Finite Group Databasebeta

← #10848717

Subgroups — #10848717

Order 768.

1216 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2C2×#5068C211yesmaximal, characteristic, complemented
3C2×#5059C211yesmaximal, characteristic, complemented
4#82077C211yesmaximal, characteristic, complemented
5#71740C211yesmaximal, characteristic, complemented
6#71725C211yesmaximal, characteristic, complemented
7#71700C211yesmaximal, characteristic, complemented
8#71699C211yesmaximal, characteristic, complemented
9#71685C211yesmaximal, characteristic, complemented
10#71684C211yesmaximal, characteristic
11#71633C211yesmaximal, characteristic, complemented
12#71632C211yesmaximal, characteristic, complemented
13#71613C211yesmaximal, characteristic, complemented
14#71612C211yesmaximal, characteristic, complemented
15C4×#830C211yesmaximal, characteristic, complemented
16#25601—31nomaximal, Sylow
17C3×#529—24no—
18C3×#529—24no—
19C2×C3×#126—21no—
20C2×C3×#125C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×#123—21no—
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4—21no—
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×#117—21no—
29C22×C3×C42C2211yescharacteristic
30C22×#216C2211yescharacteristic
31C22×#215C2211yescharacteristic
32C22×#214C2211yescharacteristic
33C22×#213C2211yescharacteristic
34C2×#930C2211yescharacteristic
35C2×#924C2211yescharacteristic
36C2×#875C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41#5213—21no—
42#5213—21no—
43C2×#830C2211yescharacteristic
44C2×#830C2211yescharacteristic
45#5068—24no—
46#5059—24no—
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51#4940—21no—
52#4940—21no—
53#4939C2211yescharacteristic
54#4936C2211yescharacteristic
55#4929C2211yescharacteristic
56C2×C4×C3⋊C8C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529D311yescharacteristic, complemented
65C2×#495—31no—
66C2×#488—31no—
67#2850—31no—
68#2001—31no—
69#2000—31no—
70#2000—31no—
71#1999—31no—
72#1991—31no—
73#1958—31no—
74#1880—31no—
75#1879—31no—
76#1878—31no—
77#1877—31no—
78C4×C22⋊C8—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4D411yescharacteristic
84C23×C3×C4D411yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×D12C2311yescharacteristic
88C22×Dic6C2311yescharacteristic
89C3×#126—28no—
90C3×#125—22no—
91C3×#125D414yescomplemented
92C3×#124—22no—
93C3×#124D414yescomplemented
94C3×#123—28no—
95C3×C22⋊Q8—22no—
96C3×C22⋊Q8—22no—
97C3×#121—22no—
98C3×#121—22no—
99C3×C4×Q8—22no—
100C3×C4×Q8—22no—
101C3×C4×D4—28no—
102C3×C4×D4—22no—
103C3×C4×D4—22no—
104C3×#117—28no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C42—21no—
117C2×C3×C42—22no—
118C2×C3×C42—22no—
119C2×C3×C42D411yescharacteristic
120C2×C3×C42D411yescharacteristic
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×#217—21no—
124C2×#216—22no—
125C2×#216—22no—
126C2×#216—41no—
127C2×#215—22no—
128C2×#215—22no—
129C2×#215—41no—
130C2×#214—22no—
131C2×#214—22no—
132C2×#214—41no—
133C2×#213—22no—
134C2×#213—22no—
135C2×#213—41no—
136#930—41no—
137#930—41no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×C4⋊Dic3C2311yescharacteristic
144C2×C4⋊Dic3C2311yescharacteristic
145#924—41no—
146#924—41no—
147C2×Dic3⋊C4—21no—
148C22×C3⋊C8C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152#875—22no—
153#875—22no—
154#835—41no—
155#835—41no—
156#832—41no—
157#832—41no—
158C3⋊#95—21no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162#830—22no—
163#830—22no—
164#810—22no—
165#810—22no—
166#809—22no—
167#809—22no—
168C4×C3⋊C8—22no—
169C4×C3⋊C8—22no—
170C22×Q16—31no—
171C22×SD16—31no—
172C22×SD16—31no—
173C22×D8—31no—
174#529—24no—
175#529—24no—
176C2×#126—21no—
177C2×#125C2×D311yescharacteristic
178C2×#124—31no—
179C2×#124C2×D311yescharacteristic
180C2×#123—21no—
181C2×C22⋊Q8—31no—
182C2×C22⋊Q8C2×D311yescharacteristic
183C2×#121—31no—
184C2×#121C2×D311yescharacteristic
185C2×C4×Q8C2×D311yescharacteristic
186C2×C4×D4—21no—
187C2×C4×D4C2×D311yescharacteristic
188C2×#117—21no—
189C22×C42C2×D311yescharacteristic
190#495—64no—
191#488—64no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×C22⋊C8—31no—
201C2×C22⋊C8—31no—
202C2×C4×C8—31no—
203C2×C4×C8—31no—
204#391—31no—
205#390—31no—
206#388—61no—
207#388—61no—
208#386—61no—
209#386—61no—
210#382—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
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—24no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—21no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4C2×D412yes—
235C22×C3×C4—24no—
236C22×C3×C4—22no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—22no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—41no—
250C22×C3×C4—41no—
251C22×C3×C4—42no—
252C22×C3×C4—42no—
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4C2411yescharacteristic
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—42no—
262C22×Dic3—21no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×Dic6—21no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—24no—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4C2×D412yes—
284C3×C4⋊C4C2×D412yes—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—24no—
288C3×C22⋊C4—24no—
289C3×C22⋊C4—24no—
290C3×C42—24no—
291C3×C42—22no—
292C3×C42—22no—
293C3×C42—21no—
294C3×C42—21no—
295C3×C42C2×D412yes—
296C3×C42C2×D412yes—
297#217—42no—
298#216—44no—
299#215—44no—
300#214—44no—
301#213—44no—
302(C2×D3)⋊C4—42no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—42no—
305(C2×D3)⋊C4—42no—
306(C2×D3)⋊C4—42no—
307C4⋊Dic3—21no—
308C4⋊Dic3—21no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311Dic3⋊C4—42no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
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#4112yes—
323C2×C3⋊C8#4112yes—
324C22×Q8—31no—
325C22×Q8C22×D311yescharacteristic
326C22×D4—21no—
327C22×D4—31no—
328C22×D4—61no—
329C22×D4C22×D311yescharacteristic
330C23×C4—21no—
331C23×C4#6711yescharacteristic
332C23×C4#6711yescharacteristic
333C23×C4C22×D311yescharacteristic
334C2×Q16—62no—
335C2×Q16—62no—
336C2×Q16—121no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—62no—
341C2×SD16—121no—
342C2×SD16—121no—
343C2×D8—62no—
344C2×D8—62no—
345C2×D8—121no—
346C22×C8—31no—
347C22×C8—31no—
348C22×C8—31no—
349C22×C8—31no—
350#126—28no—
351#125—22no—
352#125#6714yescomplemented
353#124—22no—
354#124—62no—
355#124—62no—
356#124#6714yescomplemented
357#123—28no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—121no—
361C22⋊Q8—121no—
362#121—22no—
363#121—22no—
364#121—121no—
365#121—121no—
366C4×Q8—22no—
367C4×Q8—22no—
368C4×D4—28no—
369C4×D4—22no—
370C4×D4—22no—
371#117—28no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—31no—
377C2×C4⋊C4—31no—
378C2×C4⋊C4—61no—
379C2×C4⋊C4C22×D311yescharacteristic
380C2×C4⋊C4C22×D311yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—61no—
387C2×C22⋊C4—61no—
388C2×C22⋊C4—61no—
389C2×C22⋊C4—61no—
390C2×C22⋊C4—61no—
391C2×C22⋊C4—61no—
392C2×C42—21no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42#6711yescharacteristic
396C2×C42#6711yescharacteristic
397C2×C42C22×D311yescharacteristic
398C2×C42C22×D311yescharacteristic
399#103—62no—
400#103—62no—
401#103—121no—
402#103—121no—
403#102—62no—
404#102—62no—
405#102—121no—
406#102—121no—
407C22⋊C8—62no—
408C22⋊C8—62no—
409C4×C8—62no—
410C4×C8—62no—
411#95—61no—
412#95—61no—
413#95—61no—
414#95—61no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—22no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3#13512yes—
429C23×C3C22×D411yescharacteristic
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C22×D3—41no—
436C22×D3—41no—
437C3×Q8—22no—
438C3×Q8—22no—
439C3×Q8—41no—
440C3×Q8—41no—
441C3×D4—22no—
442C3×D4—22no—
443C3×D4—48no—
444C3×D4—41no—
445C3×D4—41no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
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—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—44no—
462C2×C3×C4—44no—
463C2×C3×C4—48no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
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#12012yes—
475C2×C3×C4#12012yes—
476C2×C3×C4#13512yes—
477C2×C3×C4C22×D411yescharacteristic
478C2×C3×C4C22×D411yescharacteristic
479C2×C3×C4C2×#4111yescharacteristic
480C2×C3×C4C2×#4111yescharacteristic
481C2×C3×C4H(5,𝔽2)11yescharacteristic
482C2×C3×C4H(5,𝔽2)11yescharacteristic
483#67—84no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490C2×Dic3—41no—
491C2×Dic3—41no—
492C2×Dic3—41no—
493D12—41no—
494D12—41no—
495D12—41no—
496D12—41no—
497Dic6—41no—
498Dic6—41no—
499Dic6—41no—
500Dic6—41no—
501C3⋊C8—22no—
502C3⋊C8—22no—
503C3⋊C8—41no—
504C3⋊C8—41no—
505C24—21no—
506C24—61no—
507C24C2×#6711yescharacteristic
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—61no—
514C2×Q8—61no—
515C2×Q8—61no—
516C2×Q8—61no—
517C2×Q8—61no—
518C2×Q8—61no—
519C2×Q8C2×#6712yes—
520C2×D4—24no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—61no—
529C2×D4—61no—
530C2×D4—61no—
531C2×D4—61no—
532C2×D4—61no—
533C2×D4—61no—
534C2×D4—122no—
535C2×D4—122no—
536C2×D4—122no—
537C2×D4C2×#6712yes—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4C2×#6711yescharacteristic
560C22×C4C2×#6711yescharacteristic
561C22×C4C2×#6711yescharacteristic
562C22×C4C2×#6711yescharacteristic
563C22×C4C2×#6711yescharacteristic
564C22×C4C23×D311yescharacteristic
565Q16—124no—
566SD16—124no—
567SD16—124no—
568D8—124no—
569C2×C8—32no—
570C2×C8—32no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—61no—
577C2×C8—61no—
578C2×C8—61no—
579C2×C8—61no—
580C2×C8—61no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—122no—
592C4⋊C4C2×#6712yes—
593C4⋊C4C2×#6712yes—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—122no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C22⋊C4—122no—
605C42—24no—
606C42—22no—
607C42—22no—
608C42—21no—
609C42—21no—
610C42C2×#6712yes—
611C42C2×#6712yes—
612C22×C3—22no—
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3C2×#12011yescharacteristic
627C22×C3#53211yescharacteristic
628C22×C3#53511yescharacteristic
629C22×C3C2×#13511yescharacteristic
630C22×C3C2×#13511yescharacteristic
631C22×C3#57511yescharacteristic
632C22×C3#57511yescharacteristic
633C2×D3—81no—
634C2×D3—81no—
635C2×D3—81no—
636C2×D3—81no—
637C2×D3—81no—
638C2×D3—81no—
639C2×D3—81no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—41no—
644C3×C4—42no—
645C3×C4—41no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4#54611yescharacteristic
649C3×C4#54611yescharacteristic
650C3×C4#55011yescharacteristic
651C3×C4#55011yescharacteristic
652Dic3—81no—
653Dic3—81no—
654Dic3—81no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—22no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—121no—
672C23—121no—
673C23—121no—
674C23—121no—
675C23#95012yes—
676C23C22×#6711yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681Q8—121no—
682Q8—121no—
683Q8—121no—
684Q8—121no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4—121no—
691D4—121no—
692D4—121no—
693D4—121no—
694D4—244no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—48no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4#95012yes—
733C2×C4#95312yes—
734C2×C4#95312yes—
735C2×C4D3×#4111yescharacteristic
736C2×C4D3×#4111yescharacteristic
737C2×C4#100911yescharacteristic
738C2×C4#100911yescharacteristic
739C2×C4C22×#6711yescharacteristic
740C2×C4C22×#6711yescharacteristic
741C8—62no—
742C8—62no—
743C8—121no—
744C8—121no—
745C2×C3—42no—
746C2×C3—82no—
747C2×C3#243111yescharacteristic
748C2×C3#300211yescharacteristic
749C2×C3#300211yescharacteristic
750C2×C3#316811yescharacteristic
751C2×C3#318311yescharacteristic
752C2×C3#321111yescharacteristic
753C2×C3#321211yescharacteristic
754D3—161no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—241no—
770C22—241no—
771C22—241no—
772C22—241no—
773C22—241no—
774C22—241no—
775C22—241no—
776C22C2×#95011yescharacteristic
777C22C2×#95011yescharacteristic
778C22#582211yescharacteristic
779C22#582211yescharacteristic
780C22#583011yescharacteristic
781C22#583211yescharacteristic
782C22C2×#95311yescharacteristic
783C4—22no—
784C4—22no—
785C4—22no—
786C4—41no—
787C4—42no—
788C4—42no—
789C4—41no—
790C4—42no—
791C4—241no—
792C4—241no—
793C4—241no—
794C4#582911yescharacteristic
795C4#582911yescharacteristic
796C4#583411yescharacteristic
797C4#583411yescharacteristic
798C3#2560111yescharacteristic, complemented, Sylow
799C2—42no—
800C2—82no—
801C2—481no—
802C2#8313411yescharacteristic
803C2#8313911yescharacteristic
804C2#8314411yescharacteristic
805C2#8314511yescharacteristic
806C2#8408011yescharacteristic
807C2#8408011yescharacteristic
808C2#8409211yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#529C2
socleC23×C3C22×D4
prime radical#71684C2
hypercenterC2×#529D3
hypocenterC3#25601
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×C3×#529C2semidirect
2. C2×#5068C2semidirect
3. C2×#5059C2semidirect
4. #82077C2semidirect
5. #71740C2semidirect
6. #71725C2semidirect
7. #71700C2semidirect
8. #71699C2semidirect
9. #71685C2semidirect
11. #71633C2semidirect
12. #71632C2semidirect
13. #71613C2semidirect
14. #71612C2semidirect
15. C4×#830C2semidirect
64. C2×#529D3semidirect
91. C3×#125D4semidirect
93. C3×#124D4semidirect
352. #125#67semidirect
356. #124#67semidirect
798. C3#25601semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C2×#50682
C2×#50592
#820772
#717402
#717252
#717002
#716992
#716852
#716842
#716332
#716322
#716132
#716122
C4×#8302
#256013