Finite Group Databasebeta

← #10830631

Subgroups — #10830631

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×#5554C211yesmaximal, characteristic, complemented
2C2×C3×C4×D8C211yesmaximal, characteristic, complemented
3C2×#5158C211yesmaximal, characteristic, complemented
4C2×#5156C211yesmaximal, characteristic, complemented
5#82416C211yesmaximal, characteristic, complemented
6C2×#5016C211yesmaximal, characteristic, complemented
7#71605C211yesmaximal, characteristic, complemented
8#70635C211yesmaximal, characteristic, complemented
9#70634C211yesmaximal, characteristic, complemented
10#70205C211yesmaximal, characteristic, complemented
11#70204C211yesmaximal, characteristic, complemented
12#70199C211yesmaximal, characteristic, complemented
13#70198C211yesmaximal, characteristic, complemented
14#69787C211yesmaximal, characteristic, complemented
15#69773C211yesmaximal, characteristic, complemented
16#24245—31nomaximal, Sylow
17C22×#237C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19C22×C3×D8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic, complemented
22C2×#938C2211yescharacteristic
23C2×#938C2211yescharacteristic, complemented
24C22×#214C2211yescharacteristic, complemented
25C22×#213C2211yescharacteristic
26C2×#930—21no—
27C22×(C2×D3)⋊C4—21no—
28#5554—24no—
29#5554—24no—
30C2×#897C2211yescharacteristic
31C2×#895C2211yescharacteristic
32C2×#886—21no—
33C2×#882—21no—
34C2×#875C2211yescharacteristic
35C2×C4×D12C2211yescharacteristic
36C3×C4×D8—24no—
37C2×C3×#107C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic, complemented
40C2×C3×C4×C8C2211yescharacteristic, complemented
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43#5213—21no—
44#5213—21no—
45#5158—24no—
46#5156—24no—
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×(C2×D3)⋊C8C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C2×#816C2211yescharacteristic, complemented
54C2×#816C2211yescharacteristic, complemented
55#5016—24no—
56#4987C2211yescharacteristic
57#4987C2211yescharacteristic, complemented
58C2×#810C2211yescharacteristic, complemented
59C2×#809C2211yescharacteristic
60#4960—21no—
61#4953—21no—
62#4936C2211yescharacteristic, complemented
63C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
64#4529C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#463—31no—
68C2×#449—31no—
69C2×#447—31no—
70C2×C4×D8D311yescharacteristic, complemented
71#2535—31no—
72#2036—31no—
73#2033—31no—
74#2000—31no—
75#1999—31no—
76#1958—31no—
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×D4C2311yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C23×C3×C4—21no—
86C22×#67—21no—
87C22×#67—21no—
88C22×#67—21no—
89C22×#67—21no—
90C23×Dic3—21no—
91C2×#237—22no—
92C2×#237—22no—
93C2×#237—22no—
94C2×#237—22no—
95C2×#237—41no—
96C2×#237—41no—
97C2×D3×D4—22no—
98C2×D3×D4—22no—
99C2×D3×D4—22no—
100C2×D3×D4—22no—
101C2×D3×D4—41no—
102C2×D3×D4—41no—
103C22×D12—21no—
104C22×D12D411yescharacteristic
105C22×D12C2311yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C22×C4×D3C2311yescharacteristic
108C22×Dic6C2311yescharacteristic
109C2×C3×D8—22no—
110C2×C3×D8—22no—
111C2×C3×D8D414yescomplemented
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C3×C4×D4—22no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C3×C4×D4D414yescomplemented
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C4⋊C4C2311yescharacteristic
120C2×C3×C22⋊C4—21no—
121C2×C3×C22⋊C4—21no—
122C2×C3×C42C2311yescharacteristic
123C2×#217—21no—
124C2×#217—21no—
125#938—22no—
126#938—22no—
127#938—41no—
128#938—41no—
129C2×#214—22no—
130C2×#214—22no—
131C2×#214—41no—
132C2×#213—22no—
133C2×#213—22no—
134C2×#213—41no—
135#930—28no—
136C2×(C2×D3)⋊C4—28no—
137C2×(C2×D3)⋊C4—21no—
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×(C2×D3)⋊C4D411yescharacteristic
144C2×(C2×D3)⋊C4D411yescharacteristic
145C2×C4⋊Dic3—21no—
146C2×C4⋊Dic3D411yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150C22×C3⋊C8C2311yescharacteristic
151#897—22no—
152#897—22no—
153#895—22no—
154#895—22no—
155#886—28no—
156#882—28no—
157#875—22no—
158#875D414yescomplemented
159C4×D12—22no—
160C4×D12—22no—
161C3×#107—22no—
162C3×#102—22no—
163C3×#102—22no—
164C3×C4×C8—22no—
165#832—22no—
166#832—22no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#821—22no—
172#821—41no—
173(C2×D3)⋊C8—22no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—41no—
176(C2×D3)⋊C8—41no—
177#816—22no—
178#816—41no—
179#810—22no—
180#809—22no—
181C4⋊(C3⋊C8)—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×SD16—31no—
185C22×D8—31no—
186C22×D8C2×D311yescharacteristic
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×D4C2×D311yescharacteristic
199C2×C4×D4C2×D311yescharacteristic, complemented
200C22×C22⋊C4—61no—
201#463—64no—
202#449—64no—
203#447—64no—
204C4×D8—24no—
205C2×#107C2×D311yescharacteristic, complemented
206C2×C4⋊C8—31no—
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×#102C2×D311yescharacteristic
216C2×#102C2×D311yescharacteristic, complemented
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8—31no—
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×C3—21no—
232C24×C3—21no—
233C23×D3—21no—
234C23×D3—24no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—81no—
240C23×D3—81no—
241C23×D3C2×D411yescharacteristic
242C23×D3C2×D411yescharacteristic
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4C2×D412yes—
252C2×C3×D4C2×D412yes—
253C2×C3×D4C2×D412yes—
254C2×C3×D4#4112yes—
255C22×C3×C4—21no—
256C22×C3×C4—24no—
257C22×C3×C4—21no—
258C22×C3×C4—42no—
259C22×C3×C4—81no—
260C22×C3×C4—81no—
261C22×C3×C4—81no—
262C22×C3×C4—81no—
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C2×#67—24no—
267C2×#67—24no—
268C2×#67—42no—
269C2×#67—42no—
270C2×#67—42no—
271C2×#67—42no—
272C2×#67—42no—
273C2×#67—42no—
274C2×#67—42no—
275C2×#67—42no—
276C2×#67—81no—
277C2×#67—81no—
278C22×Dic3—24no—
279C22×Dic3—21no—
280C22×Dic3—21no—
281C22×Dic3—21no—
282C22×Dic3—42no—
283C22×Dic3—42no—
284C22×Dic3C2×D411yescharacteristic
285C22×Dic3C2×D411yescharacteristic
286#237—44no—
287#237—44no—
288#237—44no—
289#237—44no—
290D3×D4—44no—
291D3×D4—44no—
292D3×D4—44no—
293D3×D4—44no—
294C2×D12—21no—
295C2×D12—21no—
296C2×D12—21no—
297C2×D12—21no—
298C2×D12—22no—
299C2×D12—22no—
300C2×D12—21no—
301C2×D12—24no—
302C2×D12—41no—
303C2×D12—81no—
304C2×D12—81no—
305C2×D12C2×D412yes—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6—21no—
321C2×Dic6—21no—
322C2×Dic6—21no—
323C2×Dic6C2×D412yes—
324C3×D8—28no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8C2×D412yes—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4C2×D412yes—
335C3×C22⋊C4—24no—
336C3×C22⋊C4—42no—
337C3×C42C2×D412yes—
338C3×C42C2×D412yes—
339#217—42no—
340#217—42no—
341#214—44no—
342#213—44no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—24no—
345(C2×D3)⋊C4—22no—
346(C2×D3)⋊C4—22no—
347(C2×D3)⋊C4—24no—
348(C2×D3)⋊C4—24no—
349(C2×D3)⋊C4—81no—
350(C2×D3)⋊C4—81no—
351C4⋊Dic3—24no—
352C4⋊Dic3—22no—
353C4⋊Dic3—21no—
354C4⋊Dic3—21no—
355C4⋊Dic3—21no—
356C4⋊Dic3—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361C2×C3⋊C8—21no—
362C2×C3⋊C8—21no—
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—61no—
374C22×D4—61no—
375C22×D4—62no—
376C22×D4—61no—
377C22×D4—62no—
378C22×D4—62no—
379C22×D4—62no—
380C22×D4—61no—
381C22×D4—61no—
382C22×D4—121no—
383C22×D4—121no—
384C22×D4C22×D311yescharacteristic
385C22×D4C22×D311yescharacteristic
386C23×C4—21no—
387C23×C4—21no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—61no—
391C2×SD16—62no—
392C2×SD16—62no—
393C2×SD16—121no—
394C2×D8—22no—
395C2×D8—22no—
396C2×D8—62no—
397C2×D8—62no—
398C2×D8—121no—
399C2×D8D1214yescomplemented
400C22×C8—31no—
401C22×C8—31no—
402C22×C8C22×D311yescharacteristic
403C22×C8C22×D311yescharacteristic
404#124—34no—
405#124—62no—
406#123—68no—
407C22⋊Q8—62no—
408C22⋊Q8—62no—
409#121—62no—
410#121—68no—
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—22no—
420C4×D4—62no—
421C4×D4—62no—
422C4×D4#6714yescomplemented
423C2×C4⋊C4—31no—
424C2×C4⋊C4—31no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—61no—
427C2×C4⋊C4C22×D311yescharacteristic
428C2×C4⋊C4C22×D311yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—68no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4—61no—
438C2×C22⋊C4—61no—
439C2×C22⋊C4—61no—
440C2×C22⋊C4—61no—
441C2×C22⋊C4—61no—
442C2×C42C22×D311yescharacteristic
443#107—22no—
444C4⋊C8—62no—
445#103—62no—
446#103—62no—
447#103—121no—
448#102—22no—
449#102—22no—
450#102—62no—
451#102—62no—
452#102—62no—
453#102—62no—
454#102—121no—
455C22⋊C8—62no—
456C22⋊C8—62no—
457C22⋊C8—121no—
458C22⋊C8—121no—
459C4×C8—22no—
460#95—61no—
461#95—61no—
462#95—61no—
463#95—61no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—22no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3C22×D411yescharacteristic
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—22no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—48no—
494C22×D3—48no—
495C22×D3—41no—
496C22×D3—41no—
497C22×D3—41no—
498C22×D3—41no—
499C22×D3—41no—
500C22×D3—41no—
501C22×D3—84no—
502C22×D3—84no—
503C22×D3—84no—
504C22×D3—84no—
505C22×D3—84no—
506C22×D3#13512yes—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—22no—
510C3×D4—22no—
511C3×D4—22no—
512C3×D4—41no—
513C3×D4—41no—
514C3×D4#12114yes—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—84no—
526C2×C3×C4—84no—
527C2×C3×C4#12012yes—
528C2×C3×C4#12012yes—
529C2×C3×C4C22×D411yescharacteristic
530C2×C3×C4C22×D411yescharacteristic
531C2×C3×C4C22×D411yescharacteristic
532C2×C3×C4C2×#4111yescharacteristic
533C2×C3×C4H(5,𝔽2)11yescharacteristic
534C2×C3×C4H(5,𝔽2)11yescharacteristic
535#67—48no—
536#67—48no—
537#67—84no—
538#67—84no—
539C2×Dic3—21no—
540C2×Dic3—22no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—48no—
547C2×Dic3—41no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—41no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555D12—22no—
556D12—22no—
557D12—44no—
558D12—41no—
559D12—41no—
560D12—84no—
561C4×D3—41no—
562C4×D3—41no—
563C4×D3—41no—
564C4×D3—41no—
565C4×D3—41no—
566C4×D3—41no—
567C4×D3—41no—
568C4×D3—41no—
569Dic6—22no—
570Dic6—22no—
571Dic6—41no—
572Dic6—41no—
573C3×C8—22no—
574C3×C8—41no—
575C3⋊C8—41no—
576C3⋊C8—41no—
577C24—21no—
578C24—21no—
579C24—31no—
580C24—31no—
581C24—64no—
582C24—61no—
583C24—122no—
584C24—122no—
585C24—122no—
586C24—122no—
587C24—241no—
588C24—241no—
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—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—32no—
608C2×D4—62no—
609C2×D4—64no—
610C2×D4—64no—
611C2×D4—64no—
612C2×D4—62no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—121no—
619C2×D4—122no—
620C2×D4—122no—
621C2×D4—124no—
622C2×D4—124no—
623C2×D4—124no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—124no—
627C2×D4—122no—
628C2×D4—122no—
629C2×D4—122no—
630C2×D4—122no—
631C2×D4—241no—
632C2×D4—241no—
633C2×D4—241no—
634C2×D4—241no—
635C2×D4C2×D1212yes—
636C2×D4C2×D1212yes—
637C2×D4#23512yes—
638C2×D4C2×#6712yes—
639C22×C4—21no—
640C22×C4—24no—
641C22×C4—21no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—42no—
645C22×C4—64no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4—81no—
665C22×C4—122no—
666C22×C4—122no—
667C22×C4D3×D411yescharacteristic
668C22×C4D3×D411yescharacteristic
669C22×C4C23×D311yescharacteristic
670SD16—124no—
671D8—28no—
672D8—124no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—61no—
679C2×C8—61no—
680C2×C8—61no—
681C2×C8—61no—
682C2×C8—61no—
683C2×C8—61no—
684C2×C8C2×D1212yes—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—64no—
689C4⋊C4—62no—
690C4⋊C4—61no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4C2×#6712yes—
695C22⋊C4—24no—
696C22⋊C4—42no—
697C22⋊C4—64no—
698C22⋊C4—64no—
699C22⋊C4—62no—
700C22⋊C4—62no—
701C22⋊C4—64no—
702C22⋊C4—64no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—241no—
706C22⋊C4—241no—
707C42D3×D412yes—
708C42C2×#6712yes—
709C22×C3—24no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—81no—
720C22×C3—81no—
721C22×C3—81no—
722C22×C3—81no—
723C22×C3C2×#12011yescharacteristic
724C22×C3D4211yescharacteristic
725C22×C3#54611yescharacteristic
726C22×C3C2×#13511yescharacteristic
727C22×C3#57511yescharacteristic
728C22×C3#57611yescharacteristic
729C22×C3#57611yescharacteristic
730C2×D3—22no—
731C2×D3—22no—
732C2×D3—22no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
737C2×D3—41no—
738C2×D3—42no—
739C2×D3—41no—
740C2×D3—42no—
741C2×D3—41no—
742C2×D3—42no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—816no—
748C2×D3—81no—
749C2×D3—81no—
750C2×D3—81no—
751C2×D3—81no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—42no—
755C3×C4—81no—
756C3×C4C2×#12111yescharacteristic
757C3×C4#53511yescharacteristic
758C3×C4D4211yescharacteristic
759C3×C4#54611yescharacteristic
760Dic3—42no—
761Dic3—41no—
762Dic3—41no—
763Dic3—81no—
764Dic3—81no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—32no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23—61no—
785C23—61no—
786C23—61no—
787C23—61no—
788C23—61no—
789C23—61no—
790C23—62no—
791C23—61no—
792C23—61no—
793C23—61no—
794C23—128no—
795C23—128no—
796C23—121no—
797C23—121no—
798C23—121no—
799C23—121no—
800C23—121no—
801C23—121no—
802C23—244no—
803C23—244no—
804C23—244no—
805C23—244no—
806C23—244no—
807C23C2×D3×D411yescharacteristic
808Q8—62no—
809Q8—62no—
810Q8—121no—
811Q8—121no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—41no—
818D4—41no—
819D4—62no—
820D4—62no—
821D4—124no—
822D4—128no—
823D4—128no—
824D4—121no—
825D4—121no—
826D4—244no—
827D4—244no—
828D4—244no—
829D4#93014yes—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—61no—
841C2×C4—62no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—84no—
848C2×C4—84no—
849C2×C4—128no—
850C2×C4—121no—
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—121no—
865C2×C4—121no—
866C2×C4#93712yes—
867C2×C4#93712yes—
868C2×C4C22×D1211yescharacteristic
869C2×C4C2×#23511yescharacteristic
870C2×C4C2×D3×D411yescharacteristic
871C2×C4#100911yescharacteristic
872C2×C4#100911yescharacteristic
873C2×C4C22×#6711yescharacteristic
874C8—22no—
875C8—41no—
876C8—121no—
877C8—121no—
878C2×C3—44no—
879C2×C3—82no—
880C2×C3#240811yescharacteristic
881C2×C3#300211yescharacteristic
882C2×C3#300811yescharacteristic
883C2×C3#327311yescharacteristic
884C2×C3#328011yescharacteristic
885C2×C3#329711yescharacteristic
886C2×C3#332211yescharacteristic
887D3—42no—
888D3—81no—
889D3—82no—
890C22—24no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—62no—
901C22—62no—
902C22—62no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
911C22—121no—
912C22—122no—
913C22—121no—
914C22—122no—
915C22—121no—
916C22—122no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—2416no—
922C22—241no—
923C22—241no—
924C22—241no—
925C22—241no—
926C22D4×D1211yescharacteristic
927C22#555011yescharacteristic
928C22#575711yescharacteristic
929C22#575711yescharacteristic
930C22D3×#13511yescharacteristic
931C22#576811yescharacteristic
932C22C2×#93711yescharacteristic
933C4—22no—
934C4—22no—
935C4—42no—
936C4—81no—
937C4—121no—
938C4—121no—
939C4—122no—
940C4—241no—
941C4—241no—
942C4D4×D1211yescharacteristic
943C4#555011yescharacteristic
944C4C2×#93011yescharacteristic
945C4#583011yescharacteristic
946C3#2424511yescharacteristic, complemented, Sylow
947C2—44no—
948C2—82no—
949C2—122no—
950C2—241no—
951C2—242no—
952C2#7960411yescharacteristic
953C2#7960611yescharacteristic
954C2#7960911yescharacteristic
955C2#7961111yescharacteristic
956C2#8240311yescharacteristic
957C2#8383311yescharacteristic
958C2#8391111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×C4×D8C2
socleC23×C3C22×D4
hypercenterC2×C4×D8D3
hypocenterC3#24245
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#5554C2semidirect
2. C2×C3×C4×D8C2semidirect
3. C2×#5158C2semidirect
4. C2×#5156C2semidirect
5. #82416C2semidirect
6. C2×#5016C2semidirect
7. #71605C2semidirect
8. #70635C2semidirect
9. #70634C2semidirect
10. #70205C2semidirect
11. #70204C2semidirect
12. #70199C2semidirect
13. #70198C2semidirect
14. #69787C2semidirect
15. #69773C2semidirect
21. C2×C3×C4×D4C22semidirect
23. C2×#938C22semidirect
24. C22×#214C22semidirect
37. C2×C3×#107C22semidirect
39. C2×C3×#102C22semidirect
40. C2×C3×C4×C8C22semidirect
51. C2×(C2×D3)⋊C8C22semidirect
52. C2×(C2×D3)⋊C8C22semidirect
53. C2×#816C22semidirect
54. C2×#816C22semidirect
57. #4987C22semidirect
58. C2×#810C22semidirect
62. #4936C22semidirect
63. C2×C4⋊(C3⋊C8)C22semidirect
64. #4529C22semidirect
65. #4529C22semidirect
70. C2×C4×D8D3semidirect
111. C2×C3×D8D4semidirect
117. C3×C4×D4D4semidirect
158. #875D4semidirect
199. C2×C4×D4C2×D3semidirect
205. C2×#107C2×D3semidirect
216. C2×#102C2×D3semidirect
221. C2×C4×C8C2×D3semidirect
399. C2×D8D12semidirect
422. C4×D4#67semidirect
946. C3#24245semidirect

Maximal subgroups

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

subgroupindex
C2×#55542
C2×C3×C4×D82
C2×#51582
C2×#51562
#824162
C2×#50162
#716052
#706352
#706342
#702052
#702042
#701992
#701982
#697872
#697732
#242453