Finite Group Databasebeta

← C3×#81305 #11887704

Subgroups — C3×#81305 #11887704

Order 1152.

829 conjugacy classes of subgroups.

The subgroup lattice has 769 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5598C211yesmaximal, characteristic
2C3×#5513C211yesmaximal, characteristic, complemented
3C32×#480C211yesmaximal, characteristic, complemented
4C3×#5041C211yesmaximal, characteristic, complemented
5C2×C3×#810C211yesmaximal, characteristic, complemented
6C3×#4888C211yesmaximal, characteristic, complemented
7C3×#4887C211yesmaximal, characteristic, complemented
8C3×#4877C211yesmaximal, characteristic, complemented
9C3×#4873C211yesmaximal, characteristic, complemented
10C3×#4783C211yesmaximal, characteristic, complemented
11C3×#4772C211yesmaximal, characteristic, complemented
12C3×#4768C211yesmaximal, characteristic, complemented
13C3×#4767C211yesmaximal, characteristic, complemented
14C3×#4739C211yesmaximal, characteristic, complemented
15C3×#67⋊C8C211yesmaximal, characteristic, complemented
16C3×#3300—31nomaximal
17#81305C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C32×#121C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C3×#939—21no—
23C3×#936C2211yescharacteristic
24C3×D4×Dic3—21no—
25C2×C3×#214C2211yescharacteristic
26C3×#929—21no—
27C3×C4×#67C2211yescharacteristic
28C3×#926—21no—
29C3×#924C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31C2×C3×Dic12C2211yescharacteristic
32C2×C3×Dic12C2211yescharacteristic
33C2×C3×D3×C8C2211yescharacteristic
34C3×#898—21no—
35C3×#897C2211yescharacteristic
36C3×#897C2211yescharacteristic
37C3×#892C2211yescharacteristic
38C3×#890C2211yescharacteristic
39C3×#889—21no—
40C3×#887C2211yescharacteristic
41C3×#887C2211yescharacteristic
42C3×#885—21no—
43C3×#878—21no—
44C32×#107C2211yescharacteristic
45C32×#107C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C32×C22⋊C8C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#810C2211yescharacteristic
58C3×#810C2211yescharacteristic
59C3×#810C2211yescharacteristic
60C3×#808C2211yescharacteristic
61C3×#552—31no—
62C3×#548—31no—
63#5598C2×C311yescharacteristic
64#5513C2×C311yescharacteristic, complemented
65C3×#488—31no—
66C3×#485—31no—
67C3×#480—21no—
68C3×#480D311yescharacteristic, complemented
69C3×#480C2×C311yescharacteristic, complemented
70C3×#479—31no—
71C3×#467—31no—
72C3×#465—31no—
73C3×#464—31no—
74C3×#452—31no—
75C3×#451—31no—
76C3×C4×Q16—31no—
77C3×C8×D4—31no—
78C3×#416—31no—
79C2×C3×#103—31no—
80#5041C2×C311yescharacteristic, complemented
81C2×#810C2×C311yescharacteristic, complemented
82#4888C2×C311yescharacteristic, complemented
83#4887C2×C311yescharacteristic, complemented
84#4877C2×C311yescharacteristic, complemented
85#4873C2×C311yescharacteristic, complemented
86#4783C2×C311yescharacteristic, complemented
87#4772C2×C311yescharacteristic, complemented
88#4768C2×C311yescharacteristic, complemented
89#4767C2×C311yescharacteristic, complemented
90#4739C2×C311yescharacteristic, complemented
91#67⋊C8C2×C311yescharacteristic, complemented
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C22×C32×C4C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C3×#237—22no—
101C3×#237—41no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—22no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6—41no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#214—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8—41no—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×Dic12—22no—
142C3×Dic12—41no—
143C3×D3×C8—41no—
144#3300—31noSylow
145C2×C3×#41—31no—
146C22×C3×Q8—31no—
147C2×#237C22×C311yescharacteristic
148C22×Dic6C22×C311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C22×C3×C8—31no—
153C22×C3×C8—31no—
154C3×#126—61no—
155C3×#125—31no—
156C3×#125—61no—
157C3×#124—31no—
158C3×#124—61no—
159C3×#123—61no—
160C3×C22⋊Q8—31no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—61no—
164C3×#121—21no—
165C3×#121—61no—
166C3×#121C2×D311yescharacteristic
167C3×#121C22×C311yescharacteristic
168C3×C4×Q8—31no—
169C3×C4×Q8—31no—
170C3×C4×D4—31no—
171C3×C4×D4—61no—
172C3×#117—31no—
173C3×#117—61no—
174C2×C3×C4⋊C4—21no—
175C2×C3×C4⋊C4C2×D311yescharacteristic
176C2×C3×C4⋊C4C22×C311yescharacteristic
177#939—21no—
178#936C22×C311yescharacteristic
179D4×Dic3—21no—
180C2×#214C22×C311yescharacteristic
181#929—21no—
182C4×#67C22×C311yescharacteristic
183#926—21no—
184#924C22×C311yescharacteristic
185C22×C3⋊C8C22×C311yescharacteristic
186C2×Dic12C22×C311yescharacteristic
187C2×Dic12C22×C311yescharacteristic
188C2×D3×C8C22×C311yescharacteristic
189#898—21no—
190#897C22×C311yescharacteristic
191#897C22×C311yescharacteristic
192#892C22×C311yescharacteristic
193#890C22×C311yescharacteristic
194#889—21no—
195#887C22×C311yescharacteristic
196#887C22×C311yescharacteristic
197#885—21no—
198#878—21no—
199C3×#107—21no—
200C3×#107—21no—
201C3×#107C2×D311yescharacteristic
202C3×#107C2×D311yescharacteristic
203C3×#107C22×C311yescharacteristic
204C3×#107C22×C311yescharacteristic
205C3×#106—31no—
206C3×C4⋊C8—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#102—21no—
215C3×#102—21no—
216C3×#102—31no—
217C3×#102C2×D311yescharacteristic
218C3×#102C2×D311yescharacteristic
219C3×#102C22×C311yescharacteristic
220C3×#102C22×C311yescharacteristic
221C3×C22⋊C8—21no—
222C3×C22⋊C8—31no—
223C3×C22⋊C8C2×D311yescharacteristic
224C3×C22⋊C8C22×C311yescharacteristic
225C3×C4×C8—31no—
226#832C22×C311yescharacteristic
227(C2×D3)⋊C8C22×C311yescharacteristic
228#816C22×C311yescharacteristic
229#816C22×C311yescharacteristic
230Dic3⋊C8C22×C311yescharacteristic
231C8×Dic3C22×C311yescharacteristic
232#810C22×C311yescharacteristic
233#810C22×C311yescharacteristic
234#810C22×C311yescharacteristic
235#810C22×C311yescharacteristic
236#810C22×C311yescharacteristic
237#808C22×C311yescharacteristic
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×D4—21no—
242C32×D4—21no—
243C32×D4—42no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—42no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C3×#67—22no—
253C3×#67—42no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×C4×D3—21no—
264C3×C4×D3—21no—
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—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#552—31no—
277#548—31no—
278#488—31no—
279#485—31no—
280#480C3×D311yescharacteristic, complemented
281#479—31no—
282#467—31no—
283#465—31no—
284#464—31no—
285#452—31no—
286#451—31no—
287C4×Q16—31no—
288C8×D4—31no—
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—21no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—41no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C23×C311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—31no—
311C22×C3×C4—41no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C23×C311yescharacteristic
316C2×#67—21no—
317C2×#67C3×D411yescharacteristic
318C22×Dic3—21no—
319C22×Dic3—21no—
320#237—22no—
321#237—41no—
322C2×C4×D3C23×C311yescharacteristic
323C2×Dic6—22no—
324C2×Dic6—21no—
325C2×Dic6—41no—
326C2×Dic6C23×C311yescharacteristic
327C2×Dic6C23×C311yescharacteristic
328C2×Dic6C23×C311yescharacteristic
329C3×Q16—62no—
330C3×Q16—121no—
331C3×SD16—121no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—121no—
337C2×C3×C8—121no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C23×C311yescharacteristic
341C2×C3×C8C23×C311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
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⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C4⋊C4C23×C311yescharacteristic
363C3×C22⋊C4—21no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—41no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C22⋊C4—61no—
373C3×C22⋊C4—61no—
374C3×C42—31no—
375C3×C42—61no—
376C3×C42—61no—
377C3×C42—61no—
378#217—21no—
379#217—21no—
380#217—21no—
381#217C3×D411yescharacteristic
382#214—41no—
383(C2×D3)⋊C4—21no—
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
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4C3×D411yescharacteristic
396C4×Dic3—21no—
397C4×Dic3—21no—
398C4×Dic3—21no—
399C4×Dic3C23×C311yescharacteristic
400C2×C3⋊C8—41no—
401C2×C3⋊C8C23×C311yescharacteristic
402C2×C3⋊C8C23×C311yescharacteristic
403Dic12—22no—
404Dic12—41no—
405D3×C8—41no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32#13512yes—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C32×C4—21no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4H(5,𝔽2)11yescharacteristic
422C3×Dic3—22no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C2×#41—31no—
430C22×Q8—31no—
431C2×Q16—31no—
432C2×Q16—31no—
433C2×SD16—31no—
434C22×C8—31no—
435C22×C8—31no—
436#126—61no—
437#125—31no—
438#125—61no—
439#124—31no—
440#124—61no—
441#123—61no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—61no—
446#121—61no—
447#121C2×C3×D311yescharacteristic
448C4×Q8—31no—
449C4×Q8—31no—
450C4×D4—31no—
451C4×D4—61no—
452#117—31no—
453#117—61no—
454C2×C4⋊C4C2×C3×D311yescharacteristic
455#107C2×C3×D311yescharacteristic
456#107C2×C3×D311yescharacteristic
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#103—31no—
466#102—31no—
467#102C2×C3×D311yescharacteristic
468#102C2×C3×D311yescharacteristic
469C22⋊C8—31no—
470C22⋊C8C2×C3×D311yescharacteristic
471C4×C8—31no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3—41no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×C3×D411yescharacteristic
479C22×D3C2×C3×D411yescharacteristic
480C3×Q8—32no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—122no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—21no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—42no—
494C3×D4—42no—
495C3×D4—62no—
496C3×D4—82no—
497C3×D4—122no—
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—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—42no—
519C2×C3×C4—42no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—82no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×C3×D411yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C24×C311yescharacteristic
533#67—22no—
534#67—42no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—42no—
540C2×Dic3—42no—
541C2×Dic3C2×C3×D411yescharacteristic
542C2×Dic3C2×C3×D411yescharacteristic
543C2×Dic3C2×C3×D411yescharacteristic
544C4×D3—21no—
545C4×D3—21no—
546Dic6—21no—
547Dic6—21no—
548Dic6—21no—
549Dic6—21no—
550Dic6—21no—
551Dic6—42no—
552Dic6C3×#4112yes—
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—22no—
564C2×C32—81no—
565C2×C32#54611yescharacteristic
566C2×C32C2×#13511yescharacteristic
567C2×C32#57811yescharacteristic
568C3×D3—41no—
569#41—62no—
570#41—121no—
571C2×Q8—31no—
572C2×Q8—31no—
573C2×Q8—31no—
574C2×Q8—62no—
575C2×Q8—61no—
576C2×Q8—121no—
577C2×D4—21no—
578C2×D4—31no—
579C2×D4—61no—
580C2×D4C22×C3×D311yescharacteristic
581C22×C4—21no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4C22×C3×D311yescharacteristic
586Q16—62no—
587Q16—121no—
588SD16—121no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—121no—
592C2×C8—121no—
593C2×C8C22×C3×D311yescharacteristic
594C2×C8C22×C3×D311yescharacteristic
595C4⋊C4—21no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4C22×C3×D311yescharacteristic
606C4⋊C4C22×C3×D311yescharacteristic
607C4⋊C4C22×C3×D311yescharacteristic
608C22⋊C4—21no—
609C22⋊C4—31no—
610C22⋊C4—31no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C42—31no—
618C42—61no—
619C42—61no—
620C42—61no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—22no—
626C22×C3—21no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3#91212yes—
642C22×C3C3×#13512yes—
643C22×C3C2×D3×D411yescharacteristic
644C22×C3C22×C3×D411yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—62no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—81no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4D3×#4111yescharacteristic
670C3×C4#100911yescharacteristic
671C3×C4C2×C3×#4111yescharacteristic
672C3×C4C3×H(5,𝔽2)11yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—22no—
676Dic3—21no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680C32#330011yescharacteristic, complemented, Sylow
681C23—21no—
682C23—31no—
683C23C3×D3×D411yescharacteristic
684Q8—32no—
685Q8—61no—
686Q8—61no—
687Q8—61no—
688Q8—61no—
689Q8—61no—
690Q8—122no—
691D4—21no—
692D4—21no—
693D4—42no—
694D4—62no—
695D4—122no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—42no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4C3×D3×D411yescharacteristic
714C2×C4C23×C3×D311yescharacteristic
715C8—21no—
716C8—21no—
717C8—61no—
718C8—61no—
719C2×C3—22no—
720C2×C3—22no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—42no—
725C2×C3—81no—
726C2×C3—81no—
727C2×C3—121no—
728C2×C3—161no—
729C2×C3#565411yescharacteristic
730C2×C3C2×#91211yescharacteristic
731C2×C3#577911yescharacteristic
732C2×C3C3×#54611yescharacteristic
733C2×C3C2×C3×#13511yescharacteristic
734C2×C3C3×#57811yescharacteristic
735D3—41no—
736C22—21no—
737C22—21no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22C3×#91212yes—
745C22C2×C3×D3×D411yescharacteristic
746C4—21no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—62no—
754C4—121no—
755C4—121no—
756C4—121no—
757C4C3×D3×#4111yescharacteristic
758C4C3×#100911yescharacteristic
759C3—21no—
760C3#8130511yescharacteristic, direct product factor
761C3C3×#330011yescharacteristic, complemented
762C2—22no—
763C2—81no—
764C2—121no—
765C2C3×#565411yescharacteristic
766C2C2×C3×#91211yescharacteristic
767C2C3×#577911yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#480C2
socleC22×C32C22×D4
prime radicalC3×#5598C2
hypercenterC3×#480D3
hypocenterC3C3×#3300
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#480

Complements

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

NH ≅ G/Ntype
2. C3×#5513C2semidirect
3. C32×#480C2semidirect
4. C3×#5041C2semidirect
5. C2×C3×#810C2semidirect
6. C3×#4888C2semidirect
7. C3×#4887C2semidirect
8. C3×#4877C2semidirect
9. C3×#4873C2semidirect
10. C3×#4783C2semidirect
11. C3×#4772C2semidirect
12. C3×#4768C2semidirect
13. C3×#4767C2semidirect
14. C3×#4739C2semidirect
15. C3×#67⋊C8C2semidirect
17. #81305C3direct (N × H)
64. #5513C2×C3semidirect
68. C3×#480D3semidirect
69. C3×#480C2×C3semidirect
80. #5041C2×C3semidirect
81. C2×#810C2×C3semidirect
82. #4888C2×C3semidirect
83. #4887C2×C3semidirect
84. #4877C2×C3semidirect
85. #4873C2×C3semidirect
86. #4783C2×C3semidirect
87. #4772C2×C3semidirect
88. #4768C2×C3semidirect
89. #4767C2×C3semidirect
90. #4739C2×C3semidirect
91. #67⋊C8C2×C3semidirect
280. #480C3×D3semidirect
680. C32#3300semidirect
760. C3#81305direct (N × H)
761. C3C3×#3300semidirect

Maximal subgroups

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

subgroupindex
C3×#55982
C3×#55132
C32×#4802
C3×#50412
C2×C3×#8102
C3×#48882
C3×#48872
C3×#48772
C3×#48732
C3×#47832
C3×#47722
C3×#47682
C3×#47672
C3×#47392
C3×#67⋊C82
C3×#33003
#813053