Finite Group Databasebeta

← #11906131

Subgroups — #11906131

Order 1152.

3215 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3#10595997C211yesmaximal, characteristic, complemented
4C3×#5525C211yesmaximal, characteristic, complemented
5C3×#5522C211yesmaximal, characteristic, complemented
6#10595029C211yesmaximal, characteristic, complemented
7C2×#63860C211yesmaximal, characteristic, complemented
8#10594630C214yesmaximal, complemented
9#10594382C214yesmaximal, complemented
10#10594292C218yesmaximal, complemented
11#10594000C212yesmaximal, complemented
12D3×#875C212yesmaximal, complemented
13#10593897C212yesmaximal, complemented
14#10593894C212yesmaximal, complemented
15#86317—31nomaximal
16#85847—31nomaximal
17C2×#3828C2211yescharacteristic
18C22×#634C2211yescharacteristic, complemented
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic
22C2×D3×#67C2214yes—
23C2×#3805C2214yescomplemented
24#64307—28no—
25C2×#3802C2212yes—
26C2×D3×D12C2212yes—
27#64298—28no—
28C2×#3796C2212yes—
29C2×#3795C2212yes—
30C2×#3795C2212yescomplemented
31C2×#3795C2212yescomplemented
32C2×D3×Dic6C2212yescomplemented
33C2×D3×Dic6C2212yescomplemented
34C32×#117C2211yescharacteristic, complemented
35#64106C2214yescomplemented
36#64095C2214yescomplemented
37#64084C2212yescomplemented
38#64078C2212yescomplemented
39C2×C3×C4×Dic3C2211yescharacteristic, complemented
40C3×#895C2214yescomplemented
41C3×#893C2212yescomplemented
42C3×#887C2212yescomplemented
43C3×#882C2214yescomplemented
44C3×#67⋊C4C2214yescomplemented
45C3×#875C2212yescomplemented
46C3×#874C2212yescomplemented
47C3×#872C2212yescomplemented
48C3×C42×D3C2212yescomplemented
49#63978C2214yescomplemented
50C2×(C2×D3)⋊Dic3C2214yescomplemented
51#63922C2218yescomplemented
52D3×(C2×D3)⋊C4C2218yescomplemented
53#63911C2211yescharacteristic, complemented
54#63908C2218yescomplemented
55C4×#626C2214yescomplemented
56#63893C2218yescomplemented
57Dic3×D12C2218yescomplemented
58#63891C2218yescomplemented
59#63886C2218yescomplemented
60#63866C2211yescharacteristic, complemented
61#63864C2211yescharacteristic, complemented
62#63860C2214yescomplemented
63#63860C2212yescomplemented
64#63860C2212yescomplemented
65#63860C2211yescharacteristic, complemented
66#63852C2218yescomplemented
67C2×#1010—31no—
68C2×#1010—31no—
69C2×#1009—31no—
70C2×#1004—31no—
71C3×#535—31no—
72C3×C4×#41—31no—
73#5832—31no—
74C2×#936—31no—
75#5716—32no—
76#5715—32no—
77#5675—32no—
78D3×#124—32no—
79#5612—34no—
80#5598—34no—
81#5591—38no—
82#5576—34no—
83#5554—34no—
84#5554—38no—
85#5526—31no—
86#5526—31no—
87#5526—32no—
88#5526—61no—
89#5525—32no—
90#5525D311yescharacteristic, complemented
91#5522D311yescharacteristic, complemented
92#5477—31no—
93#5477—32no—
94C2×#875—31no—
95C2×#875—32no—
96C23×C3×D3C2312yes—
97C22×D32C2314yes—
98C22×C32×C4C2311yescharacteristic
99C2×#638C2312yes—
100C22×C3⋊Dic3C2312yes—
101#3828—24no—
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C4×C3⋊D3C2312yes—
104C2×#634—24no—
105C2×#634C2312yes—
106C2×#634C2312yes—
107C2×#634C2311yescharacteristic
108C2×C3×#67C2312yes—
109C2×C3×#67C2312yes—
110C22×C3×Dic3C2312yes—
111C3×#235—24no—
112C3×#235D418yescomplemented
113C2×C3×D12—24no—
114C2×C3×D12C2312yes—
115C2×C3×D12C2312yes—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2318yes—
118C2×C3×D12C2311yescharacteristic
119C2×C3×C4×D3C2312yes—
120C2×C3×C4×D3C2314yes—
121C2×C3×C4×D3C2312yes—
122C2×C3×Dic6C2311yescharacteristic
123C2×C3×Dic6C2311yescharacteristic
124D3×#67—216no—
125C2×#627C2314yes—
126C2×#626C2314yes—
127C2×#626C2314yes—
128C2×#625C2314yes—
129C2×#625C2314yes—
130#3805—216no—
131C2×D3×Dic3C2314yes—
132C2×D3×Dic3C2314yes—
133C2×D3×Dic3C2314yes—
134#3802—28no—
135D3×D12—28no—
136#3796—28no—
137#3795—28no—
138#3795—28no—
139#3795—28no—
140D3×Dic6—28no—
141D3×Dic6—28no—
142C32×C4⋊C4C2312yes—
143C32×C22⋊C4C2312yes—
144C32×C42C2312yes—
145#3752C2318yes—
146C4⋊(C3⋊Dic3)C2318yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2318yes—
149C3×Dic3⋊C4C2314yes—
150C3×C4×Dic3C2314yes—
151C3×C4×Dic3C2312yes—
152C3×C4×Dic3C2311yescharacteristic
153C3×C4×Dic3C2311yescharacteristic
154Dic3⋊Dic3C2314yes—
155#3722C2314yes—
156(C2×D3)⋊Dic3C2318yes—
157(C2×D3)⋊Dic3C2318yes—
158(C2×D3)⋊Dic3C2314yes—
159#3500—91noSylow
160C2×C3×#41—31no—
161C2×C3×#41—31no—
162C22×C3×D4—31no—
163C22×#67—34no—
164#1010—68no—
165#1010—68no—
166#1009—68no—
167C2×#239—32no—
168C2×D3×Q8—32no—
169C2×D3×Q8—32no—
170#1004—68no—
171C2×#237—34no—
172C2×#237—34no—
173C2×#237—32no—
174C2×#237—32no—
175C2×#237—32no—
176C2×#237—32no—
177C2×D3×D4—34no—
178C2×D3×D4—32no—
179C2×D3×D4—32no—
180C2×D3×D4—32no—
181C2×#235—31no—
182C2×#235—31no—
183C2×#235—32no—
184C2×#235—32no—
185C2×#235—32no—
186C2×#235—61no—
187C2×#235C2×D311yescharacteristic
188C2×#235C2×D311yescharacteristic, complemented
189C22×D12—32no—
190C22×D12C2×D311yescharacteristic
191C22×Dic6—31no—
192C22×Dic6—31no—
193C22×Dic6—32no—
194C22×Dic6—32no—
195C22×Dic6—61no—
196C3×#127—32no—
197C3×#124—32no—
198C3×#121—34no—
199C3×#120—34no—
200C3×C4×Q8—32no—
201C3×C4×D4—32no—
202C3×C4×D4—34no—
203C3×#117—21no—
204C3×#117—32no—
205C3×#117C2×D311yescharacteristic, complemented
206C3×#117C2×D311yescharacteristic, complemented
207C2×C3×C42—31no—
208C2×C3×C42—32no—
209C2×#217—34no—
210#947—31no—
211#944—31no—
212#940—31no—
213#939—34no—
214#939—38no—
215#938—38no—
216#937—38no—
217#936—32no—
218#936—32no—
219#936—31no—
220#936—34no—
221D4×Dic3—38no—
222#930—34no—
223#930—38no—
224C4×#67—34no—
225C2×(C2×D3)⋊C4—34no—
226C2×(C2×D3)⋊C4—38no—
227C2×C4×Dic3C2×D311yescharacteristic, complemented
228#897—34no—
229#897—34no—
230#897—38no—
231#897—64no—
232#895—38no—
233#895C2×D314yescomplemented
234#893C2×D312yescomplemented
235#887C2×D312yescomplemented
236#886—34no—
237#886—34no—
238#886—38no—
239#886—64no—
240#885—38no—
241#883—38no—
242#882—38no—
243#882C2×D314yescomplemented
244#67⋊C4C2×D314yescomplemented
245D3×C22⋊C4—38no—
246#878—38no—
247#875—32no—
248#875—32no—
249#875—34no—
250#875—31no—
251#875—31no—
252#875—32no—
253#875—32no—
254#875—38no—
255#875—62no—
256#875C2×D312yescomplemented
257#874—31no—
258#874C2×D312yescomplemented
259C4×D12—38no—
260C4×D12—34no—
261#872C2×D312yescomplemented
262C42×D3C2×D312yescomplemented
263#869—31no—
264#869—32no—
265#869—32no—
266#869—62no—
267C23×C32C2411yescharacteristic
268C22×C3⋊D3C2412yes—
269C22×C3×D3—24no—
270C22×C3×D3—44no—
271C22×C3×D3C2414yes—
272C22×C3×D3C2412yes—
273C22×C3×D3C2412yes—
274C2×D32—28no—
275C2×D32—48no—
276C2×C32×C4C2×D414yes—
277C2×C32×C4C2414yes—
278C2×C32×C4C2411yescharacteristic
279C2×C32×C4C2411yescharacteristic
280#638—24no—
281C2×C3⋊Dic3—24no—
282C2×C3⋊Dic3C2414yes—
283C2×C3⋊Dic3C2412yes—
284C4⋊(C3⋊D3)—22no—
285C4×C3⋊D3—24no—
286#634—24no—
287#634—24no—
288#634—22no—
289C3×#67—24no—
290C3×#67C2×D418yes—
291C2×C3×Dic3—42no—
292C2×C3×Dic3C2412yes—
293C2×C3×Dic3C2412yes—
294C2×C3×Dic3C2412yes—
295C2×C3×Dic3C2412yes—
296C3×D12—22no—
297C3×D12—24no—
298C3×D12—24no—
299C3×D12—48no—
300C3×D12C2×D414yes—
301C3×C4×D3—24no—
302C3×C4×D3—44no—
303C3×C4×D3C2×D418yes—
304C3×Dic6—22no—
305C3×Dic6C2×D414yes—
306#627—28no—
307#626—28no—
308#626—44no—
309#625—28no—
310#625—28no—
311D3×Dic3—28no—
312D3×Dic3—28no—
313D3×Dic3—28no—
314C2×2−1+4—91no—
315C2×H(5,𝔽2)—91no—
316#548—94no—
317#546—98no—
318#546—94no—
319#536—92no—
320#536—91no—
321#535—31no—
322#535—92no—
323#532—92no—
324#532—91no—
325C2×#124—92no—
326C2×#124—91no—
327C4×#41—31no—
328C24×C3—32no—
329C23×D3—34no—
330C23×D3—34no—
331C23×D3C22×D312yes—
332C3×#41—38no—
333C3×#41—64no—
334C2×C3×Q8—31no—
335C2×C3×Q8—31no—
336C2×C3×D4—32no—
337C2×C3×D4—32no—
338C2×C3×D4—31no—
339C2×C3×D4—32no—
340C2×C3×D4—32no—
341C2×C3×D4—31no—
342C2×C3×D4—38no—
343C2×C3×D4—64no—
344C22×C3×C4—21no—
345C22×C3×C4—32no—
346C22×C3×C4—32no—
347C22×C3×C4—32no—
348C22×C3×C4—34no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C2×#67—32no—
352C2×#67—32no—
353C2×#67—34no—
354C2×#67—34no—
355C2×#67—34no—
356C2×#67—34no—
357C2×#67—34no—
358C2×#67—34no—
359C2×#67—62no—
360C2×#67—616no—
361C2×#67C22×D312yes—
362C2×#67C22×D312yes—
363C22×Dic3—32no—
364C22×Dic3—32no—
365C22×Dic3—34no—
366C22×Dic3—34no—
367C22×Dic3—34no—
368C22×Dic3—62no—
369C22×Dic3C22×D312yes—
370#239—68no—
371D3×Q8—68no—
372D3×Q8—68no—
373#237—68no—
374#237—616no—
375#237—616no—
376#237—68no—
377#237—68no—
378#237—68no—
379D3×D4—68no—
380D3×D4—616no—
381D3×D4—68no—
382D3×D4—68no—
383#235—24no—
384#235—68no—
385#235—68no—
386#235—64no—
387#235—64no—
388#235—68no—
389#235—124no—
390#235D1218yescomplemented
391C2×D12—24no—
392C2×D12—34no—
393C2×D12—31no—
394C2×D12—31no—
395C2×D12—34no—
396C2×D12—61no—
397C2×D12—68no—
398C2×D12C22×D311yescharacteristic
399C2×D12C22×D312yes—
400C2×D12C22×D312yes—
401C2×D12C22×D318yes—
402C2×D12C22×D311yescharacteristic
403C2×C4×D3—34no—
404C2×C4×D3—34no—
405C2×C4×D3—34no—
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—62no—
409C2×C4×D3C22×D312yes—
410C2×C4×D3C22×D314yes—
411C2×C4×D3C22×D312yes—
412C2×Dic6—31no—
413C2×Dic6—31no—
414C2×Dic6—32no—
415C2×Dic6—32no—
416C2×Dic6—32no—
417C2×Dic6—32no—
418C2×Dic6—34no—
419C2×Dic6—34no—
420C2×Dic6—61no—
421C2×Dic6—62no—
422C2×Dic6—62no—
423C2×Dic6—68no—
424C2×Dic6—64no—
425C2×Dic6—64no—
426C2×Dic6—68no—
427C2×Dic6—124no—
428C2×Dic6C22×D311yescharacteristic
429C2×Dic6C22×D311yescharacteristic
430C3×C4⋊C4—22no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4C22×D312yes—
433C3×C4⋊C4C22×D312yes—
434C3×C22⋊C4—22no—
435C3×C22⋊C4—38no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4C22×D312yes—
438C3×C22⋊C4C22×D312yes—
439C3×C42—22no—
440C3×C42—31no—
441C3×C42—34no—
442C3×C42—32no—
443C3×C42—31no—
444C3×C42C22×D312yes—
445C3×C42C22×D312yes—
446#217—38no—
447#217—38no—
448#217—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—38no—
451(C2×D3)⋊C4—38no—
452(C2×D3)⋊C4—38no—
453(C2×D3)⋊C4—38no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—68no—
457(C2×D3)⋊C4C22×D314yes—
458(C2×D3)⋊C4C22×D318yes—
459C4⋊Dic3—38no—
460C4⋊Dic3—38no—
461C4⋊Dic3—34no—
462C4⋊Dic3—68no—
463Dic3⋊C4—34no—
464Dic3⋊C4C22×D314yes—
465C4×Dic3C22×D311yescharacteristic
466C4×Dic3C22×D314yes—
467C4×Dic3C22×D311yescharacteristic
468C4×Dic3C22×D312yes—
469C22×C32—22no—
470C22×C32C22×D412yes—
471C22×C32C2511yescharacteristic
472C2×C3⋊D3—22no—
473C2×C3⋊D3—24no—
474C2×C3×D3—24no—
475C2×C3×D3—22no—
476C2×C3×D3—24no—
477C2×C3×D3—24no—
478C2×C3×D3—28no—
479C2×C3×D3—84no—
480C2×C3×D3C22×D414yes—
481D32—88no—
482C32×C4—24no—
483C32×C4C22×D412yes—
484C32×C4C22×D412yes—
485C3⋊Dic3—22no—
486C3⋊Dic3—24no—
487C3×Dic3—22no—
488C3×Dic3—22no—
489C3×Dic3—22no—
490C3×Dic3C22×D414yes—
4912−1+4—188no—
492H(5,𝔽2)—188no—
493C2×#41—31no—
494C2×#41—31no—
495C2×#41—92no—
496C2×#41—92no—
497C2×#41—92no—
498C2×#41—94no—
499C2×#41—92no—
500C2×#41—91no—
501C22×Q8—92no—
502C22×Q8—92no—
503C22×Q8—91no—
504C22×D4—31no—
505C22×D4—92no—
506C22×D4—92no—
507C22×D4—94no—
508C4⋊Q8—91no—
509C4⋊Q8—92no—
510#127—32no—
511#127—91no—
512#124—32no—
513#124—98no—
514#124—92no—
515#124—92no—
516#124—94no—
517#124—91no—
518#124—91no—
519#124—92no—
520#123—98no—
521#123—94no—
522C22⋊Q8—98no—
523C22⋊Q8—94no—
524#121—34no—
525#121—98no—
526#121—98no—
527#121—94no—
528#120—34no—
529#120—98no—
530C4×Q8—32no—
531C4×D4—32no—
532C4×D4—34no—
533C4×D4—94no—
534C4×D4—98no—
535#117—32no—
536#117D3211yescharacteristic, complemented
537C2×C22⋊C4—98no—
538C2×C22⋊C4—94no—
539C2×C42—31no—
540C2×C42—32no—
541C23×C3—21no—
542C23×C3—32no—
543C23×C3—34no—
544C23×C3—32no—
545C23×C3—64no—
546C23×C3—124no—
547C23×C3C23×D311yescharacteristic
548C23×C3C23×D311yescharacteristic
549C22×D3—24no—
550C22×D3—32no—
551C22×D3—32no—
552C22×D3—44no—
553C22×D3—62no—
554C22×D3—68no—
555C22×D3—68no—
556C22×D3—128no—
557C22×D3—128no—
558C22×D3C23×D314yes—
559C22×D3C23×D312yes—
560C22×D3C23×D312yes—
561C3×Q8—34no—
562C3×Q8—62no—
563C3×D4—38no—
564C3×D4—34no—
565C3×D4—64no—
566C3×D4—64no—
567C3×D4—64no—
568C3×D4—62no—
569C3×D4—128no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—24no—
573C2×C3×C4—24no—
574C2×C3×C4—32no—
575C2×C3×C4—38no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—64no—
580C2×C3×C4—124no—
581C2×C3×C4—122no—
582C2×C3×C4C2×D1214yes—
583C2×C3×C4D3×D414yes—
584C2×C3×C4C23×D314yes—
585C2×C3×C4C23×D314yes—
586C2×C3×C4C23×D311yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590#67—24no—
591#67—68no—
592#67—68no—
593#67—64no—
594#67—64no—
595#67—68no—
596#67—68no—
597#67—68no—
598#67—124no—
599#67—124no—
600#67C2×D1218yes—
601C2×Dic3—32no—
602C2×Dic3—32no—
603C2×Dic3—34no—
604C2×Dic3—34no—
605C2×Dic3—42no—
606C2×Dic3—62no—
607C2×Dic3—64no—
608C2×Dic3—68no—
609C2×Dic3—64no—
610C2×Dic3—64no—
611C2×Dic3—68no—
612C2×Dic3—68no—
613C2×Dic3—124no—
614C2×Dic3C23×D312yes—
615C2×Dic3C23×D312yes—
616C2×Dic3C23×D312yes—
617C2×Dic3C23×D312yes—
618D12—24no—
619D12—24no—
620D12—22no—
621D12—48no—
622D12—68no—
623D12—62no—
624D12—62no—
625D12—122no—
626D12—124no—
627D12C2×D1214yes—
628C4×D3—24no—
629C4×D3—44no—
630C4×D3—68no—
631C4×D3—68no—
632C4×D3—68no—
633C4×D3—64no—
634C4×D3—64no—
635C4×D3—124no—
636C4×D3C2×D1218yes—
637Dic6—22no—
638Dic6—68no—
639Dic6—64no—
640Dic6—64no—
641Dic6—62no—
642Dic6—64no—
643Dic6—64no—
644Dic6—62no—
645Dic6—68no—
646Dic6—124no—
647Dic6—124no—
648Dic6—122no—
649Dic6C2×D1214yes—
650C2×C32—22no—
651C2×C32C23×D411yescharacteristic
652C2×C32#58512yes—
653C3⋊D3—42no—
654C3×D3—24no—
655C3×D3—44no—
656C3×D3—42no—
657C24—32no—
658C24—94no—
659#41—38no—
660#41—64no—
661#41—188no—
662#41—188no—
663#41—188no—
664#41—1816no—
665#41—188no—
666#41—184no—
667C2×Q8—31no—
668C2×Q8—31no—
669C2×Q8—94no—
670C2×Q8—92no—
671C2×Q8—92no—
672C2×Q8—91no—
673C2×Q8—188no—
674C2×Q8—188no—
675C2×Q8—184no—
676C2×D4—32no—
677C2×D4—32no—
678C2×D4—31no—
679C2×D4—32no—
680C2×D4—32no—
681C2×D4—31no—
682C2×D4—38no—
683C2×D4—64no—
684C2×D4—94no—
685C2×D4—94no—
686C2×D4—94no—
687C2×D4—94no—
688C2×D4—92no—
689C2×D4—91no—
690C2×D4—188no—
691C2×D4—188no—
692C2×D4—1816no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—32no—
696C22×C4—34no—
697C22×C4—94no—
698C22×C4—94no—
699C22×C4—94no—
700C22×C4—92no—
701C22×C4—92no—
702C22×C4C2×D3211yescharacteristic
703C4⋊C4—34no—
704C4⋊C4—94no—
705C4⋊C4—98no—
706C4⋊C4C2×D3212yes—
707C22⋊C4—38no—
708C22⋊C4—34no—
709C22⋊C4—94no—
710C22⋊C4—98no—
711C22⋊C4—98no—
712C22⋊C4—94no—
713C22⋊C4—98no—
714C22⋊C4C2×D3212yes—
715C42—31no—
716C42—31no—
717C42—34no—
718C42—32no—
719C42C2×D3212yes—
720C22×C3—22no—
721C22×C3—22no—
722C22×C3—22no—
723C22×C3—21no—
724C22×C3—34no—
725C22×C3—42no—
726C22×C3—64no—
727C22×C3—62no—
728C22×C3—64no—
729C22×C3—64no—
730C22×C3—68no—
731C22×C3—244no—
732C22×C3C22×D1212yes—
733C22×C3C2×D3×D412yes—
734C22×C3C24×D311yescharacteristic
735C22×C3C24×D311yescharacteristic
736C2×D3—24no—
737C2×D3—22no—
738C2×D3—24no—
739C2×D3—24no—
740C2×D3—28no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—64no—
744C2×D3—64no—
745C2×D3—84no—
746C2×D3—122no—
747C2×D3—124no—
748C2×D3—248no—
749C2×D3—248no—
750C2×D3C22×D1214yes—
751C3×C4—24no—
752C3×C4—24no—
753C3×C4—22no—
754C3×C4—22no—
755C3×C4—34no—
756C3×C4—44no—
757C3×C4—62no—
758C3×C4—62no—
759C3×C4—62no—
760C3×C4C22×D1212yes—
761C3×C4C22×D1212yes—
762C3×C4C2×D3×D412yes—
763C3×C4C2×D3×D412yes—
764Dic3—22no—
765Dic3—22no—
766Dic3—22no—
767Dic3—64no—
768Dic3—62no—
769Dic3—64no—
770Dic3—62no—
771Dic3—124no—
772Dic3—122no—
773Dic3C22×D1214yes—
774C32#350011yescharacteristic, complemented, Sylow
775C23—32no—
776C23—34no—
777C23—32no—
778C23—64no—
779C23—92no—
780C23—124no—
781C23—188no—
782C23—368no—
783C23C22×D3211yescharacteristic
784Q8—34no—
785Q8—62no—
786Q8—188no—
787Q8—184no—
788Q8—184no—
789Q8—182no—
790D4—38no—
791D4—34no—
792D4—64no—
793D4—64no—
794D4—64no—
795D4—62no—
796D4—128no—
797D4—188no—
798D4—188no—
799D4—188no—
800D4—184no—
801D4—182no—
802D4—364no—
803C2×C4—32no—
804C2×C4—38no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—64no—
809C2×C4—94no—
810C2×C4—92no—
811C2×C4—124no—
812C2×C4—122no—
813C2×C4—188no—
814C2×C4—188no—
815C2×C4—188no—
816C2×C4—184no—
817C2×C4—184no—
818C2×C4D3×D1214yes—
819C2×C4C22×D3214yes—
820C2×C4C22×D3211yescharacteristic
821C2×C4C22×D3211yescharacteristic
822C2×C3—22no—
823C2×C3—22no—
824C2×C3—21no—
825C2×C3—22no—
826C2×C3—42no—
827C2×C3—64no—
828C2×C3—124no—
829C2×C3—122no—
830C2×C3C23×D1211yescharacteristic
831C2×C3C22×D3×D411yescharacteristic
832C2×C3#596412yes—
833C2×C3#596612yes—
834D3—24no—
835D3—44no—
836D3—42no—
837D3—122no—
838D3—122no—
839D3—242no—
840C22—22no—
841C22—34no—
842C22—64no—
843C22—62no—
844C22—64no—
845C22—64no—
846C22—68no—
847C22—182no—
848C22—184no—
849C22—244no—
850C22—728no—
851C22C2×D3×D1212yes—
852C22C23×D3211yescharacteristic
853C4—24no—
854C4—34no—
855C4—62no—
856C4—62no—
857C4—62no—
858C4—182no—
859C4—184no—
860C4C2×D3×D1212yes—
861C4C2×D3×D1212yes—
862C3—21no—
863C3#8584711yescharacteristic, complemented
864C3#8631711yescharacteristic, complemented
865C2—22no—
866C2—64no—
867C2—124no—
868C2—122no—
869C2—362no—
870C2C22×D3×D1211yescharacteristic
871C2#1059669612yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3500
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C2×#64298C2semidirect
3. #10595997C2semidirect
4. C3×#5525C2semidirect
5. C3×#5522C2semidirect
6. #10595029C2semidirect
7. C2×#63860C2semidirect
8. #10594630C2semidirect
9. #10594382C2semidirect
10. #10594292C2semidirect
11. #10594000C2semidirect
12. D3×#875C2semidirect
13. #10593897C2semidirect
14. #10593894C2semidirect
18. C22×#634C22semidirect
20. C2×C3×#235C22semidirect
23. C2×#3805C22semidirect
30. C2×#3795C22semidirect
31. C2×#3795C22semidirect
32. C2×D3×Dic6C22semidirect
33. C2×D3×Dic6C22semidirect
34. C32×#117C22semidirect
35. #64106C22semidirect
36. #64095C22semidirect
37. #64084C22semidirect
38. #64078C22semidirect
39. C2×C3×C4×Dic3C22semidirect
40. C3×#895C22semidirect
41. C3×#893C22semidirect
42. C3×#887C22semidirect
43. C3×#882C22semidirect
44. C3×#67⋊C4C22semidirect
45. C3×#875C22semidirect
46. C3×#874C22semidirect
47. C3×#872C22semidirect
48. C3×C42×D3C22semidirect
49. #63978C22semidirect
50. C2×(C2×D3)⋊Dic3C22semidirect
51. #63922C22semidirect
52. D3×(C2×D3)⋊C4C22semidirect
53. #63911C22semidirect
54. #63908C22semidirect
55. C4×#626C22semidirect
56. #63893C22semidirect
57. Dic3×D12C22semidirect
58. #63891C22semidirect
59. #63886C22semidirect
60. #63866C22semidirect
61. #63864C22semidirect
62. #63860C22semidirect
63. #63860C22semidirect
64. #63860C22semidirect
65. #63860C22semidirect
66. #63852C22semidirect
90. #5525D3semidirect
91. #5522D3semidirect
112. C3×#235D4semidirect
188. C2×#235C2×D3semidirect
205. C3×#117C2×D3semidirect
206. C3×#117C2×D3semidirect
227. C2×C4×Dic3C2×D3semidirect
233. #895C2×D3semidirect
234. #893C2×D3semidirect
235. #887C2×D3semidirect
243. #882C2×D3semidirect
244. #67⋊C4C2×D3semidirect
256. #875C2×D3semidirect
258. #874C2×D3semidirect
261. #872C2×D3semidirect
262. C42×D3C2×D3semidirect
390. #235D12semidirect
536. #117D32semidirect
774. C32#3500semidirect
863. C3#85847semidirect
864. C3#86317semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
C2×#642982
#105959972
C3×#55252
C3×#55222
#105950292
C2×#638602
#105946302
#105943822
#105942922
#105940002
D3×#8752
#105938972
#105938942
#863173
#858473