Finite Group Databasebeta

← #11905892

Subgroups — #11905892

Order 1152.

3140 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64297C212yesmaximal, complemented
2#10596024C211yesmaximal, characteristic, complemented
3C3×#5548C211yesmaximal, characteristic, complemented
4C3×D4×Dic6C211yesmaximal, characteristic, complemented
5#10595143C212yesmaximal, complemented
6#10595131C212yesmaximal, complemented
7#10594916C212yesmaximal, complemented
8#10594902C212yesmaximal, complemented
9#10594894C212yesmaximal, complemented
10#10594379C212yesmaximal, complemented
11#10594369C212yesmaximal, complemented
12#10594075C214yesmaximal, complemented
13#10594059C214yesmaximal, complemented
14#10593970C211yesmaximal, characteristic, complemented
15#10593904C211yesmaximal, characteristic, complemented
16#10593902C211yesmaximal, characteristic, complemented
17C4×D3×Dic6C211yesmaximal, characteristic, complemented
18#86760—31nomaximal
19#86222—31nomaximal
20C2×#3828C2212yes—
21C2×C3×#235C2212yes—
22C22×C3×Dic6C2212yes—
23C2×#3804C2214yes—
24C2×#3804C2214yes—
25C2×#3799C2212yes—
26C2×#3799C2212yes—
27C2×#3797C2214yes—
28#64297—216no—
29C2×#3796C2214yes—
30C2×D3×Dic6C2212yes—
31C2×D3×Dic6C2211yescharacteristic
32C32×C4×D4C2211yescharacteristic
33#64149C2212yes—
34#64139C2212yes—
35#64102C2212yes—
36#64093C2214yes—
37#64083C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C3×#940C2211yescharacteristic
40C3×#938C2211yescharacteristic
41C3×D4×Dic3C2212yes—
42C3×C4×#67C2212yes—
43C3×#924C2212yes—
44C3×#895C2211yescharacteristic
45C3×#888C2212yes—
46C3×#888C2211yescharacteristic
47C3×#885C2212yes—
48C3×#884C2212yes—
49C3×#878C2214yes—
50C3×C4×D12C2211yescharacteristic
51C3×C42×D3C2211yescharacteristic
52C3×#869C2211yescharacteristic
53C3×C4×Dic6C2211yescharacteristic
54#63978C2214yes—
55#63971C2214yes—
56#63971C2214yes—
57#63958C2214yes—
58#63953C2214yes—
59#63952C2214yes—
60#63919C2212yes—
61C4×#627C2212yes—
62#63911C2212yes—
63#63910C2214yes—
64#63909C2212yes—
65#63909C2212yes—
66#63909C2212yes—
67#63907C2214yes—
68#63899C2214yes—
69#63898C2212yes—
70#63894C2212yes—
71#63894C2212yes—
72#63894C2212yes—
73D3×C4⋊Dic3C2211yescharacteristic
74#63888C2214yes—
75#63888C2214yes—
76#63886C2214yes—
77#63881C2214yes—
78D3×Dic3⋊C4C2212yes—
79C4×D3×Dic3C2212yes—
80#63865C2214yes—
81#63864C2212yes—
82#63856C2212yes—
83#63844C2211yescharacteristic
84Dic3×Dic6C2211yescharacteristic
85#63837C2212yes—
86C2×#1010—32no—
87C2×#1007—32no—
88C3×D4×Q8—31no—
89C3×#532—31no—
90#5833—32no—
91#5817—32no—
92#5727—32no—
93#5727—32no—
94#5727—31no—
95#5725—32no—
96#5725—31no—
97#5718—32no—
98#5677—34no—
99#5633—32no—
100#5633—34no—
101#5629—32no—
102#5629—34no—
103#5597—34no—
104#5596—32no—
105#5596—32no—
106#5577—31no—
107C4×D3×Q8—31no—
108#5553—31no—
109#5553—31no—
110#5553—32no—
111#5553—31no—
112#5553—61no—
113#5552—32no—
114#5552—32no—
115#5548—32no—
116#5548D311yescharacteristic, complemented
117D4×Dic6—31no—
118D4×Dic6D311yescharacteristic, complemented
119#5477—31no—
120C2×C4×Dic6—31no—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C2×#638C2314yes—
124C2×#638C2314yes—
125#3828—28no—
126C2×C4⋊(C3⋊D3)C2312yes—
127C2×C4⋊(C3⋊D3)C2312yes—
128C2×C4⋊(C3⋊D3)C2312yes—
129C2×C4×C3⋊D3C2314yes—
130C2×#634C2311yescharacteristic
131C2×C3×#67C2312yes—
132C2×C3×#67C2312yes—
133C2×C3×#67C2312yes—
134C22×C3×Dic3C2314yes—
135C3×#235—28no—
136C2×C3×D12C2312yes—
137C2×C3×D12C2311yescharacteristic
138C2×C3×C4×D3C2311yescharacteristic
139C2×C3×C4×D3C2312yes—
140C2×C3×C4×D3C2311yescharacteristic
141C2×C3×C4×D3C2311yescharacteristic
142C2×C3×Dic6—28no—
143C2×C3×Dic6C2314yes—
144C2×C3×Dic6C2312yes—
145C2×C3×Dic6C2312yes—
146C2×C3×Dic6C2311yescharacteristic
147C2×#627C2314yes—
148C2×#627C2312yes—
149C2×#626C2314yes—
150C2×#626C2314yes—
151C2×#626C2314yes—
152C2×#624C2314yes—
153C2×#624C2314yes—
154#3804—216no—
155#3804—216no—
156C2×D3×Dic3C2314yes—
157C2×D3×Dic3C2312yes—
158C2×D3×Dic3C2312yes—
159#3799—28no—
160#3799—28no—
161#3797—216no—
162#3796—216no—
163D3×Dic6—28no—
164D3×Dic6D418yescomplemented
165C32×C4⋊C4C2311yescharacteristic
166C32×C22⋊C4C2312yes—
167C32×C42C2311yescharacteristic
168#3752C2314yes—
169C4⋊(C3⋊Dic3)C2311yescharacteristic
170#3750C2312yes—
171C4×C3⋊Dic3C2312yes—
172C3×#217C2314yes—
173C3×#217C2312yes—
174C3×(C2×D3)⋊C4C2312yes—
175C3×(C2×D3)⋊C4C2312yes—
176C3×C4⋊Dic3C2312yes—
177C3×C4⋊Dic3C2312yes—
178C3×C4⋊Dic3C2311yescharacteristic
179C3×C4⋊Dic3C2311yescharacteristic
180C3×Dic3⋊C4C2312yes—
181C3×Dic3⋊C4C2314yes—
182C3×Dic3⋊C4C2312yes—
183C3×C4×Dic3C2311yescharacteristic
184C3×C4×Dic3C2312yes—
185C3×C4×Dic3C2311yescharacteristic
186C3×C4×Dic3C2311yescharacteristic
187#3724C2312yes—
188#3724C2314yes—
189Dic3⋊Dic3C2312yes—
190Dic3⋊Dic3C2312yes—
191#3722C2314yes—
192#3722C2314yes—
193#3722C2314yes—
194(C2×D3)⋊Dic3C2314yes—
195Dic32C2312yes—
196Dic32C2312yes—
197#3497—91noSylow
198C2×C3×#41—32no—
199C22×C3×Q8—32no—
200#1010—616no—
201#1007—616no—
202C2×#239—34no—
203C2×#239—32no—
204C2×#239—32no—
205C2×D3×Q8—31no—
206C2×D3×Q8—32no—
207C2×D3×Q8—34no—
208C2×D3×Q8—34no—
209C2×#237—34no—
210C2×#237—34no—
211C2×#237—34no—
212C2×#235—32no—
213C2×#235—32no—
214C2×#235—34no—
215C2×#235—34no—
216C2×#235—32no—
217C2×#235—32no—
218C2×#235—62no—
219C2×#235C2×D312yes—
220C22×Dic6—31no—
221C22×Dic6—32no—
222C22×Dic6C2×D312yes—
223C3×C4⋊Q8—32no—
224C3×C4⋊Q8—31no—
225C3×C4⋊Q8—31no—
226C3×#127—31no—
227C3×#124—32no—
228C3×C22⋊Q8—32no—
229C3×C22⋊Q8—34no—
230C3×#121—31no—
231C3×#121—31no—
232C3×#121—32no—
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#947—34no—
242#947—32no—
243#946—32no—
244#946—34no—
245#946—34no—
246Q8×Dic3—31no—
247#940—32no—
248#940—32no—
249#940—32no—
250#940—62no—
251#940C2×D311yescharacteristic
252#939—34no—
253#939—34no—
254#939—34no—
255#939—34no—
256#938—34no—
257#938C2×D311yescharacteristic
258D4×Dic3—32no—
259D4×Dic3C2×D312yes—
260#930—32no—
261#930—32no—
262#930—34no—
263#930—32no—
264#930—32no—
265#930—32no—
266#930—62no—
267C4×#67—34no—
268C4×#67C2×D312yes—
269C2×C4⋊Dic3—31no—
270#924—32no—
271#924C2×D312yes—
272C2×Dic3⋊C4—32no—
273C2×C4×Dic3—32no—
274#896—34no—
275#896—34no—
276#896—34no—
277#896—34no—
278#896—34no—
279#895—34no—
280#895—32no—
281#895—32no—
282#895—32no—
283#895—34no—
284#895C2×D311yescharacteristic
285#893—32no—
286#893—32no—
287#893—32no—
288#893—34no—
289#893—32no—
290#893—32no—
291#893—32no—
292#893—62no—
293D3×C4⋊C4—32no—
294D3×C4⋊C4—31no—
295#888—32no—
296#888—32no—
297#888C2×D311yescharacteristic
298#888C2×D312yes—
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#884—34no—
308#884—34no—
309#884—34no—
310#884—34no—
311#884—64no—
312#884C2×D312yes—
313#67⋊C4—34no—
314#67⋊C4—34no—
315#878—34no—
316#878C2×D314yes—
317#875—32no—
318#874—32no—
319#874—31no—
320#874—31no—
321#874—61no—
322C4×D12—32no—
323C4×D12—32no—
324C4×D12—32no—
325C4×D12C2×D311yescharacteristic
326C42×D3—32no—
327C42×D3C2×D311yescharacteristic
328#869C2×D311yescharacteristic
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
348#638—28no—
349#638—44no—
350C2×C3⋊Dic3C2412yes—
351C2×C3⋊Dic3C2412yes—
352C4⋊(C3⋊D3)—24no—
353C4⋊(C3⋊D3)—24no—
354C4⋊(C3⋊D3)—42no—
355C4×C3⋊D3—28no—
356#634C2×D414yes—
357C3×#67—24no—
358C3×#67—24no—
359C3×#67—42no—
360C2×C3×Dic3—28no—
361C2×C3×Dic3C2411yescharacteristic
362C2×C3×Dic3C2412yes—
363C2×C3×Dic3C2414yes—
364C2×C3×Dic3C2411yescharacteristic
365C2×C3×Dic3C2412yes—
366C2×C3×Dic3C2412yes—
367C2×C3×Dic3C2411yescharacteristic
368C3×D12—24no—
369C3×D12—22no—
370C3×C4×D3—24no—
371C3×C4×D3—22no—
372C3×C4×D3—41no—
373C3×C4×D3C2×D414yes—
374C3×Dic6—24no—
375C3×Dic6—28no—
376C3×Dic6—24no—
377C3×Dic6C2×D414yes—
378#627—28no—
379#627C2×D418yes—
380#626—28no—
381#626—28no—
382#626—44no—
383#624—28no—
384#624—28no—
385D3×Dic3—28no—
386D3×Dic3—42no—
387D3×Dic3C2×D418yes—
388C2×2−1+4—92no—
389#550—91no—
390#550—92no—
391#550—91no—
392D4×Q8—31no—
393D4×Q8—91no—
394D4×Q8—92no—
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—
406C2×C3×Q8—31no—
407C2×C3×Q8—32no—
408C2×C3×Q8—34no—
409C2×C3×Q8—32no—
410C2×C3×Q8—68no—
411C2×C3×D4—21no—
412C2×C3×D4—32no—
413C2×C3×D4—32no—
414C2×C3×D4—32no—
415C2×C3×D4—31no—
416C2×C3×D4—32no—
417C2×C3×D4C22×D311yescharacteristic
418C2×C3×D4C22×D311yescharacteristic
419C22×C3×C4—22no—
420C22×C3×C4—31no—
421C22×C3×C4—34no—
422C22×C3×C4—31no—
423C22×C3×C4—32no—
424C22×C3×C4—31no—
425C22×C3×C4C22×D312yes—
426C22×C3×C4C22×D312yes—
427C2×#67—34no—
428C2×#67—34no—
429C2×#67—34no—
430C2×#67—34no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—64no—
435C2×#67—64no—
436C2×#67C22×D312yes—
437C2×#67C22×D312yes—
438C2×#67C22×D312yes—
439C22×Dic3—32no—
440C22×Dic3—34no—
441C22×Dic3—32no—
442C22×Dic3C22×D314yes—
443#239—68no—
444#239—616no—
445#239—68no—
446D3×Q8—38no—
447D3×Q8—616no—
448D3×Q8—616no—
449D3×Q8—68no—
450#237—616no—
451#237—616no—
452#237—616no—
453#235—28no—
454#235—68no—
455#235—616no—
456#235—68no—
457#235—68no—
458#235—616no—
459#235—68no—
460#235—128no—
461C2×D12—34no—
462C2×D12—34no—
463C2×D12—32no—
464C2×D12—32no—
465C2×D12—32no—
466C2×D12—32no—
467C2×D12—34no—
468C2×D12—32no—
469C2×D12—32no—
470C2×D12—62no—
471C2×D12—62no—
472C2×D12—62no—
473C2×D12C22×D311yescharacteristic
474C2×D12C22×D312yes—
475C2×C4×D3—32no—
476C2×C4×D3—34no—
477C2×C4×D3—34no—
478C2×C4×D3—34no—
479C2×C4×D3—34no—
480C2×C4×D3—34no—
481C2×C4×D3—34no—
482C2×C4×D3—34no—
483C2×C4×D3—32no—
484C2×C4×D3—64no—
485C2×C4×D3C22×D311yescharacteristic
486C2×C4×D3C22×D312yes—
487C2×C4×D3C22×D311yescharacteristic
488C2×C4×D3C22×D311yescharacteristic
489C2×Dic6—28no—
490C2×Dic6—31no—
491C2×Dic6—31no—
492C2×Dic6—32no—
493C2×Dic6—32no—
494C2×Dic6—38no—
495C2×Dic6—34no—
496C2×Dic6—34no—
497C2×Dic6—61no—
498C2×Dic6—68no—
499C2×Dic6C22×D312yes—
500C2×Dic6C22×D314yes—
501C2×Dic6C22×D312yes—
502C2×Dic6C22×D311yescharacteristic
503C3×C4⋊C4—21no—
504C3×C4⋊C4—32no—
505C3×C4⋊C4—31no—
506C3×C4⋊C4—31no—
507C3×C4⋊C4—32no—
508C3×C4⋊C4—34no—
509C3×C4⋊C4—32no—
510C3×C4⋊C4—32no—
511C3×C4⋊C4C22×D311yescharacteristic
512C3×C4⋊C4C22×D311yescharacteristic
513C3×C22⋊C4—22no—
514C3×C22⋊C4—32no—
515C3×C22⋊C4—34no—
516C3×C22⋊C4—32no—
517C3×C22⋊C4—32no—
518C3×C22⋊C4C22×D312yes—
519C3×C22⋊C4C22×D312yes—
520C3×C42—21no—
521C3×C42—31no—
522C3×C42—31no—
523C3×C42—31no—
524C3×C42—32no—
525C3×C42C22×D311yescharacteristic
526C3×C42C22×D311yescharacteristic
527#217—34no—
528#217C22×D314yes—
529#217C22×D312yes—
530(C2×D3)⋊C4—34no—
531(C2×D3)⋊C4—34no—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4—34no—
534(C2×D3)⋊C4—34no—
535(C2×D3)⋊C4—34no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—34no—
538(C2×D3)⋊C4—34no—
539(C2×D3)⋊C4—64no—
540(C2×D3)⋊C4C22×D312yes—
541(C2×D3)⋊C4C22×D312yes—
542C4⋊Dic3—31no—
543C4⋊Dic3—31no—
544C4⋊Dic3—32no—
545C4⋊Dic3—32no—
546C4⋊Dic3—61no—
547C4⋊Dic3C22×D311yescharacteristic
548C4⋊Dic3C22×D312yes—
549C4⋊Dic3C22×D312yes—
550C4⋊Dic3C22×D311yescharacteristic
551Dic3⋊C4—32no—
552Dic3⋊C4—32no—
553Dic3⋊C4—32no—
554Dic3⋊C4—32no—
555Dic3⋊C4—32no—
556Dic3⋊C4—32no—
557Dic3⋊C4—34no—
558Dic3⋊C4—34no—
559Dic3⋊C4—62no—
560Dic3⋊C4C22×D312yes—
561Dic3⋊C4C22×D314yes—
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—24no—
579C2×C3⋊D3—24no—
580C2×C3⋊D3—24no—
581C2×C3×D3—21no—
582C2×C3×D3—21no—
583C2×C3×D3—22no—
584C2×C3×D3—22no—
585C2×C3×D3—22no—
586C2×C3×D3C22×D412yes—
587C32×C4—22no—
588C32×C4—21no—
589C32×C4C22×D412yes—
590C32×C42−1+412yescomplemented
591C3⋊Dic3—22no—
592C3⋊Dic3C22×D414yes—
593C3×Dic3—24no—
594C3×Dic3—22no—
595C3×Dic3—21no—
596C3×Dic3—22no—
597C3×Dic3—21no—
598C3×Dic3C22×D414yes—
599C3×Dic3C22×D412yes—
6002−1+4—1816no—
601C2×#41—32no—
602C2×#41—94no—
603C2×#41—94no—
604C2×#41—92no—
605C2×#41—92no—
606C2×#41—94no—
607C2×#41—92no—
608C22×Q8—32no—
609C22×Q8—91no—
610C22×Q8—92no—
611C22×Q8—94no—
612C4⋊Q8—31no—
613C4⋊Q8—32no—
614C4⋊Q8—31no—
615C4⋊Q8—92no—
616#127—31no—
617#127—92no—
618#127—92no—
619#127—91no—
620#124—32no—
621#124—92no—
622#124—94no—
623#124—94no—
624C22⋊Q8—32no—
625C22⋊Q8—34no—
626C22⋊Q8—94no—
627C22⋊Q8—94no—
628C22⋊Q8—94no—
629C22⋊Q8—94no—
630C22⋊Q8—92no—
631#121—31no—
632#121—31no—
633#121—32no—
634#121—94no—
635#121—94no—
636#121—94no—
637#121—94no—
638#121—92no—
639#121—92no—
640#121—92no—
641#121—94no—
642#121—94no—
643#121—92no—
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—32no—
669C23×C3C23×D312yes—
670C23×C3C23×D312yes—
671C22×D3—34no—
672C22×D3—34no—
673C22×D3—64no—
674C22×D3C23×D312yes—
675C22×D3C23×D311yescharacteristic
676C3×Q8—34no—
677C3×Q8—64no—
678C3×Q8—68no—
679C3×Q8—64no—
680C3×D4—22no—
681C3×D4—22no—
682C3×D4—42no—
683C3×D4—64no—
684C3×D4—64no—
685C3×D4—64no—
686C3×D4—62no—
687C3×D4—122no—
688C2×C3×C4—24no—
689C2×C3×C4—24no—
690C2×C3×C4—21no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—22no—
694C2×C3×C4—32no—
695C2×C3×C4—31no—
696C2×C3×C4—34no—
697C2×C3×C4—31no—
698C2×C3×C4—32no—
699C2×C3×C4—31no—
700C2×C3×C4—32no—
701C2×C3×C4—34no—
702C2×C3×C4—44no—
703C2×C3×C4—68no—
704C2×C3×C4—64no—
705C2×C3×C4—62no—
706C2×C3×C4—121no—
707C2×C3×C4C23×D311yescharacteristic
708C2×C3×C4C23×D311yescharacteristic
709C2×C3×C4C23×D312yes—
710C2×C3×C4C23×D312yes—
711C2×C3×C4C23×D311yescharacteristic
712C2×C3×C4C23×D311yescharacteristic
713C2×C3×C4C23×D311yescharacteristic
714C2×C3×C4C23×D311yescharacteristic
715#67—24no—
716#67—24no—
717#67—42no—
718#67—68no—
719#67—68no—
720#67—68no—
721#67—68no—
722#67—128no—
723#67—124no—
724#67—124no—
725#67—124no—
726#67—244no—
727C2×Dic3—28no—
728C2×Dic3—32no—
729C2×Dic3—32no—
730C2×Dic3—38no—
731C2×Dic3—32no—
732C2×Dic3—32no—
733C2×Dic3—62no—
734C2×Dic3—62no—
735C2×Dic3—68no—
736C2×Dic3—122no—
737C2×Dic3C23×D311yescharacteristic
738C2×Dic3C23×D312yes—
739C2×Dic3C23×D311yescharacteristic
740C2×Dic3C23×D312yes—
741C2×Dic3C23×D314yes—
742C2×Dic3C23×D312yes—
743C2×Dic3C23×D311yescharacteristic
744D12—24no—
745D12—22no—
746D12—68no—
747D12—68no—
748D12—64no—
749D12—64no—
750D12—64no—
751D12—64no—
752D12—124no—
753D12—124no—
754D12—122no—
755D12—122no—
756D12—124no—
757D12—242no—
758C4×D3—24no—
759C4×D3—22no—
760C4×D3—38no—
761C4×D3—41no—
762C4×D3—68no—
763C4×D3—68no—
764C4×D3—68no—
765C4×D3—68no—
766C4×D3—68no—
767C4×D3—68no—
768C4×D3—68no—
769C4×D3—128no—
770C4×D3—122no—
771C4×D3D3×D414yes—
772Dic6—24no—
773Dic6—28no—
774Dic6—24no—
775Dic6—34no—
776Dic6—34no—
777Dic6—38no—
778Dic6—38no—
779Dic6—64no—
780Dic6—68no—
781Dic6—68no—
782Dic6D3×D414yes—
783C2×C32—42no—
784C2×C32C23×D411yescharacteristic
785C2×C32C2×2−1+411yescharacteristic
786C2×C32#58511yescharacteristic
787C3⋊D3—44no—
788C3×D3—22no—
789C3×D3—42no—
790#41—68no—
791#41—188no—
792#41—188no—
793#41—1816no—
794#41—1816no—
795#41—188no—
796#41—1816no—
797C2×Q8—31no—
798C2×Q8—34no—
799C2×Q8—32no—
800C2×Q8—32no—
801C2×Q8—68no—
802C2×Q8—92no—
803C2×Q8—94no—
804C2×Q8—98no—
805C2×Q8—91no—
806C2×Q8—188no—
807C2×Q8—1816no—
808C2×D4—32no—
809C2×D4—32no—
810C2×D4—32no—
811C2×D4—31no—
812C2×D4—32no—
813C2×D4—94no—
814C2×D4—94no—
815C2×D4—94no—
816C2×D4—94no—
817C2×D4—94no—
818C2×D4—92no—
819C2×D4—92no—
820C2×D4—92no—
821C2×D4C2×D3211yescharacteristic
822C22×C4—31no—
823C22×C4—34no—
824C22×C4—31no—
825C22×C4—32no—
826C22×C4—31no—
827C22×C4—94no—
828C22×C4—94no—
829C22×C4—92no—
830C22×C4—94no—
831C22×C4—92no—
832C22×C4—94no—
833C22×C4C2×D3212yes—
834C4⋊C4—32no—
835C4⋊C4—31no—
836C4⋊C4—31no—
837C4⋊C4—32no—
838C4⋊C4—32no—
839C4⋊C4—34no—
840C4⋊C4—32no—
841C4⋊C4—92no—
842C4⋊C4—92no—
843C4⋊C4—92no—
844C4⋊C4—94no—
845C4⋊C4—92no—
846C4⋊C4—91no—
847C4⋊C4C2×D3211yescharacteristic
848C22⋊C4—32no—
849C22⋊C4—34no—
850C22⋊C4—32no—
851C22⋊C4—32no—
852C22⋊C4—94no—
853C22⋊C4—94no—
854C22⋊C4—94no—
855C22⋊C4—94no—
856C22⋊C4—94no—
857C22⋊C4C2×D3212yes—
858C42—31no—
859C42—31no—
860C42—31no—
861C42—32no—
862C42—92no—
863C42—92no—
864C42—92no—
865C42C2×D3211yescharacteristic
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—21no—
873C22×C3—32no—
874C22×C3—42no—
875C22×C3—42no—
876C22×C3—42no—
877C22×C3—61no—
878C22×C3—61no—
879C22×C3—62no—
880C22×C3—62no—
881C22×C3—62no—
882C22×C3C24×D311yescharacteristic
883C22×C3C24×D311yescharacteristic
884C2×D3—21no—
885C2×D3—21no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—64no—
890C2×D3—64no—
891C2×D3—64no—
892C2×D3—64no—
893C2×D3—64no—
894C2×D3—64no—
895C2×D3—124no—
896C2×D3—124no—
897C2×D3—124no—
898C2×D3C2×D3×D412yes—
899C3×C4—22no—
900C3×C4—22no—
901C3×C4—21no—
902C3×C4—21no—
903C3×C4—22no—
904C3×C4—22no—
905C3×C4—32no—
906C3×C4—34no—
907C3×C4—42no—
908C3×C4—41no—
909C3×C4—62no—
910C3×C4—64no—
911C3×C4—61no—
912C3×C4—62no—
913C3×C4—61no—
914C3×C4C2×D3×D412yes—
915C3×C4C2×D3×D412yes—
916C3×C4#100712yescomplemented
917C3×C4#101012yescomplemented
918Dic3—24no—
919Dic3—22no—
920Dic3—21no—
921Dic3—21no—
922Dic3—22no—
923Dic3—34no—
924Dic3—34no—
925Dic3—64no—
926Dic3—62no—
927Dic3—62no—
928Dic3—122no—
929Dic3C2×D3×D412yes—
930Dic3C2×D3×D414yes—
931C32#349711yescharacteristic, complemented, Sylow
932C23—31no—
933C23—32no—
934C23—94no—
935C23C22×D3212yes—
936Q8—34no—
937Q8—68no—
938Q8—64no—
939Q8—64no—
940Q8—98no—
941Q8—94no—
942Q8—188no—
943D4—22no—
944D4—64no—
945D4—64no—
946D4—64no—
947D4—62no—
948D4—122no—
949D4—188no—
950D4—188no—
951D4—188no—
952D4—184no—
953D4—184no—
954D4—362no—
955D4—364no—
956D4—364no—
957C2×C4—24no—
958C2×C4—31no—
959C2×C4—32no—
960C2×C4—34no—
961C2×C4—31no—
962C2×C4—31no—
963C2×C4—32no—
964C2×C4—32no—
965C2×C4—34no—
966C2×C4—68no—
967C2×C4—62no—
968C2×C4—64no—
969C2×C4—98no—
970C2×C4—92no—
971C2×C4—92no—
972C2×C4—121no—
973C2×C4—188no—
974C2×C4—188no—
975C2×C4—188no—
976C2×C4—188no—
977C2×C4—362no—
978C2×C4C22×D3211yescharacteristic
979C2×C4C22×D3212yes—
980C2×C4C22×D3211yescharacteristic
981C2×C4C22×D3211yescharacteristic
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—42no—
986C2×C3—42no—
987C2×C3—62no—
988C2×C3—82no—
989C2×C3—122no—
990C2×C3C22×D3×D411yescharacteristic
991C2×C3C22×D3×D411yescharacteristic
992C2×C3C2×#100711yescharacteristic
993C2×C3C2×#101011yescharacteristic
994C2×C3#596411yescharacteristic
995C2×C3#596811yescharacteristic
996D3—22no—
997D3—42no—
998D3—124no—
999D3—124no—
1000D3—244no—
1001C22—22no—
1002C22—22no—
1003C22—22no—
1004C22—32no—
1005C22—61no—
1006C22—61no—
1007C22—62no—
1008C22—62no—
1009C22—62no—
1010C22—184no—
1011C22—184no—
1012C22—184no—
1013C22C23×D3211yescharacteristic
1014C4—22no—
1015C4—21no—
1016C4—32no—
1017C4—34no—
1018C4—61no—
1019C4—62no—
1020C4—64no—
1021C4—61no—
1022C4—62no—
1023C4—94no—
1024C4—182no—
1025C4#6429712yescomplemented
1026C4D32×D412yes—
1027C3—21no—
1028C3#8622211yescharacteristic, complemented
1029C3#8676011yescharacteristic, complemented
1030C2—42no—
1031C2—62no—
1032C2—122no—
1033C2—364no—
1034C2C2×#6429711yescharacteristic
1035C2C2×D32×D411yescharacteristic
1036C2#1059669711yescharacteristic
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×#64297C2semidirect
2. #10596024C2semidirect
3. C3×#5548C2semidirect
4. C3×D4×Dic6C2semidirect
5. #10595143C2semidirect
6. #10595131C2semidirect
7. #10594916C2semidirect
8. #10594902C2semidirect
9. #10594894C2semidirect
10. #10594379C2semidirect
11. #10594369C2semidirect
12. #10594075C2semidirect
13. #10594059C2semidirect
14. #10593970C2semidirect
15. #10593904C2semidirect
16. #10593902C2semidirect
17. C4×D3×Dic6C2semidirect
116. #5548D3semidirect
118. D4×Dic6D3semidirect
164. D3×Dic6D4semidirect
590. C32×C42−1+4semidirect
916. C3×C4#1007semidirect
917. C3×C4#1010semidirect
931. C32#3497semidirect
1025. C4#64297semidirect
1028. C3#86222semidirect
1029. C3#86760semidirect

Maximal subgroups

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

subgroupindex
C2×#642972
#105960242
C3×#55482
C3×D4×Dic62
#105951432
#105951312
#105949162
#105949022
#105948942
#105943792
#105943692
#105940752
#105940592
#105939702
#105939042
#105939022
C4×D3×Dic62
#867603
#862223