Finite Group Databasebeta

← #11906022

Subgroups — #11906022

Order 1152.

3097 conjugacy classes of subgroups.

The subgroup lattice has 1025 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64315C212yesmaximal, complemented
2C3⋊D3×C4⋊Q8C211yesmaximal, characteristic, complemented
3C3×#5727C211yesmaximal, characteristic, complemented
4C3×#5726C211yesmaximal, characteristic, complemented
5#10595405C212yesmaximal, complemented
6#10595400C212yesmaximal, complemented
7#10595357C212yesmaximal, complemented
8#10594515C212yesmaximal, complemented
9#10594373C212yesmaximal, complemented
10#10594371C214yesmaximal, complemented
11#10594367C212yesmaximal, complemented
12#10594365C214yesmaximal, complemented
13D3×#888C212yesmaximal, complemented
14#10593972C211yesmaximal, characteristic, complemented
15Dic6×D12C211yesmaximal, characteristic, complemented
16#10593895C211yesmaximal, characteristic, complemented
17C4×#3796C211yesmaximal, characteristic, complemented
18#86746—31nomaximal
19#86679—31nomaximal
20C2×Q8×C3⋊D3C2212yes—
21C2×C3×#239C2212yes—
22C2×C3×D3×Q8C2212yes—
23#64315—216no—
24C2×#3798C2214yes—
25C2×#3798C2212yes—
26C2×#3796C2214yes—
27C2×#3796C2211yescharacteristic
28C2×#3795C2212yes—
29C2×#3795C2214yes—
30C2×D3×Dic6C2214yes—
31C2×D3×Dic6C2212yes—
32C32×C4⋊Q8C2211yescharacteristic
33#64153C2212yes—
34C4⋊C4×C3⋊D3C2212yes—
35C4⋊C4×C3⋊D3C2212yes—
36#64097C2212yes—
37#64097C2212yes—
38C42×C3⋊D3C2211yescharacteristic
39#64078C2211yescharacteristic
40C3×#946C2212yes—
41C3×#946C2212yes—
42C3×#896C2214yes—
43C3×#895C2212yes—
44C3×#894C2214yes—
45C3×#893C2212yes—
46C3×D3×C4⋊C4C2212yes—
47C3×#888C2212yes—
48C3×C4×D12C2211yescharacteristic
49C3×C4×D12C2211yescharacteristic
50C3×C4×D12C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic
52#63919C2211yescharacteristic
53#63918C2212yes—
54#63916C2211yescharacteristic
55#63916C2211yescharacteristic
56#63915C2212yes—
57#63914C2211yescharacteristic
58#63913C2214yes—
59#63912C2212yes—
60#63908C2212yes—
61#63905C2214yes—
62C4×#626C2212yes—
63C4×#625C2212yes—
64#63898C2211yescharacteristic
65#63893C2214yes—
66Dic3×D12C2212yes—
67#63891C2214yes—
68D3×C4⋊Dic3C2212yes—
69#63887C2214yes—
70#63885C2214yes—
71#63884C2214yes—
72#63881C2212yes—
73#63879C2214yes—
74#63878C2212yes—
75D3×Dic3⋊C4C2214yes—
76C4×D3×Dic3C2212yes—
77#63857C2212yes—
78#63857C2212yes—
79#63853C2214yes—
80#63853C2214yes—
81#63851C2214yes—
82#63849C2211yescharacteristic
83#63843C2211yescharacteristic
84#63840C2214yes—
85#63839C2214yes—
86C2×#1010—32no—
87C2×#1007—32no—
88C3×D4×Q8—31no—
89C3×#547—31no—
90#5824—32no—
91Q8×#67—32no—
92#5727D311yescharacteristic, complemented
93#5726—32no—
94#5726D311yescharacteristic, complemented
95D3×C4⋊Q8—31no—
96D3×C4⋊Q8—31no—
97D3×C4⋊Q8—32no—
98D3×C4⋊Q8—61no—
99#5655—34no—
100#5648—34no—
101#5632—32no—
102#5631—32no—
103#5631—34no—
104#5628—32no—
105#5628—32no—
106#5628—34no—
107#5611—32no—
108#5596—32no—
109Q8×D12—31no—
110C4×#239—31no—
111#5555—31no—
112#5551—32no—
113#5551—31no—
114#5548—32no—
115#5548—31no—
116#5548—31no—
117D4×Dic6—31no—
118C4×#237—31no—
119#5507—32no—
120C2×#888—32no—
121C2×C32×Q8C2312yes—
122Q8×C3⋊D3—28no—
123C2×C4×C3⋊D3C2314yes—
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×#634C2312yes—
128C2×#634C2314yes—
129C3×#239—28no—
130C3×D3×Q8—28no—
131C2×C3×D12C2311yescharacteristic
132C2×C3×D12C2314yes—
133C2×C3×D12C2311yescharacteristic
134C2×C3×D12C2311yescharacteristic
135C2×C3×C4×D3C2314yes—
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2314yes—
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2312yes—
140C2×C3×Dic6C2314yes—
141C2×C3×Dic6C2311yescharacteristic
142C2×#627C2314yes—
143C2×#627C2312yes—
144C2×#626C2312yes—
145C2×#626C2312yes—
146C2×#626C2312yes—
147C2×#625C2314yes—
148C2×#625C2312yes—
149C2×#625C2312yes—
150C2×D3×Dic3C2314yes—
151C2×D3×Dic3C2314yes—
152C2×D3×Dic3C2312yes—
153C2×D3×Dic3C2312yes—
154#3798—28no—
155#3798—216no—
156#3796—216no—
157#3796D418yescomplemented
158#3795—28no—
159#3795—216no—
160D3×Dic6—28no—
161D3×Dic6—216no—
162C32×C4⋊C4C2312yes—
163C32×C4⋊C4C2312yes—
164C32×C42C2311yescharacteristic
165C4⋊(C3⋊Dic3)C2312yes—
166C4⋊(C3⋊Dic3)C2312yes—
167#3750C2314yes—
168#3750C2314yes—
169C4×C3⋊Dic3C2311yescharacteristic
170C4×C3⋊Dic3C2311yescharacteristic
171C4×C3⋊Dic3C2311yescharacteristic
172C3×(C2×D3)⋊C4C2314yes—
173C3×(C2×D3)⋊C4C2312yes—
174C3×(C2×D3)⋊C4C2312yes—
175C3×(C2×D3)⋊C4C2314yes—
176C3×(C2×D3)⋊C4C2312yes—
177C3×C4⋊Dic3C2311yescharacteristic
178C3×C4⋊Dic3C2311yescharacteristic
179C3×C4⋊Dic3C2311yescharacteristic
180C3×C4⋊Dic3C2311yescharacteristic
181C3×Dic3⋊C4C2314yes—
182C3×Dic3⋊C4C2314yes—
183C3×Dic3⋊C4C2312yes—
184C3×C4×Dic3C2312yes—
185#3724C2312yes—
186Dic3⋊Dic3C2314yes—
187Dic3⋊Dic3C2314yes—
188Dic3⋊Dic3C2312yes—
189#3722C2312yes—
190(C2×D3)⋊Dic3C2312yes—
191(C2×D3)⋊Dic3C2314yes—
192(C2×D3)⋊Dic3C2314yes—
193(C2×D3)⋊Dic3C2312yes—
194(C2×D3)⋊Dic3C2312yes—
195Dic32C2312yes—
196Dic32C2312yes—
197#3499—91noSylow
198C2×C3×#41—32no—
199C22×C3×Q8—32no—
200#1010—616no—
201#1007—616no—
202C2×#239—31no—
203C2×#239—34no—
204C2×#239C2×D312yes—
205C2×D3×Q8—32no—
206C2×D3×Q8—32no—
207C2×D3×Q8—34no—
208C2×D3×Q8—32no—
209C2×D3×Q8—62no—
210C2×D3×Q8C2×D312yes—
211C2×#237—34no—
212C2×#237—32no—
213C2×#237—31no—
214C2×#237—34no—
215C2×#235—34no—
216C2×#235—32no—
217C2×#235—34no—
218C2×#235—32no—
219C2×#235—34no—
220C2×#235—32no—
221C22×Dic6—32no—
222C22×Dic6—34no—
223C3×C4⋊Q8—21no—
224C3×C4⋊Q8—32no—
225C3×C4⋊Q8C2×D311yescharacteristic
226C3×C4⋊Q8C2×D311yescharacteristic
227C3×#123—34no—
228C3×C22⋊Q8—32no—
229C3×C22⋊Q8—32no—
230C3×C22⋊Q8—34no—
231C3×#121—32no—
232C3×C4×Q8—31no—
233C3×C4×D4—32no—
234C3×C4×D4—31no—
235C3×C4×D4—31no—
236C3×C4×D4—31no—
237C2×C3×C4⋊C4—32no—
238#946—34no—
239#946C2×D312yes—
240#946C2×D312yes—
241Q8×Dic3—31no—
242#944—32no—
243#944—32no—
244#944—34no—
245#944—62no—
246#940—31no—
247#940—31no—
248#939—34no—
249#938—32no—
250#938—31no—
251#938—31no—
252#935—34no—
253D4×Dic3—31no—
254D4×Dic3—32no—
255#930—32no—
256#929—34no—
257C4×#67—32no—
258C4×#67—32no—
259C4×#67—34no—
260C4×#67—32no—
261C2×C4⋊Dic3—32no—
262#924—32no—
263#924—32no—
264#924—34no—
265C2×Dic3⋊C4—34no—
266C2×C4×Dic3—32no—
267#897—32no—
268#897—32no—
269#897—34no—
270#896—34no—
271#896C2×D314yes—
272#895—31no—
273#895—31no—
274#895C2×D312yes—
275#894—34no—
276#894—34no—
277#894—34no—
278#894C2×D314yes—
279#893—31no—
280#893—32no—
281#893C2×D312yes—
282#892—32no—
283#892—31no—
284#892—31no—
285D3×C4⋊C4—32no—
286D3×C4⋊C4—34no—
287D3×C4⋊C4—32no—
288D3×C4⋊C4—32no—
289D3×C4⋊C4—32no—
290D3×C4⋊C4—32no—
291D3×C4⋊C4—62no—
292D3×C4⋊C4—62no—
293D3×C4⋊C4C2×D312yes—
294#888—34no—
295#888—32no—
296#888—32no—
297#888—32no—
298#888—32no—
299#888—31no—
300#888—31no—
301#888—34no—
302#888—34no—
303#888—32no—
304#888—62no—
305#888—62no—
306#888C2×D312yes—
307#887—31no—
308#886—34no—
309#885—32no—
310#885—34no—
311#885—34no—
312#885—32no—
313#884—34no—
314#884—32no—
315#884—32no—
316#883—34no—
317#883—34no—
318#883—34no—
319#883—34no—
320#67⋊C4—34no—
321#67⋊C4—32no—
322#878—34no—
323#878—34no—
324#877—32no—
325C4×D12—32no—
326C4×D12—32no—
327C4×D12C2×D311yescharacteristic
328C4×D12C2×D311yescharacteristic
329C4×D12C2×D311yescharacteristic
330C42×D3—32no—
331C42×D3—31no—
332C42×D3—31no—
333C42×D3—61no—
334#869—31no—
335#869—31no—
336#869—32no—
337#869—61no—
338C4×Dic6C2×D311yescharacteristic
339C22×C3⋊D3C2411yescharacteristic
340C22×C3×D3C2412yes—
341C22×C3×D3C2412yes—
342C22×C3×D3C2412yes—
343C32×Q8—24no—
344C2×C32×C4C2411yescharacteristic
345C2×C32×C4C2414yes—
346C2×C32×C4C2411yescharacteristic
347C2×C32×C4C2411yescharacteristic
348C2×C3⋊Dic3C2411yescharacteristic
349C2×C3⋊Dic3C2414yes—
350C2×C3⋊Dic3C2411yescharacteristic
351C2×C3⋊Dic3C2411yescharacteristic
352C4×C3⋊D3—22no—
353C4×C3⋊D3—22no—
354C4×C3⋊D3—28no—
355C4×C3⋊D3C2×D414yes—
356#634—24no—
357#634—28no—
358C2×C3×Dic3C2412yes—
359C2×C3×Dic3C2412yes—
360C2×C3×Dic3C2412yes—
361C2×C3×Dic3C2412yes—
362C2×C3×Dic3C2412yes—
363C3×D12—28no—
364C3×D12—22no—
365C3×D12—22no—
366C3×D12C2×D414yes—
367C3×C4×D3—28no—
368C3×C4×D3—24no—
369C3×C4×D3—24no—
370C3×C4×D3—24no—
371C3×C4×D3—28no—
372C3×Dic6—28no—
373C3×Dic6C2×D414yes—
374#627—24no—
375#627—28no—
376#626—24no—
377#626—24no—
378#626C2×D418yes—
379#625—28no—
380#625—24no—
381#625—24no—
382D3×Dic3—28no—
383D3×Dic3—24no—
384D3×Dic3—28no—
385D3×Dic3C2×D418yes—
386C2×2−1+4—92no—
387D4×Q8—31no—
388D4×Q8—91no—
389D4×Q8—92no—
390#547—31no—
391#547—92no—
392#547—91no—
393#547—92no—
394#547—94no—
395#547—92no—
396#536—92no—
397#536—94no—
398#532—91no—
399#532—92no—
400C2×C4⋊Q8—92no—
401C2×C4⋊Q8—91no—
402C4×#41—91no—
403C3×#41—68no—
404C2×C3×Q8—22no—
405C2×C3×Q8—31no—
406C2×C3×Q8—34no—
407C2×C3×Q8—68no—
408C2×C3×Q8C22×D312yes—
409C2×C3×Q8C22×D312yes—
410C2×C3×D4—31no—
411C2×C3×D4—31no—
412C2×C3×D4—34no—
413C2×C3×D4—31no—
414C22×C3×C4—32no—
415C22×C3×C4—34no—
416C22×C3×C4—32no—
417C22×C3×C4—34no—
418C22×C3×C4—32no—
419C2×#67—32no—
420C2×#67—34no—
421C2×#67—32no—
422C2×#67—32no—
423C2×#67—32no—
424C2×#67—34no—
425C2×#67—32no—
426C2×#67—32no—
427C2×#67—32no—
428C22×Dic3—32no—
429C22×Dic3—34no—
430C22×Dic3—32no—
431C22×Dic3—34no—
432#239—28no—
433#239—38no—
434#239—616no—
435D3×Q8—28no—
436D3×Q8—616no—
437D3×Q8—68no—
438D3×Q8—68no—
439D3×Q8—68no—
440D3×Q8—128no—
441#237—38no—
442#237—616no—
443#237—616no—
444#237—68no—
445#235—68no—
446#235—68no—
447#235—616no—
448#235—616no—
449#235—616no—
450#235—68no—
451C2×D12—32no—
452C2×D12—32no—
453C2×D12—32no—
454C2×D12C22×D311yescharacteristic
455C2×D12C22×D311yescharacteristic
456C2×D12C22×D314yes—
457C2×D12C22×D311yescharacteristic
458C2×C4×D3—32no—
459C2×C4×D3—31no—
460C2×C4×D3—31no—
461C2×C4×D3—32no—
462C2×C4×D3—34no—
463C2×C4×D3—34no—
464C2×C4×D3—31no—
465C2×C4×D3—31no—
466C2×C4×D3—31no—
467C2×C4×D3—31no—
468C2×C4×D3—34no—
469C2×C4×D3—34no—
470C2×C4×D3—61no—
471C2×C4×D3—61no—
472C2×C4×D3—61no—
473C2×C4×D3—64no—
474C2×C4×D3C22×D312yes—
475C2×C4×D3C22×D312yes—
476C2×C4×D3C22×D312yes—
477C2×C4×D3C22×D314yes—
478C2×C4×D3C22×D314yes—
479C2×Dic6—32no—
480C2×Dic6—32no—
481C2×Dic6—34no—
482C2×Dic6—34no—
483C2×Dic6—34no—
484C2×Dic6—34no—
485C2×Dic6—32no—
486C2×Dic6—32no—
487C2×Dic6—62no—
488C2×Dic6—64no—
489C2×Dic6—616no—
490C2×Dic6—68no—
491C2×Dic6C22×D314yes—
492C2×Dic6C22×D311yescharacteristic
493C3×C4⋊C4—22no—
494C3×C4⋊C4—22no—
495C3×C4⋊C4—31no—
496C3×C4⋊C4—31no—
497C3×C4⋊C4—34no—
498C3×C4⋊C4—31no—
499C3×C4⋊C4—34no—
500C3×C4⋊C4—32no—
501C3×C4⋊C4—31no—
502C3×C4⋊C4C22×D312yes—
503C3×C4⋊C4C22×D312yes—
504C3×C4⋊C4C22×D312yes—
505C3×C4⋊C4C22×D312yes—
506C3×C22⋊C4—32no—
507C3×C22⋊C4—32no—
508C3×C22⋊C4—34no—
509C3×C22⋊C4—34no—
510C3×C22⋊C4—32no—
511C3×C42—21no—
512C3×C42—32no—
513C3×C42C22×D311yescharacteristic
514C3×C42C22×D311yescharacteristic
515#217—32no—
516#217—32no—
517#217—34no—
518#217—32no—
519#217—34no—
520(C2×D3)⋊C4—32no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—32no—
524(C2×D3)⋊C4—32no—
525(C2×D3)⋊C4—32no—
526(C2×D3)⋊C4—32no—
527(C2×D3)⋊C4C22×D312yes—
528(C2×D3)⋊C4C22×D312yes—
529(C2×D3)⋊C4C22×D312yes—
530(C2×D3)⋊C4C22×D314yes—
531(C2×D3)⋊C4C22×D314yes—
532C4⋊Dic3—32no—
533C4⋊Dic3—32no—
534C4⋊Dic3—32no—
535C4⋊Dic3—32no—
536C4⋊Dic3—34no—
537C4⋊Dic3—32no—
538C4⋊Dic3—34no—
539C4⋊Dic3—62no—
540C4⋊Dic3—62no—
541C4⋊Dic3C22×D311yescharacteristic
542C4⋊Dic3C22×D311yescharacteristic
543C4⋊Dic3C22×D311yescharacteristic
544C4⋊Dic3C22×D311yescharacteristic
545Dic3⋊C4—34no—
546Dic3⋊C4—34no—
547Dic3⋊C4—34no—
548Dic3⋊C4—34no—
549Dic3⋊C4—32no—
550Dic3⋊C4—34no—
551Dic3⋊C4—34no—
552Dic3⋊C4—32no—
553Dic3⋊C4—32no—
554Dic3⋊C4—64no—
555Dic3⋊C4—64no—
556Dic3⋊C4C22×D312yes—
557Dic3⋊C4C22×D314yes—
558Dic3⋊C4C22×D314yes—
559C4×Dic3—31no—
560C4×Dic3—31no—
561C4×Dic3—31no—
562C4×Dic3—31no—
563C4×Dic3—31no—
564C4×Dic3—31no—
565C4×Dic3—32no—
566C4×Dic3—32no—
567C4×Dic3—32no—
568C4×Dic3—32no—
569C4×Dic3—61no—
570C4×Dic3—61no—
571C4×Dic3—61no—
572C4×Dic3C22×D312yes—
573C22×C32C2511yescharacteristic
574C2×C3⋊D3—21no—
575C2×C3⋊D3—21no—
576C2×C3⋊D3C22×D412yes—
577C2×C3×D3—22no—
578C2×C3×D3—22no—
579C2×C3×D3—22no—
580C2×C3×D3—22no—
581C2×C3×D3—22no—
582C2×C3×D3—22no—
583C2×C3×D3—22no—
584C2×C3×D3—22no—
585C2×C3×D3C22×D414yes—
586C32×C4—21no—
587C32×C4—24no—
588C32×C4C22×D412yes—
589C32×C42−1+412yescomplemented
590C3⋊Dic3—21no—
591C3⋊Dic3—24no—
592C3⋊Dic3C22×D412yes—
593C3⋊Dic32−1+412yescomplemented
594C3×Dic3—22no—
595C3×Dic3—22no—
596C3×Dic3—22no—
597C3×Dic3—22no—
598C3×Dic3C22×D414yes—
5992−1+4—1816no—
600C2×#41—32no—
601C2×#41—92no—
602C2×#41—94no—
603C2×#41—94no—
604C2×#41—92no—
605C2×#41—91no—
606C2×#41—94no—
607C22×Q8—32no—
608C22×Q8—94no—
609C22×Q8—92no—
610C22×Q8—92no—
611C4⋊Q8—32no—
612C4⋊Q8—92no—
613C4⋊Q8—91no—
614C4⋊Q8—94no—
615C4⋊Q8—94no—
616C4⋊Q8—92no—
617C4⋊Q8—92no—
618C4⋊Q8—92no—
619C4⋊Q8—91no—
620C4⋊Q8D3211yescharacteristic
621#127—91no—
622#124—94no—
623#124—92no—
624#123—34no—
625#123—94no—
626#123—94no—
627#123—94no—
628#123—94no—
629#123—94no—
630C22⋊Q8—32no—
631C22⋊Q8—32no—
632C22⋊Q8—34no—
633C22⋊Q8—94no—
634C22⋊Q8—94no—
635C22⋊Q8—94no—
636C22⋊Q8—92no—
637C22⋊Q8—92no—
638#121—32no—
639#121—92no—
640#121—94no—
641#121—91no—
642#121—91no—
643#121—92no—
644C4×Q8—31no—
645C4×Q8—91no—
646C4×D4—32no—
647C4×D4—31no—
648C4×D4—31no—
649C4×D4—31no—
650C4×D4—92no—
651C4×D4—92no—
652C4×D4—92no—
653C4×D4—94no—
654C4×D4—91no—
655C4×D4—92no—
656#117—92no—
657#117—91no—
658C2×C4⋊C4—32no—
659C2×C4⋊C4—94no—
660C2×C4⋊C4—92no—
661C2×C4⋊C4—92no—
662C2×C4⋊C4—92no—
663C2×C42—92no—
664C2×C42—91no—
665C23×C3—32no—
666C23×C3—32no—
667C23×C3—32no—
668C22×D3—31no—
669C22×D3—31no—
670C22×D3—61no—
671C22×D3C23×D312yes—
672C22×D3C23×D312yes—
673C22×D3C23×D312yes—
674C3×Q8—24no—
675C3×Q8—24no—
676C3×Q8—34no—
677C3×Q8—44no—
678C3×Q8—68no—
679C3×D4—34no—
680C3×D4—68no—
681C3×D4—62no—
682C3×D4—62no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—24no—
687C2×C3×C4—32no—
688C2×C3×C4—32no—
689C2×C3×C4—32no—
690C2×C3×C4—32no—
691C2×C3×C4—32no—
692C2×C3×C4—68no—
693C2×C3×C4—68no—
694C2×C3×C4—64no—
695C2×C3×C4—64no—
696C2×C3×C4—64no—
697C2×C3×C4C23×D311yescharacteristic
698C2×C3×C4C23×D311yescharacteristic
699C2×C3×C4C23×D314yes—
700C2×C3×C4C23×D314yes—
701C2×C3×C4C23×D311yescharacteristic
702C2×C3×C4C23×D311yescharacteristic
703C2×C3×C4C23×D311yescharacteristic
704C2×C3×C4C23×D311yescharacteristic
705#67—38no—
706#67—64no—
707#67—64no—
708#67—64no—
709#67—64no—
710#67—64no—
711#67—64no—
712#67—68no—
713#67—68no—
714C2×Dic3—31no—
715C2×Dic3—31no—
716C2×Dic3—31no—
717C2×Dic3—31no—
718C2×Dic3—38no—
719C2×Dic3—31no—
720C2×Dic3—31no—
721C2×Dic3—34no—
722C2×Dic3—34no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—64no—
727C2×Dic3—64no—
728C2×Dic3—68no—
729C2×Dic3—68no—
730C2×Dic3C23×D312yes—
731C2×Dic3C23×D312yes—
732C2×Dic3C23×D312yes—
733C2×Dic3C23×D312yes—
734C2×Dic3C23×D312yes—
735D12—28no—
736D12—22no—
737D12—22no—
738D12—38no—
739D12—64no—
740D12—64no—
741D12D3×D414yes—
742C4×D3—28no—
743C4×D3—24no—
744C4×D3—24no—
745C4×D3—24no—
746C4×D3—28no—
747C4×D3—38no—
748C4×D3—34no—
749C4×D3—34no—
750C4×D3—64no—
751C4×D3—62no—
752C4×D3—62no—
753C4×D3—64no—
754C4×D3—68no—
755C4×D3—68no—
756C4×D3—64no—
757C4×D3—64no—
758C4×D3—68no—
759C4×D3—68no—
760C4×D3—62no—
761C4×D3—62no—
762C4×D3—128no—
763Dic6—28no—
764Dic6—64no—
765Dic6—64no—
766Dic6—68no—
767Dic6—68no—
768Dic6—68no—
769Dic6—64no—
770Dic6—64no—
771Dic6—68no—
772Dic6—128no—
773Dic6—124no—
774Dic6D3×D414yes—
775C2×C32C23×D411yescharacteristic
776C2×C32C2×2−1+411yescharacteristic
777C2×C32C2×2−1+411yescharacteristic
778C3⋊D3—22no—
779C3×D3—24no—
780C3×D3—42no—
781C3×D3—42no—
782#41—68no—
783#41—98no—
784#41—188no—
785#41—1816no—
786#41—1816no—
787#41—188no—
788#41—1816no—
789C2×Q8—31no—
790C2×Q8—34no—
791C2×Q8—68no—
792C2×Q8—94no—
793C2×Q8—92no—
794C2×Q8—92no—
795C2×Q8—94no—
796C2×Q8—1816no—
797C2×Q8—188no—
798C2×Q8—188no—
799C2×Q8C2×D3212yes—
800C2×D4—31no—
801C2×D4—31no—
802C2×D4—31no—
803C2×D4—34no—
804C2×D4—92no—
805C2×D4—92no—
806C2×D4—92no—
807C2×D4—92no—
808C2×D4—94no—
809C2×D4—92no—
810C22×C4—32no—
811C22×C4—34no—
812C22×C4—34no—
813C22×C4—32no—
814C22×C4—32no—
815C22×C4—92no—
816C22×C4—92no—
817C22×C4—94no—
818C22×C4—94no—
819C22×C4—91no—
820C22×C4—91no—
821C22×C4—91no—
822C22×C4—94no—
823C4⋊C4—31no—
824C4⋊C4—34no—
825C4⋊C4—31no—
826C4⋊C4—34no—
827C4⋊C4—31no—
828C4⋊C4—32no—
829C4⋊C4—31no—
830C4⋊C4—92no—
831C4⋊C4—94no—
832C4⋊C4—94no—
833C4⋊C4—92no—
834C4⋊C4—94no—
835C4⋊C4—92no—
836C4⋊C4—94no—
837C4⋊C4—92no—
838C4⋊C4C2×D3212yes—
839C4⋊C4C2×D3212yes—
840C22⋊C4—32no—
841C22⋊C4—34no—
842C22⋊C4—32no—
843C22⋊C4—32no—
844C22⋊C4—34no—
845C22⋊C4—92no—
846C22⋊C4—92no—
847C22⋊C4—94no—
848C22⋊C4—94no—
849C22⋊C4—92no—
850C22⋊C4—92no—
851C42—32no—
852C42—92no—
853C42—92no—
854C42—91no—
855C42—91no—
856C42—91no—
857C42C2×D3211yescharacteristic
858C22×C3—21no—
859C22×C3—34no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—62no—
866C22×C3—62no—
867C22×C3—62no—
868C22×C3C24×D311yescharacteristic
869C22×C3C24×D311yescharacteristic
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—32no—
879C2×D3—32no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—61no—
884C2×D3—61no—
885C2×D3—61no—
886C2×D3—61no—
887C2×D3C2×D3×D414yes—
888C3×C4—22no—
889C3×C4—24no—
890C3×C4—24no—
891C3×C4—21no—
892C3×C4—21no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—34no—
896C3×C4—44no—
897C3×C4—62no—
898C3×C4—62no—
899C3×C4—62no—
900C3×C4—62no—
901C3×C4C2×D3×D412yes—
902C3×C4C2×D3×D412yes—
903C3×C4#100712yescomplemented
904C3×C4#101012yescomplemented
905Dic3—22no—
906Dic3—22no—
907Dic3—22no—
908Dic3—22no—
909Dic3—32no—
910Dic3—32no—
911Dic3—32no—
912Dic3—32no—
913Dic3—62no—
914Dic3—62no—
915Dic3—62no—
916Dic3—64no—
917Dic3—64no—
918Dic3—61no—
919Dic3—61no—
920Dic3—124no—
921Dic3C2×D3×D414yes—
922C32#349911yescharacteristic, complemented, Sylow
923C23—32no—
924C23—32no—
925C23—32no—
926C23—91no—
927Q8—24no—
928Q8—34no—
929Q8—68no—
930Q8—188no—
931Q8—188no—
932Q8—184no—
933Q8—184no—
934D4—34no—
935D4—68no—
936D4—62no—
937D4—62no—
938D4—98no—
939D4—184no—
940D4—184no—
941D4—184no—
942D4—184no—
943D4—188no—
944C2×C4—32no—
945C2×C4—32no—
946C2×C4—32no—
947C2×C4—32no—
948C2×C4—32no—
949C2×C4—68no—
950C2×C4—68no—
951C2×C4—64no—
952C2×C4—64no—
953C2×C4—64no—
954C2×C4—98no—
955C2×C4—91no—
956C2×C4—91no—
957C2×C4—94no—
958C2×C4—91no—
959C2×C4—94no—
960C2×C4—182no—
961C2×C4—188no—
962C2×C4—188no—
963C2×C4—184no—
964C2×C4—188no—
965C2×C4—182no—
966C2×C4C22×D3211yescharacteristic
967C2×C4C22×D3214yes—
968C2×C4C22×D3211yescharacteristic
969C2×C4C22×D3211yescharacteristic
970C2×C3—21no—
971C2×C3—21no—
972C2×C3—21no—
973C2×C3—64no—
974C2×C3—122no—
975C2×C3—122no—
976C2×C3C22×D3×D411yescharacteristic
977C2×C3C22×D3×D411yescharacteristic
978C2×C3C2×#100711yescharacteristic
979C2×C3C2×#101011yescharacteristic
980C2×C3D3×2−1+411yescharacteristic
981C2×C3D3×2−1+411yescharacteristic
982D3—24no—
983D3—42no—
984D3—42no—
985D3—64no—
986D3—62no—
987D3—62no—
988C22—34no—
989C22—62no—
990C22—62no—
991C22—62no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—62no—
997C22—92no—
998C22—181no—
999C22—181no—
1000C22C23×D3211yescharacteristic
1001C4—24no—
1002C4—21no—
1003C4—34no—
1004C4—62no—
1005C4—62no—
1006C4—62no—
1007C4—62no—
1008C4—92no—
1009C4—92no—
1010C4—184no—
1011C4—181no—
1012C4D32×D412yes—
1013C4#6431512yescomplemented
1014C3—21no—
1015C3#8667911yescharacteristic, complemented
1016C3#8674611yescharacteristic, complemented
1017C2—64no—
1018C2—122no—
1019C2—122no—
1020C2—182no—
1021C2C2×D32×D411yescharacteristic
1022C2C2×#6431511yescharacteristic
1023C2#1059668711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32#3499
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64315C2semidirect
2. C3⋊D3×C4⋊Q8C2semidirect
3. C3×#5727C2semidirect
4. C3×#5726C2semidirect
5. #10595405C2semidirect
6. #10595400C2semidirect
7. #10595357C2semidirect
8. #10594515C2semidirect
9. #10594373C2semidirect
10. #10594371C2semidirect
11. #10594367C2semidirect
12. #10594365C2semidirect
13. D3×#888C2semidirect
14. #10593972C2semidirect
15. Dic6×D12C2semidirect
16. #10593895C2semidirect
17. C4×#3796C2semidirect
92. #5727D3semidirect
94. #5726D3semidirect
157. #3796D4semidirect
589. C32×C42−1+4semidirect
593. C3⋊Dic32−1+4semidirect
903. C3×C4#1007semidirect
904. C3×C4#1010semidirect
922. C32#3499semidirect
1013. C4#64315semidirect
1015. C3#86679semidirect
1016. C3#86746semidirect

Maximal subgroups

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

subgroupindex
C2×#643152
C3⋊D3×C4⋊Q82
C3×#57272
C3×#57262
#105954052
#105954002
#105953572
#105945152
#105943732
#105943712
#105943672
#105943652
D3×#8882
#105939722
Dic6×D122
#105938952
C4×#37962
#867463
#866793