Finite Group Databasebeta

← C3×#81544 #11888012

Subgroups — C3×#81544 #11888012

Order 1152.

820 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5631C211yesmaximal, characteristic
2C3×#5533C211yesmaximal, characteristic, complemented
3C32×#485C211yesmaximal, characteristic, complemented
4C3×#5051C211yesmaximal, characteristic, complemented
5C3×#5002C211yesmaximal, characteristic, complemented
6C3×#4890C211yesmaximal, characteristic, complemented
7C3×#4887C211yesmaximal, characteristic, complemented
8C3×#4868C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4808C211yesmaximal, characteristic, complemented
11C3×#4804C211yesmaximal, characteristic, complemented
12C3×#4795C211yesmaximal, characteristic, complemented
13C3×#4792C211yesmaximal, characteristic, complemented
14C3×#4733C211yesmaximal, characteristic, complemented
15C3×#67⋊C8C211yesmaximal, characteristic, complemented
16C3×#3302—31nomaximal
17#81544C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C32×#117C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#894—21no—
33C3×#893C2211yescharacteristic
34C3×#892C2211yescharacteristic
35C3×D3×C4⋊C4—21no—
36C3×#888C2211yescharacteristic
37C3×#887C2211yescharacteristic
38C3×#885—21no—
39C3×#884—21no—
40C3×#883—21no—
41C3×#879—21no—
42C3×#876—21no—
43C3×C4×Dic6—21no—
44C32×#107C2211yescharacteristic
45C32×#106C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×C22⋊C8C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#809C2211yescharacteristic
59C3×#809C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#556—31no—
62C3×#547—31no—
63#5631C2×C311yescharacteristic
64#5533C2×C311yescharacteristic, complemented
65C3×#487—31no—
66C3×#485—21no—
67C3×#485—31no—
68C3×#485D311yescharacteristic, complemented
69C3×#485C2×C311yescharacteristic, complemented
70C3×#474—31no—
71C3×#467—31no—
72C3×#467—31no—
73C3×#462—31no—
74C3×#452—31no—
75C3×#452—31no—
76C3×C4×SD16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C3×#416—31no—
80#5051C2×C311yescharacteristic, complemented
81#5002C2×C311yescharacteristic, complemented
82#4890C2×C311yescharacteristic, complemented
83#4887C2×C311yescharacteristic, complemented
84#4868C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4808C2×C311yescharacteristic, complemented
87#4804C2×C311yescharacteristic, complemented
88#4795C2×C311yescharacteristic, complemented
89#4792C2×C311yescharacteristic, complemented
90#4733C2×C311yescharacteristic, complemented
91#67⋊C8C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67D411yescharacteristic
96C3×#239—22no—
97C3×#239—41no—
98C3×#235—22no—
99C3×#235—41no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C22⋊C4—21no—
117C32×C42—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#216—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×Dic12—41no—
142C3×#204—22no—
143C3×D3×C8—41no—
144#3302—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#239C22×C311yescharacteristic
148C2×#235C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C22×C3×C8—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×C4⋊Q8—31no—
156C3×#126—61no—
157C3×#126—61no—
158C3×#124—61no—
159C3×#123—61no—
160C3×#123—61no—
161C3×C22⋊Q8—21no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8C2×D311yescharacteristic
166C3×C22⋊Q8C22×C311yescharacteristic
167C3×#121—61no—
168C3×C4×Q8—31no—
169C3×C4×Q8—61no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×#117—21no—
173C3×#117—31no—
174C3×#117C2×D311yescharacteristic
175C3×#117C22×C311yescharacteristic
176C2×C3×C4⋊C4—61no—
177#944C22×C311yescharacteristic
178C2×#216C22×C311yescharacteristic
179C4×#67C22×C311yescharacteristic
180#924C22×C311yescharacteristic
181C22×C3⋊C8C22×C311yescharacteristic
182C2×Dic12C22×C311yescharacteristic
183C2×#204C22×C311yescharacteristic
184C2×D3×C8C22×C311yescharacteristic
185#897C22×C311yescharacteristic
186#897C22×C311yescharacteristic
187#894—21no—
188#893C22×C311yescharacteristic
189#892C22×C311yescharacteristic
190D3×C4⋊C4—21no—
191#888C22×C311yescharacteristic
192#887C22×C311yescharacteristic
193#885—21no—
194#884—21no—
195#883—21no—
196#879—21no—
197#876—21no—
198C4×Dic6—21no—
199C3×#107—21no—
200C3×#107—31no—
201C3×#107C2×D311yescharacteristic
202C3×#107C22×C311yescharacteristic
203C3×#106—21no—
204C3×#106C2×D311yescharacteristic
205C3×#106C22×C311yescharacteristic
206C3×C4⋊C8—31no—
207C3×#103—21no—
208C3×#103—21no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103C2×D311yescharacteristic
215C3×#103C2×D311yescharacteristic
216C3×#103C22×C311yescharacteristic
217C3×#103C22×C311yescharacteristic
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×C22⋊C8—21no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8C2×D311yescharacteristic
224C3×C22⋊C8C22×C311yescharacteristic
225C3×C4×C8—31no—
226#835C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231C8×Dic3C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#809C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C3×#67—22no—
252C3×#67—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—42no—
261C3×D12#4112yes—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#556—31no—
277#547—31no—
278#487—31no—
279#485—31no—
280#485C3×D311yescharacteristic, complemented
281#474—31no—
282#467—31no—
283#467—31no—
284#462—31no—
285#452—31no—
286#452—31no—
287C4×SD16—31no—
288C8×D4—31no—
289#416—31no—
290#416—31no—
291C3×#41—62no—
292C3×#41—62no—
293C3×#41—121no—
294C3×#41—121no—
295C2×C3×Q8—21no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C23×C311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C23×C311yescharacteristic
312C2×#67—21no—
313C2×#67C3×D411yescharacteristic
314#239—22no—
315#239—41no—
316#235—22no—
317#235—41no—
318C2×D12—21no—
319C2×D12C23×C311yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3C23×C311yescharacteristic
324C2×Dic6—21no—
325C2×Dic6C23×C311yescharacteristic
326C2×Dic6C23×C311yescharacteristic
327C3×Q16—121no—
328C3×Q16—121no—
329C3×SD16—62no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—121no—
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—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—41no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4—61no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C23×C311yescharacteristic
359C3×C4⋊C4C23×C311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C42—21no—
375C3×C42—21no—
376C3×C42—31no—
377C3×C42—41no—
378C3×C42—61no—
379C3×C42—61no—
380#217—21no—
381#217C3×D411yescharacteristic
382#216—41no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4C3×D411yescharacteristic
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3C23×C311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4C3×D411yescharacteristic
397C4×Dic3—21no—
398C4×Dic3—21no—
399C4×Dic3C23×C311yescharacteristic
400C2×C3⋊C8—41no—
401C2×C3⋊C8C23×C311yescharacteristic
402C2×C3⋊C8C23×C311yescharacteristic
403Dic12—41no—
404#204—22no—
405D3×C8—41no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—21no—
411C2×C3×D3—22no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C32×C4—21no—
417C32×C4—41no—
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#13512yes—
429C2×#41—31no—
430C2×#41—31no—
431C2×Q16—31no—
432C2×Q16—31no—
433C2×SD16—31no—
434C22×C8—31no—
435C22×C8—31no—
436C4⋊Q8—31no—
437C4⋊Q8—31no—
438#126—61no—
439#126—61no—
440#124—61no—
441#123—61no—
442#123—61no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—31no—
446C22⋊Q8C2×C3×D311yescharacteristic
447#121—61no—
448C4×Q8—31no—
449C4×Q8—61no—
450C4×D4—31no—
451C4×D4—31no—
452#117—31no—
453#117C2×C3×D311yescharacteristic
454C2×C4⋊C4—61no—
455#107—31no—
456#107C2×C3×D311yescharacteristic
457#106C2×C3×D311yescharacteristic
458C4⋊C8—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103C2×C3×D311yescharacteristic
465#103C2×C3×D311yescharacteristic
466#102—31no—
467#102—31no—
468#102—31no—
469C22⋊C8—31no—
470C22⋊C8C2×C3×D311yescharacteristic
471C4×C8—31no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—61no—
475C23×C3D3×D411yescharacteristic
476C23×C3C2×C3×D411yescharacteristic
477C22×D3—21no—
478C22×D3C2×C3×D411yescharacteristic
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—122no—
490C3×D4—32no—
491C3×D4—62no—
492C3×D4—61no—
493C3×D4—122no—
494C3×D4—122no—
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—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—122no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C2×C3×D411yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C24×C311yescharacteristic
530#67—22no—
531#67—42no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3C2×C3×D411yescharacteristic
536C2×Dic3C2×C3×D411yescharacteristic
537C2×Dic3C2×C3×D411yescharacteristic
538D12—21no—
539D12—42no—
540D12C3×#4112yes—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—42no—
544C4×D3—42no—
545C4×D3—42no—
546Dic6—21no—
547Dic6—21no—
548Dic6—21no—
549Dic6—21no—
550Dic6—42no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—41no—
556C3×C8—41no—
557C3×C8—61no—
558C3×C8—61no—
559C3⋊C8—21no—
560C3⋊C8—21no—
561C2×C32—41no—
562C2×C32#54611yescharacteristic
563C2×C32C2×#13511yescharacteristic
564C2×C32#57811yescharacteristic
565C3×D3—41no—
566C3×D3—42no—
567#41—62no—
568#41—62no—
569#41—121no—
570#41—121no—
571C2×Q8—31no—
572C2×Q8—31no—
573C2×Q8—61no—
574C2×Q8C22×C3×D311yescharacteristic
575C2×D4—31no—
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—61no—
579C22×C4—31no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4C22×C3×D311yescharacteristic
584Q16—121no—
585Q16—121no—
586SD16—62no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—121no—
590C2×C8—121no—
591C2×C8C22×C3×D311yescharacteristic
592C2×C8C22×C3×D311yescharacteristic
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⋊C4C22×C3×D311yescharacteristic
604C4⋊C4C22×C3×D311yescharacteristic
605C4⋊C4C22×C3×D311yescharacteristic
606C22⋊C4—21no—
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—21no—
616C42—31no—
617C42—61no—
618C42—61no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—62no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C2×D3×D411yescharacteristic
636C22×C3C22×C3×D411yescharacteristic
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—22no—
641C2×D3—41no—
642C2×D3—41no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—32no—
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—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4—81no—
662C3×C4—81no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4D3×#4111yescharacteristic
667C3×C4#100911yescharacteristic
668C3×C4C2×C3×#4111yescharacteristic
669C3×C4C3×H(5,𝔽2)11yescharacteristic
670Dic3—21no—
671Dic3—21no—
672Dic3—41no—
673Dic3—41no—
674Dic3—41no—
675Dic3C3×#13512yes—
676C32#330211yescharacteristic, complemented, Sylow
677C23—31no—
678C23—61no—
679C23C3×D3×D411yescharacteristic
680Q8—21no—
681Q8—21no—
682Q8—61no—
683Q8—61no—
684Q8—61no—
685Q8—61no—
686Q8—122no—
687D4—32no—
688D4—62no—
689D4—61no—
690D4—122no—
691D4—122no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—122no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4C3×D3×D411yescharacteristic
710C2×C4C23×C3×D311yescharacteristic
711C8—21no—
712C8—21no—
713C8—61no—
714C8—61no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—81no—
721C2×C3—121no—
722C2×C3—122no—
723C2×C3#565411yescharacteristic
724C2×C3D3×#13511yescharacteristic
725C2×C3#577911yescharacteristic
726C2×C3C3×#54611yescharacteristic
727C2×C3C2×C3×#13511yescharacteristic
728C2×C3C3×#57811yescharacteristic
729D3—41no—
730D3—42no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—61no—
735C22—61no—
736C22—61no—
737C22—62no—
738C22—121no—
739C22—121no—
740C22C2×C3×D3×D411yescharacteristic
741C4—21no—
742C4—32no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—61no—
748C4—61no—
749C4—121no—
750C4—121no—
751C4—121no—
752C4C3×D3×#4111yescharacteristic
753C4C3×#100911yescharacteristic
754C3—21no—
755C3#8154411yescharacteristic, direct product factor
756C3C3×#330211yescharacteristic, complemented
757C2—41no—
758C2—121no—
759C2—122no—
760C2C3×#565411yescharacteristic
761C2C3×D3×#13511yescharacteristic
762C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#485C2
socleC22×C32C22×D4
prime radicalC3×#5631C2
hypercenterC3×#485D3
hypocenterC3C3×#3302
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#485

Complements

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

NH ≅ G/Ntype
2. C3×#5533C2semidirect
3. C32×#485C2semidirect
4. C3×#5051C2semidirect
5. C3×#5002C2semidirect
6. C3×#4890C2semidirect
7. C3×#4887C2semidirect
8. C3×#4868C2semidirect
9. C3×#4852C2semidirect
10. C3×#4808C2semidirect
11. C3×#4804C2semidirect
12. C3×#4795C2semidirect
13. C3×#4792C2semidirect
14. C3×#4733C2semidirect
15. C3×#67⋊C8C2semidirect
17. #81544C3direct (N × H)
64. #5533C2×C3semidirect
68. C3×#485D3semidirect
69. C3×#485C2×C3semidirect
80. #5051C2×C3semidirect
81. #5002C2×C3semidirect
82. #4890C2×C3semidirect
83. #4887C2×C3semidirect
84. #4868C2×C3semidirect
85. #4852C2×C3semidirect
86. #4808C2×C3semidirect
87. #4804C2×C3semidirect
88. #4795C2×C3semidirect
89. #4792C2×C3semidirect
90. #4733C2×C3semidirect
91. #67⋊C8C2×C3semidirect
280. #485C3×D3semidirect
676. C32#3302semidirect
755. C3#81544direct (N × H)
756. C3C3×#3302semidirect

Maximal subgroups

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

subgroupindex
C3×#56312
C3×#55332
C32×#4852
C3×#50512
C3×#50022
C3×#48902
C3×#48872
C3×#48682
C3×#48522
C3×#48082
C3×#48042
C3×#47952
C3×#47922
C3×#47332
C3×#67⋊C82
C3×#33023
#815443