Finite Group Databasebeta

← C3×#79449 #11887716

Subgroups — C3×#79449 #11887716

Order 1152.

839 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5552C211yesmaximal, characteristic
2C3×#5541C211yesmaximal, characteristic, complemented
3C32×C8×D4C211yesmaximal, characteristic, complemented
4C3×#5116C211yesmaximal, characteristic, complemented
5C3×#5114C211yesmaximal, characteristic, complemented
6C3×#5113C211yesmaximal, characteristic, complemented
7C2×C3×#816C211yesmaximal, characteristic, complemented
8C3×#4845C211yesmaximal, characteristic, complemented
9C3×#4829C211yesmaximal, characteristic, complemented
10C3×#4739C211yesmaximal, characteristic, complemented
11C3×#4736C211yesmaximal, characteristic, complemented
12C3×#4733C211yesmaximal, characteristic, complemented
13C3×#4723C211yesmaximal, characteristic, complemented
14C3×C4×Dic12C211yesmaximal, characteristic, complemented
15C3×#4697C211yesmaximal, characteristic, complemented
16C3×#3300—31nomaximal
17#79449C311yesmaximal, characteristic, direct product factor
18C2×C3×#235C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C3×#939—21no—
24C3×#935—21no—
25C3×#930C2211yescharacteristic
26C3×#926C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C2×C3×Dic12C2211yescharacteristic
32C2×C3×Dic12C2211yescharacteristic
33C2×C3×#204C2211yescharacteristic
34C3×#896—21no—
35C3×#889—21no—
36C3×#885—21no—
37C3×#67⋊C4—21no—
38C3×#879—21no—
39C3×#877—21no—
40C3×#875C2211yescharacteristic
41C3×#870C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×C4×Dic6C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C32×C22⋊C8C2211yescharacteristic
47C32×C4×C8C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#818C2211yescharacteristic
53C3×#817C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×#816C2211yescharacteristic
57C3×#816C2211yescharacteristic
58C3×#816C2211yescharacteristic
59C3×#816C2211yescharacteristic
60C3×#816C2211yescharacteristic
61C3×#552—31no—
62C3×#548—31no—
63#5552C2×C311yescharacteristic
64#5541C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#485—31no—
67C3×#480—31no—
68C3×#479—31no—
69C3×#467—31no—
70C3×#465—31no—
71C3×#464—31no—
72C3×#452—31no—
73C3×#451—31no—
74C3×C4×Q16—31no—
75C3×C8×D4—21no—
76C3×C8×D4D311yescharacteristic, complemented
77C3×C8×D4C2×C311yescharacteristic, complemented
78C3×#416—31no—
79C2×C3×#103—31no—
80#5116C2×C311yescharacteristic, complemented
81#5114C2×C311yescharacteristic, complemented
82#5113C2×C311yescharacteristic, complemented
83C2×#816C2×C311yescharacteristic, complemented
84#4845C2×C311yescharacteristic, complemented
85#4829C2×C311yescharacteristic, complemented
86#4739C2×C311yescharacteristic, complemented
87#4736C2×C311yescharacteristic, complemented
88#4733C2×C311yescharacteristic, complemented
89#4723C2×C311yescharacteristic, complemented
90C4×Dic12C2×C311yescharacteristic, complemented
91#4697C2×C311yescharacteristic, complemented
92C2×C32×D4D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×#235—22no—
100C3×#235—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6—22no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6—41no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C32×C8—41no—
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4D411yescharacteristic
116C32×C22⋊C4D411yescharacteristic
117C32×C22⋊C4D411yescharacteristic
118C32×C42C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3—21no—
141C3×Dic12—22no—
142C3×Dic12—41no—
143C3×#204—41no—
144#3300—31noSylow
145C2×C3×#41—31no—
146C22×C3×Q8—31no—
147C2×#235C22×C311yescharacteristic
148C22×Dic6C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C22×C3×C8—21no—
153C22×C3×C8—21no—
154C22×C3×C8C2×D311yescharacteristic
155C22×C3×C8C2×D311yescharacteristic
156C22×C3×C8C22×C311yescharacteristic
157C22×C3×C8C22×C311yescharacteristic
158C3×#126—61no—
159C3×#125—31no—
160C3×#125—61no—
161C3×#124—31no—
162C3×#124—61no—
163C3×#123—61no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—61no—
168C3×#121—31no—
169C3×#121—61no—
170C3×C4×Q8—31no—
171C3×C4×Q8—31no—
172C3×C4×D4—21no—
173C3×C4×D4—61no—
174C3×C4×D4C2×D311yescharacteristic
175C3×C4×D4C22×C311yescharacteristic
176C3×#117—31no—
177C3×#117—61no—
178C2×C3×C4⋊C4—31no—
179#939—21no—
180#935—21no—
181#930C22×C311yescharacteristic
182#926C22×C311yescharacteristic
183C2×C4⋊Dic3C22×C311yescharacteristic
184#924C22×C311yescharacteristic
185#924C22×C311yescharacteristic
186#924C22×C311yescharacteristic
187C2×Dic12C22×C311yescharacteristic
188C2×Dic12C22×C311yescharacteristic
189C2×#204C22×C311yescharacteristic
190#896—21no—
191#889—21no—
192#885—21no—
193#67⋊C4—21no—
194#879—21no—
195#877—21no—
196#875C22×C311yescharacteristic
197#870C22×C311yescharacteristic
198C4×Dic6C22×C311yescharacteristic
199C4×Dic6C22×C311yescharacteristic
200C3×#107—31no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—21no—
204C3×C4⋊C8C2×D311yescharacteristic
205C3×C4⋊C8C22×C311yescharacteristic
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×C22⋊C8—21no—
217C3×C22⋊C8—21no—
218C3×C22⋊C8C2×D311yescharacteristic
219C3×C22⋊C8C2×D311yescharacteristic
220C3×C22⋊C8C22×C311yescharacteristic
221C3×C22⋊C8C22×C311yescharacteristic
222C3×C4×C8—21no—
223C3×C4×C8C2×D311yescharacteristic
224C3×C4×C8C22×C311yescharacteristic
225#821C22×C311yescharacteristic
226#821C22×C311yescharacteristic
227#821C22×C311yescharacteristic
228#818C22×C311yescharacteristic
229#818C22×C311yescharacteristic
230#817C22×C311yescharacteristic
231#816C22×C311yescharacteristic
232#816C22×C311yescharacteristic
233#816C22×C311yescharacteristic
234#816C22×C311yescharacteristic
235#816C22×C311yescharacteristic
236#816C22×C311yescharacteristic
237#816C22×C311yescharacteristic
238C23×C32C2×D411yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C32×D4—22no—
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×C4C2×D411yescharacteristic
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2411yescharacteristic
251C3×#67—42no—
252C3×#67—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3—42no—
262C3×D12—21no—
263C3×D12—21no—
264C3×C4×D3—42no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271C3×Dic6#4112yes—
272C32×C8—21no—
273C32×C8—21no—
274C32×C8—21no—
275C32×C8—21no—
276#552—31no—
277#548—31no—
278#488—31no—
279#485—31no—
280#480—31no—
281#479—31no—
282#467—31no—
283#465—31no—
284#464—31no—
285#452—31no—
286#451—31no—
287C4×Q16—31no—
288C8×D4C3×D311yescharacteristic, complemented
289#416—31no—
290C2×#103—31no—
291C3×#41—62no—
292C3×#41—121no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×Q8—62no—
297C2×C3×Q8—61no—
298C2×C3×Q8—121no—
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4D1211yescharacteristic
304C2×C3×D4C3×D411yescharacteristic
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C23×C311yescharacteristic
313C22×C3×C4C23×C311yescharacteristic
314C2×#67—21no—
315C2×#67—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318#235—22no—
319#235—41no—
320C2×D12C23×C311yescharacteristic
321C2×C4×D3—21no—
322C2×Dic6—22no—
323C2×Dic6—21no—
324C2×Dic6—41no—
325C2×Dic6C23×C311yescharacteristic
326C2×Dic6C23×C311yescharacteristic
327C2×Dic6C23×C311yescharacteristic
328C3×Q16—62no—
329C3×Q16—121no—
330C3×SD16—121no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—41no—
336C2×C3×C8—41no—
337C2×C3×C8—41no—
338C2×C3×C8—41no—
339C2×C3×C8—42no—
340C2×C3×C8—42no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C23×C311yescharacteristic
346C2×C3×C8C23×C311yescharacteristic
347C2×C3×C8C23×C311yescharacteristic
348C2×C3×C8C23×C311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
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⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4D1211yescharacteristic
363C3×C4⋊C4C3×D411yescharacteristic
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4D1211yescharacteristic
374C3×C22⋊C4D1211yescharacteristic
375C3×C22⋊C4C3×D411yescharacteristic
376C3×C22⋊C4C3×D411yescharacteristic
377C3×C42—21no—
378C3×C42—61no—
379C3×C42—61no—
380C3×C42—61no—
381C3×C42C22×D311yescharacteristic
382C3×C42C23×C311yescharacteristic
383#217—21no—
384#217—21no—
385#217—21no—
386#217—21no—
387(C2×D3)⋊C4—21no—
388(C2×D3)⋊C4—21no—
389(C2×D3)⋊C4—21no—
390C4⋊Dic3—21no—
391C4⋊Dic3C23×C311yescharacteristic
392C4⋊Dic3C23×C311yescharacteristic
393C4⋊Dic3C23×C311yescharacteristic
394C4⋊Dic3C23×C311yescharacteristic
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—21no—
401Dic3⋊C4—21no—
402C4×Dic3—21no—
403C4×Dic3—21no—
404C4×Dic3—21no—
405Dic12—22no—
406Dic12—41no—
407#204—41no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32#13512yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C32×C4—21no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4C2×#4111yescharacteristic
423C32×C4H(5,𝔽2)11yescharacteristic
424C3×Dic3—22no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C2×#41—31no—
432C22×Q8—31no—
433C2×Q16—31no—
434C2×Q16—31no—
435C2×SD16—31no—
436C22×C8C2×C3×D311yescharacteristic
437C22×C8C2×C3×D311yescharacteristic
438#126—61no—
439#125—31no—
440#125—61no—
441#124—31no—
442#124—61no—
443#123—61no—
444C22⋊Q8—31no—
445C22⋊Q8—31no—
446C22⋊Q8—31no—
447C22⋊Q8—61no—
448#121—31no—
449#121—61no—
450C4×Q8—31no—
451C4×Q8—31no—
452C4×D4—61no—
453C4×D4C2×C3×D311yescharacteristic
454#117—31no—
455#117—61no—
456C2×C4⋊C4—31no—
457#107—31no—
458#107—31no—
459#106—31no—
460C4⋊C8C2×C3×D311yescharacteristic
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—31no—
468#102—31no—
469#102—31no—
470#102—31no—
471C22⋊C8C2×C3×D311yescharacteristic
472C22⋊C8C2×C3×D311yescharacteristic
473C4×C8C2×C3×D311yescharacteristic
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—61no—
477C23×C3C2×D1211yescharacteristic
478C23×C3C2×D1211yescharacteristic
479C23×C3C2×C3×D411yescharacteristic
480C23×C3C2×C3×D411yescharacteristic
481C22×D3—21no—
482C3×Q8—32no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—122no—
489C3×D4—24no—
490C3×D4—22no—
491C3×D4—22no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—122no—
495C3×D4—122no—
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—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4—122no—
522C2×C3×C4—122no—
523C2×C3×C4C2×D1211yescharacteristic
524C2×C3×C4C2×D1211yescharacteristic
525C2×C3×C4C2×D1211yescharacteristic
526C2×C3×C4C2×D1211yescharacteristic
527C2×C3×C4C2×C3×D411yescharacteristic
528C2×C3×C4C2×C3×D411yescharacteristic
529C2×C3×C4C2×C3×D411yescharacteristic
530C2×C3×C4C2×C3×D411yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C24×C311yescharacteristic
533#67—42no—
534#67—42no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—42no—
543C2×Dic3—42no—
544D12—21no—
545D12—21no—
546C4×D3—42no—
547Dic6—21no—
548Dic6—21no—
549Dic6—21no—
550Dic6—21no—
551Dic6—21no—
552Dic6—42no—
553Dic6C3×#4112yes—
554C3×C8—22no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—41no—
564C3×C8—41no—
565C3×C8—41no—
566C2×C32—22no—
567C2×C32—41no—
568C2×C32#54611yescharacteristic
569C2×C32C2×#13511yescharacteristic
570C2×C32#57811yescharacteristic
571C3×D3—81no—
572#41—62no—
573#41—121no—
574C2×Q8—31no—
575C2×Q8—31no—
576C2×Q8—31no—
577C2×Q8—62no—
578C2×Q8—61no—
579C2×Q8—121no—
580C2×D4—31no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4C3×D1211yescharacteristic
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—61no—
587C22×C4C22×C3×D311yescharacteristic
588C22×C4C22×C3×D311yescharacteristic
589Q16—62no—
590Q16—121no—
591SD16—121no—
592C2×C8—41no—
593C2×C8—41no—
594C2×C8C22×C3×D311yescharacteristic
595C2×C8C22×C3×D311yescharacteristic
596C2×C8C22×C3×D311yescharacteristic
597C2×C8C22×C3×D311yescharacteristic
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4C3×D1211yescharacteristic
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4C3×D1211yescharacteristic
619C22⋊C4C3×D1211yescharacteristic
620C42—61no—
621C42—61no—
622C42—61no—
623C42C22×C3×D311yescharacteristic
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—22no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—22no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3#90412yes—
645C22×C3C3×#13512yes—
646C22×C3C22×D1211yescharacteristic
647C22×C3C22×C3×D411yescharacteristic
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C3×C4—22no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—62no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4#100411yescharacteristic
673C3×C4D3×#4111yescharacteristic
674C3×C4C2×C3×#4111yescharacteristic
675C3×C4C3×H(5,𝔽2)11yescharacteristic
676Dic3—22no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—41no—
683C32#330011yescharacteristic, complemented, Sylow
684C23—61no—
685C23C2×C3×D1211yescharacteristic
686C23C2×C3×D1211yescharacteristic
687Q8—32no—
688Q8—61no—
689Q8—61no—
690Q8—61no—
691Q8—61no—
692Q8—61no—
693Q8—122no—
694D4—22no—
695D4—61no—
696D4—61no—
697D4—122no—
698D4—122no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4C2×C3×D1211yescharacteristic
714C2×C4C2×C3×D1211yescharacteristic
715C2×C4C2×C3×D1211yescharacteristic
716C2×C4C2×C3×D1211yescharacteristic
717C2×C4C23×C3×D311yescharacteristic
718C8—21no—
719C8—21no—
720C8—21no—
721C8—21no—
722C2×C3—22no—
723C2×C3—22no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—42no—
728C2×C3—42no—
729C2×C3—41no—
730C2×C3—41no—
731C2×C3—241no—
732C2×C3#555411yescharacteristic
733C2×C3C2×#90411yescharacteristic
734C2×C3#575311yescharacteristic
735C2×C3C3×#54611yescharacteristic
736C2×C3C2×C3×#13511yescharacteristic
737C2×C3C3×#57811yescharacteristic
738D3—81no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22C3×#90412yes—
748C22C22×C3×D1211yescharacteristic
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—62no—
754C4—121no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4—121no—
760C4C3×#100411yescharacteristic
761C4C3×D3×#4111yescharacteristic
762C3—21no—
763C3#7944911yescharacteristic, direct product factor
764C3C3×#330011yescharacteristic, complemented
765C2—22no—
766C2—41no—
767C2—241no—
768C2C3×#555411yescharacteristic
769C2C2×C3×#90411yescharacteristic
770C2C3×#575311yescharacteristic
subgroupG/H
centerC22×C3C22×D12
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×C8×D4C2
socleC22×C32C22×D4
prime radicalC3×#5552C2
hypercenterC3×C8×D4D3
hypocenterC3C3×#3300
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C4×D4 ◁ C3×C8×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5541C2semidirect
3. C32×C8×D4C2semidirect
4. C3×#5116C2semidirect
5. C3×#5114C2semidirect
6. C3×#5113C2semidirect
7. C2×C3×#816C2semidirect
8. C3×#4845C2semidirect
9. C3×#4829C2semidirect
10. C3×#4739C2semidirect
11. C3×#4736C2semidirect
12. C3×#4733C2semidirect
13. C3×#4723C2semidirect
14. C3×C4×Dic12C2semidirect
15. C3×#4697C2semidirect
17. #79449C3direct (N × H)
64. #5541C2×C3semidirect
76. C3×C8×D4D3semidirect
77. C3×C8×D4C2×C3semidirect
80. #5116C2×C3semidirect
81. #5114C2×C3semidirect
82. #5113C2×C3semidirect
83. C2×#816C2×C3semidirect
84. #4845C2×C3semidirect
85. #4829C2×C3semidirect
86. #4739C2×C3semidirect
87. #4736C2×C3semidirect
88. #4733C2×C3semidirect
89. #4723C2×C3semidirect
90. C4×Dic12C2×C3semidirect
91. #4697C2×C3semidirect
288. C8×D4C3×D3semidirect
683. C32#3300semidirect
763. C3#79449direct (N × H)
764. C3C3×#3300semidirect

Maximal subgroups

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

subgroupindex
C3×#55522
C3×#55412
C32×C8×D42
C3×#51162
C3×#51142
C3×#51132
C2×C3×#8162
C3×#48452
C3×#48292
C3×#47392
C3×#47362
C3×#47332
C3×#47232
C3×C4×Dic122
C3×#46972
C3×#33003
#794493