Finite Group Databasebeta

← #11905922

Subgroups — #11905922

Order 1152.

3139 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64297C212yesmaximal, complemented
2#10595948C211yesmaximal, characteristic, complemented
3C3×#5477C211yesmaximal, characteristic, complemented
4C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
5#10595043C212yesmaximal, complemented
6#10594911C214yesmaximal, complemented
7#10594910C214yesmaximal, complemented
8#10593903C212yesmaximal, complemented
9#10593902C212yesmaximal, complemented
10#10593901C214yesmaximal, complemented
11#10593900C212yesmaximal, complemented
12#10593899C214yesmaximal, complemented
13Dic6×D12C212yesmaximal, complemented
14#86222—31nomaximal
15#85818—31nomaximal
16C2×#3828C2212yes—
17C2×C3×#235C2212yes—
18C22×C3×Dic6C2211yescharacteristic
19C2×#3804C2218yes—
20C2×#3799C2214yes—
21C2×#3797C2214yes—
22#64297—216no—
23C2×#3796C2214yes—
24C2×D3×Dic6C2214yes—
25C2×C32×C42C2211yescharacteristic
26#64139C2212yes—
27#64139C2212yes—
28#64084C2212yes—
29#64083C2211yescharacteristic
30C4×C4⋊(C3⋊D3)C2212yes—
31C4×C4⋊(C3⋊D3)C2212yes—
32#64078C2211yescharacteristic
33C3×#930C2212yes—
34C3×#930C2212yes—
35C2×C3×C4⋊Dic3C2211yescharacteristic
36C2×C3×Dic3⋊C4C2212yes—
37C2×C3×C4×Dic3C2212yes—
38C3×#875C2212yes—
39C3×#874C2211yescharacteristic
40C3×C4×D12C2212yes—
41C3×C4×D12C2212yes—
42C3×#869C2211yescharacteristic
43C3×C4×Dic6C2212yes—
44C3×C4×Dic6C2212yes—
45C3×C4×Dic6C2212yes—
46C3×C4×Dic6C2212yes—
47#63978C2218yes—
48#63918C2214yes—
49#63916C2214yes—
50#63911C2214yes—
51#63910C2218yes—
52#63909C2214yes—
53#63895C2218yes—
54#63894C2214yes—
55#63893C2218yes—
56Dic3×D12C2214yes—
57#63886C2218yes—
58#63880C2218yes—
59#63871C2214yes—
60#63857C2214yes—
61#63852C2218yes—
62C2×#1010—32no—
63C2×#1007—32no—
64C3×#532—31no—
65C2×C3×C4×Q8—31no—
66#5833—32no—
67#5727—32no—
68#5718—32no—
69#5677—34no—
70#5597—34no—
71#5596—34no—
72#5577—32no—
73#5577—32no—
74#5576—34no—
75#5576—34no—
76Q8×D12—32no—
77Q8×D12—32no—
78#5553—32no—
79#5552—34no—
80D4×Dic6—32no—
81#5510—32no—
82#5510—34no—
83#5477—31no—
84#5477—31no—
85#5477—34no—
86#5477—61no—
87#5477D311yescharacteristic, complemented
88C2×C4×Dic6D311yescharacteristic, complemented
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C2×#638C2314yes—
93#3828—28no—
94C2×C4⋊(C3⋊D3)C2312yes—
95C2×C4⋊(C3⋊D3)C2312yes—
96C2×C4⋊(C3⋊D3)C2312yes—
97C2×C4×C3⋊D3C2314yes—
98C2×#634C2312yes—
99C2×C3×#67C2314yes—
100C22×C3×Dic3C2312yes—
101C22×C3×Dic3C2312yes—
102C3×#235—28no—
103C2×C3×D12C2312yes—
104C2×C3×D12C2312yes—
105C2×C3×D12C2312yes—
106C2×C3×C4×D3C2314yes—
107C2×C3×Dic6D418yescomplemented
108C2×C3×Dic6C2312yes—
109C2×C3×Dic6C2312yes—
110C2×C3×Dic6C2312yes—
111C2×#627C2318yes—
112C2×#626C2318yes—
113C2×#626C2318yes—
114C2×#624C2318yes—
115#3804—232no—
116C2×D3×Dic3C2318yes—
117#3799—216no—
118#3797—216no—
119#3796—216no—
120D3×Dic6—216no—
121C32×C42C2311yescharacteristic
122C32×C42C2311yescharacteristic
123C32×C42C2311yescharacteristic
124C32×C42C2311yescharacteristic
125#3752C2314yes—
126#3752C2314yes—
127C4⋊(C3⋊Dic3)C2312yes—
128C4⋊(C3⋊Dic3)C2312yes—
129C3×(C2×D3)⋊C4C2314yes—
130C3×(C2×D3)⋊C4C2314yes—
131C3×C4⋊Dic3C2312yes—
132C3×C4⋊Dic3C2312yes—
133C3×C4⋊Dic3C2312yes—
134C3×C4⋊Dic3C2312yes—
135C3×Dic3⋊C4C2314yes—
136C3×Dic3⋊C4C2314yes—
137C3×C4×Dic3C2314yes—
138C3×C4×Dic3C2314yes—
139Dic3⋊Dic3C2318yes—
140#3722C2318yes—
141(C2×D3)⋊Dic3C2318yes—
142#3497—91noSylow
143C2×C3×#41—32no—
144C22×C3×Q8—31no—
145#1010—616no—
146#1007—616no—
147C2×#239—34no—
148C2×#239—34no—
149C2×D3×Q8—34no—
150C2×D3×Q8—34no—
151C2×D3×Q8—34no—
152C2×#237—38no—
153C2×#237—34no—
154C2×#235—32no—
155C2×#235—32no—
156C2×#235—38no—
157C2×#235—34no—
158C2×#235—62no—
159C2×#235C2×D312yes—
160C22×Dic6—34no—
161C22×Dic6C2×D311yescharacteristic
162C3×C4⋊Q8—31no—
163C3×#127—31no—
164C3×#124—32no—
165C3×#121—32no—
166C3×#121—32no—
167C3×C4×Q8—32no—
168C3×C4×Q8—32no—
169C3×C4×Q8—32no—
170C3×C4×Q8—32no—
171C3×C4×D4—32no—
172C3×C4×D4—32no—
173C2×C3×C4⋊C4—32no—
174C2×C3×C4⋊C4—31no—
175C2×C3×C42—21no—
176C2×C3×C42—32no—
177C2×C3×C42C2×D311yescharacteristic
178C2×C3×C42C2×D311yescharacteristic
179#946—34no—
180#940—34no—
181#939—38no—
182#939—38no—
183#938—34no—
184D4×Dic3—34no—
185#930—32no—
186#930—32no—
187#930—32no—
188#930—32no—
189#930—38no—
190#930—34no—
191#930—62no—
192#930—62no—
193#930C2×D312yes—
194#930C2×D312yes—
195C2×C4⋊Dic3C2×D311yescharacteristic
196#924—34no—
197C2×Dic3⋊C4C2×D312yes—
198C2×C4×Dic3C2×D312yes—
199#897—34no—
200#897—34no—
201#897—38no—
202#897—38no—
203#896—38no—
204#895—38no—
205#895—34no—
206#895—34no—
207#895—38no—
208#893—34no—
209#888—34no—
210#885—38no—
211#884—38no—
212#67⋊C4—38no—
213#878—38no—
214#875—32no—
215#875—32no—
216#875—38no—
217#875—62no—
218#875C2×D312yes—
219#874—34no—
220#874—31no—
221#874—31no—
222#874—61no—
223#874C2×D311yescharacteristic
224C4×D12—34no—
225C4×D12—32no—
226C4×D12—32no—
227C4×D12—32no—
228C4×D12—32no—
229C4×D12—38no—
230C4×D12—34no—
231C4×D12—62no—
232C4×D12—62no—
233C4×D12C2×D312yes—
234C4×D12C2×D312yes—
235#869—31no—
236#869—31no—
237#869—34no—
238#869—61no—
239#869C2×D311yescharacteristic
240C4×Dic6C2×D312yes—
241C4×Dic6C2×D312yes—
242C4×Dic6C2×D312yes—
243C4×Dic6C2×D312yes—
244C23×C32C2411yescharacteristic
245C22×C3⋊D3C2414yes—
246C22×C3×D3C2414yes—
247C2×C32×C4—22no—
248C2×C32×C4—41no—
249C2×C32×C4C2×D414yes—
250C2×C32×C4C2411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C32×C4C2411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638—28no—
257C2×C3⋊Dic3C2414yes—
258C4⋊(C3⋊D3)—24no—
259C4⋊(C3⋊D3)—24no—
260C4⋊(C3⋊D3)—42no—
261C4×C3⋊D3—28no—
262#634—24no—
263C3×#67—28no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3C2×D418yes—
266C2×C3×Dic3C2414yes—
267C2×C3×Dic3C2414yes—
268C2×C3×Dic3C2414yes—
269C3×D12—24no—
270C3×D12—24no—
271C3×D12—42no—
272C3×C4×D3—28no—
273C3×Dic6—24no—
274C3×Dic6C2×D418yes—
275C3×Dic6C2×D418yes—
276#627—216no—
277#626—216no—
278#626—48no—
279#624—216no—
280D3×Dic3—216no—
281C2×2−1+4—92no—
282#550—92no—
283#550—92no—
284D4×Q8—92no—
285D4×Q8—92no—
286#548—94no—
287#548—94no—
288#537—94no—
289#537—92no—
290#532—31no—
291#532—94no—
292#532—91no—
293C2×C4×Q8—31no—
294C3×#41—68no—
295C2×C3×Q8—38no—
296C2×C3×Q8—32no—
297C2×C3×Q8—32no—
298C2×C3×Q8—32no—
299C2×C3×D4—34no—
300C2×C3×D4—32no—
301C2×C3×D4—32no—
302C2×C3×D4—32no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—32no—
307C22×C3×C4—32no—
308C22×C3×C4—34no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×C3×C4C22×D311yescharacteristic
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—34no—
316C2×#67—34no—
317C2×#67—38no—
318C2×#67—38no—
319C2×#67—64no—
320C2×#67C22×D314yes—
321C22×Dic3—38no—
322C22×Dic3C22×D312yes—
323C22×Dic3C22×D312yes—
324#239—616no—
325#239—616no—
326D3×Q8—616no—
327D3×Q8—616no—
328D3×Q8—616no—
329#237—632no—
330#237—616no—
331#235—28no—
332#235—632no—
333#235—68no—
334#235—68no—
335#235—616no—
336#235—128no—
337C2×D12—38no—
338C2×D12—32no—
339C2×D12—32no—
340C2×D12—32no—
341C2×D12—32no—
342C2×D12—38no—
343C2×D12—32no—
344C2×D12—32no—
345C2×D12—62no—
346C2×D12—62no—
347C2×D12—62no—
348C2×D12C22×D312yes—
349C2×D12C22×D312yes—
350C2×D12C22×D312yes—
351C2×C4×D3—38no—
352C2×C4×D3—34no—
353C2×C4×D3—34no—
354C2×C4×D3—38no—
355C2×C4×D3—38no—
356C2×C4×D3—64no—
357C2×C4×D3C22×D314yes—
358C2×Dic6—32no—
359C2×Dic6—32no—
360C2×Dic6—38no—
361C2×Dic6—38no—
362C2×Dic6—62no—
363C2×Dic6—616no—
364C2×Dic6D1218yescomplemented
365C2×Dic6C22×D312yes—
366C2×Dic6C22×D312yes—
367C2×Dic6C22×D312yes—
368C3×C4⋊C4—32no—
369C3×C4⋊C4—34no—
370C3×C4⋊C4—34no—
371C3×C4⋊C4—32no—
372C3×C4⋊C4—32no—
373C3×C4⋊C4—32no—
374C3×C22⋊C4—34no—
375C3×C22⋊C4—34no—
376C3×C42—21no—
377C3×C42—21no—
378C3×C42—21no—
379C3×C42—21no—
380C3×C42—34no—
381C3×C42—34no—
382C3×C42C22×D311yescharacteristic
383C3×C42C22×D311yescharacteristic
384C3×C42C22×D311yescharacteristic
385C3×C42C22×D311yescharacteristic
386C3×C42C22×D311yescharacteristic
387C3×C42C22×D311yescharacteristic
388C3×C42C22×D311yescharacteristic
389C3×C42C22×D311yescharacteristic
390#217—38no—
391(C2×D3)⋊C4—38no—
392(C2×D3)⋊C4—34no—
393(C2×D3)⋊C4—34no—
394(C2×D3)⋊C4—34no—
395(C2×D3)⋊C4—34no—
396(C2×D3)⋊C4—38no—
397(C2×D3)⋊C4—38no—
398(C2×D3)⋊C4—64no—
399(C2×D3)⋊C4—64no—
400(C2×D3)⋊C4C22×D314yes—
401(C2×D3)⋊C4C22×D314yes—
402C4⋊Dic3—32no—
403C4⋊Dic3—32no—
404C4⋊Dic3—32no—
405C4⋊Dic3—32no—
406C4⋊Dic3—38no—
407C4⋊Dic3—62no—
408C4⋊Dic3—62no—
409C4⋊Dic3C22×D312yes—
410C4⋊Dic3C22×D312yes—
411C4⋊Dic3C22×D312yes—
412C4⋊Dic3C22×D312yes—
413Dic3⋊C4—38no—
414Dic3⋊C4C22×D314yes—
415Dic3⋊C4C22×D314yes—
416C4×Dic3C22×D314yes—
417C4×Dic3C22×D314yes—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32C22×D412yes—
421C22×C32C2511yescharacteristic
422C2×C3⋊D3—24no—
423C2×C3⋊D3—24no—
424C2×C3⋊D3—24no—
425C2×C3×D3—24no—
426C2×C3×D3—24no—
427C2×C3×D3—24no—
428C32×C4—21no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4C22×D412yes—
432C32×C4C22×D412yes—
433C32×C42−1+412yescomplemented
434C3⋊Dic3—24no—
435C3×Dic3—24no—
436C3×Dic3—24no—
437C3×Dic3C22×D418yes—
4382−1+4—1816no—
439C2×#41—32no—
440C2×#41—98no—
441C2×#41—94no—
442C2×#41—94no—
443C2×#41—92no—
444C22×Q8—31no—
445C22×Q8—94no—
446C22×Q8—94no—
447C4⋊Q8—31no—
448C4⋊Q8—94no—
449C4⋊Q8—91no—
450#127—31no—
451#127—94no—
452#127—91no—
453#124—32no—
454#124—98no—
455#124—92no—
456C22⋊Q8—98no—
457C22⋊Q8—98no—
458C22⋊Q8—94no—
459C22⋊Q8—94no—
460#121—32no—
461#121—32no—
462#121—98no—
463#121—94no—
464#121—94no—
465#121—98no—
466#121—98no—
467#121—92no—
468#121—92no—
469C4×Q8—32no—
470C4×Q8—32no—
471C4×Q8—32no—
472C4×Q8—32no—
473C4×D4—32no—
474C4×D4—32no—
475C4×D4—98no—
476C4×D4—94no—
477C4×D4—94no—
478C4×D4—92no—
479C4×D4—92no—
480C2×C4⋊C4—32no—
481C2×C4⋊C4—31no—
482C2×C42—32no—
483C2×C42D3211yescharacteristic
484C23×C3—21no—
485C23×C3—34no—
486C23×C3C23×D311yescharacteristic
487C23×C3C23×D311yescharacteristic
488C22×D3—34no—
489C22×D3—34no—
490C22×D3—64no—
491C22×D3C23×D314yes—
492C3×Q8—38no—
493C3×Q8—38no—
494C3×Q8—64no—
495C3×D4—68no—
496C3×D4—64no—
497C3×D4—64no—
498C3×D4—122no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—24no—
508C2×C3×C4—38no—
509C2×C3×C4—34no—
510C2×C3×C4—34no—
511C2×C3×C4—34no—
512C2×C3×C4—42no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—42no—
516C2×C3×C4—68no—
517C2×C3×C4—122no—
518C2×C3×C4C2×D1214yes—
519C2×C3×C4D3×D414yes—
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—28no—
533#67—68no—
534#67—68no—
535#67—616no—
536#67—128no—
537#67—128no—
538C2×Dic3—34no—
539C2×Dic3—34no—
540C2×Dic3—42no—
541C2×Dic3—64no—
542C2×Dic3—616no—
543C2×Dic3C2×D1218yes—
544C2×Dic3C23×D314yes—
545C2×Dic3C23×D314yes—
546C2×Dic3C23×D314yes—
547D12—24no—
548D12—24no—
549D12—42no—
550D12—616no—
551D12—64no—
552D12—64no—
553D12—64no—
554D12—64no—
555D12—124no—
556D12—124no—
557D12—122no—
558D12—122no—
559D12—124no—
560D12—128no—
561C4×D3—28no—
562C4×D3—616no—
563C4×D3—616no—
564C4×D3—68no—
565C4×D3—68no—
566C4×D3—616no—
567C4×D3—128no—
568Dic6—24no—
569Dic6—616no—
570Dic6—64no—
571Dic6—64no—
572Dic6—616no—
573Dic6—124no—
574Dic6C2×D1218yes—
575Dic6C2×D1218yes—
576C2×C32—22no—
577C2×C32C23×D411yescharacteristic
578C2×C32C2×2−1+411yescharacteristic
579C2×C32#58511yescharacteristic
580C3⋊D3—44no—
581C3×D3—44no—
582#41—68no—
583#41—1832no—
584#41—1816no—
585#41—1816no—
586#41—188no—
587C2×Q8—32no—
588C2×Q8—32no—
589C2×Q8—32no—
590C2×Q8—38no—
591C2×Q8—98no—
592C2×Q8—92no—
593C2×Q8—1816no—
594C2×Q8—1816no—
595C2×D4—34no—
596C2×D4—32no—
597C2×D4—32no—
598C2×D4—32no—
599C2×D4—98no—
600C2×D4—98no—
601C2×D4—94no—
602C2×D4—92no—
603C2×D4—92no—
604C2×D4—92no—
605C22×C4—32no—
606C22×C4—32no—
607C22×C4—34no—
608C22×C4—98no—
609C22×C4—98no—
610C22×C4—94no—
611C22×C4C2×D3211yescharacteristic
612C22×C4C2×D3211yescharacteristic
613C22×C4C2×D3211yescharacteristic
614C4⋊C4—34no—
615C4⋊C4—34no—
616C4⋊C4—32no—
617C4⋊C4—32no—
618C4⋊C4—32no—
619C4⋊C4—32no—
620C4⋊C4—98no—
621C4⋊C4—92no—
622C4⋊C4—92no—
623C22⋊C4—34no—
624C22⋊C4—34no—
625C22⋊C4—98no—
626C22⋊C4—98no—
627C22⋊C4—94no—
628C22⋊C4—94no—
629C42—34no—
630C42—34no—
631C42C2×D3211yescharacteristic
632C42C2×D3211yescharacteristic
633C42C2×D3211yescharacteristic
634C42C2×D3211yescharacteristic
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—64no—
644C22×C3—64no—
645C22×C3—64no—
646C22×C3C22×D1212yes—
647C22×C3C2×D3×D412yes—
648C22×C3C24×D311yescharacteristic
649C22×C3C24×D311yescharacteristic
650C2×D3—24no—
651C2×D3—24no—
652C2×D3—24no—
653C2×D3—64no—
654C2×D3—64no—
655C2×D3—64no—
656C2×D3—64no—
657C2×D3—64no—
658C2×D3—64no—
659C2×D3—124no—
660C2×D3—124no—
661C2×D3—124no—
662C3×C4—22no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—22no—
672C3×C4—38no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—64no—
676C3×C4—64no—
677C3×C4C22×D1212yes—
678C3×C4C22×D1212yes—
679C3×C4C2×D3×D412yes—
680C3×C4C2×D3×D412yes—
681C3×C4#100712yescomplemented
682C3×C4#101012yescomplemented
683Dic3—24no—
684Dic3—24no—
685Dic3—64no—
686Dic3—64no—
687Dic3—124no—
688Dic3C22×D1218yes—
689C32#349711yescharacteristic, complemented, Sylow
690C23—34no—
691C23—94no—
692C23C22×D3211yescharacteristic
693Q8—38no—
694Q8—38no—
695Q8—64no—
696Q8—1816no—
697Q8—184no—
698D4—68no—
699D4—64no—
700D4—64no—
701D4—122no—
702D4—1816no—
703D4—188no—
704D4—184no—
705D4—184no—
706D4—362no—
707D4—368no—
708C2×C4—22no—
709C2×C4—38no—
710C2×C4—34no—
711C2×C4—34no—
712C2×C4—34no—
713C2×C4—41no—
714C2×C4—68no—
715C2×C4—94no—
716C2×C4—122no—
717C2×C4—1816no—
718C2×C4—1816no—
719C2×C4—188no—
720C2×C4D3×D1214yes—
721C2×C4C22×D3211yescharacteristic
722C2×C4C22×D3211yescharacteristic
723C2×C4C22×D3211yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C2×C4C22×D3211yescharacteristic
726C2×C4C22×D3211yescharacteristic
727C2×C3—22no—
728C2×C3—22no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—42no—
733C2×C3—124no—
734C2×C3C23×D1211yescharacteristic
735C2×C3C22×D3×D411yescharacteristic
736C2×C3C2×#100711yescharacteristic
737C2×C3C2×#101011yescharacteristic
738C2×C3#596411yescharacteristic
739C2×C3#596411yescharacteristic
740D3—44no—
741D3—124no—
742D3—124no—
743D3—244no—
744C22—21no—
745C22—21no—
746C22—64no—
747C22—64no—
748C22—64no—
749C22—184no—
750C22—184no—
751C22—184no—
752C22C2×D3×D1212yes—
753C22C23×D3211yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—38no—
758C4—64no—
759C4—64no—
760C4—184no—
761C4#6429712yescomplemented
762C4C2×D3×D1212yes—
763C4C2×D3×D1212yes—
764C3—21no—
765C3#8581811yescharacteristic, complemented
766C3#8622211yescharacteristic, complemented
767C2—22no—
768C2—124no—
769C2—364no—
770C2C2×#6429711yescharacteristic
771C2C22×D3×D1211yescharacteristic
772C2#1059666911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3497
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64297C2semidirect
2. #10595948C2semidirect
3. C3×#5477C2semidirect
4. C2×C3×C4×Dic6C2semidirect
5. #10595043C2semidirect
6. #10594911C2semidirect
7. #10594910C2semidirect
8. #10593903C2semidirect
9. #10593902C2semidirect
10. #10593901C2semidirect
11. #10593900C2semidirect
12. #10593899C2semidirect
13. Dic6×D12C2semidirect
87. #5477D3semidirect
88. C2×C4×Dic6D3semidirect
107. C2×C3×Dic6D4semidirect
364. C2×Dic6D12semidirect
433. C32×C42−1+4semidirect
681. C3×C4#1007semidirect
682. C3×C4#1010semidirect
689. C32#3497semidirect
761. C4#64297semidirect
765. C3#85818semidirect
766. C3#86222semidirect

Maximal subgroups

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

subgroupindex
C2×#642972
#105959482
C3×#54772
C2×C3×C4×Dic62
#105950432
#105949112
#105949102
#105939032
#105939022
#105939012
#105939002
#105938992
Dic6×D122
#862223
#858183