Finite Group Databasebeta

← C2×#13091425 #72243954

Subgroups — C2×#13091425 #72243954

Order 2916.

1027 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13091425C212yesmaximal, direct product factor
2C2×#10624869C211yesmaximal, characteristic, complemented
3C2×C3⋊#4208C311yesmaximal, characteristic, complemented
4C2×C3×C9×C3⋊D3—31nomaximal
5C2×#92305C311yesmaximal, characteristic, complemented
6C2×#92305C311yesmaximal, characteristic, complemented
7C2×#92300C311yesmaximal, characteristic
8C2×C9×(C3⋊D3)⋊C3—31nomaximal
9C2×C9×(C3⋊D3)⋊C3—31nomaximal
10C2×C9×(C3⋊D3)⋊C3—31nomaximal
11#10624869C2211yescharacteristic, complemented, Sylow
12C2×C3×#737—21no—
13C2×C3×#737C2×C311yescharacteristic, complemented
14C2×C33×C9D311yescharacteristic, complemented
15C3⋊#4208C2×C312yescomplemented
16C3×C9×C3⋊D3—32no—
17C2×#6893—21no—
18C2×#6893—21no—
19C2×#6893C2×C311yescharacteristic, complemented
20C2×#6893C2×C311yescharacteristic, complemented
21C2×C9⋊H(3,𝔽3)—21no—
22C2×C9⋊H(3,𝔽3)—21no—
23C2×C9⋊H(3,𝔽3)—21no—
24C2×C9⋊H(3,𝔽3)—21no—
25C2×C9⋊H(3,𝔽3)—21no—
26C2×C9⋊H(3,𝔽3)—21no—
27C2×C9⋊H(3,𝔽3)—21no—
28C2×C9⋊H(3,𝔽3)—21no—
29C2×C9⋊H(3,𝔽3)—21no—
30C2×#6891—21no—
31C2×C32⋊H(3,𝔽3)C2×C311yescharacteristic
32C2×C9×H(3,𝔽3)—21no—
33C2×C9×H(3,𝔽3)—21no—
34C2×C9×H(3,𝔽3)—21no—
35C2×C9×H(3,𝔽3)D311yescharacteristic, complemented
36C2×C9×H(3,𝔽3)D311yescharacteristic, complemented
37C2×C9×H(3,𝔽3)D311yescharacteristic, complemented
38#92305C2×C312yescomplemented
39#92305C2×C312yescomplemented
40#92300C2×C312yes—
41C9×(C3⋊D3)⋊C3—32no—
42C9×(C3⋊D3)⋊C3—32no—
43C9×(C3⋊D3)⋊C3—32no—
44C2×C32×C3⋊D3—31no—
45C2×C3⋊#272C3211yescharacteristic
46C2×#4208—91no—
47C2×#4208—91no—
48C2×#4208—91no—
49C2×C9×C3⋊D3—31no—
50C2×C9×C3⋊D3—31no—
51C2×C9×C3⋊D3—31no—
52C2×C9×C3⋊D3—31no—
53C2×C9×C3⋊D3—31no—
54C2×C9×C3⋊D3—31no—
55C2×C3×(C3⋊D3)⋊C3—31no—
56C2×C3×(C3⋊D3)⋊C3—31no—
57C2×C3×(C3⋊D3)⋊C3—31no—
58C2×C3×D3×C9—91no—
59C2×C3×D3×C9—91no—
60C2×C3×D3×C9—91no—
61C2×C3×D3×C9—91no—
62C2×(C3⋊D3)⋊C9—31no—
63C2×(C3⋊D3)⋊C9—31no—
64C2×(C3⋊D3)⋊C9—31no—
65C2×(C3⋊D3)⋊C9—31no—
66C2×(C3⋊D3)⋊C9—31no—
67C2×(C3⋊D3)⋊C9—31no—
68C3×#737—21no—
69C3×#737C22×C311yescharacteristic, complemented
70C33×C9C2×D311yescharacteristic, complemented
71#6893—21no—
72#6893—21no—
73#6893C22×C311yescharacteristic, complemented
74#6893C22×C311yescharacteristic, complemented
75C9⋊H(3,𝔽3)—21no—
76C9⋊H(3,𝔽3)—21no—
77C9⋊H(3,𝔽3)—21no—
78C9⋊H(3,𝔽3)—21no—
79C9⋊H(3,𝔽3)—21no—
80C9⋊H(3,𝔽3)—21no—
81C9⋊H(3,𝔽3)—21no—
82C9⋊H(3,𝔽3)—21no—
83C9⋊H(3,𝔽3)—21no—
84#6891—21no—
85C32⋊H(3,𝔽3)C22×C311yescharacteristic
86C9×H(3,𝔽3)—21no—
87C9×H(3,𝔽3)—21no—
88C9×H(3,𝔽3)—21no—
89C9×H(3,𝔽3)C2×D311yescharacteristic, complemented
90C9×H(3,𝔽3)C2×D311yescharacteristic, complemented
91C9×H(3,𝔽3)C2×D311yescharacteristic, complemented
92C2×C34C3×D311yescharacteristic
93C32×C3⋊D3—32no—
94C2×#737—31no—
95C2×#737—31no—
96C2×#737—31no—
97C2×#737—61no—
98C2×#737—61no—
99C2×#737—61no—
100C2×#737—61no—
101C2×#737—61no—
102C2×#737—61no—
103C2×#737—61no—
104C2×#737—61no—
105C2×#737—61no—
106C2×#737—61no—
107C2×#737—61no—
108C2×#737—61no—
109C2×C3×3−1+2—21no—
110C2×C3×3−1+2—21no—
111C2×C3×3−1+2—21no—
112C2×C3×3−1+2—21no—
113C2×C3×3−1+2—21no—
114C2×C3×3−1+2—21no—
115C2×C3×3−1+2—21no—
116C2×C3×3−1+2—21no—
117C2×C3×3−1+2—21no—
118C2×C3×3−1+2—21no—
119C2×C3×3−1+2—21no—
120C2×C3×3−1+2—21no—
121C2×C3×H(3,𝔽3)—21no—
122C2×C3×H(3,𝔽3)—21no—
123C2×C3×H(3,𝔽3)—21no—
124C2×C3×H(3,𝔽3)—21no—
125C2×C3×H(3,𝔽3)C3×D311yescharacteristic
126C2×C3×H(3,𝔽3)C3×D311yescharacteristic
127C2×C3×H(3,𝔽3)C3×D311yescharacteristic
128C2×C3×H(3,𝔽3)C2×C3211yescharacteristic
129C2×C32×C9—21no—
130C2×C32×C9—21no—
131C2×C32×C9—21no—
132C2×C32×C9—21no—
133C2×C32×C9—21no—
134C2×C32×C9—21no—
135C2×C32×C9—21no—
136C2×C32×C9—61no—
137C2×C32×C9—61no—
138C2×C32×C9—61no—
139C2×C32×C9—61no—
140C2×C32×C9—61no—
141C2×C32×C9—61no—
142C2×C32×C9C3×D311yescharacteristic
143C2×C32×C9C3×D311yescharacteristic
144C2×C32×C9C3×D311yescharacteristic
145C2×C32×C9C3×D311yescharacteristic, complemented
146C2×C32×C9C3×D311yescharacteristic, complemented
147C2×C32×C9C3×D311yescharacteristic, complemented
148C2×C32×C9C3⋊D311yescharacteristic
149C3⋊#272C2×C3212yes—
150#4208—92no—
151#4208—92no—
152#4208—92no—
153C9×C3⋊D3—32no—
154C9×C3⋊D3—32no—
155C9×C3⋊D3—32no—
156C9×C3⋊D3—32no—
157C9×C3⋊D3—32no—
158C9×C3⋊D3—32no—
159C3×(C3⋊D3)⋊C3—32no—
160C3×(C3⋊D3)⋊C3—32no—
161C3×(C3⋊D3)⋊C3—32no—
162C3×D3×C9—92no—
163C3×D3×C9—92no—
164C3×D3×C9—92no—
165C3×D3×C9—92no—
166C2×C32⋊C9—21no—
167C2×C32⋊C9—21no—
168C2×C32⋊C9—21no—
169C2×C32⋊C9—21no—
170C2×C32⋊C9—21no—
171C2×C32⋊C9—21no—
172C2×C32⋊C9—21no—
173C2×C32⋊C9—21no—
174C2×C32⋊C9—21no—
175C2×C32⋊C9—21no—
176C2×C32⋊C9—21no—
177C2×C32⋊C9—21no—
178C2×C32⋊C9—21no—
179C2×C32⋊C9—21no—
180C2×C32⋊C9—21no—
181C2×C32⋊C9—21no—
182C2×C32⋊C9—21no—
183C2×C32⋊C9—21no—
184C2×C32⋊C9—21no—
185C2×C32⋊C9—21no—
186C2×C32⋊C9—21no—
187C2×C32⋊C9—21no—
188C2×C32⋊C9—21no—
189C2×C32⋊C9—21no—
190C2×C32⋊C9—21no—
191C2×C32⋊C9—21no—
192C2×C32⋊C9—21no—
193C2×C32⋊C9—21no—
194C2×C32⋊C9—21no—
195C2×C32⋊C9—21no—
196C2×C32⋊C9—21no—
197C2×C32⋊C9—21no—
198C2×C32⋊C9—21no—
199C2×C32⋊C9C3×D311yescharacteristic, complemented
200C2×C32⋊C9C3×D311yescharacteristic, complemented
201C2×C32⋊C9C3×D311yescharacteristic, complemented
202C2×C32⋊C9C3×D311yescharacteristic, complemented
203C2×C32⋊C9C3×D311yescharacteristic, complemented
204C2×C32⋊C9C3×D311yescharacteristic, complemented
205(C3⋊D3)⋊C9—32no—
206(C3⋊D3)⋊C9—32no—
207(C3⋊D3)⋊C9—32no—
208(C3⋊D3)⋊C9—32no—
209(C3⋊D3)⋊C9—32no—
210(C3⋊D3)⋊C9—32no—
211C2×C3×C3⋊D3—31no—
212C2×C3×C3⋊D3—31no—
213C2×C3×C3⋊D3—31no—
214C2×C3×C3⋊D3—31no—
215C2×C3×C3⋊D3—31no—
216C2×C3×C3⋊D3—31no—
217C2×C3×C3⋊D3—31no—
218C2×C32×D3—91no—
219C2×C32×D3—91no—
220C2×C32×D3—91no—
221C2×C32×D3—91no—
222C22×C3×C9—271no—
223C2×#272—91no—
224C2×#272—91no—
225C2×#272—91no—
226C2×(C3⋊D3)⋊C3—31no—
227C2×(C3⋊D3)⋊C3—31no—
228C2×(C3⋊D3)⋊C3—31no—
229C2×(C3⋊D3)⋊C3—31no—
230C2×(C3⋊D3)⋊C3—31no—
231C2×(C3⋊D3)⋊C3—31no—
232C2×(C3⋊D3)⋊C3—31no—
233C2×(C3⋊D3)⋊C3—31no—
234C2×(C3⋊D3)⋊C3—31no—
235C2×D3×C9—91no—
236C2×D3×C9—91no—
237C2×D3×C9—91no—
238C2×D3×C9—91no—
239C2×D3×C9—91no—
240C2×D3×C9—91no—
241C2×D3×C9—91no—
242C2×D3×C9—91no—
243C2×D3×C9—91no—
244C2×D3×C9—91no—
245C2×D3×C9—91no—
246C2×D3×C9—91no—
247C2×D3×C9—271no—
248C2×D3×C9—271no—
249C2×D3×C9—271no—
250C34C2×C3×D311yescharacteristic
251#737—31no—
252#737—31no—
253#737—31no—
254#737—61no—
255#737—61no—
256#737—61no—
257#737—61no—
258#737—61no—
259#737—61no—
260#737—61no—
261#737—61no—
262#737—61no—
263#737—61no—
264#737—61no—
265#737—61no—
266C3×3−1+2—21no—
267C3×3−1+2—21no—
268C3×3−1+2—21no—
269C3×3−1+2—21no—
270C3×3−1+2—21no—
271C3×3−1+2—21no—
272C3×3−1+2—21no—
273C3×3−1+2—21no—
274C3×3−1+2—21no—
275C3×3−1+2—21no—
276C3×3−1+2—21no—
277C3×3−1+2—21no—
278C3×H(3,𝔽3)—21no—
279C3×H(3,𝔽3)—21no—
280C3×H(3,𝔽3)—21no—
281C3×H(3,𝔽3)—21no—
282C3×H(3,𝔽3)C2×C3×D311yescharacteristic
283C3×H(3,𝔽3)C2×C3×D311yescharacteristic
284C3×H(3,𝔽3)C2×C3×D311yescharacteristic
285C3×H(3,𝔽3)C22×C3211yescharacteristic
286C32×C9—21no—
287C32×C9—21no—
288C32×C9—21no—
289C32×C9—21no—
290C32×C9—21no—
291C32×C9—21no—
292C32×C9—21no—
293C32×C9—61no—
294C32×C9—61no—
295C32×C9—61no—
296C32×C9—61no—
297C32×C9—61no—
298C32×C9—61no—
299C32×C9C2×C3×D311yescharacteristic
300C32×C9C2×C3×D311yescharacteristic
301C32×C9C2×C3×D311yescharacteristic
302C32×C9C2×C3×D311yescharacteristic, complemented
303C32×C9C2×C3×D311yescharacteristic, complemented
304C32×C9C2×C3×D311yescharacteristic, complemented
305C32×C9C2×C3⋊D311yescharacteristic
306C32⋊C9—21no—
307C32⋊C9—21no—
308C32⋊C9—21no—
309C32⋊C9—21no—
310C32⋊C9—21no—
311C32⋊C9—21no—
312C32⋊C9—21no—
313C32⋊C9—21no—
314C32⋊C9—21no—
315C32⋊C9—21no—
316C32⋊C9—21no—
317C32⋊C9—21no—
318C32⋊C9—21no—
319C32⋊C9—21no—
320C32⋊C9—21no—
321C32⋊C9—21no—
322C32⋊C9—21no—
323C32⋊C9—21no—
324C32⋊C9—21no—
325C32⋊C9—21no—
326C32⋊C9—21no—
327C32⋊C9—21no—
328C32⋊C9—21no—
329C32⋊C9—21no—
330C32⋊C9—21no—
331C32⋊C9—21no—
332C32⋊C9—21no—
333C32⋊C9—21no—
334C32⋊C9—21no—
335C32⋊C9—21no—
336C32⋊C9—21no—
337C32⋊C9—21no—
338C32⋊C9—21no—
339C32⋊C9C2×C3×D311yescharacteristic, complemented
340C32⋊C9C2×C3×D311yescharacteristic, complemented
341C32⋊C9C2×C3×D311yescharacteristic, complemented
342C32⋊C9C2×C3×D311yescharacteristic, complemented
343C32⋊C9C2×C3×D311yescharacteristic, complemented
344C32⋊C9C2×C3×D311yescharacteristic, complemented
345C2×C33—21no—
346C2×C33—21no—
347C2×C33—21no—
348C2×C33—21no—
349C2×C33—31no—
350C2×C33—61no—
351C2×C33—61no—
352C2×C33—61no—
353C2×C33—61no—
354C2×C33—61no—
355C2×C33—61no—
356C2×C33—61no—
357C2×C33—61no—
358C2×C33C32×D311yescharacteristic
359C2×C33C32×D311yescharacteristic
360C2×C33C32×D311yescharacteristic
361C2×C33C32×D311yescharacteristic
362C2×C33C3×C3⋊D311yescharacteristic
363C3×C3⋊D3—32no—
364C3×C3⋊D3—32no—
365C3×C3⋊D3—32no—
366C3×C3⋊D3—32no—
367C3×C3⋊D3—32no—
368C3×C3⋊D3—32no—
369C3×C3⋊D3—32no—
370C32×D3—92no—
371C32×D3—92no—
372C32×D3—92no—
373C32×D3—92no—
374C2×3−1+2—61no—
375C2×3−1+2—61no—
376C2×3−1+2—61no—
377C2×3−1+2—61no—
378C2×3−1+2—61no—
379C2×3−1+2—61no—
380C2×3−1+2—61no—
381C2×3−1+2—61no—
382C2×3−1+2—61no—
383C2×3−1+2—61no—
384C2×3−1+2—61no—
385C2×3−1+2—61no—
386C2×3−1+2—61no—
387C2×3−1+2—61no—
388C2×3−1+2—61no—
389C2×3−1+2—61no—
390C2×3−1+2—61no—
391C2×3−1+2—61no—
392C2×3−1+2—61no—
393C2×3−1+2—61no—
394C2×3−1+2—61no—
395C2×3−1+2—61no—
396C2×3−1+2—61no—
397C2×3−1+2—61no—
398C2×3−1+2—61no—
399C2×3−1+2—61no—
400C2×3−1+2—61no—
401C2×3−1+2—61no—
402C2×3−1+2—61no—
403C2×3−1+2—61no—
404C2×3−1+2—61no—
405C2×3−1+2—61no—
406C2×3−1+2—61no—
407C2×3−1+2—61no—
408C2×3−1+2—61no—
409C2×3−1+2—61no—
410C2×H(3,𝔽3)—31no—
411C2×H(3,𝔽3)—31no—
412C2×H(3,𝔽3)—31no—
413C2×H(3,𝔽3)—31no—
414C2×H(3,𝔽3)—61no—
415C2×H(3,𝔽3)—61no—
416C2×H(3,𝔽3)—61no—
417C2×H(3,𝔽3)—61no—
418C2×H(3,𝔽3)—61no—
419C2×H(3,𝔽3)—61no—
420C2×H(3,𝔽3)—61no—
421C2×H(3,𝔽3)—61no—
422C2×H(3,𝔽3)—61no—
423C2×H(3,𝔽3)—61no—
424C2×H(3,𝔽3)—61no—
425C2×H(3,𝔽3)—61no—
426C2×H(3,𝔽3)—61no—
427C2×H(3,𝔽3)—61no—
428C2×H(3,𝔽3)—61no—
429C2×H(3,𝔽3)—61no—
430C2×H(3,𝔽3)—61no—
431C2×H(3,𝔽3)—61no—
432C2×H(3,𝔽3)—61no—
433C2×H(3,𝔽3)—61no—
434C2×C3×C9—21no—
435C2×C3×C9—21no—
436C2×C3×C9—21no—
437C2×C3×C9—21no—
438C2×C3×C9—21no—
439C2×C3×C9—21no—
440C2×C3×C9—21no—
441C2×C3×C9—21no—
442C2×C3×C9—21no—
443C2×C3×C9—21no—
444C2×C3×C9—21no—
445C2×C3×C9—21no—
446C2×C3×C9—21no—
447C2×C3×C9—21no—
448C2×C3×C9—21no—
449C2×C3×C9—31no—
450C2×C3×C9—31no—
451C2×C3×C9—31no—
452C2×C3×C9—31no—
453C2×C3×C9—31no—
454C2×C3×C9—61no—
455C2×C3×C9—61no—
456C2×C3×C9—61no—
457C2×C3×C9—61no—
458C2×C3×C9—62no—
459C2×C3×C9—61no—
460C2×C3×C9—61no—
461C2×C3×C9—61no—
462C2×C3×C9—61no—
463C2×C3×C9—61no—
464C2×C3×C9—61no—
465C2×C3×C9—61no—
466C2×C3×C9—61no—
467C2×C3×C9—61no—
468C2×C3×C9—61no—
469C2×C3×C9—61no—
470C2×C3×C9—61no—
471C2×C3×C9—61no—
472C2×C3×C9—61no—
473C2×C3×C9—61no—
474C2×C3×C9—61no—
475C2×C3×C9—61no—
476C2×C3×C9—61no—
477C2×C3×C9—61no—
478C2×C3×C9—61no—
479C2×C3×C9—61no—
480C2×C3×C9—61no—
481C2×C3×C9—61no—
482C2×C3×C9—61no—
483C2×C3×C9—272no—
484C2×C3×C9(C3⋊D3)⋊C311yescharacteristic, complemented
485C2×C3×C9(C3⋊D3)⋊C311yescharacteristic, complemented
486C2×C3×C9(C3⋊D3)⋊C311yescharacteristic, complemented
487C2×C3×C9C3×C3⋊D311yescharacteristic
488C2×C3×C9C3×C3⋊D311yescharacteristic
489C2×C3×C9C3×C3⋊D311yescharacteristic
490#272—92no—
491#272—92no—
492#272—92no—
493(C3⋊D3)⋊C3—32no—
494(C3⋊D3)⋊C3—32no—
495(C3⋊D3)⋊C3—32no—
496(C3⋊D3)⋊C3—32no—
497(C3⋊D3)⋊C3—32no—
498(C3⋊D3)⋊C3—32no—
499(C3⋊D3)⋊C3—32no—
500(C3⋊D3)⋊C3—32no—
501(C3⋊D3)⋊C3—32no—
502D3×C9—92no—
503D3×C9—92no—
504D3×C9—92no—
505D3×C9—92no—
506D3×C9—92no—
507D3×C9—92no—
508D3×C9—92no—
509D3×C9—92no—
510D3×C9—92no—
511D3×C9—92no—
512D3×C9—92no—
513D3×C9—92no—
514D3×C9—272no—
515D3×C9—272no—
516D3×C9—272no—
517C22×C32—271no—
518C2×C3⋊D3—31no—
519C2×C3⋊D3—31no—
520C2×C3⋊D3—31no—
521C2×C3⋊D3—31no—
522C2×C3×D3—91no—
523C2×C3×D3—91no—
524C2×C3×D3—91no—
525C2×C3×D3—91no—
526C2×C3×D3—91no—
527C2×C3×D3—91no—
528C2×C3×D3—91no—
529C2×C3×D3—91no—
530C2×C3×D3—91no—
531C2×C3×D3—91no—
532C2×C3×D3—91no—
533C2×C3×D3—91no—
534C2×C3×D3—91no—
535C2×C3×D3—91no—
536C2×C3×D3—91no—
537C2×C3×D3—91no—
538C2×C3×D3—271no—
539C2×C3×D3—271no—
540C2×C3×D3—271no—
541C22×C9—271no—
542C22×C9—271no—
543C22×C9—271no—
544C33—21no—
545C33—21no—
546C33—21no—
547C33—21no—
548C33—31no—
549C33—61no—
550C33—61no—
551C33—61no—
552C33—61no—
553C33—61no—
554C33—61no—
555C33—61no—
556C33—61no—
557C33C2×C32×D311yescharacteristic
558C33C2×C32×D311yescharacteristic
559C33C2×C32×D311yescharacteristic
560C33C2×C32×D311yescharacteristic
561C33C2×C3×C3⋊D311yescharacteristic
5623−1+2—61no—
5633−1+2—61no—
5643−1+2—61no—
5653−1+2—61no—
5663−1+2—61no—
5673−1+2—61no—
5683−1+2—61no—
5693−1+2—61no—
5703−1+2—61no—
5713−1+2—61no—
5723−1+2—61no—
5733−1+2—61no—
5743−1+2—61no—
5753−1+2—61no—
5763−1+2—61no—
5773−1+2—61no—
5783−1+2—61no—
5793−1+2—61no—
5803−1+2—61no—
5813−1+2—61no—
5823−1+2—61no—
5833−1+2—61no—
5843−1+2—61no—
5853−1+2—61no—
5863−1+2—61no—
5873−1+2—61no—
5883−1+2—61no—
5893−1+2—61no—
5903−1+2—61no—
5913−1+2—61no—
5923−1+2—61no—
5933−1+2—61no—
5943−1+2—61no—
5953−1+2—61no—
5963−1+2—61no—
5973−1+2—61no—
598H(3,𝔽3)—31no—
599H(3,𝔽3)—31no—
600H(3,𝔽3)—31no—
601H(3,𝔽3)—31no—
602H(3,𝔽3)—61no—
603H(3,𝔽3)—61no—
604H(3,𝔽3)—61no—
605H(3,𝔽3)—61no—
606H(3,𝔽3)—61no—
607H(3,𝔽3)—61no—
608H(3,𝔽3)—61no—
609H(3,𝔽3)—61no—
610H(3,𝔽3)—61no—
611H(3,𝔽3)—61no—
612H(3,𝔽3)—61no—
613H(3,𝔽3)—61no—
614H(3,𝔽3)—61no—
615H(3,𝔽3)—61no—
616H(3,𝔽3)—61no—
617H(3,𝔽3)—61no—
618H(3,𝔽3)—61no—
619H(3,𝔽3)—61no—
620H(3,𝔽3)—61no—
621H(3,𝔽3)—61no—
622C3×C9—21no—
623C3×C9—21no—
624C3×C9—21no—
625C3×C9—21no—
626C3×C9—21no—
627C3×C9—21no—
628C3×C9—21no—
629C3×C9—21no—
630C3×C9—21no—
631C3×C9—21no—
632C3×C9—21no—
633C3×C9—21no—
634C3×C9—21no—
635C3×C9—21no—
636C3×C9—21no—
637C3×C9—31no—
638C3×C9—31no—
639C3×C9—31no—
640C3×C9—31no—
641C3×C9—31no—
642C3×C9—61no—
643C3×C9—61no—
644C3×C9—61no—
645C3×C9—61no—
646C3×C9—62no—
647C3×C9—61no—
648C3×C9—61no—
649C3×C9—61no—
650C3×C9—61no—
651C3×C9—61no—
652C3×C9—61no—
653C3×C9—61no—
654C3×C9—61no—
655C3×C9—61no—
656C3×C9—61no—
657C3×C9—61no—
658C3×C9—61no—
659C3×C9—61no—
660C3×C9—61no—
661C3×C9—61no—
662C3×C9—61no—
663C3×C9—61no—
664C3×C9—61no—
665C3×C9—61no—
666C3×C9—61no—
667C3×C9—61no—
668C3×C9—61no—
669C3×C9—61no—
670C3×C9—61no—
671C3×C9C2×(C3⋊D3)⋊C311yescharacteristic, complemented
672C3×C9C2×(C3⋊D3)⋊C311yescharacteristic, complemented
673C3×C9C2×(C3⋊D3)⋊C311yescharacteristic, complemented
674C3×C9C2×C3×C3⋊D311yescharacteristic
675C3×C9C2×C3×C3⋊D311yescharacteristic
676C3×C9C2×C3×C3⋊D311yescharacteristic
677C2×C32—21no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—31no—
681C2×C32—31no—
682C2×C32—31no—
683C2×C32—31no—
684C2×C32—31no—
685C2×C32—31no—
686C2×C32—31no—
687C2×C32—31no—
688C2×C32—61no—
689C2×C32—61no—
690C2×C32—61no—
691C2×C32—61no—
692C2×C32—61no—
693C2×C32—61no—
694C2×C32—61no—
695C2×C32—61no—
696C2×C32—61no—
697C2×C32—61no—
698C2×C32—61no—
699C2×C32—61no—
700C2×C32—61no—
701C2×C32—61no—
702C2×C32—61no—
703C2×C32—61no—
704C2×C32—61no—
705C2×C32—61no—
706C2×C32—61no—
707C2×C32—61no—
708C2×C32—61no—
709C2×C32—61no—
710C2×C32—61no—
711C2×C32—61no—
712C2×C32—61no—
713C2×C32—61no—
714C2×C32—61no—
715C2×C32—61no—
716C2×C32—61no—
717C2×C32—61no—
718C2×C32—61no—
719C2×C32—61no—
720C2×C32—61no—
721C2×C32—61no—
722C2×C32—61no—
723C2×C32—61no—
724C2×C32—61no—
725C2×C32—61no—
726C2×C32—272no—
727C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
728C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
729C2×C32C3×(C3⋊D3)⋊C311yescharacteristic
730C2×C32#420811yescharacteristic, complemented
731C2×C32#420811yescharacteristic, complemented
732C2×C32#420811yescharacteristic, complemented
733C2×C32C32×C3⋊D311yescharacteristic
734C3⋊D3—32no—
735C3⋊D3—32no—
736C3⋊D3—32no—
737C3⋊D3—32no—
738C3×D3—92no—
739C3×D3—92no—
740C3×D3—92no—
741C3×D3—92no—
742C3×D3—92no—
743C3×D3—92no—
744C3×D3—92no—
745C3×D3—92no—
746C3×D3—92no—
747C3×D3—92no—
748C3×D3—92no—
749C3×D3—92no—
750C3×D3—92no—
751C3×D3—92no—
752C3×D3—92no—
753C3×D3—92no—
754C3×D3—272no—
755C3×D3—272no—
756C3×D3—272no—
757C2×C9—21no—
758C2×C9—21no—
759C2×C9—21no—
760C2×C9—21no—
761C2×C9—31no—
762C2×C9—61no—
763C2×C9—61no—
764C2×C9—61no—
765C2×C9—61no—
766C2×C9—61no—
767C2×C9—61no—
768C2×C9—61no—
769C2×C9—61no—
770C2×C9—61no—
771C2×C9—61no—
772C2×C9—61no—
773C2×C9—61no—
774C2×C9—272no—
775C2×C9—272no—
776C2×C9—272no—
777C2×C9C3⋊((C3⋊D3)⋊C3)11yescharacteristic
778C22×C3—271no—
779C22×C3—271no—
780C22×C3—271no—
781C22×C3—271no—
782C2×D3—91no—
783C2×D3—91no—
784C2×D3—91no—
785C2×D3—91no—
786C2×D3—271no—
787C2×D3—271no—
788C2×D3—271no—
789C32—21no—
790C32—21no—
791C32—21no—
792C32—31no—
793C32—31no—
794C32—31no—
795C32—31no—
796C32—31no—
797C32—31no—
798C32—31no—
799C32—31no—
800C32—61no—
801C32—61no—
802C32—61no—
803C32—61no—
804C32—61no—
805C32—61no—
806C32—61no—
807C32—61no—
808C32—61no—
809C32—61no—
810C32—61no—
811C32—61no—
812C32—61no—
813C32—61no—
814C32—61no—
815C32—61no—
816C32—61no—
817C32—61no—
818C32—61no—
819C32—61no—
820C32—61no—
821C32—61no—
822C32—61no—
823C32—61no—
824C32—61no—
825C32—61no—
826C32—61no—
827C32—61no—
828C32—61no—
829C32—61no—
830C32—61no—
831C32—61no—
832C32—61no—
833C32—61no—
834C32—61no—
835C32—61no—
836C32—61no—
837C32—61no—
838C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
839C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
840C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
841C32C2×#420811yescharacteristic, complemented
842C32C2×#420811yescharacteristic, complemented
843C32C2×#420811yescharacteristic, complemented
844C32C2×C32×C3⋊D311yescharacteristic
845C9—21no—
846C9—21no—
847C9—21no—
848C9—21no—
849C9—31no—
850C9—61no—
851C9—61no—
852C9—61no—
853C9—61no—
854C9—61no—
855C9—61no—
856C9—61no—
857C9—61no—
858C9—61no—
859C9—61no—
860C9—61no—
861C9—61no—
862C9C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
863C2×C3—21no—
864C2×C3—31no—
865C2×C3—31no—
866C2×C3—31no—
867C2×C3—31no—
868C2×C3—61no—
869C2×C3—61no—
870C2×C3—61no—
871C2×C3—61no—
872C2×C3—61no—
873C2×C3—91no—
874C2×C3—91no—
875C2×C3—181no—
876C2×C3—181no—
877C2×C3—181no—
878C2×C3—181no—
879C2×C3—272no—
880C2×C3—272no—
881C2×C3—272no—
882C2×C3—272no—
883C2×C3C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
884C2×C3C3×#420811yescharacteristic
885D3—92no—
886D3—92no—
887D3—92no—
888D3—92no—
889D3—272no—
890D3—272no—
891D3—272no—
892C22—271noSylow
893C3—21no—
894C3—31no—
895C3—31no—
896C3—31no—
897C3—31no—
898C3—61no—
899C3—61no—
900C3—61no—
901C3—61no—
902C3—61no—
903C3—91no—
904C3—91no—
905C3—181no—
906C3—181no—
907C3—181no—
908C3—181no—
909C3C2×C3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
910C3C2×C3×#420811yescharacteristic
911C2—272no—
912C2#1309142511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C9C3⋊((C3⋊D3)⋊C3)
commutator, cosocle, hypocenterC3×H(3,𝔽3)C22×C32
FrattiniC32C2×C32×C3⋊D3
FittingC2×#10624869C2
socleC2×C32C32×C3⋊D3
prime radicalC2×#92300C3
LCSG ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2×C9

Complements

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

NH ≅ G/Ntype
1. #13091425C2direct (N × H)
2. C2×#10624869C2semidirect
3. C2×C3⋊#4208C3semidirect
5. C2×#92305C3semidirect
6. C2×#92305C3semidirect
11. #10624869C22semidirect
13. C2×C3×#737C2×C3semidirect
14. C2×C33×C9D3semidirect
15. C3⋊#4208C2×C3semidirect
19. C2×#6893C2×C3semidirect
20. C2×#6893C2×C3semidirect
35. C2×C9×H(3,𝔽3)D3semidirect
36. C2×C9×H(3,𝔽3)D3semidirect
37. C2×C9×H(3,𝔽3)D3semidirect
38. #92305C2×C3semidirect
39. #92305C2×C3semidirect
69. C3×#737C22×C3semidirect
70. C33×C9C2×D3semidirect
73. #6893C22×C3semidirect
74. #6893C22×C3semidirect
89. C9×H(3,𝔽3)C2×D3semidirect
90. C9×H(3,𝔽3)C2×D3semidirect
91. C9×H(3,𝔽3)C2×D3semidirect
145. C2×C32×C9C3×D3semidirect
146. C2×C32×C9C3×D3semidirect
147. C2×C32×C9C3×D3semidirect
199. C2×C32⋊C9C3×D3semidirect
200. C2×C32⋊C9C3×D3semidirect
201. C2×C32⋊C9C3×D3semidirect
202. C2×C32⋊C9C3×D3semidirect
203. C2×C32⋊C9C3×D3semidirect
204. C2×C32⋊C9C3×D3semidirect
302. C32×C9C2×C3×D3semidirect
303. C32×C9C2×C3×D3semidirect
304. C32×C9C2×C3×D3semidirect
339. C32⋊C9C2×C3×D3semidirect
340. C32⋊C9C2×C3×D3semidirect
341. C32⋊C9C2×C3×D3semidirect
342. C32⋊C9C2×C3×D3semidirect
343. C32⋊C9C2×C3×D3semidirect
344. C32⋊C9C2×C3×D3semidirect
484. C2×C3×C9(C3⋊D3)⋊C3semidirect
485. C2×C3×C9(C3⋊D3)⋊C3semidirect
486. C2×C3×C9(C3⋊D3)⋊C3semidirect
671. C3×C9C2×(C3⋊D3)⋊C3semidirect
672. C3×C9C2×(C3⋊D3)⋊C3semidirect
673. C3×C9C2×(C3⋊D3)⋊C3semidirect
730. C2×C32#4208semidirect
731. C2×C32#4208semidirect
732. C2×C32#4208semidirect
841. C32C2×#4208semidirect
842. C32C2×#4208semidirect
843. C32C2×#4208semidirect
912. C2#13091425direct (N × H)

Maximal subgroups

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

subgroupindex
#130914252
C2×#106248692
C2×C3⋊#42083
C2×C3×C9×C3⋊D33
C2×#923053
C2×#923003
C2×C9×(C3⋊D3)⋊C33