Finite Group Databasebeta

← #11660628

Subgroups — #11660628

Order 768.

1816 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5479C211yesmaximal, characteristic
2C3×#2920C211yesmaximal, characteristic, complemented
3C2×#4925C211yesmaximal, characteristic, complemented
4#79333C214yesmaximal, complemented
5#79325C214yesmaximal, complemented
6#79296C214yesmaximal, complemented
7#79288C211yesmaximal, characteristic, complemented
8#79286C211yesmaximal, characteristic, complemented
9#79264C211yesmaximal, characteristic, complemented
10#79263C211yesmaximal, characteristic, complemented
11#79053C214yesmaximal, complemented
12#78633C214yesmaximal, complemented
13#78511C214yesmaximal, complemented
14#60290—31nomaximal, Sylow
15C22×C3×C42C2211yescharacteristic
16C2×#930C411yescharacteristic
17C2×#929C412yes—
18C2×C4×#67C2212yes—
19C2×#924C411yescharacteristic
20#5479C412yes—
21#5479C412yes—
22#5479C412yes—
23#5479C412yes—
24#5479C2212yes—
25#5479C2212yes—
26#5479C2212yes—
27#5479C2212yes—
28C2×#876C412yes—
29C2×#875C411yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C2×#872C2212yes—
32C2×#870C411yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C3×#432C2212yes—
35C3×#432C2212yescomplemented
36C3×#431C2211yescharacteristic
37C3×#431C2211yescharacteristic
38C3×#431C2212yescomplemented
39C3×#423C2212yescomplemented
40C3×#407C2212yes—
41C3×C4×M16C2212yescomplemented
42C2×#830C2212yes—
43#5128C2218yescomplemented
44#5127C2218yescomplemented
45#4925C2211yescharacteristic
46#4925C2211yescharacteristic
47#4925C2212yes—
48#4925C2212yescomplemented
49#4925C2212yescomplemented
50C2×C4⋊(C3⋊C8)C2212yescomplemented
51C2×C4×C3⋊C8C2212yescomplemented
52#4840C2218yescomplemented
53#4839C2218yescomplemented
54#4838C2214yescomplemented
55#4834C2214yescomplemented
56#4831C2214yescomplemented
57#4830C2214yescomplemented
58#4730C2218yescomplemented
59#4726C2214yes—
60#67⋊C8C2218yescomplemented
61D3×C22⋊C8C2214yes—
62#4719C2214yes—
63#4718C2214yes—
64#4709C2218yescomplemented
65#4708C2218yescomplemented
66#4688C2214yescomplemented
67C8×D12C2214yescomplemented
68#4679C2214yescomplemented
69C8×Dic6C2214yescomplemented
70C2×#529—31no—
71#2994—34no—
72#2993—34no—
73#2983—31no—
74#2982—31no—
75#2975—31no—
76#2974—34no—
77#2972—31no—
78#2969—34no—
79#2966—34no—
80#2924—34no—
81#2920D311yescharacteristic, complemented
82C2×#431—31no—
83C23×C3×C4C2×C411yescharacteristic
84C23×C3×C4C2×C411yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67C2×C412yes—
87C22×D12C2×C411yescharacteristic
88C22×C4×D3C2312yes—
89C22×Dic6C2×C411yescharacteristic
90C2×C3×M16C2314yes—
91C2×C3×C42C2×C411yescharacteristic
92C2×C3×C42C2×C411yescharacteristic
93C2×C3×C42C2×C411yescharacteristic
94C2×C3×C42C2×C411yescharacteristic
95C2×C3×C42C2×C411yescharacteristic
96C2×C3×C42C2×C411yescharacteristic
97C2×C3×C42C2311yescharacteristic
98C2×C3×C42C2311yescharacteristic
99C2×C3×C42C2311yescharacteristic
100C2×C3×C42C2311yescharacteristic
101C2×C3×C42C2311yescharacteristic
102C2×C3×C42C2311yescharacteristic
103C2×#217C2×C412yes—
104#930C2×C412yes—
105#930C2×C412yes—
106#930C2×C412yes—
107#930C2×C412yes—
108#929C2×C414yes—
109#929C2×C414yes—
110#929C2×C414yes—
111#929C2×C414yes—
112C4×#67C2×C414yes—
113C4×#67C2×C414yes—
114C4×#67C2314yes—
115C4×#67C2314yes—
116C2×(C2×D3)⋊C4C2×C412yes—
117C2×(C2×D3)⋊C4C2×C412yes—
118C2×(C2×D3)⋊C4C2×C412yes—
119C2×(C2×D3)⋊C4C2×C412yes—
120C2×C4⋊Dic3C2×C411yescharacteristic
121C2×C4⋊Dic3C2×C411yescharacteristic
122#924C2×C412yes—
123#924C2×C412yes—
124#924C2×C412yes—
125#924C2×C412yes—
126C2×Dic3⋊C4C2×C412yes—
127C2×Dic3⋊C4C2×C412yes—
128C2×Dic3⋊C4C2×C412yes—
129C2×Dic3⋊C4C2×C412yes—
130C2×C4×Dic3C2312yes—
131C22×C3⋊C8C2314yes—
132C2×ΓL(1,𝔽25)C2318yes—
133C2×D3×C8C2318yes—
134#876C2×C414yes—
135#876C2×C414yes—
136#876C2×C414yes—
137#876C2×C414yes—
138#875C2×C412yes—
139#875C2×C412yes—
140#875C2×C412yes—
141#875C2×C412yes—
142C4×D12C2×C412yes—
143C4×D12C2×C412yes—
144C4×D12C2312yes—
145C4×D12C2312yes—
146#872C2×C414yes—
147#872C2×C414yes—
148#872C2314yes—
149#872C2314yes—
150#870C2×C412yes—
151#870C2×C412yes—
152#870C2×C412yes—
153#870C2×C412yes—
154C4×Dic6C2×C412yes—
155C4×Dic6C2×C412yes—
156C4×Dic6C2312yes—
157C4×Dic6C2312yes—
158C3×C4⋊C8C2312yes—
159C3×C4⋊C8C2312yes—
160C3×C4⋊C8C2314yes—
161C3×C22⋊C8C2312yes—
162C3×C22⋊C8C2312yes—
163C3×C22⋊C8C2314yes—
164C3×#97C2314yes—
165C3×C4×C8C2312yes—
166C3×C4×C8C2312yes—
167#830C2314yes—
168#830C2312yes—
169#830C2312yes—
170(C2×D3)⋊C8C2318yes—
171(C2×D3)⋊C8C2318yes—
172#815C2318yes—
173Dic3⋊C8C2318yes—
174Dic3⋊C8C2318yes—
175C8×Dic3C2318yes—
176C4⋊(C3⋊C8)C2312yes—
177C4⋊(C3⋊C8)C2312yes—
178C4⋊(C3⋊C8)C2314yes—
179C4×C3⋊C8C2314yes—
180C4×C3⋊C8C2312yes—
181C4×C3⋊C8C2312yes—
182#529—32no—
183#529—32no—
184#529—32no—
185#529—32no—
186#529—32no—
187#529—32no—
188#529—32no—
189#529—32no—
190C2×#126—32no—
191C2×#125—31no—
192C2×#124—31no—
193C2×#123—32no—
194C2×C22⋊Q8—31no—
195C2×#121—31no—
196C2×C4×Q8—31no—
197C2×C4×D4—32no—
198C2×C4×D4—31no—
199C2×#117—32no—
200C22×C42C2×D311yescharacteristic
201#446—34no—
202#446—34no—
203C8×Q8—34no—
204C8×Q8—34no—
205#436—38no—
206#436—34no—
207#436—34no—
208#435—38no—
209#435—38no—
210C8×D4—34no—
211C8×D4—38no—
212C8×D4—34no—
213#433—38no—
214#433—38no—
215#432—34no—
216#432C2×D312yes—
217#432C2×D312yescomplemented
218#431—32no—
219#431—31no—
220#431—31no—
221#431—32no—
222#431—32no—
223#431—34no—
224#431C2×D311yescharacteristic
225#431C2×D311yescharacteristic
226#431C2×D312yescomplemented
227#424—38no—
228#423C2×D312yescomplemented
229C2×C4⋊C8—32no—
230#407—34no—
231#407C2×D312yes—
232C2×C22⋊C8—32no—
233C2×C22⋊C8—34no—
234#405—38no—
235C4×M16C2×D312yescomplemented
236C2×C4×C8—32no—
237C24×C3C22×C411yescharacteristic
238C23×D3C22×C412yes—
239C22×C3×C4—24no—
240C22×C3×C4—42no—
241C22×C3×C4—42no—
242C22×C3×C4C22×C411yescharacteristic
243C22×C3×C4C22×C411yescharacteristic
244C22×C3×C4C22×C411yescharacteristic
245C22×C3×C4C22×C411yescharacteristic
246C22×C3×C4C22×C411yescharacteristic
247C22×C3×C4C22×C411yescharacteristic
248C22×C3×C4C22×C411yescharacteristic
249C22×C3×C4C22×C411yescharacteristic
250C22×C3×C4C22×C411yescharacteristic
251C22×C3×C4C22×C411yescharacteristic
252C22×C3×C4C22×C411yescharacteristic
253C22×C3×C4C22×C411yescharacteristic
254C22×C3×C4C22×C411yescharacteristic
255C22×C3×C4C22×C411yescharacteristic
256C22×C3×C4C22×C411yescharacteristic
257C22×C3×C4C2411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C2×#67—44no—
261C2×#67C22×C414yes—
262C2×#67C22×C414yes—
263C22×Dic3C22×C412yes—
264C22×Dic3C22×C412yes—
265C22×Dic3C22×C412yes—
266C2×D12—24no—
267C2×D12C22×C412yes—
268C2×D12C22×C412yes—
269C2×C4×D3—44no—
270C2×C4×D3C22×C414yes—
271C2×C4×D3C2414yes—
272C2×Dic6—24no—
273C2×Dic6C22×C412yes—
274C2×Dic6C22×C412yes—
275C3×M16—44no—
276C2×C3×C8C2414yes—
277C2×C3×C8C2414yes—
278C3×C42C22×C411yescharacteristic
279C3×C42C22×C411yescharacteristic
280C3×C42C22×C411yescharacteristic
281C3×C42C22×C411yescharacteristic
282C3×C42C22×C411yescharacteristic
283C3×C42C22×C411yescharacteristic
284C3×C42C22×C411yescharacteristic
285C3×C42C22×C411yescharacteristic
286C3×C42C22×C411yescharacteristic
287C3×C42C22×C411yescharacteristic
288C3×C42C22×C411yescharacteristic
289C3×C42C22×C411yescharacteristic
290C3×C42C2411yescharacteristic
291C3×C42C2411yescharacteristic
292C3×C42C2411yescharacteristic
293C3×C42C2411yescharacteristic
294#217C22×C414yes—
295#217C22×C414yes—
296(C2×D3)⋊C4C22×C414yes—
297(C2×D3)⋊C4C22×C414yes—
298(C2×D3)⋊C4C22×C414yes—
299(C2×D3)⋊C4C22×C414yes—
300(C2×D3)⋊C4C22×C414yes—
301(C2×D3)⋊C4C22×C414yes—
302(C2×D3)⋊C4C22×C414yes—
303(C2×D3)⋊C4C22×C414yes—
304C4⋊Dic3C22×C412yes—
305C4⋊Dic3C22×C412yes—
306C4⋊Dic3C22×C412yes—
307C4⋊Dic3C22×C412yes—
308Dic3⋊C4C22×C414yes—
309Dic3⋊C4C22×C414yes—
310Dic3⋊C4C22×C414yes—
311Dic3⋊C4C22×C414yes—
312Dic3⋊C4C22×C414yes—
313Dic3⋊C4C22×C414yes—
314Dic3⋊C4C22×C414yes—
315Dic3⋊C4C22×C414yes—
316C4×Dic3C22×C414yes—
317C4×Dic3C2414yes—
318C2×C3⋊C8—44no—
319C2×C3⋊C8C2414yes—
320C2×C3⋊C8C2414yes—
321ΓL(1,𝔽25)—48no—
322D3×C8—48no—
323C22×Q8—31no—
324C22×D4—32no—
325C22×D4—31no—
326C23×C4—32no—
327C23×C4C4×D311yescharacteristic
328C23×C4C4×D311yescharacteristic
329C23×C4C22×D311yescharacteristic
330C2×M16—38no—
331C2×M16C22×D314yes—
332C22×C8—34no—
333C22×C8—38no—
334#126—34no—
335#126—34no—
336#126—34no—
337#126—34no—
338#125—32no—
339#125—32no—
340#125—32no—
341#125—32no—
342#124—32no—
343#124—32no—
344#124—32no—
345#124—32no—
346#123—34no—
347#123—34no—
348#123—34no—
349#123—34no—
350C22⋊Q8—32no—
351C22⋊Q8—32no—
352C22⋊Q8—32no—
353C22⋊Q8—32no—
354#121—32no—
355#121—32no—
356#121—32no—
357#121—32no—
358C4×Q8—32no—
359C4×Q8—32no—
360C4×Q8—32no—
361C4×Q8—32no—
362C4×D4—34no—
363C4×D4—34no—
364C4×D4—34no—
365C4×D4—34no—
366C4×D4—32no—
367C4×D4—32no—
368C4×D4—32no—
369C4×D4—32no—
370#117—34no—
371#117—34no—
372#117—34no—
373#117—34no—
374C2×C4⋊C4—32no—
375C2×C4⋊C4—32no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—32no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—32no—
380C2×C22⋊C4—32no—
381C2×C22⋊C4—32no—
382C2×C22⋊C4—32no—
383C2×C22⋊C4—32no—
384C2×C22⋊C4—32no—
385C2×C42—32no—
386C2×C42C4×D311yescharacteristic
387C2×C42C4×D311yescharacteristic
388C2×C42C4×D311yescharacteristic
389C2×C42C4×D311yescharacteristic
390C2×C42C4×D311yescharacteristic
391C2×C42C4×D311yescharacteristic
392C2×C42C22×D311yescharacteristic
393C2×C42C22×D311yescharacteristic
394C2×C42C22×D311yescharacteristic
395C2×C42C22×D311yescharacteristic
396C2×C42C22×D311yescharacteristic
397C2×C42C22×D311yescharacteristic
398C4⋊C8—38no—
399C4⋊C8—38no—
400C4⋊C8—34no—
401C4⋊C8—32no—
402C4⋊C8—32no—
403C4⋊C8C22×D314yes—
404C4⋊C8C22×D312yes—
405C4⋊C8C22×D312yes—
406C22⋊C8—32no—
407C22⋊C8—32no—
408C22⋊C8—34no—
409C22⋊C8—38no—
410C22⋊C8—38no—
411C22⋊C8C22×D312yes—
412C22⋊C8C22×D312yes—
413C22⋊C8C22×D314yes—
414#97—38no—
415#97C22×D314yes—
416C4×C8—38no—
417C4×C8—34no—
418C4×C8—32no—
419C4×C8—32no—
420C4×C8C22×D312yes—
421C4×C8C22×D312yes—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—41no—
425C23×C3C23×C411yescharacteristic
426C23×C3C23×C411yescharacteristic
427C23×C3C23×C411yescharacteristic
428C22×D3—24no—
429C22×D3—42no—
430C22×D3—42no—
431C22×D3C23×C414yes—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4#13114yes—
450C2×C3×C4C23×C411yescharacteristic
451C2×C3×C4C23×C411yescharacteristic
452C2×C3×C4C23×C411yescharacteristic
453C2×C3×C4C23×C411yescharacteristic
454C2×C3×C4C23×C411yescharacteristic
455C2×C3×C4C23×C411yescharacteristic
456C2×C3×C4C23×C411yescharacteristic
457C2×C3×C4C23×C411yescharacteristic
458C2×C3×C4C23×C411yescharacteristic
459C2×C3×C4C23×C411yescharacteristic
460C2×C3×C4C23×C411yescharacteristic
461C2×C3×C4C2511yescharacteristic
462#67—28no—
463#67—44no—
464C2×Dic3—24no—
465C2×Dic3—42no—
466C2×Dic3—42no—
467C2×Dic3C23×C414yes—
468C2×Dic3C23×C414yes—
469C2×Dic3C23×C414yes—
470D12—24no—
471D12—24no—
472C4×D3—28no—
473C4×D3—44no—
474Dic6—24no—
475Dic6—24no—
476C3×C8—24no—
477C3×C8—24no—
478C3⋊C8—24no—
479C3⋊C8—24no—
480C24—32no—
481C24C2×C4×D311yescharacteristic
482C2×Q8—32no—
483C2×Q8—32no—
484C2×Q8—64no—
485C2×D4—34no—
486C2×D4—34no—
487C2×D4—32no—
488C2×D4—32no—
489C2×D4—64no—
490C2×D4—124no—
491C22×C4—24no—
492C22×C4—32no—
493C22×C4—32no—
494C22×C4—32no—
495C22×C4—34no—
496C22×C4—34no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—124no—
500C22×C4C2×C4×D311yescharacteristic
501C22×C4C2×C4×D311yescharacteristic
502C22×C4C2×C4×D311yescharacteristic
503C22×C4C2×C4×D311yescharacteristic
504C22×C4C2×C4×D311yescharacteristic
505C22×C4C2×C4×D311yescharacteristic
506C22×C4C2×C4×D311yescharacteristic
507C22×C4C2×C4×D311yescharacteristic
508C22×C4C2×C4×D311yescharacteristic
509C22×C4C2×C4×D311yescharacteristic
510C22×C4C2×C4×D311yescharacteristic
511C22×C4C2×C4×D311yescharacteristic
512C22×C4C2×C4×D311yescharacteristic
513C22×C4C2×C4×D311yescharacteristic
514C22×C4C2×C4×D311yescharacteristic
515C22×C4C23×D311yescharacteristic
516C22×C4C23×D311yescharacteristic
517C22×C4C23×D311yescharacteristic
518M16—44no—
519M16—128no—
520C2×C8—34no—
521C2×C8—34no—
522C2×C8—128no—
523C2×C8—124no—
524C2×C8C23×D314yes—
525C2×C8C23×D314yes—
526C4⋊C4—34no—
527C4⋊C4—34no—
528C4⋊C4—34no—
529C4⋊C4—34no—
530C4⋊C4—32no—
531C4⋊C4—32no—
532C4⋊C4—34no—
533C4⋊C4—34no—
534C4⋊C4—32no—
535C4⋊C4—32no—
536C4⋊C4—34no—
537C4⋊C4—34no—
538C22⋊C4—34no—
539C22⋊C4—34no—
540C22⋊C4—34no—
541C22⋊C4—34no—
542C22⋊C4—34no—
543C22⋊C4—34no—
544C22⋊C4—34no—
545C22⋊C4—34no—
546C22⋊C4—34no—
547C22⋊C4—34no—
548C42—34no—
549C42—34no—
550C42C2×C4×D311yescharacteristic
551C42C2×C4×D311yescharacteristic
552C42C2×C4×D311yescharacteristic
553C42C2×C4×D311yescharacteristic
554C42C2×C4×D311yescharacteristic
555C42C2×C4×D311yescharacteristic
556C42C2×C4×D311yescharacteristic
557C42C2×C4×D311yescharacteristic
558C42C2×C4×D311yescharacteristic
559C42C2×C4×D311yescharacteristic
560C42C2×C4×D311yescharacteristic
561C42C2×C4×D311yescharacteristic
562C42C23×D311yescharacteristic
563C42C23×D311yescharacteristic
564C42C23×D311yescharacteristic
565C42C23×D311yescharacteristic
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—44no—
574C22×C3C2×#13112yes—
575C22×C3#56812yes—
576C22×C3C24×C411yescharacteristic
577C2×D3—24no—
578C2×D3—24no—
579C2×D3—24no—
580C2×D3—84no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—21no—
586C3×C4—21no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4C2×#13112yes—
591C3×C4C2×#13112yes—
592C3×C4#58512yes—
593Dic3—24no—
594Dic3—24no—
595Dic3—24no—
596C23—22no—
597C23—22no—
598C23—34no—
599C23—41no—
600C23—64no—
601C23—122no—
602C23—122no—
603C23C22×C4×D311yescharacteristic
604C23C22×C4×D311yescharacteristic
605C23C22×C4×D311yescharacteristic
606Q8—64no—
607Q8—64no—
608D4—68no—
609D4—64no—
610D4—64no—
611D4—124no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—34no—
623C2×C4—34no—
624C2×C4—34no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—64no—
633C2×C4—68no—
634C2×C4—124no—
635C2×C4—122no—
636C2×C4—122no—
637C2×C4#90714yes—
638C2×C4C22×C4×D311yescharacteristic
639C2×C4C22×C4×D311yescharacteristic
640C2×C4C22×C4×D311yescharacteristic
641C2×C4C22×C4×D311yescharacteristic
642C2×C4C22×C4×D311yescharacteristic
643C2×C4C22×C4×D311yescharacteristic
644C2×C4C22×C4×D311yescharacteristic
645C2×C4C22×C4×D311yescharacteristic
646C2×C4C22×C4×D311yescharacteristic
647C2×C4C22×C4×D311yescharacteristic
648C2×C4C22×C4×D311yescharacteristic
649C2×C4C24×D311yescharacteristic
650C8—24no—
651C8—24no—
652C8—64no—
653C8—64no—
654C2×C3—22no—
655C2×C3—22no—
656C2×C3—41no—
657C2×C3#342811yescharacteristic
658C2×C3C22×#13111yescharacteristic
659C2×C3C2×#56811yescharacteristic
660D3—44no—
661C22—21no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—44no—
669C22—64no—
670C22—64no—
671C22—64no—
672C22—244no—
673C22C2×#90712yes—
674C22#574512yes—
675C22C23×C4×D311yescharacteristic
676C4—21no—
677C4—21no—
678C4—21no—
679C4—21no—
680C4—21no—
681C4—21no—
682C4—21no—
683C4—21no—
684C4—21no—
685C4—64no—
686C4—64no—
687C4—64no—
688C4C2×#90712yes—
689C4C2×#90712yes—
690C4#596412yes—
691C3#6029011yescharacteristic, complemented, Sylow
692C2—22no—
693C2—22no—
694C2—41no—
695C2—124no—
696C2#8573111yescharacteristic
697C2C22×#90711yescharacteristic
698C2C2×#574511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC3×#2920C2
prime radicalC2×#930C4
cosocleC2×C3×C4C25
hypercenter#2920D3
hypocenterC3#60290
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #2920

Complements

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

NH ≅ G/Ntype
2. C3×#2920C2semidirect
3. C2×#4925C2semidirect
4. #79333C2semidirect
5. #79325C2semidirect
6. #79296C2semidirect
7. #79288C2semidirect
8. #79286C2semidirect
9. #79264C2semidirect
10. #79263C2semidirect
11. #79053C2semidirect
12. #78633C2semidirect
13. #78511C2semidirect
35. C3×#432C22semidirect
38. C3×#431C22semidirect
39. C3×#423C22semidirect
41. C3×C4×M16C22semidirect
43. #5128C22semidirect
44. #5127C22semidirect
48. #4925C22semidirect
49. #4925C22semidirect
50. C2×C4⋊(C3⋊C8)C22semidirect
51. C2×C4×C3⋊C8C22semidirect
52. #4840C22semidirect
53. #4839C22semidirect
54. #4838C22semidirect
55. #4834C22semidirect
56. #4831C22semidirect
57. #4830C22semidirect
58. #4730C22semidirect
60. #67⋊C8C22semidirect
64. #4709C22semidirect
65. #4708C22semidirect
66. #4688C22semidirect
67. C8×D12C22semidirect
68. #4679C22semidirect
69. C8×Dic6C22semidirect
81. #2920D3semidirect
217. #432C2×D3semidirect
226. #431C2×D3semidirect
228. #423C2×D3semidirect
235. C4×M16C2×D3semidirect
691. C3#60290semidirect

Maximal subgroups

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

subgroupindex
C2×#54792
C3×#29202
C2×#49252
#793332
#793252
#792962
#792882
#792862
#792642
#792632
#790532
#786332
#785112
#602903