Finite Group Databasebeta

← #11703581

Subgroups — #11703581

Order 768.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#41C211yesmaximal, characteristic, complemented
2#87275C212yesmaximal, complemented
3#85853C212yesmaximal, complemented
4#85852C216yesmaximal, complemented
5#85850C213yesmaximal, complemented
6#85848C213yesmaximal, complemented
7#85846C211yesmaximal, characteristic, complemented
8#85845C212yesmaximal, complemented
9#85843C216yesmaximal, complemented
10#85838C216yesmaximal, complemented
11C4×#1009C212yesmaximal, complemented
12#85828C211yesmaximal, characteristic, complemented
13#85821C212yesmaximal, complemented
14#85802C212yesmaximal, complemented
15#85790C216yesmaximal, complemented
16D4×#235C216yesmaximal, complemented
17#85747C216yesmaximal, complemented
18#85680C213yesmaximal, complemented
19C2×#5477C213yesmaximal, complemented
20#62800—31nomaximal, Sylow
21C22×C3×#41C2211yescharacteristic
22C2×#1009C2212yes—
23C22×#235C2216yescomplemented
24C3×C4×#41C2211yescharacteristic
25C3×C4×#41C2211yescharacteristic
26C3×C4×#41C2213yescomplemented
27C3×C4×#41C2213yescomplemented
28C3×C4×#41C2211yescharacteristic, complemented
29C3×C4×#41C2213yescomplemented
30C3×C4×#41C2213yescomplemented
31C3×C4×#41C2211yescharacteristic, complemented
32C2×C3×C4×Q8C2211yescharacteristic, complemented
33C2×C3×C4×Q8C2211yescharacteristic, complemented
34C2×C3×C4×D4C2213yescomplemented
35C2×C3×C4×D4C2213yescomplemented
36C2×C3×#117C2213yescomplemented
37C22×C3×C42C2213yescomplemented
38#5834C2214yescomplemented
39#5833C2216yescomplemented
40#5830C2216yescomplemented
41#5829C22112yescomplemented
42#5827C2212yes—
43#5817C2214yescomplemented
44D4×#67C22112yescomplemented
45#5791C2216yescomplemented
46#5791C2216yescomplemented
47#5791C2216yescomplemented
48C2×#930C2216yescomplemented
49C2×#930C2216yescomplemented
50#5585C2216yescomplemented
51#5585C2216yescomplemented
52#5584C2216yescomplemented
53#5582C22112yescomplemented
54#5580C22112yescomplemented
55#5579C2216yescomplemented
56#5577C2212yescomplemented
57#5577C2212yescomplemented
58#5574C2214yescomplemented
59C4×#239C2214yescomplemented
60#5570C2212yescomplemented
61Q8×Dic6C2212yescomplemented
62#5565C22112yescomplemented
63#5563C2216yescomplemented
64#5562C22112yescomplemented
65#5560C22124yescomplemented
66#5553C2216yescomplemented
67#5553C2216yescomplemented
68#5552C22112yescomplemented
69#5551C2216yescomplemented
70#5550C22112yescomplemented
71#5550C22112yescomplemented
72D4×D12C2216yescomplemented
73D4×D12C2216yescomplemented
74#5548C22112yescomplemented
75#5547C22124yescomplemented
76#5545C22112yescomplemented
77C4×D3×D4C22112yescomplemented
78#5543C2216yescomplemented
79D4×Dic6C2216yescomplemented
80#5535C22112yescomplemented
81#5534C22112yescomplemented
82#5532C22112yescomplemented
83#5530C22112yescomplemented
84#5527C22124yescomplemented
85#5525C2216yescomplemented
86#5523C2216yescomplemented
87#5521C2216yescomplemented
88#5519C2216yescomplemented
89#5514C22112yescomplemented
90#5507C22112yescomplemented
91#5490C22124yescomplemented
92#5479C2216yescomplemented
93#5479C2216yescomplemented
94#5479C2216yescomplemented
95#5479C2216yescomplemented
96#5479C2216yescomplemented
97#5479C2216yescomplemented
98#5477C2216yescomplemented
99#5477C2216yescomplemented
100#5477C2216yescomplemented
101#5477C2216yescomplemented
102#5477C2213yescomplemented
103#5477C2213yescomplemented
104#5477C2216yescomplemented
105#5477C2216yescomplemented
106#5477C2213yescomplemented
107#5477C2216yescomplemented
108C2×#875C2216yescomplemented
109C2×#874C2213yescomplemented
110C4×#235C2216yescomplemented
111C4×#235C2216yescomplemented
112C4×#235C2216yescomplemented
113C2×C4×D12C2216yescomplemented
114C2×C4×D12C2216yescomplemented
115#5470C2213yescomplemented
116#5470C2213yescomplemented
117#5470C2211yescharacteristic, complemented
118C2×#869C2213yescomplemented
119#3522—32no—
120#3519—36no—
121#3517—32no—
122#3514—36no—
123#3511—33no—
124#3508—33no—
125#3503—31no—
126#3498—31no—
127#3494—36no—
128#3488—32no—
129#3483—32no—
130#3481—36no—
131#3480—32no—
132D4×#41—36no—
133#3460—36no—
134#3444—33no—
135C2×#532—33no—
136C4×H(5,𝔽2)—32no—
137C2×C4×#41D311yescharacteristic, complemented
138C2×C3×#41—28no—
139C2×C3×#41C2313yes—
140C2×C3×#41C2313yes—
141C2×C3×#41C2311yescharacteristic
142C2×C3×#41C2311yescharacteristic
143C22×C3×Q8C2311yescharacteristic
144C22×C3×D4C2313yes—
145C23×C3×C4C2313yes—
146C23×C3×C4C2313yes—
147C23×C3×C4C2313yes—
148C22×#67C23112yes—
149#1009—216no—
150C2×#239C2314yes—
151C2×D3×D4C23112yes—
152C2×#235—424no—
153C2×#235C2316yes—
154C2×#235C2316yes—
155C2×#235C23112yes—
156C2×#235C23112yes—
157C2×#235C23112yes—
158C2×#235C2316yes—
159C22×D12C2316yes—
160C22×D12C2316yes—
161C22×D12C2316yes—
162C22×C4×D3C23112yes—
163C22×Dic6C2316yes—
164C3×C4×Q8C2311yescharacteristic
165C3×C4×Q8C2311yescharacteristic
166C3×C4×Q8C2311yescharacteristic
167C3×C4×Q8C2311yescharacteristic
168C3×C4×Q8C2313yes—
169C3×C4×Q8C2313yes—
170C3×C4×Q8C2313yes—
171C3×C4×Q8C2313yes—
172C3×C4×D4C2313yes—
173C3×C4×D4C2313yes—
174C3×C4×D4C2313yes—
175C3×C4×D4C2313yes—
176C3×C4×D4C2316yes—
177C3×C4×D4C2313yes—
178C3×C4×D4C2316yes—
179C3×C4×D4C2316yes—
180C3×C4×D4C2313yes—
181C3×C4×D4C2313yes—
182C3×C4×D4C2316yes—
183C3×C4×D4C2313yes—
184C3×#117C2313yes—
185C3×#117C2313yes—
186C3×#117C2316yes—
187C3×#117C2313yes—
188C3×#117C2313yes—
189C3×#117C2316yes—
190C2×C3×C4⋊C4C2313yes—
191C2×C3×C4⋊C4C2313yes—
192C2×C3×C22⋊C4C2316yes—
193C2×C3×C42C2313yes—
194C2×C3×C42C2311yescharacteristic
195C2×C3×C42C2313yes—
196C2×C3×C42C2313yes—
197C2×C3×C42C2313yes—
198C2×C3×C42C2313yes—
199C2×C3×C42C2313yes—
200C2×C3×C42C2313yes—
201C2×C3×C42C2313yes—
202C2×C3×C42C2313yes—
203C2×C3×C42C2313yes—
204C2×C3×C42C2313yes—
205#953C23112yes—
206#947C23112yes—
207#946C23112yes—
208Q8×Dic3C2314yes—
209#940C23112yes—
210#939C23124yes—
211#938C23112yes—
212#937C23124yes—
213D4×Dic3C23112yes—
214#930C2316yes—
215#930C2316yes—
216#930C23112yes—
217#930C23112yes—
218#930C23112yes—
219#930C23112yes—
220#930C23112yes—
221#930C23112yes—
222#930C2316yes—
223#930C2316yes—
224#930C2316yes—
225#930C2316yes—
226#929C23112yes—
227#929C23112yes—
228#929C23112yes—
229C4×#67C23112yes—
230C4×#67C23112yes—
231C4×#67C23112yes—
232C4×#67C23112yes—
233C4×#67C23112yes—
234C4×#67C23112yes—
235C2×(C2×D3)⋊C4C23112yes—
236C2×(C2×D3)⋊C4C23112yes—
237#926C2312yes—
238#926C2316yes—
239#926C2316yes—
240C2×C4⋊Dic3C2316yes—
241C2×C4⋊Dic3C2316yes—
242#924C2312yes—
243#924C2312yes—
244#924C2316yes—
245#924C2316yes—
246#924C2316yes—
247#924C2316yes—
248#898C23124yes—
249#896C23124yes—
250#895C23112yes—
251#895C23112yes—
252#894C23124yes—
253#894C23124yes—
254#893C23112yes—
255#893C23112yes—
256#892C23112yes—
257D3×C4⋊C4C23112yes—
258#890C23112yes—
259#888C23112yes—
260#885C23124yes—
261#884C23124yes—
262#884C23124yes—
263#883C23124yes—
264#882C23124yes—
265#67⋊C4C23124yes—
266D3×C22⋊C4C23124yes—
267#878C23124yes—
268#876C23112yes—
269#876C23112yes—
270#875C2316yes—
271#875C23112yes—
272#875C23112yes—
273#875C23112yes—
274#875C2316yes—
275#875C2316yes—
276#874C2313yes—
277#874C2316yes—
278#874C2316yes—
279#874C2316yes—
280C4×D12C2316yes—
281C4×D12C2316yes—
282C4×D12C23112yes—
283C4×D12C23112yes—
284C4×D12C23112yes—
285C4×D12C23112yes—
286C4×D12C23112yes—
287C4×D12C23112yes—
288C4×D12C2316yes—
289C4×D12C2316yes—
290C4×D12C2316yes—
291C4×D12C2316yes—
292#872C23112yes—
293#872C23112yes—
294#872C23112yes—
295C42×D3C23112yes—
296#870C2312yes—
297#870C2316yes—
298#870C2316yes—
299#869C2313yes—
300#869C2316yes—
301#869C2316yes—
302#869C2316yes—
303#869C2311yescharacteristic
304#869C2311yescharacteristic
305C4×Dic6C2312yes—
306C4×Dic6C2312yes—
307C4×Dic6C2316yes—
308C4×Dic6C2316yes—
309C4×Dic6C2316yes—
310C4×Dic6C2316yes—
311C2×H(5,𝔽2)—32no—
312C22×#41—36no—
313C22×#41C2×D311yescharacteristic
314#559—36no—
315#559—36no—
316Q82—32no—
317#557—32no—
318#556—36no—
319#555—36no—
320#555—312no—
321#554—36no—
322#554—36no—
323#553—312no—
324#553—312no—
325#553—312no—
326#551—324no—
327#550—34no—
328#550—32no—
329#550—32no—
330#550—36no—
331#550—36no—
332D4×Q8—36no—
333#548—34no—
334#548—312no—
335#547—36no—
336#547—312no—
337#546—312no—
338#546—312no—
339#546—312no—
340#546—324no—
341D42—312no—
342D42—36no—
343D42—36no—
344#544—36no—
345#542—312no—
346#542—312no—
347#540—312no—
348#540—312no—
349#538—324no—
350#537—36no—
351#535—36no—
352#535—36no—
353#533—31no—
354#533—33no—
355#533—33no—
356#532—312no—
357#532—33no—
358#532—36no—
359#532—36no—
360#532—36no—
361#532—36no—
362#532—36no—
363#532—36no—
364#532—36no—
365#532—33no—
366#532—33no—
367C2×C4⋊Q8—33no—
368C2×#127—33no—
369#529—312no—
370#529—36no—
371#529—36no—
372#529—36no—
373#529—36no—
374#529—36no—
375#529—36no—
376C2×#124—36no—
377#525—36no—
378#525—36no—
379#525—36no—
380#525—324no—
381C2×#121—36no—
382C2×#121—36no—
383#520—32no—
384#520—34no—
385#520—36no—
386#518—312no—
387#518—36no—
388C4×#41—34no—
389C4×#41—36no—
390C4×#41—36no—
391C4×#41—36no—
392C4×#41C2×D311yescharacteristic
393C4×#41C2×D311yescharacteristic
394C4×#41C2×D313yescomplemented
395C4×#41C2×D313yescomplemented
396C4×#41C2×D311yescharacteristic, complemented
397C4×#41C2×D313yescomplemented
398C4×#41C2×D313yescomplemented
399C4×#41C2×D311yescharacteristic, complemented
400C2×C4×Q8C2×D311yescharacteristic, complemented
401C2×C4×Q8C2×D311yescharacteristic, complemented
402C2×C4×D4—312no—
403C2×C4×D4—36no—
404C2×C4×D4—36no—
405C2×C4×D4C2×D313yescomplemented
406C2×C4×D4C2×D313yescomplemented
407C2×#117C2×D313yescomplemented
408C22×C42C2×D313yescomplemented
409C24×C3C2413yes—
410C23×D3C24112yes—
411C3×#41—24no—
412C3×#41—212no—
413C3×#41—212no—
414C3×#41#4118yescomplemented
415C2×C3×Q8—24no—
416C2×C3×Q8C2413yes—
417C2×C3×Q8C2411yescharacteristic
418C2×C3×D4—212no—
419C2×C3×D4C2416yes—
420C2×C3×D4C2413yes—
421C2×C3×D4C2413yes—
422C22×C3×C4—212no—
423C22×C3×C4—212no—
424C22×C3×C4—46no—
425C22×C3×C4C2413yes—
426C22×C3×C4C2411yescharacteristic
427C22×C3×C4C2411yescharacteristic
428C22×C3×C4C2413yes—
429C22×C3×C4C2413yes—
430C22×C3×C4C2413yes—
431C22×C3×C4C2413yes—
432C22×C3×C4C2413yes—
433C22×C3×C4C2413yes—
434C22×C3×C4C2413yes—
435C22×C3×C4C2413yes—
436C22×C3×C4C2413yes—
437C22×C3×C4C2413yes—
438C22×C3×C4C2413yes—
439C22×C3×C4C2413yes—
440C22×C3×C4C2413yes—
441C22×C3×C4C2413yes—
442C22×C3×C4C2411yescharacteristic
443C2×#67—424no—
444C2×#67C24112yes—
445C2×#67C24112yes—
446C2×#67C24124yes—
447C2×#67C24112yes—
448C22×Dic3C24112yes—
449#239—216no—
450D3×D4—248no—
451#235—224no—
452#235—224no—
453#235—424no—
454#235—412no—
455#235—424no—
456#235—424no—
457C2×D12—224no—
458C2×D12—412no—
459C2×D12—412no—
460C2×D12C2416yes—
461C2×D12C2416yes—
462C2×D12C2416yes—
463C2×D12C24112yes—
464C2×D12C24112yes—
465C2×D12C24112yes—
466C2×C4×D3—424no—
467C2×C4×D3C24112yes—
468C2×C4×D3C24112yes—
469C2×C4×D3C24112yes—
470C2×C4×D3C24124yes—
471C2×Dic6—412no—
472C2×Dic6C2412yes—
473C2×Dic6C2412yes—
474C2×Dic6C2416yes—
475C2×Dic6C24112yes—
476C3×C4⋊C4C2413yes—
477C3×C4⋊C4C2413yes—
478C3×C4⋊C4C2413yes—
479C3×C4⋊C4C2413yes—
480C3×C4⋊C4C2416yes—
481C3×C4⋊C4C2416yes—
482C3×C22⋊C4C2416yes—
483C3×C22⋊C4C2416yes—
484C3×C22⋊C4C2416yes—
485C3×C22⋊C4C2416yes—
486C3×C42C2413yes—
487C3×C42C2413yes—
488C3×C42C2411yescharacteristic
489C3×C42C2411yescharacteristic
490C3×C42C2413yes—
491C3×C42C2413yes—
492C3×C42C2411yescharacteristic
493C3×C42C2413yes—
494C3×C42C2413yes—
495C3×C42C2411yescharacteristic
496C3×C42C2413yes—
497C3×C42C2413yes—
498C3×C42C2413yes—
499C3×C42C2413yes—
500C3×C42C2413yes—
501C3×C42C2413yes—
502#217C24112yes—
503#217C24112yes—
504#217C2414yes—
505(C2×D3)⋊C4C24112yes—
506(C2×D3)⋊C4C24112yes—
507(C2×D3)⋊C4C24112yes—
508(C2×D3)⋊C4C24112yes—
509(C2×D3)⋊C4C24112yes—
510(C2×D3)⋊C4C24112yes—
511(C2×D3)⋊C4C24124yes—
512(C2×D3)⋊C4C24124yes—
513C4⋊Dic3C2412yes—
514C4⋊Dic3C2412yes—
515C4⋊Dic3C2416yes—
516C4⋊Dic3C2416yes—
517C4⋊Dic3C2412yes—
518C4⋊Dic3C2412yes—
519C4⋊Dic3C24112yes—
520C4⋊Dic3C24112yes—
521Dic3⋊C4C2414yes—
522Dic3⋊C4C2414yes—
523Dic3⋊C4C24112yes—
524Dic3⋊C4C24112yes—
525Dic3⋊C4C24112yes—
526Dic3⋊C4C24112yes—
527C4×Dic3C2414yes—
528C4×Dic3C24112yes—
529C4×Dic3C24112yes—
530H(5,𝔽2)—616no—
531C2×#41—28no—
532C2×#41—34no—
533C2×#41—36no—
534C2×#41—36no—
535C2×#41—36no—
536C2×#41—312no—
537C2×#41—312no—
538C2×#41—312no—
539C2×#41—1224no—
540C2×#41C22×D313yes—
541C2×#41C22×D313yes—
542C2×#41C22×D311yescharacteristic
543C2×#41C22×D311yescharacteristic
544C22×Q8—36no—
545C22×Q8C22×D311yescharacteristic
546C22×D4—312no—
547C22×D4—312no—
548C22×D4—36no—
549C22×D4—36no—
550C22×D4—36no—
551C22×D4C22×D313yes—
552C23×C4—312no—
553C23×C4C22×D313yes—
554C23×C4C22×D313yes—
555C23×C4C22×D313yes—
556C4⋊Q8—312no—
557C4⋊Q8—33no—
558C4⋊Q8—36no—
559C4⋊Q8—36no—
560C4⋊Q8—36no—
561C4⋊Q8—31no—
562C4⋊Q8—31no—
563#127—312no—
564#127—33no—
565#127—36no—
566#127—36no—
567#127—36no—
568#126—324no—
569#126—312no—
570#126—312no—
571#125—312no—
572#125—32no—
573#125—36no—
574#125—36no—
575#124—312no—
576#124—324no—
577#124—36no—
578#124—312no—
579#124—312no—
580#124—312no—
581#124—36no—
582#124—36no—
583#123—312no—
584#123—312no—
585#123—312no—
586#123—324no—
587#123—324no—
588#123—324no—
589C22⋊Q8—312no—
590C22⋊Q8—32no—
591C22⋊Q8—32no—
592C22⋊Q8—36no—
593C22⋊Q8—36no—
594C22⋊Q8—36no—
595C22⋊Q8—36no—
596C22⋊Q8—324no—
597C22⋊Q8—324no—
598#121—324no—
599#121—312no—
600#121—36no—
601#121—36no—
602#121—312no—
603#121—312no—
604#121—312no—
605#121—312no—
606#121—312no—
607#121—312no—
608#121—36no—
609#121—36no—
610#121—36no—
611#121—36no—
612#121—312no—
613#121—312no—
614#121—324no—
615#121—324no—
616#120—312no—
617#120—324no—
618#120—324no—
619C4×Q8—34no—
620C4×Q8—32no—
621C4×Q8—32no—
622C4×Q8—36no—
623C4×Q8—36no—
624C4×Q8—36no—
625C4×Q8—36no—
626C4×Q8C22×D311yescharacteristic
627C4×Q8C22×D311yescharacteristic
628C4×Q8C22×D311yescharacteristic
629C4×Q8C22×D311yescharacteristic
630C4×Q8C22×D313yes—
631C4×Q8C22×D313yes—
632C4×Q8C22×D313yes—
633C4×Q8C22×D313yes—
634C4×D4—312no—
635C4×D4—312no—
636C4×D4—312no—
637C4×D4—312no—
638C4×D4—312no—
639C4×D4—312no—
640C4×D4—312no—
641C4×D4—312no—
642C4×D4—312no—
643C4×D4—324no—
644C4×D4—312no—
645C4×D4—36no—
646C4×D4—36no—
647C4×D4—312no—
648C4×D4—312no—
649C4×D4—312no—
650C4×D4—312no—
651C4×D4—312no—
652C4×D4—36no—
653C4×D4—36no—
654C4×D4—36no—
655C4×D4—36no—
656C4×D4C22×D313yes—
657C4×D4C22×D313yes—
658C4×D4C22×D313yes—
659C4×D4C22×D313yes—
660C4×D4C22×D316yes—
661C4×D4C22×D313yes—
662C4×D4C22×D316yes—
663C4×D4C22×D313yes—
664C4×D4C22×D316yes—
665C4×D4C22×D316yes—
666C4×D4C22×D313yes—
667C4×D4C22×D313yes—
668#117—32no—
669#117—36no—
670#117—36no—
671#117—312no—
672#117—312no—
673#117—312no—
674#117—312no—
675#117C22×D313yes—
676#117C22×D313yes—
677#117C22×D316yes—
678#117C22×D316yes—
679#117C22×D313yes—
680#117C22×D313yes—
681C2×C4⋊C4—36no—
682C2×C4⋊C4—36no—
683C2×C4⋊C4—312no—
684C2×C4⋊C4C22×D313yes—
685C2×C4⋊C4C22×D313yes—
686C2×C22⋊C4—312no—
687C2×C22⋊C4—312no—
688C2×C22⋊C4—324no—
689C2×C22⋊C4C22×D316yes—
690C2×C42—312no—
691C2×C42C22×D313yes—
692C2×C42C22×D313yes—
693C2×C42C22×D313yes—
694C2×C42C22×D313yes—
695C2×C42C22×D313yes—
696C2×C42C22×D313yes—
697C2×C42C22×D313yes—
698C2×C42C22×D313yes—
699C2×C42C22×D313yes—
700C2×C42C22×D313yes—
701C2×C42C22×D313yes—
702C2×C42C22×D311yescharacteristic
703C23×C3—26no—
704C23×C3—26no—
705C23×C3—43no—
706C23×C3C2513yes—
707C23×C3C2513yes—
708C23×C3C2511yescharacteristic
709C22×D3—224no—
710C22×D3—412no—
711C22×D3—412no—
712C22×D3C25112yes—
713C3×Q8—26no—
714C3×Q8C2×#4114yescomplemented
715C3×D4—212no—
716C3×D4—26no—
717C3×D4C2×#41112yescomplemented
718C2×C3×C4—26no—
719C2×C3×C4—26no—
720C2×C3×C4—22no—
721C2×C3×C4—26no—
722C2×C3×C4—26no—
723C2×C3×C4—26no—
724C2×C3×C4—26no—
725C2×C3×C4—26no—
726C2×C3×C4—26no—
727C2×C3×C4—26no—
728C2×C3×C4—26no—
729C2×C3×C4—26no—
730C2×C3×C4—22no—
731C2×C3×C4—43no—
732C2×C3×C4—43no—
733C2×C3×C4—43no—
734C2×C3×C4C2×#41112yescomplemented
735C2×C3×C4H(5,𝔽2)14yescomplemented
736C2×C3×C4C2513yes—
737C2×C3×C4C2513yes—
738C2×C3×C4C2511yescharacteristic
739C2×C3×C4C2511yescharacteristic
740C2×C3×C4C2513yes—
741C2×C3×C4C2513yes—
742C2×C3×C4C2513yes—
743C2×C3×C4C2513yes—
744C2×C3×C4C2511yescharacteristic
745C2×C3×C4C2511yescharacteristic
746C2×C3×C4C2511yescharacteristic
747C2×C3×C4C2511yescharacteristic
748#67—224no—
749#67—224no—
750#67—424no—
751#67—412no—
752C2×Dic3—412no—
753C2×Dic3C2514yes—
754C2×Dic3C2514yes—
755C2×Dic3C25112yes—
756D12—212no—
757D12—224no—
758D12—212no—
759D12—212no—
760D12—412no—
761D12—412no—
762C4×D3—224no—
763C4×D3—224no—
764C4×D3—424no—
765C4×D3—412no—
766Dic6—24no—
767Dic6—212no—
768Dic6—24no—
769Dic6—412no—
770C24—312no—
771C24C23×D313yes—
772#41—24no—
773#41—212no—
774#41—212no—
775#41—616no—
776#41—624no—
777#41—624no—
778#41—1224no—
779#41—1224no—
780#41—1224no—
781#41—1212no—
782#41#23518yescomplemented
783C2×Q8—24no—
784C2×Q8—32no—
785C2×Q8—32no—
786C2×Q8—36no—
787C2×Q8—312no—
788C2×Q8—1212no—
789C2×Q8C23×D313yes—
790C2×Q8C23×D311yescharacteristic
791C2×D4—212no—
792C2×D4—312no—
793C2×D4—312no—
794C2×D4—312no—
795C2×D4—324no—
796C2×D4—312no—
797C2×D4—36no—
798C2×D4—36no—
799C2×D4—36no—
800C2×D4—312no—
801C2×D4—312no—
802C2×D4—648no—
803C2×D4—624no—
804C2×D4—1212no—
805C2×D4—1212no—
806C2×D4—1224no—
807C2×D4C23×D316yes—
808C2×D4C23×D313yes—
809C2×D4C23×D313yes—
810C22×C4—212no—
811C22×C4—212no—
812C22×C4—312no—
813C22×C4—312no—
814C22×C4—312no—
815C22×C4—312no—
816C22×C4—324no—
817C22×C4—46no—
818C22×C4—1224no—
819C22×C4C23×D311yescharacteristic
820C22×C4C23×D311yescharacteristic
821C22×C4C23×D313yes—
822C22×C4C23×D313yes—
823C22×C4C23×D313yes—
824C22×C4C23×D313yes—
825C22×C4C23×D313yes—
826C22×C4C23×D313yes—
827C22×C4C23×D313yes—
828C22×C4C23×D313yes—
829C22×C4C23×D313yes—
830C22×C4C23×D313yes—
831C22×C4C23×D313yes—
832C22×C4C23×D313yes—
833C22×C4C23×D313yes—
834C22×C4C23×D313yes—
835C22×C4C23×D313yes—
836C22×C4C23×D311yescharacteristic
837C4⋊C4—312no—
838C4⋊C4—36no—
839C4⋊C4—36no—
840C4⋊C4—312no—
841C4⋊C4—312no—
842C4⋊C4—32no—
843C4⋊C4—32no—
844C4⋊C4—34no—
845C4⋊C4—34no—
846C4⋊C4—32no—
847C4⋊C4—32no—
848C4⋊C4—312no—
849C4⋊C4—312no—
850C4⋊C4—312no—
851C4⋊C4C23×D313yes—
852C4⋊C4C23×D313yes—
853C4⋊C4C23×D313yes—
854C4⋊C4C23×D313yes—
855C4⋊C4C23×D316yes—
856C4⋊C4C23×D316yes—
857C22⋊C4—312no—
858C22⋊C4—34no—
859C22⋊C4—312no—
860C22⋊C4—312no—
861C22⋊C4—324no—
862C22⋊C4—312no—
863C22⋊C4—312no—
864C22⋊C4—324no—
865C22⋊C4—312no—
866C22⋊C4—312no—
867C22⋊C4—312no—
868C22⋊C4C23×D316yes—
869C22⋊C4C23×D316yes—
870C22⋊C4C23×D316yes—
871C22⋊C4C23×D316yes—
872C42—312no—
873C42—312no—
874C42—34no—
875C42C23×D311yescharacteristic
876C42C23×D311yescharacteristic
877C42C23×D313yes—
878C42C23×D313yes—
879C42C23×D313yes—
880C42C23×D313yes—
881C42C23×D313yes—
882C42C23×D313yes—
883C42C23×D313yes—
884C42C23×D313yes—
885C42C23×D313yes—
886C42C23×D313yes—
887C42C23×D313yes—
888C42C23×D311yescharacteristic
889C42C23×D311yescharacteristic
890C42C23×D313yes—
891C22×C3—21no—
892C22×C3—23no—
893C22×C3—21no—
894C22×C3—23no—
895C22×C3—23no—
896C22×C3—23no—
897C22×C3—23no—
898C22×C3—412no—
899C22×C3C22×#4116yes—
900C22×C3C2×H(5,𝔽2)12yes—
901C22×C3C2611yescharacteristic
902C2×D3—212no—
903C2×D3—212no—
904C2×D3—212no—
905C2×D3—824no—
906C3×C4—21no—
907C3×C4—23no—
908C3×C4—23no—
909C3×C4—23no—
910C3×C4—23no—
911C3×C4—23no—
912C3×C4—21no—
913C3×C4C22×#4112yes—
914C3×C4C22×#4116yes—
915C3×C4C2×H(5,𝔽2)12yes—
916C3×C4C2×H(5,𝔽2)12yes—
917C3×C4#58512yes—
918Dic3—24no—
919Dic3—212no—
920Dic3—24no—
921C23—26no—
922C23—26no—
923C23—312no—
924C23—43no—
925C23—624no—
926C23—1212no—
927C23—1212no—
928C23C24×D313yes—
929C23C24×D313yes—
930C23C24×D311yescharacteristic
931Q8—26no—
932Q8—64no—
933Q8—612no—
934Q8—64no—
935Q8—1212no—
936Q8C2×#23514yescomplemented
937D4—212no—
938D4—26no—
939D4—624no—
940D4—624no—
941D4—612no—
942D4—624no—
943D4—612no—
944D4—612no—
945D4—1212no—
946D4—1212no—
947D4—1224no—
948D4—1212no—
949D4C2×#235112yescomplemented
950C2×C4—26no—
951C2×C4—26no—
952C2×C4—22no—
953C2×C4—26no—
954C2×C4—26no—
955C2×C4—26no—
956C2×C4—26no—
957C2×C4—26no—
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—22no—
961C2×C4—26no—
962C2×C4—26no—
963C2×C4—34no—
964C2×C4—34no—
965C2×C4—312no—
966C2×C4—43no—
967C2×C4—43no—
968C2×C4—43no—
969C2×C4—624no—
970C2×C4—624no—
971C2×C4—1224no—
972C2×C4—1212no—
973C2×C4—1212no—
974C2×C4C2×#235112yescomplemented
975C2×C4#100914yescomplemented
976C2×C4C24×D313yes—
977C2×C4C24×D311yescharacteristic
978C2×C4C24×D311yescharacteristic
979C2×C4C24×D313yes—
980C2×C4C24×D313yes—
981C2×C4C24×D313yes—
982C2×C4C24×D313yes—
983C2×C4C24×D313yes—
984C2×C4C24×D311yescharacteristic
985C2×C4C24×D311yescharacteristic
986C2×C4C24×D311yescharacteristic
987C2×C4C24×D311yescharacteristic
988C2×C3—26no—
989C2×C3—22no—
990C2×C3—43no—
991C2×C3C23×#4111yescharacteristic
992C2×C3C22×H(5,𝔽2)11yescharacteristic
993C2×C3C2×#58511yescharacteristic
994D3—412no—
995C22—21no—
996C22—23no—
997C22—21no—
998C22—23no—
999C22—23no—
1000C22—23no—
1001C22—23no—
1002C22—412no—
1003C22—612no—
1004C22—612no—
1005C22—612no—
1006C22—2424no—
1007C22C22×#23516yes—
1008C22C2×#100912yes—
1009C22C25×D311yescharacteristic
1010C4—21no—
1011C4—23no—
1012C4—23no—
1013C4—23no—
1014C4—21no—
1015C4—23no—
1016C4—23no—
1017C4—64no—
1018C4—612no—
1019C4—64no—
1020C4C22×#23512yes—
1021C4C22×#23516yes—
1022C4C2×#100912yes—
1023C4C2×#100912yes—
1024C4#596412yes—
1025C3#6280011yescharacteristic, complemented, Sylow
1026C2—22no—
1027C2—26no—
1028C2—43no—
1029C2—1212no—
1030C2C23×#23511yescharacteristic
1031C2C22×#100911yescharacteristic
1032C2C2×#596411yescharacteristic
subgroupG/H
centerC2×C4C24×D3
commutator, socle, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×C4×#41C2
hypercenterC2×C4×#41D3
hypocenterC3#62800
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×#41C2semidirect
2. #87275C2semidirect
3. #85853C2semidirect
4. #85852C2semidirect
5. #85850C2semidirect
6. #85848C2semidirect
7. #85846C2semidirect
8. #85845C2semidirect
9. #85843C2semidirect
10. #85838C2semidirect
11. C4×#1009C2semidirect
12. #85828C2semidirect
13. #85821C2semidirect
14. #85802C2semidirect
15. #85790C2semidirect
16. D4×#235C2semidirect
17. #85747C2semidirect
18. #85680C2semidirect
19. C2×#5477C2semidirect
23. C22×#235C22semidirect
26. C3×C4×#41C22semidirect
27. C3×C4×#41C22semidirect
28. C3×C4×#41C22semidirect
29. C3×C4×#41C22semidirect
30. C3×C4×#41C22semidirect
31. C3×C4×#41C22semidirect
32. C2×C3×C4×Q8C22semidirect
33. C2×C3×C4×Q8C22semidirect
34. C2×C3×C4×D4C22semidirect
35. C2×C3×C4×D4C22semidirect
36. C2×C3×#117C22semidirect
37. C22×C3×C42C22semidirect
38. #5834C22semidirect
39. #5833C22semidirect
40. #5830C22semidirect
41. #5829C22semidirect
43. #5817C22semidirect
44. D4×#67C22semidirect
45. #5791C22semidirect
46. #5791C22semidirect
47. #5791C22semidirect
48. C2×#930C22semidirect
49. C2×#930C22semidirect
50. #5585C22semidirect
51. #5585C22semidirect
52. #5584C22semidirect
53. #5582C22semidirect
54. #5580C22semidirect
55. #5579C22semidirect
56. #5577C22semidirect
57. #5577C22semidirect
58. #5574C22semidirect
59. C4×#239C22semidirect
60. #5570C22semidirect
61. Q8×Dic6C22semidirect
62. #5565C22semidirect
63. #5563C22semidirect
64. #5562C22semidirect
65. #5560C22semidirect
66. #5553C22semidirect
67. #5553C22semidirect
68. #5552C22semidirect
69. #5551C22semidirect
70. #5550C22semidirect
71. #5550C22semidirect
72. D4×D12C22semidirect
73. D4×D12C22semidirect
74. #5548C22semidirect
75. #5547C22semidirect
76. #5545C22semidirect
77. C4×D3×D4C22semidirect
78. #5543C22semidirect
79. D4×Dic6C22semidirect
80. #5535C22semidirect
81. #5534C22semidirect
82. #5532C22semidirect
83. #5530C22semidirect
84. #5527C22semidirect
85. #5525C22semidirect
86. #5523C22semidirect
87. #5521C22semidirect
88. #5519C22semidirect
89. #5514C22semidirect
90. #5507C22semidirect
91. #5490C22semidirect
92. #5479C22semidirect
93. #5479C22semidirect
94. #5479C22semidirect
95. #5479C22semidirect
96. #5479C22semidirect
97. #5479C22semidirect
98. #5477C22semidirect
99. #5477C22semidirect
100. #5477C22semidirect
101. #5477C22semidirect
102. #5477C22semidirect
103. #5477C22semidirect
104. #5477C22semidirect
105. #5477C22semidirect
106. #5477C22semidirect
107. #5477C22semidirect
108. C2×#875C22semidirect
109. C2×#874C22semidirect
110. C4×#235C22semidirect
111. C4×#235C22semidirect
112. C4×#235C22semidirect
113. C2×C4×D12C22semidirect
114. C2×C4×D12C22semidirect
115. #5470C22semidirect
116. #5470C22semidirect
117. #5470C22semidirect
118. C2×#869C22semidirect
137. C2×C4×#41D3semidirect
394. C4×#41C2×D3semidirect
395. C4×#41C2×D3semidirect
396. C4×#41C2×D3semidirect
397. C4×#41C2×D3semidirect
398. C4×#41C2×D3semidirect
399. C4×#41C2×D3semidirect
400. C2×C4×Q8C2×D3semidirect
401. C2×C4×Q8C2×D3semidirect
405. C2×C4×D4C2×D3semidirect
406. C2×C4×D4C2×D3semidirect
407. C2×#117C2×D3semidirect
408. C22×C42C2×D3semidirect
414. C3×#41#41semidirect
714. C3×Q8C2×#41semidirect
717. C3×D4C2×#41semidirect
734. C2×C3×C4C2×#41semidirect
735. C2×C3×C4H(5,𝔽2)semidirect
782. #41#235semidirect
936. Q8C2×#235semidirect
949. D4C2×#235semidirect
974. C2×C4C2×#235semidirect
975. C2×C4#1009semidirect
1025. C3#62800semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#412
#872752
#858532
#858522
#858502
#858482
#858462
#858452
#858432
#858382
C4×#10092
#858282
#858212
#858022
#857902
D4×#2352
#857472
#856802
C2×#54772
#628003