Finite Group Databasebeta

← C3×#81527 #11889355

Subgroups — C3×#81527 #11889355

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5632C211yesmaximal, characteristic
2C3×#5529C211yesmaximal, characteristic
3C32×#485C211yesmaximal, characteristic, complemented
4C3×#5052C211yesmaximal, characteristic, complemented
5C3×#5004C211yesmaximal, characteristic, complemented
6C3×#4887C211yesmaximal, characteristic, complemented
7C3×#4877C211yesmaximal, characteristic, complemented
8C3×#4862C211yesmaximal, characteristic, complemented
9C3×#4853C211yesmaximal, characteristic, complemented
10C3×#4809C211yesmaximal, characteristic, complemented
11C3×D3×#103C211yesmaximal, characteristic, complemented
12C3×#4797C211yesmaximal, characteristic, complemented
13C3×#4795C211yesmaximal, characteristic, complemented
14C3×#4739C211yesmaximal, characteristic, complemented
15C3×#4728C211yesmaximal, characteristic
16C3×#3312—31nomaximal
17#81527C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C32×#117C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic
28C2×C3×Dic12C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#897C2211yescharacteristic
32C3×#896—21no—
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×#890C2211yescharacteristic
35C3×#888—21no—
36C3×#887C2211yescharacteristic
37C3×#887C2211yescharacteristic
38C3×#883—21no—
39C3×#67⋊C4—21no—
40C3×#879—21no—
41C3×#878—21no—
42C3×#872—21no—
43C3×#870—21no—
44C32×#107C2211yescharacteristic
45C32×#106C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×C22⋊C8C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#815C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#810C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#552—31no—
62C3×D4×Q8—31no—
63#5632C2×C311yescharacteristic
64#5529C2×C311yescharacteristic
65C3×#491—31no—
66C3×#485—21no—
67C3×#485D311yescharacteristic, complemented
68C3×#485C2×C311yescharacteristic, complemented
69C3×#483—31no—
70C3×#479—31no—
71C3×#470—31no—
72C3×#467—31no—
73C3×#462—31no—
74C3×#451—31no—
75C3×#451—31no—
76C3×#441—31no—
77C3×#435—31no—
78C3×#419—31no—
79C2×C3×#103—31no—
80#5052C2×C311yescharacteristic, complemented
81#5004C2×C311yescharacteristic, complemented
82#4887C2×C311yescharacteristic, complemented
83#4877C2×C311yescharacteristic, complemented
84#4862C2×C311yescharacteristic, complemented
85#4853C2×C311yescharacteristic, complemented
86#4809C2×C311yescharacteristic, complemented
87D3×#103C2×C311yescharacteristic, complemented
88#4797C2×C311yescharacteristic, complemented
89#4795C2×C311yescharacteristic, complemented
90#4739C2×C311yescharacteristic, complemented
91#4728C2×C311yescharacteristic
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67D411yescharacteristic
95C22×C3×Dic3—21no—
96C3×D3×Q8—22no—
97C3×D3×Q8—41no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6—22no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6—41no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C22⋊C4—21no—
116C32×C42—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
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
138C3×#208—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×Dic12—22no—
142C3×Dic12—41no—
143C3×D3×C8—41no—
144#3312—31noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C22×C311yescharacteristic
148C22×Dic6C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×C4⋊Q8—61no—
156C3×#126—61no—
157C3×#125—31no—
158C3×#125—61no—
159C3×#123—61no—
160C3×C22⋊Q8—21no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—61no—
165C3×C22⋊Q8—61no—
166C3×C22⋊Q8C2×D311yescharacteristic
167C3×C22⋊Q8C22×C311yescharacteristic
168C3×C4×Q8—31no—
169C3×C4×Q8—31no—
170C3×C4×D4—31no—
171C3×C4×D4—61no—
172C3×#117—21no—
173C3×#117—61no—
174C3×#117C2×D311yescharacteristic
175C3×#117C22×C311yescharacteristic
176C2×C3×C4⋊C4—31no—
177#944C22×C311yescharacteristic
178C2×#216C22×C311yescharacteristic
179C4×#67C22×C311yescharacteristic
180#924C22×C311yescharacteristic
181C2×#208C22×C311yescharacteristic
182C2×Dic12C22×C311yescharacteristic
183C2×Dic12C22×C311yescharacteristic
184C2×D3×C8C22×C311yescharacteristic
185#897C22×C311yescharacteristic
186#897C22×C311yescharacteristic
187#896—21no—
188D3×C4⋊C4C22×C311yescharacteristic
189#890C22×C311yescharacteristic
190#888—21no—
191#887C22×C311yescharacteristic
192#887C22×C311yescharacteristic
193#883—21no—
194#67⋊C4—21no—
195#879—21no—
196#878—21no—
197#872—21no—
198#870—21no—
199C3×#107—21no—
200C3×#107C2×D311yescharacteristic
201C3×#107C22×C311yescharacteristic
202C3×#106—21no—
203C3×#106—31no—
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×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103C2×D311yescharacteristic
218C3×#103C2×D311yescharacteristic
219C3×#103C22×C311yescharacteristic
220C3×#103C22×C311yescharacteristic
221C3×C22⋊C8—21no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8C2×D311yescharacteristic
224C3×C22⋊C8C22×C311yescharacteristic
225C3×#97—31no—
226#835C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230#815C22×C311yescharacteristic
231Dic3⋊C8C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#810C22×C311yescharacteristic
237#808C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C3×#67—22no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—42no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—42no—
262C3×C4×D3—42no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269C3×Dic6—42no—
270C3×Dic6#4112yes—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—31no—
276D4×Q8—31no—
277#491—31no—
278#485C3×D311yescharacteristic, complemented
279#483—31no—
280#479—31no—
281#470—31no—
282#467—31no—
283#462—31no—
284#451—31no—
285#451—31no—
286#441—31no—
287#435—31no—
288#419—31no—
289C2×#103—31no—
290C2×C3×Q8—21no—
291C2×C3×Q8—31no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—62no—
296C2×C3×Q8—61no—
297C2×C3×Q8—62no—
298C2×C3×Q8—121no—
299C2×C3×Q8—121no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C23×C311yescharacteristic
302C2×C3×D4—31no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C23×C311yescharacteristic
310C2×#67C3×D411yescharacteristic
311C22×Dic3—21no—
312D3×Q8—22no—
313D3×Q8—41no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3C23×C311yescharacteristic
317C2×Dic6—22no—
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6—41no—
321C2×Dic6C23×C311yescharacteristic
322C2×Dic6C23×C311yescharacteristic
323C2×Dic6C23×C311yescharacteristic
324C3×Q16—62no—
325C3×Q16—121no—
326C3×Q16—121no—
327C3×M16—121no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C2×C3×C8—121no—
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C22×D311yescharacteristic
335C2×C3×C8C23×C311yescharacteristic
336C2×C3×C8C23×C311yescharacteristic
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—41no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
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×C42—21no—
373C3×C42—21no—
374C3×C42—31no—
375C3×C42—41no—
376C3×C42—61no—
377C3×C42—61no—
378#217—21no—
379#217C3×D411yescharacteristic
380#216—41no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4C3×D411yescharacteristic
384C4⋊Dic3—21no—
385C4⋊Dic3—21no—
386C4⋊Dic3—21no—
387C4⋊Dic3C23×C311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4C3×D411yescharacteristic
396C4×Dic3—21no—
397C4×Dic3—21no—
398C4×Dic3C23×C311yescharacteristic
399#208—41no—
400C2×C3⋊C8C23×C311yescharacteristic
401C2×C3⋊C8C23×C311yescharacteristic
402Dic12—22no—
403Dic12—41no—
404D3×C8—41no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32C22×D411yescharacteristic
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3#13712yes—
412C32×C4—21no—
413C32×C4—41no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4H(5,𝔽2)11yescharacteristic
419C3×Dic3—22no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×Q8—31no—
427C22×Q8—31no—
428C2×Q16—31no—
429C2×Q16—31no—
430C2×Q16—31no—
431C2×M16—31no—
432C22×C8—31no—
433C4⋊Q8—31no—
434C4⋊Q8—61no—
435#126—61no—
436#125—31no—
437#125—61no—
438#123—61no—
439C22⋊Q8—31no—
440C22⋊Q8—31no—
441C22⋊Q8—31no—
442C22⋊Q8—61no—
443C22⋊Q8—61no—
444C22⋊Q8C2×C3×D311yescharacteristic
445C4×Q8—31no—
446C4×Q8—31no—
447C4×D4—31no—
448C4×D4—61no—
449#117—61no—
450#117C2×C3×D311yescharacteristic
451C2×C4⋊C4—31no—
452#107C2×C3×D311yescharacteristic
453#106—31no—
454#106C2×C3×D311yescharacteristic
455C4⋊C8—31no—
456#103—31no—
457#103—31no—
458#103—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103C2×C3×D311yescharacteristic
465#103C2×C3×D311yescharacteristic
466C22⋊C8—31no—
467C22⋊C8C2×C3×D311yescharacteristic
468#97—31no—
469C23×C3—21no—
470C23×C3—31no—
471C23×C3D3×D411yescharacteristic
472C23×C3C2×C3×D411yescharacteristic
473C22×D3C2×C3×D411yescharacteristic
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—32no—
479C3×Q8—41no—
480C3×Q8—41no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—122no—
487C3×Q8—122no—
488C3×D4—62no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
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—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
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—122no—
519C2×C3×C4—122no—
520C2×C3×C4—122no—
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C2×C3×D411yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C24×C311yescharacteristic
525#67—22no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—42no—
531C2×Dic3C2×C3×D411yescharacteristic
532C2×Dic3C2×C3×D411yescharacteristic
533C2×Dic3C2×C3×D411yescharacteristic
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—42no—
537C4×D3—42no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6—21no—
542Dic6—21no—
543Dic6—42no—
544Dic6—42no—
545Dic6C3×#4112yes—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—21no—
549C3×C8—21no—
550C3×C8—41no—
551C3×C8—41no—
552C3×C8—61no—
553C3×C8—61no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C2×C32—41no—
557C2×C32#54611yescharacteristic
558C2×C32C2×#13711yescharacteristic
559C2×C32#57811yescharacteristic
560C3×D3—22no—
561C2×Q8—31no—
562C2×Q8—31no—
563C2×Q8—31no—
564C2×Q8—61no—
565C2×Q8—62no—
566C2×Q8—61no—
567C2×Q8—62no—
568C2×Q8—121no—
569C2×Q8—121no—
570C2×Q8C22×C3×D311yescharacteristic
571C2×D4—31no—
572C22×C4—31no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4C22×C3×D311yescharacteristic
577Q16—62no—
578Q16—121no—
579Q16—121no—
580M16—121no—
581C2×C8—31no—
582C2×C8—31no—
583C2×C8—121no—
584C2×C8C22×C3×D311yescharacteristic
585C2×C8C22×C3×D311yescharacteristic
586C4⋊C4—21no—
587C4⋊C4—31no—
588C4⋊C4—31no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4C22×C3×D311yescharacteristic
600C4⋊C4C22×C3×D311yescharacteristic
601C4⋊C4C22×C3×D311yescharacteristic
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C42—21no—
610C42—31no—
611C42—61no—
612C42—61no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—32no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3C2×D3×D411yescharacteristic
627C22×C3C22×C3×D411yescharacteristic
628C2×D3—21no—
629C2×D3—21no—
630C2×D3C3×#13712yes—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—62no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—81no—
651C3×C4—81no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4D3×#4111yescharacteristic
656C3×C4#100911yescharacteristic
657C3×C4C2×C3×#4111yescharacteristic
658C3×C4C3×H(5,𝔽2)11yescharacteristic
659Dic3—21no—
660Dic3—21no—
661Dic3—22no—
662Dic3—21no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666C32#331211yescharacteristic, complemented, Sylow
667C23—31no—
668C23C3×D3×D411yescharacteristic
669Q8—21no—
670Q8—21no—
671Q8—32no—
672Q8—61no—
673Q8—61no—
674Q8—61no—
675Q8—61no—
676Q8—61no—
677Q8—122no—
678Q8—122no—
679D4—62no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—122no—
696C2×C4—122no—
697C2×C4—122no—
698C2×C4C3×D3×D411yescharacteristic
699C2×C4C23×C3×D311yescharacteristic
700C8—21no—
701C8—21no—
702C8—61no—
703C8—61no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—41no—
708C2×C3—41no—
709C2×C3—62no—
710C2×C3—81no—
711C2×C3#565411yescharacteristic
712C2×C3#577111yescharacteristic
713C2×C3D3×#13711yescharacteristic
714C2×C3C3×#54611yescharacteristic
715C2×C3C2×C3×#13711yescharacteristic
716C2×C3C3×#57811yescharacteristic
717D3—22no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—32no—
722C22—61no—
723C22—61no—
724C22C2×C3×D3×D411yescharacteristic
725C4—21no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—61no—
731C4—61no—
732C4—61no—
733C4—62no—
734C4—121no—
735C4—121no—
736C4—121no—
737C4C3×D3×#4111yescharacteristic
738C4C3×#100911yescharacteristic
739C3—21no—
740C3#8152711yescharacteristic, direct product factor
741C3C3×#331211yescharacteristic, complemented
742C2—41no—
743C2—62no—
744C2C3×#565411yescharacteristic
745C2C3×#577111yescharacteristic
746C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#485C2
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC3×#485D3
hypocenterC3C3×#3312
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
3. C32×#485C2semidirect
4. C3×#5052C2semidirect
5. C3×#5004C2semidirect
6. C3×#4887C2semidirect
7. C3×#4877C2semidirect
8. C3×#4862C2semidirect
9. C3×#4853C2semidirect
10. C3×#4809C2semidirect
11. C3×D3×#103C2semidirect
12. C3×#4797C2semidirect
13. C3×#4795C2semidirect
14. C3×#4739C2semidirect
17. #81527C3direct (N × H)
67. C3×#485D3semidirect
68. C3×#485C2×C3semidirect
80. #5052C2×C3semidirect
81. #5004C2×C3semidirect
82. #4887C2×C3semidirect
83. #4877C2×C3semidirect
84. #4862C2×C3semidirect
85. #4853C2×C3semidirect
86. #4809C2×C3semidirect
87. D3×#103C2×C3semidirect
88. #4797C2×C3semidirect
89. #4795C2×C3semidirect
90. #4739C2×C3semidirect
278. #485C3×D3semidirect
666. C32#3312semidirect
740. C3#81527direct (N × H)
741. C3C3×#3312semidirect

Maximal subgroups

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

subgroupindex
C3×#56322
C3×#55292
C32×#4852
C3×#50522
C3×#50042
C3×#48872
C3×#48772
C3×#48622
C3×#48532
C3×#48092
C3×D3×#1032
C3×#47972
C3×#47952
C3×#47392
C3×#47282
C3×#33123
#815273