Finite Group Databasebeta

← #10830638

Subgroups — #10830638

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×#5829C211yesmaximal, characteristic, complemented
2C2×#5238C211yesmaximal, characteristic, complemented
3C2×#4819C211yesmaximal, characteristic, complemented
4C2×#4773C211yesmaximal, characteristic, complemented
5C2×#4756C211yesmaximal, characteristic, complemented
6#73933C211yesmaximal, characteristic, complemented
7C3×#1788C211yesmaximal, characteristic, complemented
8#70275C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70226C211yesmaximal, characteristic, complemented
11#70198C211yesmaximal, characteristic, complemented
12#70154C211yesmaximal, characteristic, complemented
13#69961C211yesmaximal, characteristic, complemented
14#69916C211yesmaximal, characteristic, complemented
15#69523C211yesmaximal, characteristic, complemented
16#24245—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×D3×D4C2211yescharacteristic
19#5829—24no—
20#5829—24no—
21C2×#947C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C22×#215C2211yescharacteristic, complemented
24C2×#939—21no—
25C2×#937—21no—
26C2×D4×Dic3C2211yescharacteristic
27C22×#213C2211yescharacteristic
28C2×#930C2211yescharacteristic
29C2×#930C2211yescharacteristic, complemented
30C2×#929—21no—
31C2×C4×#67C2211yescharacteristic
32C22×(C2×D3)⋊C4—21no—
33C22×D24C2211yescharacteristic
34C2×#895C2211yescharacteristic
35C2×#893C2211yescharacteristic, complemented
36C2×C3×#103C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic, complemented
41C3×#380C2211yescharacteristic, complemented
42#5238—24no—
43C2×#835C2211yescharacteristic, complemented
44C2×#832C2211yescharacteristic
45C2×#830C2211yescharacteristic, complemented
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic, complemented
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×Dic3⋊C8C2211yescharacteristic, complemented
51C2×C8×Dic3C2211yescharacteristic, complemented
52#4987C2211yescharacteristic
53#4977C2211yescharacteristic, complemented
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56C2×#807C2211yescharacteristic, complemented
57#4960—21no—
58#4956—21no—
59#4819—24no—
60#4773—24no—
61#4756—24no—
62#4675—21no—
63#4665—21no—
64#4551C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, 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#1954—31no—
78#1804—31no—
79#1788D311yescharacteristic, complemented
80#1786—31no—
81C24×D3—21no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41—22no—
86C2×C3×#41—41no—
87C2×C3×#41—41no—
88C22×C3×Q8C2311yescharacteristic
89C22×C3×D4—21no—
90C22×C3×D4C2311yescharacteristic
91C23×C3×C4—21no—
92C23×C3×C4C2311yescharacteristic
93C22×#67—21no—
94C22×#67—21no—
95C22×#67—21no—
96C22×#67D411yescharacteristic
97C23×Dic3—21no—
98C2×D3×D4—22no—
99C2×D3×D4—22no—
100C2×D3×D4—22no—
101C2×D3×D4—22no—
102C2×D3×D4—41no—
103C2×D3×D4—41no—
104C22×D12—21no—
105C22×D12C2311yescharacteristic
106C22×D12C2311yescharacteristic
107C22×C4×D3—21no—
108C22×C4×D3C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×#217—21no—
115C2×#217D411yescharacteristic
116#947—22no—
117#947D414yescomplemented
118#946—22no—
119#946—22no—
120C2×#215—22no—
121C2×#215—22no—
122C2×#215—41no—
123#939—28no—
124#937—28no—
125D4×Dic3—22no—
126D4×Dic3D414yescomplemented
127C2×#213—22no—
128C2×#213—22no—
129C2×#213D414yescomplemented
130#930—22no—
131#930—22no—
132#930—22no—
133#930—41no—
134#929—28no—
135C4×#67—22no—
136C4×#67—22no—
137C2×(C2×D3)⋊C4—28no—
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)⋊C4—21no—
144C2×(C2×D3)⋊C4—21no—
145C2×(C2×D3)⋊C4—21no—
146C2×(C2×D3)⋊C4D411yescharacteristic
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×Dic3⋊C4—21no—
150C2×Dic3⋊C4D411yescharacteristic
151C2×C4×Dic3C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C2×D24—22no—
155C2×D24—22no—
156C2×D24—41no—
157#895—22no—
158#895—41no—
159#893—22no—
160#893—22no—
161C3×#103—22no—
162C3×#103—41no—
163C3×#102—22no—
164C3×#102—22no—
165C3×C22⋊C8—41no—
166C3×#95—21no—
167#835—22no—
168#832—22no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171C3⋊#95—21no—
172#830—22no—
173#821—22no—
174#821—41no—
175(C2×D3)⋊C8—22no—
176(C2×D3)⋊C8—41no—
177Dic3⋊C8—22no—
178C8×Dic3—22no—
179#809—22no—
180#809—22no—
181#807—22no—
182C22×#41C2×D311yescharacteristic
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×D4—31no—
200C22×C22⋊C4—61no—
201#463—64no—
202#449—64no—
203#447—64no—
204C4×D8—64no—
205C2×#107—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103C2×D311yescharacteristic, complemented
209C2×#103C2×D311yescharacteristic, complemented
210C2×#102—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102C2×D311yescharacteristic
216C2×#102C2×D311yescharacteristic
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8C2×D311yescharacteristic, complemented
221C2×C4×C8—31no—
222#397—61no—
223#392—61no—
224#386—61no—
225#386—61no—
226#382—31no—
227#380—31no—
228#380C2×D311yescharacteristic, complemented
229#340—31no—
230#340—31no—
231C24×C3—21no—
232C24×C3C2×D411yescharacteristic
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—24no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—42no—
240C23×D3—81no—
241C23×D3—81no—
242C23×D3C2×D411yescharacteristic
243C3×#41—44no—
244C3×#41—44no—
245C3×#41—44no—
246C3×#41—44no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8C2×D412yes—
253C2×C3×D4—24no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—42no—
258C2×C3×D4—42no—
259C2×C3×D4C2×D412yes—
260C2×C3×D4C2×D412yes—
261C2×C3×D4#4112yes—
262C22×C3×C4—24no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C2×#67—24no—
277C2×#67—22no—
278C2×#67—24no—
279C2×#67—22no—
280C2×#67—41no—
281C2×#67—42no—
282C2×#67—42no—
283C2×#67—42no—
284C2×#67—42no—
285C2×#67—81no—
286C2×#67—81no—
287C2×#67—81no—
288C22×Dic3—21no—
289C22×Dic3—24no—
290C22×Dic3—21no—
291C22×Dic3—81no—
292C22×Dic3—81no—
293C22×Dic3C2×D411yescharacteristic
294C22×Dic3C2×D411yescharacteristic
295C22×Dic3C2×D411yescharacteristic
296D3×D4—44no—
297D3×D4—44no—
298D3×D4—44no—
299D3×D4—44no—
300C2×D12—21no—
301C2×D12—21no—
302C2×D12—21no—
303C2×D12—21no—
304C2×D12—21no—
305C2×D12—21no—
306C2×D12—21no—
307C2×D12—21no—
308C2×D12—21no—
309C2×D12—21no—
310C2×D12—42no—
311C2×D12—42no—
312C2×D12—81no—
313C2×D12C2×D412yes—
314C2×D12C2×D412yes—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—21no—
320C2×C4×D3—21no—
321C2×C4×D3—42no—
322C2×C4×D3—81no—
323C2×C4×D3—81no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C22⋊C4—81no—
335#217—22no—
336#217—24no—
337#215—44no—
338#213—28no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—24no—
343(C2×D3)⋊C4—24no—
344(C2×D3)⋊C4—42no—
345(C2×D3)⋊C4—42no—
346(C2×D3)⋊C4—42no—
347(C2×D3)⋊C4—81no—
348C4⋊Dic3—21no—
349C4⋊Dic3—21no—
350C4⋊Dic3—21no—
351C4⋊Dic3C2×D412yes—
352Dic3⋊C4—24no—
353Dic3⋊C4—22no—
354C4×Dic3C2×D412yes—
355C4×Dic3C2×D412yes—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361C2×C3⋊C8C2×D412yes—
362D24—44no—
363C25—61no—
364C2×#41—22no—
365C2×#41—22no—
366C2×#41—22no—
367C2×#41—22no—
368C2×#41—41no—
369C2×#41—41no—
370C22×Q8C22×D311yescharacteristic
371C22×D4—21no—
372C22×D4—31no—
373C22×D4—31no—
374C22×D4—31no—
375C22×D4—61no—
376C22×D4—61no—
377C22×D4—62no—
378C22×D4—61no—
379C22×D4—62no—
380C22×D4—62no—
381C22×D4—62no—
382C22×D4—61no—
383C22×D4—121no—
384C22×D4—121no—
385C22×D4C22×D311yescharacteristic
386C23×C4—21no—
387C23×C4—31no—
388C23×C4—61no—
389C23×C4—61no—
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×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—62no—
411#121—68no—
412#121—62no—
413#121—62no—
414#121—121no—
415#121—121no—
416#120—68no—
417C4×D4—34no—
418C4×D4—62no—
419C4×D4—62no—
420C4×D4—62no—
421C4×D4—62no—
422C4×D4—62no—
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—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—61no—
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×C42—31no—
443#107—62no—
444C4⋊C8—62no—
445#103—22no—
446#103—41no—
447#103—62no—
448#102—22no—
449#102—22no—
450#102—62no—
451#102—62no—
452#102—62no—
453#102—62no—
454#102—121no—
455C22⋊C8—41no—
456C22⋊C8—62no—
457C22⋊C8—62no—
458C22⋊C8—121no—
459C4×C8—62no—
460#95—21no—
461#95—61no—
462#95—61no—
463#95—61no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
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—22no—
487C22×D3—48no—
488C22×D3—48no—
489C22×D3—41no—
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—84no—
502C22×D3—84no—
503C22×D3—84no—
504C22×D3—84no—
505C22×D3—84no—
506C22×D3#13512yes—
507C3×Q8—22no—
508C3×Q8—22no—
509C3×Q8—41no—
510C3×Q8—41no—
511C3×D4—22no—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—48no—
515C3×D4#12114yes—
516C2×C3×C4—21no—
517C2×C3×C4—22no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—48no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4C22×D411yescharacteristic
534C2×C3×C4C22×D411yescharacteristic
535C2×C3×C4C22×D411yescharacteristic
536C2×C3×C4C2×#4111yescharacteristic
537C2×C3×C4H(5,𝔽2)11yescharacteristic
538C2×C3×C4H(5,𝔽2)11yescharacteristic
539#67—44no—
540#67—48no—
541#67—84no—
542#67—84no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—22no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—41no—
552C2×Dic3—41no—
553C2×Dic3—41no—
554C2×Dic3—41no—
555C2×Dic3—41no—
556C2×Dic3—84no—
557C2×Dic3#12012yes—
558C2×Dic3#12012yes—
559D12—22no—
560D12—22no—
561D12—22no—
562D12—22no—
563D12—41no—
564D12—41no—
565D12—41no—
566D12—41no—
567D12—84no—
568C4×D3—41no—
569C4×D3—41no—
570C4×D3—41no—
571C4×D3—41no—
572C4×D3—84no—
573C3×C8—41no—
574C3×C8—41no—
575C3⋊C8—22no—
576C3⋊C8—41no—
577C24—21no—
578C24—31no—
579C24—64no—
580C24—61no—
581C24—61no—
582C24—122no—
583C24—122no—
584C24—122no—
585C24—122no—
586C24—241no—
587C24—241no—
588C24D3×D411yescharacteristic
589#41—44no—
590#41—44no—
591#41—44no—
592#41—44no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8D3×D412yes—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—32no—
604C2×D4—32no—
605C2×D4—42no—
606C2×D4—42no—
607C2×D4—62no—
608C2×D4—62no—
609C2×D4—64no—
610C2×D4—64no—
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—122no—
622C2×D4—122no—
623C2×D4—121no—
624C2×D4—122no—
625C2×D4—122no—
626C2×D4—124no—
627C2×D4—124no—
628C2×D4—124no—
629C2×D4—124no—
630C2×D4—122no—
631C2×D4—122no—
632C2×D4—241no—
633C2×D4—241no—
634C2×D4—241no—
635C2×D4—241no—
636C2×D4#23512yes—
637C2×D4D3×D412yes—
638C2×D4D3×D412yes—
639C22×C4—24no—
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—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—64no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—61no—
662C22×C4—61no—
663C22×C4—122no—
664C22×C4—241no—
665C22×C4—241no—
666C22×C4—241no—
667C22×C4—241no—
668C22×C4D3×D411yescharacteristic
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—32no—
680C2×C8—61no—
681C2×C8—61no—
682C2×C8—61no—
683C2×C8—61no—
684C2×C8—61no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—32no—
690C4⋊C4—62no—
691C4⋊C4—64no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C22⋊C4—62no—
696C22⋊C4—64no—
697C22⋊C4—64no—
698C22⋊C4—64no—
699C22⋊C4—64no—
700C22⋊C4—62no—
701C22⋊C4—64no—
702C22⋊C4—81no—
703C22⋊C4—122no—
704C22⋊C4—122no—
705C22⋊C4—122no—
706C22⋊C4—241no—
707C42—32no—
708C42—32no—
709C22×C3—24no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
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—22no—
731C2×D3—22no—
732C2×D3—22no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—41no—
736C2×D3—41no—
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—41no—
753C3×C4—42no—
754C3×C4—81no—
755C3×C4—81no—
756C3×C4C2×#12111yescharacteristic
757C3×C4#53511yescharacteristic
758C3×C4D4211yescharacteristic
759C3×C4#54611yescharacteristic
760Dic3—22no—
761Dic3—22no—
762Dic3—41no—
763Dic3—42no—
764Dic3—81no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—32no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—61no—
781C23—61no—
782C23—61no—
783C23—61no—
784C23—61no—
785C23—61no—
786C23—62no—
787C23—62no—
788C23—128no—
789C23—128no—
790C23—121no—
791C23—121no—
792C23—121no—
793C23—121no—
794C23—121no—
795C23—121no—
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—22no—
809Q8—22no—
810Q8—41no—
811Q8—41no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—62no—
817D4—62no—
818D4—62no—
819D4—62no—
820D4—124no—
821D4—128no—
822D4—121no—
823D4—121no—
824D4—121no—
825D4—121no—
826D4—244no—
827D4—244no—
828D4—244no—
829D4#88414yes—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—48no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
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—41no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—62no—
855C2×C4—61no—
856C2×C4—61no—
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—244no—
867C2×C4—244no—
868C2×C4C2×#23511yescharacteristic
869C2×C4C2×D3×D411yescharacteristic
870C2×C4C2×D3×D411yescharacteristic
871C2×C4C2×D3×D411yescharacteristic
872C2×C4#100411yescharacteristic
873C2×C4#100411yescharacteristic
874C8—41no—
875C8—41no—
876C8—62no—
877C8—121no—
878C2×C3—44no—
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—42no—
888D3—82no—
889D3—82no—
890C22—24no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—62no—
905C22—62no—
906C22—62no—
907C22—121no—
908C22—121no—
909C22—121no—
910C22—121no—
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—
926C22#549011yescharacteristic
927C22D3×#12011yescharacteristic
928C22#559011yescharacteristic
929C22D3×#13511yescharacteristic
930C22#576911yescharacteristic
931C22#577411yescharacteristic
932C22#577711yescharacteristic
933C4—41no—
934C4—42no—
935C4—62no—
936C4—62no—
937C4—81no—
938C4—81no—
939C4—121no—
940C4—122no—
941C4—241no—
942C4C2×#88411yescharacteristic
943C4#549011yescharacteristic
944C4#559011yescharacteristic
945C4#559211yescharacteristic
946C3#2424511yescharacteristic, complemented, Sylow
947C2—44no—
948C2—81no—
949C2—122no—
950C2—242no—
951C2—242no—
952C2#7382411yescharacteristic
953C2#7884611yescharacteristic
954C2#7890211yescharacteristic
955C2#8008511yescharacteristic
956C2#8010111yescharacteristic
957C2#8022611yescharacteristic
958C2#8024311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1788C2
socleC23×C3C22×D4
hypercenter#1788D3
hypocenterC3#24245
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
1. C2×#5829C2semidirect
2. C2×#5238C2semidirect
3. C2×#4819C2semidirect
4. C2×#4773C2semidirect
5. C2×#4756C2semidirect
6. #73933C2semidirect
7. C3×#1788C2semidirect
8. #70275C2semidirect
9. #70272C2semidirect
10. #70226C2semidirect
11. #70198C2semidirect
12. #70154C2semidirect
13. #69961C2semidirect
14. #69916C2semidirect
15. #69523C2semidirect
23. C22×#215C22semidirect
29. C2×#930C22semidirect
35. C2×#893C22semidirect
36. C2×C3×#103C22semidirect
37. C2×C3×#103C22semidirect
40. C2×C3×C22⋊C8C22semidirect
41. C3×#380C22semidirect
43. C2×#835C22semidirect
45. C2×#830C22semidirect
47. C2×#821C22semidirect
50. C2×Dic3⋊C8C22semidirect
51. C2×C8×Dic3C22semidirect
53. #4977C22semidirect
56. C2×#807C22semidirect
64. #4551C22semidirect
65. #4529C22semidirect
79. #1788D3semidirect
117. #947D4semidirect
126. D4×Dic3D4semidirect
129. C2×#213D4semidirect
208. C2×#103C2×D3semidirect
209. C2×#103C2×D3semidirect
220. C2×C22⋊C8C2×D3semidirect
228. #380C2×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×#58292
C2×#52382
C2×#48192
C2×#47732
C2×#47562
#739332
C3×#17882
#702752
#702722
#702262
#701982
#701542
#699612
#699162
#695232
#242453