Finite Group Databasebeta

← C3×#83600 #11889790

Subgroups — C3×#83600 #11889790

Order 1152.

871 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#552C211yesmaximal, characteristic, complemented
2C3×#5551C211yesmaximal, characteristic
3C3×#5069C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5052C211yesmaximal, characteristic, complemented
6C3×#5051C211yesmaximal, characteristic, complemented
7C3×#5047C211yesmaximal, characteristic, complemented
8C3×#5047C211yesmaximal, characteristic, complemented
9C3×#5031C211yesmaximal, characteristic, complemented
10C3×#5026C211yesmaximal, characteristic, complemented
11C3×#5011C211yesmaximal, characteristic, complemented
12C3×#5002C211yesmaximal, characteristic, complemented
13C3×#4996C211yesmaximal, characteristic, complemented
14C3×#4970C211yesmaximal, characteristic, complemented
15C3×#4966C211yesmaximal, characteristic, complemented
16C3×#3315—31nomaximal
17#83600C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×#126—21no—
21C32×#125—21no—
22C32×#125C2211yescharacteristic
23C32×#123—21no—
24C32×C22⋊Q8C2211yescharacteristic
25C32×C22⋊Q8C2211yescharacteristic
26C32×C4×Q8C2211yescharacteristic
27C32×C4×D4C2211yescharacteristic
28C32×#117—21no—
29C32×#117C2211yescharacteristic
30C2×C32×C4⋊C4C2211yescharacteristic
31C2×C3×#216C2211yescharacteristic
32C2×C3×#216C2211yescharacteristic
33C2×C3×#215C2211yescharacteristic
34C3×#938—21no—
35C3×#924C2211yescharacteristic
36C3×#924C2211yescharacteristic
37C2×C3×#208C2211yescharacteristic
38C22×C3×C3⋊C8C2211yescharacteristic
39C3×D3×C4⋊C4—21no—
40C3×#883—21no—
41C3×#883—21no—
42C3×C4×D12C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#830C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#809C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#808C2211yescharacteristic
57C3×#807C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×C4⋊(C3⋊C8)C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#552—21no—
62C3×#552D311yescharacteristic, complemented
63C3×#552C2×C311yescharacteristic, complemented
64C3×#547—31no—
65#5551C2×C311yescharacteristic
66C3×#491—31no—
67C3×#485—31no—
68C3×#484—31no—
69C3×#478—31no—
70C3×#470—31no—
71C3×#467—31no—
72C3×#462—31no—
73C3×#452—31no—
74C3×#452—31no—
75C3×#440—31no—
76C3×#435—31no—
77C3×#417—31no—
78C3×#416—31no—
79#5069C2×C311yescharacteristic, complemented
80#5066C2×C311yescharacteristic, complemented
81#5052C2×C311yescharacteristic, complemented
82#5051C2×C311yescharacteristic, complemented
83#5047C2×C311yescharacteristic, complemented
84#5047C2×C311yescharacteristic, complemented
85#5031C2×C311yescharacteristic, complemented
86#5026C2×C311yescharacteristic, complemented
87#5011C2×C311yescharacteristic, complemented
88#5002C2×C311yescharacteristic, complemented
89#4996C2×C311yescharacteristic, complemented
90#4970C2×C311yescharacteristic, complemented
91#4966C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4D411yescharacteristic
94C22×C32×C4—21no—
95C22×C32×C4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C3×#235—22no—
100C3×#235—22no—
101C3×#235—41no—
102C3×#235—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C32×C4⋊C4—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4D411yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C4⋊C4C2311yescharacteristic
119C32×C22⋊C4—21no—
120C32×C22⋊C4—21no—
121C32×C22⋊C4—21no—
122C32×C22⋊C4D411yescharacteristic
123C32×C22⋊C4D411yescharacteristic
124C32×C42—21no—
125C32×C42—21no—
126C32×C42C2311yescharacteristic
127C3×#217—21no—
128C3×#217—21no—
129C3×#216—41no—
130C3×#216—41no—
131C3×#215—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×#208—41no—
139C2×C3×C3⋊C8—41no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3315—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#235C22×C311yescharacteristic
148C2×#235C22×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—22no—
156C3×#126—21no—
157C3×#126—21no—
158C3×#125—22no—
159C3×#125—21no—
160C3×#125—21no—
161C3×#125—21no—
162C3×#125C2×D311yescharacteristic
163C3×#125C22×C311yescharacteristic
164C3×#123—22no—
165C3×#123—21no—
166C3×#123—21no—
167C3×#123—61no—
168C3×#123—61no—
169C3×C22⋊Q8—21no—
170C3×C22⋊Q8—21no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8C2×D311yescharacteristic
174C3×C22⋊Q8C2×D311yescharacteristic
175C3×C22⋊Q8C22×C311yescharacteristic
176C3×C22⋊Q8C22×C311yescharacteristic
177C3×#121—61no—
178C3×C4×Q8—21no—
179C3×C4×Q8C2×D311yescharacteristic
180C3×C4×Q8C22×C311yescharacteristic
181C3×C4×D4—21no—
182C3×C4×D4—31no—
183C3×C4×D4C2×D311yescharacteristic
184C3×C4×D4C22×C311yescharacteristic
185C3×#117—22no—
186C3×#117—21no—
187C3×#117—21no—
188C3×#117—21no—
189C3×#117C2×D311yescharacteristic
190C3×#117C22×C311yescharacteristic
191C2×C3×C4⋊C4—21no—
192C2×C3×C4⋊C4—61no—
193C2×C3×C4⋊C4C2×D311yescharacteristic
194C2×C3×C4⋊C4C22×C311yescharacteristic
195C2×#216C22×C311yescharacteristic
196C2×#216C22×C311yescharacteristic
197C2×#215C22×C311yescharacteristic
198#938—21no—
199#924C22×C311yescharacteristic
200#924C22×C311yescharacteristic
201C2×#208C22×C311yescharacteristic
202C22×C3⋊C8C22×C311yescharacteristic
203D3×C4⋊C4—21no—
204#883—21no—
205#883—21no—
206C4×D12C22×C311yescharacteristic
207#869C22×C311yescharacteristic
208C3×#107—31no—
209C3×#107—31no—
210C3×#106—31no—
211C3×C4⋊C8—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×#103—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102—31no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×#97—31no—
225#835C22×C311yescharacteristic
226#830C22×C311yescharacteristic
227#830C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#810C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#809C22×C311yescharacteristic
235#809C22×C311yescharacteristic
236#809C22×C311yescharacteristic
237#808C22×C311yescharacteristic
238#807C22×C311yescharacteristic
239#807C22×C311yescharacteristic
240C4⋊(C3⋊C8)C22×C311yescharacteristic
241#803C22×C311yescharacteristic
242C23×C32C2×D411yescharacteristic
243C23×C32C2×D411yescharacteristic
244C22×C3×D3—21no—
245C32×Q8—21no—
246C32×Q8—21no—
247C32×D4—41no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—42no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2411yescharacteristic
262C3×#67—42no—
263C3×#67—42no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C3×D12—21no—
268C3×D12#4112yes—
269C3×C4×D3—42no—
270C3×C4×D3—42no—
271C3×C4×D3—42no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280#552C3×D311yescharacteristic, complemented
281#547—31no—
282#491—31no—
283#485—31no—
284#484—31no—
285#478—31no—
286#470—31no—
287#467—31no—
288#462—31no—
289#452—31no—
290#452—31no—
291#440—31no—
292#435—31no—
293#417—31no—
294#416—31no—
295C3×#41—62no—
296C3×#41—62no—
297C3×#41—121no—
298C3×#41—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C23×C311yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—61no—
307C2×C3×D4—61no—
308C2×C3×D4#6711yescharacteristic
309C2×C3×D4C3×D411yescharacteristic
310C22×C3×C4—22no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C23×C311yescharacteristic
321C22×C3×C4C23×C311yescharacteristic
322C2×#67—21no—
323C2×#67—21no—
324#235—22no—
325#235—22no—
326#235—41no—
327#235—41no—
328C2×D12C23×C311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×Dic6C23×C311yescharacteristic
333C2×Dic6C23×C311yescharacteristic
334C3×Q16—121no—
335C3×Q16—121no—
336C3×SD16—62no—
337C3×M16—121no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—121no—
343C3×C4⋊C4—22no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—22no—
346C3×C4⋊C4—22no—
347C3×C4⋊C4—22no—
348C3×C4⋊C4—22no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—21no—
351C3×C4⋊C4—21no—
352C3×C4⋊C4—21no—
353C3×C4⋊C4—21no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—61no—
367C3×C4⋊C4—61no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4#6711yescharacteristic
371C3×C4⋊C4C3×D411yescharacteristic
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C4⋊C4C22×D311yescharacteristic
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C23×C311yescharacteristic
376C3×C4⋊C4C23×C311yescharacteristic
377C3×C4⋊C4C23×C311yescharacteristic
378C3×C22⋊C4—22no—
379C3×C22⋊C4—22no—
380C3×C22⋊C4—22no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—21no—
384C3×C22⋊C4—21no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—61no—
390C3×C22⋊C4—61no—
391C3×C22⋊C4—61no—
392C3×C22⋊C4#6711yescharacteristic
393C3×C22⋊C4#6711yescharacteristic
394C3×C22⋊C4C3×D411yescharacteristic
395C3×C22⋊C4C3×D411yescharacteristic
396C3×C42—22no—
397C3×C42—22no—
398C3×C42—21no—
399C3×C42—21no—
400C3×C42—21no—
401C3×C42—21no—
402C3×C42—21no—
403C3×C42C22×D311yescharacteristic
404C3×C42C23×C311yescharacteristic
405#217—21no—
406#217—21no—
407#216—41no—
408#216—41no—
409#215—22no—
410(C2×D3)⋊C4—21no—
411C4⋊Dic3—21no—
412C4⋊Dic3—21no—
413C4⋊Dic3C23×C311yescharacteristic
414Dic3⋊C4—21no—
415Dic3⋊C4—21no—
416#208—41no—
417C2×C3⋊C8—41no—
418C2×C3⋊C8C23×C311yescharacteristic
419C2×C3⋊C8C23×C311yescharacteristic
420C2×C3⋊C8C23×C311yescharacteristic
421C2×C3⋊C8C23×C311yescharacteristic
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32C22×D411yescharacteristic
429C2×C3×D3—22no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—21no—
435C32×C4—21no—
436C32×C4—41no—
437C32×C4—41no—
438C32×C4—41no—
439C32×C4—41no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3×Dic3—41no—
443C3×Dic3—41no—
444C3×Dic3—41no—
445C2×#41—31no—
446C2×#41—31no—
447C2×Q16—31no—
448C2×Q16—31no—
449C2×SD16—31no—
450C2×M16—31no—
451C22×C8—31no—
452C4⋊Q8—31no—
453#126—21no—
454#125—21no—
455#125C2×C3×D311yescharacteristic
456#123—21no—
457#123—61no—
458#123—61no—
459C22⋊Q8—31no—
460C22⋊Q8—31no—
461C22⋊Q8C2×C3×D311yescharacteristic
462C22⋊Q8C2×C3×D311yescharacteristic
463#121—61no—
464C4×Q8C2×C3×D311yescharacteristic
465C4×D4—31no—
466C4×D4C2×C3×D311yescharacteristic
467#117—21no—
468#117C2×C3×D311yescharacteristic
469C2×C4⋊C4—61no—
470C2×C4⋊C4C2×C3×D311yescharacteristic
471#107—31no—
472#107—31no—
473#106—31no—
474C4⋊C8—31no—
475#103—31no—
476#103—31no—
477#103—31no—
478#103—31no—
479#103—31no—
480#103—31no—
481#103—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485C22⋊C8—31no—
486C22⋊C8—31no—
487#97—31no—
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—61no—
491C23×C3C2×#6711yescharacteristic
492C23×C3C2×#6711yescharacteristic
493C23×C3C2×C3×D411yescharacteristic
494C23×C3C2×C3×D411yescharacteristic
495C22×D3—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—21no—
500C3×Q8—41no—
501C3×Q8—41no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×Q8—61no—
506C3×D4—32no—
507C3×D4—41no—
508C3×D4—41no—
509C3×D4—42no—
510C3×D4—61no—
511C3×D4—122no—
512C3×D4—122no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—22no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—44no—
543C2×C3×C4—42no—
544C2×C3×C4—42no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—122no—
549C2×C3×C4—122no—
550C2×C3×C4—122no—
551C2×C3×C4C2×#6711yescharacteristic
552C2×C3×C4C2×#6711yescharacteristic
553C2×C3×C4C2×#6711yescharacteristic
554C2×C3×C4C2×#6711yescharacteristic
555C2×C3×C4C2×C3×D411yescharacteristic
556C2×C3×C4C2×C3×D411yescharacteristic
557C2×C3×C4C2×C3×D411yescharacteristic
558C2×C3×C4C2×C3×D411yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560C2×C3×C4C24×C311yescharacteristic
561#67—42no—
562#67—42no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566D12—21no—
567D12C3×#4112yes—
568C4×D3—42no—
569C4×D3—42no—
570C4×D3—42no—
571Dic6—21no—
572Dic6—21no—
573Dic6—21no—
574Dic6—21no—
575C3×C8—61no—
576C3×C8—61no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C3⋊C8—21no—
583C2×C32—41no—
584C2×C32—41no—
585C2×C32#54611yescharacteristic
586C2×C32#57511yescharacteristic
587C2×C32#57811yescharacteristic
588C3×D3—42no—
589#41—62no—
590#41—62no—
591#41—121no—
592#41—121no—
593C2×Q8—31no—
594C2×Q8—31no—
595C2×Q8C22×C3×D311yescharacteristic
596C2×D4—31no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4C3×#6711yescharacteristic
600C22×C4—21no—
601C22×C4—61no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4C22×C3×D311yescharacteristic
605C22×C4C22×C3×D311yescharacteristic
606Q16—121no—
607Q16—121no—
608SD16—62no—
609M16—121no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—121no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4C3×#6711yescharacteristic
627C4⋊C4C22×C3×D311yescharacteristic
628C4⋊C4C22×C3×D311yescharacteristic
629C4⋊C4C22×C3×D311yescharacteristic
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4C3×#6711yescharacteristic
637C22⋊C4C3×#6711yescharacteristic
638C42—21no—
639C42—21no—
640C42C22×C3×D311yescharacteristic
641C22×C3—22no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—62no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3C22×#6711yescharacteristic
664C22×C3C22×C3×D411yescharacteristic
665C2×D3—22no—
666C2×D3—41no—
667C2×D3—41no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—42no—
683C3×C4—42no—
684C3×C4—42no—
685C3×C4—42no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—41no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4D3×#4111yescharacteristic
698C3×C4#100911yescharacteristic
699C3×C4C2×C3×#4111yescharacteristic
700C3×C4C3×H(5,𝔽2)11yescharacteristic
701Dic3—41no—
702Dic3—41no—
703Dic3—41no—
704C32#331511yescharacteristic, complemented, Sylow
705C23—61no—
706C23C2×C3×#6711yescharacteristic
707C23C2×C3×#6711yescharacteristic
708Q8—21no—
709Q8—21no—
710Q8—61no—
711Q8—61no—
712Q8—61no—
713Q8—61no—
714D4—32no—
715D4—41no—
716D4—61no—
717D4—122no—
718D4—122no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—42no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—122no—
734C2×C4C2×C3×#6711yescharacteristic
735C2×C4C2×C3×#6711yescharacteristic
736C2×C4C2×C3×#6711yescharacteristic
737C2×C4C2×C3×#6711yescharacteristic
738C2×C4C23×C3×D311yescharacteristic
739C8—61no—
740C8—61no—
741C8—61no—
742C8—61no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—42no—
747C2×C3—41no—
748C2×C3—41no—
749C2×C3—41no—
750C2×C3—41no—
751C2×C3—81no—
752C2×C3—122no—
753C2×C3#582211yescharacteristic
754C2×C3#582911yescharacteristic
755C2×C3#583811yescharacteristic
756C2×C3C3×#54611yescharacteristic
757C2×C3C3×#57511yescharacteristic
758C2×C3C3×#57811yescharacteristic
759D3—42no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—62no—
767C22—121no—
768C22—121no—
769C22C22×C3×#6711yescharacteristic
770C4—21no—
771C4—21no—
772C4—21no—
773C4—21no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4C3×D3×#4111yescharacteristic
782C4C3×#100911yescharacteristic
783C3—21no—
784C3#8360011yescharacteristic, direct product factor
785C3C3×#331511yescharacteristic, complemented
786C2—41no—
787C2—41no—
788C2—122no—
789C2C3×#582211yescharacteristic
790C2C3×#582911yescharacteristic
791C2C3×#583811yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#552C2
socleC22×C32C22×D4
prime radicalC3×#5551C2
hypercenterC3×#552D3
hypocenterC3C3×#3315
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#552

Complements

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

NH ≅ G/Ntype
1. C32×#552C2semidirect
3. C3×#5069C2semidirect
4. C3×#5066C2semidirect
5. C3×#5052C2semidirect
6. C3×#5051C2semidirect
7. C3×#5047C2semidirect
8. C3×#5047C2semidirect
9. C3×#5031C2semidirect
10. C3×#5026C2semidirect
11. C3×#5011C2semidirect
12. C3×#5002C2semidirect
13. C3×#4996C2semidirect
14. C3×#4970C2semidirect
15. C3×#4966C2semidirect
17. #83600C3direct (N × H)
62. C3×#552D3semidirect
63. C3×#552C2×C3semidirect
79. #5069C2×C3semidirect
80. #5066C2×C3semidirect
81. #5052C2×C3semidirect
82. #5051C2×C3semidirect
83. #5047C2×C3semidirect
84. #5047C2×C3semidirect
85. #5031C2×C3semidirect
86. #5026C2×C3semidirect
87. #5011C2×C3semidirect
88. #5002C2×C3semidirect
89. #4996C2×C3semidirect
90. #4970C2×C3semidirect
91. #4966C2×C3semidirect
280. #552C3×D3semidirect
704. C32#3315semidirect
784. C3#83600direct (N × H)
785. C3C3×#3315semidirect

Maximal subgroups

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

subgroupindex
C32×#5522
C3×#55512
C3×#50692
C3×#50662
C3×#50522
C3×#50512
C3×#50472
C3×#50312
C3×#50262
C3×#50112
C3×#50022
C3×#49962
C3×#49702
C3×#49662
C3×#33153
#836003