Finite Group Databasebeta

← C3×#78966 #11889349

Subgroups — C3×#78966 #11889349

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 755 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic
2C3×#5529C211yesmaximal, characteristic
3C32×#419C211yesmaximal, characteristic, complemented
4C3×#5228C211yesmaximal, characteristic, complemented
5C3×#5137C211yesmaximal, characteristic, complemented
6C3×#5127C211yesmaximal, characteristic
7C3×#4996C211yesmaximal, characteristic, complemented
8C3×#4813C211yesmaximal, characteristic, complemented
9C3×#4809C211yesmaximal, characteristic, complemented
10C3×#4805C211yesmaximal, characteristic, complemented
11C3×D3×#103C211yesmaximal, characteristic, complemented
12C3×#4799C211yesmaximal, characteristic, complemented
13C3×#4797C211yesmaximal, characteristic, complemented
14C3×#4795C211yesmaximal, characteristic, complemented
15C3×#4789C211yesmaximal, characteristic, complemented
16C3×#3312—31nomaximal
17#78966C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C32×M16C2211yescharacteristic
21C32×#117C2211yescharacteristic
22C3×#946—21no—
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×#944—21no—
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C3×C4×#67—21no—
30C3×C4×#67C2211yescharacteristic
31C3×#924—21no—
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic
34C2×C3×Dic12C2211yescharacteristic
35C2×C3×D3×C8C2211yescharacteristic
36C3×#897C2211yescharacteristic
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#890C2211yescharacteristic
39C3×#887C2211yescharacteristic
40C3×#883—21no—
41C3×#879—21no—
42C3×#872—21no—
43C3×#870—21no—
44C32×#103C2211yescharacteristic
45C32×#103C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#815C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#808C2211yescharacteristic
60C3×#807C2211yescharacteristic
61C3×#552—31no—
62C3×D4×Q8—31no—
63Q8×#67C2×C311yescharacteristic
64#5529C2×C311yescharacteristic
65C3×#491—31no—
66C3×#485—31no—
67C3×#483—31no—
68C3×#479—31no—
69C3×#470—31no—
70C3×#467—31no—
71C3×#462—31no—
72C3×#451—31no—
73C3×#451—31no—
74C3×#441—31no—
75C3×#435—31no—
76C3×#419—21no—
77C3×#419D311yescharacteristic, complemented
78C3×#419C2×C311yescharacteristic, complemented
79C2×C3×#103—31no—
80#5228C2×C311yescharacteristic, complemented
81#5137C2×C311yescharacteristic, complemented
82#5127C2×C311yescharacteristic
83#4996C2×C311yescharacteristic, complemented
84#4813C2×C311yescharacteristic, complemented
85#4809C2×C311yescharacteristic, complemented
86#4805C2×C311yescharacteristic, complemented
87D3×#103C2×C311yescharacteristic, complemented
88#4799C2×C311yescharacteristic, complemented
89#4797C2×C311yescharacteristic, complemented
90#4795C2×C311yescharacteristic, complemented
91#4789C2×C311yescharacteristic, complemented
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×C3×#67D411yescharacteristic
100C3×D3×Q8—22no—
101C3×D3×Q8—41no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C32×M16—41no—
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42—21no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#217D411yescharacteristic
118C3×#216—22no—
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×C4⋊Dic3C2311yescharacteristic
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⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4D411yescharacteristic
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×Dic12—41no—
143C3×D3×C8—41no—
144#3312—31noSylow
145C22×C3×Q8—21no—
146C22×C3×Q8—31no—
147C22×C3×Q8C2×D311yescharacteristic
148C22×C3×Q8C22×C311yescharacteristic
149C2×D3×Q8C22×C311yescharacteristic
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C2×C3×Q16—31no—
153C2×C3×M16—21no—
154C2×C3×M16C2×D311yescharacteristic
155C2×C3×M16C22×C311yescharacteristic
156C22×C3×C8—31no—
157C3×C4⋊Q8—31no—
158C3×C4⋊Q8—61no—
159C3×#126—61no—
160C3×#125—31no—
161C3×#125—61no—
162C3×#123—61no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—61no—
168C3×C22⋊Q8—61no—
169C3×C4×Q8—31no—
170C3×C4×Q8—31no—
171C3×C4×D4—31no—
172C3×C4×D4—61no—
173C3×#117—21no—
174C3×#117—61no—
175C3×#117C2×D311yescharacteristic
176C3×#117C22×C311yescharacteristic
177C2×C3×C4⋊C4—31no—
178#946—21no—
179#946C22×C311yescharacteristic
180Q8×Dic3C22×C311yescharacteristic
181#944—21no—
182#944C22×C311yescharacteristic
183C2×#216C22×C311yescharacteristic
184C2×#216C22×C311yescharacteristic
185C4×#67—21no—
186C4×#67C22×C311yescharacteristic
187#924—21no—
188#924C22×C311yescharacteristic
189#924C22×C311yescharacteristic
190C2×Dic12C22×C311yescharacteristic
191C2×D3×C8C22×C311yescharacteristic
192#897C22×C311yescharacteristic
193D3×C4⋊C4C22×C311yescharacteristic
194#890C22×C311yescharacteristic
195#887C22×C311yescharacteristic
196#883—21no—
197#879—21no—
198#872—21no—
199#870—21no—
200C3×#107—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#103—21no—
205C3×#103—21no—
206C3×#103—21no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103C2×D311yescharacteristic
215C3×#103C2×D311yescharacteristic
216C3×#103C2×D311yescharacteristic
217C3×#103C2×D311yescharacteristic
218C3×#103C22×C311yescharacteristic
219C3×#103C22×C311yescharacteristic
220C3×#103C22×C311yescharacteristic
221C3×#103C22×C311yescharacteristic
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×#97—31no—
225#835C22×C311yescharacteristic
226#835C22×C311yescharacteristic
227#830C22×C311yescharacteristic
228(C2×D3)⋊C8C22×C311yescharacteristic
229#817C22×C311yescharacteristic
230#816C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232#815C22×C311yescharacteristic
233Dic3⋊C8C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#808C22×C311yescharacteristic
237#807C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—42no—
244C32×Q8#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—42no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C3×#67—22no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
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#479—31no—
281#470—31no—
282#467—31no—
283#462—31no—
284#451—31no—
285#451—31no—
286#441—31no—
287#435—31no—
288#419C3×D311yescharacteristic, complemented
289C2×#103—31no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—24no—
293C2×C3×Q8—22no—
294C2×C3×Q8—22no—
295C2×C3×Q8—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—41no—
300C2×C3×Q8—41no—
301C2×C3×Q8—41no—
302C2×C3×Q8—42no—
303C2×C3×Q8—61no—
304C2×C3×Q8—62no—
305C2×C3×Q8—121no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C23×C311yescharacteristic
309C2×C3×Q8C23×C311yescharacteristic
310C2×C3×D4—31no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—41no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C23×C311yescharacteristic
320C2×#67C3×D411yescharacteristic
321D3×Q8—22no—
322D3×Q8—41no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3C23×C311yescharacteristic
326C2×Dic6—21no—
327C2×Dic6C23×C311yescharacteristic
328C2×Dic6C23×C311yescharacteristic
329C3×Q16—62no—
330C3×Q16—121no—
331C3×Q16—121no—
332C3×M16—41no—
333C3×M16—41no—
334C3×M16—42no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—121no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C23×C311yescharacteristic
343C2×C3×C8C23×C311yescharacteristic
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
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⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C4⋊C4C23×C311yescharacteristic
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—41no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C42—21no—
374C3×C42—21no—
375C3×C42—31no—
376C3×C42—41no—
377C3×C42—61no—
378C3×C42—61no—
379#217—21no—
380#217—21no—
381#217C3×D411yescharacteristic
382#216—22no—
383#216—41no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4C3×D411yescharacteristic
387C4⋊Dic3—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3C23×C311yescharacteristic
391C4⋊Dic3C23×C311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4C3×D411yescharacteristic
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3C23×C311yescharacteristic
404C2×C3⋊C8C23×C311yescharacteristic
405C2×C3⋊C8C23×C311yescharacteristic
406Dic12—41no—
407D3×C8—41no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32C22×D411yescharacteristic
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3#13712yes—
415C32×C4—21no—
416C32×C4—22no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4H(5,𝔽2)11yescharacteristic
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C22×Q8—31no—
430C22×Q8C2×C3×D311yescharacteristic
431C2×Q16—31no—
432C2×Q16—31no—
433C2×Q16—31no—
434C2×M16C2×C3×D311yescharacteristic
435C22×C8—31no—
436C4⋊Q8—31no—
437C4⋊Q8—61no—
438#126—61no—
439#125—31no—
440#125—61no—
441#123—61no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—31no—
446C22⋊Q8—61no—
447C22⋊Q8—61no—
448C4×Q8—31no—
449C4×Q8—31no—
450C4×D4—31no—
451C4×D4—61no—
452#117—61no—
453#117C2×C3×D311yescharacteristic
454C2×C4⋊C4—31no—
455#107—31no—
456#106—31no—
457#106—31no—
458C4⋊C8—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103C2×C3×D311yescharacteristic
466#103C2×C3×D311yescharacteristic
467#103C2×C3×D311yescharacteristic
468#103C2×C3×D311yescharacteristic
469C22⋊C8—31no—
470C22⋊C8—31no—
471#97—31no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3D3×D411yescharacteristic
475C23×C3C2×C3×D411yescharacteristic
476C22×D3C2×C3×D411yescharacteristic
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—22no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—22no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×Q8—42no—
488C3×Q8—42no—
489C3×Q8—44no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—122no—
495C3×Q8#23512yes—
496C3×Q8C3×#4112yes—
497C3×D4—62no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
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—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—42no—
522C2×C3×C4—42no—
523C2×C3×C4—44no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—122no—
531C2×C3×C4—122no—
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C2×C3×D411yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535C2×C3×C4C24×C311yescharacteristic
536#67—22no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3C2×C3×D411yescharacteristic
542C2×Dic3C2×C3×D411yescharacteristic
543C2×Dic3C2×C3×D411yescharacteristic
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—42no—
547C4×D3—42no—
548Dic6—21no—
549Dic6—21no—
550Dic6—21no—
551Dic6—21no—
552Dic6—42no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—41no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C2×C32—41no—
564C2×C32#54611yescharacteristic
565C2×C32C2×#13711yescharacteristic
566C2×C32#57811yescharacteristic
567C3×D3—22no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—31no—
571C2×Q8—31no—
572C2×Q8—41no—
573C2×Q8—61no—
574C2×Q8—62no—
575C2×Q8—121no—
576C2×Q8C22×C3×D311yescharacteristic
577C2×Q8C22×C3×D311yescharacteristic
578C2×D4—31no—
579C22×C4—21no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4C22×C3×D311yescharacteristic
584Q16—62no—
585Q16—121no—
586Q16—121no—
587M16—41no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—121no—
591C2×C8C22×C3×D311yescharacteristic
592C2×C8C22×C3×D311yescharacteristic
593C4⋊C4—31no—
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⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4C22×C3×D311yescharacteristic
608C4⋊C4C22×C3×D311yescharacteristic
609C22⋊C4—21no—
610C22⋊C4—31no—
611C22⋊C4—31no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C42—21no—
617C42—31no—
618C42—61no—
619C42—61no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—32no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3C2×D3×D411yescharacteristic
634C22×C3C22×C3×D411yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3C3×#13712yes—
638C3×C4—22no—
639C3×C4—21no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—81no—
657C3×C4—81no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4C2×#23511yescharacteristic
663C3×C4#100411yescharacteristic
664C3×C4C2×C3×#4111yescharacteristic
665C3×C4C3×H(5,𝔽2)11yescharacteristic
666Dic3—21no—
667Dic3—21no—
668Dic3—21no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673C32#331211yescharacteristic, complemented, Sylow
674C23—31no—
675C23C3×D3×D411yescharacteristic
676Q8—21no—
677Q8—21no—
678Q8—21no—
679Q8—42no—
680Q8—61no—
681Q8—61no—
682Q8—61no—
683Q8—61no—
684Q8—122no—
685Q8C3×#23512yes—
686D4—62no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—42no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—122no—
704C2×C4—122no—
705C2×C4C3×D3×D411yescharacteristic
706C2×C4C23×C3×D311yescharacteristic
707C8—21no—
708C8—21no—
709C8—61no—
710C8—61no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—42no—
715C2×C3—41no—
716C2×C3—41no—
717C2×C3—62no—
718C2×C3#549011yescharacteristic
719C2×C3D3×#13711yescharacteristic
720C2×C3#577911yescharacteristic
721C2×C3C3×#54611yescharacteristic
722C2×C3C2×C3×#13711yescharacteristic
723C2×C3C3×#57811yescharacteristic
724D3—22no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—32no—
729C22—61no—
730C22—61no—
731C22C2×C3×D3×D411yescharacteristic
732C4—21no—
733C4—22no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—61no—
738C4—61no—
739C4—61no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—121no—
744C4C2×C3×#23511yescharacteristic
745C4C3×#100411yescharacteristic
746C3—21no—
747C3#7896611yescharacteristic, direct product factor
748C3C3×#331211yescharacteristic, complemented
749C2—41no—
750C2—62no—
751C2C3×#549011yescharacteristic
752C2C3×D3×#13711yescharacteristic
753C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#419C2
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC3×#419D3
hypocenterC3C3×#3312
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#419

Complements

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

NH ≅ G/Ntype
3. C32×#419C2semidirect
4. C3×#5228C2semidirect
5. C3×#5137C2semidirect
7. C3×#4996C2semidirect
8. C3×#4813C2semidirect
9. C3×#4809C2semidirect
10. C3×#4805C2semidirect
11. C3×D3×#103C2semidirect
12. C3×#4799C2semidirect
13. C3×#4797C2semidirect
14. C3×#4795C2semidirect
15. C3×#4789C2semidirect
17. #78966C3direct (N × H)
77. C3×#419D3semidirect
78. C3×#419C2×C3semidirect
80. #5228C2×C3semidirect
81. #5137C2×C3semidirect
83. #4996C2×C3semidirect
84. #4813C2×C3semidirect
85. #4809C2×C3semidirect
86. #4805C2×C3semidirect
87. D3×#103C2×C3semidirect
88. #4799C2×C3semidirect
89. #4797C2×C3semidirect
90. #4795C2×C3semidirect
91. #4789C2×C3semidirect
288. #419C3×D3semidirect
673. C32#3312semidirect
747. C3#78966direct (N × H)
748. C3C3×#3312semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#672
C3×#55292
C32×#4192
C3×#52282
C3×#51372
C3×#51272
C3×#49962
C3×#48132
C3×#48092
C3×#48052
C3×D3×#1032
C3×#47992
C3×#47972
C3×#47952
C3×#47892
C3×#33123
#789663