Finite Group Databasebeta

← #11660183

Subgroups — #11660183

Order 768.

1704 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#533C211yesmaximal, characteristic
2C3×#2985C211yesmaximal, characteristic, complemented
3#83331C211yesmaximal, characteristic, complemented
4#79964C212yesmaximal, complemented
5#79963C214yesmaximal, complemented
6#79960C212yesmaximal, complemented
7#79959C214yesmaximal, complemented
8#79921C212yesmaximal, complemented
9#79918C212yesmaximal, complemented
10#79374C214yesmaximal
11#79361C214yesmaximal, complemented
12D3×#432C211yesmaximal, characteristic
13#79316C211yesmaximal, characteristic, complemented
14#79282C211yesmaximal, characteristic
15#79266C211yesmaximal, characteristic, complemented
16#60251—31nomaximal, Sylow
17C3×#533C2211yescharacteristic
18#5728C411yescharacteristic
19#5728C411yescharacteristic
20D3×C4⋊Q8C411yescharacteristic
21D3×C4⋊Q8C411yescharacteristic
22#5688C412yes—
23D3×#125C412yes—
24D3×C22⋊Q8C412yes—
25D3×C22⋊Q8C412yes—
26#5622C412yes—
27#5622C412yes—
28#5578C2212yes—
29#5578C2212yes—
30C4×D3×Q8C2212yes—
31C4×D3×Q8C2212yes—
32D3×#117C2212yes—
33#5517C2212yes—
34C2×C42×D3C2211yescharacteristic
35#5470C2211yescharacteristic
36C3×#446C2214yescomplemented
37C3×#446C2212yescomplemented
38C3×C8×Q8C2212yescomplemented
39C3×#433C2214yes—
40C3×#432C2211yescharacteristic
41C3×#431C2211yescharacteristic
42#5024C2212yescomplemented
43#5024C2214yescomplemented
44Q8×C3⋊C8C2212yescomplemented
45#5000C2214yes—
46#4926C2211yescharacteristic
47#4925C2211yescharacteristic
48#4839C2214yes—
49#4839C2214yes—
50#4837C2212yes—
51#4835C2214yes—
52#4835C2212yes—
53#4835C2212yes—
54#4833C2214yes—
55D3×C4⋊C8C2212yes—
56#4831C2214yescomplemented
57#4831C2214yescomplemented
58#4831C2212yescomplemented
59#4830C2212yescomplemented
60#4828C2214yescomplemented
61#4828C2214yescomplemented
62#4828C2214yescomplemented
63#4726C2212yes—
64D3×C22⋊C8C2212yes—
65#4720C2214yes—
66#4720C2214yes—
67#4719C2212yes—
68#4719C2212yes—
69#4708C2214yes—
70#4705C2214yes—
71#4705C2212yes—
72D3×#97C2212yes—
73#4701C2214yescomplemented
74#4701C2214yescomplemented
75#4701C2214yescomplemented
76#4689C2214yes—
77C4×ΓL(1,𝔽25)C2211yescharacteristic
78C4×ΓL(1,𝔽25)C2211yescharacteristic
79#4685C2214yes—
80#4685C2211yescharacteristic
81#4685C2211yescharacteristic
82#4679C2214yescomplemented
83#4679C2214yescomplemented
84#4679C2212yescomplemented
85C8×Dic6C2212yescomplemented
86C2×#533—31no—
87#2987—34no—
88#2985—31no—
89#2985—31no—
90#2985—31no—
91#2985D311yescharacteristic, complemented
92#2984—32no—
93#2984—32no—
94#2983—34no—
95#2962—32no—
96#2962—32no—
97#2961—34no—
98#2924—34no—
99#2920—31no—
100C2×#432—31no—
101C2×D3×Q8C2×C412yes—
102C2×D3×Q8C2×C412yes—
103C22×C4×D3C2×C411yescharacteristic
104C22×C4×D3C2×C411yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C3×C4⋊Q8C2×C411yescharacteristic
107C3×C4⋊Q8C2×C411yescharacteristic
108C3×#125C2×C412yes—
109C3×C22⋊Q8C2×C412yes—
110C3×C22⋊Q8C2×C412yes—
111C3×C4×Q8C2312yes—
112C3×C4×Q8C2312yes—
113C3×#117C2312yes—
114C2×C3×C42C2311yescharacteristic
115#946C2×C412yes—
116#946C2×C412yes—
117Q8×Dic3C2×C412yes—
118Q8×Dic3C2×C412yes—
119#944C2×C412yes—
120#944C2×C412yes—
121#926C2312yes—
122#924C2×C412yes—
123#924C2×C412yes—
124C2×C4×Dic3C2×C411yescharacteristic
125C2×C4×Dic3C2×C411yescharacteristic
126C2×C4×Dic3C2311yescharacteristic
127C2×ΓL(1,𝔽25)C2312yes—
128C2×ΓL(1,𝔽25)C2312yes—
129C2×D3×C8C2314yes—
130#897C2×C412yes—
131#897C2×C412yes—
132#896C2×C414yes—
133#896C2×C414yes—
134#892C2×C412yes—
135#892C2×C412yes—
136D3×C4⋊C4C2×C412yes—
137D3×C4⋊C4C2×C412yes—
138D3×C4⋊C4C2×C414yes—
139D3×C4⋊C4C2×C414yes—
140D3×C4⋊C4C2×C412yes—
141D3×C4⋊C4C2×C412yes—
142#890C2×C412yes—
143#890C2×C412yes—
144#889C2×C414yes—
145#889C2×C414yes—
146#888C2×C412yes—
147#888C2×C412yes—
148#888C2×C412yes—
149#888C2×C412yes—
150#887C2×C414yes—
151#887C2×C414yes—
152#887C2×C412yes—
153#887C2×C412yes—
154D3×C22⋊C4C2×C414yes—
155#878C2×C414yes—
156#878C2×C414yes—
157#877C2×C414yes—
158#872C2314yes—
159C42×D3C2×C411yescharacteristic
160C42×D3C2×C411yescharacteristic
161C42×D3C2×C411yescharacteristic
162C42×D3C2×C411yescharacteristic
163C42×D3C2311yescharacteristic
164C42×D3C2314yes—
165C42×D3C2311yescharacteristic
166C42×D3C2311yescharacteristic
167C42×D3C2311yescharacteristic
168#870C2×C412yes—
169#869C2×C411yescharacteristic
170#869C2×C411yescharacteristic
171C4×Dic6C2312yes—
172C4×Dic6C2314yes—
173C4×Dic6C2314yes—
174C4×Dic6C2312yes—
175C3×C4⋊C8C2312yes—
176C3×C4⋊C8C2312yes—
177C3×C4⋊C8C2314yes—
178C3×C4⋊C8C2314yes—
179C3×C22⋊C8C2312yes—
180C3×C22⋊C8C2312yes—
181C3×#97C2312yes—
182C3×#97C2314yes—
183C3×C4×C8C2311yescharacteristic
184C3×C4×C8C2311yescharacteristic
185C3×C4×C8C2314yes—
186#830C2312yes—
187#830C2312yes—
188(C2×D3)⋊C8C2312yes—
189(C2×D3)⋊C8C2314yes—
190(C2×D3)⋊C8C2312yes—
191#815C2312yes—
192#815C2314yes—
193#815C2314yes—
194#815C2314yes—
195#815C2312yes—
196Dic3⋊C8C2314yes—
197Dic3⋊C8C2312yes—
198Dic3⋊C8C2314yes—
199Dic3⋊C8C2314yes—
200Dic3⋊C8C2314yes—
201Dic3⋊C8C2312yes—
202Dic3⋊C8C2314yes—
203C8×Dic3C2314yes—
204C8×Dic3C2314yes—
205C4⋊(C3⋊C8)C2312yes—
206C4⋊(C3⋊C8)C2312yes—
207C4⋊(C3⋊C8)C2314yes—
208C4⋊(C3⋊C8)C2314yes—
209#803C2312yes—
210#803C2314yes—
211C4×C3⋊C8C2311yescharacteristic
212C4×C3⋊C8C2311yescharacteristic
213C4×C3⋊C8C2314yes—
214#533—31no—
215#533—31no—
216#533—32no—
217#533—32no—
218#533—32no—
219#533—32no—
220#533—32no—
221#533—32no—
222#533—31no—
223#533C2×D311yescharacteristic
224C2×C4⋊Q8—31no—
225C2×C4⋊Q8—31no—
226C2×#125—32no—
227C2×C22⋊Q8—32no—
228C2×C22⋊Q8—32no—
229C2×C4×Q8—32no—
230C2×C4×Q8—32no—
231C2×#117—32no—
232C22×C42—31no—
233#446—34no—
234#446—32no—
235#446—34no—
236#446—34no—
237#446—34no—
238#446—34no—
239#446—34no—
240#446—32no—
241#446—34no—
242#446—34no—
243#446—34no—
244#446—34no—
245#446—34no—
246#446—32no—
247#446C2×D314yescomplemented
248#446C2×D312yescomplemented
249C8×Q8—32no—
250C8×Q8—32no—
251C8×Q8—32no—
252C8×Q8C2×D312yescomplemented
253#433—34no—
254#433—34no—
255#433—34no—
256#433C2×D314yes—
257#432—31no—
258#432—32no—
259#432—32no—
260#432—34no—
261#432—32no—
262#432—32no—
263#432—32no—
264#432—34no—
265#432C2×D311yescharacteristic
266#431—31no—
267#431—34no—
268#431—31no—
269#431—31no—
270#431—34no—
271#431C2×D311yescharacteristic
272#424—34no—
273#424—34no—
274#423—32no—
275C2×C4⋊C8—32no—
276#407—32no—
277C2×C22⋊C8—32no—
278#405—34no—
279#405—34no—
280C4×M16—31no—
281C4×M16—31no—
282C2×#97—32no—
283C23×D3C22×C411yescharacteristic
284C2×C3×Q8C22×C412yes—
285C2×C3×Q8C22×C412yes—
286C22×C3×C4C22×C411yescharacteristic
287C22×C3×C4C22×C411yescharacteristic
288C22×C3×C4C2411yescharacteristic
289C22×Dic3C22×C411yescharacteristic
290C22×Dic3C22×C411yescharacteristic
291C22×Dic3C22×C411yescharacteristic
292D3×Q8—44no—
293D3×Q8—44no—
294C2×C4×D3—24no—
295C2×C4×D3—42no—
296C2×C4×D3—42no—
297C2×C4×D3C22×C411yescharacteristic
298C2×C4×D3C22×C411yescharacteristic
299C2×C4×D3C22×C411yescharacteristic
300C2×C4×D3C22×C411yescharacteristic
301C2×C4×D3C22×C411yescharacteristic
302C2×C4×D3C22×C411yescharacteristic
303C2×C4×D3C22×C414yes—
304C2×C4×D3C22×C411yescharacteristic
305C2×C4×D3C22×C411yescharacteristic
306C2×C4×D3C22×C411yescharacteristic
307C2×C4×D3C22×C411yescharacteristic
308C2×C4×D3C22×C414yes—
309C2×C4×D3C2411yescharacteristic
310C2×C4×D3C2411yescharacteristic
311C2×Dic6C22×C412yes—
312C2×Dic6C22×C412yes—
313C2×Dic6C22×C414yes—
314C2×Dic6C22×C414yes—
315C2×C3×C8C2412yes—
316C2×C3×C8C2414yes—
317C2×C3×C8C2412yes—
318C3×C4⋊C4C22×C412yes—
319C3×C4⋊C4C22×C412yes—
320C3×C4⋊C4C22×C414yes—
321C3×C4⋊C4C22×C414yes—
322C3×C4⋊C4C22×C412yes—
323C3×C4⋊C4C22×C412yes—
324C3×C22⋊C4C22×C414yes—
325C3×C42C22×C411yescharacteristic
326C3×C42C22×C411yescharacteristic
327C3×C42C2411yescharacteristic
328C3×C42C2414yes—
329C3×C42C2411yescharacteristic
330#217C22×C414yes—
331(C2×D3)⋊C4C22×C414yes—
332(C2×D3)⋊C4C22×C414yes—
333C4⋊Dic3C22×C412yes—
334C4⋊Dic3C22×C412yes—
335C4⋊Dic3C22×C414yes—
336C4⋊Dic3C22×C414yes—
337C4⋊Dic3C22×C412yes—
338C4⋊Dic3C22×C412yes—
339Dic3⋊C4C22×C414yes—
340Dic3⋊C4C22×C414yes—
341Dic3⋊C4C22×C414yes—
342Dic3⋊C4C22×C414yes—
343Dic3⋊C4C22×C414yes—
344Dic3⋊C4C22×C414yes—
345Dic3⋊C4C22×C414yes—
346Dic3⋊C4C22×C414yes—
347C4×Dic3C22×C411yescharacteristic
348C4×Dic3C22×C411yescharacteristic
349C4×Dic3C22×C411yescharacteristic
350C4×Dic3C22×C411yescharacteristic
351C4×Dic3C22×C411yescharacteristic
352C4×Dic3C22×C411yescharacteristic
353C4×Dic3C22×C411yescharacteristic
354C4×Dic3C22×C411yescharacteristic
355C4×Dic3C22×C411yescharacteristic
356C4×Dic3C22×C411yescharacteristic
357C4×Dic3C22×C414yes—
358C4×Dic3C22×C414yes—
359C4×Dic3C2414yes—
360C4×Dic3C2411yescharacteristic
361C4×Dic3C2411yescharacteristic
362C2×C3⋊C8C2412yes—
363C2×C3⋊C8C2412yes—
364C2×C3⋊C8C2414yes—
365ΓL(1,𝔽25)—24no—
366ΓL(1,𝔽25)—24no—
367D3×C8—28no—
368C22×Q8—32no—
369C22×Q8—32no—
370C23×C4—31no—
371C23×C4—31no—
372C23×C4—31no—
373C2×M16—32no—
374C2×M16—32no—
375C22×C8—34no—
376C4⋊Q8—32no—
377C4⋊Q8—32no—
378C4⋊Q8—32no—
379C4⋊Q8—32no—
380C4⋊Q8—32no—
381C4⋊Q8—32no—
382C4⋊Q8—31no—
383C4⋊Q8—31no—
384C4⋊Q8C4×D311yescharacteristic
385C4⋊Q8C4×D311yescharacteristic
386#125—34no—
387#125—34no—
388#125—32no—
389#125—32no—
390#125—32no—
391#125C4×D312yes—
392C22⋊Q8—32no—
393C22⋊Q8—32no—
394C22⋊Q8—32no—
395C22⋊Q8—32no—
396C22⋊Q8—34no—
397C22⋊Q8—34no—
398C22⋊Q8—32no—
399C22⋊Q8—32no—
400C22⋊Q8—34no—
401C22⋊Q8—34no—
402C22⋊Q8C4×D312yes—
403C22⋊Q8C4×D312yes—
404C4×Q8—32no—
405C4×Q8—32no—
406C4×Q8—32no—
407C4×Q8—32no—
408C4×Q8—34no—
409C4×Q8—34no—
410C4×Q8—32no—
411C4×Q8—32no—
412C4×Q8—34no—
413C4×Q8—34no—
414C4×Q8C22×D312yes—
415C4×Q8C22×D312yes—
416#117—32no—
417#117—32no—
418#117—32no—
419#117—34no—
420#117—34no—
421#117C22×D312yes—
422C2×C4⋊C4—32no—
423C2×C4⋊C4—32no—
424C2×C4⋊C4—34no—
425C2×C4⋊C4—34no—
426C2×C4⋊C4—32no—
427C2×C4⋊C4—32no—
428C2×C22⋊C4—34no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—31no—
432C2×C42—31no—
433C2×C42—31no—
434C2×C42—31no—
435C2×C42—31no—
436C2×C42—34no—
437C2×C42—31no—
438C2×C42—31no—
439C2×C42—31no—
440C2×C42—31no—
441C2×C42C22×D311yescharacteristic
442C4⋊C8—34no—
443C4⋊C8—32no—
444C4⋊C8—32no—
445C4⋊C8—34no—
446C4⋊C8—34no—
447C4⋊C8—34no—
448C4⋊C8—34no—
449C4⋊C8—32no—
450C4⋊C8—32no—
451C4⋊C8—34no—
452C4⋊C8—34no—
453C4⋊C8C22×D312yes—
454C4⋊C8C22×D312yes—
455C4⋊C8C22×D314yes—
456C4⋊C8C22×D314yes—
457C22⋊C8—32no—
458C22⋊C8—32no—
459C22⋊C8—34no—
460C22⋊C8—32no—
461C22⋊C8—32no—
462C22⋊C8C22×D312yes—
463C22⋊C8C22×D312yes—
464#97—34no—
465#97—32no—
466#97—32no—
467#97—34no—
468#97—34no—
469#97—32no—
470#97—34no—
471#97C22×D312yes—
472#97C22×D314yes—
473C4×C8—34no—
474C4×C8—34no—
475C4×C8—31no—
476C4×C8—31no—
477C4×C8—34no—
478C4×C8C22×D311yescharacteristic
479C4×C8C22×D311yescharacteristic
480C4×C8C22×D314yes—
481C23×C3C23×C411yescharacteristic
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—41no—
485C22×D3C23×C411yescharacteristic
486C22×D3C23×C411yescharacteristic
487C3×Q8—24no—
488C3×Q8—42no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—41no—
492C2×C3×C4C23×C411yescharacteristic
493C2×C3×C4C23×C411yescharacteristic
494C2×C3×C4C23×C411yescharacteristic
495C2×C3×C4C23×C411yescharacteristic
496C2×C3×C4C23×C414yes—
497C2×C3×C4C23×C414yes—
498C2×C3×C4C23×C411yescharacteristic
499C2×C3×C4C2511yescharacteristic
500C2×Dic3—22no—
501C2×Dic3—41no—
502C2×Dic3—41no—
503C2×Dic3C23×C411yescharacteristic
504C2×Dic3C23×C411yescharacteristic
505C2×Dic3C23×C411yescharacteristic
506C2×Dic3C23×C411yescharacteristic
507C2×Dic3C23×C411yescharacteristic
508C2×Dic3C23×C414yes—
509C2×Dic3C23×C414yes—
510C2×Dic3C23×C411yescharacteristic
511C4×D3—22no—
512C4×D3—22no—
513C4×D3—22no—
514C4×D3—28no—
515C4×D3—22no—
516C4×D3—22no—
517C4×D3—22no—
518C4×D3—22no—
519C4×D3—41no—
520C4×D3—41no—
521C4×D3—41no—
522C4×D3—41no—
523C4×D3—44no—
524C4×D32−1+414yes—
525Dic6—24no—
526Dic6—44no—
527Dic6—44no—
528Dic6—42no—
529C3×C8—24no—
530C3×C8—22no—
531C3×C8—22no—
532C3⋊C8—24no—
533C3⋊C8—22no—
534C3⋊C8—22no—
535C24—31no—
536C2×Q8—32no—
537C2×Q8—34no—
538C2×Q8—34no—
539C2×Q8—32no—
540C2×Q8—124no—
541C2×Q8—124no—
542C2×Q8C2×C4×D312yes—
543C2×Q8C2×C4×D312yes—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—31no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—31no—
554C22×C4—34no—
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—34no—
561C22×C4—64no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4C2×C4×D311yescharacteristic
565C22×C4C2×C4×D311yescharacteristic
566C22×C4C23×D311yescharacteristic
567M16—64no—
568M16—64no—
569C2×C8—32no—
570C2×C8—32no—
571C2×C8—34no—
572C2×C8—68no—
573C2×C8C23×D312yes—
574C2×C8C23×D314yes—
575C2×C8C23×D312yes—
576C4⋊C4—34no—
577C4⋊C4—34no—
578C4⋊C4—32no—
579C4⋊C4—32no—
580C4⋊C4—34no—
581C4⋊C4—34no—
582C4⋊C4—34no—
583C4⋊C4—34no—
584C4⋊C4—34no—
585C4⋊C4—34no—
586C4⋊C4—34no—
587C4⋊C4—34no—
588C4⋊C4—32no—
589C4⋊C4—32no—
590C4⋊C4C2×C4×D312yes—
591C4⋊C4C2×C4×D312yes—
592C4⋊C4C2×C4×D314yes—
593C4⋊C4C2×C4×D314yes—
594C4⋊C4C2×C4×D312yes—
595C4⋊C4C2×C4×D312yes—
596C22⋊C4—34no—
597C22⋊C4—34no—
598C22⋊C4—34no—
599C22⋊C4C2×C4×D314yes—
600C42—31no—
601C42—31no—
602C42—31no—
603C42—31no—
604C42—31no—
605C42—31no—
606C42—31no—
607C42—31no—
608C42—31no—
609C42—31no—
610C42—34no—
611C42—34no—
612C42—34no—
613C42—31no—
614C42—31no—
615C42C2×C4×D311yescharacteristic
616C42C2×C4×D311yescharacteristic
617C42C23×D311yescharacteristic
618C42C23×D314yes—
619C42C23×D311yescharacteristic
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3C24×C411yescharacteristic
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—44no—
629C2×D3#51912yes—
630C2×D3#56812yes—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—24no—
634C3×C4—24no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4#56812yes—
638C3×C4C2×2−1+412yes—
639Dic3—21no—
640Dic3—24no—
641Dic3—21no—
642Dic3—21no—
643Dic3—24no—
644Dic3—21no—
645Dic3—21no—
646Dic3#51912yes—
647C23—31no—
648C23—31no—
649C23—62no—
650C23—62no—
651C23—121no—
652C23C22×C4×D311yescharacteristic
653Q8—24no—
654Q8—42no—
655Q8—64no—
656Q8—124no—
657Q8—122no—
658Q8—124no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—31no—
662C2×C4—34no—
663C2×C4—31no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—34no—
669C2×C4—34no—
670C2×C4—41no—
671C2×C4—62no—
672C2×C4—62no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—68no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—124no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4C22×C4×D311yescharacteristic
688C2×C4C22×C4×D311yescharacteristic
689C2×C4C22×C4×D311yescharacteristic
690C2×C4C22×C4×D311yescharacteristic
691C2×C4C22×C4×D314yes—
692C2×C4C22×C4×D314yes—
693C2×C4C22×C4×D311yescharacteristic
694C2×C4C24×D311yescharacteristic
695C8—24no—
696C8—22no—
697C8—22no—
698C8—64no—
699C8—62no—
700C8—62no—
701C2×C3—41no—
702C2×C3C2×#51911yescharacteristic
703C2×C3C2×#56811yescharacteristic
704C2×C3C2×#56811yescharacteristic
705D3—22no—
706D3—22no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—32no—
711C22—32no—
712C22—61no—
713C22—61no—
714C22—61no—
715C22—61no—
716C22—124no—
717C22C23×C4×D311yescharacteristic
718C4—21no—
719C4—24no—
720C4—21no—
721C4—21no—
722C4—21no—
723C4—24no—
724C4—32no—
725C4—61no—
726C4—61no—
727C4—64no—
728C4—61no—
729C4—61no—
730C4—61no—
731C4—64no—
732C4#575012yes—
733C4D3×2−1+412yes—
734C3#6025111yescharacteristic, complemented, Sylow
735C2—41no—
736C2—62no—
737C2—62no—
738C2D3×#51911yescharacteristic
739C2C2×#575011yescharacteristic
740C2D3×#56811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D3
commutator, socleC22×C3C24×C4
FittingC3×#2985C2
prime radicalC23×D3C22×C4
cosocleC2×C3×C4C25
hypercenter#2985D3
hypocenterC3#60251
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #2985

Complements

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

NH ≅ G/Ntype
2. C3×#2985C2semidirect
3. #83331C2semidirect
4. #79964C2semidirect
5. #79963C2semidirect
6. #79960C2semidirect
7. #79959C2semidirect
8. #79921C2semidirect
9. #79918C2semidirect
11. #79361C2semidirect
13. #79316C2semidirect
15. #79266C2semidirect
36. C3×#446C22semidirect
37. C3×#446C22semidirect
38. C3×C8×Q8C22semidirect
42. #5024C22semidirect
43. #5024C22semidirect
44. Q8×C3⋊C8C22semidirect
56. #4831C22semidirect
57. #4831C22semidirect
58. #4831C22semidirect
59. #4830C22semidirect
60. #4828C22semidirect
61. #4828C22semidirect
62. #4828C22semidirect
73. #4701C22semidirect
74. #4701C22semidirect
75. #4701C22semidirect
82. #4679C22semidirect
83. #4679C22semidirect
84. #4679C22semidirect
85. C8×Dic6C22semidirect
91. #2985D3semidirect
247. #446C2×D3semidirect
248. #446C2×D3semidirect
252. C8×Q8C2×D3semidirect
734. C3#60251semidirect

Maximal subgroups

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

subgroupindex
D3×#5332
C3×#29852
#833312
#799642
#799632
#799602
#799592
#799212
#799182
#793742
#793612
D3×#4322
#793162
#792822
#792662
#602513