Finite Group Databasebeta

← #11905894

Subgroups — #11905894

Order 1152.

3124 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C212yesmaximal, complemented
2D4×#634C211yesmaximal, characteristic, complemented
3C3×#5553C211yesmaximal, characteristic, complemented
4C3×#5548C211yesmaximal, characteristic, complemented
5#10595144C212yesmaximal, complemented
6#10595133C212yesmaximal, complemented
7#10595004C212yesmaximal, complemented
8#10594918C212yesmaximal, complemented
9#10594899C212yesmaximal, complemented
10#10594376C212yesmaximal, complemented
11#10594367C212yesmaximal, complemented
12#10594076C214yesmaximal, complemented
13#10594060C214yesmaximal, complemented
14#10593906C211yesmaximal, characteristic, complemented
15Dic6×D12C211yesmaximal, characteristic, complemented
16#10593897C211yesmaximal, characteristic, complemented
17C4×D3×Dic6C211yesmaximal, characteristic, complemented
18#86784—31nomaximal
19#86222—31nomaximal
20C22×#634C2212yes—
21C2×C3×#235C2212yes—
22C2×C3×#235C2212yes—
23C2×#3805C2214yes—
24C2×#3805C2214yes—
25#64298—216no—
26C2×#3795C2214yes—
27C2×#3795C2212yes—
28C2×#3795C2212yes—
29C2×D3×Dic6C2214yes—
30C2×D3×Dic6C2212yes—
31C2×D3×Dic6C2211yescharacteristic
32C32×C4×D4C2211yescharacteristic
33D4×C3⋊Dic3C2212yes—
34#64133C2212yes—
35#64097C2212yes—
36#64087C2214yes—
37#64078C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C3×#940C2212yes—
40C3×#940C2211yescharacteristic
41C3×#938C2211yescharacteristic
42C3×#930C2212yes—
43C3×C4×#67C2212yes—
44C3×#895C2211yescharacteristic
45C3×#893C2212yes—
46C3×#888C2211yescharacteristic
47C3×#885C2212yes—
48C3×#884C2212yes—
49C3×#884C2214yes—
50C3×#874C2211yescharacteristic
51C3×C4×D12C2211yescharacteristic
52C3×C42×D3C2211yescharacteristic
53C3×C4×Dic6C2211yescharacteristic
54#63980C2214yes—
55#67⋊Dic3C2214yes—
56#63970C2214yes—
57#63970C2214yes—
58#63970C2214yes—
59#63959C2214yes—
60#63918C2212yes—
61C4×#627C2212yes—
62#63914C2212yes—
63#63913C2214yes—
64#63908C2212yes—
65#63908C2212yes—
66#63908C2212yes—
67#63898C2212yes—
68#63896C2214yes—
69#63893C2214yes—
70Dic3×D12C2212yes—
71Dic3×D12C2212yes—
72Dic3×D12C2212yes—
73D3×C4⋊Dic3C2211yescharacteristic
74#63887C2214yes—
75#63885C2214yes—
76#63885C2214yes—
77#63879C2214yes—
78D3×Dic3⋊C4C2212yes—
79C4×D3×Dic3C2212yes—
80#63860C2212yes—
81#63857C2212yes—
82#63851C2214yes—
83#63844C2211yescharacteristic
84Dic3×Dic6C2211yescharacteristic
85#63837C2212yes—
86C2×#1010—32no—
87C2×#1010—32no—
88C3×#550—31no—
89C3×#532—31no—
90#5833—32no—
91#5831—32no—
92#5727—32no—
93#5718—32no—
94#5718—32no—
95#5718—31no—
96#5716—32no—
97#5716—31no—
98#5677—34no—
99#5608—32no—
100#5608—34no—
101#5598—32no—
102#5598—34no—
103#5597—34no—
104#5596—32no—
105#5596—32no—
106Q8×D12—31no—
107C4×D3×Q8—31no—
108#5553—31no—
109#5553D311yescharacteristic, complemented
110#5552—32no—
111#5552—32no—
112#5548—32no—
113#5548D311yescharacteristic, complemented
114D4×Dic6—31no—
115D4×Dic6—31no—
116D4×Dic6—32no—
117D4×Dic6—31no—
118D4×Dic6—61no—
119#5477—31no—
120C2×C4×Dic6—31no—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C22×C3⋊Dic3C2314yes—
124C2×#634—28no—
125C2×#634C2312yes—
126C2×#634C2314yes—
127C2×#634C2311yescharacteristic
128C2×C3×#67C2312yes—
129C2×C3×#67C2314yes—
130C2×C3×#67C2312yes—
131C2×C3×#67C2312yes—
132C2×C3×#67C2314yes—
133C3×#235—28no—
134C3×#235—28no—
135C2×C3×D12C2312yes—
136C2×C3×D12C2312yes—
137C2×C3×D12C2311yescharacteristic
138C2×C3×D12C2312yes—
139C2×C3×D12C2312yes—
140C2×C3×C4×D3C2314yes—
141C2×C3×C4×D3C2311yescharacteristic
142C2×C3×C4×D3C2312yes—
143C2×C3×C4×D3C2311yescharacteristic
144C2×C3×C4×D3C2311yescharacteristic
145C2×C3×Dic6C2312yes—
146C2×C3×Dic6C2311yescharacteristic
147C2×#627C2314yes—
148C2×#627C2312yes—
149C2×#625C2314yes—
150C2×#625C2314yes—
151C2×#625C2314yes—
152#3805—216no—
153#3805—216no—
154C2×D3×Dic3C2314yes—
155C2×D3×Dic3C2314yes—
156C2×D3×Dic3C2314yes—
157C2×D3×Dic3C2312yes—
158C2×D3×Dic3C2312yes—
159#3795—28no—
160#3795—28no—
161#3795—216no—
162D3×Dic6—28no—
163D3×Dic6—216no—
164D3×Dic6D418yescomplemented
165C32×C4⋊C4C2311yescharacteristic
166C32×C22⋊C4C2312yes—
167C32×C42C2311yescharacteristic
168#3757C2314yes—
169C4⋊(C3⋊Dic3)C2311yescharacteristic
170C4⋊(C3⋊Dic3)C2312yes—
171C4⋊(C3⋊Dic3)C2312yes—
172#3750C2312yes—
173#3750C2314yes—
174C4×C3⋊Dic3C2312yes—
175C3×#217C2312yes—
176C3×(C2×D3)⋊C4C2312yes—
177C3×(C2×D3)⋊C4C2314yes—
178C3×(C2×D3)⋊C4C2312yes—
179C3×C4⋊Dic3C2311yescharacteristic
180C3×C4⋊Dic3C2311yescharacteristic
181C3×Dic3⋊C4C2312yes—
182C3×Dic3⋊C4C2312yes—
183C3×C4×Dic3C2311yescharacteristic
184C3×C4×Dic3C2311yescharacteristic
185C3×C4×Dic3C2312yes—
186C3×C4×Dic3C2311yescharacteristic
187#3724C2312yes—
188Dic3⋊Dic3C2312yes—
189Dic3⋊Dic3C2312yes—
190Dic3⋊Dic3C2314yes—
191(C2×D3)⋊Dic3C2314yes—
192(C2×D3)⋊Dic3C2314yes—
193(C2×D3)⋊Dic3C2314yes—
194(C2×D3)⋊Dic3C2314yes—
195Dic32C2312yes—
196Dic32C2312yes—
197#3497—91noSylow
198C2×C3×#41—32no—
199C2×C3×#41—32no—
200#1010—616no—
201#1010—616no—
202C2×D3×Q8—31no—
203C2×D3×Q8—34no—
204C2×D3×Q8—32no—
205C2×#237—34no—
206C2×#237—34no—
207C2×#237—34no—
208C2×#237—34no—
209C2×#237—32no—
210C2×#237—32no—
211C2×#237—34no—
212C2×#235—32no—
213C2×#235—34no—
214C2×#235—32no—
215C2×#235C2×D312yes—
216C2×#235C2×D312yes—
217C22×Dic6—31no—
218C22×Dic6—32no—
219C22×Dic6—32no—
220C22×Dic6—32no—
221C22×Dic6—34no—
222C22×Dic6—62no—
223C3×C4⋊Q8—31no—
224C3×#127—32no—
225C3×#127—31no—
226C3×#127—31no—
227C3×#124—32no—
228C3×#121—31no—
229C3×#121—32no—
230C3×#121—31no—
231C3×#121—32no—
232C3×#121—34no—
233C3×C4×Q8—31no—
234C3×C4×D4—21no—
235C3×C4×D4—32no—
236C3×C4×D4—32no—
237C3×C4×D4—31no—
238C3×C4×D4C2×D311yescharacteristic
239C3×C4×D4C2×D311yescharacteristic
240C2×C3×C42—31no—
241#946—34no—
242Q8×Dic3—31no—
243#940—32no—
244#940—32no—
245#940C2×D311yescharacteristic
246#940C2×D312yes—
247#939—34no—
248#939—34no—
249#939—34no—
250#939—34no—
251#939—34no—
252#939—34no—
253#939—34no—
254#938—34no—
255#938—34no—
256#938—34no—
257#938—32no—
258#938—32no—
259#938—32no—
260#938C2×D311yescharacteristic
261#936—34no—
262#936—32no—
263D4×Dic3—32no—
264D4×Dic3—32no—
265D4×Dic3—34no—
266D4×Dic3—32no—
267D4×Dic3—32no—
268D4×Dic3—32no—
269D4×Dic3—32no—
270D4×Dic3—62no—
271#930—32no—
272#930—32no—
273#930—32no—
274#930C2×D312yes—
275C4×#67—34no—
276C4×#67C2×D312yes—
277C2×C4⋊Dic3—31no—
278#924—32no—
279#924—32no—
280#924—32no—
281#924—34no—
282#924—62no—
283C2×Dic3⋊C4—32no—
284C2×C4×Dic3—32no—
285#897—32no—
286#897—34no—
287#896—34no—
288#896—34no—
289#895C2×D311yescharacteristic
290#893—32no—
291#893C2×D312yes—
292D3×C4⋊C4—32no—
293D3×C4⋊C4—31no—
294#888—32no—
295#888—32no—
296#888—32no—
297#888—62no—
298#888C2×D311yescharacteristic
299#887—32no—
300#887—31no—
301#885—34no—
302#885—34no—
303#885—34no—
304#885C2×D312yes—
305#884—34no—
306#884—34no—
307#884C2×D314yes—
308#884C2×D312yes—
309#67⋊C4—34no—
310#67⋊C4—34no—
311#878—34no—
312#878—34no—
313#878—34no—
314#878—34no—
315#878—34no—
316#878—64no—
317#875—32no—
318#874C2×D311yescharacteristic
319C4×D12—32no—
320C4×D12—32no—
321C4×D12—32no—
322C4×D12C2×D311yescharacteristic
323C42×D3—32no—
324C42×D3C2×D311yescharacteristic
325#869—31no—
326#869—31no—
327#869—32no—
328#869—61no—
329C4×Dic6—31no—
330C4×Dic6—31no—
331C4×Dic6—31no—
332C4×Dic6—31no—
333C4×Dic6—32no—
334C4×Dic6—32no—
335C4×Dic6—32no—
336C4×Dic6—61no—
337C4×Dic6C2×D311yescharacteristic
338C23×C32C2412yes—
339C22×C3×D3C2414yes—
340C22×C3×D3C2412yes—
341C22×C3×D3C2411yescharacteristic
342C32×D4—22no—
343C2×C32×C4—24no—
344C2×C32×C4C2411yescharacteristic
345C2×C32×C4C2412yes—
346C2×C32×C4C2411yescharacteristic
347C2×C32×C4C2411yescharacteristic
348C2×C3⋊Dic3—28no—
349C2×C3⋊Dic3C2412yes—
350C2×C3⋊Dic3C2414yes—
351C2×C3⋊Dic3C2412yes—
352#634—24no—
353#634—28no—
354#634C2×D414yes—
355C3×#67—24no—
356C3×#67—24no—
357C3×#67—28no—
358C3×#67—44no—
359C3×#67—42no—
360C2×C3×Dic3C2411yescharacteristic
361C2×C3×Dic3C2412yes—
362C2×C3×Dic3C2411yescharacteristic
363C2×C3×Dic3C2412yes—
364C2×C3×Dic3C2412yes—
365C2×C3×Dic3C2411yescharacteristic
366C3×D12—24no—
367C3×D12—24no—
368C3×D12—24no—
369C3×D12—22no—
370C3×D12—42no—
371C3×C4×D3—24no—
372C3×C4×D3—22no—
373C3×C4×D3—28no—
374C3×C4×D3—41no—
375C3×C4×D3C2×D414yes—
376C3×Dic6—24no—
377C3×Dic6C2×D414yes—
378#627—28no—
379#627C2×D418yes—
380#625—28no—
381#625—28no—
382#625—44no—
383D3×Dic3—28no—
384D3×Dic3—28no—
385D3×Dic3—28no—
386D3×Dic3—42no—
387D3×Dic3C2×D418yes—
388C2×2−1+4—92no—
389#550—31no—
390#550—91no—
391#550—92no—
392D4×Q8—91no—
393D4×Q8—92no—
394D4×Q8—91no—
395#548—92no—
396#548—92no—
397#548—94no—
398#537—94no—
399#537—92no—
400#532—31no—
401#532—91no—
402#532—92no—
403#532—92no—
404C2×C4×Q8—91no—
405C3×#41—68no—
406C3×#41—68no—
407C2×C3×Q8—31no—
408C2×C3×Q8—32no—
409C2×C3×D4—21no—
410C2×C3×D4—34no—
411C2×C3×D4—32no—
412C2×C3×D4—32no—
413C2×C3×D4—34no—
414C2×C3×D4—32no—
415C2×C3×D4—32no—
416C2×C3×D4—31no—
417C2×C3×D4—32no—
418C2×C3×D4—32no—
419C2×C3×D4—32no—
420C2×C3×D4C22×D311yescharacteristic
421C2×C3×D4C22×D311yescharacteristic
422C22×C3×C4—22no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—34no—
426C22×C3×C4—32no—
427C22×C3×C4—31no—
428C22×C3×C4C22×D312yes—
429C22×C3×C4C22×D312yes—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67C22×D314yes—
437C2×#67C22×D312yes—
438C2×#67C22×D312yes—
439C2×#67C22×D314yes—
440C2×#67C22×D312yes—
441C22×Dic3—32no—
442C22×Dic3—34no—
443C22×Dic3—34no—
444C22×Dic3—34no—
445C22×Dic3—34no—
446C22×Dic3—34no—
447C22×Dic3—32no—
448C22×Dic3—64no—
449D3×Q8—38no—
450D3×Q8—616no—
451D3×Q8—68no—
452#237—68no—
453#237—616no—
454#237—616no—
455#237—616no—
456#237—616no—
457#237—616no—
458#237—68no—
459#235—28no—
460#235—28no—
461#235—68no—
462#235—616no—
463#235—68no—
464C2×D12C22×D311yescharacteristic
465C2×D12C22×D312yes—
466C2×D12C22×D312yes—
467C2×D12C22×D312yes—
468C2×D12C22×D312yes—
469C2×C4×D3—32no—
470C2×C4×D3—34no—
471C2×C4×D3—34no—
472C2×C4×D3—34no—
473C2×C4×D3—32no—
474C2×C4×D3C22×D311yescharacteristic
475C2×C4×D3C22×D312yes—
476C2×C4×D3C22×D314yes—
477C2×C4×D3C22×D311yescharacteristic
478C2×C4×D3C22×D311yescharacteristic
479C2×Dic6—31no—
480C2×Dic6—31no—
481C2×Dic6—32no—
482C2×Dic6—32no—
483C2×Dic6—38no—
484C2×Dic6—32no—
485C2×Dic6—32no—
486C2×Dic6—34no—
487C2×Dic6—34no—
488C2×Dic6—34no—
489C2×Dic6—34no—
490C2×Dic6—61no—
491C2×Dic6—62no—
492C2×Dic6—64no—
493C2×Dic6—616no—
494C2×Dic6—68no—
495C2×Dic6—68no—
496C2×Dic6—68no—
497C2×Dic6—128no—
498C2×Dic6C22×D312yes—
499C2×Dic6C22×D311yescharacteristic
500C3×C4⋊C4—21no—
501C3×C4⋊C4—32no—
502C3×C4⋊C4—31no—
503C3×C4⋊C4—31no—
504C3×C4⋊C4—32no—
505C3×C4⋊C4C22×D311yescharacteristic
506C3×C4⋊C4C22×D311yescharacteristic
507C3×C22⋊C4—22no—
508C3×C22⋊C4—32no—
509C3×C22⋊C4—32no—
510C3×C22⋊C4—34no—
511C3×C22⋊C4—32no—
512C3×C22⋊C4C22×D312yes—
513C3×C22⋊C4C22×D312yes—
514C3×C42—21no—
515C3×C42—31no—
516C3×C42—31no—
517C3×C42—31no—
518C3×C42—32no—
519C3×C42C22×D311yescharacteristic
520C3×C42C22×D311yescharacteristic
521#217—34no—
522#217—34no—
523#217—34no—
524#217—34no—
525#217—34no—
526#217—34no—
527#217—64no—
528#217C22×D312yes—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—34no—
531(C2×D3)⋊C4—34no—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4C22×D312yes—
534(C2×D3)⋊C4C22×D314yes—
535(C2×D3)⋊C4C22×D312yes—
536C4⋊Dic3—31no—
537C4⋊Dic3—31no—
538C4⋊Dic3—32no—
539C4⋊Dic3—32no—
540C4⋊Dic3—32no—
541C4⋊Dic3—32no—
542C4⋊Dic3—32no—
543C4⋊Dic3—32no—
544C4⋊Dic3—34no—
545C4⋊Dic3—61no—
546C4⋊Dic3—62no—
547C4⋊Dic3—62no—
548C4⋊Dic3C22×D311yescharacteristic
549C4⋊Dic3C22×D311yescharacteristic
550Dic3⋊C4—32no—
551Dic3⋊C4—32no—
552Dic3⋊C4—34no—
553Dic3⋊C4—34no—
554Dic3⋊C4—32no—
555Dic3⋊C4—32no—
556Dic3⋊C4—32no—
557Dic3⋊C4—32no—
558Dic3⋊C4—34no—
559Dic3⋊C4—62no—
560Dic3⋊C4—64no—
561Dic3⋊C4C22×D312yes—
562Dic3⋊C4C22×D312yes—
563C4×Dic3—32no—
564C4×Dic3—32no—
565C4×Dic3—32no—
566C4×Dic3—32no—
567C4×Dic3—32no—
568C4×Dic3—32no—
569C4×Dic3—62no—
570C4×Dic3C22×D311yescharacteristic
571C4×Dic3C22×D312yes—
572C4×Dic3C22×D311yescharacteristic
573C4×Dic3C22×D311yescharacteristic
574C22×C32—22no—
575C22×C32—22no—
576C22×C32—22no—
577C22×C32C2511yescharacteristic
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—24no—
581C2×C3×D3—22no—
582C2×C3×D3—24no—
583C2×C3×D3—22no—
584C2×C3×D3—22no—
585C2×C3×D3—24no—
586C2×C3×D3C22×D412yes—
587C32×C4—22no—
588C32×C4—21no—
589C32×C4C22×D412yes—
590C32×C42−1+412yescomplemented
591C3⋊Dic3—24no—
592C3⋊Dic3—22no—
593C3⋊Dic3C22×D414yes—
594C3×Dic3—22no—
595C3×Dic3—21no—
596C3×Dic3—22no—
597C3×Dic3—21no—
598C3×Dic3C22×D412yes—
599C3×Dic3C22×D414yes—
6002−1+4—1816no—
601C2×#41—32no—
602C2×#41—32no—
603C2×#41—92no—
604C2×#41—94no—
605C2×#41—92no—
606C2×#41—94no—
607C2×#41—94no—
608C22×Q8—91no—
609C22×Q8—92no—
610C22×Q8—94no—
611C22×Q8—92no—
612C4⋊Q8—31no—
613C4⋊Q8—92no—
614C4⋊Q8—92no—
615C4⋊Q8—91no—
616#127—31no—
617#127—32no—
618#127—31no—
619#127—92no—
620#124—32no—
621#124—92no—
622#124—94no—
623#124—94no—
624C22⋊Q8—94no—
625C22⋊Q8—94no—
626C22⋊Q8—94no—
627C22⋊Q8—94no—
628C22⋊Q8—92no—
629C22⋊Q8—92no—
630C22⋊Q8—94no—
631#121—31no—
632#121—32no—
633#121—31no—
634#121—32no—
635#121—34no—
636#121—94no—
637#121—94no—
638#121—92no—
639#121—92no—
640#121—92no—
641#121—94no—
642#121—94no—
643#121—94no—
644#121—94no—
645C4×Q8—31no—
646C4×Q8—92no—
647C4×Q8—91no—
648C4×Q8—92no—
649C4×Q8—91no—
650C4×Q8—91no—
651C4×D4—32no—
652C4×D4—32no—
653C4×D4—31no—
654C4×D4—92no—
655C4×D4—92no—
656C4×D4—92no—
657C4×D4—94no—
658C4×D4—94no—
659C4×D4—92no—
660C4×D4—92no—
661C4×D4D3211yescharacteristic
662C2×C4⋊C4—92no—
663C2×C4⋊C4—91no—
664C2×C42—31no—
665C2×C42—92no—
666C23×C3—22no—
667C23×C3—31no—
668C23×C3—34no—
669C23×C3—32no—
670C23×C3C23×D312yes—
671C23×C3C23×D312yes—
672C22×D3C23×D314yes—
673C22×D3C23×D312yes—
674C22×D3C23×D311yescharacteristic
675C3×Q8—34no—
676C3×Q8—64no—
677C3×D4—24no—
678C3×D4—22no—
679C3×D4—22no—
680C3×D4—64no—
681C3×D4—64no—
682C3×D4—68no—
683C3×D4—64no—
684C3×D4—64no—
685C3×D4—64no—
686C3×D4—62no—
687C3×D4—122no—
688C3×D4—124no—
689C3×D4—122no—
690C2×C3×C4—24no—
691C2×C3×C4—24no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—22no—
696C2×C3×C4—32no—
697C2×C3×C4—31no—
698C2×C3×C4—34no—
699C2×C3×C4—31no—
700C2×C3×C4—32no—
701C2×C3×C4—31no—
702C2×C3×C4—32no—
703C2×C3×C4—44no—
704C2×C3×C4—68no—
705C2×C3×C4—64no—
706C2×C3×C4—62no—
707C2×C3×C4—121no—
708C2×C3×C4C23×D311yescharacteristic
709C2×C3×C4C23×D311yescharacteristic
710C2×C3×C4C23×D312yes—
711C2×C3×C4C23×D312yes—
712C2×C3×C4C23×D311yescharacteristic
713C2×C3×C4C23×D311yescharacteristic
714C2×C3×C4C23×D311yescharacteristic
715C2×C3×C4C23×D311yescharacteristic
716#67—24no—
717#67—24no—
718#67—28no—
719#67—42no—
720#67—44no—
721#67—68no—
722#67—68no—
723#67—68no—
724#67—68no—
725#67—124no—
726#67—124no—
727C2×Dic3—32no—
728C2×Dic3—32no—
729C2×Dic3—38no—
730C2×Dic3—32no—
731C2×Dic3—32no—
732C2×Dic3—34no—
733C2×Dic3—34no—
734C2×Dic3—62no—
735C2×Dic3—62no—
736C2×Dic3—64no—
737C2×Dic3—68no—
738C2×Dic3—68no—
739C2×Dic3—68no—
740C2×Dic3—68no—
741C2×Dic3—68no—
742C2×Dic3—128no—
743C2×Dic3—122no—
744C2×Dic3C23×D311yescharacteristic
745C2×Dic3C23×D312yes—
746C2×Dic3C23×D311yescharacteristic
747C2×Dic3C23×D312yes—
748C2×Dic3C23×D312yes—
749C2×Dic3C23×D311yescharacteristic
750D12—24no—
751D12—24no—
752D12—22no—
753D12—24no—
754D12—42no—
755C4×D3—24no—
756C4×D3—22no—
757C4×D3—28no—
758C4×D3—38no—
759C4×D3—41no—
760C4×D3—68no—
761C4×D3—68no—
762C4×D3—68no—
763C4×D3—122no—
764C4×D3D3×D414yes—
765Dic6—24no—
766Dic6—34no—
767Dic6—34no—
768Dic6—38no—
769Dic6—38no—
770Dic6—64no—
771Dic6—68no—
772Dic6—68no—
773Dic6—68no—
774Dic6—64no—
775Dic6—64no—
776Dic6—68no—
777Dic6—128no—
778Dic6—124no—
779Dic6D3×D414yes—
780C2×C32—42no—
781C2×C32C23×D411yescharacteristic
782C2×C32C2×2−1+411yescharacteristic
783C2×C32#58511yescharacteristic
784C3×D3—22no—
785C3×D3—44no—
786C3×D3—42no—
787#41—68no—
788#41—68no—
789#41—188no—
790#41—1816no—
791#41—188no—
792#41—1816no—
793#41—1816no—
794C2×Q8—31no—
795C2×Q8—32no—
796C2×Q8—92no—
797C2×Q8—94no—
798C2×Q8—98no—
799C2×Q8—91no—
800C2×Q8—94no—
801C2×Q8—92no—
802C2×Q8—188no—
803C2×Q8—188no—
804C2×Q8—1816no—
805C2×D4—32no—
806C2×D4—34no—
807C2×D4—32no—
808C2×D4—32no—
809C2×D4—34no—
810C2×D4—31no—
811C2×D4—32no—
812C2×D4—32no—
813C2×D4—32no—
814C2×D4—32no—
815C2×D4—94no—
816C2×D4—94no—
817C2×D4—94no—
818C2×D4C2×D3211yescharacteristic
819C22×C4—31no—
820C22×C4—31no—
821C22×C4—32no—
822C22×C4—34no—
823C22×C4—31no—
824C22×C4—92no—
825C22×C4—94no—
826C22×C4—94no—
827C22×C4—94no—
828C22×C4—92no—
829C22×C4—94no—
830C22×C4C2×D3212yes—
831C4⋊C4—32no—
832C4⋊C4—31no—
833C4⋊C4—31no—
834C4⋊C4—32no—
835C4⋊C4—92no—
836C4⋊C4—92no—
837C4⋊C4—92no—
838C4⋊C4—94no—
839C4⋊C4—92no—
840C4⋊C4—91no—
841C4⋊C4—92no—
842C4⋊C4—94no—
843C4⋊C4—92no—
844C4⋊C4C2×D3211yescharacteristic
845C22⋊C4—32no—
846C22⋊C4—32no—
847C22⋊C4—34no—
848C22⋊C4—32no—
849C22⋊C4—94no—
850C22⋊C4—94no—
851C22⋊C4—94no—
852C22⋊C4—94no—
853C22⋊C4—94no—
854C22⋊C4C2×D3212yes—
855C42—31no—
856C42—31no—
857C42—31no—
858C42—32no—
859C42—92no—
860C42—92no—
861C42—92no—
862C42C2×D3211yescharacteristic
863C22×C3—24no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—21no—
871C22×C3—32no—
872C22×C3—42no—
873C22×C3—42no—
874C22×C3—61no—
875C22×C3—61no—
876C22×C3—62no—
877C22×C3—64no—
878C22×C3—62no—
879C22×C3—64no—
880C22×C3—64no—
881C22×C3—62no—
882C22×C3C24×D311yescharacteristic
883C22×C3C24×D311yescharacteristic
884C2×D3—21no—
885C2×D3—21no—
886C2×D3—24no—
887C2×D3—22no—
888C2×D3—24no—
889C2×D3—22no—
890C2×D3—22no—
891C2×D3—24no—
892C2×D3C2×D3×D412yes—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—21no—
896C3×C4—21no—
897C3×C4—22no—
898C3×C4—22no—
899C3×C4—32no—
900C3×C4—34no—
901C3×C4—42no—
902C3×C4—41no—
903C3×C4—62no—
904C3×C4—61no—
905C3×C4—62no—
906C3×C4—61no—
907C3×C4C2×D3×D412yes—
908C3×C4C2×D3×D412yes—
909C3×C4#101012yescomplemented
910C3×C4#101012yescomplemented
911Dic3—22no—
912Dic3—21no—
913Dic3—21no—
914Dic3—22no—
915Dic3—34no—
916Dic3—34no—
917Dic3—64no—
918Dic3—64no—
919Dic3—64no—
920Dic3—62no—
921Dic3—62no—
922Dic3—124no—
923Dic3—122no—
924Dic3C2×D3×D412yes—
925Dic3C2×D3×D414yes—
926C32#349711yescharacteristic, complemented, Sylow
927C23—31no—
928C23—32no—
929C23—34no—
930C23C22×D3212yes—
931Q8—34no—
932Q8—64no—
933Q8—98no—
934Q8—94no—
935Q8—188no—
936Q8—188no—
937Q8—184no—
938D4—22no—
939D4—64no—
940D4—64no—
941D4—68no—
942D4—64no—
943D4—62no—
944D4—64no—
945D4—64no—
946D4—122no—
947D4—122no—
948D4—124no—
949D4—188no—
950D4—188no—
951D4—364no—
952C2×C4—24no—
953C2×C4—31no—
954C2×C4—32no—
955C2×C4—34no—
956C2×C4—31no—
957C2×C4—31no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—68no—
961C2×C4—62no—
962C2×C4—64no—
963C2×C4—98no—
964C2×C4—92no—
965C2×C4—92no—
966C2×C4—94no—
967C2×C4—121no—
968C2×C4—188no—
969C2×C4—188no—
970C2×C4—188no—
971C2×C4—188no—
972C2×C4—362no—
973C2×C4C22×D3211yescharacteristic
974C2×C4C22×D3212yes—
975C2×C4C22×D3211yescharacteristic
976C2×C4C22×D3211yescharacteristic
977C2×C3—21no—
978C2×C3—21no—
979C2×C3—21no—
980C2×C3—44no—
981C2×C3—42no—
982C2×C3—42no—
983C2×C3—62no—
984C2×C3—122no—
985C2×C3—124no—
986C2×C3C22×D3×D411yescharacteristic
987C2×C3C22×D3×D411yescharacteristic
988C2×C3C2×#101011yescharacteristic
989C2×C3C2×#101011yescharacteristic
990C2×C3#596411yescharacteristic
991C2×C3#596611yescharacteristic
992D3—22no—
993D3—44no—
994D3—42no—
995C22—22no—
996C22—22no—
997C22—22no—
998C22—32no—
999C22—61no—
1000C22—61no—
1001C22—62no—
1002C22—64no—
1003C22—64no—
1004C22—62no—
1005C22—64no—
1006C22—62no—
1007C22C23×D3211yescharacteristic
1008C4—22no—
1009C4—21no—
1010C4—32no—
1011C4—34no—
1012C4—61no—
1013C4—62no—
1014C4—61no—
1015C4—62no—
1016C4—94no—
1017C4—184no—
1018C4—182no—
1019C4#6429812yescomplemented
1020C4D32×D412yes—
1021C3—21no—
1022C3#8622211yescharacteristic, complemented
1023C3#8678411yescharacteristic, complemented
1024C2—42no—
1025C2—62no—
1026C2—124no—
1027C2—122no—
1028C2C2×#6429811yescharacteristic
1029C2C2×D32×D411yescharacteristic
1030C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3497
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64298C2semidirect
2. D4×#634C2semidirect
3. C3×#5553C2semidirect
4. C3×#5548C2semidirect
5. #10595144C2semidirect
6. #10595133C2semidirect
7. #10595004C2semidirect
8. #10594918C2semidirect
9. #10594899C2semidirect
10. #10594376C2semidirect
11. #10594367C2semidirect
12. #10594076C2semidirect
13. #10594060C2semidirect
14. #10593906C2semidirect
15. Dic6×D12C2semidirect
16. #10593897C2semidirect
17. C4×D3×Dic6C2semidirect
109. #5553D3semidirect
113. #5548D3semidirect
164. D3×Dic6D4semidirect
590. C32×C42−1+4semidirect
909. C3×C4#1010semidirect
910. C3×C4#1010semidirect
926. C32#3497semidirect
1019. C4#64298semidirect
1022. C3#86222semidirect
1023. C3#86784semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
D4×#6342
C3×#55532
C3×#55482
#105951442
#105951332
#105950042
#105949182
#105948992
#105943762
#105943672
#105940762
#105940602
#105939062
Dic6×D122
#105938972
C4×D3×Dic62
#867843
#862223