Finite Group Databasebeta

← C3×#81248 #11889337

Subgroups — C3×#81248 #11889337

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 743 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5694C211yesmaximal, characteristic
2C3×Q8×D12C211yesmaximal, characteristic
3C32×#479C211yesmaximal, characteristic, complemented
4C3×#5069C211yesmaximal, characteristic, complemented
5C3×#5030C211yesmaximal, characteristic, complemented
6C3×#4888C211yesmaximal, characteristic, complemented
7C3×#4887C211yesmaximal, characteristic, complemented
8C3×#4867C211yesmaximal, characteristic, complemented
9C3×#4862C211yesmaximal, characteristic, complemented
10C3×#4849C211yesmaximal, characteristic, complemented
11C3×#4836C211yesmaximal, characteristic
12C3×#4809C211yesmaximal, characteristic, complemented
13C3×#4809C211yesmaximal, characteristic, complemented
14C3×#4802C211yesmaximal, characteristic, complemented
15C3×D3×#103C211yesmaximal, characteristic, complemented
16C3×#3312—31nomaximal
17#81248C311yesmaximal, characteristic, direct product factor
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C32×#125C2211yescharacteristic
21C32×C4×Q8C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×Dic12C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×#898—21no—
28C3×#897—21no—
29C3×#897—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×C4×D12—21no—
40C3×C4×D12C2211yescharacteristic
41C3×#869—21no—
42C3×#869C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C32×#107C2211yescharacteristic
45C32×#106C2211yescharacteristic
46C32×C4⋊C8C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C32×#103C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#552—31no—
62C3×D4×Q8—31no—
63#5694C2×C311yescharacteristic
64Q8×D12C2×C311yescharacteristic
65C3×#491—31no—
66C3×#485—31no—
67C3×#483—31no—
68C3×#479—21no—
69C3×#479D311yescharacteristic, complemented
70C3×#479C2×C311yescharacteristic, complemented
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#5069C2×C311yescharacteristic, complemented
81#5030C2×C311yescharacteristic, complemented
82#4888C2×C311yescharacteristic, complemented
83#4887C2×C311yescharacteristic, complemented
84#4867C2×C311yescharacteristic, complemented
85#4862C2×C311yescharacteristic, complemented
86#4849C2×C311yescharacteristic, complemented
87#4836C2×C311yescharacteristic
88#4809C2×C311yescharacteristic, complemented
89#4809C2×C311yescharacteristic, complemented
90#4802C2×C311yescharacteristic, complemented
91D3×#103C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C3×D3×Q8—22no—
94C3×D3×Q8—22no—
95C3×D3×Q8—41no—
96C3×D3×Q8—41no—
97C2×C3×D12D411yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C42—21no—
117C32×C42C2311yescharacteristic
118C3×#216—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#3312—31noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C22×C311yescharacteristic
148C2×D3×Q8C22×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—21no—
158C3×#125—61no—
159C3×#125C2×D311yescharacteristic
160C3×#125C22×C311yescharacteristic
161C3×#123—61no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—61no—
167C3×C22⋊Q8—61no—
168C3×C4×Q8—21no—
169C3×C4×Q8—31no—
170C3×C4×Q8C2×D311yescharacteristic
171C3×C4×Q8C22×C311yescharacteristic
172C3×C4×D4—31no—
173C3×C4×D4—61no—
174C3×#117—31no—
175C3×#117—61no—
176C2×C3×C4⋊C4—31no—
177C2×#216C22×C311yescharacteristic
178C2×Dic12C22×C311yescharacteristic
179C2×Dic12C22×C311yescharacteristic
180C2×ΓL(1,𝔽25)C22×C311yescharacteristic
181C2×D3×C8C22×C311yescharacteristic
182#898—21no—
183#897—21no—
184#897—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—
194C4×D12—21no—
195C4×D12C22×C311yescharacteristic
196#869—21no—
197#869C22×C311yescharacteristic
198C4×Dic6C22×C311yescharacteristic
199C3×#107—21no—
200C3×#107C2×D311yescharacteristic
201C3×#107C22×C311yescharacteristic
202C3×#106—21no—
203C3×#106—31no—
204C3×#106C2×D311yescharacteristic
205C3×#106C22×C311yescharacteristic
206C3×C4⋊C8—21no—
207C3×C4⋊C8C2×D311yescharacteristic
208C3×C4⋊C8C22×C311yescharacteristic
209C3×#103—21no—
210C3×#103—21no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103—31no—
219C3×#103C2×D311yescharacteristic
220C3×#103C2×D311yescharacteristic
221C3×#103C22×C311yescharacteristic
222C3×#103C22×C311yescharacteristic
223C3×C22⋊C8—31no—
224C3×C22⋊C8—31no—
225C3×#97—31no—
226#835C22×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#808C22×C311yescharacteristic
237#803C22×C311yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8#4112yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—22no—
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—42no—
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—21no—
269C3×Dic6—42no—
270C3×Dic6—42no—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—31no—
276D4×Q8—31no—
277#491—31no—
278#485—31no—
279#483—31no—
280#479C3×D311yescharacteristic, complemented
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—61no—
296C2×C3×Q8—62no—
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—31no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308D3×Q8—22no—
309D3×Q8—22no—
310D3×Q8—41no—
311D3×Q8—41no—
312C2×D12C3×D411yescharacteristic
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3C23×C311yescharacteristic
317C2×C4×D3C23×C311yescharacteristic
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6C23×C311yescharacteristic
321C2×Dic6C23×C311yescharacteristic
322C2×Dic6C23×C311yescharacteristic
323C3×Q16—62no—
324C3×Q16—121no—
325C3×Q16—121no—
326C3×M16—121no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C2×C3×C8—121no—
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C23×C311yescharacteristic
335C2×C3×C8C23×C311yescharacteristic
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
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—41no—
349C3×C4⋊C4—41no—
350C3×C4⋊C4—61no—
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⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C4⋊C4C23×C311yescharacteristic
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—21no—
374C3×C42—41no—
375C3×C42—61no—
376C3×C42—61no—
377C3×C42C22×D311yescharacteristic
378C3×C42C23×C311yescharacteristic
379#216—22no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4C3×D411yescharacteristic
386(C2×D3)⋊C4C3×D411yescharacteristic
387C4⋊Dic3—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3C3×D411yescharacteristic
394C4⋊Dic3C23×C311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397C4×Dic3—21no—
398C4×Dic3—21no—
399C2×C3⋊C8C23×C311yescharacteristic
400C2×C3⋊C8C23×C311yescharacteristic
401Dic12—41no—
402Dic12—41no—
403ΓL(1,𝔽25)—41no—
404D3×C8—41no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3#13712yes—
412C32×C4—22no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—41no—
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—61no—
437#125C2×C3×D311yescharacteristic
438#123—61no—
439C22⋊Q8—31no—
440C22⋊Q8—31no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
443C22⋊Q8—61no—
444C22⋊Q8—61no—
445C4×Q8—31no—
446C4×Q8C2×C3×D311yescharacteristic
447C4×D4—31no—
448C4×D4—61no—
449#117—31no—
450#117—61no—
451C2×C4⋊C4—31no—
452#107C2×C3×D311yescharacteristic
453#106—31no—
454#106C2×C3×D311yescharacteristic
455C4⋊C8C2×C3×D311yescharacteristic
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⋊C8—31no—
468#97—31no—
469C23×C3—31no—
470C23×C3—31no—
471C22×D3C2×C3×D411yescharacteristic
472C22×D3C2×C3×D411yescharacteristic
473C3×Q8—21no—
474C3×Q8—21no—
475C3×Q8—22no—
476C3×Q8—41no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—122no—
484C3×Q8—122no—
485C3×Q8#23912yes—
486C3×Q8C3×#4112yes—
487C3×D4—62no—
488C2×C3×C4—21no—
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—31no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4—122no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×C3×D411yescharacteristic
519C2×C3×C4C2×C3×D411yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C24×C311yescharacteristic
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3C2×C3×D411yescharacteristic
527C2×Dic3C2×C3×D411yescharacteristic
528D12—22no—
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—42no—
534C4×D3—42no—
535C4×D3—42no—
536Dic6—21no—
537Dic6—21no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6—21no—
542Dic6—42no—
543Dic6—42no—
544C3×C8—21no—
545C3×C8—21no—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—41no—
549C3×C8—41no—
550C3×C8—61no—
551C3×C8—61no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C2×C32#54611yescharacteristic
555C2×C32C2×#13711yescharacteristic
556C2×C32#57811yescharacteristic
557C3×D3—22no—
558C3×D3—41no—
559C2×Q8—31no—
560C2×Q8—31no—
561C2×Q8—31no—
562C2×Q8—61no—
563C2×Q8—61no—
564C2×Q8—62no—
565C2×Q8—62no—
566C2×Q8—121no—
567C2×Q8—121no—
568C2×Q8C22×C3×D311yescharacteristic
569C2×D4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575Q16—62no—
576Q16—121no—
577Q16—121no—
578M16—121no—
579C2×C8—31no—
580C2×C8—31no—
581C2×C8—121no—
582C2×C8C22×C3×D311yescharacteristic
583C2×C8C22×C3×D311yescharacteristic
584C4⋊C4—21no—
585C4⋊C4—21no—
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⋊C4C22×C3×D311yescharacteristic
598C4⋊C4C22×C3×D311yescharacteristic
599C4⋊C4C22×C3×D311yescharacteristic
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C42—21no—
608C42—61no—
609C42—61no—
610C42C22×C3×D311yescharacteristic
611C22×C3—21no—
612C22×C3—32no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3C2×D3×D411yescharacteristic
619C22×C3C22×C3×D411yescharacteristic
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—21no—
625C2×D3C3×#13712yes—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—42no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—81no—
646C3×C4—81no—
647C3×C4—81no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4C2×#23911yescharacteristic
653C3×C4#100911yescharacteristic
654C3×C4C2×C3×#4111yescharacteristic
655C3×C4C3×H(5,𝔽2)11yescharacteristic
656Dic3—21no—
657Dic3—21no—
658Dic3—41no—
659Dic3—41no—
660Dic3—41no—
661Dic3—41no—
662C32#331211yescharacteristic, complemented, Sylow
663C23—31no—
664C23—31no—
665Q8—21no—
666Q8—61no—
667Q8—61no—
668Q8—61no—
669Q8—61no—
670Q8—61no—
671Q8—61no—
672Q8—122no—
673Q8—122no—
674Q8C3×#23912yes—
675D4—62no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—122no—
691C2×C4—122no—
692C2×C4—122no—
693C2×C4C3×D3×D411yescharacteristic
694C2×C4C3×D3×D411yescharacteristic
695C2×C4C23×C3×D311yescharacteristic
696C8—21no—
697C8—21no—
698C8—61no—
699C8—61no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—62no—
704C2×C3—121no—
705C2×C3#563011yescharacteristic
706C2×C3#577111yescharacteristic
707C2×C3D3×#13711yescharacteristic
708C2×C3C3×#54611yescharacteristic
709C2×C3C2×C3×#13711yescharacteristic
710C2×C3C3×#57811yescharacteristic
711D3—22no—
712D3—41no—
713C22—32no—
714C22—61no—
715C22—61no—
716C22—61no—
717C22—61no—
718C22—61no—
719C22C2×C3×D3×D411yescharacteristic
720C4—21no—
721C4—21no—
722C4—22no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—61no—
727C4—61no—
728C4—121no—
729C4—121no—
730C4—121no—
731C4—121no—
732C4C2×C3×#23911yescharacteristic
733C4C3×#100911yescharacteristic
734C3—21no—
735C3#8124811yescharacteristic, direct product factor
736C3C3×#331211yescharacteristic, complemented
737C2—62no—
738C2—121no—
739C2C3×#563011yescharacteristic
740C2C3×#577111yescharacteristic
741C2C3×D3×#13711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#479C2
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC3×#479D3
hypocenterC3C3×#3312
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#479

Complements

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

NH ≅ G/Ntype
3. C32×#479C2semidirect
4. C3×#5069C2semidirect
5. C3×#5030C2semidirect
6. C3×#4888C2semidirect
7. C3×#4887C2semidirect
8. C3×#4867C2semidirect
9. C3×#4862C2semidirect
10. C3×#4849C2semidirect
12. C3×#4809C2semidirect
13. C3×#4809C2semidirect
14. C3×#4802C2semidirect
15. C3×D3×#103C2semidirect
17. #81248C3direct (N × H)
69. C3×#479D3semidirect
70. C3×#479C2×C3semidirect
80. #5069C2×C3semidirect
81. #5030C2×C3semidirect
82. #4888C2×C3semidirect
83. #4887C2×C3semidirect
84. #4867C2×C3semidirect
85. #4862C2×C3semidirect
86. #4849C2×C3semidirect
88. #4809C2×C3semidirect
89. #4809C2×C3semidirect
90. #4802C2×C3semidirect
91. D3×#103C2×C3semidirect
280. #479C3×D3semidirect
662. C32#3312semidirect
735. C3#81248direct (N × H)
736. C3C3×#3312semidirect

Maximal subgroups

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

subgroupindex
C3×#56942
C3×Q8×D122
C32×#4792
C3×#50692
C3×#50302
C3×#48882
C3×#48872
C3×#48672
C3×#48622
C3×#48492
C3×#48362
C3×#48092
C3×#48022
C3×D3×#1032
C3×#33123
#812483