Finite Group Databasebeta

← #10827556

Subgroups — #10827556

Order 768.

1262 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#552C211yesmaximal, characteristic, complemented
2C2×#5047C211yesmaximal, characteristic, complemented
3#82402C211yesmaximal, characteristic
4C2×#4966C211yesmaximal, characteristic, complemented
5#71744C211yesmaximal, characteristic, complemented
6#71743C211yesmaximal, characteristic, complemented
7#71700C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71697C211yesmaximal, characteristic, complemented
10#71633C211yesmaximal, characteristic, complemented
11#71632C211yesmaximal, characteristic, complemented
12#71611C211yesmaximal, characteristic, complemented
13#71586C211yesmaximal, characteristic, complemented
14#71585C211yesmaximal, characteristic, complemented
15#71554C211yesmaximal, characteristic, complemented
16#23978—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C3×#552—24no—
19C3×#552—24no—
20C2×C3×#126—21no—
21C2×C3×#125—21no—
22C2×C3×#125C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×#117—21no—
29C2×C3×#117C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C22×#216C2211yescharacteristic
32C22×#215C2211yescharacteristic
33C2×#930C2211yescharacteristic
34C2×#924C2211yescharacteristic
35C22×#208C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#835C2211yescharacteristic
38#5223—21no—
39#5212C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5047—24no—
44#4989—21no—
45C2×#810C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#810C2211yescharacteristic
48#4966—24no—
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#809C2211yescharacteristic
52#4959—21no—
53#4956—21no—
54#4939C2211yescharacteristic
55#4929C2211yescharacteristic
56#4529C2211yescharacteristic
57#4529C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#552D311yescharacteristic, complemented
65C2×#452—31no—
66C2×#417—31no—
67#2407—31no—
68#2026—31no—
69#2025—31no—
70#2001—31no—
71#2000—31no—
72#1894—31no—
73#1880—31no—
74#1878—31no—
75#1875—31no—
76#1873—31no—
77#1870—31no—
78#1824—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4D411yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67—21no—
85C22×#67—21no—
86C2×#235—22no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—41no—
91C2×#235—41no—
92C22×D12C2311yescharacteristic
93C22×C4×D3—21no—
94C22×Dic6C2311yescharacteristic
95C3×#126—28no—
96C3×#125—28no—
97C3×#125—22no—
98C3×#125—22no—
99C3×#123—28no—
100C3×C22⋊Q8—22no—
101C3×C22⋊Q8—22no—
102C3×C22⋊Q8—22no—
103C3×C22⋊Q8D414yescomplemented
104C3×C4×Q8—22no—
105C3×C4×Q8—22no—
106C3×C4×D4—22no—
107C3×C4×D4—22no—
108C3×#117—28no—
109C3×#117—22no—
110C3×#117—22no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—22no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—21no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4D411yescharacteristic
119C2×C3×C4⋊C4D414yescomplemented
120C2×C3×C4⋊C4C2311yescharacteristic
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4D411yescharacteristic
127C2×C3×C22⋊C4D411yescharacteristic
128C2×C3×C42—21no—
129C2×C3×C42—21no—
130C2×C3×C42C2311yescharacteristic
131C2×#217—21no—
132C2×#217—21no—
133C2×#216—22no—
134C2×#216—22no—
135C2×#216—41no—
136C2×#215—22no—
137C2×#215—22no—
138C2×#215—41no—
139#930—22no—
140#930—41no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×C4⋊Dic3C2311yescharacteristic
145C2×C4⋊Dic3C2311yescharacteristic
146#924—22no—
147#924—41no—
148C2×Dic3⋊C4—21no—
149C2×#208—22no—
150C2×#208—41no—
151C2×#208—41no—
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155C22×C3⋊C8C2311yescharacteristic
156#835—41no—
157#835—41no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161#830—22no—
162#830—41no—
163#830—41no—
164#810—22no—
165#810—22no—
166#810—22no—
167#809—22no—
168#809—22no—
169#809—22no—
170C22×#41—31no—
171C22×Q16—31no—
172C22×SD16—31no—
173C22×M16—31no—
174#552—24no—
175#552—24no—
176C2×#126—21no—
177C2×#125—21no—
178C2×#125C2×D311yescharacteristic
179C2×#123—21no—
180C2×C22⋊Q8—31no—
181C2×C22⋊Q8C2×D311yescharacteristic
182C2×C22⋊Q8C2×D311yescharacteristic
183C2×#121—31no—
184C2×C4×Q8C2×D311yescharacteristic
185C2×C4×D4C2×D311yescharacteristic
186C2×#117—21no—
187C2×#117C2×D311yescharacteristic
188C22×C4⋊C4C2×D311yescharacteristic
189#452—64no—
190#417—64no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×C22⋊C8—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202#394—61no—
203#392—61no—
204#391—31no—
205#390—31no—
206#386—61no—
207#385—61no—
208#380—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3C2×D411yescharacteristic
218C24×C3C2×D411yescharacteristic
219C23×D3—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8C2×D412yes—
226C2×C3×D4—22no—
227C2×C3×D4—41no—
228C2×C3×D4—41no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—24no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—42no—
245C22×C3×C4—42no—
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D412yes—
251C22×C3×C4C2×D412yes—
252C22×C3×C4C2411yescharacteristic
253C2×#67—42no—
254C2×#67—42no—
255C2×#67—42no—
256C2×#67—42no—
257C2×#67—42no—
258C2×#67—81no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—21no—
262#235—28no—
263#235—44no—
264#235—44no—
265#235—44no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×D12#4112yes—
272C2×C4×D3—42no—
273C2×C4×D3—42no—
274C2×C4×D3—42no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C2×Dic6—21no—
278C2×Dic6—21no—
279C2×Dic6—21no—
280C2×Dic6#4112yes—
281C3×C4⋊C4—24no—
282C3×C4⋊C4—24no—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—24no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—24no—
287C3×C4⋊C4—22no—
288C3×C4⋊C4—21no—
289C3×C4⋊C4—21no—
290C3×C4⋊C4—21no—
291C3×C4⋊C4C2×D412yes—
292C3×C4⋊C4C2×D412yes—
293C3×C4⋊C4C2×D412yes—
294C3×C22⋊C4—24no—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—24no—
297C3×C22⋊C4—22no—
298C3×C22⋊C4—22no—
299C3×C42—24no—
300C3×C42—24no—
301C3×C42—21no—
302C3×C42—21no—
303#217—42no—
304#217—81no—
305#216—44no—
306#215—44no—
307(C2×D3)⋊C4—42no—
308(C2×D3)⋊C4—42no—
309(C2×D3)⋊C4—81no—
310C4⋊Dic3—21no—
311C4⋊Dic3—21no—
312C4⋊Dic3—21no—
313C4⋊Dic3—21no—
314Dic3⋊C4—42no—
315#208—44no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—21no—
322C2×C3⋊C8—21no—
323C2×C3⋊C8—21no—
324C2×C3⋊C8—21no—
325C2×C3⋊C8—21no—
326C2×C3⋊C8—21no—
327C2×C3⋊C8—21no—
328C2×#41—62no—
329C2×#41—62no—
330C2×#41—62no—
331C2×#41—62no—
332C2×#41—121no—
333C2×#41—121no—
334C22×Q8—31no—
335C22×Q8C22×D311yescharacteristic
336C22×D4—31no—
337C22×D4—61no—
338C22×D4—61no—
339C22×D4#6711yescharacteristic
340C23×C4—21no—
341C23×C4—61no—
342C23×C4C22×D311yescharacteristic
343C23×C4C22×D311yescharacteristic
344C2×Q16—62no—
345C2×Q16—62no—
346C2×Q16—121no—
347C2×SD16—62no—
348C2×SD16—62no—
349C2×SD16—121no—
350C2×M16—62no—
351C2×M16—121no—
352C2×M16—121no—
353C22×C8—31no—
354C22×C8—31no—
355C22×C8—31no—
356C22×C8—31no—
357#126—28no—
358#125—28no—
359#125—22no—
360#125—22no—
361#123—28no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C22⋊Q8—22no—
365C22⋊Q8—62no—
366C22⋊Q8—121no—
367C22⋊Q8#6714yescomplemented
368#121—62no—
369#121—121no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×D4—22no—
373C4×D4—22no—
374#117—28no—
375#117—22no—
376#117—22no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—31no—
385C2×C4⋊C4—31no—
386C2×C4⋊C4—61no—
387C2×C4⋊C4#6711yescharacteristic
388C2×C4⋊C4#6714yescomplemented
389C2×C4⋊C4C22×D311yescharacteristic
390C2×C4⋊C4C22×D311yescharacteristic
391C2×C4⋊C4C22×D311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—61no—
396C2×C22⋊C4—61no—
397C2×C22⋊C4—61no—
398C2×C22⋊C4—61no—
399C2×C22⋊C4—61no—
400C2×C22⋊C4#6711yescharacteristic
401C2×C22⋊C4#6711yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42C22×D311yescharacteristic
405#103—62no—
406#103—62no—
407#103—62no—
408#103—121no—
409#103—121no—
410#102—62no—
411#102—62no—
412#102—62no—
413C22⋊C8—62no—
414C22⋊C8—121no—
415C22⋊C8—121no—
416#95—61no—
417#95—61no—
418#95—61no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3—21no—
424C23×C3—21no—
425C23×C3—21no—
426C23×C3—21no—
427C23×C3—21no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3#12012yes—
433C23×C3C22×D411yescharacteristic
434C22×D3—22no—
435C22×D3—41no—
436C22×D3—41no—
437C22×D3—41no—
438C22×D3—41no—
439C22×D3—41no—
440C22×D3—41no—
441C3×Q8—22no—
442C3×Q8—22no—
443C3×Q8—41no—
444C3×Q8—41no—
445C3×D4—44no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—21no—
458C2×C3×C4—22no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—48no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4#12012yes—
479C2×C3×C4C22×D411yescharacteristic
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C2×#4111yescharacteristic
482C2×C3×C4C2×#4111yescharacteristic
483C2×C3×C4H(5,𝔽2)11yescharacteristic
484C2×C3×C4H(5,𝔽2)11yescharacteristic
485#67—48no—
486#67—84no—
487C2×Dic3—22no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493C2×Dic3—41no—
494C2×Dic3—41no—
495C2×Dic3—41no—
496D12—22no—
497D12—22no—
498D12—41no—
499D12—41no—
500C4×D3—48no—
501Dic6—22no—
502Dic6—22no—
503Dic6—41no—
504Dic6—41no—
505C3⋊C8—41no—
506C3⋊C8—41no—
507C3⋊C8—41no—
508C3⋊C8—41no—
509C24—61no—
510C24C2×#6711yescharacteristic
511C24C2×#6711yescharacteristic
512#41—68no—
513#41—124no—
514#41—124no—
515#41—124no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—32no—
522C2×Q8—61no—
523C2×Q8—61no—
524C2×Q8—61no—
525C2×Q8—61no—
526C2×Q8—61no—
527C2×Q8C2×#6712yes—
528C2×D4—22no—
529C2×D4—32no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—61no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4—122no—
538C2×D4—122no—
539C2×D4—122no—
540C2×D4—122no—
541C2×D4—122no—
542C2×D4—241no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—122no—
564C22×C4—122no—
565C22×C4—122no—
566C22×C4C2×#6711yescharacteristic
567C22×C4C2×#6711yescharacteristic
568C22×C4C2×#6711yescharacteristic
569C22×C4C2×#6711yescharacteristic
570C22×C4C2×#6712yes—
571C22×C4C2×#6712yes—
572C22×C4C23×D311yescharacteristic
573Q16—124no—
574SD16—124no—
575M16—124no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C2×C8—61no—
582C2×C8—61no—
583C2×C8—61no—
584C2×C8—61no—
585C2×C8—61no—
586C2×C8—61no—
587C2×C8—61no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—122no—
603C4⋊C4C2×#6712yes—
604C4⋊C4C2×#6712yes—
605C4⋊C4C2×#6712yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—24no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—122no—
612C22⋊C4—122no—
613C22⋊C4—122no—
614C22⋊C4—241no—
615C22⋊C4—241no—
616C42—24no—
617C42—24no—
618C42—21no—
619C42—21no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3C2×#12011yescharacteristic
635C22×C3#54611yescharacteristic
636C22×C3#54611yescharacteristic
637C22×C3#57511yescharacteristic
638C22×C3#57511yescharacteristic
639C22×C3#57711yescharacteristic
640C22×C3#57811yescharacteristic
641C2×D3—42no—
642C2×D3—42no—
643C2×D3—42no—
644C2×D3—81no—
645C2×D3—81no—
646C2×D3—81no—
647C2×D3—81no—
648C3×C4—22no—
649C3×C4—41no—
650C3×C4—42no—
651C3×C4—41no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4—41no—
655C3×C4—42no—
656C3×C4#52511yescharacteristic
657C3×C4#53511yescharacteristic
658C3×C4#54611yescharacteristic
659C3×C4#54611yescharacteristic
660Dic3—42no—
661Dic3—81no—
662Dic3—81no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—62no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23#95312yes—
684C23C22×#6711yescharacteristic
685Q8—22no—
686Q8—22no—
687Q8—41no—
688Q8—41no—
689Q8—62no—
690Q8—62no—
691Q8—121no—
692Q8—121no—
693D4—44no—
694D4—62no—
695D4—62no—
696D4—128no—
697D4—121no—
698D4—121no—
699D4—244no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—48no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—62no—
733C2×C4—128no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—121no—
740C2×C4—121no—
741C2×C4—121no—
742C2×C4#95312yes—
743C2×C4D3×#4111yescharacteristic
744C2×C4D3×#4111yescharacteristic
745C2×C4#100911yescharacteristic
746C2×C4#100911yescharacteristic
747C2×C4C22×#6711yescharacteristic
748C2×C4C22×#6711yescharacteristic
749C8—121no—
750C8—121no—
751C8—121no—
752C8—121no—
753C2×C3—42no—
754C2×C3—81no—
755C2×C3#240411yescharacteristic
756C2×C3#300511yescharacteristic
757C2×C3#301311yescharacteristic
758C2×C3#331511yescharacteristic
759C2×C3#331711yescharacteristic
760C2×C3#332311yescharacteristic
761C2×C3#332711yescharacteristic
762D3—82no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—122no—
778C22—122no—
779C22—122no—
780C22—241no—
781C22—241no—
782C22—241no—
783C22—241no—
784C22#582211yescharacteristic
785C22#582211yescharacteristic
786C22#582911yescharacteristic
787C22#582911yescharacteristic
788C22#583711yescharacteristic
789C22#583811yescharacteristic
790C22C2×#95311yescharacteristic
791C4—22no—
792C4—41no—
793C4—42no—
794C4—42no—
795C4—41no—
796C4—42no—
797C4—41no—
798C4—42no—
799C4—122no—
800C4—241no—
801C4—241no—
802C4#582811yescharacteristic
803C4#582911yescharacteristic
804C4#582911yescharacteristic
805C4#583011yescharacteristic
806C3#2397811yescharacteristic, complemented, Sylow
807C2—42no—
808C2—81no—
809C2—242no—
810C2#8360011yescharacteristic
811C2#8360111yescharacteristic
812C2#8360411yescharacteristic
813C2#8360511yescharacteristic
814C2#8408111yescharacteristic
815C2#8409611yescharacteristic
816C2#8411411yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#552C2
socleC23×C3C22×D4
prime radical#82402C2
hypercenterC2×#552D3
hypocenterC3#23978
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×C3×#552C2semidirect
2. C2×#5047C2semidirect
4. C2×#4966C2semidirect
5. #71744C2semidirect
6. #71743C2semidirect
7. #71700C2semidirect
8. #71699C2semidirect
9. #71697C2semidirect
10. #71633C2semidirect
11. #71632C2semidirect
12. #71611C2semidirect
13. #71586C2semidirect
14. #71585C2semidirect
15. #71554C2semidirect
64. C2×#552D3semidirect
103. C3×C22⋊Q8D4semidirect
119. C2×C3×C4⋊C4D4semidirect
367. C22⋊Q8#67semidirect
388. C2×C4⋊C4#67semidirect
806. C3#23978semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5522
C2×#50472
#824022
C2×#49662
#717442
#717432
#717002
#716992
#716972
#716332
#716322
#716112
#715862
#715852
#715542
#239783