Finite Group Databasebeta

← #10830637

Subgroups — #10830637

Order 768.

1628 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5550C211yesmaximal, characteristic, complemented
2#82415C211yesmaximal, characteristic, complemented
3C2×#4844C211yesmaximal, characteristic, complemented
4C2×#4734C211yesmaximal, characteristic, complemented
5C2×#4732C211yesmaximal, characteristic, complemented
6C2×C4×D24C211yesmaximal, characteristic, complemented
7C3×#1954C211yesmaximal, characteristic, complemented
8#70480C211yesmaximal, characteristic, complemented
9#69962C211yesmaximal, characteristic, complemented
10#69961C211yesmaximal, characteristic, complemented
11#69960C211yesmaximal, characteristic, complemented
12#69959C211yesmaximal, characteristic, complemented
13#69937C211yesmaximal, characteristic, complemented
14#69934C211yesmaximal, characteristic, complemented
15#69773C211yesmaximal, characteristic, complemented
16#24245—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#937—21no—
21C2×#930C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#930C2211yescharacteristic, complemented
24C2×#924C2211yescharacteristic
25C22×D24C2211yescharacteristic
26C22×D24C2211yescharacteristic
27C22×#204C2211yescharacteristic, complemented
28#5550—24no—
29#5550—24no—
30C2×#894—21no—
31C2×#884—21no—
32C2×D3×C22⋊C4—21no—
33C2×#875C2211yescharacteristic
34C2×C4×D12C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic, complemented
36C2×C3×C4⋊C8C2211yescharacteristic, complemented
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40C2×C3×C22⋊C8C2211yescharacteristic, complemented
41C2×C3×C4×C8C2211yescharacteristic, complemented
42#5223—21no—
43#5212C2211yescharacteristic
44#5212C2211yescharacteristic, complemented
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C2×#821C2211yescharacteristic
50C2×#821C2211yescharacteristic
51C2×#821C2211yescharacteristic, complemented
52C2×#818C2211yescharacteristic, complemented
53C2×#816C2211yescharacteristic, complemented
54C2×#816C2211yescharacteristic, complemented
55C2×#816C2211yescharacteristic, complemented
56#4992—21no—
57#4956—21no—
58#4956—21no—
59#4936C2211yescharacteristic, complemented
60#4844—24no—
61#4734—24no—
62#4732—24no—
63C4×D24—24no—
64#4551C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#463—31no—
68C2×#449—31no—
69C2×#447—31no—
70C2×C4×D8—31no—
71#2535—31no—
72#2036—31no—
73#2033—31no—
74#2000—31no—
75#1999—31no—
76#1958—31no—
77#1954D311yescharacteristic, complemented
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×D4D411yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C22×#67—21no—
88C22×#67—21no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—22no—
93C2×#235—41no—
94C2×#235—41no—
95C22×D12—21no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—22no—
100C22×D12—41no—
101C22×D12—41no—
102C22×D12C2311yescharacteristic
103C22×D12C2311yescharacteristic
104C22×D12C2311yescharacteristic
105C22×C4×D3—21no—
106C22×C4×D3—21no—
107C22×C4×D3—21no—
108C22×Dic6C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C3×C4×D4—22no—
114C3×C4×D4—22no—
115C2×C3×C4⋊C4D411yescharacteristic
116C2×C3×C22⋊C4D411yescharacteristic
117C2×C3×C22⋊C4D411yescharacteristic
118C2×C3×C42C2311yescharacteristic
119C2×#217—21no—
120C2×#217—21no—
121C2×#217—21no—
122#937—28no—
123#930—22no—
124#930—22no—
125#930—22no—
126#930—22no—
127#930—41no—
128#930—41no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140#924—22no—
141#924—22no—
142C2×Dic3⋊C4—21no—
143C2×D24—22no—
144C2×D24—22no—
145C2×D24—22no—
146C2×D24—22no—
147C2×D24—41no—
148C2×D24D414yescomplemented
149C2×#204—22no—
150C2×#204—22no—
151C2×#204—41no—
152#894—28no—
153#884—28no—
154D3×C22⋊C4—28no—
155#875—22no—
156#875D414yescomplemented
157C4×D12—22no—
158C4×D12—22no—
159C4×D12—22no—
160C4×D12D414yescomplemented
161C3×C4⋊C8—22no—
162C3×C22⋊C8—22no—
163C3×C22⋊C8—22no—
164C3×C22⋊C8—41no—
165C3×C22⋊C8—41no—
166C3×C4×C8—22no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#821—22no—
172#821—22no—
173#821—22no—
174#821—22no—
175#821—22no—
176#821—22no—
177#821—41no—
178#818—22no—
179#816—22no—
180#816—22no—
181#816—41no—
182C22×#41—31no—
183C23×D4—31no—
184C22×SD16—31no—
185C22×D8—31no—
186C22×D8—31no—
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×D4—31no—
198C2×C4×D4—31no—
199C2×C4×D4C2×D311yescharacteristic
200C22×C22⋊C4—61no—
201#463—64no—
202#449—64no—
203#447—64no—
204C4×D8—64no—
205C2×#107—31no—
206C2×C4⋊C8C2×D311yescharacteristic, complemented
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#102—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102—31no—
216C2×#102—31no—
217C2×C22⋊C8C2×D311yescharacteristic
218C2×C22⋊C8C2×D311yescharacteristic
219C2×C22⋊C8C2×D311yescharacteristic, complemented
220C2×C22⋊C8C2×D311yescharacteristic, complemented
221C2×C4×C8C2×D311yescharacteristic, complemented
222#397—61no—
223#392—61no—
224#386—61no—
225#386—61no—
226#382—31no—
227#380—31no—
228#380—31no—
229#340—31no—
230#340—31no—
231C24×C3C2×D411yescharacteristic
232C24×C3C2×D411yescharacteristic
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—21no—
236C23×D3—24no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—42no—
240C23×D3—42no—
241C23×D3—81no—
242C23×D3—81no—
243C2×C3×D4—22no—
244C2×C3×D4—22no—
245C2×C3×D4—41no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2411yescharacteristic
263C2×#67—24no—
264C2×#67—24no—
265C2×#67—42no—
266C2×#67—42no—
267C2×#67—42no—
268C2×#67—42no—
269C2×#67—42no—
270C2×#67—42no—
271C2×#67—81no—
272C2×#67—81no—
273C2×#67—81no—
274C2×#67—81no—
275C22×Dic3—21no—
276C22×Dic3—21no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280#235—44no—
281#235—44no—
282#235—44no—
283#235—44no—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12—21no—
289C2×D12—21no—
290C2×D12—21no—
291C2×D12—21no—
292C2×D12—21no—
293C2×D12—21no—
294C2×D12—21no—
295C2×D12—24no—
296C2×D12—21no—
297C2×D12—21no—
298C2×D12—44no—
299C2×D12—44no—
300C2×D12—44no—
301C2×D12—42no—
302C2×D12—42no—
303C2×D12—44no—
304C2×D12C2×D412yes—
305C2×D12C2×D412yes—
306C2×D12C2×D412yes—
307C2×D12C2×D412yes—
308C2×D12#4112yes—
309C2×C4×D3—24no—
310C2×C4×D3—24no—
311C2×C4×D3—42no—
312C2×C4×D3—42no—
313C2×C4×D3—42no—
314C2×C4×D3—81no—
315C2×C4×D3—81no—
316C2×C4×D3—81no—
317C2×C4×D3—81no—
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6—21no—
321C2×Dic6—21no—
322C2×Dic6—21no—
323C2×Dic6C2×D412yes—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8C2×D412yes—
336C3×C4⋊C4—22no—
337C3×C22⋊C4—22no—
338C3×C22⋊C4—22no—
339C3×C42C2×D412yes—
340C3×C42C2×D412yes—
341#217—24no—
342#217—81no—
343#217—81no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—24no—
346(C2×D3)⋊C4—24no—
347(C2×D3)⋊C4—24no—
348(C2×D3)⋊C4—42no—
349(C2×D3)⋊C4—42no—
350(C2×D3)⋊C4—42no—
351C4⋊Dic3—21no—
352C4⋊Dic3—21no—
353C4⋊Dic3—21no—
354C4⋊Dic3—21no—
355C4⋊Dic3—21no—
356C4⋊Dic3—21no—
357C4⋊Dic3—21no—
358C4⋊Dic3C2×D412yes—
359Dic3⋊C4—24no—
360D24—28no—
361D24—44no—
362#204—44no—
363C25—61no—
364C2×#41—62no—
365C2×#41—62no—
366C2×#41—62no—
367C2×#41—62no—
368C2×#41—121no—
369C2×#41—121no—
370C22×Q8—31no—
371C22×D4—31no—
372C22×D4—31no—
373C22×D4—31no—
374C22×D4—62no—
375C22×D4—62no—
376C22×D4—62no—
377C22×D4—62no—
378C22×D4—61no—
379C22×D4—61no—
380C22×D4—61no—
381C22×D4—61no—
382C22×D4—61no—
383C22×D4—121no—
384C22×D4—121no—
385C22×D4D1211yescharacteristic
386C23×C4—61no—
387C23×C4—61no—
388C23×C4—61no—
389C23×C4C22×D311yescharacteristic
390C23×C4C22×D311yescharacteristic
391C2×SD16—62no—
392C2×SD16—62no—
393C2×SD16—121no—
394C2×D8—34no—
395C2×D8—62no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—62no—
399C2×D8—121no—
400C22×C8C22×D311yescharacteristic
401C22×C8C22×D311yescharacteristic
402C22×C8C22×D311yescharacteristic
403C22×C8C22×D311yescharacteristic
404#124—34no—
405#124—62no—
406#123—68no—
407C22⋊Q8—62no—
408C22⋊Q8—62no—
409#121—68no—
410#121—62no—
411#121—62no—
412#121—62no—
413#121—62no—
414#121—121no—
415#121—121no—
416#120—68no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—34no—
420C4×D4—62no—
421C4×D4—62no—
422C4×D4—62no—
423C2×C4⋊C4—31no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—61no—
428C2×C4⋊C4D1211yescharacteristic
429C2×C22⋊C4—68no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C22⋊C4D1211yescharacteristic
441C2×C22⋊C4D1211yescharacteristic
442C2×C42C22×D311yescharacteristic
443#107—62no—
444C4⋊C8—22no—
445#103—62no—
446#103—62no—
447#103—121no—
448#102—62no—
449#102—62no—
450#102—62no—
451#102—62no—
452#102—62no—
453#102—62no—
454#102—121no—
455C22⋊C8—22no—
456C22⋊C8—22no—
457C22⋊C8—41no—
458C22⋊C8—41no—
459C4×C8—22no—
460#95—61no—
461#95—61no—
462#95—61no—
463#95—61no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3#13512yes—
478C23×C3C22×D411yescharacteristic
479C22×D3—22no—
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—22no—
483C22×D3—22no—
484C22×D3—48no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—48no—
490C22×D3—41no—
491C22×D3—41no—
492C22×D3—41no—
493C22×D3—41no—
494C22×D3—41no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—41no—
502C22×D3—84no—
503C22×D3—84no—
504C22×D3—84no—
505C22×D3—84no—
506C22×D3—84no—
507C3×D4—44no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4#12012yes—
527C2×C3×C4#12012yes—
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C22×D411yescharacteristic
530C2×C3×C4C22×D411yescharacteristic
531C2×C3×C4C2×#4111yescharacteristic
532C2×C3×C4H(5,𝔽2)11yescharacteristic
533C2×C3×C4H(5,𝔽2)11yescharacteristic
534#67—48no—
535#67—84no—
536#67—84no—
537#67—84no—
538C2×Dic3—22no—
539C2×Dic3—22no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3—41no—
545C2×Dic3—41no—
546C2×Dic3—41no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553D12—22no—
554D12—22no—
555D12—22no—
556D12—22no—
557D12—22no—
558D12—22no—
559D12—22no—
560D12—48no—
561D12—41no—
562D12—41no—
563D12—41no—
564D12—41no—
565D12#12114yes—
566C4×D3—48no—
567C4×D3—84no—
568C4×D3—84no—
569Dic6—22no—
570Dic6—22no—
571Dic6—41no—
572Dic6—41no—
573C3×C8—22no—
574C3×C8—41no—
575C3×C8—41no—
576C3×C8—41no—
577C24—64no—
578C24—61no—
579C24—61no—
580C24—61no—
581C24—122no—
582C24—122no—
583C24—122no—
584C24—122no—
585C24—241no—
586C24—241no—
587C24C2×D1211yescharacteristic
588C24C2×D1211yescharacteristic
589#41—124no—
590#41—124no—
591#41—124no—
592#41—124no—
593C2×Q8—32no—
594C2×Q8—61no—
595C2×Q8—61no—
596C2×Q8—61no—
597C2×Q8—61no—
598C2×Q8—61no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—32no—
602C2×D4—32no—
603C2×D4—32no—
604C2×D4—32no—
605C2×D4—32no—
606C2×D4—41no—
607C2×D4—64no—
608C2×D4—64no—
609C2×D4—64no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—61no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—61no—
622C2×D4—61no—
623C2×D4—122no—
624C2×D4—122no—
625C2×D4—124no—
626C2×D4—124no—
627C2×D4—124no—
628C2×D4—124no—
629C2×D4—122no—
630C2×D4—122no—
631C2×D4—122no—
632C2×D4—122no—
633C2×D4—122no—
634C2×D4—122no—
635C2×D4—241no—
636C2×D4—241no—
637C2×D4—241no—
638C2×D4—241no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—64no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—64no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—122no—
659C22×C4—122no—
660C22×C4—122no—
661C22×C4—241no—
662C22×C4—241no—
663C22×C4—241no—
664C22×C4—241no—
665C22×C4C2×D1211yescharacteristic
666C22×C4C2×D1211yescharacteristic
667C22×C4C2×D1211yescharacteristic
668C22×C4C2×D1211yescharacteristic
669C22×C4C23×D311yescharacteristic
670SD16—124no—
671D8—68no—
672D8—124no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8D3×D412yes—
685C4⋊C4—22no—
686C4⋊C4—32no—
687C4⋊C4—64no—
688C4⋊C4—61no—
689C4⋊C4—61no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—64no—
698C22⋊C4—64no—
699C22⋊C4—64no—
700C22⋊C4—64no—
701C22⋊C4—64no—
702C22⋊C4—122no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—241no—
706C22⋊C4—241no—
707C42D3×D412yes—
708C42D3×D412yes—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3C2×#12011yescharacteristic
724C22×C3D4211yescharacteristic
725C22×C3#54611yescharacteristic
726C22×C3C2×#13511yescharacteristic
727C22×C3#57511yescharacteristic
728C22×C3#57611yescharacteristic
729C22×C3#57611yescharacteristic
730C2×D3—24no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—42no—
734C2×D3—42no—
735C2×D3—42no—
736C2×D3—42no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—42no—
741C2×D3—42no—
742C2×D3—42no—
743C2×D3—816no—
744C2×D3—81no—
745C2×D3—81no—
746C2×D3—81no—
747C2×D3—81no—
748C2×D3—81no—
749C2×D3—81no—
750C2×D3—81no—
751C2×D3—81no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4C2×#12111yescharacteristic
757C3×C4#53511yescharacteristic
758C3×C4D4211yescharacteristic
759C3×C4#54611yescharacteristic
760Dic3—42no—
761Dic3—42no—
762Dic3—81no—
763Dic3—81no—
764Dic3—81no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—62no—
779C23—62no—
780C23—62no—
781C23—62no—
782C23—62no—
783C23—128no—
784C23—128no—
785C23—121no—
786C23—121no—
787C23—121no—
788C23—121no—
789C23—121no—
790C23—121no—
791C23—121no—
792C23—121no—
793C23—121no—
794C23—121no—
795C23—121no—
796C23—121no—
797C23—121no—
798C23—121no—
799C23—121no—
800C23—121no—
801C23—244no—
802C23—244no—
803C23—244no—
804C23—244no—
805C23—244no—
806C23#90412yes—
807C23C22×D1211yescharacteristic
808Q8—62no—
809Q8—62no—
810Q8—121no—
811Q8—121no—
812D4—34no—
813D4—44no—
814D4—62no—
815D4—62no—
816D4—62no—
817D4—62no—
818D4—62no—
819D4—62no—
820D4—62no—
821D4—128no—
822D4—128no—
823D4—121no—
824D4—121no—
825D4—121no—
826D4—121no—
827D4—244no—
828D4—244no—
829D4—244no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—62no—
849C2×C4—62no—
850C2×C4—128no—
851C2×C4—121no—
852C2×C4—121no—
853C2×C4—121no—
854C2×C4—121no—
855C2×C4—121no—
856C2×C4—121no—
857C2×C4—121no—
858C2×C4—121no—
859C2×C4—121no—
860C2×C4—121no—
861C2×C4—121no—
862C2×C4—121no—
863C2×C4—121no—
864C2×C4—244no—
865C2×C4—244no—
866C2×C4#88212yes—
867C2×C4#88212yes—
868C2×C4C2×D3×D411yescharacteristic
869C2×C4C2×D3×D411yescharacteristic
870C2×C4C2×D3×D411yescharacteristic
871C2×C4#100411yescharacteristic
872C2×C4D3×#4111yescharacteristic
873C2×C4#100911yescharacteristic
874C8—22no—
875C8—41no—
876C8—41no—
877C8—41no—
878C2×C3—42no—
879C2×C3—81no—
880C2×C3#240811yescharacteristic
881C2×C3#300211yescharacteristic
882C2×C3#300811yescharacteristic
883C2×C3#327311yescharacteristic
884C2×C3#328011yescharacteristic
885C2×C3#329711yescharacteristic
886C2×C3#332211yescharacteristic
887D3—44no—
888D3—82no—
889D3—82no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—64no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—122no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—122no—
916C22—122no—
917C22—2416no—
918C22—241no—
919C22—241no—
920C22—241no—
921C22—241no—
922C22—241no—
923C22—241no—
924C22—241no—
925C22—241no—
926C22C2×#88211yescharacteristic
927C22D4×D1211yescharacteristic
928C22#555411yescharacteristic
929C22C2×#90411yescharacteristic
930C22#574811yescharacteristic
931C22#575211yescharacteristic
932C22#575211yescharacteristic
933C4—22no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—122no—
938C4—122no—
939C4—241no—
940C4—241no—
941C4—241no—
942C4D3×#12111yescharacteristic
943C4#560711yescharacteristic
944C4#567611yescharacteristic
945C4#571711yescharacteristic
946C3#2424511yescharacteristic, complemented, Sylow
947C2—42no—
948C2—81no—
949C2—124no—
950C2—242no—
951C2—242no—
952C2#7643611yescharacteristic
953C2#7861011yescharacteristic
954C2#7867011yescharacteristic
955C2#7943311yescharacteristic
956C2#7944111yescharacteristic
957C2#7954911yescharacteristic
958C2#7955311yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1954C2
socleC23×C3C22×D4
hypercenter#1954D3
hypocenterC3#24245
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1954

Complements

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

NH ≅ G/Ntype
1. C2×#5550C2semidirect
2. #82415C2semidirect
3. C2×#4844C2semidirect
4. C2×#4734C2semidirect
5. C2×#4732C2semidirect
6. C2×C4×D24C2semidirect
7. C3×#1954C2semidirect
8. #70480C2semidirect
9. #69962C2semidirect
10. #69961C2semidirect
11. #69960C2semidirect
12. #69959C2semidirect
13. #69937C2semidirect
14. #69934C2semidirect
15. #69773C2semidirect
23. C2×#930C22semidirect
27. C22×#204C22semidirect
35. C2×C4×D12C22semidirect
36. C2×C3×C4⋊C8C22semidirect
39. C2×C3×C22⋊C8C22semidirect
40. C2×C3×C22⋊C8C22semidirect
41. C2×C3×C4×C8C22semidirect
44. #5212C22semidirect
51. C2×#821C22semidirect
52. C2×#818C22semidirect
53. C2×#816C22semidirect
54. C2×#816C22semidirect
55. C2×#816C22semidirect
59. #4936C22semidirect
64. #4551C22semidirect
65. #4551C22semidirect
77. #1954D3semidirect
148. C2×D24D4semidirect
156. #875D4semidirect
160. C4×D12D4semidirect
206. C2×C4⋊C8C2×D3semidirect
219. C2×C22⋊C8C2×D3semidirect
220. C2×C22⋊C8C2×D3semidirect
221. C2×C4×C8C2×D3semidirect
946. C3#24245semidirect

Maximal subgroups

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

subgroupindex
C2×#55502
#824152
C2×#48442
C2×#47342
C2×#47322
C2×C4×D242
C3×#19542
#704802
#699622
#699612
#699602
#699592
#699372
#699342
#697732
#242453