Finite Group Databasebeta

← C3×#83615 #11888558

Subgroups — C3×#83615 #11888558

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#553C211yesmaximal, characteristic, complemented
2C3×#5551C211yesmaximal, characteristic, complemented
3C3×#5069C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5042C211yesmaximal, characteristic, complemented
6C3×#5041C211yesmaximal, characteristic, complemented
7C3×#5037C211yesmaximal, characteristic, complemented
8C3×#5037C211yesmaximal, characteristic, complemented
9C3×#5019C211yesmaximal, characteristic, complemented
10C3×#5014C211yesmaximal, characteristic, complemented
11C3×#5011C211yesmaximal, characteristic, complemented
12C3×#5002C211yesmaximal, characteristic, complemented
13C3×#4996C211yesmaximal, characteristic, complemented
14C3×#4971C211yesmaximal, characteristic, complemented
15C3×#4966C211yesmaximal, characteristic, complemented
16C3×#3307—31nomaximal
17#83615C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C32×#126—21no—
21C32×#125C2211yescharacteristic
22C32×#123—21no—
23C32×#121—21no—
24C32×#121C2211yescharacteristic
25C32×#121C2211yescharacteristic
26C32×C4×D4—21no—
27C32×C4×D4C2211yescharacteristic
28C32×C4×D4C2211yescharacteristic
29C32×#117C2211yescharacteristic
30C2×C32×C4⋊C4C2211yescharacteristic
31C3×#938—21no—
32C2×C3×#214C2211yescharacteristic
33C2×C3×#214C2211yescharacteristic
34C2×C3×#213C2211yescharacteristic
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×#832C2211yescharacteristic
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×#808C2211yescharacteristic
58C3×#807C2211yescharacteristic
59C3×C4⋊(C3⋊C8)C2211yescharacteristic
60C3×#803C2211yescharacteristic
61C3×#553—21no—
62C3×#553D311yescharacteristic, complemented
63C3×#553C2×C311yescharacteristic, complemented
64C3×#547—31no—
65#5551C2×C311yescharacteristic, complemented
66C3×#491—31no—
67C3×#485—31no—
68C3×#483—31no—
69C3×#478—31no—
70C3×#468—31no—
71C3×#465—31no—
72C3×#461—31no—
73C3×#449—31no—
74C3×#449—31no—
75C3×#442—31no—
76C3×#435—31no—
77C3×#417—31no—
78C3×#416—31no—
79#5069C2×C311yescharacteristic, complemented
80#5066C2×C311yescharacteristic, complemented
81#5042C2×C311yescharacteristic, complemented
82#5041C2×C311yescharacteristic, complemented
83#5037C2×C311yescharacteristic, complemented
84#5037C2×C311yescharacteristic, complemented
85#5019C2×C311yescharacteristic, complemented
86#5014C2×C311yescharacteristic, complemented
87#5011C2×C311yescharacteristic, complemented
88#5002C2×C311yescharacteristic, complemented
89#4996C2×C311yescharacteristic, complemented
90#4971C2×C311yescharacteristic, complemented
91#4966C2×C311yescharacteristic, complemented
92C2×C32×D4—21no—
93C2×C32×D4—21no—
94C2×C32×D4D411yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×#235—22no—
103C3×#235—22no—
104C3×#235—41no—
105C3×#235—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
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⋊C4—21no—
123C32×C22⋊C4D411yescharacteristic
124C32×C22⋊C4D411yescharacteristic
125C32×C42—21no—
126C32×C42C2311yescharacteristic
127C3×#217—21no—
128C3×#217—21no—
129C3×#214—41no—
130C3×#214—41no—
131C3×#213—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#3307—31noSylow
145C2×C3×#41—31no—
146C2×C3×#41—31no—
147C2×#235C22×C311yescharacteristic
148C2×#235C22×C311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C2×C3×D8—31no—
152C2×C3×M16—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×#126—22no—
156C3×#126—21no—
157C3×#126—21no—
158C3×#125—21no—
159C3×#125C2×D311yescharacteristic
160C3×#125C22×C311yescharacteristic
161C3×#123—22no—
162C3×#123—21no—
163C3×#123—21no—
164C3×#123—61no—
165C3×#123—61no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—31no—
168C3×#121—22no—
169C3×#121—21no—
170C3×#121—21no—
171C3×#121—21no—
172C3×#121—21no—
173C3×#121—61no—
174C3×#121C2×D311yescharacteristic
175C3×#121C2×D311yescharacteristic
176C3×#121C22×C311yescharacteristic
177C3×#121C22×C311yescharacteristic
178C3×C4×D4—22no—
179C3×C4×D4—21no—
180C3×C4×D4—21no—
181C3×C4×D4—21no—
182C3×C4×D4—21no—
183C3×C4×D4—31no—
184C3×C4×D4C2×D311yescharacteristic
185C3×C4×D4C2×D311yescharacteristic
186C3×C4×D4C22×C311yescharacteristic
187C3×C4×D4C22×C311yescharacteristic
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
195#938—21no—
196C2×#214C22×C311yescharacteristic
197C2×#214C22×C311yescharacteristic
198C2×#213C22×C311yescharacteristic
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×#106—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×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102—31no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8—31no—
224C3×#97—31no—
225#832C22×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#808C22×C311yescharacteristic
239#807C22×C311yescharacteristic
240C4⋊(C3⋊C8)C22×C311yescharacteristic
241#803C22×C311yescharacteristic
242C23×C32—21no—
243C23×C32C2×D411yescharacteristic
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C32×D4—21no—
247C32×D4—21no—
248C32×D4—41no—
249C32×D4—42no—
250C32×D4—81no—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—81no—
259C2×C32×C4—81no—
260C2×C32×C4C2×D411yescharacteristic
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2×D411yescharacteristic
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C3×#67—42no—
266C3×#67—42no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C3×D12—21no—
271C3×D12#4112yes—
272C3×C4×D3—42no—
273C3×C4×D3—42no—
274C3×C4×D3—42no—
275C3×Dic6—21no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#553C3×D311yescharacteristic, complemented
284#547—31no—
285#491—31no—
286#485—31no—
287#483—31no—
288#478—31no—
289#468—31no—
290#465—31no—
291#461—31no—
292#449—31no—
293#449—31no—
294#442—31no—
295#435—31no—
296#417—31no—
297#416—31no—
298C3×#41—62no—
299C3×#41—62no—
300C3×#41—121no—
301C3×#41—121no—
302C2×C3×Q8—31no—
303C2×C3×Q8—31no—
304C2×C3×D4—22no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—22no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C2×C3×D4—61no—
315C2×C3×D4#6711yescharacteristic
316C2×C3×D4C3×D411yescharacteristic
317C2×C3×D4C22×D311yescharacteristic
318C2×C3×D4C23×C311yescharacteristic
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—21no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C23×C311yescharacteristic
333C22×C3×C4C23×C311yescharacteristic
334C2×#67—21no—
335C2×#67—21no—
336#235—22no—
337#235—22no—
338#235—41no—
339#235—41no—
340C2×D12C23×C311yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3—21no—
343C2×C4×D3—21no—
344C2×Dic6C23×C311yescharacteristic
345C2×Dic6C23×C311yescharacteristic
346C3×SD16—121no—
347C3×SD16—121no—
348C3×D8—62no—
349C3×M16—121no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—121no—
355C3×C4⋊C4—22no—
356C3×C4⋊C4—22no—
357C3×C4⋊C4—22no—
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—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4#6711yescharacteristic
374C3×C4⋊C4C3×D411yescharacteristic
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C4⋊C4C23×C311yescharacteristic
379C3×C4⋊C4C23×C311yescharacteristic
380C3×C4⋊C4C23×C311yescharacteristic
381C3×C22⋊C4—22no—
382C3×C22⋊C4—22no—
383C3×C22⋊C4—22no—
384C3×C22⋊C4—22no—
385C3×C22⋊C4—21no—
386C3×C22⋊C4—21no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C22⋊C4—21no—
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—21no—
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4#6711yescharacteristic
399C3×C22⋊C4#6711yescharacteristic
400C3×C22⋊C4C3×D411yescharacteristic
401C3×C22⋊C4C3×D411yescharacteristic
402C3×C42—22no—
403C3×C42—21no—
404C3×C42—21no—
405C3×C42—21no—
406C3×C42C22×D311yescharacteristic
407C3×C42C23×C311yescharacteristic
408#217—21no—
409#217—21no—
410#214—41no—
411#214—41no—
412#213—22no—
413(C2×D3)⋊C4—21no—
414C4⋊Dic3—21no—
415C4⋊Dic3—21no—
416C4⋊Dic3C23×C311yescharacteristic
417Dic3⋊C4—21no—
418Dic3⋊C4—21no—
419#208—41no—
420C2×C3⋊C8—41no—
421C2×C3⋊C8C23×C311yescharacteristic
422C2×C3⋊C8C23×C311yescharacteristic
423C2×C3⋊C8C23×C311yescharacteristic
424C2×C3⋊C8C23×C311yescharacteristic
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32C22×D411yescharacteristic
435C2×C3×D3—22no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C32×C4—21no—
439C32×C4—21no—
440C32×C4—21no—
441C32×C4—21no—
442C32×C4—41no—
443C32×C4—41no—
444C32×C4—41no—
445C32×C4C2×#4111yescharacteristic
446C32×C4H(5,𝔽2)11yescharacteristic
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C2×#41—31no—
451C2×#41—31no—
452C2×SD16—31no—
453C2×SD16—31no—
454C2×D8—31no—
455C2×M16—31no—
456C22×C8—31no—
457C4⋊Q8—31no—
458#126—21no—
459#125C2×C3×D311yescharacteristic
460#123—21no—
461#123—61no—
462#123—61no—
463C22⋊Q8—31no—
464C22⋊Q8—31no—
465#121—21no—
466#121—61no—
467#121C2×C3×D311yescharacteristic
468#121C2×C3×D311yescharacteristic
469C4×D4—21no—
470C4×D4—31no—
471C4×D4C2×C3×D311yescharacteristic
472C4×D4C2×C3×D311yescharacteristic
473#117C2×C3×D311yescharacteristic
474C2×C4⋊C4—61no—
475C2×C4⋊C4C2×C3×D311yescharacteristic
476#107—31no—
477#106—31no—
478#106—31no—
479C4⋊C8—31no—
480#103—31no—
481#103—31no—
482#103—31no—
483#103—31no—
484#103—31no—
485#103—31no—
486#102—31no—
487#102—31no—
488#102—31no—
489#102—31no—
490C22⋊C8—31no—
491C22⋊C8—31no—
492#97—31no—
493C23×C3—22no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—61no—
499C23×C3C2×#6711yescharacteristic
500C23×C3C2×#6711yescharacteristic
501C23×C3C2×C3×D411yescharacteristic
502C23×C3C2×C3×D411yescharacteristic
503C22×D3—21no—
504C3×Q8—61no—
505C3×Q8—61no—
506C3×Q8—61no—
507C3×Q8—61no—
508C3×D4—21no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—32no—
513C3×D4—41no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—41no—
517C3×D4—42no—
518C3×D4—44no—
519C3×D4—42no—
520C3×D4—42no—
521C3×D4—61no—
522C3×D4—81no—
523C3×D4—81no—
524C3×D4—82no—
525C3×D4—122no—
526C3×D4—122no—
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—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—81no—
557C2×C3×C4—81no—
558C2×C3×C4—81no—
559C2×C3×C4—81no—
560C2×C3×C4—82no—
561C2×C3×C4—82no—
562C2×C3×C4—122no—
563C2×C3×C4—122no—
564C2×C3×C4—122no—
565C2×C3×C4C2×#6711yescharacteristic
566C2×C3×C4C2×#6711yescharacteristic
567C2×C3×C4C2×#6711yescharacteristic
568C2×C3×C4C2×#6711yescharacteristic
569C2×C3×C4C2×C3×D411yescharacteristic
570C2×C3×C4C2×C3×D411yescharacteristic
571C2×C3×C4C2×C3×D411yescharacteristic
572C2×C3×C4C2×C3×D411yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574C2×C3×C4C24×C311yescharacteristic
575#67—42no—
576#67—42no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580D12—21no—
581D12C3×#4112yes—
582C4×D3—42no—
583C4×D3—42no—
584C4×D3—42no—
585Dic6—21no—
586Dic6—21no—
587Dic6—21no—
588Dic6—21no—
589C3×C8—61no—
590C3×C8—61no—
591C3×C8—61no—
592C3×C8—61no—
593C3⋊C8—21no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8—21no—
597C2×C32—41no—
598C2×C32—41no—
599C2×C32—81no—
600C2×C32#54611yescharacteristic
601C2×C32#57511yescharacteristic
602C2×C32#57711yescharacteristic
603C3×D3—42no—
604#41—62no—
605#41—62no—
606#41—121no—
607#41—121no—
608C2×Q8—31no—
609C2×Q8—31no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—31no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4C3×#6711yescharacteristic
616C2×D4C22×C3×D311yescharacteristic
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4C22×C3×D311yescharacteristic
623C22×C4C22×C3×D311yescharacteristic
624SD16—121no—
625SD16—121no—
626D8—62no—
627M16—121no—
628C2×C8—31no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—121no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4C3×#6711yescharacteristic
642C4⋊C4C22×C3×D311yescharacteristic
643C4⋊C4C22×C3×D311yescharacteristic
644C4⋊C4C22×C3×D311yescharacteristic
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—61no—
652C22⋊C4C3×#6711yescharacteristic
653C22⋊C4C3×#6711yescharacteristic
654C42—21no—
655C42C22×C3×D311yescharacteristic
656C22×C3—22no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—42no—
676C22×C3—42no—
677C22×C3—42no—
678C22×C3—41no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—62no—
685C22×C3—121no—
686C22×C3—121no—
687C22×C3C22×#6711yescharacteristic
688C22×C3C22×C3×D411yescharacteristic
689C2×D3—22no—
690C2×D3—41no—
691C2×D3—41no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—42no—
707C3×C4—42no—
708C3×C4—42no—
709C3×C4—41no—
710C3×C4—41no—
711C3×C4—41no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—121no—
716C3×C4—121no—
717C3×C4—121no—
718C3×C4D3×#4111yescharacteristic
719C3×C4#100911yescharacteristic
720C3×C4C2×C3×#4111yescharacteristic
721C3×C4C3×H(5,𝔽2)11yescharacteristic
722Dic3—41no—
723Dic3—41no—
724Dic3—41no—
725C32#330711yescharacteristic, complemented, Sylow
726C23—21no—
727C23—61no—
728C23C2×C3×#6711yescharacteristic
729C23C2×C3×#6711yescharacteristic
730Q8—61no—
731Q8—61no—
732Q8—61no—
733Q8—61no—
734D4—21no—
735D4—21no—
736D4—32no—
737D4—41no—
738D4—42no—
739D4—61no—
740D4—81no—
741D4—122no—
742D4—122no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4C2×C3×#6711yescharacteristic
759C2×C4C2×C3×#6711yescharacteristic
760C2×C4C2×C3×#6711yescharacteristic
761C2×C4C2×C3×#6711yescharacteristic
762C2×C4C23×C3×D311yescharacteristic
763C8—61no—
764C8—61no—
765C8—61no—
766C8—61no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—42no—
771C2×C3—41no—
772C2×C3—41no—
773C2×C3—41no—
774C2×C3—41no—
775C2×C3—81no—
776C2×C3—82no—
777C2×C3—81no—
778C2×C3—81no—
779C2×C3—122no—
780C2×C3#582211yescharacteristic
781C2×C3#582911yescharacteristic
782C2×C3#583611yescharacteristic
783C2×C3C3×#54611yescharacteristic
784C2×C3C3×#57511yescharacteristic
785C2×C3C3×#57711yescharacteristic
786D3—42no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—21no—
792C22—21no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—62no—
797C22—121no—
798C22—121no—
799C22C22×C3×#6711yescharacteristic
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—121no—
808C4—121no—
809C4—121no—
810C4C3×D3×#4111yescharacteristic
811C4C3×#100911yescharacteristic
812C3—21no—
813C3#8361511yescharacteristic, direct product factor
814C3C3×#330711yescharacteristic, complemented
815C2—41no—
816C2—41no—
817C2—81no—
818C2—122no—
819C2C3×#582211yescharacteristic
820C2C3×#582911yescharacteristic
821C2C3×#583611yescharacteristic
subgroupG/H
centerC22×C3C22×#67
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#553C2
socleC22×C32C22×D4
hypercenterC3×#553D3
hypocenterC3C3×#3307
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×#553

Complements

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

NH ≅ G/Ntype
1. C32×#553C2semidirect
2. C3×#5551C2semidirect
3. C3×#5069C2semidirect
4. C3×#5066C2semidirect
5. C3×#5042C2semidirect
6. C3×#5041C2semidirect
7. C3×#5037C2semidirect
8. C3×#5037C2semidirect
9. C3×#5019C2semidirect
10. C3×#5014C2semidirect
11. C3×#5011C2semidirect
12. C3×#5002C2semidirect
13. C3×#4996C2semidirect
14. C3×#4971C2semidirect
15. C3×#4966C2semidirect
17. #83615C3direct (N × H)
62. C3×#553D3semidirect
63. C3×#553C2×C3semidirect
65. #5551C2×C3semidirect
79. #5069C2×C3semidirect
80. #5066C2×C3semidirect
81. #5042C2×C3semidirect
82. #5041C2×C3semidirect
83. #5037C2×C3semidirect
84. #5037C2×C3semidirect
85. #5019C2×C3semidirect
86. #5014C2×C3semidirect
87. #5011C2×C3semidirect
88. #5002C2×C3semidirect
89. #4996C2×C3semidirect
90. #4971C2×C3semidirect
91. #4966C2×C3semidirect
283. #553C3×D3semidirect
725. C32#3307semidirect
813. C3#83615direct (N × H)
814. C3C3×#3307semidirect

Maximal subgroups

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

subgroupindex
C32×#5532
C3×#55512
C3×#50692
C3×#50662
C3×#50422
C3×#50412
C3×#50372
C3×#50192
C3×#50142
C3×#50112
C3×#50022
C3×#49962
C3×#49712
C3×#49662
C3×#33073
#836153