Finite Group Databasebeta

← #11906024

Subgroups — #11906024

Order 1152.

3098 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64297C212yesmaximal, complemented
2#10596022C211yesmaximal, characteristic, complemented
3C3×#5548C211yesmaximal, characteristic, complemented
4C3×D4×Dic6C211yesmaximal, characteristic, complemented
5#10595139C212yesmaximal, complemented
6#10595136C212yesmaximal, complemented
7Dic6×#67C212yesmaximal, complemented
8#10594884C212yesmaximal, complemented
9#10594834C212yesmaximal, complemented
10#10594374C212yesmaximal, complemented
11#10594373C212yesmaximal, complemented
12#10594070C214yesmaximal, complemented
13#10594065C214yesmaximal, complemented
14C4×#3799C211yesmaximal, characteristic, complemented
15Dic6×D12C211yesmaximal, characteristic, complemented
16D3×#869C211yesmaximal, characteristic, complemented
17#10593869C211yesmaximal, characteristic, complemented
18#86746—31nomaximal
19#86243—31nomaximal
20C2×#3828C2212yes—
21C2×C3×#235C2212yes—
22C22×C3×Dic6C2212yes—
23C2×#3804C2214yes—
24C2×#3804C2214yes—
25C2×#3799C2212yes—
26C2×#3799C2211yescharacteristic
27C2×#3797C2214yes—
28#64297—216no—
29C2×#3796C2214yes—
30C2×D3×Dic6C2212yes—
31C2×D3×Dic6C2212yes—
32C32×C4×D4C2211yescharacteristic
33#64147C2212yes—
34#64133C2212yes—
35C4⋊C4×C3⋊D3C2212yes—
36#64092C2214yes—
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38#64078C2211yescharacteristic
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#63975C2214yes—
55Dic3×#67C2214yes—
56#63969C2214yes—
57#63964C2214yes—
58#63959C2214yes—
59#63958C2214yes—
60#63918C2212yes—
61#63918C2212yes—
62#63918C2212yes—
63#63916C2212yes—
64#63904C2212yes—
65C4×#626C2212yes—
66#63900C2212yes—
67#63894C2211yescharacteristic
68#63893C2214yes—
69Dic3×D12C2212yes—
70D3×C4⋊Dic3C2212yes—
71D3×C4⋊Dic3C2212yes—
72#63887C2214yes—
73#63884C2214yes—
74#63883C2214yes—
75C4×#624C2212yes—
76#63866C2212yes—
77#63857C2212yes—
78#63856C2212yes—
79#63854C2214yes—
80#63853C2214yes—
81Dic3×Dic6C2211yescharacteristic
82#63841C2211yescharacteristic
83#63839C2214yes—
84#63839C2214yes—
85#63836C2212yes—
86C2×#1010—32no—
87C2×#1007—32no—
88C3×D4×Q8—31no—
89C3×#532—31no—
90#5825—32no—
91Q8×#67—32no—
92#5726—32no—
93#5726—31no—
94D3×C4⋊Q8—32no—
95D3×C4⋊Q8—32no—
96D3×C4⋊Q8—31no—
97#5716—32no—
98#5675—34no—
99#5631—32no—
100#5631—34no—
101#5628—32no—
102#5628—34no—
103#5611—32no—
104#5611—32no—
105#5611—34no—
106Q8×D12—31no—
107C4×#239—31no—
108#5551—31no—
109#5551—31no—
110#5551—32no—
111#5551—32no—
112#5551—31no—
113#5551—61no—
114#5548—32no—
115#5548D311yescharacteristic, complemented
116D4×Dic6—32no—
117D4×Dic6—31no—
118D4×Dic6D311yescharacteristic, complemented
119C4×#235—31no—
120C2×#869—31no—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C2×#638C2314yes—
124#3828—28no—
125C2×C4⋊(C3⋊D3)C2311yescharacteristic
126C2×C4×C3⋊D3C2314yes—
127C2×C4×C3⋊D3C2312yes—
128C2×#634C2312yes—
129C2×C3×#67C2312yes—
130C2×C3×#67C2312yes—
131C2×C3×#67C2312yes—
132C22×C3×Dic3C2314yes—
133C3×#235—28no—
134C2×C3×D12C2312yes—
135C2×C3×D12C2311yescharacteristic
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×Dic6—28no—
141C2×C3×Dic6C2314yes—
142C2×C3×Dic6C2312yes—
143C2×C3×Dic6C2312yes—
144C2×C3×Dic6C2311yescharacteristic
145C2×#627C2314yes—
146C2×#627C2314yes—
147C2×#626C2314yes—
148C2×#626C2312yes—
149C2×#624C2314yes—
150C2×#624C2312yes—
151C2×#624C2312yes—
152#3804—216no—
153#3804—216no—
154C2×D3×Dic3C2314yes—
155C2×D3×Dic3C2314yes—
156#3799—28no—
157#3799D418yescomplemented
158#3797—216no—
159#3796—216no—
160D3×Dic6—28no—
161D3×Dic6—28no—
162C32×C4⋊C4C2311yescharacteristic
163C32×C22⋊C4C2312yes—
164C32×C42C2311yescharacteristic
165#3757C2314yes—
166#3752C2312yes—
167C4⋊(C3⋊Dic3)C2312yes—
168C4⋊(C3⋊Dic3)C2312yes—
169C4⋊(C3⋊Dic3)C2311yescharacteristic
170#3750C2314yes—
171C3×#217C2314yes—
172C3×#217C2312yes—
173C3×(C2×D3)⋊C4C2312yes—
174C3×(C2×D3)⋊C4C2312yes—
175C3×C4⋊Dic3C2312yes—
176C3×C4⋊Dic3C2312yes—
177C3×C4⋊Dic3C2311yescharacteristic
178C3×C4⋊Dic3C2311yescharacteristic
179C3×Dic3⋊C4C2312yes—
180C3×Dic3⋊C4C2314yes—
181C3×Dic3⋊C4C2312yes—
182C3×C4×Dic3C2311yescharacteristic
183C3×C4×Dic3C2312yes—
184C3×C4×Dic3C2311yescharacteristic
185C3×C4×Dic3C2311yescharacteristic
186#3724C2314yes—
187Dic3⋊Dic3C2312yes—
188Dic3⋊Dic3C2314yes—
189Dic3⋊Dic3C2314yes—
190Dic3⋊Dic3C2314yes—
191#3722C2312yes—
192(C2×D3)⋊Dic3C2312yes—
193(C2×D3)⋊Dic3C2314yes—
194(C2×D3)⋊Dic3C2314yes—
195Dic32C2312yes—
196Dic32C2312yes—
197#3499—91noSylow
198C2×C3×#41—32no—
199C22×C3×Q8—32no—
200#1010—616no—
201#1007—616no—
202C2×#239—34no—
203C2×#239—31no—
204C2×#239—32no—
205C2×D3×Q8—32no—
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—31no—
217C2×#235—32no—
218C2×#235—62no—
219C2×#235C2×D312yes—
220C22×Dic6—32no—
221C22×Dic6—32no—
222C22×Dic6C2×D312yes—
223C3×C4⋊Q8—31no—
224C3×C4⋊Q8—32no—
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#946—32no—
242#946—34no—
243Q8×Dic3—31no—
244#944—34no—
245#944—34no—
246#944—32no—
247#940C2×D311yescharacteristic
248#938—32no—
249#938—32no—
250#938—34no—
251#938—32no—
252#938—62no—
253#938C2×D311yescharacteristic
254#936—34no—
255#935—34no—
256#935—34no—
257D4×Dic3—34no—
258D4×Dic3—32no—
259D4×Dic3C2×D312yes—
260C4×#67—34no—
261C4×#67—32no—
262C4×#67—32no—
263C4×#67C2×D312yes—
264#926—31no—
265C2×C4⋊Dic3—32no—
266C2×C4⋊Dic3—32no—
267#924—32no—
268#924—32no—
269#924—32no—
270#924—34no—
271#924—32no—
272#924—62no—
273#924C2×D312yes—
274#897—32no—
275#897—34no—
276#895—32no—
277#895C2×D311yescharacteristic
278#894—34no—
279#894—34no—
280#894—34no—
281#893—32no—
282#893—31no—
283#892—31no—
284#892—32no—
285D3×C4⋊C4—32no—
286D3×C4⋊C4—32no—
287D3×C4⋊C4—32no—
288D3×C4⋊C4—32no—
289D3×C4⋊C4—32no—
290D3×C4⋊C4—32no—
291D3×C4⋊C4—34no—
292D3×C4⋊C4—34no—
293D3×C4⋊C4—62no—
294#888—34no—
295#888—34no—
296#888—32no—
297#888—32no—
298#888—32no—
299#888C2×D311yescharacteristic
300#888C2×D312yes—
301#885—34no—
302#885C2×D312yes—
303#884—34no—
304#884C2×D312yes—
305#883—34no—
306#883—34no—
307#883—34no—
308#883—34no—
309#883—34no—
310#883—34no—
311#883—34no—
312#883—64no—
313#878—34no—
314#878—34no—
315#878—34no—
316#878C2×D314yes—
317C4×D12—32no—
318C4×D12—32no—
319C4×D12—31no—
320C4×D12—31no—
321C4×D12—31no—
322C4×D12—61no—
323C4×D12C2×D311yescharacteristic
324#872—32no—
325C42×D3—32no—
326C42×D3—32no—
327C42×D3C2×D311yescharacteristic
328#869—32no—
329#869—31no—
330#869—31no—
331#869—32no—
332#869—32no—
333#869—32no—
334#869—61no—
335#869C2×D311yescharacteristic
336C4×Dic6—31no—
337C4×Dic6C2×D311yescharacteristic
338C23×C32C2412yes—
339C22×C3⋊D3C2412yes—
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—
349C2×C3⋊Dic3C2412yes—
350C2×C3⋊Dic3C2414yes—
351C4⋊(C3⋊D3)C2×D414yes—
352C4×C3⋊D3—28no—
353C4×C3⋊D3—24no—
354#634—24no—
355C3×#67—24no—
356C3×#67—24no—
357C3×#67—24no—
358C2×C3×Dic3—28no—
359C2×C3×Dic3C2412yes—
360C2×C3×Dic3C2414yes—
361C2×C3×Dic3C2411yescharacteristic
362C2×C3×Dic3C2412yes—
363C2×C3×Dic3C2411yescharacteristic
364C2×C3×Dic3C2412yes—
365C2×C3×Dic3C2411yescharacteristic
366C3×D12—24no—
367C3×D12—22no—
368C3×C4×D3—24no—
369C3×C4×D3—22no—
370C3×C4×D3—22no—
371C3×C4×D3C2×D414yes—
372C3×Dic6—24no—
373C3×Dic6—28no—
374C3×Dic6—24no—
375C3×Dic6C2×D414yes—
376#627—28no—
377#627—28no—
378#626—28no—
379#626C2×D418yes—
380#624—28no—
381#624—24no—
382#624C2×D418yes—
383D3×Dic3—28no—
384D3×Dic3—28no—
385C2×2−1+4—92no—
386D4×Q8—31no—
387D4×Q8—91no—
388D4×Q8—92no—
389#547—92no—
390#547—92no—
391#547—91no—
392#547—94no—
393#547—92no—
394#547—91no—
395#536—94no—
396#536—92no—
397#532—31no—
398#532—92no—
399C2×C4⋊Q8—91no—
400C2×C4⋊Q8—92no—
401C4×#41—91no—
402C3×#41—68no—
403C2×C3×Q8—31no—
404C2×C3×Q8—32no—
405C2×C3×Q8—34no—
406C2×C3×Q8—32no—
407C2×C3×Q8—68no—
408C2×C3×D4—21no—
409C2×C3×D4—32no—
410C2×C3×D4—32no—
411C2×C3×D4—32no—
412C2×C3×D4—31no—
413C2×C3×D4—32no—
414C2×C3×D4C22×D311yescharacteristic
415C2×C3×D4C22×D311yescharacteristic
416C22×C3×C4—22no—
417C22×C3×C4—31no—
418C22×C3×C4—34no—
419C22×C3×C4—32no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4C22×D312yes—
423C22×C3×C4C22×D312yes—
424C2×#67—34no—
425C2×#67—34no—
426C2×#67—32no—
427C2×#67—34no—
428C2×#67—64no—
429C2×#67C22×D312yes—
430C2×#67C22×D312yes—
431C2×#67C22×D312yes—
432C22×Dic3—34no—
433C22×Dic3—34no—
434C22×Dic3C22×D314yes—
435#239—38no—
436#239—68no—
437#239—616no—
438D3×Q8—616no—
439D3×Q8—616no—
440D3×Q8—68no—
441D3×Q8—68no—
442#237—616no—
443#237—616no—
444#237—616no—
445#235—28no—
446#235—38no—
447#235—68no—
448#235—616no—
449#235—616no—
450#235—68no—
451#235—68no—
452#235—128no—
453C2×D12—32no—
454C2×D12—31no—
455C2×D12—31no—
456C2×D12—34no—
457C2×D12—61no—
458C2×D12C22×D311yescharacteristic
459C2×D12C22×D312yes—
460C2×C4×D3—32no—
461C2×C4×D3—32no—
462C2×C4×D3—34no—
463C2×C4×D3—34no—
464C2×C4×D3—32no—
465C2×C4×D3—32no—
466C2×C4×D3—34no—
467C2×C4×D3—34no—
468C2×C4×D3—32no—
469C2×C4×D3—32no—
470C2×C4×D3—34no—
471C2×C4×D3—34no—
472C2×C4×D3—62no—
473C2×C4×D3—64no—
474C2×C4×D3C22×D311yescharacteristic
475C2×C4×D3C22×D311yescharacteristic
476C2×C4×D3C22×D312yes—
477C2×C4×D3C22×D311yescharacteristic
478C2×Dic6—28no—
479C2×Dic6—32no—
480C2×Dic6—32no—
481C2×Dic6—34no—
482C2×Dic6—34no—
483C2×Dic6—34no—
484C2×Dic6—34no—
485C2×Dic6—62no—
486C2×Dic6—68no—
487C2×Dic6—68no—
488C2×Dic6C22×D312yes—
489C2×Dic6C22×D314yes—
490C2×Dic6C22×D312yes—
491C2×Dic6C22×D311yescharacteristic
492C3×C4⋊C4—21no—
493C3×C4⋊C4—32no—
494C3×C4⋊C4—31no—
495C3×C4⋊C4—32no—
496C3×C4⋊C4—34no—
497C3×C4⋊C4—32no—
498C3×C4⋊C4—32no—
499C3×C4⋊C4—31no—
500C3×C4⋊C4C22×D311yescharacteristic
501C3×C4⋊C4C22×D311yescharacteristic
502C3×C22⋊C4—22no—
503C3×C22⋊C4—32no—
504C3×C22⋊C4—34no—
505C3×C22⋊C4—32no—
506C3×C22⋊C4—32no—
507C3×C22⋊C4C22×D312yes—
508C3×C22⋊C4C22×D312yes—
509C3×C42—21no—
510C3×C42—31no—
511C3×C42—31no—
512C3×C42—31no—
513C3×C42—32no—
514C3×C42C22×D311yescharacteristic
515C3×C42C22×D311yescharacteristic
516#217—34no—
517#217—34no—
518#217—34no—
519#217—34no—
520#217—32no—
521#217—64no—
522#217C22×D314yes—
523#217C22×D312yes—
524(C2×D3)⋊C4—32no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—32no—
528(C2×D3)⋊C4—32no—
529(C2×D3)⋊C4—32no—
530(C2×D3)⋊C4—32no—
531(C2×D3)⋊C4—62no—
532(C2×D3)⋊C4C22×D312yes—
533(C2×D3)⋊C4C22×D312yes—
534C4⋊Dic3—31no—
535C4⋊Dic3—32no—
536C4⋊Dic3—32no—
537C4⋊Dic3—32no—
538C4⋊Dic3—32no—
539C4⋊Dic3—31no—
540C4⋊Dic3—34no—
541C4⋊Dic3—34no—
542C4⋊Dic3—34no—
543C4⋊Dic3—32no—
544C4⋊Dic3—62no—
545C4⋊Dic3—62no—
546C4⋊Dic3—61no—
547C4⋊Dic3C22×D311yescharacteristic
548C4⋊Dic3C22×D311yescharacteristic
549C4⋊Dic3C22×D312yes—
550C4⋊Dic3C22×D312yes—
551Dic3⋊C4—34no—
552Dic3⋊C4—34no—
553Dic3⋊C4—32no—
554Dic3⋊C4—34no—
555Dic3⋊C4—34no—
556Dic3⋊C4—34no—
557Dic3⋊C4—34no—
558Dic3⋊C4—34no—
559Dic3⋊C4—64no—
560Dic3⋊C4C22×D312yes—
561Dic3⋊C4C22×D314yes—
562Dic3⋊C4C22×D312yes—
563C4×Dic3—32no—
564C4×Dic3—32no—
565C4×Dic3—32no—
566C4×Dic3—32no—
567C4×Dic3C22×D312yes—
568C4×Dic3C22×D311yescharacteristic
569C4×Dic3C22×D311yescharacteristic
570C4×Dic3C22×D311yescharacteristic
571C22×C32—22no—
572C22×C32—22no—
573C22×C32—22no—
574C22×C32C2511yescharacteristic
575C2×C3⋊D3—22no—
576C2×C3⋊D3—22no—
577C2×C3⋊D3C22×D414yes—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—22no—
581C2×C3×D3—22no—
582C2×C3×D3—22no—
583C2×C3×D3C22×D412yes—
584C32×C4—22no—
585C32×C4—21no—
586C32×C4C22×D412yes—
587C32×C42−1+412yescomplemented
588C3⋊Dic3—24no—
589C3⋊Dic3—22no—
590C3×Dic3—24no—
591C3×Dic3—22no—
592C3×Dic3—22no—
593C3×Dic3—21no—
594C3×Dic3C22×D414yes—
595C3×Dic3C22×D412yes—
596C3×Dic32−1+412yescomplemented
5972−1+4—1816no—
598C2×#41—32no—
599C2×#41—94no—
600C2×#41—94no—
601C2×#41—91no—
602C2×#41—92no—
603C2×#41—94no—
604C2×#41—92no—
605C22×Q8—32no—
606C22×Q8—92no—
607C22×Q8—92no—
608C22×Q8—94no—
609C4⋊Q8—31no—
610C4⋊Q8—32no—
611C4⋊Q8—31no—
612C4⋊Q8—92no—
613C4⋊Q8—92no—
614C4⋊Q8—92no—
615C4⋊Q8—92no—
616C4⋊Q8—94no—
617C4⋊Q8—94no—
618C4⋊Q8—91no—
619#127—31no—
620#124—32no—
621#124—94no—
622#123—94no—
623#123—94no—
624#123—94no—
625#123—94no—
626#123—94no—
627#123—94no—
628C22⋊Q8—32no—
629C22⋊Q8—34no—
630C22⋊Q8—94no—
631C22⋊Q8—94no—
632C22⋊Q8—94no—
633C22⋊Q8—92no—
634C22⋊Q8—92no—
635C22⋊Q8—92no—
636#121—31no—
637#121—31no—
638#121—32no—
639#121—94no—
640#121—92no—
641#121—92no—
642C4×Q8—31no—
643C4×Q8—91no—
644C4×D4—32no—
645C4×D4—32no—
646C4×D4—31no—
647C4×D4—91no—
648C4×D4—92no—
649C4×D4—92no—
650C4×D4—92no—
651C4×D4—94no—
652C4×D4—91no—
653C4×D4D3211yescharacteristic
654#117—92no—
655#117—91no—
656C2×C4⋊C4—94no—
657C2×C4⋊C4—92no—
658C2×C4⋊C4—92no—
659C2×C4⋊C4—92no—
660C2×C4⋊C4—92no—
661C2×C42—31no—
662C2×C42—92no—
663C23×C3—22no—
664C23×C3—31no—
665C23×C3—32no—
666C23×C3C23×D312yes—
667C23×C3C23×D312yes—
668C22×D3—32no—
669C22×D3—32no—
670C22×D3—62no—
671C22×D3C23×D312yes—
672C22×D3C23×D311yescharacteristic
673C3×Q8—34no—
674C3×Q8—64no—
675C3×Q8—68no—
676C3×Q8—64no—
677C3×D4—22no—
678C3×D4—22no—
679C3×D4—42no—
680C3×D4—64no—
681C3×D4—64no—
682C3×D4—64no—
683C3×D4—64no—
684C3×D4—62no—
685C2×C3×C4—24no—
686C2×C3×C4—24no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—22no—
690C2×C3×C4—21no—
691C2×C3×C4—31no—
692C2×C3×C4—31no—
693C2×C3×C4—32no—
694C2×C3×C4—34no—
695C2×C3×C4—32no—
696C2×C3×C4—32no—
697C2×C3×C4—34no—
698C2×C3×C4—31no—
699C2×C3×C4—44no—
700C2×C3×C4—62no—
701C2×C3×C4—68no—
702C2×C3×C4—64no—
703C2×C3×C4—62no—
704C2×C3×C4C23×D311yescharacteristic
705C2×C3×C4C23×D312yes—
706C2×C3×C4C23×D312yes—
707C2×C3×C4C23×D311yescharacteristic
708C2×C3×C4C23×D311yescharacteristic
709C2×C3×C4C23×D311yescharacteristic
710C2×C3×C4C23×D311yescharacteristic
711C2×C3×C4C23×D311yescharacteristic
712#67—24no—
713#67—24no—
714#67—24no—
715#67—38no—
716#67—68no—
717#67—68no—
718#67—68no—
719#67—128no—
720C2×Dic3—28no—
721C2×Dic3—32no—
722C2×Dic3—32no—
723C2×Dic3—34no—
724C2×Dic3—34no—
725C2×Dic3—62no—
726C2×Dic3—64no—
727C2×Dic3—68no—
728C2×Dic3—68no—
729C2×Dic3C23×D312yes—
730C2×Dic3C23×D311yescharacteristic
731C2×Dic3C23×D312yes—
732C2×Dic3C23×D314yes—
733C2×Dic3C23×D311yescharacteristic
734C2×Dic3C23×D312yes—
735C2×Dic3C23×D311yescharacteristic
736D12—24no—
737D12—22no—
738D12—38no—
739D12—34no—
740D12—34no—
741D12—64no—
742D12—68no—
743C4×D3—24no—
744C4×D3—22no—
745C4×D3—22no—
746C4×D3—38no—
747C4×D3—38no—
748C4×D3—64no—
749C4×D3—68no—
750C4×D3—68no—
751C4×D3—68no—
752C4×D3—68no—
753C4×D3—68no—
754C4×D3—68no—
755C4×D3—64no—
756C4×D3—64no—
757C4×D3—64no—
758C4×D3—124no—
759C4×D3—128no—
760C4×D3D3×D414yes—
761Dic6—24no—
762Dic6—28no—
763Dic6—24no—
764Dic6—68no—
765Dic6—68no—
766Dic6—64no—
767Dic6—64no—
768Dic6—68no—
769Dic6—68no—
770Dic6—124no—
771Dic6D3×D414yes—
772C2×C32—42no—
773C2×C32C23×D411yescharacteristic
774C2×C32C2×2−1+411yescharacteristic
775C2×C32C2×2−1+411yescharacteristic
776C3⋊D3—24no—
777C3×D3—22no—
778C3×D3—42no—
779#41—68no—
780#41—98no—
781#41—188no—
782#41—1816no—
783#41—1816no—
784#41—188no—
785#41—1816no—
786C2×Q8—31no—
787C2×Q8—34no—
788C2×Q8—32no—
789C2×Q8—32no—
790C2×Q8—68no—
791C2×Q8—94no—
792C2×Q8—94no—
793C2×Q8—92no—
794C2×Q8—188no—
795C2×Q8—188no—
796C2×Q8—1816no—
797C2×D4—32no—
798C2×D4—32no—
799C2×D4—32no—
800C2×D4—31no—
801C2×D4—32no—
802C2×D4—92no—
803C2×D4—94no—
804C2×D4—94no—
805C2×D4—91no—
806C2×D4C2×D3211yescharacteristic
807C22×C4—31no—
808C22×C4—34no—
809C22×C4—31no—
810C22×C4—31no—
811C22×C4—32no—
812C22×C4—92no—
813C22×C4—92no—
814C22×C4—94no—
815C22×C4—94no—
816C22×C4—94no—
817C22×C4—92no—
818C22×C4—94no—
819C22×C4C2×D3212yes—
820C4⋊C4—32no—
821C4⋊C4—31no—
822C4⋊C4—32no—
823C4⋊C4—34no—
824C4⋊C4—32no—
825C4⋊C4—32no—
826C4⋊C4—31no—
827C4⋊C4—94no—
828C4⋊C4—94no—
829C4⋊C4—94no—
830C4⋊C4—94no—
831C4⋊C4—92no—
832C4⋊C4—92no—
833C4⋊C4—94no—
834C4⋊C4—92no—
835C4⋊C4—91no—
836C4⋊C4C2×D3211yescharacteristic
837C22⋊C4—32no—
838C22⋊C4—34no—
839C22⋊C4—32no—
840C22⋊C4—32no—
841C22⋊C4—92no—
842C22⋊C4—92no—
843C22⋊C4—94no—
844C22⋊C4—94no—
845C22⋊C4—94no—
846C22⋊C4—92no—
847C22⋊C4C2×D3212yes—
848C42—31no—
849C42—31no—
850C42—31no—
851C42—32no—
852C42—92no—
853C42—92no—
854C42C2×D3211yescharacteristic
855C22×C3—22no—
856C22×C3—22no—
857C22×C3—22no—
858C22×C3—22no—
859C22×C3—22no—
860C22×C3—22no—
861C22×C3—21no—
862C22×C3—32no—
863C22×C3—42no—
864C22×C3—42no—
865C22×C3—42no—
866C22×C3—61no—
867C22×C3—61no—
868C22×C3—62no—
869C22×C3—62no—
870C22×C3—62no—
871C22×C3C24×D311yescharacteristic
872C22×C3C24×D311yescharacteristic
873C2×D3—21no—
874C2×D3—21no—
875C2×D3—22no—
876C2×D3—22no—
877C2×D3—22no—
878C2×D3—34no—
879C2×D3—34no—
880C2×D3—64no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3C2×D3×D412yes—
888C3×C4—22no—
889C3×C4—22no—
890C3×C4—21no—
891C3×C4—21no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—32no—
895C3×C4—34no—
896C3×C4—32no—
897C3×C4—42no—
898C3×C4—41no—
899C3×C4—62no—
900C3×C4—64no—
901C3×C4—61no—
902C3×C4—62no—
903C3×C4C2×D3×D412yes—
904C3×C4C2×D3×D412yes—
905C3×C4#100712yescomplemented
906C3×C4#101012yescomplemented
907Dic3—24no—
908Dic3—22no—
909Dic3—21no—
910Dic3—22no—
911Dic3—64no—
912Dic3—64no—
913Dic3—62no—
914Dic3—62no—
915Dic3—124no—
916Dic3—122no—
917Dic3C2×D3×D412yes—
918Dic3C2×D3×D414yes—
919Dic3#101012yescomplemented
920C32#349911yescharacteristic, complemented, Sylow
921C23—31no—
922C23—32no—
923C23—92no—
924C23C22×D3212yes—
925Q8—34no—
926Q8—68no—
927Q8—64no—
928Q8—64no—
929Q8—188no—
930Q8—188no—
931Q8—184no—
932D4—22no—
933D4—64no—
934D4—64no—
935D4—64no—
936D4—64no—
937D4—62no—
938D4—98no—
939D4—94no—
940D4—188no—
941D4—188no—
942C2×C4—24no—
943C2×C4—31no—
944C2×C4—31no—
945C2×C4—32no—
946C2×C4—34no—
947C2×C4—31no—
948C2×C4—32no—
949C2×C4—32no—
950C2×C4—34no—
951C2×C4—62no—
952C2×C4—68no—
953C2×C4—62no—
954C2×C4—64no—
955C2×C4—98no—
956C2×C4—92no—
957C2×C4—94no—
958C2×C4—188no—
959C2×C4—184no—
960C2×C4—188no—
961C2×C4—188no—
962C2×C4—188no—
963C2×C4—184no—
964C2×C4C22×D3211yescharacteristic
965C2×C4C22×D3212yes—
966C2×C4C22×D3211yescharacteristic
967C2×C4C22×D3211yescharacteristic
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—42no—
972C2×C3—42no—
973C2×C3—62no—
974C2×C3—82no—
975C2×C3—122no—
976C2×C3C22×D3×D411yescharacteristic
977C2×C3C22×D3×D411yescharacteristic
978C2×C3C2×#100711yescharacteristic
979C2×C3C2×#101011yescharacteristic
980C2×C3C2×#101011yescharacteristic
981C2×C3D3×2−1+411yescharacteristic
982D3—22no—
983D3—42no—
984D3—64no—
985D3—64no—
986D3—124no—
987C22—22no—
988C22—22no—
989C22—22no—
990C22—32no—
991C22—61no—
992C22—61no—
993C22—62no—
994C22—62no—
995C22—62no—
996C22—94no—
997C22—182no—
998C22—182no—
999C22C23×D3211yescharacteristic
1000C4—22no—
1001C4—21no—
1002C4—32no—
1003C4—34no—
1004C4—32no—
1005C4—61no—
1006C4—62no—
1007C4—64no—
1008C4—62no—
1009C4—182no—
1010C4—184no—
1011C4#6429712yescomplemented
1012C4D32×D412yes—
1013C3—21no—
1014C3#8624311yescharacteristic, complemented
1015C3#8674611yescharacteristic, complemented
1016C2—42no—
1017C2—62no—
1018C2—122no—
1019C2—184no—
1020C2C2×#6429711yescharacteristic
1021C2C2×D32×D411yescharacteristic
1022C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3499
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. #10596022C2semidirect
3. C3×#5548C2semidirect
4. C3×D4×Dic6C2semidirect
5. #10595139C2semidirect
6. #10595136C2semidirect
7. Dic6×#67C2semidirect
8. #10594884C2semidirect
9. #10594834C2semidirect
10. #10594374C2semidirect
11. #10594373C2semidirect
12. #10594070C2semidirect
13. #10594065C2semidirect
14. C4×#3799C2semidirect
15. Dic6×D12C2semidirect
16. D3×#869C2semidirect
17. #10593869C2semidirect
115. #5548D3semidirect
118. D4×Dic6D3semidirect
157. #3799D4semidirect
587. C32×C42−1+4semidirect
596. C3×Dic32−1+4semidirect
905. C3×C4#1007semidirect
906. C3×C4#1010semidirect
919. Dic3#1010semidirect
920. C32#3499semidirect
1011. C4#64297semidirect
1014. C3#86243semidirect
1015. C3#86746semidirect

Maximal subgroups

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

subgroupindex
C2×#642972
#105960222
C3×#55482
C3×D4×Dic62
#105951392
#105951362
Dic6×#672
#105948842
#105948342
#105943742
#105943732
#105940702
#105940652
C4×#37992
Dic6×D122
D3×#8692
#105938692
#867463
#862433