Finite Group Databasebeta

← #11703722

Subgroups — #11703722

Order 768.

11534 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×#5968C211yesmaximal, characteristic, complemented
2C23×#239C211yesmaximal, characteristic, complemented
3C3×#3486C211yesmaximal, characteristic, complemented
4#87290C211yesmaximal, characteristic, complemented
5#87251C211yesmaximal, characteristic, complemented
6#86745C218yesmaximal, complemented
7D4×#239C218yesmaximal, complemented
8#86713C218yesmaximal, complemented
9#86710C218yesmaximal, complemented
10#86354C216yesmaximal, complemented
11#86338C216yesmaximal, complemented
12#86039C216yesmaximal, complemented
13D3×#525C216yesmaximal, complemented
14#85874C211yesmaximal, characteristic, complemented
15#85872C211yesmaximal, characteristic, complemented
16#62811—31nomaximal, Sylow
17C2×C3×2−1+4C2211yescharacteristic, complemented
18C23×C3×Q8C2211yescharacteristic, complemented
19#5968—216no—
20C2×#1009C2216yescomplemented
21C2×#1009C2214yescomplemented
22C2×D3×#41C2216yescomplemented
23C2×D3×#41C2214yescomplemented
24C2×#1007C2211yescharacteristic, complemented
25C2×#1007C2214yescomplemented
26C22×#239—216no—
27C22×#239C2211yescharacteristic
28C22×#239C2213yescomplemented
29C22×#239C2213yescomplemented
30C22×#239C2211yescharacteristic, complemented
31C22×#239C2218yescomplemented
32C22×#239C2218yescomplemented
33C22×#239C2214yescomplemented
34C23×D12C2213yescomplemented
35C23×C4×D3C2213yescomplemented
36C3×D4×Q8C2218yescomplemented
37C3×#548C2218yescomplemented
38C3×#536C2216yescomplemented
39C3×#525C2216yescomplemented
40C3×#519C2211yescharacteristic, complemented
41#5834C2218yescomplemented
42#5830C2216yescomplemented
43#5828C2216yescomplemented
44#5817C2218yescomplemented
45#5817C2218yescomplemented
46#5816C2216yescomplemented
47Q8×#67C2218yescomplemented
48#5812C2211yescharacteristic, complemented
49#5791C2216yescomplemented
50#5726C22124yescomplemented
51#5725C22112yescomplemented
52#5724C22112yescomplemented
53#5676C22124yescomplemented
54#5674C22112yescomplemented
55#5668C22112yescomplemented
56#5656C22112yescomplemented
57#5653C22124yescomplemented
58D3×#123C22112yescomplemented
59#5631C22124yescomplemented
60#5630C22124yescomplemented
61#5630C22124yescomplemented
62#5629C22124yescomplemented
63#5627C22112yescomplemented
64#5627C22124yescomplemented
65D3×C22⋊Q8C22112yescomplemented
66#5609C22124yescomplemented
67#5606C22112yescomplemented
68D3×#121C22112yescomplemented
69D3×#120C22112yescomplemented
70#5586C2214yescomplemented
71#5577C2218yescomplemented
72#5576C2218yescomplemented
73#5574C2218yescomplemented
74C4×#239C2218yescomplemented
75#5550C22124yescomplemented
76D4×D12C22124yescomplemented
77#5547C22124yescomplemented
78C4×D3×D4C22124yescomplemented
79#5525C2216yescomplemented
80#5524C2216yescomplemented
81#5521C2216yescomplemented
82D3×#117C2216yescomplemented
83C2×#585—31no—
84C23×#41—31no—
85#3489—38no—
86#3488—38no—
87#3487—31no—
88#3487—31no—
89#3486—31no—
90#3486D311yescharacteristic, complemented
91#3485—36no—
92#3484—36no—
93D4×#41—38no—
94D4×#41—38no—
95#3449—36no—
96C2×#525—36no—
97#3428—31no—
98C24×D3C2313yes—
99C3×2−1+4—28no—
100C2×C3×#41C2316yes—
101C2×C3×#41C2314yescomplemented
102C22×C3×Q8—28no—
103C22×C3×Q8C2318yes—
104C22×C3×Q8C2313yes—
105C22×C3×Q8C2311yescharacteristic
106C22×C3×Q8C2314yescomplemented
107C23×C3×C4C2313yes—
108C23×Dic3C2311yescharacteristic
109#1009—232no—
110#1009—248no—
111D3×#41—232no—
112D3×#41—248no—
113#1007—28no—
114#1007—232no—
115C2×#239—28no—
116C2×#239—264no—
117C2×#239—264no—
118C2×#239—232no—
119C2×#239—224no—
120C2×#239—224no—
121C2×#239D4116yescomplemented
122C2×#239C23112yes—
123C2×#239C23112yes—
124C2×#239C23124yes—
125C2×#239C2318yes—
126C2×#239C2314yes—
127C2×#239C2314yes—
128C2×#239C2316yescomplemented
129C2×#239C23112yescomplemented
130C2×#239C2314yescomplemented
131C2×D3×Q8C2316yescomplemented
132C2×D3×Q8C2314yescomplemented
133C2×#237C2314yes—
134C2×#237C2316yescomplemented
135C2×D3×D4C23112yes—
136C2×D3×D4C23124yes—
137C2×D3×D4C2316yescomplemented
138C2×D3×D4C23112yescomplemented
139C2×#235C2316yes—
140C2×#235C23112yescomplemented
141C2×#235C23112yescomplemented
142C22×D12—224no—
143C22×D12C2316yes—
144C22×D12C2313yes—
145C22×D12C23124yes—
146C22×D12C2313yes—
147C22×D12C23112yescomplemented
148C22×C4×D3—224no—
149C22×C4×D3C2313yes—
150C22×C4×D3C2313yes—
151C22×C4×D3C2313yes—
152C22×C4×D3C23112yes—
153C22×C4×D3C23112yes—
154C22×C4×D3C2313yes—
155C22×C4×D3C23112yescomplemented
156C3×C4⋊Q8C23112yescomplemented
157C3×#124C23112yescomplemented
158C3×#123C23112yes—
159C3×C22⋊Q8C23112yes—
160C3×C22⋊Q8C23124yescomplemented
161C3×#121C23112yes—
162C3×#120C2314yes—
163C3×C4×Q8C2318yescomplemented
164C3×C4×D4C23124yes—
165C3×#117C2316yes—
166#953C2314yes—
167#947C23112yescomplemented
168#947C23112yescomplemented
169#946C23124yescomplemented
170#946C23112yescomplemented
171Q8×Dic3C2318yescomplemented
172#944C23112yescomplemented
173#940C23112yescomplemented
174#939C2318yes—
175#938C23112yescomplemented
176#937C23112yes—
177#937C23124yes—
178#935C2314yes—
179D4×Dic3C2318yes—
180#930C23112yes—
181#930C23124yescomplemented
182#929C23112yes—
183C4×#67C23124yes—
184C4×#67C23124yescomplemented
185#926C2316yes—
186#924C23112yes—
187#897C23112yescomplemented
188#896C23124yescomplemented
189#895C23148yescomplemented
190#895C23112yescomplemented
191#895C23124yescomplemented
192#894C23124yescomplemented
193#894C23148yescomplemented
194#893C23124yescomplemented
195#893C23124yescomplemented
196#892C23112yescomplemented
197D3×C4⋊C4C23124yescomplemented
198D3×C4⋊C4C23112yescomplemented
199#886C2314yes—
200#884C23148yescomplemented
201#884C23124yescomplemented
202#883C23124yescomplemented
203#882C23112yes—
204#882C23124yes—
205#882C23148yescomplemented
206#67⋊C4C2318yes—
207#67⋊C4C23124yescomplemented
208D3×C22⋊C4C23112yes—
209D3×C22⋊C4C23124yes—
210D3×C22⋊C4C23124yescomplemented
211#878C2318yes—
212#877C2314yes—
213#875C23112yescomplemented
214#874C23112yescomplemented
215C4×D12C23124yescomplemented
216C4×D12C23124yescomplemented
217#872C23112yescomplemented
218C42×D3C23112yescomplemented
219#585—616no—
220C2×2−1+4—31no—
221C2×2−1+4—34no—
222C2×2−1+4C2×D311yescharacteristic, complemented
223C2×H(5,𝔽2)—36no—
224C2×H(5,𝔽2)—34no—
225C22×#41—36no—
226C22×#41—34no—
227C22×#41—31no—
228C22×#41—33no—
229C22×#41—38no—
230C22×#41—33no—
231C22×#41—31no—
232C22×#41—38no—
233C22×#41—34no—
234C22×#41—616no—
235C23×Q8C2×D311yescharacteristic, complemented
236C23×D4—33no—
237C24×C4—33no—
238#550—38no—
239#550—38no—
240D4×Q8—38no—
241D4×Q8C2×D318yescomplemented
242#548—38no—
243#548—38no—
244#548—38no—
245#548C2×D318yescomplemented
246#547—324no—
247#547—324no—
248#546—324no—
249#546—324no—
250#546—324no—
251#546—324no—
252D42—324no—
253D42—324no—
254#537—324no—
255#536—36no—
256#536—312no—
257#536C2×D316yescomplemented
258#535—36no—
259#535—312no—
260#535—36no—
261#534—324no—
262#532—312no—
263#532—312no—
264#525—36no—
265#525—36no—
266#525—312no—
267#525—312no—
268#525—324no—
269#525—312no—
270#525—34no—
271#525—324no—
272#525—36no—
273#525C2×D316yescomplemented
274C2×#123—312no—
275C2×C22⋊Q8—312no—
276C2×#121—312no—
277C2×#120—312no—
278#520—38no—
279#519—31no—
280#519C2×D311yescharacteristic, complemented
281#518—36no—
282C4×#41—38no—
283C2×C4×D4—324no—
284C2×#117—36no—
285C24×C3C2411yescharacteristic
286C23×D3—212no—
287C23×D3—412no—
288C23×D3C24112yes—
289C23×D3C24112yes—
290C23×D3C2413yes—
291C23×D3C2413yes—
292C3×#41—216no—
293C3×#41—224no—
294C2×C3×Q8—232no—
295C2×C3×Q8—216no—
296C2×C3×Q8—212no—
297C2×C3×Q8C2×D418yescomplemented
298C2×C3×Q8C24112yes—
299C2×C3×Q8C2416yes—
300C2×C3×Q8C2414yes—
301C2×C3×D4C2418yes—
302C2×C3×D4C2414yes—
303C2×C3×D4C2416yes—
304C22×C3×C4—212no—
305C22×C3×C4C24112yes—
306C22×C3×C4C24112yes—
307C22×C3×C4C2413yes—
308C22×C3×C4C2413yes—
309C2×#67C2418yes—
310C2×#67C2414yes—
311C2×#67C24112yes—
312C2×#67C2414yes—
313C2×#67C24124yes—
314C22×Dic3—24no—
315C22×Dic3C2412yes—
316C22×Dic3C2412yes—
317C22×Dic3C2414yes—
318C22×Dic3C2411yescharacteristic
319C22×Dic3C2411yescharacteristic
320#239—232no—
321#239—216no—
322#239—296no—
323#239—248no—
324#239—248no—
325#239—248no—
326#239—224no—
327#239C2×D4132yescomplemented
328#239C2×D4132yescomplemented
329D3×Q8—216no—
330D3×Q8—224no—
331#237—216no—
332#237—224no—
333D3×D4—248no—
334D3×D4—248no—
335D3×D4—224no—
336D3×D4—448no—
337#235—224no—
338#235—248no—
339#235—248no—
340C2×D12—224no—
341C2×D12—212no—
342C2×D12—296no—
343C2×D12—248no—
344C2×D12C2×D4124yescomplemented
345C2×D12C2416yes—
346C2×D12C24112yes—
347C2×D12C24112yes—
348C2×D12C24124yes—
349C2×D12C24124yes—
350C2×D12C24112yes—
351C2×C4×D3—212no—
352C2×C4×D3—212no—
353C2×C4×D3—212no—
354C2×C4×D3—248no—
355C2×C4×D3—248no—
356C2×C4×D3—248no—
357C2×C4×D3C2×D4124yescomplemented
358C2×C4×D3C24112yes—
359C2×C4×D3C24112yes—
360C2×C4×D3C24112yes—
361C2×C4×D3C24112yes—
362C2×C4×D3C2414yes—
363C2×C4×D3C2416yes—
364C2×C4×D3C2416yes—
365C2×C4×D3C24124yes—
366C2×C4×D3C2416yes—
367C2×C4×D3C2416yes—
368C2×Dic6C2416yes—
369C2×Dic6C2414yes—
370C3×C4⋊C4C24112yes—
371C3×C4⋊C4C24124yes—
372C3×C22⋊C4C2414yes—
373C3×C22⋊C4C2418yes—
374C3×C22⋊C4C24124yes—
375C3×C42C24112yes—
376#217C2414yes—
377#217C2418yes—
378#217C2418yes—
379(C2×D3)⋊C4C24124yes—
380(C2×D3)⋊C4C2418yes—
381(C2×D3)⋊C4C24124yes—
382(C2×D3)⋊C4C24124yes—
383(C2×D3)⋊C4C24124yes—
384C4⋊Dic3C2418yes—
385C4⋊Dic3C24112yes—
386Dic3⋊C4C2418yes—
387Dic3⋊C4C2418yes—
388Dic3⋊C4C24124yes—
389C4×Dic3C2418yes—
390C4×Dic3C24112yes—
391C25—33no—
3922−1+4—28no—
3932−1+4—632no—
3942−1+4—68no—
395H(5,𝔽2)—648no—
396H(5,𝔽2)—632no—
397C2×#41—316no—
398C2×#41—34no—
399C2×#41—34no—
400C2×#41—312no—
401C2×#41—36no—
402C2×#41—312no—
403C2×#41—324no—
404C2×#41—312no—
405C2×#41—38no—
406C2×#41—34no—
407C2×#41—34no—
408C2×#41—36no—
409C2×#41—36no—
410C2×#41—312no—
411C2×#41—312no—
412C2×#41—624no—
413C2×#41—648no—
414C2×#41—624no—
415C2×#41—664no—
416C2×#41—664no—
417C2×#41—632no—
418C2×#41—632no—
419C2×#41—68no—
420C2×#41C22×D316yes—
421C2×#41C22×D314yescomplemented
422C22×Q8—28no—
423C22×Q8—36no—
424C22×Q8—34no—
425C22×Q8C22×D313yes—
426C22×Q8C22×D318yes—
427C22×Q8C22×D311yescharacteristic
428C22×Q8C22×D314yescomplemented
429C22×D4—312no—
430C22×D4—36no—
431C22×D4—312no—
432C22×D4—324no—
433C22×D4—33no—
434C22×D4—36no—
435C22×D4—33no—
436C22×D4—324no—
437C22×D4—312no—
438C22×D4—624no—
439C23×C4—33no—
440C23×C4—31no—
441C23×C4—312no—
442C23×C4—312no—
443C23×C4—312no—
444C23×C4—33no—
445C23×C4—33no—
446C23×C4—33no—
447C23×C4—624no—
448C23×C4C22×D313yes—
449C4⋊Q8—312no—
450C4⋊Q8C22×D3112yescomplemented
451#127—312no—
452#127—312no—
453#124—312no—
454#124—312no—
455#124—312no—
456#124C22×D3112yescomplemented
457#123—34no—
458#123—312no—
459#123—324no—
460#123—348no—
461#123—34no—
462#123—324no—
463#123C22×D3112yes—
464C22⋊Q8—312no—
465C22⋊Q8—324no—
466C22⋊Q8—312no—
467C22⋊Q8—324no—
468C22⋊Q8—312no—
469C22⋊Q8—38no—
470C22⋊Q8C22×D3112yes—
471C22⋊Q8C22×D3124yescomplemented
472#121—38no—
473#121—312no—
474#121—312no—
475#121—324no—
476#121—312no—
477#121—324no—
478#121—348no—
479#121—324no—
480#121—348no—
481#121C22×D3112yes—
482#120—34no—
483#120—312no—
484#120—324no—
485#120—312no—
486#120—324no—
487#120—348no—
488#120C22×D314yes—
489C4×Q8—38no—
490C4×Q8C22×D318yescomplemented
491C4×D4—38no—
492C4×D4—324no—
493C4×D4—324no—
494C4×D4—324no—
495C4×D4—324no—
496C4×D4—38no—
497C4×D4—324no—
498C4×D4—324no—
499C4×D4—324no—
500C4×D4C22×D3124yes—
501#117—36no—
502#117—312no—
503#117—34no—
504#117—312no—
505#117C22×D316yes—
506C2×C4⋊C4—312no—
507C2×C4⋊C4—324no—
508C2×C22⋊C4—312no—
509C2×C22⋊C4—324no—
510C2×C22⋊C4—324no—
511C2×C42—312no—
512C23×C3—22no—
513C23×C3—24no—
514C23×C3C2514yes—
515C23×C3C2511yescharacteristic
516C23×C3C2512yes—
517C22×D3—26no—
518C22×D3—224no—
519C22×D3—224no—
520C22×D3—224no—
521C22×D3—46no—
522C22×D3—412no—
523C22×D3—46no—
524C22×D3—424no—
525C22×D3—448no—
526C22×D3C22×D4112yes—
527C22×D3C2516yes—
528C22×D3C2514yes—
529C22×D3C2516yes—
530C3×Q8—212no—
531C3×Q8—224no—
532C3×Q8C22×D4116yes—
533C3×D4—28no—
534C3×D4—216no—
535C3×D4—212no—
536C2×C3×C4—26no—
537C2×C3×C4—224no—
538C2×C3×C4—224no—
539C2×C3×C4C22×D4112yes—
540C2×C3×C4C2518yes—
541C2×C3×C4C2516yes—
542C2×C3×C4C2514yes—
543C2×C3×C4C2516yes—
544#67—28no—
545#67—216no—
546#67—224no—
547#67—28no—
548#67—424no—
549C2×Dic3—22no—
550C2×Dic3—24no—
551C2×Dic3—24no—
552C2×Dic3—28no—
553C2×Dic3C22×D414yes—
554C2×Dic3C2518yes—
555C2×Dic3C2514yes—
556C2×Dic3C2512yes—
557C2×Dic3C2511yescharacteristic
558C2×Dic3C2511yescharacteristic
559D12—248no—
560D12—224no—
561D12—224no—
562D12—212no—
563D12—424no—
564D12C22×D4148yes—
565C4×D3—224no—
566C4×D3—224no—
567C4×D3—224no—
568C4×D3—224no—
569C4×D3—28no—
570C4×D3—212no—
571C4×D3—212no—
572C4×D3—424no—
573C4×D3C22×D4124yes—
574C4×D3C22×D4124yes—
575Dic6—212no—
576Dic6—28no—
577C24—33no—
578C24—312no—
579C24—312no—
580C24—33no—
581C24—612no—
582C24—1212no—
583C24C23×D311yescharacteristic
584#41—216no—
585#41—224no—
586#41—332no—
587#41—332no—
588#41—648no—
589#41—648no—
590#41—616no—
591#41—624no—
592#41—648no—
593#41—624no—
594#41—648no—
595#41—696no—
596#41—648no—
597#41—632no—
598#41—616no—
599#41—624no—
600C2×Q8—232no—
601C2×Q8—216no—
602C2×Q8—212no—
603C2×Q8—34no—
604C2×Q8—36no—
605C2×Q8—624no—
606C2×Q8—616no—
607C2×Q8D3×D418yescomplemented
608C2×Q8C23×D316yes—
609C2×Q8C23×D3112yes—
610C2×Q8C23×D314yes—
611C2×D4—38no—
612C2×D4—34no—
613C2×D4—312no—
614C2×D4—34no—
615C2×D4—324no—
616C2×D4—324no—
617C2×D4—312no—
618C2×D4—312no—
619C2×D4—324no—
620C2×D4—36no—
621C2×D4—312no—
622C2×D4—324no—
623C2×D4—696no—
624C2×D4—648no—
625C2×D4—624no—
626C2×D4—624no—
627C2×D4—648no—
628C2×D4—648no—
629C2×D4—612no—
630C2×D4—1248no—
631C2×D4C23×D318yes—
632C2×D4C23×D314yes—
633C2×D4C23×D316yes—
634C22×C4—212no—
635C22×C4—31no—
636C22×C4—324no—
637C22×C4—36no—
638C22×C4—36no—
639C22×C4—32no—
640C22×C4—34no—
641C22×C4—32no—
642C22×C4—31no—
643C22×C4—312no—
644C22×C4—312no—
645C22×C4—34no—
646C22×C4—36no—
647C22×C4—312no—
648C22×C4—312no—
649C22×C4—36no—
650C22×C4—324no—
651C22×C4—612no—
652C22×C4—648no—
653C22×C4—648no—
654C22×C4—648no—
655C22×C4—612no—
656C22×C4—64no—
657C22×C4—612no—
658C22×C4C23×D3112yes—
659C22×C4C23×D3112yes—
660C22×C4C23×D313yes—
661C22×C4C23×D313yes—
662C4⋊C4—38no—
663C4⋊C4—38no—
664C4⋊C4—38no—
665C4⋊C4—312no—
666C4⋊C4—324no—
667C4⋊C4C23×D3112yes—
668C4⋊C4C23×D3124yes—
669C22⋊C4—34no—
670C22⋊C4—38no—
671C22⋊C4—38no—
672C22⋊C4—38no—
673C22⋊C4—324no—
674C22⋊C4—324no—
675C22⋊C4—324no—
676C22⋊C4—324no—
677C22⋊C4C23×D314yes—
678C22⋊C4C23×D318yes—
679C22⋊C4C23×D3124yes—
680C42—38no—
681C42—312no—
682C42C23×D3112yes—
683C22×C3—28no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—24no—
688C22×C3—28no—
689C22×C3C23×D412yes—
690C22×C3#58514yescomplemented
691C22×C3C2611yescharacteristic
692C2×D3—212no—
693C2×D3—26no—
694C2×D3—24no—
695C2×D3—28no—
696C2×D3—212no—
697C2×D3—412no—
698C2×D3—448no—
699C2×D3—412no—
700C2×D3—824no—
701C2×D3C23×D4112yes—
702C3×C4—24no—
703C3×C4—26no—
704C3×C4—28no—
705C3×C4C23×D4112yes—
706Dic3—24no—
707Dic3—22no—
708Dic3—28no—
709Dic3C23×D412yes—
710Dic3C23×D412yes—
711C23—22no—
712C23—24no—
713C23—36no—
714C23—312no—
715C23—34no—
716C23—36no—
717C23—624no—
718C23—624no—
719C23—66no—
720C23—624no—
721C23—126no—
722C23—1212no—
723C23—126no—
724C23—1224no—
725C23—1248no—
726C23C24×D314yes—
727C23C24×D311yescharacteristic
728C23C24×D312yes—
729Q8—224no—
730Q8—212no—
731Q8—68no—
732Q8—612no—
733Q8C2×D3×D4116yes—
734D4—28no—
735D4—216no—
736D4—212no—
737D4—348no—
738D4—624no—
739D4—648no—
740D4—68no—
741D4—624no—
742D4—68no—
743D4—616no—
744D4—624no—
745D4—612no—
746D4—1224no—
747D4—1224no—
748C2×C4—26no—
749C2×C4—224no—
750C2×C4—224no—
751C2×C4—34no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—324no—
755C2×C4—324no—
756C2×C4—38no—
757C2×C4—32no—
758C2×C4—34no—
759C2×C4—68no—
760C2×C4—612no—
761C2×C4—612no—
762C2×C4—624no—
763C2×C4—624no—
764C2×C4—64no—
765C2×C4—64no—
766C2×C4—68no—
767C2×C4—62no—
768C2×C4—624no—
769C2×C4—624no—
770C2×C4—1224no—
771C2×C4C2×D3×D4112yes—
772C2×C4C24×D318yes—
773C2×C4C24×D314yes—
774C2×C4C24×D316yes—
775C2×C4C24×D316yes—
776C2×C3—22no—
777C2×C3—24no—
778C2×C3—44no—
779C2×C3C24×D411yescharacteristic
780C2×C3C2×#58512yes—
781D3—212no—
782D3—46no—
783D3—44no—
784C22—28no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—24no—
789C22—28no—
790C22—312no—
791C22—612no—
792C22—66no—
793C22—64no—
794C22—68no—
795C22—612no—
796C22—1212no—
797C22—1248no—
798C22—1212no—
799C22—2424no—
800C22C22×D3×D412yes—
801C22#596814yescomplemented
802C22C25×D311yescharacteristic
803C4—24no—
804C4—26no—
805C4—28no—
806C4—32no—
807C4—32no—
808C4—62no—
809C4—64no—
810C4—68no—
811C4C22×D3×D4112yes—
812C3#6281111yescharacteristic, complemented, Sylow
813C2—22no—
814C2—24no—
815C2—44no—
816C2—612no—
817C2—126no—
818C2—124no—
819C2C23×D3×D411yescharacteristic
820C2C2×#596812yes—
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3486C2
hypercenter#3486D3
hypocenterC3#62811
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. C2×#5968C2semidirect
2. C23×#239C2semidirect
3. C3×#3486C2semidirect
4. #87290C2semidirect
5. #87251C2semidirect
6. #86745C2semidirect
7. D4×#239C2semidirect
8. #86713C2semidirect
9. #86710C2semidirect
10. #86354C2semidirect
11. #86338C2semidirect
12. #86039C2semidirect
13. D3×#525C2semidirect
14. #85874C2semidirect
15. #85872C2semidirect
17. C2×C3×2−1+4C22semidirect
18. C23×C3×Q8C22semidirect
20. C2×#1009C22semidirect
21. C2×#1009C22semidirect
22. C2×D3×#41C22semidirect
23. C2×D3×#41C22semidirect
24. C2×#1007C22semidirect
25. C2×#1007C22semidirect
28. C22×#239C22semidirect
29. C22×#239C22semidirect
30. C22×#239C22semidirect
31. C22×#239C22semidirect
32. C22×#239C22semidirect
33. C22×#239C22semidirect
34. C23×D12C22semidirect
35. C23×C4×D3C22semidirect
36. C3×D4×Q8C22semidirect
37. C3×#548C22semidirect
38. C3×#536C22semidirect
39. C3×#525C22semidirect
40. C3×#519C22semidirect
41. #5834C22semidirect
42. #5830C22semidirect
43. #5828C22semidirect
44. #5817C22semidirect
45. #5817C22semidirect
46. #5816C22semidirect
47. Q8×#67C22semidirect
48. #5812C22semidirect
49. #5791C22semidirect
50. #5726C22semidirect
51. #5725C22semidirect
52. #5724C22semidirect
53. #5676C22semidirect
54. #5674C22semidirect
55. #5668C22semidirect
56. #5656C22semidirect
57. #5653C22semidirect
58. D3×#123C22semidirect
59. #5631C22semidirect
60. #5630C22semidirect
61. #5630C22semidirect
62. #5629C22semidirect
63. #5627C22semidirect
64. #5627C22semidirect
65. D3×C22⋊Q8C22semidirect
66. #5609C22semidirect
67. #5606C22semidirect
68. D3×#121C22semidirect
69. D3×#120C22semidirect
70. #5586C22semidirect
71. #5577C22semidirect
72. #5576C22semidirect
73. #5574C22semidirect
74. C4×#239C22semidirect
75. #5550C22semidirect
76. D4×D12C22semidirect
77. #5547C22semidirect
78. C4×D3×D4C22semidirect
79. #5525C22semidirect
80. #5524C22semidirect
81. #5521C22semidirect
82. D3×#117C22semidirect
90. #3486D3semidirect
101. C2×C3×#41C23semidirect
106. C22×C3×Q8C23semidirect
121. C2×#239D4semidirect
128. C2×#239C23semidirect
129. C2×#239C23semidirect
130. C2×#239C23semidirect
131. C2×D3×Q8C23semidirect
132. C2×D3×Q8C23semidirect
134. C2×#237C23semidirect
137. C2×D3×D4C23semidirect
138. C2×D3×D4C23semidirect
140. C2×#235C23semidirect
141. C2×#235C23semidirect
147. C22×D12C23semidirect
155. C22×C4×D3C23semidirect
156. C3×C4⋊Q8C23semidirect
157. C3×#124C23semidirect
160. C3×C22⋊Q8C23semidirect
163. C3×C4×Q8C23semidirect
167. #947C23semidirect
168. #947C23semidirect
169. #946C23semidirect
170. #946C23semidirect
171. Q8×Dic3C23semidirect
172. #944C23semidirect
173. #940C23semidirect
175. #938C23semidirect
181. #930C23semidirect
184. C4×#67C23semidirect
187. #897C23semidirect
188. #896C23semidirect
189. #895C23semidirect
190. #895C23semidirect
191. #895C23semidirect
192. #894C23semidirect
193. #894C23semidirect
194. #893C23semidirect
195. #893C23semidirect
196. #892C23semidirect
197. D3×C4⋊C4C23semidirect
198. D3×C4⋊C4C23semidirect
200. #884C23semidirect
201. #884C23semidirect
202. #883C23semidirect
205. #882C23semidirect
207. #67⋊C4C23semidirect
210. D3×C22⋊C4C23semidirect
213. #875C23semidirect
214. #874C23semidirect
215. C4×D12C23semidirect
216. C4×D12C23semidirect
217. #872C23semidirect
218. C42×D3C23semidirect
222. C2×2−1+4C2×D3semidirect
235. C23×Q8C2×D3semidirect
241. D4×Q8C2×D3semidirect
245. #548C2×D3semidirect
257. #536C2×D3semidirect
273. #525C2×D3semidirect
280. #519C2×D3semidirect
297. C2×C3×Q8C2×D4semidirect
327. #239C2×D4semidirect
328. #239C2×D4semidirect
344. C2×D12C2×D4semidirect
357. C2×C4×D3C2×D4semidirect
421. C2×#41C22×D3semidirect
428. C22×Q8C22×D3semidirect
450. C4⋊Q8C22×D3semidirect
456. #124C22×D3semidirect
471. C22⋊Q8C22×D3semidirect
490. C4×Q8C22×D3semidirect
607. C2×Q8D3×D4semidirect
690. C22×C3#585semidirect
801. C22#5968semidirect
812. C3#62811semidirect

Maximal subgroups

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

subgroupindex
C2×#59682
C23×#2392
C3×#34862
#872902
#872512
#867452
D4×#2392
#867132
#867102
#863542
#863382
#860392
D3×#5252
#858742
#858722
#628113