Finite Group Databasebeta

← C3×#81190 #11889799

Subgroups — C3×#81190 #11889799

Order 1152.

815 conjugacy classes of subgroups.

The subgroup lattice has 763 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5694C211yesmaximal, characteristic, complemented
2C3×#5555C211yesmaximal, characteristic
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5069C211yesmaximal, characteristic, complemented
5C3×#5018C211yesmaximal, characteristic, complemented
6C3×#4887C211yesmaximal, characteristic, complemented
7C3×#4884C211yesmaximal, characteristic, complemented
8C3×#4868C211yesmaximal, characteristic, complemented
9C3×#4867C211yesmaximal, characteristic, complemented
10C3×#4849C211yesmaximal, characteristic, complemented
11C3×#4836C211yesmaximal, characteristic, complemented
12C3×#4783C211yesmaximal, characteristic, complemented
13C3×#4783C211yesmaximal, characteristic, complemented
14C3×#4772C211yesmaximal, characteristic, complemented
15C3×#4771C211yesmaximal, characteristic, complemented
16C3×#3315—31nomaximal
17#81190C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C32×#125C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C3×#930—21no—
24C2×C3×C4⋊Dic3—21no—
25C2×C3×Dic12C2211yescharacteristic
26C2×C3×Dic12C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#898—21no—
30C3×#897C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#897C2211yescharacteristic
34C3×#894—21no—
35C3×#892—21no—
36C3×#892C2211yescharacteristic
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#890—21no—
39C3×#886—21no—
40C3×#886—21no—
41C3×C4×D12C2211yescharacteristic
42C3×#869C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C32×#107C2211yescharacteristic
45C32×#106C2211yescharacteristic
46C32×C4⋊C8C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C32×#102C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#552—31no—
62C3×#547—31no—
63#5694C2×C311yescharacteristic, complemented
64#5555C2×C311yescharacteristic
65C3×#491—31no—
66C3×#485—31no—
67C3×#484—31no—
68C3×#478—21no—
69C3×#478D311yescharacteristic, complemented
70C3×#478C2×C311yescharacteristic, complemented
71C3×#470—31no—
72C3×#467—31no—
73C3×#462—31no—
74C3×#452—31no—
75C3×#452—31no—
76C3×#440—31no—
77C3×#435—31no—
78C3×#417—31no—
79C3×#416—31no—
80#5069C2×C311yescharacteristic, complemented
81#5018C2×C311yescharacteristic, complemented
82#4887C2×C311yescharacteristic, complemented
83#4884C2×C311yescharacteristic, complemented
84#4868C2×C311yescharacteristic, complemented
85#4867C2×C311yescharacteristic, complemented
86#4849C2×C311yescharacteristic, complemented
87#4836C2×C311yescharacteristic, complemented
88#4783C2×C311yescharacteristic, complemented
89#4783C2×C311yescharacteristic, complemented
90#4772C2×C311yescharacteristic, complemented
91#4771C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C3×#237—22no—
99C3×#237—22no—
100C3×#237—41no—
101C3×#237—41no—
102C2×C3×D12D411yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C42C2311yescharacteristic
118C3×#214—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3D411yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3—21no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×Dic12—41no—
141C3×Dic12—41no—
142C3×ΓL(1,𝔽25)—41no—
143C3×D3×C8—41no—
144#3315—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#237C22×C311yescharacteristic
148C2×#237C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×#126—61no—
156C3×#125—21no—
157C3×#125—61no—
158C3×#125C2×D311yescharacteristic
159C3×#125C22×C311yescharacteristic
160C3×#123—61no—
161C3×#123—61no—
162C3×#123—61no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×#121—61no—
168C3×C4×Q8—31no—
169C3×C4×D4—21no—
170C3×C4×D4—31no—
171C3×C4×D4C2×D311yescharacteristic
172C3×C4×D4C22×C311yescharacteristic
173C3×#117—31no—
174C3×#117—61no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C4⋊C4—61no—
177C2×#214C22×C311yescharacteristic
178#930—21no—
179C2×C4⋊Dic3—21no—
180C2×Dic12C22×C311yescharacteristic
181C2×Dic12C22×C311yescharacteristic
182C2×ΓL(1,𝔽25)C22×C311yescharacteristic
183C2×D3×C8C22×C311yescharacteristic
184#898—21no—
185#897C22×C311yescharacteristic
186#897C22×C311yescharacteristic
187#897C22×C311yescharacteristic
188#897C22×C311yescharacteristic
189#894—21no—
190#892—21no—
191#892C22×C311yescharacteristic
192D3×C4⋊C4C22×C311yescharacteristic
193#890—21no—
194#886—21no—
195#886—21no—
196C4×D12C22×C311yescharacteristic
197#869C22×C311yescharacteristic
198C4×Dic6C22×C311yescharacteristic
199C3×#107—21no—
200C3×#107—31no—
201C3×#107C2×D311yescharacteristic
202C3×#107C22×C311yescharacteristic
203C3×#106—21no—
204C3×#106C2×D311yescharacteristic
205C3×#106C22×C311yescharacteristic
206C3×C4⋊C8—21no—
207C3×C4⋊C8C2×D311yescharacteristic
208C3×C4⋊C8C22×C311yescharacteristic
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#102—21no—
217C3×#102—21no—
218C3×#102—31no—
219C3×#102C2×D311yescharacteristic
220C3×#102C2×D311yescharacteristic
221C3×#102C22×C311yescharacteristic
222C3×#102C22×C311yescharacteristic
223C3×C22⋊C8—31no—
224C3×C22⋊C8—31no—
225C3×#97—31no—
226#832C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#807C22×C311yescharacteristic
237#803C22×C311yescharacteristic
238C23×C32—21no—
239C22×C3×D3C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×D4—21no—
242C32×D4#4112yes—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—42no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C3×#67—42no—
251C3×#67—42no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—42no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—41no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#552—31no—
277#547—31no—
278#491—31no—
279#485—31no—
280#484—31no—
281#478C3×D311yescharacteristic, complemented
282#470—31no—
283#467—31no—
284#462—31no—
285#452—31no—
286#452—31no—
287#440—31no—
288#435—31no—
289#417—31no—
290#416—31no—
291C3×#41—62no—
292C3×#41—62no—
293C3×#41—121no—
294C3×#41—121no—
295C2×C3×Q8—31no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×D4—21no—
299C2×C3×D4—31no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C23×C311yescharacteristic
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—41no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C2×#67—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316#237—22no—
317#237—22no—
318#237—41no—
319#237—41no—
320C2×D12C3×D411yescharacteristic
321C2×C4×D3—21no—
322C2×C4×D3C23×C311yescharacteristic
323C2×C4×D3C23×C311yescharacteristic
324C2×Dic6C23×C311yescharacteristic
325C2×Dic6C23×C311yescharacteristic
326C2×Dic6C23×C311yescharacteristic
327C3×Q16—121no—
328C3×Q16—121no—
329C3×SD16—62no—
330C3×M16—121no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—121no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C23×C311yescharacteristic
339C2×C3×C8C23×C311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—41no—
350C3×C4⋊C4—41no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C4⋊C4C23×C311yescharacteristic
364C3×C4⋊C4C23×C311yescharacteristic
365C3×C22⋊C4—21no—
366C3×C22⋊C4—21no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—31no—
369C3×C22⋊C4—41no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C42—21no—
376C3×C42—61no—
377C3×C42—61no—
378C3×C42C22×D311yescharacteristic
379C3×C42C23×C311yescharacteristic
380#214—22no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4C3×D411yescharacteristic
387(C2×D3)⋊C4C3×D411yescharacteristic
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3—21no—
394C4⋊Dic3C3×D411yescharacteristic
395C4⋊Dic3C23×C311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398C4×Dic3—21no—
399C4×Dic3—21no—
400C2×C3⋊C8C23×C311yescharacteristic
401C2×C3⋊C8C23×C311yescharacteristic
402Dic12—41no—
403Dic12—41no—
404ΓL(1,𝔽25)—41no—
405D3×C8—41no—
406C22×C32—22no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4—41no—
421C32×C4C2×#4111yescharacteristic
422C32×C4H(5,𝔽2)11yescharacteristic
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C2×#41—31no—
430C2×#41—31no—
431C2×Q16—31no—
432C2×Q16—31no—
433C2×SD16—31no—
434C2×M16—31no—
435C22×C8—31no—
436C4⋊Q8—31no—
437#126—61no—
438#125—61no—
439#125C2×C3×D311yescharacteristic
440#123—61no—
441#123—61no—
442#123—61no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—31no—
446C22⋊Q8—31no—
447#121—61no—
448C4×Q8—31no—
449C4×D4—31no—
450C4×D4C2×C3×D311yescharacteristic
451#117—31no—
452#117—61no—
453C2×C4⋊C4—31no—
454C2×C4⋊C4—61no—
455#107—31no—
456#107C2×C3×D311yescharacteristic
457#106C2×C3×D311yescharacteristic
458C4⋊C8C2×C3×D311yescharacteristic
459#103—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#102—31no—
467#102C2×C3×D311yescharacteristic
468#102C2×C3×D311yescharacteristic
469C22⋊C8—31no—
470C22⋊C8—31no—
471#97—31no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—31no—
475C23×C3—31no—
476C23×C3—41no—
477C22×D3C2×C3×D411yescharacteristic
478C22×D3C2×C3×D411yescharacteristic
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—22no—
488C3×D4—41no—
489C3×D4—121no—
490C3×D4—122no—
491C3×D4—122no—
492C3×D4#23912yes—
493C3×D4C3×#4112yes—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—42no—
509C2×C3×C4—42no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—82no—
519C2×C3×C4—122no—
520C2×C3×C4—122no—
521C2×C3×C4—122no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4C2×C3×D411yescharacteristic
525C2×C3×C4C2×C3×D411yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C24×C311yescharacteristic
528#67—42no—
529#67—42no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—42no—
535C2×Dic3—42no—
536C2×Dic3C2×C3×D411yescharacteristic
537C2×Dic3C2×C3×D411yescharacteristic
538D12—41no—
539C4×D3—21no—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—42no—
544Dic6—21no—
545Dic6—21no—
546Dic6—21no—
547Dic6—21no—
548Dic6—21no—
549Dic6—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—41no—
555C3×C8—41no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C2×C32—42no—
561C2×C32#54611yescharacteristic
562C2×C32#57511yescharacteristic
563C2×C32#57811yescharacteristic
564C3×D3—41no—
565C3×D3—41no—
566#41—62no—
567#41—62no—
568#41—121no—
569#41—121no—
570C2×Q8—31no—
571C2×Q8—31no—
572C2×Q8—31no—
573C2×D4—31no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4C22×C3×D311yescharacteristic
577C22×C4—21no—
578C22×C4—31no—
579C22×C4—31no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583Q16—121no—
584Q16—121no—
585SD16—62no—
586M16—121no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—121no—
590C2×C8C22×C3×D311yescharacteristic
591C2×C8C22×C3×D311yescharacteristic
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4C22×C3×D311yescharacteristic
605C4⋊C4C22×C3×D311yescharacteristic
606C4⋊C4C22×C3×D311yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—31no—
609C22⋊C4—31no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C42—61no—
616C42—61no—
617C42C22×C3×D311yescharacteristic
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—21no—
621C22×C3—42no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C22×C3×D411yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—81no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4C2×#23911yescharacteristic
666C3×C4#100911yescharacteristic
667C3×C4C2×C3×#4111yescharacteristic
668C3×C4C3×H(5,𝔽2)11yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—41no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675C32#331511yescharacteristic, complemented, Sylow
676C23—21no—
677C23—31no—
678C23—31no—
679Q8—61no—
680Q8—61no—
681Q8—61no—
682Q8—61no—
683Q8—61no—
684Q8—61no—
685D4—21no—
686D4—121no—
687D4—122no—
688D4—122no—
689D4C3×#23912yes—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—42no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—122no—
705C2×C4—122no—
706C2×C4—122no—
707C2×C4C3×D3×D411yescharacteristic
708C2×C4C3×D3×D411yescharacteristic
709C2×C4C23×C3×D311yescharacteristic
710C8—21no—
711C8—21no—
712C8—61no—
713C8—61no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—42no—
718C2×C3—42no—
719C2×C3—82no—
720C2×C3—121no—
721C2×C3—121no—
722C2×C3#563011yescharacteristic
723C2×C3#577111yescharacteristic
724C2×C3#577311yescharacteristic
725C2×C3C3×#54611yescharacteristic
726C2×C3C3×#57511yescharacteristic
727C2×C3C3×#57811yescharacteristic
728D3—41no—
729D3—41no—
730C22—22no—
731C22—41no—
732C22—41no—
733C22—61no—
734C22—61no—
735C22—61no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22C2×C3×D3×D411yescharacteristic
740C4—21no—
741C4—21no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—61no—
746C4—61no—
747C4—121no—
748C4—121no—
749C4—121no—
750C4—121no—
751C4C2×C3×#23911yescharacteristic
752C4C3×#100911yescharacteristic
753C3—21no—
754C3#8119011yescharacteristic, direct product factor
755C3C3×#331511yescharacteristic, complemented
756C2—42no—
757C2—121no—
758C2—121no—
759C2C3×#563011yescharacteristic
760C2C3×#577111yescharacteristic
761C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC3×#5555C2
hypercenterC3×#478D3
hypocenterC3C3×#3315
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#478

Complements

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

NH ≅ G/Ntype
1. C3×#5694C2semidirect
3. C32×#478C2semidirect
4. C3×#5069C2semidirect
5. C3×#5018C2semidirect
6. C3×#4887C2semidirect
7. C3×#4884C2semidirect
8. C3×#4868C2semidirect
9. C3×#4867C2semidirect
10. C3×#4849C2semidirect
11. C3×#4836C2semidirect
12. C3×#4783C2semidirect
13. C3×#4783C2semidirect
14. C3×#4772C2semidirect
15. C3×#4771C2semidirect
17. #81190C3direct (N × H)
63. #5694C2×C3semidirect
69. C3×#478D3semidirect
70. C3×#478C2×C3semidirect
80. #5069C2×C3semidirect
81. #5018C2×C3semidirect
82. #4887C2×C3semidirect
83. #4884C2×C3semidirect
84. #4868C2×C3semidirect
85. #4867C2×C3semidirect
86. #4849C2×C3semidirect
87. #4836C2×C3semidirect
88. #4783C2×C3semidirect
89. #4783C2×C3semidirect
90. #4772C2×C3semidirect
91. #4771C2×C3semidirect
281. #478C3×D3semidirect
675. C32#3315semidirect
754. C3#81190direct (N × H)
755. C3C3×#3315semidirect

Maximal subgroups

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

subgroupindex
C3×#56942
C3×#55552
C32×#4782
C3×#50692
C3×#50182
C3×#48872
C3×#48842
C3×#48682
C3×#48672
C3×#48492
C3×#48362
C3×#47832
C3×#47722
C3×#47712
C3×#33153
#811903