Finite Group Databasebeta

← #10974280

Subgroups — #10974280

Order 768.

2834 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5798C211yesmaximal, characteristic
2C22×#924C211yesmaximal, characteristic, complemented
3C2×C3×#386C211yesmaximal, characteristic
4#84043C211yesmaximal, characteristic
5C2×#5210C211yesmaximal, characteristic, complemented
6#82110C214yesmaximal, complemented
7#82095C211yesmaximal, characteristic, complemented
8#82094C211yesmaximal, characteristic, complemented
9#74770C212yesmaximal, complemented
10#74769C212yesmaximal, complemented
11#74738C212yesmaximal, complemented
12#74711C214yesmaximal, complemented
13#74709C214yesmaximal, complemented
14#74689C212yesmaximal, complemented
15#73350C214yesmaximal, complemented
16#35349—31nomaximal, Sylow
17C23×C3×D4C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C23×Dic6C2211yescharacteristic, complemented
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yes—
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2211yescharacteristic
25C22×#217C2212yes—
26C22×#217C2211yescharacteristic
27#5798—28no—
28C2×D4×Dic3C2212yes—
29C2×D4×Dic3C2212yes—
30C2×D4×Dic3C2212yes—
31C2×D4×Dic3C2212yes—
32C2×#926C2212yes—
33C22×C4⋊Dic3C2211yescharacteristic, complemented
34C2×#924—28no—
35C2×#924C2214yes—
36C2×#924C2214yescomplemented
37C22×Dic3⋊C4C2211yescharacteristic, complemented
38C22×Dic3⋊C4C2211yescharacteristic, complemented
39C22×Dic3⋊C4C2212yescomplemented
40C2×#878C2214yescomplemented
41C3×#386C2212yes—
42C3×#386C2212yes—
43C3×#386C2214yes—
44C2×C3×#95C2212yes—
45#5247C2212yes—
46#5220C2212yes—
47#5220C2212yes—
48#5220C2214yes—
49#5212C2214yes—
50#5211C2212yes—
51#5210C2214yes—
52#5210C2214yes—
53#5210C2212yescomplemented
54#5210C2212yescomplemented
55C2×C3⋊#95C2212yescomplemented
56#4950C2212yescomplemented
57#4950C2214yescomplemented
58#4950C2212yescomplemented
59#4950C2212yescomplemented
60#4950C2212yescomplemented
61#4949C2214yescomplemented
62#4948C2214yescomplemented
63#4948C2214yescomplemented
64#4947C2214yescomplemented
65#4946C2214yescomplemented
66#4946C2214yescomplemented
67#4942C2212yescomplemented
68#4942C2212yescomplemented
69#4942C2214yescomplemented
70#4661C2214yescomplemented
71#4660C2214yescomplemented
72#4657C2214yescomplemented
73#4656C2214yescomplemented
74#4655C2214yescomplemented
75#4654C2214yescomplemented
76#4647C2214yescomplemented
77#4646C2214yescomplemented
78C22×C22⋊Q8—31no—
79C2×#518—31no—
80#2579—32no—
81#2579—32no—
82#2487—32no—
83#2450—34no—
84#2449—34no—
85#2438—34no—
86#2437—34no—
87#2409—32no—
88#2315—31no—
89#2315—31no—
90#2308—31no—
91C2×#386D311yescharacteristic
92C2×#385—31no—
93C25×C3C2311yescharacteristic
94C25×C3C2311yescharacteristic
95C22×C3×D4—24no—
96C22×C3×D4—24no—
97C22×C3×D4Q818yescomplemented
98C22×C3×D4C2312yes—
99C22×C3×D4C2312yes—
100C23×C3×C4—24no—
101C23×C3×C4—44no—
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2312yes—
104C23×C3×C4C2312yes—
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2312yes—
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2312yes—
110C23×Dic3C2312yes—
111C23×Dic3C2312yes—
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C22×Dic6—24no—
118C22×Dic6—44no—
119C22×Dic6C2314yes—
120C2×C3×C22⋊C4—24no—
121C2×C3×C22⋊C4—44no—
122C2×C3×C22⋊C4C2312yes—
123C2×C3×C22⋊C4C2312yes—
124C2×C3×C22⋊C4C2314yes—
125C2×C3×C22⋊C4C2314yes—
126C2×#217—24no—
127C2×#217—24no—
128C2×#217—24no—
129C2×#217—28no—
130C2×#217D418yes—
131C2×#217C2312yes—
132C2×#217C2312yes—
133C2×#217C2312yes—
134C2×#217C2312yes—
135C2×#217C2312yes—
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2312yes—
139C2×#217C2314yes—
140C2×#217C2314yes—
141C2×#217C2312yes—
142C2×#217C2312yes—
143D4×Dic3—28no—
144D4×Dic3—28no—
145D4×Dic3—28no—
146D4×Dic3—28no—
147#926—28no—
148C2×C4⋊Dic3—24no—
149C2×C4⋊Dic3C2314yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2314yes—
153C2×C4⋊Dic3C2314yes—
154#924—216no—
155#924—216no—
156C2×Dic3⋊C4—24no—
157C2×Dic3⋊C4—24no—
158C2×Dic3⋊C4—44no—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2314yes—
165C2×C4×Dic3C2312yes—
166C2×C4×Dic3C2312yes—
167#878—48no—
168C3×#95C2314yes—
169C3×#95C2314yes—
170C3⋊#95C2314yes—
171C3⋊#95C2314yes—
172C3⋊#95C2314yes—
173C3⋊#95C2314yes—
174C3⋊#95C2314yes—
175C3⋊#95C2314yes—
176C3⋊#95C2314yes—
177C3⋊#95C2314yes—
178C23×Q8—31no—
179C23×D4C2×D311yescharacteristic
180C24×C4C2×D311yescharacteristic
181C2×C22⋊Q8—34no—
182C2×C22⋊Q8—34no—
183C2×C22⋊Q8—34no—
184C2×C22⋊Q8—68no—
185#518—68no—
186C2×C4×D4—32no—
187C2×C4×D4—32no—
188C2×C4×D4—32no—
189C2×C4×D4—32no—
190C2×#117—32no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—32no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—32no—
200C22×C22⋊C4C2×D311yescharacteristic
201C22×C22⋊C4C2×D312yes—
202#400—34no—
203#399—34no—
204#398—34no—
205#398—34no—
206#396—34no—
207#396—34no—
208#395—34no—
209#393—34no—
210#391—34no—
211#389—34no—
212#387—34no—
213#387—34no—
214#386—32no—
215#386—32no—
216#386—34no—
217#386C2×D312yes—
218#386C2×D312yes—
219#386C2×D314yes—
220#385—34no—
221#385—32no—
222#385—32no—
223#385—34no—
224#385—32no—
225#385—34no—
226#385—32no—
227#385—32no—
228#385—32no—
229#385—34no—
230#385—34no—
231#381—32no—
232#380—34no—
233#380—32no—
234#380—32no—
235#380—34no—
236#379—32no—
237C2×#95—32no—
238C2×#95C2×D312yes—
239C24×C3—22no—
240C24×C3—22no—
241C24×C3—42no—
242C24×C3—42no—
243C24×C3—42no—
244C24×C3—42no—
245C24×C3C2×D414yes—
246C24×C3C2×Q814yes—
247C24×C3C2×Q814yescomplemented
248C24×C3#4114yes—
249C24×C3C2412yes—
250C24×C3C2411yescharacteristic
251C24×C3C2411yescharacteristic
252C24×C3C2411yescharacteristic
253C2×C3×D4—232no—
254C2×C3×D4—24no—
255C2×C3×D4—24no—
256C2×C3×D4—24no—
257C2×C3×D4—24no—
258C2×C3×D4C2×Q818yes—
259C2×C3×D4C2×Q818yescomplemented
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4—22no—
263C22×C3×C4—24no—
264C22×C3×C4—22no—
265C22×C3×C4—24no—
266C22×C3×C4—24no—
267C22×C3×C4—24no—
268C22×C3×C4—24no—
269C22×C3×C4—24no—
270C22×C3×C4—42no—
271C22×C3×C4—42no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4—42no—
275C22×C3×C4—416no—
276C22×C3×C4C2×Q814yescomplemented
277C22×C3×C4C2414yes—
278C22×C3×C4C2412yes—
279C22×C3×C4C2412yes—
280C22×C3×C4C2412yes—
281C22×Dic3—22no—
282C22×Dic3—22no—
283C22×Dic3—24no—
284C22×Dic3—22no—
285C22×Dic3—22no—
286C22×Dic3—24no—
287C22×Dic3—24no—
288C22×Dic3—42no—
289C22×Dic3—42no—
290C22×Dic3—42no—
291C22×Dic3—42no—
292C22×Dic3—42no—
293C22×Dic3—42no—
294C22×Dic3—44no—
295C22×Dic3—42no—
296C22×Dic3—44no—
297C22×Dic3—42no—
298C22×Dic3C2×D414yes—
299C22×Dic3C2×D414yes—
300C22×Dic3C2412yes—
301C22×Dic3C2414yes—
302C22×Dic3C2412yes—
303C22×Dic3C2412yes—
304C22×Dic3C2412yes—
305C22×Dic3C2412yes—
306C22×Dic3C2412yes—
307C2×Dic6—28no—
308C2×Dic6—28no—
309C2×Dic6—44no—
310C2×Dic6—416no—
311C3×C22⋊C4—24no—
312C3×C22⋊C4—24no—
313C3×C22⋊C4—28no—
314C3×C22⋊C4—44no—
315#217—24no—
316#217—24no—
317#217—24no—
318#217—24no—
319#217—24no—
320#217—24no—
321#217—24no—
322#217—24no—
323#217—44no—
324#217—44no—
325#217C2×D418yes—
326#217C2×D418yes—
327C4⋊Dic3—28no—
328C4⋊Dic3—24no—
329C4⋊Dic3—24no—
330C4⋊Dic3—44no—
331C4⋊Dic3—44no—
332Dic3⋊C4—28no—
333Dic3⋊C4—28no—
334Dic3⋊C4—28no—
335Dic3⋊C4—44no—
336Dic3⋊C4—44no—
337Dic3⋊C4—44no—
338C4×Dic3—24no—
339C4×Dic3—24no—
340C25C22×D311yescharacteristic
341C25C22×D311yescharacteristic
342C22×Q8—34no—
343C22×Q8—64no—
344C22×Q8—124no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4Dic618yescomplemented
348C22×D4C22×D312yes—
349C22×D4C22×D312yes—
350C23×C4—24no—
351C23×C4—31no—
352C23×C4—31no—
353C23×C4—31no—
354C23×C4—31no—
355C23×C4—31no—
356C23×C4—32no—
357C23×C4—32no—
358C23×C4—31no—
359C23×C4—32no—
360C23×C4—44no—
361C23×C4C22×D311yescharacteristic
362C23×C4C22×D312yes—
363C23×C4C22×D312yes—
364C23×C4C22×D311yescharacteristic
365C23×C4C22×D312yes—
366C23×C4C22×D311yescharacteristic
367C22⋊Q8—616no—
368C22⋊Q8—616no—
369C22⋊Q8—128no—
370C4×D4—68no—
371C4×D4—68no—
372C4×D4—68no—
373C4×D4—68no—
374#117—68no—
375C2×C4⋊C4—34no—
376C2×C4⋊C4—34no—
377C2×C4⋊C4—34no—
378C2×C4⋊C4—34no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—32no—
381C2×C4⋊C4—34no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—64no—
387C2×C4⋊C4—64no—
388C2×C4⋊C4—64no—
389C2×C4⋊C4—124no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—38no—
392C2×C22⋊C4—32no—
393C2×C22⋊C4—32no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—32no—
397C2×C22⋊C4—32no—
398C2×C22⋊C4—32no—
399C2×C22⋊C4—32no—
400C2×C22⋊C4—32no—
401C2×C22⋊C4—32no—
402C2×C22⋊C4—34no—
403C2×C22⋊C4—34no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—68no—
406C2×C22⋊C4—64no—
407C2×C22⋊C4—64no—
408C2×C22⋊C4—64no—
409C2×C22⋊C4C22×D314yes—
410C2×C22⋊C4C22×D312yes—
411C2×C22⋊C4C22×D312yes—
412C2×C22⋊C4C22×D314yes—
413C2×C42—32no—
414C2×C42—32no—
415#95—34no—
416#95—34no—
417#95—34no—
418#95—34no—
419#95—34no—
420#95—34no—
421#95—34no—
422#95—34no—
423#95C22×D314yes—
424#95C22×D314yes—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—24no—
434C23×C3—24no—
435C23×C3—28no—
436C23×C3—44no—
437C23×C3—44no—
438C23×C3—48no—
439C23×C3—48no—
440C23×C3—48no—
441C23×C3—82no—
442C23×C3—82no—
443C23×C3—84no—
444C23×C3C22⋊Q8116yescomplemented
445C23×C3C22×D412yes—
446C23×C3C22×D412yes—
447C23×C3C22×D412yes—
448C23×C3C22×Q814yes—
449C23×C3C22×Q812yes—
450C23×C3C22×Q812yes—
451C23×C3C22×Q812yes—
452C23×C3C2×#4112yes—
453C23×C3C2×#4112yes—
454C23×C3C2×#4112yes—
455C23×C3C2511yescharacteristic
456C3×D4—216no—
457C3×D4—216no—
458C2×C3×C4—28no—
459C2×C3×C4—28no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—24no—
466C2×C3×C4—22no—
467C2×C3×C4—24no—
468C2×C3×C4—22no—
469C2×C3×C4—24no—
470C2×C3×C4—48no—
471C2×C3×C4—48no—
472C2×C3×C4—44no—
473C2×C3×C4—84no—
474C2×C3×C4C22×Q814yes—
475C2×C3×C4H(5,𝔽2)14yes—
476C2×Dic3—24no—
477C2×Dic3—24no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—22no—
481C2×Dic3—22no—
482C2×Dic3—24no—
483C2×Dic3—24no—
484C2×Dic3—24no—
485C2×Dic3—24no—
486C2×Dic3—24no—
487C2×Dic3—24no—
488C2×Dic3—24no—
489C2×Dic3—44no—
490C2×Dic3—44no—
491C2×Dic3—44no—
492C2×Dic3—44no—
493C2×Dic3—48no—
494C2×Dic3—84no—
495C2×Dic3—84no—
496C2×Dic3—82no—
497C2×Dic3—82no—
498C2×Dic3C22×D414yes—
499C2×Dic3C22×D414yes—
500Dic6—416no—
501C24—22no—
502C24—22no—
503C24—42no—
504C24—42no—
505C24—42no—
506C24—42no—
507C24C2×Dic614yes—
508C24C2×Dic614yescomplemented
509C24D3×D414yes—
510C24#23714yes—
511C24C23×D312yes—
512C24C23×D311yescharacteristic
513C24C23×D311yescharacteristic
514C24C23×D311yescharacteristic
515C2×Q8—68no—
516C2×Q8—68no—
517C2×Q8—124no—
518C2×Q8—1216no—
519C2×D4—232no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—24no—
523C2×D4—24no—
524C2×D4C2×Dic618yes—
525C2×D4C2×Dic618yescomplemented
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—32no—
537C22×C4—32no—
538C22×C4—34no—
539C22×C4—34no—
540C22×C4—32no—
541C22×C4—34no—
542C22×C4—32no—
543C22×C4—32no—
544C22×C4—32no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—416no—
551C22×C4—64no—
552C22×C4—64no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—64no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—122no—
559C22×C4—122no—
560C22×C4—122no—
561C22×C4—122no—
562C22×C4—122no—
563C22×C4—122no—
564C22×C4—122no—
565C22×C4—124no—
566C22×C4—124no—
567C22×C4—122no—
568C22×C4C2×Dic614yescomplemented
569C22×C4C23×D314yes—
570C22×C4C23×D312yes—
571C22×C4C23×D312yes—
572C22×C4C23×D312yes—
573C4⋊C4—68no—
574C4⋊C4—68no—
575C4⋊C4—68no—
576C4⋊C4—64no—
577C4⋊C4—64no—
578C4⋊C4—68no—
579C4⋊C4—124no—
580C4⋊C4—124no—
581C4⋊C4—124no—
582C4⋊C4—124no—
583C4⋊C4—124no—
584C22⋊C4—24no—
585C22⋊C4—24no—
586C22⋊C4—28no—
587C22⋊C4—38no—
588C22⋊C4—38no—
589C22⋊C4—44no—
590C22⋊C4—64no—
591C22⋊C4—64no—
592C22⋊C4—64no—
593C22⋊C4—64no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—124no—
599C22⋊C4—124no—
600C42—64no—
601C42—64no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—24no—
609C22×C3—24no—
610C22×C3—24no—
611C22×C3—24no—
612C22×C3—24no—
613C22×C3—24no—
614C22×C3—24no—
615C22×C3—28no—
616C22×C3—416no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—44no—
620C22×C3—88no—
621C22×C3C2×C22⋊Q814yes—
622C22×C3C2×C22⋊Q814yes—
623C22×C3C2×C22⋊Q814yes—
624C22×C3C23×D411yescharacteristic
625C22×C3C23×Q811yescharacteristic
626C22×C3C22×#4111yescharacteristic
627C22×C3C2×H(5,𝔽2)12yes—
628C22×C3#58512yes—
629C3×C4—24no—
630C3×C4—24no—
631C3×C4—42no—
632C3×C4—44no—
633Dic3—24no—
634Dic3—24no—
635Dic3—42no—
636Dic3—42no—
637Dic3—42no—
638Dic3—42no—
639Dic3—44no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—28no—
651C23—44no—
652C23—48no—
653C23—44no—
654C23—48no—
655C23—48no—
656C23—82no—
657C23—84no—
658C23—82no—
659C23#878116yescomplemented
660C23C22×Dic614yes—
661C23C22×Dic612yes—
662C23C22×Dic612yes—
663C23C22×Dic612yes—
664C23C2×D3×D412yes—
665C23C2×D3×D412yes—
666C23C2×D3×D412yes—
667C23C2×#23712yes—
668C23C2×#23712yes—
669C23C2×#23712yes—
670C23C24×D311yescharacteristic
671Q8—1216no—
672D4—216no—
673D4—216no—
674C2×C4—28no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—28no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—34no—
687C2×C4—34no—
688C2×C4—48no—
689C2×C4—48no—
690C2×C4—44no—
691C2×C4—64no—
692C2×C4—64no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—62no—
696C2×C4—62no—
697C2×C4—64no—
698C2×C4—64no—
699C2×C4—64no—
700C2×C4—64no—
701C2×C4—64no—
702C2×C4—64no—
703C2×C4—64no—
704C2×C4—84no—
705C2×C4—124no—
706C2×C4—124no—
707C2×C4—124no—
708C2×C4—128no—
709C2×C4—124no—
710C2×C4—244no—
711C2×C4—244no—
712C2×C4—242no—
713C2×C4—242no—
714C2×C4C22×Dic614yes—
715C2×C4#100414yes—
716C2×C3—24no—
717C2×C3—24no—
718C2×C3—24no—
719C2×C3—44no—
720C2×C3C22×C22⋊Q811yescharacteristic
721C2×C3#348411yescharacteristic
722C2×C3#348511yescharacteristic
723C2×C3#350112yes—
724C2×C3#350512yes—
725C22—24no—
726C22—24no—
727C22—24no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—28no—
738C22—24no—
739C22—416no—
740C22—42no—
741C22—44no—
742C22—42no—
743C22—88no—
744C22C2×#87814yes—
745C22C2×#87814yes—
746C22C2×#87814yes—
747C22C23×Dic611yescharacteristic
748C22C22×D3×D411yescharacteristic
749C22C22×#23711yescharacteristic
750C22C2×#100412yes—
751C22#596412yes—
752C4—24no—
753C4—24no—
754C4—42no—
755C4—44no—
756C4—64no—
757C4—64no—
758C4—122no—
759C4—122no—
760C4—124no—
761C4—122no—
762C4—122no—
763C3#3534911yescharacteristic, complemented, Sylow
764C2—24no—
765C2—24no—
766C2—24no—
767C2—44no—
768C2C22×#87811yescharacteristic
769C2#8576612yes—
770C2#8591911yescharacteristic
771C2#8593712yes—
772C2#8601211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#386C2
prime radicalC23×C3×D4C22
hypercenterC2×#386D3
hypocenterC3#35349
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C22×#924C2semidirect
5. C2×#5210C2semidirect
6. #82110C2semidirect
7. #82095C2semidirect
8. #82094C2semidirect
9. #74770C2semidirect
10. #74769C2semidirect
11. #74738C2semidirect
12. #74711C2semidirect
13. #74709C2semidirect
14. #74689C2semidirect
15. #73350C2semidirect
19. C23×Dic6C22semidirect
33. C22×C4⋊Dic3C22semidirect
36. C2×#924C22semidirect
37. C22×Dic3⋊C4C22semidirect
38. C22×Dic3⋊C4C22semidirect
39. C22×Dic3⋊C4C22semidirect
40. C2×#878C22semidirect
53. #5210C22semidirect
54. #5210C22semidirect
55. C2×C3⋊#95C22semidirect
56. #4950C22semidirect
57. #4950C22semidirect
58. #4950C22semidirect
59. #4950C22semidirect
60. #4950C22semidirect
61. #4949C22semidirect
62. #4948C22semidirect
63. #4948C22semidirect
64. #4947C22semidirect
65. #4946C22semidirect
66. #4946C22semidirect
67. #4942C22semidirect
68. #4942C22semidirect
69. #4942C22semidirect
70. #4661C22semidirect
71. #4660C22semidirect
72. #4657C22semidirect
73. #4656C22semidirect
74. #4655C22semidirect
75. #4654C22semidirect
76. #4647C22semidirect
77. #4646C22semidirect
97. C22×C3×D4Q8semidirect
247. C24×C3C2×Q8semidirect
259. C2×C3×D4C2×Q8semidirect
276. C22×C3×C4C2×Q8semidirect
347. C22×D4Dic6semidirect
444. C23×C3C22⋊Q8semidirect
508. C24C2×Dic6semidirect
525. C2×D4C2×Dic6semidirect
568. C22×C4C2×Dic6semidirect
659. C23#878semidirect
763. C3#35349semidirect

Maximal subgroups

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

subgroupindex
C2×#57982
C22×#9242
C2×C3×#3862
#840432
C2×#52102
#821102
#820952
#820942
#747702
#747692
#747382
#747112
#747092
#746892
#733502
#353493