Finite Group Databasebeta

← #10829310

Subgroups — #10829310

Order 768.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#553C211yesmaximal, characteristic, complemented
2C2×#5066C211yesmaximal, characteristic, complemented
3#82417C211yesmaximal, characteristic, complemented
4C2×#5014C211yesmaximal, characteristic, complemented
5#71741C211yesmaximal, characteristic, complemented
6#71684C211yesmaximal, characteristic, complemented
7#71684C211yesmaximal, characteristic, complemented
8#71680C211yesmaximal, characteristic, complemented
9#71679C211yesmaximal, characteristic, complemented
10#71615C211yesmaximal, characteristic, complemented
11#71604C211yesmaximal, characteristic, complemented
12#71586C211yesmaximal, characteristic, complemented
13#71576C211yesmaximal, characteristic, complemented
14#71560C211yesmaximal, characteristic, complemented
15#71556C211yesmaximal, characteristic, complemented
16#24136—31nomaximal, Sylow
17C3×#553—24no—
18C3×#553—24no—
19C2×C3×#126—21no—
20C2×C3×#125C2211yescharacteristic
21C2×C3×#123—21no—
22C2×C3×#121—21no—
23C2×C3×#121C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×C4×D4—21no—
26C2×C3×C4×D4C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×#117C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C2×#938—21no—
31C22×#213C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×#930C2211yescharacteristic
34C2×C4×D12C2211yescharacteristic
35C2×#832C2211yescharacteristic
36C2×#832C2211yescharacteristic
37C2×#832C2211yescharacteristic
38#5212C2211yescharacteristic
39#5212C2211yescharacteristic
40C2×#830C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44#5066—24no—
45#5014—24no—
46#4987—21no—
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#808C2211yescharacteristic
51C2×#808C2211yescharacteristic
52C2×#807C2211yescharacteristic
53#4961—21no—
54#4961—21no—
55#4935C2211yescharacteristic
56C2×C4⋊(C3⋊C8)C2211yescharacteristic
57C2×#803C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#553D311yescharacteristic, complemented
65C2×#478—31no—
66C2×#442—31no—
67#2537—31no—
68#2034—31no—
69#2033—31no—
70#1999—31no—
71#1999—31no—
72#1992—31no—
73#1955—31no—
74#1875—31no—
75#1874—31no—
76#1854—31no—
77#1853—31no—
78#1802—31no—
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4D411yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4—21no—
85C23×C3×C4C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—21no—
88C22×#67—21no—
89C22×D12C2311yescharacteristic
90C22×C4×D3—21no—
91C3×#126—28no—
92C3×#125—22no—
93C3×#125D414yescomplemented
94C3×#123—28no—
95C3×#121—28no—
96C3×#121—22no—
97C3×#121—22no—
98C3×#121—22no—
99C3×#121—22no—
100C3×C4×D4—28no—
101C3×C4×D4—22no—
102C3×C4×D4—22no—
103C3×C4×D4—22no—
104C3×C4×D4D414yescomplemented
105C3×#117—22no—
106C3×#117—22no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C4⋊C4—22no—
111C2×C3×C4⋊C4—22no—
112C2×C3×C4⋊C4D411yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C4⋊C4C2311yescharacteristic
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4D411yescharacteristic
121C2×C3×C22⋊C4D411yescharacteristic
122C2×C3×C42—21no—
123C2×C3×C42C2311yescharacteristic
124C2×#217—21no—
125C2×#217—21no—
126#938—44no—
127C2×#213—22no—
128C2×#213—22no—
129C2×#213—22no—
130#930—22no—
131#930—22no—
132#930—41no—
133#930—41no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×(C2×D3)⋊C4—21no—
137C2×C4⋊Dic3—21no—
138C2×C4⋊Dic3—21no—
139C2×C4⋊Dic3C2311yescharacteristic
140C2×C4⋊Dic3C2311yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C4×D12—22no—
147C4×D12—22no—
148#832—22no—
149#832—41no—
150#832—41no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153#830—22no—
154#830—22no—
155#830—41no—
156#830—41no—
157#809—22no—
158#809—22no—
159#809—22no—
160#808—22no—
161#808—22no—
162#807—22no—
163C4⋊(C3⋊C8)—22no—
164#803—22no—
165C22×D8—31no—
166#553—24no—
167#553—24no—
168C2×#126—21no—
169C2×#125C2×D311yescharacteristic
170C2×#123—21no—
171C2×#121—21no—
172C2×#121—31no—
173C2×#121—31no—
174C2×#121—61no—
175C2×#121C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×C4×D4—21no—
178C2×C4×D4—31no—
179C2×C4×D4C2×D311yescharacteristic
180C2×C4×D4C2×D311yescharacteristic
181C2×#117C2×D311yescharacteristic
182C22×C4⋊C4C2×D311yescharacteristic
183#478—64no—
184#442—64no—
185C2×#107—31no—
186C2×#106—31no—
187C2×#106—31no—
188C2×C4⋊C8—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×#102—31no—
194C2×#102—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8—31no—
197C2×C22⋊C8—31no—
198C2×C22⋊C8—31no—
199C2×#97—31no—
200#394—61no—
201#394—61no—
202#384—31no—
203#380—31no—
204#380—31no—
205#380—61no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340—31no—
210#340—31no—
211#340—31no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C24×C3C2×D411yescharacteristic
215C23×D3—21no—
216C2×C3×D4—24no—
217C2×C3×D4—22no—
218C2×C3×D4—24no—
219C2×C3×D4—22no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—41no—
226C2×C3×D4—42no—
227C2×C3×D4—42no—
228C2×C3×D4—81no—
229C2×C3×D4—81no—
230C2×C3×D4C2×D412yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—24no—
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—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—24no—
248C22×C3×C4—81no—
249C22×C3×C4—81no—
250C22×C3×C4—81no—
251C22×C3×C4—81no—
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4C2411yescharacteristic
257C2×#67—42no—
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—81no—
262C2×#67—81no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—21no—
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—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4C2×D412yes—
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—22no—
290C3×C22⋊C4—22no—
291C3×C42—24no—
292C3×C42C2×D412yes—
293C3×C42C2×D412yes—
294#217—42no—
295#217—42no—
296#213—28no—
297(C2×D3)⋊C4—42no—
298(C2×D3)⋊C4—42no—
299(C2×D3)⋊C4—42no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4⋊Dic3—21no—
306C4⋊Dic3—42no—
307C4⋊Dic3—81no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
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#4112yes—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—31no—
323C22×D4—61no—
324C22×D4—61no—
325C22×D4#6711yescharacteristic
326C22×D4C22×D311yescharacteristic
327C23×C4—21no—
328C23×C4—21no—
329C23×C4—61no—
330C23×C4C22×D311yescharacteristic
331C23×C4C22×D311yescharacteristic
332C2×D8—62no—
333C2×D8—62no—
334C2×D8—62no—
335C22×C8—31no—
336C22×C8—31no—
337C22×C8—31no—
338C22×C8—31no—
339#126—28no—
340#125—22no—
341#125#6714yescomplemented
342#123—28no—
343#121—28no—
344#121—22no—
345#121—22no—
346#121—22no—
347#121—22no—
348#121—62no—
349#121—62no—
350#121—121no—
351#121—121no—
352#121—124no—
353C4×D4—28no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—62no—
358C4×D4—62no—
359C4×D4#6714yescomplemented
360#117—22no—
361#117—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—61no—
371C2×C4⋊C4—61no—
372C2×C4⋊C4#6711yescharacteristic
373C2×C4⋊C4C22×D311yescharacteristic
374C2×C4⋊C4C22×D311yescharacteristic
375C2×C4⋊C4C22×D311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C22⋊C4#6711yescharacteristic
386C2×C22⋊C4#6711yescharacteristic
387C2×C42—21no—
388C2×C42C22×D311yescharacteristic
389#107—62no—
390#106—62no—
391#106—62no—
392C4⋊C8—62no—
393#102—62no—
394#102—62no—
395#102—62no—
396#102—62no—
397#102—121no—
398#102—121no—
399C22⋊C8—62no—
400C22⋊C8—62no—
401C22⋊C8—121no—
402C22⋊C8—121no—
403#97—62no—
404#95—61no—
405#95—61no—
406C23×C3—21no—
407C23×C3—21no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—22no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—41no—
424C23×C3—41no—
425C23×C3—41no—
426C23×C3AGL(1,ℤ/8)12yes—
427C23×C3C22×D411yescharacteristic
428C22×D3—22no—
429C22×D3—41no—
430C22×D3—41no—
431C22×D3—41no—
432C22×D3—41no—
433C22×D3—41no—
434C22×D3—41no—
435C3×D4—22no—
436C3×D4—22no—
437C3×D4—44no—
438C3×D4—48no—
439C3×D4—41no—
440C3×D4—41no—
441C3×D4—84no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—21no—
450C2×C3×C4—22no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—84no—
470C2×C3×C4—84no—
471C2×C3×C4#12012yes—
472C2×C3×C4#12012yes—
473C2×C3×C4C22×D411yescharacteristic
474C2×C3×C4C22×D411yescharacteristic
475C2×C3×C4C2×#4111yescharacteristic
476C2×C3×C4C2×#4111yescharacteristic
477C2×C3×C4H(5,𝔽2)11yescharacteristic
478C2×C3×C42−1+411yescharacteristic
479#67—84no—
480#67—84no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C2×Dic3—41no—
488C2×Dic3—41no—
489C2×Dic3—41no—
490D12—22no—
491D12—22no—
492D12—41no—
493D12—41no—
494C4×D3—84no—
495C3⋊C8—22no—
496C3⋊C8—41no—
497C3⋊C8—41no—
498C3⋊C8—41no—
499C24—21no—
500C24—61no—
501C24C2×#6711yescharacteristic
502C24C2×#6711yescharacteristic
503C2×D4—24no—
504C2×D4—22no—
505C2×D4—24no—
506C2×D4—22no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—32no—
513C2×D4—41no—
514C2×D4—42no—
515C2×D4—42no—
516C2×D4—61no—
517C2×D4—61no—
518C2×D4—61no—
519C2×D4—61no—
520C2×D4—61no—
521C2×D4—81no—
522C2×D4—81no—
523C2×D4—122no—
524C2×D4—122no—
525C2×D4—122no—
526C2×D4—122no—
527C2×D4—241no—
528C2×D4—241no—
529C2×D4C2×#6712yes—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—61no—
548C22×C4—61no—
549C22×C4—61no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—81no—
554C22×C4—122no—
555C22×C4—122no—
556C22×C4—122no—
557C22×C4C2×#6711yescharacteristic
558C22×C4C2×#6711yescharacteristic
559C22×C4C2×#6711yescharacteristic
560C22×C4C2×#6711yescharacteristic
561C22×C4C23×D311yescharacteristic
562D8—68no—
563C2×C8—32no—
564C2×C8—61no—
565C2×C8—61no—
566C2×C8—61no—
567C2×C8—61no—
568C2×C8—61no—
569C2×C8—61no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—22no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—122no—
589C4⋊C4—241no—
590C4⋊C4C2×#6712yes—
591C4⋊C4C2×#6712yes—
592C4⋊C4C2×#6712yes—
593C22⋊C4—24no—
594C22⋊C4—24no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—122no—
600C22⋊C4—122no—
601C22⋊C4—122no—
602C22⋊C4—122no—
603C22⋊C4—122no—
604C42—24no—
605C42C2×#6712yes—
606C42C2×#6712yes—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—42no—
618C22×C3—41no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—81no—
625C22×C3—81no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3C2×#12011yescharacteristic
629C22×C3#54611yescharacteristic
630C22×C3#54711yescharacteristic
631C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
632C22×C3#57511yescharacteristic
633C22×C3#57611yescharacteristic
634C22×C3#57711yescharacteristic
635C2×D3—42no—
636C2×D3—42no—
637C2×D3—42no—
638C2×D3—81no—
639C2×D3—81no—
640C2×D3—81no—
641C2×D3—81no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4#52511yescharacteristic
650C3×C4#53711yescharacteristic
651C3×C4#54811yescharacteristic
652C3×C4#55011yescharacteristic
653Dic3—81no—
654Dic3—81no—
655Dic3—81no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—62no—
677C23—121no—
678C23—121no—
679C23—121no—
680C23—121no—
681C23—121no—
682C23—121no—
683C23#94912yes—
684C23C22×#6711yescharacteristic
685D4—22no—
686D4—22no—
687D4—44no—
688D4—48no—
689D4—41no—
690D4—41no—
691D4—62no—
692D4—62no—
693D4—84no—
694D4—121no—
695D4—121no—
696D4—244no—
697D4—244no—
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—21no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—41no—
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—41no—
724C2×C4—41no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—121no—
731C2×C4—121no—
732C2×C4—121no—
733C2×C4—121no—
734C2×C4—121no—
735C2×C4—121no—
736C2×C4—244no—
737C2×C4#95312yes—
738C2×C4#95312yes—
739C2×C4D3×#4111yescharacteristic
740C2×C4D3×#4111yescharacteristic
741C2×C4#100911yescharacteristic
742C2×C4#101011yescharacteristic
743C2×C4C22×#6711yescharacteristic
744C2×C4C22×#6711yescharacteristic
745C8—62no—
746C8—121no—
747C8—121no—
748C8—121no—
749C2×C3—42no—
750C2×C3—81no—
751C2×C3—82no—
752C2×C3#240711yescharacteristic
753C2×C3#300611yescharacteristic
754C2×C3#301211yescharacteristic
755C2×C3#330711yescharacteristic
756C2×C3#331811yescharacteristic
757C2×C3#334511yescharacteristic
758C2×C3#334711yescharacteristic
759D3—82no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—42no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—122no—
782C22—122no—
783C22—122no—
784C22—241no—
785C22—241no—
786C22—241no—
787C22—241no—
788C22C2×#94911yescharacteristic
789C22#582211yescharacteristic
790C22#582411yescharacteristic
791C22#582911yescharacteristic
792C22#583511yescharacteristic
793C22#583611yescharacteristic
794C22C2×#95311yescharacteristic
795C4—22no—
796C4—22no—
797C4—42no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—241no—
803C4—241no—
804C4—241no—
805C4#582811yescharacteristic
806C4#583111yescharacteristic
807C4#583311yescharacteristic
808C4#583411yescharacteristic
809C3#2413611yescharacteristic, complemented, Sylow
810C2—42no—
811C2—81no—
812C2—82no—
813C2—242no—
814C2#8360811yescharacteristic
815C2#8361011yescharacteristic
816C2#8361511yescharacteristic
817C2#8361611yescharacteristic
818C2#8408211yescharacteristic
819C2#8409711yescharacteristic
820C2#8410211yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#553C2
socleC23×C3C22×D4
hypercenterC2×#553D3
hypocenterC3#24136
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×C3×#553C2semidirect
2. C2×#5066C2semidirect
3. #82417C2semidirect
4. C2×#5014C2semidirect
5. #71741C2semidirect
6. #71684C2semidirect
7. #71684C2semidirect
8. #71680C2semidirect
9. #71679C2semidirect
10. #71615C2semidirect
11. #71604C2semidirect
12. #71586C2semidirect
13. #71576C2semidirect
14. #71560C2semidirect
15. #71556C2semidirect
64. C2×#553D3semidirect
93. C3×#125D4semidirect
104. C3×C4×D4D4semidirect
341. #125#67semidirect
359. C4×D4#67semidirect
809. C3#24136semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5532
C2×#50662
#824172
C2×#50142
#717412
#716842
#716802
#716792
#716152
#716042
#715862
#715762
#715602
#715562
#241363