349C2×C3×C3⋊D3—33no—
350C2×C3×C3⋊D3—62no—
351C2×C3×C3⋊D3—62no—
352C2×C3×C3⋊D3—66no—
353C2×C3×C3⋊D3—61no—
354C2×C3×C3⋊D3—61no—
355C2×C3×C3⋊D3—62no—
356C2×C3×C3⋊D3—62no—
357C2×C3×C3⋊D3—91no—
358C2×C3×C3⋊D3—91no—
359C2×C3×C3⋊D3—91no—
360C2×C3×C3⋊D3—91no—
361C2×C3×C3⋊D3—91no—
362C2×C3×C3⋊D3—91no—
363C2×C3×C3⋊D3—91no—
364C2×C3×C3⋊D3—91no—
365C2×C3×C3⋊D3—91no—
366C2×C3×C3⋊D3—91no—
367C2×C3×C3⋊D3—91no—
368C2×C3×C3⋊D3—182no—
369C2×C3×C3⋊D3—182no—
370C2×C3×C3⋊D3—182no—
371C2×C3×C3⋊D3—182no—
372C2×C3×C3⋊D3—181no—
373C2×C3×C3⋊D3—181no—
374C2×C3×C3⋊D3—181no—
375C2×C3×C3⋊D3—181no—
376C2×C32×D3—21no—
377C2×C32×D3—23no—
378C2×C32×D3—31no—
379C2×C32×D3—31no—
380C2×C32×D3—31no—
381C2×C32×D3—31no—
382C2×C32×D3—61no—
383C2×C32×D3—61no—
384C2×C32×D3—61no—
385C2×C32×D3—61no—
386C2×C32×D3—61no—
387C2×C32×D3—91no—
388C2×C32×D3—91no—
389C2×C32×D3—91no—
390C2×C32×D3—91no—
391C2×C32×D3—91no—
392C2×C32×D3—91no—
393C2×C32×D3—91no—
394C2×C32×D3—91no—
395C2×C32×D3—182no—
396C2×C32×D3—182no—
397C2×C32×D3—182no—
398C2×C32×D3—182no—
399C2×C32×D3C2×C3×D311yescharacteristic
400C2×C32×D3C2×C3×D313yescomplemented
401C2×C32×D3C2×C3⋊D311yescharacteristic, complemented
402D3×C3⋊D3—62no—
403D3×C3⋊D3—66no—
404D3×C3⋊D3—182no—
405D3×C3⋊D3—182no—
406D3×C3⋊D3—182no—
407C3×D32—182no—
408C3×D32—182no—
409C3×D32—182no—
410C3×D32—182no—
411C33×C4—31no—
412C33×C4—31no—
413C33×C4—61no—
414C3⋊(C3⋊Dic3)—31no—
415C3⋊(C3⋊Dic3)—31no—
416C3⋊(C3⋊Dic3)—33no—
417C3⋊(C3⋊Dic3)—61no—
418C3⋊(C3⋊Dic3)—63no—
419C3⋊(C3⋊Dic3)—91no—
420C3⋊(C3⋊Dic3)—91no—
421C3⋊(C3⋊Dic3)—91no—
422C3⋊(C3⋊Dic3)—181no—
423C3⋊(C3⋊Dic3)—181no—
424C3⋊(C3⋊Dic3)—181no—
425C3×C3⋊Dic3—91no—
426C3×C3⋊Dic3—91no—
427C3×C3⋊Dic3—91no—
428C3×C3⋊Dic3—91no—
429C3×C3⋊Dic3—91no—
430C3×C3⋊Dic3—181no—
431C3×C3⋊Dic3—181no—
432C3×C3⋊Dic3—181no—
433C3×C3⋊Dic3—181no—
434C32×Dic3—21no—
435C32×Dic3—23no—
436C32×Dic3—31no—
437C32×Dic3—31no—
438C32×Dic3—31no—
439C32×Dic3—31no—
440C32×Dic3—61no—
441C32×Dic3—61no—
442C32×Dic3—61no—
443C32×Dic3—61no—
444C32×Dic3—61no—
445C32×Dic3C2×C3×D311yescharacteristic
446C32×Dic3C2×C3×D313yescomplemented
447C32×Dic3C2×C3⋊D311yescharacteristic, complemented
448C22×H(3,𝔽3)—23no—
449C22×H(3,𝔽3)—23no—
450C22×H(3,𝔽3)—23no—
451C22×H(3,𝔽3)—33no—
452C22×H(3,𝔽3)—43no—
453C22×H(3,𝔽3)—43no—
454C22×H(3,𝔽3)—46no—
455C22×H(3,𝔽3)—43no—
456C22×H(3,𝔽3)—63no—
457C22×H(3,𝔽3)D3213yescomplemented
458C2×(C3⋊D3)⋊C3—33no—
459C2×(C3⋊D3)⋊C3—33no—
460C2×(C3⋊D3)⋊C3—66no—
461C2×(C3⋊D3)⋊C3—63no—
462C2×(C3⋊D3)⋊C3—63no—
463C2×(C3⋊D3)⋊C3—66no—
464C2×(C3⋊D3)⋊C3—66no—
465C2×(C3⋊D3)⋊C3—93no—
466C2×(C3⋊D3)⋊C3—186no—
467C2×(C3⋊D3)⋊C3—183no—
468C4×H(3,𝔽3)—33no—
469C4×H(3,𝔽3)—63no—
470(C3⋊Dic3)⋊C3—93no—
471(C3⋊Dic3)⋊C3—183no—
472C34—21no—
473C34D3×D411yescharacteristic, complemented
474C34C2×C3×D411yescharacteristic, complemented
475C3×H(3,𝔽3)—21no—
476C3×H(3,𝔽3)—21no—
477C3×H(3,𝔽3)—23no—
478C3×H(3,𝔽3)—23no—
479C3×H(3,𝔽3)—43no—
480C3×H(3,𝔽3)—41no—
481C3×H(3,𝔽3)D3×D413yescomplemented
482C3×H(3,𝔽3)C2×#6711yescharacteristic, complemented
483C23×C32—271no—
484C22×C3⋊D3—31no—
485C22×C3⋊D3—33no—
486C22×C3⋊D3—91no—
487C22×C3⋊D3—91no—
488C22×C3⋊D3—91no—
489C22×C3⋊D3—91no—
490C22×C3⋊D3—93no—
491C22×C3⋊D3—271no—
492C22×C3⋊D3—271no—
493C22×C3⋊D3—271no—
494C22×C3×D3—91no—
495C22×C3×D3—91no—
496C22×C3×D3—91no—
497C22×C3×D3—91no—
498C22×C3×D3—91no—
499C22×C3×D3—91no—
500C22×C3×D3—91no—
501C22×C3×D3—91no—
502C22×C3×D3—181no—
503C22×C3×D3—181no—
504C22×C3×D3—181no—
505C22×C3×D3—181no—
506C22×C3×D3—273no—
507C22×C3×D3—271no—
508C22×C3×D3—271no—
509C22×C3×D3—271no—
510C22×C3×D3—271no—
511C22×C3×D3—271no—
512C2×D32—91no—
513C2×D32—91no—
514C2×D32—91no—
515C2×D32—91no—
516C2×D32—273no—
517C32×D4—31no—
518C32×D4—33no—
519C32×D4—31no—
520C32×D4—63no—
521C32×D4—61no—
522C32×D4—91no—
523C32×D4—91no—
524C32×D4—91no—
525C32×D4—181no—
526C32×D4—181no—
527C32×D4—181no—
528C32×D4—181no—
529C32×D4—181no—
530C32×D4—181no—
531#638—91no—
532#638—91no—
533#638—91no—
534#638—91no—
535#638—91no—
536#638—91no—
537#638—93no—
538#638—93no—
539#638—181no—
540#638—181no—
541#638—181no—
542#638—181no—
543#638—183no—
544#638—271no—
545#638—271no—
546#638—271no—
547#638—271no—
548#638—271no—
549#638—271no—
550#638—273no—
551#638—541no—
552#638—541no—
553#638—541no—
554#638—543no—
555#638—543no—
556#638—543no—
557#638—543no—
558C4⋊(C3⋊D3)—91no—
559C4⋊(C3⋊D3)—93no—
560C4⋊(C3⋊D3)—271no—
561C4⋊(C3⋊D3)—271no—
562C4⋊(C3⋊D3)—271no—
563C4×C3⋊D3—91no—
564C4×C3⋊D3—93no—
565C4×C3⋊D3—271no—
566C4×C3⋊D3—271no—
567C4×C3⋊D3—271no—
568C3×#67—33no—
569C3×#67—31no—
570C3×#67—61no—
571C3×#67—63no—
572C3×#67—271no—
573C3×#67—271no—
574C3×#67—271no—
575C3×#67—271no—
576C3×#67—271no—
577C3×#67—271no—
578C3×#67—271no—
579C3×#67—271no—
580C3×#67—271no—
581C3×#67—271no—
582C3×#67—271no—
583C3×#67—541no—
584C3×#67—541no—
585C3×#67—541no—
586C3×#67—541no—
587C3×#67(C3⋊D3)⋊C311yescharacteristic, complemented
588C3×#67(C3⋊D3)⋊C311yescharacteristic, complemented
589C3×#67(C3⋊D3)⋊C311yescharacteristic, complemented
590C3×#67C3×C3⋊D311yescharacteristic
591C2×C3×Dic3—271no—
592C3×D12—271no—
593C3×D12—271no—
594C3×D12—271no—
595C3×D12—271no—
596C3×C4×D3—271no—
597C3×C4×D3—271no—
598C3×C4×D3—271no—
599C3×C4×D3—271no—
600#626—91no—
601#626—91no—
602#626—91no—
603#626—91no—
604#626—273no—
605#625—91no—
606#625—91no—
607#625—91no—
608#625—91no—
609#625—273no—
610D3×Dic3—91no—
611D3×Dic3—91no—
612D3×Dic3—91no—
613D3×Dic3—91no—
614D3×Dic3—273no—
615C2×C33—21no—
616C2×C33—21no—
617C2×C33—21no—
618C2×C33—23no—
619C2×C33—21no—
620C2×C33—21no—
621C2×C33—21no—
622C2×C33—23no—
623C2×C33—21no—
624C2×C33—21no—
625C2×C33—21no—
626C2×C33—21no—
627C2×C33—23no—
628C2×C33—21no—
629C2×C33—31no—
630C2×C33—31no—
631C2×C33—31no—
632C2×C33—31no—
633C2×C33—41no—
634C2×C33—43no—
635C2×C33—41no—
636C2×C33—43no—
637C2×C33—41no—
638C2×C33—41no—
639C2×C33—43no—
640C2×C33—41no—
641C2×C33—41no—
642C2×C33—41no—
643C2×C33—41no—
644C2×C33—41no—
645C2×C33—46no—
646C2×C33—41no—
647C2×C33—61no—
648C2×C33—61no—
649C2×C33—61no—
650C2×C33—61no—
651C2×C33—61no—
652C2×C33—61no—
653C2×C33—61no—
654C2×C33—61no—
655C2×C33—61no—
656C2×C33—61no—
657C2×C33—61no—
658C2×C33—61no—
659C2×C33—61no—
660C2×C33—61no—
661C2×C33—61no—
662C2×C33—121no—
663C2×C33—121no—
664C2×C33—121no—
665C2×C33—121no—
666C2×C33—121no—
667C2×C33—121no—
668C2×C33—121no—
669C2×C33—121no—
670C2×C33—121no—
671C2×C33—121no—
672C2×C33—121no—
673C2×C33—121no—
674C2×C33—121no—
675C2×C33—121no—
676C2×C33—121no—
677C2×C33—121no—
678C2×C33—122no—
679C2×C33—122no—
680C2×C33—122no—
681C2×C33—121no—
682C2×C33C2×D3211yescharacteristic
683C2×C33C22×C3×D311yescharacteristic
684C2×C33C22×C3×D313yes—
685C2×C33C22×C3×D311yescharacteristic
686C2×C33C22×C3⋊D311yescharacteristic
687C3⋊(C3⋊D3)—21no—
688C3⋊(C3⋊D3)—61no—
689C3⋊(C3⋊D3)—61no—
690C3⋊(C3⋊D3)—63no—
691C3⋊(C3⋊D3)—121no—
692C3⋊(C3⋊D3)—123no—
693C3⋊(C3⋊D3)—181no—
694C3⋊(C3⋊D3)—181no—
695C3⋊(C3⋊D3)—181no—
696C3⋊(C3⋊D3)—361no—
697C3⋊(C3⋊D3)—361no—
698C3⋊(C3⋊D3)—361no—
699C3⋊(C3⋊D3)C3×#6712yescomplemented
700C3×C3⋊D3—32no—
701C3×C3⋊D3—32no—
702C3×C3⋊D3—36no—
703C3×C3⋊D3—62no—
704C3×C3⋊D3—62no—
705C3×C3⋊D3—61no—
706C3×C3⋊D3—61no—
707C3×C3⋊D3—63no—
708C3×C3⋊D3—92no—
709C3×C3⋊D3—92no—
710C3×C3⋊D3—92no—
711C3×C3⋊D3—181no—
712C3×C3⋊D3—181no—
713C3×C3⋊D3—181no—
714C3×C3⋊D3—181no—
715C3×C3⋊D3—181no—
716C3×C3⋊D3—181no—
717C3×C3⋊D3—181no—
718C3×C3⋊D3—181no—
719C3×C3⋊D3—361no—
720C3×C3⋊D3—361no—
721C3×C3⋊D3—361no—
722C3×C3⋊D3—361no—
723C32×D3—21no—
724C32×D3—23no—
725C32×D3—21no—
726C32×D3—43no—
727C32×D3—41no—
728C32×D3—61no—
729C32×D3—61no—
730C32×D3—61no—
731C32×D3—61no—
732C32×D3—92no—
733C32×D3—92no—
734C32×D3—92no—
735C32×D3—92no—
736C32×D3—121no—
737C32×D3—121no—
738C32×D3—121no—
739C32×D3—121no—
740C32×D3—121no—
741C32×D3—181no—
742C32×D3—181no—
743C32×D3—181no—
744C32×D3—181no—
745C2×H(3,𝔽3)—23no—
746C2×H(3,𝔽3)—23no—
747C2×H(3,𝔽3)—23no—
748C2×H(3,𝔽3)—23no—
749C2×H(3,𝔽3)—23no—
750C2×H(3,𝔽3)—23no—
751C2×H(3,𝔽3)—43no—
752C2×H(3,𝔽3)—43no—
753C2×H(3,𝔽3)—46no—
754C2×H(3,𝔽3)—43no—
755C2×H(3,𝔽3)—43no—
756C2×H(3,𝔽3)—43no—
757C2×H(3,𝔽3)—43no—
758C2×H(3,𝔽3)—43no—
759C2×H(3,𝔽3)—43no—
760C2×H(3,𝔽3)—46no—
761C2×H(3,𝔽3)—46no—
762C2×H(3,𝔽3)—46no—
763C2×H(3,𝔽3)—43no—
764C2×H(3,𝔽3)—63no—
765C2×H(3,𝔽3)—123no—
766C2×H(3,𝔽3)C2×D3213yes—
767(C3⋊D3)⋊C3—36no—
768(C3⋊D3)⋊C3—66no—
769(C3⋊D3)⋊C3—66no—
770(C3⋊D3)⋊C3—63no—
771(C3⋊D3)⋊C3—183no—
772(C3⋊D3)⋊C3—363no—
773C2×C3×D4—811no—
774C2×#67—271no—
775D3×D4—271no—
776D3×D4—271no—
777D3×D4—271no—
778D3×D4—271no—
779D3×D4—813no—
780C22×C32—21no—
781C22×C32—21no—
782C22×C32—21no—
783C22×C32—21no—
784C22×C32—21no—
785C22×C32—21no—
786C22×C32—23no—
787C22×C32—23no—
788C22×C32—31no—
789C22×C32—31no—
790C22×C32—31no—
791C22×C32—31no—
792C22×C32—33no—
793C22×C32—31no—
794C22×C32—33no—
795C22×C32—31no—
796C22×C32—43no—
797C22×C32—41no—
798C22×C32—63no—
799C22×C32—63no—
800C22×C32—63no—
801C22×C32—63no—
802C22×C32—61no—
803C22×C32—61no—
804C22×C32—61no—
805C22×C32—61no—
806C22×C32—61no—
807C22×C32—63no—
808C22×C32—61no—
809C22×C32—61no—
810C22×C32—61no—
811C22×C32—61no—
812C22×C32—61no—
813C22×C32—61no—
814C22×C32—61no—
815C22×C32—61no—
816C22×C32—63no—
817C22×C32—91no—
818C22×C32—91no—
819C22×C32—91no—
820C22×C32—121no—
821C22×C32—121no—
822C22×C32—121no—
823C22×C32—121no—
824C22×C32—121no—
825C22×C32—123no—
826C22×C32—123no—
827C22×C32—123no—
828C22×C32—121no—
829C22×C32—123no—
830C22×C32—121no—
831C22×C32—121no—
832C22×C32—121no—
833C22×C32—121no—
834C22×C32—121no—
835C22×C32—121no—
836C22×C32—181no—
837C22×C32—181no—
838C22×C32—181no—
839C22×C32—181no—
840C22×C32—181no—
841C22×C32—181no—
842C22×C32—271no—
843C22×C32—271no—
844C22×C32—542no—
845C22×C32C2×(C3⋊D3)⋊C311yescharacteristic, complemented
846C22×C32C2×(C3⋊D3)⋊C311yescharacteristic, complemented
847C22×C32C2×(C3⋊D3)⋊C311yescharacteristic, complemented
848C22×C32C3×D3211yescharacteristic
849C22×C32C3×D3213yescomplemented
850C22×C32D3×C3⋊D311yescharacteristic, complemented
851C22×C32C2×C3×C3⋊D311yescharacteristic
852C2×C3⋊D3—31no—
853C2×C3⋊D3—31no—
854C2×C3⋊D3—33no—
855C2×C3⋊D3—33no—
856C2×C3⋊D3—62no—
857C2×C3⋊D3—66no—
858C2×C3⋊D3—91no—
859C2×C3⋊D3—91no—
860C2×C3⋊D3—91no—
861C2×C3⋊D3—91no—
862C2×C3⋊D3—91no—
863C2×C3⋊D3—91no—
864C2×C3⋊D3—91no—
865C2×C3⋊D3—91no—
866C2×C3⋊D3—91no—
867C2×C3⋊D3—91no—
868C2×C3⋊D3—91no—
869C2×C3⋊D3—93no—
870C2×C3⋊D3—182no—
871C2×C3⋊D3—182no—
872C2×C3⋊D3—182no—
873C2×C3⋊D3—181no—
874C2×C3⋊D3—181no—
875C2×C3⋊D3—181no—
876C2×C3⋊D3—181no—
877C2×C3⋊D3—183no—
878C2×C3⋊D3—182no—
879C2×C3⋊D3—186no—
880C2×C3⋊D3—271no—
881C2×C3⋊D3—271no—
882C2×C3⋊D3—271no—
883C2×C3⋊D3—273no—
884C2×C3⋊D3—541no—
885C2×C3⋊D3—541no—
886C2×C3⋊D3—541no—
887C2×C3⋊D3—543no—
888C2×C3⋊D3—543no—
889C2×C3⋊D3—543no—
890C2×C3⋊D3—543no—
891C2×C3⋊D3—542no—
892C2×C3⋊D3—542no—
893C2×C3⋊D3—542no—
894C2×C3×D3—33no—
895C2×C3×D3—31no—
896C2×C3×D3—61no—
897C2×C3×D3—63no—
898C2×C3×D3—91no—
899C2×C3×D3—91no—
900C2×C3×D3—91no—
901C2×C3×D3—91no—
902C2×C3×D3—91no—
903C2×C3×D3—91no—
904C2×C3×D3—91no—
905C2×C3×D3—91no—
906C2×C3×D3—91no—
907C2×C3×D3—91no—
908C2×C3×D3—91no—
909C2×C3×D3—91no—
910C2×C3×D3—91no—
911C2×C3×D3—91no—
912C2×C3×D3—91no—
913C2×C3×D3—91no—
914C2×C3×D3—181no—
915C2×C3×D3—181no—
916C2×C3×D3—181no—
917C2×C3×D3—181no—
918C2×C3×D3—181no—
919C2×C3×D3—181no—
920C2×C3×D3—181no—
921C2×C3×D3—181no—
922C2×C3×D3—182no—
923C2×C3×D3—182no—
924C2×C3×D3—182no—
925C2×C3×D3—182no—
926C2×C3×D3—182no—
927C2×C3×D3—182no—
928C2×C3×D3—182no—
929C2×C3×D3—182no—
930C2×C3×D3—182no—
931C2×C3×D3—182no—
932C2×C3×D3—182no—
933C2×C3×D3—182no—
934C2×C3×D3—182no—
935C2×C3×D3—182no—
936C2×C3×D3—182no—
937C2×C3×D3—182no—
938C2×C3×D3—273no—
939C2×C3×D3—273no—
940C2×C3×D3—271no—
941C2×C3×D3—271no—
942C2×C3×D3—271no—
943C2×C3×D3—271no—
944C2×C3×D3—271no—
945C2×C3×D3—546no—
946C2×C3×D3—541no—
947C2×C3×D3—541no—
948C2×C3×D3—541no—
949C2×C3×D3—541no—
950C2×C3×D3—542no—
951C2×C3×D3—542no—
952C2×C3×D3—542no—
953C2×C3×D3—542no—
954C2×C3×D3—542no—
955C2×C3×D3C2×(C3⋊D3)⋊C311yescharacteristic, complemented
956C2×C3×D3C2×(C3⋊D3)⋊C311yescharacteristic, complemented
957C2×C3×D3C2×(C3⋊D3)⋊C311yescharacteristic, complemented
958C2×C3×D3C2×C3×C3⋊D311yescharacteristic
959D32—182no—
960D32—182no—
961D32—182no—
962D32—182no—
963D32—546no—
964C32×C4—31no—
965C32×C4—33no—
966C32×C4—31no—
967C32×C4—63no—
968C32×C4—61no—
969C32×C4—91no—
970C32×C4—91no—
971C32×C4—91no—
972C32×C4—181no—
973C32×C4—181no—
974C32×C4—181no—
975C32×C4—181no—
976C32×C4—181no—
977C32×C4—181no—
978C3⋊Dic3—91no—
979C3⋊Dic3—91no—
980C3⋊Dic3—91no—
981C3⋊Dic3—91no—
982C3⋊Dic3—91no—
983C3⋊Dic3—93no—
984C3⋊Dic3—181no—
985C3⋊Dic3—181no—
986C3⋊Dic3—181no—
987C3⋊Dic3—181no—
988C3⋊Dic3—183no—
989C3⋊Dic3—271no—
990C3⋊Dic3—271no—
991C3⋊Dic3—271no—
992C3⋊Dic3—273no—
993C3⋊Dic3—541no—
994C3⋊Dic3—541no—
995C3⋊Dic3—541no—
996C3⋊Dic3—543no—
997C3⋊Dic3—543no—
998C3⋊Dic3—543no—
999C3⋊Dic3—543no—
1000C3×Dic3—33no—
1001C3×Dic3—31no—
1002C3×Dic3—61no—
1003C3×Dic3—63no—
1004C3×Dic3—271no—
1005C3×Dic3—271no—
1006C3×Dic3—271no—
1007C3×Dic3—271no—
1008C3×Dic3—271no—
1009C3×Dic3—541no—
1010C3×Dic3—541no—
1011C3×Dic3—541no—
1012C3×Dic3—541no—
1013C3×Dic3C2×(C3⋊D3)⋊C311yescharacteristic, complemented
1014C3×Dic3C2×(C3⋊D3)⋊C311yescharacteristic, complemented
1015C3×Dic3C2×(C3⋊D3)⋊C311yescharacteristic, complemented
1016C3×Dic3C2×C3×C3⋊D311yescharacteristic
1017C33—21no—
1018C33—21no—
1019C33—23no—
1020C33—21no—
1021C33—21no—
1022C33—23no—
1023C33—21no—
1024C33—31no—
1025C33—31no—
1026C33—31no—
1027C33—31no—
1028C33—41no—
1029C33—43no—
1030C33—41no—
1031C33—61no—
1032C33—61no—
1033C33—61no—
1034C33—61no—
1035C33—61no—
1036C33—61no—
1037C33—61no—
1038C33—61no—
1039C33—61no—
1040C33—121no—
1041C33—121no—
1042C33—121no—
1043C33—121no—
1044C33—121no—
1045C33D3×#6711yescharacteristic, complemented
1046C33C3×D3×D411yescharacteristic
1047C33C3×D3×D413yescomplemented
1048C33C2×C3×#6711yescharacteristic, complemented
1049C33D4×C3⋊D311yescharacteristic, complemented
1050H(3,𝔽3)—23no—
1051H(3,𝔽3)—23no—
1052H(3,𝔽3)—23no—
1053H(3,𝔽3)—43no—
1054H(3,𝔽3)—43no—
1055H(3,𝔽3)—46no—
1056H(3,𝔽3)—43no—
1057H(3,𝔽3)D3×#6713yescomplemented
1058C23×C3—271no—
1059C23×C3—271no—
1060C23×C3—541no—
1061C23×C3—811no—
1062C22×D3—91no—
1063C22×D3—91no—
1064C22×D3—91no—
1065C22×D3—91no—
1066C22×D3—273no—
1067C22×D3—271no—
1068C22×D3—271no—
1069C22×D3—271no—
1070C22×D3—271no—
1071C22×D3—271no—
1072C22×D3—813no—
1073C3×D4—31no—
1074C3×D4—31no—
1075C3×D4—31no—
1076C3×D4—31no—
1077C3×D4—93no—
1078C3×D4—91no—
1079C3×D4—181no—
1080C3×D4—183no—
1081C3×D4—811no—
1082C3×D4—811no—
1083C3×D4—811no—
1084C2×C3×C4—811no—
1085#67—271no—
1086#67—271no—
1087#67—271no—
1088#67—271no—
1089#67—271no—
1090#67—271no—
1091#67—271no—
1092#67—271no—
1093#67—271no—
1094#67—271no—
1095#67—271no—
1096#67—541no—
1097#67—541no—
1098#67—541no—
1099#67—541no—
1100#67—813no—
1101#67—813no—
1102#67—1623no—
1103#67C3⋊((C3⋊D3)⋊C3)11yescharacteristic, direct product factor
1104C2×Dic3—271no—
1105D12—271no—
1106D12—271no—
1107D12—271no—
1108D12—271no—
1109D12—813no—
1110C4×D3—271no—
1111C4×D3—271no—
1112C4×D3—271no—
1113C4×D3—271no—
1114C4×D3—813no—
1115C2×C32—21no—
1116C2×C32—21no—
1117C2×C32—21no—
1118C2×C32—21no—
1119C2×C32—21no—
1120C2×C32—21no—
1121C2×C32—21no—
1122C2×C32—21no—
1123C2×C32—21no—
1124C2×C32—21no—
1125C2×C32—23no—
1126C2×C32—21no—
1127C2×C32—21no—
1128C2×C32—21no—
1129C2×C32—21no—
1130C2×C32—23no—
1131C2×C32—23no—
1132C2×C32—31no—
1133C2×C32—31no—
1134C2×C32—31no—
1135C2×C32—33no—
1136C2×C32—31no—
1137C2×C32—41no—
1138C2×C32—41no—
1139C2×C32—41no—
1140C2×C32—41no—
1141C2×C32—43no—
1142C2×C32—43no—
1143C2×C32—41no—
1144C2×C32—43no—
1145C2×C32—43no—
1146C2×C32—41no—
1147C2×C32—41no—
1148C2×C32—43no—
1149C2×C32—41no—
1150C2×C32—63no—
1151C2×C32—63no—
1152C2×C32—63no—
1153C2×C32—63no—
1154C2×C32—61no—
1155C2×C32—61no—
1156C2×C32—61no—
1157C2×C32—61no—
1158C2×C32—61no—
1159C2×C32—61no—
1160C2×C32—63no—
1161C2×C32—61no—
1162C2×C32—61no—
1163C2×C32—61no—
1164C2×C32—61no—
1165C2×C32—61no—
1166C2×C32—61no—
1167C2×C32—61no—
1168C2×C32—61no—
1169C2×C32—61no—
1170C2×C32—61no—
1171C2×C32—61no—
1172C2×C32—61no—
1173C2×C32—61no—
1174C2×C32—63no—
1175C2×C32—63no—
1176C2×C32—61no—
1177C2×C32—121no—
1178C2×C32—121no—
1179C2×C32—121no—
1180C2×C32—121no—
1181C2×C32—121no—
1182C2×C32—123no—
1183C2×C32—123no—
1184C2×C32—123no—
1185C2×C32—121no—
1186C2×C32—121no—
1187C2×C32—121no—
1188C2×C32—121no—
1189C2×C32—121no—
1190C2×C32—123no—
1191C2×C32—121no—
1192C2×C32—121no—
1193C2×C32—121no—
1194C2×C32—121no—
1195C2×C32—121no—
1196C2×C32—121no—
1197C2×C32—121no—
1198C2×C32—121no—
1199C2×C32—121no—
1200C2×C32—123no—
1201C2×C32—121no—
1202C2×C32—121no—
1203C2×C32—121no—
1204C2×C32—121no—
1205C2×C32—121no—
1206C2×C32—121no—
1207C2×C32—121no—
1208C2×C32—121no—
1209C2×C32—123no—
1210C2×C32—123no—
1211C2×C32—123no—
1212C2×C32—121no—
1213C2×C32—121no—
1214C2×C32—121no—
1215C2×C32—121no—
1216C2×C32—121no—
1217C2×C32—121no—
1218C2×C32—123no—
1219C2×C32—121no—
1220C2×C32—121no—
1221C2×C32—121no—
1222C2×C32—122no—
1223C2×C32—126no—
1224C2×C32—126no—
1225C2×C32—126no—
1226C2×C32—126no—
1227C2×C32—121no—
1228C2×C32—121no—
1229C2×C32—121no—
1230C2×C32—123no—
1231C2×C32—121no—
1232C2×C32—121no—
1233C2×C32—121no—
1234C2×C32—121no—
1235C2×C32—181no—
1236C2×C32—181no—
1237C2×C32—181no—
1238C2×C32—272no—
1239C2×C32—361no—
1240C2×C32—361no—
1241C2×C32—361no—
1242C2×C32—361no—
1243C2×C32—361no—
1244C2×C32—361no—
1245C2×C32—541no—
1246C2×C32C22×(C3⋊D3)⋊C311yescharacteristic
1247C2×C32C22×(C3⋊D3)⋊C311yescharacteristic
1248C2×C32C22×(C3⋊D3)⋊C311yescharacteristic
1249C2×C32C2×C3×D3213yes—
1250C2×C32C2×C3×D3211yescharacteristic
1251C2×C32C2×D3×C3⋊D311yescharacteristic
1252C2×C32C22×C3×C3⋊D311yescharacteristic
1253C3⋊D3—32no—
1254C3⋊D3—36no—
1255C3⋊D3—61no—
1256C3⋊D3—63no—
1257C3⋊D3—92no—
1258C3⋊D3—92no—
1259C3⋊D3—92no—
1260C3⋊D3—181no—
1261C3⋊D3—181no—
1262C3⋊D3—181no—
1263C3⋊D3—181no—
1264C3⋊D3—181no—
1265C3⋊D3—181no—
1266C3⋊D3—181no—
1267C3⋊D3—181no—
1268C3⋊D3—183no—
1269C3⋊D3—363no—
1270C3⋊D3—361no—
1271C3⋊D3—361no—
1272C3⋊D3—361no—
1273C3⋊D3—361no—
1274C3⋊D3—543no—
1275C3⋊D3—541no—
1276C3⋊D3—541no—
1277C3⋊D3—541no—
1278C3⋊D3—1081no—
1279C3⋊D3—1081no—
1280C3⋊D3—1081no—
1281C3⋊D3—1083no—
1282C3⋊D3—1083no—
1283C3⋊D3—1083no—
1284C3⋊D3—1083no—
1285C3×D3—21no—
1286C3×D3—21no—
1287C3×D3—21no—
1288C3×D3—21no—
1289C3×D3—63no—
1290C3×D3—61no—
1291C3×D3—92no—
1292C3×D3—92no—
1293C3×D3—92no—
1294C3×D3—92no—
1295C3×D3—92no—
1296C3×D3—92no—
1297C3×D3—92no—
1298C3×D3—92no—
1299C3×D3—121no—
1300C3×D3—123no—
1301C3×D3—182no—
1302C3×D3—182no—
1303C3×D3—182no—
1304C3×D3—182no—
1305C3×D3—182no—
1306C3×D3—181no—
1307C3×D3—181no—
1308C3×D3—181no—
1309C3×D3—182no—
1310C3×D3—182no—
1311C3×D3—182no—
1312C3×D3—181no—
1313C3×D3—181no—
1314C3×D3—181no—
1315C3×D3—181no—
1316C3×D3—181no—
1317C3×D3—276no—
1318C3×D3—543no—
1319C3×D3—541no—
1320C3×D3—541no—
1321C3×D3—541no—
1322C3×D3—541no—
1323C3×D3—541no—
1324C3×D3—1081no—
1325C3×D3—1081no—
1326C3×D3—1081no—
1327C3×D3—1081no—
1328C2×D4—811noSylow
1329C22×C3—21no—
1330C22×C3—21no—
1331C22×C3—21no—
1332C22×C3—21no—
1333C22×C3—31no—
1334C22×C3—31no—
1335C22×C3—31no—
1336C22×C3—31no—
1337C22×C3—33no—
1338C22×C3—31no—
1339C22×C3—61no—
1340C22×C3—63no—
1341C22×C3—61no—
1342C22×C3—63no—
1343C22×C3—93no—
1344C22×C3—91no—
1345C22×C3—121no—
1346C22×C3—123no—
1347C22×C3—181no—
1348C22×C3—183no—
1349C22×C3—271no—
1350C22×C3—271no—
1351C22×C3—271no—
1352C22×C3—271no—
1353C22×C3—541no—
1354C22×C3—541no—
1355C22×C3—542no—
1356C22×C3—542no—
1357C22×C3—542no—
1358C22×C3—542no—
1359C22×C3—811no—
1360C22×C3—1622no—
1361C22×C3D3×(C3⋊D3)⋊C311yescharacteristic, complemented
1362C22×C3D3×(C3⋊D3)⋊C311yescharacteristic, complemented
1363C22×C3D3×(C3⋊D3)⋊C311yescharacteristic, complemented
1364C22×C3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
1365C22×C3C3×D3×C3⋊D311yescharacteristic
1366C2×D3—91no—
1367C2×D3—91no—
1368C2×D3—91no—
1369C2×D3—91no—
1370C2×D3—91no—
1371C2×D3—91no—
1372C2×D3—91no—
1373C2×D3—91no—
1374C2×D3—182no—
1375C2×D3—182no—
1376C2×D3—182no—
1377C2×D3—182no—
1378C2×D3—273no—
1379C2×D3—273no—
1380C2×D3—271no—
1381C2×D3—271no—
1382C2×D3—271no—
1383C2×D3—271no—
1384C2×D3—271no—
1385C2×D3—546no—
1386C2×D3—541no—
1387C2×D3—541no—
1388C2×D3—541no—
1389C2×D3—541no—
1390C2×D3—542no—
1391C2×D3—542no—
1392C2×D3—542no—
1393C2×D3—542no—
1394C2×D3—542no—
1395C2×D3—813no—
1396C2×D3—1623no—
1397C2×D3—1626no—
1398C2×D3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
1399C3×C4—31no—
1400C3×C4—31no—
1401C3×C4—31no—
1402C3×C4—31no—
1403C3×C4—93no—
1404C3×C4—91no—
1405C3×C4—181no—
1406C3×C4—183no—
1407C3×C4—811no—
1408Dic3—271no—
1409Dic3—271no—
1410Dic3—271no—
1411Dic3—271no—
1412Dic3—271no—
1413Dic3—541no—
1414Dic3—541no—
1415Dic3—541no—
1416Dic3—541no—
1417Dic3—813no—
1418Dic3—1623no—
1419Dic3C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
1420C32—21no—
1421C32—21no—
1422C32—21no—
1423C32—21no—
1424C32—21no—
1425C32—23no—
1426C32—21no—
1427C32—23no—
1428C32—31no—
1429C32—31no—
1430C32—31no—
1431C32—33no—
1432C32—31no—
1433C32—43no—
1434C32—41no—
1435C32—63no—
1436C32—63no—
1437C32—63no—
1438C32—63no—
1439C32—61no—
1440C32—61no—
1441C32—61no—
1442C32—61no—
1443C32—61no—
1444C32—61no—
1445C32—61no—
1446C32—61no—
1447C32—61no—
1448C32—61no—
1449C32—61no—
1450C32—61no—
1451C32—63no—
1452C32—121no—
1453C32—121no—
1454C32—121no—
1455C32—121no—
1456C32—121no—
1457C32—121no—
1458C32—123no—
1459C32—123no—
1460C32—123no—
1461C32—123no—
1462C32—121no—
1463C32—121no—
1464C32—121no—
1465C32—121no—
1466C32—121no—
1467C32—121no—
1468C32D4×(C3⋊D3)⋊C311yescharacteristic, complemented
1469C32D4×(C3⋊D3)⋊C311yescharacteristic, complemented
1470C32D4×(C3⋊D3)⋊C311yescharacteristic, complemented
1471C32C3×D3×#6711yescharacteristic
1472C32C3×D3×#6713yescomplemented
1473C32C3⋊D3×#6711yescharacteristic, complemented
1474C32C3×D4×C3⋊D311yescharacteristic
1475C23—271no—
1476C23—811no—
1477D4—31no—
1478D4—811no—
1479D4—811no—
1480D4—811no—
1481C2×C4—811no—
1482C2×C3—21no—
1483C2×C3—21no—
1484C2×C3—21no—
1485C2×C3—21no—
1486C2×C3—21no—
1487C2×C3—21no—
1488C2×C3—21no—
1489C2×C3—21no—
1490C2×C3—21no—
1491C2×C3—33no—
1492C2×C3—31no—
1493C2×C3—41no—
1494C2×C3—41no—
1495C2×C3—41no—
1496C2×C3—41no—
1497C2×C3—63no—
1498C2×C3—61no—
1499C2×C3—61no—
1500C2×C3—61no—
1501C2×C3—61no—
1502C2×C3—61no—
1503C2×C3—61no—
1504C2×C3—63no—
1505C2×C3—61no—
1506C2×C3—63no—
1507C2×C3—61no—
1508C2×C3—121no—
1509C2×C3—123no—
1510C2×C3—123no—
1511C2×C3—121no—
1512C2×C3—121no—
1513C2×C3—121no—
1514C2×C3—123no—
1515C2×C3—123no—
1516C2×C3—121no—
1517C2×C3—123no—
1518C2×C3—183no—
1519C2×C3—181no—
1520C2×C3—272no—
1521C2×C3—272no—
1522C2×C3—361no—
1523C2×C3—363no—
1524C2×C3—542no—
1525C2×C3—541no—
1526C2×C3—542no—
1527C2×C3—541no—
1528C2×C3—1621no—
1529C2×C3C2×D3×(C3⋊D3)⋊C311yescharacteristic
1530C2×C3C2×D3×(C3⋊D3)⋊C311yescharacteristic
1531C2×C3C2×D3×(C3⋊D3)⋊C311yescharacteristic
1532C2×C3C22×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
1533C2×C3C2×C3×D3×C3⋊D311yescharacteristic
1534D3—21no—
1535D3—92no—
1536D3—92no—
1537D3—92no—
1538D3—92no—
1539D3—181no—
1540D3—181no—
1541D3—181no—
1542D3—181no—
1543D3—276no—
1544D3—543no—
1545D3—541no—
1546D3—541no—
1547D3—541no—
1548D3—541no—
1549D3—541no—
1550D3—3243no—
1551D3—1081no—
1552D3—1081no—
1553D3—1081no—
1554D3—1081no—
1555D3—1623no—
1556C22—31no—
1557C22—271no—
1558C22—271no—
1559C22—542no—
1560C22—811no—
1561C22—1622no—
1562C22D3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
1563C4—31no—
1564C4—811no—
1565C3—21no—
1566C3—21no—
1567C3—21no—
1568C3—21no—
1569C3—33no—
1570C3—31no—
1571C3—63no—
1572C3—61no—
1573C3—61no—
1574C3—63no—
1575C3—121no—
1576C3—123no—
1577C3#67×(C3⋊D3)⋊C311yescharacteristic, complemented
1578C3#67×(C3⋊D3)⋊C311yescharacteristic, complemented
1579C3#67×(C3⋊D3)⋊C311yescharacteristic, complemented
1580C3D4×C3⋊((C3⋊D3)⋊C3)11yescharacteristic, complemented
1581C3C3×C3⋊D3×#6711yescharacteristic
1582C2—21no—
1583C2—61no—
1584C2—272no—
1585C2—541no—
1586C2—1621no—
1587C2C2×D3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
subgroupG/H
centerC2C2×D3×C3⋊((C3⋊D3)⋊C3)
commutator, cosocleC2×C34C23×C3
FrattiniC2×C3C2×C3×D3×C3⋊D3
FittingC22×C32×H(3,𝔽3)C22
socleC2×C33C22×C3×D3
hypercenterC22D3×C3⋊((C3⋊D3)⋊C3)
hypocenterC34C2×C3×D4
LCSG ▷ C2×C34 ▷ C34
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C3×C3⋊((C3⋊D3)⋊C3)C2semidirect
2. C2×D3×C3⋊((C3⋊D3)⋊C3)C2semidirect
3. #14518999C2semidirect
4. C3×#67×H(3,𝔽3)C2semidirect
5. #14518681C2semidirect
6. #14518676C2semidirect
7. Dic3×C3⋊((C3⋊D3)⋊C3)C2semidirect
8. #67×C3⋊(C3⋊D3)C3semidirect
12. C22×C32×H(3,𝔽3)C22semidirect
13. C2×C3⋊(C3⋊((C3⋊D3)⋊C3))C22semidirect
16. C2×C3×C3⋊((C3⋊D3)⋊C3)C22semidirect
17. C2×C3×D3×H(3,𝔽3)C22semidirect
19. C3⋊(C3⋊((C3⋊Dic3)⋊C3))C22semidirect
20. C3×Dic3×H(3,𝔽3)C22semidirect
21. C22×C3×C3⋊(C3⋊D3)C2×C3semidirect
23. C2×D3×C3⋊(C3⋊D3)C2×C3semidirect
25. #10620179C2×C3semidirect
28. C33×#67D3semidirect
29. C33×#67C2×C3semidirect
30. #10620147C2×C3semidirect
31. #10620145C2×C3semidirect
32. Dic3×C3⋊(C3⋊D3)C2×C3semidirect
38. C22×C3⋊((C3⋊D3)⋊C3)D3semidirect
50. #67×H(3,𝔽3)D3semidirect
58. C3×C3⋊((C3⋊D3)⋊C3)D4semidirect
73. C22×C34C2×D3semidirect
74. C22×C34C22×C3semidirect
75. C2×C3⋊(C3⋊(C3⋊D3))C22×C3semidirect
79. C2×C3×C3⋊(C3⋊D3)C22×C3semidirect
84. C2×C33×D3C2×D3semidirect
85. C2×C33×D3C22×C3semidirect
88. C3⋊(C3⋊(C3⋊Dic3))C22×C3semidirect
91. C33×Dic3C2×D3semidirect
92. C33×Dic3C22×C3semidirect
100. C22×C3×H(3,𝔽3)C2×D3semidirect
101. C22×C3×H(3,𝔽3)C2×D3semidirect
113. C2×C3⋊((C3⋊D3)⋊C3)C2×D3semidirect
115. C2×D3×H(3,𝔽3)C2×D3semidirect
126. Dic3×H(3,𝔽3)C2×D3semidirect
127. C32×H(3,𝔽3)C2×D4semidirect
129. C22×C3⋊(C3⋊D3)C3×D3semidirect
192. C32×#67C3×D3semidirect
193. C32×#67C3⋊D3semidirect
240. C3×C3⋊(C3⋊D3)C3×D4semidirect
273. C3⋊((C3⋊D3)⋊C3)#67direct (N × H)
324. C22×C33D32semidirect
326. C22×C33C2×C3×D3semidirect
327. C22×C33C2×C3×D3semidirect
328. C22×C33C2×C3⋊D3semidirect
343. C2×C3⋊(C3⋊D3)C2×C3×D3semidirect
400. C2×C32×D3C2×C3×D3semidirect
401. C2×C32×D3C2×C3⋊D3semidirect
446. C32×Dic3C2×C3×D3semidirect
447. C32×Dic3C2×C3⋊D3semidirect
457. C22×H(3,𝔽3)D32semidirect
473. C34D3×D4semidirect
474. C34C2×C3×D4semidirect
481. C3×H(3,𝔽3)D3×D4semidirect
482. C3×H(3,𝔽3)C2×#67semidirect
587. C3×#67(C3⋊D3)⋊C3semidirect
588. C3×#67(C3⋊D3)⋊C3semidirect
589. C3×#67(C3⋊D3)⋊C3semidirect
699. C3⋊(C3⋊D3)C3×#67semidirect
845. C22×C32C2×(C3⋊D3)⋊C3semidirect
846. C22×C32C2×(C3⋊D3)⋊C3semidirect
847. C22×C32C2×(C3⋊D3)⋊C3semidirect
849. C22×C32C3×D32semidirect
850. C22×C32D3×C3⋊D3semidirect
955. C2×C3×D3C2×(C3⋊D3)⋊C3semidirect
956. C2×C3×D3C2×(C3⋊D3)⋊C3semidirect
957. C2×C3×D3C2×(C3⋊D3)⋊C3semidirect
1013. C3×Dic3C2×(C3⋊D3)⋊C3semidirect
1014. C3×Dic3C2×(C3⋊D3)⋊C3semidirect
1015. C3×Dic3C2×(C3⋊D3)⋊C3semidirect
1045. C33D3×#67semidirect
1047. C33C3×D3×D4semidirect
1048. C33C2×C3×#67semidirect
1049. C33D4×C3⋊D3semidirect
1057. H(3,𝔽3)D3×#67semidirect
1103. #67C3⋊((C3⋊D3)⋊C3)direct (N × H)
1361. C22×C3D3×(C3⋊D3)⋊C3semidirect
1362. C22×C3D3×(C3⋊D3)⋊C3semidirect
1363. C22×C3D3×(C3⋊D3)⋊C3semidirect
1364. C22×C3C2×C3⋊((C3⋊D3)⋊C3)semidirect
1398. C2×D3C2×C3⋊((C3⋊D3)⋊C3)semidirect
1419. Dic3C2×C3⋊((C3⋊D3)⋊C3)semidirect
1468. C32D4×(C3⋊D3)⋊C3semidirect
1469. C32D4×(C3⋊D3)⋊C3semidirect
1470. C32D4×(C3⋊D3)⋊C3semidirect
1472. C32C3×D3×#67semidirect
1473. C32C3⋊D3×#67semidirect
1562. C22D3×C3⋊((C3⋊D3)⋊C3)semidirect
1577. C3#67×(C3⋊D3)⋊C3semidirect
1578. C3#67×(C3⋊D3)⋊C3semidirect
1579. C3#67×(C3⋊D3)⋊C3semidirect
1580. C3D4×C3⋊((C3⋊D3)⋊C3)semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C3⋊((C3⋊D3)⋊C3)2
C2×D3×C3⋊((C3⋊D3)⋊C3)2
#145189992
C3×#67×H(3,𝔽3)2
#145186812
#145186762
Dic3×C3⋊((C3⋊D3)⋊C3)2
#67×C3⋊(C3⋊D3)3
C3×C3⋊D3×#673
D4×C3⋊((C3⋊D3)⋊C3)3
#67×(C3⋊D3)⋊C33