Finite Group Databasebeta

← C3×#81148 #11882307

Subgroups — C3×#81148 #11882307

Order 1152.

847 conjugacy classes of subgroups.

The subgroup lattice has 775 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5691C211yesmaximal, characteristic, complemented
2C3×#5548C211yesmaximal, characteristic, complemented
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5016C211yesmaximal, characteristic, complemented
6C3×#4883C211yesmaximal, characteristic, complemented
7C3×#4875C211yesmaximal, characteristic, complemented
8C3×#4870C211yesmaximal, characteristic, complemented
9C3×#4864C211yesmaximal, characteristic, complemented
10C3×#4844C211yesmaximal, characteristic, complemented
11C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
12C3×#4786C211yesmaximal, characteristic, complemented
13C3×#4778C211yesmaximal, characteristic, complemented
14C3×#4775C211yesmaximal, characteristic, complemented
15C3×#4762C211yesmaximal, characteristic, complemented
16C3×#3247—31nomaximal
17#81148C311yesmaximal, characteristic, direct product factor
18C2×C3×#235—21no—
19C32×#125C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C3×#940C2211yescharacteristic
22C3×#938C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C3×C4×#67—21no—
26C2×C3×D24C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C2×C3×D3×C8C2211yescharacteristic
30C3×#898—21no—
31C3×#897C2211yescharacteristic
32C3×#895C2211yescharacteristic
33C3×#895C2211yescharacteristic
34C3×#894—21no—
35C3×#893—21no—
36C3×#893C2211yescharacteristic
37C3×#892—21no—
38C3×#888C2211yescharacteristic
39C3×#887C2211yescharacteristic
40C3×#885—21no—
41C3×#884—21no—
42C3×#875C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic
44C3×C42×D3C2211yescharacteristic
45C32×#107C2211yescharacteristic
46C32×#106C2211yescharacteristic
47C32×C4⋊C8C2211yescharacteristic
48C32×#102C2211yescharacteristic
49C32×#102C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#532—31no—
62C3×#529—31no—
63#5691C2×C311yescharacteristic, complemented
64#5548C2×C311yescharacteristic, complemented
65C3×#478—21no—
66C3×#478—31no—
67C3×#478D311yescharacteristic, complemented
68C3×#478C2×C311yescharacteristic, complemented
69C3×#477—31no—
70C3×#476—31no—
71C3×#466—31no—
72C3×#466—31no—
73C3×#465—31no—
74C3×#465—31no—
75C3×#463—31no—
76C3×#463—31no—
77C3×#460—31no—
78C3×#459—31no—
79C2×C3×C4⋊C8—31no—
80#5066C2×C311yescharacteristic, complemented
81#5016C2×C311yescharacteristic, complemented
82#4883C2×C311yescharacteristic, complemented
83#4875C2×C311yescharacteristic, complemented
84#4870C2×C311yescharacteristic, complemented
85#4864C2×C311yescharacteristic, complemented
86#4844C2×C311yescharacteristic, complemented
87D3×C4⋊C8C2×C311yescharacteristic, complemented
88#4786C2×C311yescharacteristic, complemented
89#4778C2×C311yescharacteristic, complemented
90#4775C2×C311yescharacteristic, complemented
91#4762C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×#67—21no—
97C3×#235—44no—
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4—21no—
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C32×C42C2311yescharacteristic
118C3×#217—21no—
119C3×#214—41no—
120C3×#213—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3D411yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×D24—41no—
139C3×#204—41no—
140C3×D3×C8—41no—
141C3×D3×C8—41no—
142#3247—31noSylow
143C2×C3×#41—61no—
144C2×#235—21no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×D8—31no—
148C2×C3×D8—31no—
149C22×C3×C8—31no—
150C22×C3×C8—31no—
151C3×C4⋊Q8—31no—
152C3×#127—31no—
153C3×#126—61no—
154C3×#125—21no—
155C3×#125C2×D311yescharacteristic
156C3×#125C22×C311yescharacteristic
157C3×#124—31no—
158C3×#124—61no—
159C3×#123—61no—
160C3×C22⋊Q8—31no—
161C3×#121—31no—
162C3×#121—31no—
163C3×#121—31no—
164C3×#121—61no—
165C3×C4×Q8—31no—
166C3×C4×D4—21no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4—61no—
170C3×C4×D4—61no—
171C3×C4×D4C2×D311yescharacteristic
172C3×C4×D4C22×C311yescharacteristic
173C3×#117—61no—
174C2×C3×C42—31no—
175#940C22×C311yescharacteristic
176#938C22×C311yescharacteristic
177C2×#214C22×C311yescharacteristic
178C2×#213C22×C311yescharacteristic
179C4×#67—21no—
180C2×D24C22×C311yescharacteristic
181C2×#204C22×C311yescharacteristic
182C2×D3×C8C22×C311yescharacteristic
183C2×D3×C8C22×C311yescharacteristic
184#898—21no—
185#897C22×C311yescharacteristic
186#895C22×C311yescharacteristic
187#895C22×C311yescharacteristic
188#894—21no—
189#893—21no—
190#893C22×C311yescharacteristic
191#892—21no—
192#888C22×C311yescharacteristic
193#887C22×C311yescharacteristic
194#885—21no—
195#884—21no—
196#875C22×C311yescharacteristic
197C4×D12C22×C311yescharacteristic
198C42×D3C22×C311yescharacteristic
199C3×#107—21no—
200C3×#107—31no—
201C3×#107C2×D311yescharacteristic
202C3×#107C22×C311yescharacteristic
203C3×#106—21no—
204C3×#106—31no—
205C3×#106C2×D311yescharacteristic
206C3×#106C22×C311yescharacteristic
207C3×C4⋊C8—21no—
208C3×C4⋊C8—31no—
209C3×C4⋊C8—31no—
210C3×C4⋊C8—31no—
211C3×C4⋊C8C2×D311yescharacteristic
212C3×C4⋊C8C22×C311yescharacteristic
213C3×#103—31no—
214C3×#103—31no—
215C3×#102—21no—
216C3×#102—21no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102C2×D311yescharacteristic
222C3×#102C2×D311yescharacteristic
223C3×#102C22×C311yescharacteristic
224C3×#102C22×C311yescharacteristic
225#821C22×C311yescharacteristic
226#816C22×C311yescharacteristic
227Dic3⋊C8C22×C311yescharacteristic
228Dic3⋊C8C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#809C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#809C22×C311yescharacteristic
233#808C22×C311yescharacteristic
234#807C22×C311yescharacteristic
235C4⋊(C3⋊C8)C22×C311yescharacteristic
236C23×C32—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3C2×D411yescharacteristic
240C32×D4—21no—
241C32×D4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—42no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C3×#67—42no—
250C3×#67—42no—
251C3×#67—42no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—42no—
262C3×D12—42no—
263C3×C4×D3—22no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—22no—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#532—31no—
277#529—31no—
278#478—31no—
279#478C3×D311yescharacteristic, complemented
280#477—31no—
281#476—31no—
282#466—31no—
283#466—31no—
284#465—31no—
285#465—31no—
286#463—31no—
287#463—31no—
288#460—31no—
289#459—31no—
290C2×C4⋊C8—31no—
291C3×#41—124no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×D4—21no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C23×C311yescharacteristic
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—41no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—21no—
315#235—44no—
316C2×D12—21no—
317C2×D12—21no—
318C2×D12C23×C311yescharacteristic
319C2×D12C23×C311yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3C3×D411yescharacteristic
323C2×C4×D3C3×D411yescharacteristic
324C2×C4×D3C23×C311yescharacteristic
325C2×Dic6—21no—
326C2×Dic6C23×C311yescharacteristic
327C3×SD16—121no—
328C3×SD16—121no—
329C3×D8—121no—
330C3×D8—121no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—121no—
336C2×C3×C8—121no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C23×C311yescharacteristic
340C2×C3×C8C23×C311yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—41no—
350C3×C4⋊C4—41no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C23×C311yescharacteristic
358C3×C4⋊C4C23×C311yescharacteristic
359C3×C4⋊C4C23×C311yescharacteristic
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—21no—
372C3×C42—31no—
373C3×C42—31no—
374C3×C42—31no—
375C3×C42—61no—
376C3×C42C22×D311yescharacteristic
377C3×C42C23×C311yescharacteristic
378#217—21no—
379#214—41no—
380#213—41no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3C23×C311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—21no—
392C4×Dic3—21no—
393C4×Dic3C3×D411yescharacteristic
394C4×Dic3C3×D411yescharacteristic
395C4×Dic3C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397C2×C3⋊C8C23×C311yescharacteristic
398D24—41no—
399#204—41no—
400D3×C8—41no—
401D3×C8—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3AGL(1,ℤ/8)12yes—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4H(5,𝔽2)11yescharacteristic
421C32×C42−1+411yescharacteristic
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3#13512yes—
427C2×#41—61no—
428C2×SD16—31no—
429C2×SD16—31no—
430C2×D8—31no—
431C2×D8—31no—
432C22×C8—31no—
433C22×C8—31no—
434C4⋊Q8—31no—
435#127—31no—
436#126—61no—
437#125C2×C3×D311yescharacteristic
438#124—31no—
439#124—61no—
440#123—61no—
441C22⋊Q8—31no—
442#121—31no—
443#121—31no—
444#121—31no—
445#121—61no—
446C4×Q8—31no—
447C4×D4—31no—
448C4×D4—31no—
449C4×D4—61no—
450C4×D4—61no—
451C4×D4C2×C3×D311yescharacteristic
452#117—61no—
453C2×C42—31no—
454#107—31no—
455#107C2×C3×D311yescharacteristic
456#106—31no—
457#106C2×C3×D311yescharacteristic
458C4⋊C8—31no—
459C4⋊C8—31no—
460C4⋊C8—31no—
461C4⋊C8C2×C3×D311yescharacteristic
462#103—31no—
463#103—31no—
464#102—31no—
465#102—31no—
466#102—31no—
467#102—31no—
468#102C2×C3×D311yescharacteristic
469#102C2×C3×D311yescharacteristic
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3—41no—
474C23×C3—61no—
475C23×C3—61no—
476C22×D3—21no—
477C22×D3—21no—
478C22×D3C2×C3×D411yescharacteristic
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—122no—
482C3×D4—22no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—41no—
488C3×D4—61no—
489C3×D4—61no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—122no—
493C3×D4—122no—
494C3×D4—122no—
495C3×D4—122no—
496C3×D4—122no—
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—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—42no—
513C2×C3×C4—42no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—82no—
521C2×C3×C4—122no—
522C2×C3×C4—122no—
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C2×C3×D411yescharacteristic
526C2×C3×C4C2×C3×D411yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C24×C311yescharacteristic
529#67—42no—
530#67—42no—
531#67—42no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3C2×C3×D411yescharacteristic
535C2×Dic3C2×C3×D411yescharacteristic
536C2×Dic3C2×C3×D411yescharacteristic
537D12—21no—
538D12—21no—
539D12—21no—
540D12—21no—
541D12—42no—
542D12—42no—
543C4×D3—22no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—22no—
547C4×D3—42no—
548C4×D3—42no—
549Dic6—21no—
550Dic6—21no—
551Dic6—42no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—41no—
557C3×C8—41no—
558C3×C8—61no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C2×C32—81no—
563C2×C32#53711yescharacteristic
564C2×C32C2×#13511yescharacteristic
565C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
566C3×D3—22no—
567C3×D3—81no—
568C3×D3—81no—
569#41—124no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×D4—31no—
573C2×D4—31no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4C22×C3×D311yescharacteristic
580C22×C4—21no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586SD16—121no—
587SD16—121no—
588D8—121no—
589D8—121no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—121no—
593C2×C8—121no—
594C2×C8C22×C3×D311yescharacteristic
595C2×C8C22×C3×D311yescharacteristic
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4C22×C3×D311yescharacteristic
603C4⋊C4C22×C3×D311yescharacteristic
604C4⋊C4C22×C3×D311yescharacteristic
605C22⋊C4—21no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C42—31no—
615C42—31no—
616C42—31no—
617C42—61no—
618C42C22×C3×D311yescharacteristic
619C22×C3—21no—
620C22×C3—32no—
621C22×C3—42no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C22×C3×D411yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3C3×AGL(1,ℤ/8)12yes—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—32no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—81no—
667C3×C4—81no—
668C3×C4—81no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4#100711yescharacteristic
672C3×C4#100911yescharacteristic
673C3×C4C3×H(5,𝔽2)11yescharacteristic
674C3×C4C3×2−1+411yescharacteristic
675Dic3—21no—
676Dic3—21no—
677Dic3—41no—
678Dic3—41no—
679Dic3C3×#13512yes—
680C32#324711yescharacteristic, complemented, Sylow
681C23—21no—
682C23—31no—
683C23—61no—
684C23—61no—
685Q8—61no—
686Q8—61no—
687Q8—122no—
688D4—21no—
689D4—21no—
690D4—61no—
691D4—61no—
692D4—61no—
693D4—61no—
694D4—122no—
695D4—122no—
696D4—122no—
697D4—122no—
698D4—122no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—42no—
706C2×C4—62no—
707C2×C4—62no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4C3×D3×D411yescharacteristic
715C2×C4C3×D3×D411yescharacteristic
716C2×C4C23×C3×D311yescharacteristic
717C8—21no—
718C8—21no—
719C8—61no—
720C8—61no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—62no—
725C2×C3—82no—
726C2×C3—81no—
727C2×C3—81no—
728C2×C3—241no—
729C2×C3—241no—
730C2×C3#562911yescharacteristic
731C2×C3D3×#13511yescharacteristic
732C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
733C2×C3C3×#53711yescharacteristic
734C2×C3C2×C3×#13511yescharacteristic
735C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
736D3—22no—
737D3—81no—
738D3—81no—
739C22—32no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—61no—
744C22—61no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22C2×C3×D3×D411yescharacteristic
752C4—21no—
753C4—21no—
754C4—32no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—61no—
759C4—61no—
760C4—121no—
761C4—121no—
762C4C3×#100711yescharacteristic
763C4C3×#100911yescharacteristic
764C3—21no—
765C3#8114811yescharacteristic, direct product factor
766C3C3×#324711yescharacteristic, complemented
767C2—62no—
768C2—81no—
769C2—241no—
770C2—241no—
771C2C3×#562911yescharacteristic
772C2C3×D3×#13511yescharacteristic
773C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
hypercenterC3×#478D3
hypocenterC3C3×#3247
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#478

Complements

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

NH ≅ G/Ntype
1. C3×#5691C2semidirect
2. C3×#5548C2semidirect
3. C32×#478C2semidirect
4. C3×#5066C2semidirect
5. C3×#5016C2semidirect
6. C3×#4883C2semidirect
7. C3×#4875C2semidirect
8. C3×#4870C2semidirect
9. C3×#4864C2semidirect
10. C3×#4844C2semidirect
11. C3×D3×C4⋊C8C2semidirect
12. C3×#4786C2semidirect
13. C3×#4778C2semidirect
14. C3×#4775C2semidirect
15. C3×#4762C2semidirect
17. #81148C3direct (N × H)
63. #5691C2×C3semidirect
64. #5548C2×C3semidirect
67. C3×#478D3semidirect
68. C3×#478C2×C3semidirect
80. #5066C2×C3semidirect
81. #5016C2×C3semidirect
82. #4883C2×C3semidirect
83. #4875C2×C3semidirect
84. #4870C2×C3semidirect
85. #4864C2×C3semidirect
86. #4844C2×C3semidirect
87. D3×C4⋊C8C2×C3semidirect
88. #4786C2×C3semidirect
89. #4778C2×C3semidirect
90. #4775C2×C3semidirect
91. #4762C2×C3semidirect
279. #478C3×D3semidirect
680. C32#3247semidirect
765. C3#81148direct (N × H)
766. C3C3×#3247semidirect

Maximal subgroups

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

subgroupindex
C3×#56912
C3×#55482
C32×#4782
C3×#50662
C3×#50162
C3×#48832
C3×#48752
C3×#48702
C3×#48642
C3×#48442
C3×D3×C4⋊C82
C3×#47862
C3×#47782
C3×#47752
C3×#47622
C3×#32473
#811483