Finite Group Databasebeta

← #10827336

Subgroups — #10827336

Order 768.

1690 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5551C211yesmaximal, characteristic, complemented
2C2×#5156C211yesmaximal, characteristic, complemented
3C2×D3×#102C211yesmaximal, characteristic, complemented
4#76436C211yesmaximal, characteristic, complemented
5C3×#1879C211yesmaximal, characteristic, complemented
6#72043C211yesmaximal, characteristic, complemented
7#71613C211yesmaximal, characteristic, complemented
8#70204C211yesmaximal, characteristic, complemented
9#70202C211yesmaximal, characteristic, complemented
10#70200C211yesmaximal, characteristic, complemented
11#69638C211yesmaximal, characteristic, complemented
12#68880C211yesmaximal, characteristic, complemented
13#68871C211yesmaximal, characteristic, complemented
14#68678C211yesmaximal, characteristic, complemented
15#68668C211yesmaximal, characteristic, complemented
16#23960—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×#235—21no—
19C22×C3×D8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic, complemented
21C2×#938C2211yescharacteristic
22C2×#938C2211yescharacteristic
23C2×#938C2211yescharacteristic, complemented
24C22×#213C2211yescharacteristic
25C2×#924—21no—
26C22×D3×C8C2211yescharacteristic
27#5551—24no—
28#5551—24no—
29C2×#895C2211yescharacteristic
30C2×D3×C4⋊C4C2211yescharacteristic
31C2×D3×C4⋊C4C2211yescharacteristic, complemented
32C2×#883—21no—
33C2×#883—21no—
34C2×#882—21no—
35C2×C4×D12C2211yescharacteristic
36C2×#869C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic, complemented
39C3×#390C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic, complemented
43#5156—24no—
44C2×#821C2211yescharacteristic
45C2×#821C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
48C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
49#4987C2211yescharacteristic
50C2×#809C2211yescharacteristic
51#4961—21no—
52#4960—21no—
53#4955—21no—
54#4939C2211yescharacteristic
55D3×#102—24no—
56C3×#340C2211yescharacteristic, complemented
57C3×#336C2211yescharacteristic, complemented
58#4551C2211yescharacteristic, complemented
59#4551C2211yescharacteristic, complemented
60#4529C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4524C2211yescharacteristic, complemented
64C2×#547—31no—
65C2×#447—31no—
66C22×#102—31no—
67#2408—31no—
68#2023—31no—
69#2023—31no—
70#1999—31no—
71#1999—31no—
72#1893—31no—
73#1879—31no—
74#1879D311yescharacteristic, complemented
75#1874—31no—
76#1874—31no—
77#1869—31no—
78#1823—31no—
79C24×D3—21no—
80C22×C3×D4C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C22×#67—21no—
84C22×#67—21no—
85C22×#67—21no—
86C22×#67—21no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—41no—
92C2×D3×D4—41no—
93C2×#235—28no—
94C2×#235—44no—
95C2×#235—44no—
96C22×D12—21no—
97C22×D12D411yescharacteristic
98C22×D12C2311yescharacteristic
99C22×C4×D3—21no—
100C22×C4×D3—21no—
101C22×C4×D3C2311yescharacteristic
102C22×C4×D3C2311yescharacteristic
103C22×Dic6—21no—
104C2×C3×D8—22no—
105C2×C3×D8—22no—
106C2×C3×D8—41no—
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C3×C4×D4—22no—
110C3×C4×D4—22no—
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C42C2311yescharacteristic
117C2×#217—21no—
118C2×#217—21no—
119C2×#217—21no—
120#938—22no—
121#938—22no—
122#938—22no—
123#938—22no—
124#938—41no—
125#938D414yescomplemented
126C2×#213—22no—
127C2×#213—22no—
128C2×#213—41no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4D411yescharacteristic
134C2×(C2×D3)⋊C4D411yescharacteristic
135C2×C4⋊Dic3—21no—
136C2×C4⋊Dic3D411yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140#924—28no—
141C2×Dic3⋊C4—21no—
142C2×Dic3⋊C4—21no—
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×D3×C8—22no—
146C2×D3×C8—41no—
147C2×D3×C8—41no—
148#895—22no—
149#895—41no—
150D3×C4⋊C4—22no—
151D3×C4⋊C4—22no—
152D3×C4⋊C4—22no—
153D3×C4⋊C4D414yescomplemented
154#883—28no—
155#883—28no—
156#882—44no—
157C4×D12—22no—
158C4×D12—22no—
159#869—22no—
160#869—22no—
161C3×#102—22no—
162C3×#102—41no—
163#832—22no—
164#832—22no—
165#832—41no—
166C3⋊#95—21no—
167#821—22no—
168#821—22no—
169(C2×D3)⋊C8—22no—
170(C2×D3)⋊C8—41no—
171(C2×D3)⋊C8—41no—
172#809—22no—
173C22×#41—61no—
174C23×D4—31no—
175C22×D8—31no—
176C22×D8C2×D311yescharacteristic
177C23×C8—31no—
178#547—64no—
179#547—64no—
180C2×C4⋊Q8—31no—
181C2×#123—61no—
182C2×#123—61no—
183C2×C22⋊Q8—61no—
184C2×#121—31no—
185C2×#121—31no—
186C2×#121—31no—
187C2×#121—31no—
188C2×#120—61no—
189C2×C4×D4—31no—
190C2×C4×D4C2×D311yescharacteristic, complemented
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193#447—64no—
194C2×#102—31no—
195C2×#102—31no—
196C2×#102—31no—
197C2×#102—31no—
198C2×#102—31no—
199C2×#102—31no—
200C2×#102—64no—
201C2×#102C2×D311yescharacteristic
202C2×#102C2×D311yescharacteristic, complemented
203C2×C22⋊C8—31no—
204C2×C22⋊C8—31no—
205C2×C22⋊C8—31no—
206#394—61no—
207#392—61no—
208#390—31no—
209#390C2×D311yescharacteristic
210#380—31no—
211#379—61no—
212#340—31no—
213#340—31no—
214#340—31no—
215#340—31no—
216#340—31no—
217#340C2×D311yescharacteristic, complemented
218#336—31no—
219#336C2×D311yescharacteristic, complemented
220C24×C3—21no—
221C24×C3—21no—
222C23×D3—21no—
223C23×D3—42no—
224C23×D3—42no—
225C23×D3—42no—
226C23×D3—42no—
227C23×D3—42no—
228C23×D3—81no—
229C23×D3—81no—
230C23×D3C2×D411yescharacteristic
231C23×D3C2×D411yescharacteristic
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4C2×D412yes—
243C2×C3×D4#4112yescomplemented
244C22×C3×C4—24no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—42no—
248C22×C3×C4—42no—
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2411yescharacteristic
252C2×#67—24no—
253C2×#67—24no—
254C2×#67—42no—
255C2×#67—42no—
256C2×#67—42no—
257C2×#67—42no—
258C2×#67—42no—
259C2×#67—42no—
260C2×#67—42no—
261C2×#67—42no—
262C2×#67—42no—
263C2×#67—81no—
264C22×Dic3—21no—
265C22×Dic3—21no—
266C22×Dic3—21no—
267C22×Dic3C2×D411yescharacteristic
268C22×Dic3C2×D411yescharacteristic
269D3×D4—28no—
270D3×D4—44no—
271D3×D4—44no—
272D3×D4—44no—
273#235—432no—
274C2×D12—22no—
275C2×D12—22no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—42no—
282C2×D12—42no—
283C2×D12—81no—
284C2×D12D814yescomplemented
285C2×D12#4112yescomplemented
286C2×C4×D3—21no—
287C2×C4×D3—21no—
288C2×C4×D3—21no—
289C2×C4×D3—21no—
290C2×C4×D3—24no—
291C2×C4×D3—24no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—42no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3—42no—
302C2×C4×D3C2×D412yes—
303C2×C4×D3C2×D412yes—
304C2×Dic6—24no—
305C2×Dic6—42no—
306C2×Dic6—42no—
307C3×D8—44no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C3×C4⋊C4—21no—
315C3×C4⋊C4—21no—
316C3×C4⋊C4—21no—
317C3×C4⋊C4C2×D412yes—
318C3×C22⋊C4—24no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—81no—
321C3×C42—21no—
322C3×C42—21no—
323#217—24no—
324#217—24no—
325#217—42no—
326#213—44no—
327(C2×D3)⋊C4—22no—
328(C2×D3)⋊C4—22no—
329(C2×D3)⋊C4—42no—
330(C2×D3)⋊C4—42no—
331(C2×D3)⋊C4—42no—
332(C2×D3)⋊C4—81no—
333C4⋊Dic3—24no—
334C4⋊Dic3—21no—
335C4⋊Dic3—21no—
336C4⋊Dic3—22no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3C2×D412yes—
340C4⋊Dic3C2×D412yes—
341Dic3⋊C4—24no—
342Dic3⋊C4—24no—
343C2×C3⋊C8—21no—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349D3×C8—44no—
350C25—61no—
351C2×#41—68no—
352C2×#41—124no—
353C2×#41—124no—
354C22×Q8—61no—
355C22×D4—31no—
356C22×D4—31no—
357C22×D4—61no—
358C22×D4—62no—
359C22×D4—62no—
360C22×D4—61no—
361C22×D4—62no—
362C22×D4—62no—
363C22×D4—61no—
364C22×D4—61no—
365C22×D4—61no—
366C22×D4—121no—
367C22×D4—121no—
368C22×D4C22×D311yescharacteristic
369C22×D4C22×D311yescharacteristic
370C23×C4—21no—
371C23×C4—31no—
372C23×C4—31no—
373C23×C4—61no—
374C23×C4—61no—
375C2×D8—22no—
376C2×D8—22no—
377C2×D8—41no—
378C2×D8—62no—
379C2×D8—62no—
380C2×D8—121no—
381C22×C8—31no—
382C22×C8—31no—
383C22×C8—62no—
384C22×C8—121no—
385C22×C8—121no—
386C22×C8C22×D311yescharacteristic
387C22×C8C22×D311yescharacteristic
388C4⋊Q8—62no—
389C4⋊Q8—62no—
390#123—68no—
391#123—68no—
392C22⋊Q8—68no—
393#121—34no—
394#121—62no—
395#121—62no—
396#121—62no—
397#121—62no—
398#121—62no—
399#121—121no—
400#121—121no—
401#120—124no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4—62no—
405C4×D4—62no—
406C2×C4⋊C4—31no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—62no—
412C2×C4⋊C4—62no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4—62no—
417C2×C4⋊C4C22×D311yescharacteristic
418C2×C4⋊C4C22×D311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—31no—
423C2×C22⋊C4—31no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C42C22×D311yescharacteristic
432#102—22no—
433#102—41no—
434#102—62no—
435#102—62no—
436#102—62no—
437#102—62no—
438#102—62no—
439#102—121no—
440C22⋊C8—62no—
441C22⋊C8—121no—
442C22⋊C8—121no—
443#95—61no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3—41no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3C22×D411yescharacteristic
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3—22no—
470C22×D3—48no—
471C22×D3—41no—
472C22×D3—41no—
473C22×D3—41no—
474C22×D3—41no—
475C22×D3—41no—
476C22×D3—41no—
477C22×D3—84no—
478C22×D3—84no—
479C22×D3—84no—
480C22×D3—84no—
481C22×D3—84no—
482C22×D3—84no—
483C22×D3#12012yes—
484C22×D3C2×D812yes—
485C22×D3C2×D812yes—
486C22×D3AGL(1,ℤ/8)12yes—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—22no—
490C3×D4—22no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—41no—
494C3×D4—41no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—22no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—48no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4C2×D812yes—
508C2×C3×C4C22×D411yescharacteristic
509C2×C3×C4C22×D411yescharacteristic
510C2×C3×C4C2×#4111yescharacteristic
511C2×C3×C4C2×#4111yescharacteristic
512C2×C3×C4H(5,𝔽2)11yescharacteristic
513C2×C3×C4H(5,𝔽2)11yescharacteristic
514#67—48no—
515#67—48no—
516#67—48no—
517#67—84no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—41no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3#12012yes—
533D12—28no—
534D12—22no—
535D12—22no—
536D12—41no—
537D12—41no—
538D12—84no—
539C4×D3—22no—
540C4×D3—22no—
541C4×D3—22no—
542C4×D3—22no—
543C4×D3—48no—
544C4×D3—48no—
545C4×D3—41no—
546C4×D3—41no—
547C4×D3—41no—
548C4×D3—41no—
549Dic6—48no—
550C3×C8—41no—
551C3×C8—41no—
552C3⋊C8—41no—
553C3⋊C8—41no—
554C24—21no—
555C24—21no—
556C24—31no—
557C24—31no—
558C24—61no—
559C24—122no—
560C24—122no—
561C24—122no—
562C24—122no—
563C24—122no—
564C24—241no—
565C24—241no—
566#41—1232no—
567C2×Q8—64no—
568C2×Q8—122no—
569C2×Q8—122no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—34no—
581C2×D4—32no—
582C2×D4—62no—
583C2×D4—62no—
584C2×D4—68no—
585C2×D4—64no—
586C2×D4—64no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—122no—
593C2×D4—122no—
594C2×D4—122no—
595C2×D4—124no—
596C2×D4—124no—
597C2×D4—124no—
598C2×D4—122no—
599C2×D4—122no—
600C2×D4—122no—
601C2×D4—122no—
602C2×D4—122no—
603C2×D4—122no—
604C2×D4—122no—
605C2×D4—122no—
606C2×D4—241no—
607C2×D4—241no—
608C2×D4#23512yescomplemented
609C2×D4D3×D412yes—
610C22×C4—24no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—31no—
614C22×C4—32no—
615C22×C4—32no—
616C22×C4—31no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—64no—
620C22×C4—64no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—61no—
627C22×C4—61no—
628C22×C4—61no—
629C22×C4—61no—
630C22×C4—61no—
631C22×C4—61no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—122no—
635C22×C4—122no—
636C22×C4—122no—
637C22×C4—122no—
638C22×C4D3×D411yescharacteristic
639C22×C4D3×D411yescharacteristic
640C22×C4C23×D311yescharacteristic
641D8—44no—
642D8—124no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—61no—
650C2×C8—61no—
651C2×C8—61no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—124no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—32no—
660C4⋊C4—32no—
661C4⋊C4—64no—
662C4⋊C4—62no—
663C4⋊C4—64no—
664C4⋊C4—64no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4D3×D412yes—
670C22⋊C4—24no—
671C22⋊C4—42no—
672C22⋊C4—62no—
673C22⋊C4—62no—
674C22⋊C4—64no—
675C22⋊C4—64no—
676C22⋊C4—81no—
677C22⋊C4—122no—
678C22⋊C4—122no—
679C22⋊C4—122no—
680C22⋊C4—122no—
681C22⋊C4—241no—
682C42—21no—
683C42—21no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—42no—
687C22×C3—42no—
688C22×C3—42no—
689C22×C3—42no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3C2×#12011yescharacteristic
699C22×C3#54611yescharacteristic
700C22×C3#54611yescharacteristic
701C22×C3C22×D811yescharacteristic
702C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
703C22×C3#57711yescharacteristic
704C22×C3#57711yescharacteristic
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—22no—
708C2×D3—22no—
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3—42no—
721C2×D3—816no—
722C2×D3—81no—
723C2×D3—81no—
724C2×D3—81no—
725C2×D3—81no—
726C2×D3#44714yes—
727C3×C4—22no—
728C3×C4—42no—
729C3×C4—41no—
730C3×C4—81no—
731C3×C4#52511yescharacteristic
732C3×C4#53511yescharacteristic
733C3×C4#54611yescharacteristic
734C3×C4#54611yescharacteristic
735Dic3—22no—
736Dic3—41no—
737Dic3—42no—
738Dic3—42no—
739Dic3—81no—
740C23—22no—
741C23—22no—
742C23—32no—
743C23—32no—
744C23—32no—
745C23—32no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—61no—
762C23—61no—
763C23—61no—
764C23—61no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—62no—
769C23—128no—
770C23—121no—
771C23—121no—
772C23—121no—
773C23—121no—
774C23—121no—
775C23—121no—
776C23—244no—
777C23—244no—
778C23—244no—
779C23—244no—
780C23—244no—
781C23—244no—
782C23C2×D3×D411yescharacteristic
783Q8—128no—
784D4—22no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—68no—
793D4—62no—
794D4—62no—
795D4—128no—
796D4—128no—
797D4—128no—
798D4—121no—
799D4—121no—
800D4—244no—
801D4—244no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—32no—
809C2×C4—48no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—62no—
818C2×C4—62no—
819C2×C4—62no—
820C2×C4—62no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—61no—
826C2×C4—128no—
827C2×C4—128no—
828C2×C4—121no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—121no—
834C2×C4—121no—
835C2×C4—121no—
836C2×C4—121no—
837C2×C4—121no—
838C2×C4—121no—
839C2×C4D3×D812yes—
840C2×C4C2×#23511yescharacteristic
841C2×C4C2×D3×D411yescharacteristic
842C2×C4C2×D3×D411yescharacteristic
843C2×C4#100411yescharacteristic
844C2×C4D3×#4111yescharacteristic
845C2×C4#100911yescharacteristic
846C8—41no—
847C8—41no—
848C8—121no—
849C8—121no—
850C2×C3—82no—
851C2×C3—82no—
852C2×C3#240411yescharacteristic
853C2×C3C2×#44711yescharacteristic
854C2×C3#301011yescharacteristic
855C2×C3#329411yescharacteristic
856C2×C3#329411yescharacteristic
857C2×C3#330611yescharacteristic
858C2×C3#330611yescharacteristic
859D3—24no—
860D3—42no—
861D3—82no—
862C22—34no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—62no—
870C22—62no—
871C22—62no—
872C22—62no—
873C22—62no—
874C22—62no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—121no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—122no—
891C22—122no—
892C22—122no—
893C22—2416no—
894C22—241no—
895C22—241no—
896C22—241no—
897C22—241no—
898C22#555011yescharacteristic
899C22D3×#12011yescharacteristic
900C22#561211yescharacteristic
901C22C2×D3×D811yescharacteristic
902C22#577011yescharacteristic
903C22D3×AGL(1,ℤ/8)11yescharacteristic
904C22#577511yescharacteristic
905C4—22no—
906C4—42no—
907C4—41no—
908C4—62no—
909C4—81no—
910C4—122no—
911C4—122no—
912C4—121no—
913C4—241no—
914C4#549011yescharacteristic
915C4#554711yescharacteristic
916C4#560711yescharacteristic
917C4#565411yescharacteristic
918C3#2396011yescharacteristic, complemented, Sylow
919C2—64no—
920C2—82no—
921C2—82no—
922C2—122no—
923C2—242no—
924C2#7488611yescharacteristic
925C2#7960811yescharacteristic
926C2#7988011yescharacteristic
927C2D3×#44711yescharacteristic
928C2#8008611yescharacteristic
929C2#8035211yescharacteristic
930C2#8056111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1879C2
socleC23×C3C22×D4
hypercenter#1879D3
hypocenterC3#23960
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. C2×#5551C2semidirect
2. C2×#5156C2semidirect
3. C2×D3×#102C2semidirect
4. #76436C2semidirect
5. C3×#1879C2semidirect
6. #72043C2semidirect
7. #71613C2semidirect
8. #70204C2semidirect
9. #70202C2semidirect
10. #70200C2semidirect
11. #69638C2semidirect
12. #68880C2semidirect
13. #68871C2semidirect
14. #68678C2semidirect
15. #68668C2semidirect
20. C2×C3×C4×D4C22semidirect
23. C2×#938C22semidirect
31. C2×D3×C4⋊C4C22semidirect
36. C2×#869C22semidirect
38. C2×C3×#102C22semidirect
42. C2×#832C22semidirect
47. C2×(C2×D3)⋊C8C22semidirect
48. C2×(C2×D3)⋊C8C22semidirect
56. C3×#340C22semidirect
57. C3×#336C22semidirect
58. #4551C22semidirect
59. #4551C22semidirect
60. #4529C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4524C22semidirect
74. #1879D3semidirect
125. #938D4semidirect
153. D3×C4⋊C4D4semidirect
190. C2×C4×D4C2×D3semidirect
202. C2×#102C2×D3semidirect
217. #340C2×D3semidirect
219. #336C2×D3semidirect
243. C2×C3×D4#41semidirect
284. C2×D12D8semidirect
285. C2×D12#41semidirect
608. C2×D4#235semidirect
918. C3#23960semidirect

Maximal subgroups

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

subgroupindex
C2×#55512
C2×#51562
C2×D3×#1022
#764362
C3×#18792
#720432
#716132
#702042
#702022
#702002
#696382
#688802
#688712
#686782
#686682
#239603