Finite Group Databasebeta

← #11905890

Subgroups — #11905890

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×#64309C212yesmaximal, complemented
2#10596189C211yesmaximal, characteristic, complemented
3C3×#5718C211yesmaximal, characteristic, complemented
4C3×#5716C211yesmaximal, characteristic, complemented
5D4×#627C212yesmaximal, complemented
6#10595237C212yesmaximal, complemented
7#10595232C212yesmaximal, complemented
8#10595161C212yesmaximal, complemented
9#10595143C212yesmaximal, complemented
10#10595141C214yesmaximal, complemented
11#10595133C212yesmaximal, complemented
12#10595132C214yesmaximal, complemented
13#10595131C212yesmaximal, complemented
14#10593968C211yesmaximal, characteristic, complemented
15#10593904C211yesmaximal, characteristic, complemented
16#10593903C211yesmaximal, characteristic, complemented
17C4×D3×Dic6C211yesmaximal, characteristic, complemented
18#86784—31nomaximal
19#86222—31nomaximal
20C2×#3830C2212yes—
21C2×C3×#237C2212yes—
22C2×C3×#237C2212yes—
23C22×#627C2214yes—
24C2×#3805C2214yes—
25C2×#3804C2214yes—
26C2×#3804C2214yes—
27#64309—216no—
28C2×#3798C2212yes—
29C2×#3797C2212yes—
30C2×D3×Dic6C2212yes—
31C2×D3×Dic6C2211yescharacteristic
32C32×#127C2211yescharacteristic
33#64149C2212yes—
34#64148C2214yes—
35#64147C2212yes—
36D4×C3⋊Dic3C2212yes—
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C3×#940C2212yes—
40C3×#939C2214yes—
41C3×#938C2212yes—
42C3×#938C2212yes—
43C3×#938C2212yes—
44C3×#936C2212yes—
45C3×D4×Dic3C2212yes—
46C3×D4×Dic3C2212yes—
47C3×D4×Dic3C2212yes—
48C3×C4×D12C2211yescharacteristic
49C3×C42×D3C2211yescharacteristic
50C3×#869C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic
52#63982C2214yes—
53#63978C2214yes—
54#67⋊Dic3C2214yes—
55#63971C2214yes—
56#63971C2214yes—
57#63970C2214yes—
58#63964C2214yes—
59#63964C2214yes—
60#63959C2214yes—
61#63958C2214yes—
62#63953C2214yes—
63#63952C2214yes—
64#63919C2212yes—
65#63918C2212yes—
66#63918C2211yescharacteristic
67C4×#627C2212yes—
68#63911C2211yescharacteristic
69#63909C2211yescharacteristic
70#63908C2211yescharacteristic
71#63906C2212yes—
72C4×#626C2212yes—
73#63899C2214yes—
74#63898C2212yes—
75#63895C2214yes—
76#63894C2212yes—
77D3×C4⋊Dic3C2211yescharacteristic
78D3×Dic3⋊C4C2212yes—
79C4×D3×Dic3C2212yes—
80#63871C2212yes—
81#63856C2212yes—
82#63852C2212yes—
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—31no—
93#5727—31no—
94#5718—31no—
95#5718—31no—
96#5718—32no—
97#5718—61no—
98#5718D311yescharacteristic, complemented
99#5716—32no—
100#5716D311yescharacteristic, complemented
101#5677—32no—
102#5677—32no—
103#5608—32no—
104#5608—34no—
105#5598—32no—
106#5598—34no—
107#5597—34no—
108#5596—32no—
109#5596—32no—
110Q8×D12—31no—
111C4×D3×Q8—31no—
112#5553—32no—
113#5552—34no—
114#5548—32no—
115#5548—31no—
116D4×Dic6—32no—
117D4×Dic6—32no—
118D4×Dic6—31no—
119#5477—31no—
120C2×C4×Dic6—31no—
121C2×C32×D4C2312yes—
122C2×C32×D4C2312yes—
123C2×C32×D4C2312yes—
124C2×#638C2314yes—
125C2×#638C2314yes—
126C22×C3⋊Dic3C2314yes—
127#3830—28no—
128C2×C4⋊(C3⋊D3)C2311yescharacteristic
129C2×C4×C3⋊D3C2312yes—
130C2×#634C2311yescharacteristic
131C2×C3×#67C2314yes—
132C2×C3×#67C2314yes—
133C2×C3×#67C2314yes—
134C22×C3×Dic3C2314yes—
135C22×C3×Dic3C2314yes—
136C3×#237—28no—
137C3×#237—28no—
138C2×C3×D12C2311yescharacteristic
139C2×C3×C4×D3C2312yes—
140C2×C3×C4×D3C2311yescharacteristic
141C2×C3×C4×D3C2311yescharacteristic
142C2×C3×C4×D3C2311yescharacteristic
143C2×C3×Dic6C2312yes—
144C2×C3×Dic6C2311yescharacteristic
145C2×#627—216no—
146C2×#627C2314yes—
147C2×#627C2314yes—
148C2×#627C2312yes—
149C2×#627C2312yes—
150C2×#626C2312yes—
151C2×#626C2312yes—
152C2×#626C2312yes—
153C2×#625C2312yes—
154C2×#624C2314yes—
155#3805—216no—
156#3804—216no—
157#3804—216no—
158C2×D3×Dic3C2314yes—
159C2×D3×Dic3C2312yes—
160C2×D3×Dic3C2312yes—
161#3798—28no—
162#3797—28no—
163D3×Dic6—28no—
164D3×Dic6D418yescomplemented
165C32×C42C2311yescharacteristic
166#3757C2314yes—
167#3752C2312yes—
168C4⋊(C3⋊Dic3)C2311yescharacteristic
169C4⋊(C3⋊Dic3)C2311yescharacteristic
170#3750C2312yes—
171C4×C3⋊Dic3C2312yes—
172C3×#217C2314yes—
173C3×#217C2314yes—
174C3×#217C2314yes—
175C3×(C2×D3)⋊C4C2312yes—
176C3×C4⋊Dic3C2311yescharacteristic
177C3×C4⋊Dic3C2312yes—
178C3×C4⋊Dic3C2312yes—
179C3×C4⋊Dic3C2311yescharacteristic
180C3×Dic3⋊C4C2312yes—
181C3×C4×Dic3C2311yescharacteristic
182C3×C4×Dic3C2311yescharacteristic
183C3×C4×Dic3C2312yes—
184C3×C4×Dic3C2311yescharacteristic
185#3724C2312yes—
186#3724C2314yes—
187Dic3⋊Dic3C2312yes—
188Dic3⋊Dic3C2312yes—
189Dic3⋊Dic3C2314yes—
190Dic3⋊Dic3C2312yes—
191#3722C2312yes—
192#3722C2314yes—
193(C2×D3)⋊Dic3C2312yes—
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—32no—
204C2×D3×Q8—32no—
205C2×D3×Q8—32no—
206C2×#237—32no—
207C2×#237—32no—
208C2×#237—34no—
209C2×#237—34no—
210C2×#237—34no—
211C2×#237—34no—
212C2×#237—62no—
213C2×#237C2×D312yes—
214C2×#237C2×D312yes—
215C2×#235—34no—
216C2×#235—34no—
217C2×#235—32no—
218C2×#235—32no—
219C22×Dic6—31no—
220C22×Dic6—34no—
221C22×Dic6—34no—
222C22×Dic6—32no—
223C3×C4⋊Q8—31no—
224C3×#127—21no—
225C3×#127—32no—
226C3×#127C2×D311yescharacteristic
227C3×#127C2×D311yescharacteristic
228C3×#124—32no—
229C3×#121—32no—
230C3×#121—32no—
231C3×#121—32no—
232C3×#121—34no—
233C3×C4×Q8—31no—
234C3×C4×D4—32no—
235C3×C4×D4—32no—
236C3×C4×D4—32no—
237C3×C4×D4—31no—
238C2×C3×C42—31no—
239#946—32no—
240#946—32no—
241Q8×Dic3—31no—
242#940—32no—
243#940—32no—
244#940—31no—
245#940—62no—
246#940C2×D312yes—
247#939—34no—
248#939—34no—
249#939—34no—
250#939—34no—
251#939—34no—
252#939—34no—
253#939—64no—
254#939C2×D314yes—
255#938—32no—
256#938—32no—
257#938—34no—
258#938—31no—
259#938—34no—
260#938—62no—
261#938C2×D312yes—
262#938C2×D312yes—
263#938C2×D312yes—
264#936—34no—
265#936C2×D312yes—
266D4×Dic3—32no—
267D4×Dic3—32no—
268D4×Dic3—34no—
269D4×Dic3—32no—
270D4×Dic3—62no—
271D4×Dic3C2×D312yes—
272D4×Dic3C2×D312yes—
273D4×Dic3C2×D312yes—
274#930—34no—
275#930—31no—
276#930—32no—
277#930—31no—
278C4×#67—34no—
279C4×#67—32no—
280C2×C4⋊Dic3—31no—
281#924—32no—
282#924—34no—
283#924—34no—
284C2×Dic3⋊C4—32no—
285C2×C4×Dic3—32no—
286#897—32no—
287#897—34no—
288#896—34no—
289#896—34no—
290#895—31no—
291#893—32no—
292#893—32no—
293D3×C4⋊C4—32no—
294D3×C4⋊C4—31no—
295#888—32no—
296#888—32no—
297#888—32no—
298#888—31no—
299#887—32no—
300#887—31no—
301#885—34no—
302#885—34no—
303#885—34no—
304#885—32no—
305#884—34no—
306#884—34no—
307#884—34no—
308#884—32no—
309#67⋊C4—34no—
310#67⋊C4—34no—
311#878—34no—
312#878—34no—
313#878—34no—
314#878—34no—
315#878—34no—
316#875—32no—
317#874—31no—
318C4×D12—32no—
319C4×D12—31no—
320C4×D12—31no—
321C4×D12—32no—
322C4×D12—61no—
323C4×D12C2×D311yescharacteristic
324C42×D3—32no—
325C42×D3C2×D311yescharacteristic
326#869—32no—
327#869—31no—
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×C32C2414yes—
339C22×C3⋊D3C2412yes—
340C22×C3×D3C2412yes—
341C22×C3×D3C2411yescharacteristic
342C32×D4—24no—
343C32×D4—24no—
344C32×D4—42no—
345C2×C32×C4C2411yescharacteristic
346C2×C32×C4C2411yescharacteristic
347C2×C32×C4C2411yescharacteristic
348#638—28no—
349#638—44no—
350C2×C3⋊Dic3—28no—
351C2×C3⋊Dic3C2412yes—
352C2×C3⋊Dic3C2412yes—
353C2×C3⋊Dic3C2412yes—
354C4⋊(C3⋊D3)—22no—
355C4×C3⋊D3—24no—
356#634C2×D414yes—
357C3×#67—28no—
358C3×#67—28no—
359C3×#67—44no—
360C2×C3×Dic3—28no—
361C2×C3×Dic3—28no—
362C2×C3×Dic3C2411yescharacteristic
363C2×C3×Dic3C2412yes—
364C2×C3×Dic3C2414yes—
365C2×C3×Dic3C2412yes—
366C2×C3×Dic3C2411yescharacteristic
367C2×C3×Dic3C2412yes—
368C2×C3×Dic3C2411yescharacteristic
369C3×D12—22no—
370C3×C4×D3—24no—
371C3×C4×D3—22no—
372C3×C4×D3—41no—
373C3×C4×D3C2×D414yes—
374C3×Dic6—24no—
375C3×Dic6C2×D414yes—
376#627—28no—
377#627—28no—
378#627—24no—
379#627C2×D418yes—
380#626—24no—
381#626—24no—
382#626—42no—
383#625—24no—
384#624—28no—
385D3×Dic3—28no—
386D3×Dic3—42no—
387D3×Dic3C2×D418yes—
388C2×2−1+4—92no—
389#550—31no—
390#550—92no—
391#550—91no—
392D4×Q8—92no—
393D4×Q8—91no—
394D4×Q8—91no—
395#548—94no—
396#548—92no—
397#548—92no—
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—22no—
410C2×C3×D4—22no—
411C2×C3×D4—22no—
412C2×C3×D4—34no—
413C2×C3×D4—34no—
414C2×C3×D4—34no—
415C2×C3×D4—31no—
416C2×C3×D4C22×D312yes—
417C2×C3×D4C22×D312yes—
418C2×C3×D4C22×D312yes—
419C2×C3×D4C22×D312yes—
420C2×C3×D4C22×D312yes—
421C2×C3×D4C22×D312yes—
422C22×C3×C4—31no—
423C22×C3×C4—34no—
424C22×C3×C4—34no—
425C22×C3×C4—31no—
426C22×C3×C4—32no—
427C22×C3×C4—31no—
428C2×#67—34no—
429C2×#67—34no—
430C2×#67—32no—
431C2×#67—32no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—32no—
435C2×#67—32no—
436C2×#67—32no—
437C2×#67—64no—
438C2×#67—64no—
439C2×#67C22×D314yes—
440C2×#67C22×D314yes—
441C2×#67C22×D314yes—
442C22×Dic3—32no—
443C22×Dic3—34no—
444C22×Dic3—34no—
445C22×Dic3—34no—
446C22×Dic3—32no—
447C22×Dic3—64no—
448C22×Dic3C22×D314yes—
449C22×Dic3C22×D314yes—
450D3×Q8—38no—
451D3×Q8—68no—
452D3×Q8—68no—
453D3×Q8—68no—
454#237—28no—
455#237—28no—
456#237—616no—
457#237—68no—
458#237—68no—
459#237—616no—
460#237—616no—
461#237—616no—
462#237—128no—
463#235—616no—
464#235—68no—
465#235—616no—
466#235—68no—
467C2×D12—32no—
468C2×D12—32no—
469C2×D12—31no—
470C2×D12—31no—
471C2×D12—32no—
472C2×D12—61no—
473C2×D12C22×D311yescharacteristic
474C2×C4×D3—32no—
475C2×C4×D3—34no—
476C2×C4×D3—32no—
477C2×C4×D3—32no—
478C2×C4×D3—34no—
479C2×C4×D3—34no—
480C2×C4×D3—32no—
481C2×C4×D3—62no—
482C2×C4×D3C22×D311yescharacteristic
483C2×C4×D3C22×D312yes—
484C2×C4×D3C22×D311yescharacteristic
485C2×C4×D3C22×D311yescharacteristic
486C2×Dic6—31no—
487C2×Dic6—31no—
488C2×Dic6—32no—
489C2×Dic6—32no—
490C2×Dic6—38no—
491C2×Dic6—32no—
492C2×Dic6—34no—
493C2×Dic6—34no—
494C2×Dic6—32no—
495C2×Dic6—34no—
496C2×Dic6—34no—
497C2×Dic6—61no—
498C2×Dic6—68no—
499C2×Dic6—616no—
500C2×Dic6—616no—
501C2×Dic6C22×D312yes—
502C2×Dic6C22×D311yescharacteristic
503C3×C4⋊C4—32no—
504C3×C4⋊C4—31no—
505C3×C4⋊C4—31no—
506C3×C4⋊C4—32no—
507C3×C4⋊C4—32no—
508C3×C22⋊C4—34no—
509C3×C22⋊C4—34no—
510C3×C22⋊C4—34no—
511C3×C22⋊C4—32no—
512C3×C42—21no—
513C3×C42—31no—
514C3×C42—31no—
515C3×C42—31no—
516C3×C42—32no—
517C3×C42C22×D311yescharacteristic
518C3×C42C22×D311yescharacteristic
519#217—34no—
520#217—34no—
521#217—34no—
522#217—32no—
523#217—64no—
524#217C22×D314yes—
525#217C22×D314yes—
526#217C22×D314yes—
527(C2×D3)⋊C4—32no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—32no—
530(C2×D3)⋊C4—32no—
531(C2×D3)⋊C4—32no—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4—34no—
534(C2×D3)⋊C4—32no—
535(C2×D3)⋊C4—62no—
536(C2×D3)⋊C4C22×D312yes—
537C4⋊Dic3—31no—
538C4⋊Dic3—31no—
539C4⋊Dic3—31no—
540C4⋊Dic3—31no—
541C4⋊Dic3—32no—
542C4⋊Dic3—32no—
543C4⋊Dic3—32no—
544C4⋊Dic3—34no—
545C4⋊Dic3—61no—
546C4⋊Dic3—61no—
547C4⋊Dic3C22×D311yescharacteristic
548C4⋊Dic3C22×D312yes—
549C4⋊Dic3C22×D311yescharacteristic
550C4⋊Dic3C22×D312yes—
551Dic3⋊C4—32no—
552Dic3⋊C4—32no—
553Dic3⋊C4—32no—
554Dic3⋊C4—32no—
555Dic3⋊C4—32no—
556Dic3⋊C4—32no—
557Dic3⋊C4—32no—
558Dic3⋊C4—34no—
559Dic3⋊C4—34no—
560Dic3⋊C4—34no—
561Dic3⋊C4—62no—
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—24no—
575C22×C32—24no—
576C22×C32—24no—
577C22×C32C2511yescharacteristic
578C2×C3⋊D3—22no—
579C2×C3⋊D3—22no—
580C2×C3⋊D3—22no—
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—21no—
588C32×C4C22×D412yes—
589C32×C42−1+412yescomplemented
590C3⋊Dic3—22no—
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—32no—
603C2×#41—92no—
604C2×#41—94no—
605C2×#41—94no—
606C2×#41—94no—
607C2×#41—92no—
608C22×Q8—94no—
609C22×Q8—91no—
610C22×Q8—92no—
611C22×Q8—92no—
612C4⋊Q8—31no—
613C4⋊Q8—91no—
614C4⋊Q8—92no—
615C4⋊Q8—92no—
616#127—32no—
617#127—91no—
618#127—92no—
619#127D3211yescharacteristic
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—94no—
629C22⋊Q8—92no—
630C22⋊Q8—92no—
631#121—32no—
632#121—32no—
633#121—32no—
634#121—34no—
635#121—92no—
636#121—94no—
637#121—94no—
638#121—94no—
639#121—91no—
640#121—91no—
641#121—94no—
642#121—94no—
643#121—92no—
644#121—94no—
645C4×Q8—31no—
646C4×Q8—92no—
647C4×Q8—92no—
648C4×Q8—91no—
649C4×Q8—91no—
650C4×Q8—91no—
651C4×D4—32no—
652C4×D4—32no—
653C4×D4—32no—
654C4×D4—31no—
655C4×D4—92no—
656C4×D4—92no—
657C4×D4—94no—
658C4×D4—94no—
659C4×D4—92no—
660C4×D4—92no—
661C4×D4—91no—
662C2×C4⋊C4—92no—
663C2×C4⋊C4—91no—
664C2×C42—31no—
665C2×C42—92no—
666C23×C3—24no—
667C23×C3—31no—
668C23×C3—32no—
669C23×C3C23×D314yes—
670C23×C3C23×D314yes—
671C22×D3—32no—
672C22×D3—32no—
673C22×D3—62no—
674C22×D3C23×D312yes—
675C22×D3C23×D311yescharacteristic
676C3×Q8—34no—
677C3×Q8—64no—
678C3×D4—24no—
679C3×D4—24no—
680C3×D4—24no—
681C3×D4—24no—
682C3×D4—44no—
683C3×D4—44no—
684C3×D4—42no—
685C3×D4—42no—
686C3×D4—68no—
687C3×D4—68no—
688C3×D4—62no—
689C3×D4—82no—
690C3×D4—124no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
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—68no—
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×D311yescharacteristic
710C2×C3×C4C23×D311yescharacteristic
711C2×C3×C4C23×D311yescharacteristic
712C2×C3×C4C23×D311yescharacteristic
713#67—28no—
714#67—28no—
715#67—44no—
716#67—64no—
717#67—68no—
718#67—68no—
719#67—64no—
720#67—64no—
721#67—64no—
722#67—128no—
723#67—122no—
724#67—124no—
725#67—124no—
726#67—244no—
727C2×Dic3—28no—
728C2×Dic3—28no—
729C2×Dic3—32no—
730C2×Dic3—32no—
731C2×Dic3—38no—
732C2×Dic3—32no—
733C2×Dic3—32no—
734C2×Dic3—32no—
735C2×Dic3—32no—
736C2×Dic3—62no—
737C2×Dic3—62no—
738C2×Dic3—62no—
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×D314yes—
749C2×Dic3C23×D312yes—
750C2×Dic3C23×D311yescharacteristic
751D12—22no—
752D12—64no—
753D12—64no—
754D12—62no—
755D12—62no—
756D12—122no—
757D12—122no—
758C4×D3—24no—
759C4×D3—22no—
760C4×D3—38no—
761C4×D3—41no—
762C4×D3—68no—
763C4×D3—68no—
764C4×D3—64no—
765C4×D3—64no—
766C4×D3—68no—
767C4×D3—124no—
768C4×D3—122no—
769C4×D3D3×D414yes—
770Dic6—24no—
771Dic6—34no—
772Dic6—34no—
773Dic6—38no—
774Dic6—38no—
775Dic6—64no—
776Dic6—68no—
777Dic6—68no—
778Dic6—64no—
779Dic6—68no—
780Dic6—64no—
781Dic6—68no—
782Dic6D3×D414yes—
783C2×C32—44no—
784C2×C32C23×D411yescharacteristic
785C2×C32C2×2−1+411yescharacteristic
786C2×C32#58511yescharacteristic
787C3⋊D3—42no—
788C3×D3—22no—
789C3×D3—42no—
790#41—68no—
791#41—68no—
792#41—188no—
793#41—1816no—
794#41—1816no—
795#41—1816no—
796#41—188no—
797C2×Q8—31no—
798C2×Q8—32no—
799C2×Q8—92no—
800C2×Q8—92no—
801C2×Q8—94no—
802C2×Q8—94no—
803C2×Q8—98no—
804C2×Q8—91no—
805C2×Q8—1816no—
806C2×Q8—188no—
807C2×Q8—188no—
808C2×D4—34no—
809C2×D4—34no—
810C2×D4—34no—
811C2×D4—31no—
812C2×D4—92no—
813C2×D4—92no—
814C2×D4—92no—
815C2×D4—92no—
816C2×D4—94no—
817C2×D4—94no—
818C2×D4—91no—
819C2×D4C2×D3212yes—
820C2×D4C2×D3212yes—
821C2×D4C2×D3212yes—
822C22×C4—31no—
823C22×C4—34no—
824C22×C4—34no—
825C22×C4—31no—
826C22×C4—32no—
827C22×C4—31no—
828C22×C4—94no—
829C22×C4—92no—
830C22×C4—94no—
831C22×C4—92no—
832C22×C4—94no—
833C22×C4—92no—
834C4⋊C4—32no—
835C4⋊C4—31no—
836C4⋊C4—31no—
837C4⋊C4—32no—
838C4⋊C4—32no—
839C4⋊C4—92no—
840C4⋊C4—92no—
841C4⋊C4—92no—
842C4⋊C4—94no—
843C4⋊C4—92no—
844C4⋊C4—94no—
845C4⋊C4—92no—
846C4⋊C4—91no—
847C4⋊C4—91no—
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—34no—
851C22⋊C4—32no—
852C22⋊C4—92no—
853C22⋊C4—94no—
854C22⋊C4—92no—
855C22⋊C4—94no—
856C22⋊C4—94no—
857C22⋊C4—92no—
858C42—31no—
859C42—31no—
860C42—31no—
861C42—32no—
862C42—92no—
863C42—92no—
864C42—92no—
865C42C2×D3211yescharacteristic
866C22×C3—24no—
867C22×C3—24no—
868C22×C3—24no—
869C22×C3—24no—
870C22×C3—24no—
871C22×C3—24no—
872C22×C3—21no—
873C22×C3—32no—
874C22×C3—44no—
875C22×C3—44no—
876C22×C3—44no—
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—62no—
890C2×D3—62no—
891C2×D3—62no—
892C2×D3—62no—
893C2×D3—62no—
894C2×D3—62no—
895C2×D3—122no—
896C2×D3—122no—
897C2×D3—122no—
898C2×D3C2×D3×D412yes—
899C3×C4—21no—
900C3×C4—21no—
901C3×C4—22no—
902C3×C4—22no—
903C3×C4—32no—
904C3×C4—34no—
905C3×C4—41no—
906C3×C4—62no—
907C3×C4—64no—
908C3×C4—61no—
909C3×C4—62no—
910C3×C4—61no—
911C3×C4C2×D3×D412yes—
912C3×C4C2×D3×D412yes—
913C3×C4#101012yescomplemented
914C3×C4#101012yescomplemented
915Dic3—24no—
916Dic3—22no—
917Dic3—21no—
918Dic3—21no—
919Dic3—22no—
920Dic3—34no—
921Dic3—34no—
922Dic3—64no—
923Dic3—62no—
924Dic3—62no—
925Dic3—62no—
926Dic3—62no—
927Dic3—122no—
928Dic3—122no—
929Dic3C2×D3×D412yes—
930Dic3C2×D3×D414yes—
931C32#349711yescharacteristic, complemented, Sylow
932C23—31no—
933C23—32no—
934C23—92no—
935C23C22×D3214yes—
936Q8—34no—
937Q8—64no—
938Q8—98no—
939Q8—94no—
940Q8—184no—
941Q8—188no—
942Q8—188no—
943D4—24no—
944D4—24no—
945D4—42no—
946D4—68no—
947D4—68no—
948D4—62no—
949D4—124no—
950D4—184no—
951D4—184no—
952D4—188no—
953D4—184no—
954D4—182no—
955D4—362no—
956D4—364no—
957C2×C4—31no—
958C2×C4—32no—
959C2×C4—34no—
960C2×C4—31no—
961C2×C4—31no—
962C2×C4—32no—
963C2×C4—32no—
964C2×C4—34no—
965C2×C4—68no—
966C2×C4—68no—
967C2×C4—62no—
968C2×C4—64no—
969C2×C4—98no—
970C2×C4—92no—
971C2×C4—92no—
972C2×C4—92no—
973C2×C4—121no—
974C2×C4—188no—
975C2×C4—188no—
976C2×C4—188no—
977C2×C4—184no—
978C2×C4—362no—
979C2×C4C22×D3211yescharacteristic
980C2×C4C22×D3211yescharacteristic
981C2×C4C22×D3211yescharacteristic
982C2×C3—21no—
983C2×C3—21no—
984C2×C3—21no—
985C2×C3—44no—
986C2×C3—44no—
987C2×C3—62no—
988C2×C3—84no—
989C2×C3—122no—
990C2×C3C22×D3×D411yescharacteristic
991C2×C3C22×D3×D411yescharacteristic
992C2×C3C2×#101011yescharacteristic
993C2×C3C2×#101011yescharacteristic
994C2×C3#596411yescharacteristic
995C2×C3#596611yescharacteristic
996D3—22no—
997D3—42no—
998D3—122no—
999D3—122no—
1000D3—242no—
1001C22—24no—
1002C22—24no—
1003C22—24no—
1004C22—32no—
1005C22—61no—
1006C22—61no—
1007C22—62no—
1008C22—62no—
1009C22—62no—
1010C22—182no—
1011C22—182no—
1012C22—182no—
1013C22C23×D3211yescharacteristic
1014C4—21no—
1015C4—32no—
1016C4—34no—
1017C4—61no—
1018C4—62no—
1019C4—64no—
1020C4—61no—
1021C4—62no—
1022C4—94no—
1023C4—182no—
1024C4—182no—
1025C4#6430912yescomplemented
1026C4D32×D412yes—
1027C3—21no—
1028C3#8622211yescharacteristic, complemented
1029C3#8678411yescharacteristic, complemented
1030C2—44no—
1031C2—62no—
1032C2—122no—
1033C2—362no—
1034C2C2×#6430911yescharacteristic
1035C2C2×D32×D411yescharacteristic
1036C2#1059667811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32#3497
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C2×#64309C2semidirect
2. #10596189C2semidirect
3. C3×#5718C2semidirect
4. C3×#5716C2semidirect
5. D4×#627C2semidirect
6. #10595237C2semidirect
7. #10595232C2semidirect
8. #10595161C2semidirect
9. #10595143C2semidirect
10. #10595141C2semidirect
11. #10595133C2semidirect
12. #10595132C2semidirect
13. #10595131C2semidirect
14. #10593968C2semidirect
15. #10593904C2semidirect
16. #10593903C2semidirect
17. C4×D3×Dic6C2semidirect
98. #5718D3semidirect
100. #5716D3semidirect
164. D3×Dic6D4semidirect
589. C32×C42−1+4semidirect
913. C3×C4#1010semidirect
914. C3×C4#1010semidirect
931. C32#3497semidirect
1025. C4#64309semidirect
1028. C3#86222semidirect
1029. C3#86784semidirect

Maximal subgroups

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

subgroupindex
C2×#643092
#105961892
C3×#57182
C3×#57162
D4×#6272
#105952372
#105952322
#105951612
#105951432
#105951412
#105951332
#105951322
#105951312
#105939682
#105939042
#105939032
C4×D3×Dic62
#867843
#862223