Finite Group Databasebeta

← C2×#10595317 #11918765

Subgroups — C2×#10595317 #11918765

Order 1152.

3097 conjugacy classes of subgroups.

The subgroup lattice has 965 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic, complemented
3C2×#64151C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5C2×#63949C212yesmaximal, complemented
6C2×#63947C212yesmaximal, complemented
7C2×#63943C212yesmaximal, complemented
8#10595317C2116yesmaximal, direct product factor
9C2×#63939C212yesmaximal, complemented
10C2×#63830C211yesmaximal, characteristic, complemented
11C2×#63823C211yesmaximal, characteristic, complemented
12C2×D3×#208C211yesmaximal, characteristic, complemented
13C2×#5822—31nomaximal
14C2×#5777—31nomaximal
15C22×C32×Q8C2211yescharacteristic, complemented
16C2×#3828C2211yescharacteristic
17C2×C3×#239—21no—
18C2×C3×#239—21no—
19C2×C3×#239—24no—
20C2×C3×#239C2212yes—
21C2×C3×#239C2212yescomplemented
22C2×C3×#239C2218yescomplemented
23C2×C3×#235C2211yescharacteristic
24C22×C3×D12—21no—
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×C4×D3—21no—
27C22×C3×C4×D3C2211yescharacteristic
28C2×D3×#67—21no—
29C2×#3804—21no—
30D3×#235—24no—
31D3×#235C2218yescomplemented
32C2×D3×D12C2211yescharacteristic, complemented
33C2×C4×D32—21no—
34C2×#3799C2211yescharacteristic, complemented
35C2×#3798—21no—
36C2×#3795C2211yescharacteristic, complemented
37C2×D3×Dic6C2211yescharacteristic, complemented
38C2×#3756C2212yescomplemented
39#64151C2218yescomplemented
40C2×#3755C2212yescomplemented
41C2×#3748C2211yescharacteristic, complemented
42C2×C3×#216C2212yescomplemented
43C3×#942C2218yescomplemented
44C2×C3×#215C2212yescomplemented
45C2×C3×#208C2211yescharacteristic, complemented
46#63949C22116yescomplemented
47#63947C22116yescomplemented
48#63943C22116yescomplemented
49#63939C22116yescomplemented
50#63830C2218yescomplemented
51C2×#3716C2212yescomplemented
52C2×#3715C2212yescomplemented
53C2×#3714C2212yescomplemented
54#63823C2218yescomplemented
55C2×#3713C2212yescomplemented
56C2×#3711C2212yescomplemented
57D3×#208C2218yescomplemented
58C2×D3×C3⋊C8C2212yescomplemented
59C22×C3×#41—31no—
60C2×D3×#41—31no—
61C22×#239D311yescharacteristic, complemented
62C22×#235—31no—
63C2×C3×#137—31no—
64C2×#951—32no—
65#5822—316no—
66C2×#950—32no—
67C2×#950—32no—
68C2×#949—31no—
69C2×#949—32no—
70C2×#942—31no—
71C2×#942—31no—
72C2×#942—61no—
73C2×#942D311yescharacteristic, complemented
74C2×#932—31no—
75C2×#932—31no—
76C22×#208—31no—
77#5777—316no—
78C2×#919—32no—
79C2×#918—32no—
80C2×#916—32no—
81C2×#914—32no—
82C2×#908—31no—
83C2×D3×M16—31no—
84C23×C3×D3—21no—
85C23×C3×D3D411yescharacteristic
86C22×D32—21no—
87C2×C32×Q8—21no—
88C2×C32×Q8—22no—
89C2×C32×Q8C2312yes—
90C2×C32×Q8C2314yescomplemented
91C22×C32×C4—21no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94#3828—22no—
95#3828C2314yes—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C22×C3×Dic3D411yescharacteristic
101C3×#239—24no—
102C3×#239—28no—
103C3×#239—24no—
104C3×#239—28no—
105C3×#239C2318yes—
106C3×#239C2318yescomplemented
107C3×#235—22no—
108C3×#235C2314yes—
109C2×C3×D12—22no—
110C2×C3×D12—28no—
111C2×C3×D12—22no—
112C2×C3×D12—22no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2312yes—
116C2×C3×D12C2314yescomplemented
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—28no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3D411yescharacteristic
122C2×C3×C4×D3D411yescharacteristic
123C2×C3×C4×D3D414yes—
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2314yes—
127C2×C3×Dic6C2311yescharacteristic
128D3×#67—28no—
129C2×#627—21no—
130C2×#626—21no—
131C2×#626—21no—
132C2×#625—21no—
133C2×#624—21no—
134#3804—28no—
135C2×D3×Dic3—21no—
136C2×D3×Dic3—21no—
137D3×D12—22no—
138D3×D12C2314yescomplemented
139C4×D32—28no—
140#3799—22no—
141#3799C2314yescomplemented
142#3798—28no—
143#3795—22no—
144#3795C2314yescomplemented
145D3×Dic6—22no—
146D3×Dic6C2314yescomplemented
147#3756C2318yescomplemented
148#3755C2318yescomplemented
149#3748C2314yescomplemented
150C2×C3⋊(C3⋊C8)C2312yes—
151C3×#216C2318yescomplemented
152C3×#215C2318yescomplemented
153C3×#208C2314yescomplemented
154C2×C3×C3⋊C8C2312yes—
155#3716C2318yescomplemented
156#3715C2318yescomplemented
157#3714C2318yescomplemented
158#3713C2318yescomplemented
159#3711C2318yescomplemented
160D3×C3⋊C8C2318yescomplemented
161C2×#575—91noSylow
162C2×C3×#41—32no—
163C2×C3×#41—32no—
164C2×C3×#41—38no—
165C2×C3×#41—31no—
166C2×C3×#41—61no—
167C2×C3×#41—61no—
168C2×C3×#41—64no—
169C22×C3×Q8—21no—
170C22×C3×Q8C2×D311yescharacteristic, complemented
171C22×C3×Q8C2×D311yescharacteristic, complemented
172C22×C3×D4—31no—
173C22×C3×D4—61no—
174C23×C3×C4—31no—
175C23×C3×C4—61no—
176C22×#67—61no—
177D3×#41—38no—
178D3×#41—64no—
179C2×#239—21no—
180C2×#239—21no—
181C2×#239—24no—
182C2×#239—31no—
183C2×#239C2×D312yes—
184C2×#239C2×D312yescomplemented
185C2×#239C2×D318yescomplemented
186C2×D3×Q8—31no—
187C2×#237—31no—
188C2×#237—61no—
189C2×D3×D4—31no—
190C2×D3×D4—61no—
191C2×#235—31no—
192C2×#235—31no—
193C2×#235—38no—
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—61no—
197C2×#235—61no—
198C2×#235—64no—
199C2×#235—61no—
200C2×#235—61no—
201C2×#235C2×D311yescharacteristic
202C22×D12—21no—
203C22×D12—31no—
204C22×D12C2×D311yescharacteristic, complemented
205C22×C4×D3—21no—
206C22×C4×D3—61no—
207C22×C4×D3—61no—
208C22×C4×D3C2×D311yescharacteristic
209C22×Dic6—31no—
210C3×#137—38no—
211C2×C3×Q16—32no—
212C2×C3×SD16—32no—
213C2×C3×M16—31no—
214#951—316no—
215#950—316no—
216#950—316no—
217#949—38no—
218#949—316no—
219C2×#216—32no—
220C2×#216—32no—
221C2×#216—62no—
222C2×#216C2×D312yescomplemented
223#942—38no—
224#942—38no—
225#942—68no—
226#942C2×D318yescomplemented
227C2×#215—32no—
228C2×#215—32no—
229C2×#215—32no—
230C2×#215—62no—
231C2×#215C2×D312yescomplemented
232C2×#214—32no—
233C2×#214—32no—
234#932—38no—
235#932—38no—
236C2×#213—32no—
237C2×#213—32no—
238C2×#213—32no—
239C2×#208—31no—
240C2×#208—31no—
241C2×#208—38no—
242C2×#208—32no—
243C2×#208—61no—
244C2×#208C2×D311yescharacteristic, complemented
245C22×C3⋊C8—32no—
246#919—316no—
247#918—316no—
248#916—316no—
249#914—316no—
250#908—38no—
251D3×M16—38no—
252C2×D24—32no—
253C2×#204—32no—
254C2×ΓL(1,𝔽25)—32no—
255C2×D3×C8—32no—
256C23×C32C2×D411yescharacteristic
257C22×C3⋊D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—22no—
260C22×C3×D3—24no—
261C22×C3×D3—42no—
262C22×C3×D3—44no—
263C22×C3×D3C2×D411yescharacteristic
264C22×C3×D3C2×D411yescharacteristic
265C22×C3×D3C2×D414yes—
266C2×D32—24no—
267C2×D32—44no—
268C32×Q8—22no—
269C32×Q8—24no—
270C32×Q8C2414yes—
271C2×C32×C4—22no—
272C2×C32×C4—24no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2×D412yes—
275C2×C32×C4C2411yescharacteristic
276C2×C32×C4C2412yes—
277#638—24no—
278C2×C3⋊Dic3—21no—
279C4⋊(C3⋊D3)—21no—
280C4⋊(C3⋊D3)C2412yes—
281C4×C3⋊D3—24no—
282#634—21no—
283#634C2412yes—
284C3×#67—24no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3C2×D411yescharacteristic
287C2×C3×Dic3C2×D414yes—
288C2×C3×Dic3C2×D411yescharacteristic
289C3×D12—28no—
290C3×D12—28no—
291C3×D12—21no—
292C3×D12—22no—
293C3×D12—24no—
294C3×D12C2412yes—
295C3×D12C2414yes—
296C3×C4×D3—24no—
297C3×C4×D3—28no—
298C3×C4×D3—28no—
299C3×C4×D3C2×D412yes—
300C3×C4×D3C2×D412yes—
301C3×C4×D3C2×D414yes—
302C3×C4×D3C2×D414yes—
303C3×C4×D3C2412yes—
304C3×C4×D3C2412yes—
305C3×Dic6—21no—
306C3×Dic6C2412yes—
307#627—24no—
308#626—24no—
309#626—24no—
310#625—24no—
311#624—24no—
312D3×Dic3—24no—
313D3×Dic3—24no—
314C3⋊(C3⋊C8)C2414yes—
315C3×C3⋊C8C2414yes—
316C22×#41—31no—
317C22×#41—91no—
318#575—916no—
319C2×#137—31no—
320C2×#137—92no—
321C2×#137—91no—
322C2×AGL(1,ℤ/8)—91no—
323C2×AGL(1,ℤ/8)—92no—
324C2×AGL(1,ℤ/8)—91no—
325C2×#135—92no—
326C2×#135—92no—
327C22×M16—91no—
328C24×C3—31no—
329C24×C3—61no—
330C23×D3—21no—
331C23×D3—61no—
332C23×D3—61no—
333C23×D3#6711yescharacteristic
334C3×#41—38no—
335C3×#41—38no—
336C3×#41—34no—
337C3×#41—64no—
338C3×#41—68no—
339C3×#41—64no—
340C3×#41—68no—
341C3×#41—62no—
342C2×C3×Q8—21no—
343C2×C3×Q8—22no—
344C2×C3×Q8—21no—
345C2×C3×Q8—22no—
346C2×C3×Q8—22no—
347C2×C3×Q8—24no—
348C2×C3×Q8—31no—
349C2×C3×Q8—41no—
350C2×C3×Q8—42no—
351C2×C3×Q8C22×D312yes—
352C2×C3×Q8C22×D312yes—
353C2×C3×Q8C22×D314yescomplemented
354C2×C3×Q8C22×D314yescomplemented
355C2×C3×D4—32no—
356C2×C3×D4—31no—
357C2×C3×D4—34no—
358C2×C3×D4—62no—
359C2×C3×D4—62no—
360C2×C3×D4—68no—
361C2×C3×D4—61no—
362C2×C3×D4—61no—
363C2×C3×D4—62no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—34no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—34no—
374C22×C3×C4—41no—
375C22×C3×C4—62no—
376C22×C3×C4—62no—
377C22×C3×C4—68no—
378C22×C3×C4—61no—
379C22×C3×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C2×#67—21no—
382C2×#67—61no—
383C2×#67—68no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—121no—
390C22×Dic3—61no—
391C22×Dic3—61no—
392C22×Dic3#6711yescharacteristic
393#239—24no—
394#239—28no—
395#239—28no—
396#239—24no—
397#239—34no—
398#239—62no—
399#239C22×D318yes—
400#239C22×D318yescomplemented
401D3×Q8—34no—
402D3×Q8—62no—
403#237—34no—
404#237—68no—
405#237—62no—
406D3×D4—34no—
407D3×D4—68no—
408D3×D4—62no—
409#235—22no—
410#235—34no—
411#235—34no—
412#235—34no—
413#235—34no—
414#235—64no—
415#235—62no—
416#235—68no—
417#235—62no—
418#235—68no—
419#235—62no—
420#235—62no—
421#235—68no—
422#235—122no—
423#235C22×D314yes—
424C2×D12—22no—
425C2×D12—28no—
426C2×D12—22no—
427C2×D12—22no—
428C2×D12—21no—
429C2×D12—31no—
430C2×D12—31no—
431C2×D12—34no—
432C2×D12—61no—
433C2×D12—62no—
434C2×D12—61no—
435C2×D12—61no—
436C2×D12C22×D312yes—
437C2×D12C22×D311yescharacteristic
438C2×D12C22×D314yescomplemented
439C2×C4×D3—21no—
440C2×C4×D3—22no—
441C2×C4×D3—28no—
442C2×C4×D3—22no—
443C2×C4×D3—68no—
444C2×C4×D3—61no—
445C2×C4×D3—61no—
446C2×C4×D3—61no—
447C2×C4×D3—61no—
448C2×C4×D3—61no—
449C2×C4×D3—61no—
450C2×C4×D3—68no—
451C2×C4×D3—121no—
452C2×C4×D3#6711yescharacteristic
453C2×C4×D3#6711yescharacteristic
454C2×C4×D3#6714yes—
455C2×C4×D3C22×D311yescharacteristic
456C2×C4×D3C22×D311yescharacteristic
457C2×C4×D3C22×D314yes—
458C2×Dic6—31no—
459C2×Dic6—31no—
460C2×Dic6—34no—
461C2×Dic6—61no—
462C2×Dic6—62no—
463C2×Dic6—61no—
464C2×Dic6—61no—
465C2×Dic6C22×D311yescharacteristic
466C3×Q16—38no—
467C3×SD16—38no—
468C3×M16—34no—
469C2×C3×C8—32no—
470#216—38no—
471#216—38no—
472#216—68no—
473#216C22×D318yescomplemented
474#215—38no—
475#215—38no—
476#215—38no—
477#215—68no—
478#215C22×D318yescomplemented
479#214—38no—
480#214—38no—
481#213—38no—
482#213—38no—
483#213—38no—
484#208—34no—
485#208—34no—
486#208—38no—
487#208—64no—
488#208C22×D314yescomplemented
489C2×C3⋊C8—32no—
490C2×C3⋊C8—32no—
491C2×C3⋊C8—38no—
492C2×C3⋊C8—62no—
493C2×C3⋊C8C22×D312yes—
494D24—38no—
495#204—38no—
496ΓL(1,𝔽25)—38no—
497D3×C8—38no—
498C22×C32—22no—
499C22×C32C22×D412yes—
500C22×C32C22×D411yescharacteristic
501C2×C3⋊D3—22no—
502C2×C3⋊D3—42no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—24no—
507C2×C3×D3—44no—
508C2×C3×D3—48no—
509C2×C3×D3—42no—
510C2×C3×D3—44no—
511C2×C3×D3C22×D412yes—
512C2×C3×D3C22×D412yes—
513D32—48no—
514C32×C4—24no—
515C32×C4C22×D411yescharacteristic
516C32×C4C22×D412yes—
517C32×C4C2511yescharacteristic
518C3⋊Dic3—22no—
519C3×Dic3—22no—
520C3×Dic3C22×D412yes—
521C3×Dic3C22×D412yes—
522C2×#41—32no—
523C2×#41—32no—
524C2×#41—38no—
525C2×#41—31no—
526C2×#41—61no—
527C2×#41—64no—
528C2×#41—61no—
529C2×#41—91no—
530C2×#41—91no—
531C2×#41—98no—
532C2×#41—91no—
533C2×#41—181no—
534C2×#41—181no—
535C2×#41—184no—
536C22×Q8—91no—
537C22×Q8D3211yescharacteristic, complemented
538C22×D4—31no—
539C22×D4—61no—
540C22×D4—91no—
541C22×D4—181no—
542C23×C4—31no—
543C23×C4—61no—
544C23×C4—181no—
545#137—38no—
546#137—916no—
547#137—98no—
548AGL(1,ℤ/8)—98no—
549AGL(1,ℤ/8)—916no—
550AGL(1,ℤ/8)—98no—
551#135—916no—
552#135—916no—
553C2×Q16—32no—
554C2×Q16—92no—
555C2×SD16—32no—
556C2×SD16—92no—
557C2×SD16—92no—
558C2×SD16—92no—
559C2×D8—92no—
560C2×D8—92no—
561C2×M16—31no—
562C2×M16—92no—
563C2×M16—98no—
564C2×M16—91no—
565C22×C8—92no—
566C23×C3—21no—
567C23×C3—31no—
568C23×C3—31no—
569C23×C3—34no—
570C23×C3—64no—
571C23×C3—62no—
572C23×C3—61no—
573C23×C3—122no—
574C23×C3—124no—
575C23×C3D3×D411yescharacteristic
576C23×C3C2×#6711yescharacteristic
577C22×D3—21no—
578C22×D3—22no—
579C22×D3—24no—
580C22×D3—42no—
581C22×D3—44no—
582C22×D3—64no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—64no—
586C22×D3—121no—
587C22×D3—124no—
588C22×D3—124no—
589C22×D3C2×#6711yescharacteristic
590C22×D3C2×#6711yescharacteristic
591C22×D3C2×#6714yes—
592C3×Q8—22no—
593C3×Q8—24no—
594C3×Q8—22no—
595C3×Q8—24no—
596C3×Q8—24no—
597C3×Q8—32no—
598C3×Q8—42no—
599C3×Q8—44no—
600C3×Q8—61no—
601C3×Q8C23×D314yes—
602C3×Q8C23×D314yes—
603C3×D4—34no—
604C3×D4—32no—
605C3×D4—68no—
606C3×D4—68no—
607C3×D4—64no—
608C3×D4—62no—
609C3×D4—64no—
610C3×D4—61no—
611C2×C3×C4—22no—
612C2×C3×C4—24no—
613C2×C3×C4—22no—
614C2×C3×C4—24no—
615C2×C3×C4—21no—
616C2×C3×C4—22no—
617C2×C3×C4—21no—
618C2×C3×C4—22no—
619C2×C3×C4—31no—
620C2×C3×C4—31no—
621C2×C3×C4—34no—
622C2×C3×C4—32no—
623C2×C3×C4—34no—
624C2×C3×C4—34no—
625C2×C3×C4—32no—
626C2×C3×C4—32no—
627C2×C3×C4—32no—
628C2×C3×C4—44no—
629C2×C3×C4—42no—
630C2×C3×C4—68no—
631C2×C3×C4—68no—
632C2×C3×C4—61no—
633C2×C3×C4—64no—
634C2×C3×C4D3×D411yescharacteristic
635C2×C3×C4D3×D412yes—
636C2×C3×C4C2×#6711yescharacteristic
637C2×C3×C4C2×#6712yes—
638C2×C3×C4C23×D311yescharacteristic
639C2×C3×C4C23×D312yes—
640C2×C3×C4C23×D311yescharacteristic
641C2×C3×C4C23×D312yes—
642#67—24no—
643#67—64no—
644#67—64no—
645#67—64no—
646#67—64no—
647#67—64no—
648#67—64no—
649#67—124no—
650C2×Dic3—21no—
651C2×Dic3—64no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—64no—
655C2×Dic3—121no—
656C2×Dic3C2×#6711yescharacteristic
657C2×Dic3C2×#6711yescharacteristic
658C2×Dic3C2×#6714yes—
659D12—28no—
660D12—28no—
661D12—21no—
662D12—22no—
663D12—24no—
664D12—32no—
665D12—32no—
666D12—62no—
667D12—64no—
668D12—64no—
669D12—61no—
670D12—61no—
671D12—121no—
672D12C23×D314yes—
673D12C23×D312yes—
674C4×D3—24no—
675C4×D3—28no—
676C4×D3—28no—
677C4×D3—64no—
678C4×D3—64no—
679C4×D3—64no—
680C4×D3—64no—
681C4×D3—64no—
682C4×D3—64no—
683C4×D3—124no—
684C4×D3C2×#6714yes—
685C4×D3C2×#6714yes—
686C4×D3C2×#6712yes—
687C4×D3C2×#6712yes—
688C4×D3C23×D312yes—
689C4×D3C23×D312yes—
690Dic6—21no—
691Dic6—32no—
692Dic6—32no—
693Dic6—62no—
694Dic6—64no—
695Dic6—61no—
696Dic6—61no—
697Dic6—64no—
698Dic6—121no—
699Dic6C23×D312yes—
700C3×C8—34no—
701C3⋊C8—34no—
702C3⋊C8—34no—
703C3⋊C8—64no—
704C3⋊C8C23×D314yes—
705C2×C32—22no—
706C2×C32#57512yescomplemented
707C2×C32C23×D411yescharacteristic
708C3⋊D3—42no—
709C3×D3—22no—
710C3×D3—22no—
711C3×D3—42no—
712C3×D3—44no—
713C24—31no—
714C24—61no—
715C24—181no—
716#41—38no—
717#41—38no—
718#41—34no—
719#41—68no—
720#41—64no—
721#41—64no—
722#41—68no—
723#41—62no—
724#41—94no—
725#41—94no—
726#41—94no—
727#41—188no—
728#41—188no—
729#41—182no—
730#41—182no—
731#41—182no—
732C2×Q8—22no—
733C2×Q8—21no—
734C2×Q8—31no—
735C2×Q8—94no—
736C2×Q8—91no—
737C2×Q8—181no—
738C2×Q8—182no—
739C2×Q8C2×D3212yes—
740C2×Q8C2×D3214yescomplemented
741C2×D4—31no—
742C2×D4—32no—
743C2×D4—34no—
744C2×D4—68no—
745C2×D4—62no—
746C2×D4—62no—
747C2×D4—61no—
748C2×D4—62no—
749C2×D4—61no—
750C2×D4—94no—
751C2×D4—91no—
752C2×D4—182no—
753C2×D4—181no—
754C2×D4—181no—
755C2×D4—188no—
756C2×D4—181no—
757C2×D4—181no—
758C22×C4—21no—
759C22×C4—31no—
760C22×C4—31no—
761C22×C4—31no—
762C22×C4—34no—
763C22×C4—31no—
764C22×C4—34no—
765C22×C4—31no—
766C22×C4—68no—
767C22×C4—62no—
768C22×C4—62no—
769C22×C4—61no—
770C22×C4—181no—
771C22×C4—188no—
772C22×C4—181no—
773C22×C4—181no—
774C22×C4—181no—
775C22×C4C2×D3211yescharacteristic
776Q16—38no—
777Q16—98no—
778SD16—38no—
779SD16—98no—
780SD16—98no—
781SD16—98no—
782D8—98no—
783D8—98no—
784M16—34no—
785M16—98no—
786M16—94no—
787C2×C8—32no—
788C2×C8—98no—
789C2×C8—92no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—22no—
793C22×C3—21no—
794C22×C3—32no—
795C22×C3—32no—
796C22×C3—42no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—64no—
800C22×C3—62no—
801C22×C3—124no—
802C22×C3—128no—
803C22×C3—124no—
804C22×C3—122no—
805C22×C3C2×D3×D412yes—
806C22×C3C2×D3×D411yescharacteristic
807C22×C3C22×#6712yes—
808C22×C3C22×#6711yescharacteristic
809C2×D3—22no—
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—24no—
813C2×D3—44no—
814C2×D3—48no—
815C2×D3—42no—
816C2×D3—44no—
817C2×D3—62no—
818C2×D3—62no—
819C2×D3—122no—
820C2×D3—128no—
821C2×D3—128no—
822C2×D3—122no—
823C2×D3—122no—
824C2×D3—242no—
825C2×D3C22×#6712yes—
826C2×D3C22×#6712yes—
827C3×C4—24no—
828C3×C4—24no—
829C3×C4—21no—
830C3×C4—22no—
831C3×C4—21no—
832C3×C4—32no—
833C3×C4—32no—
834C3×C4—44no—
835C3×C4—62no—
836C3×C4C2×D3×D411yescharacteristic
837C3×C4C2×D3×D412yes—
838C3×C4C22×#6711yescharacteristic
839C3×C4C22×#6712yes—
840C3×C4C24×D311yescharacteristic
841C3×C4C24×D311yescharacteristic
842Dic3—22no—
843Dic3—62no—
844Dic3—62no—
845Dic3—122no—
846Dic3C22×#6712yes—
847Dic3C22×#6712yes—
848C32C2×#57511yescharacteristic, complemented, Sylow
849C23—31no—
850C23—31no—
851C23—34no—
852C23—64no—
853C23—62no—
854C23—61no—
855C23—122no—
856C23—124no—
857C23—184no—
858C23—181no—
859C23—364no—
860C23D3×#6711yescharacteristic
861Q8—22no—
862Q8—24no—
863Q8—32no—
864Q8—61no—
865Q8—92no—
866Q8—184no—
867Q8—181no—
868Q8C22×D3214yes—
869D4—32no—
870D4—34no—
871D4—68no—
872D4—68no—
873D4—64no—
874D4—64no—
875D4—62no—
876D4—61no—
877D4—92no—
878D4—184no—
879D4—184no—
880D4—184no—
881D4—184no—
882D4—181no—
883C2×C4—24no—
884C2×C4—22no—
885C2×C4—34no—
886C2×C4—31no—
887C2×C4—31no—
888C2×C4—34no—
889C2×C4—32no—
890C2×C4—32no—
891C2×C4—34no—
892C2×C4—32no—
893C2×C4—32no—
894C2×C4—68no—
895C2×C4—68no—
896C2×C4—61no—
897C2×C4—64no—
898C2×C4—184no—
899C2×C4—184no—
900C2×C4—184no—
901C2×C4—181no—
902C2×C4—184no—
903C2×C4D3×#6712yes—
904C2×C4D3×#6711yescharacteristic
905C2×C4C22×D3212yes—
906C2×C4C22×D3211yescharacteristic
907C8—34no—
908C8—94no—
909C2×C3—22no—
910C2×C3—22no—
911C2×C3—21no—
912C2×C3—22no—
913C2×C3—42no—
914C2×C3—62no—
915C2×C3—62no—
916C2×C3—124no—
917C2×C3—122no—
918C2×C3#577712yescomplemented
919C2×C3#582212yescomplemented
920C2×C3C22×D3×D411yescharacteristic
921C2×C3C23×#6711yescharacteristic
922D3—22no—
923D3—22no—
924D3—42no—
925D3—44no—
926D3—122no—
927D3—122no—
928D3—242no—
929C22—22no—
930C22—32no—
931C22—32no—
932C22—62no—
933C22—62no—
934C22—64no—
935C22—62no—
936C22—124no—
937C22—128no—
938C22—124no—
939C22—122no—
940C22—182no—
941C22—368no—
942C22—362no—
943C22C2×D3×#6712yes—
944C22C2×D3×#6711yescharacteristic
945C4—24no—
946C4—32no—
947C4—32no—
948C4—62no—
949C4—182no—
950C4C2×D3×#6712yes—
951C4C2×D3×#6711yescharacteristic
952C4C23×D3211yescharacteristic
953C3—21no—
954C3C2×#577711yescharacteristic, complemented
955C3C2×#582211yescharacteristic, complemented
956C2—22no—
957C2—62no—
958C2—62no—
959C2—124no—
960C2—122no—
961C2—362no—
962C2#1059531712yesdirect product factor
963C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
hypercenterC22×Q8D32
hypocenterC32C2×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C2×D3×#235C2semidirect
3. C2×#64151C2semidirect
4. C2×C3×#942C2semidirect
5. C2×#63949C2semidirect
6. C2×#63947C2semidirect
7. C2×#63943C2semidirect
8. #10595317C2direct (N × H)
9. C2×#63939C2semidirect
10. C2×#63830C2semidirect
11. C2×#63823C2semidirect
12. C2×D3×#208C2semidirect
15. C22×C32×Q8C22semidirect
21. C2×C3×#239C22semidirect
22. C2×C3×#239C22semidirect
25. C22×C3×D12C22semidirect
31. D3×#235C22semidirect
32. C2×D3×D12C22semidirect
34. C2×#3799C22semidirect
36. C2×#3795C22semidirect
37. C2×D3×Dic6C22semidirect
38. C2×#3756C22semidirect
39. #64151C22semidirect
40. C2×#3755C22semidirect
41. C2×#3748C22semidirect
42. C2×C3×#216C22semidirect
43. C3×#942C22semidirect
44. C2×C3×#215C22semidirect
45. C2×C3×#208C22semidirect
46. #63949C22semidirect
47. #63947C22semidirect
48. #63943C22semidirect
49. #63939C22semidirect
50. #63830C22semidirect
51. C2×#3716C22semidirect
52. C2×#3715C22semidirect
53. C2×#3714C22semidirect
54. #63823C22semidirect
55. C2×#3713C22semidirect
56. C2×#3711C22semidirect
57. D3×#208C22semidirect
58. C2×D3×C3⋊C8C22semidirect
61. C22×#239D3semidirect
73. C2×#942D3semidirect
90. C2×C32×Q8C23semidirect
106. C3×#239C23semidirect
116. C2×C3×D12C23semidirect
138. D3×D12C23semidirect
141. #3799C23semidirect
144. #3795C23semidirect
146. D3×Dic6C23semidirect
147. #3756C23semidirect
148. #3755C23semidirect
149. #3748C23semidirect
151. C3×#216C23semidirect
152. C3×#215C23semidirect
153. C3×#208C23semidirect
155. #3716C23semidirect
156. #3715C23semidirect
157. #3714C23semidirect
158. #3713C23semidirect
159. #3711C23semidirect
160. D3×C3⋊C8C23semidirect
170. C22×C3×Q8C2×D3semidirect
171. C22×C3×Q8C2×D3semidirect
184. C2×#239C2×D3semidirect
185. C2×#239C2×D3semidirect
204. C22×D12C2×D3semidirect
222. C2×#216C2×D3semidirect
226. #942C2×D3semidirect
231. C2×#215C2×D3semidirect
244. C2×#208C2×D3semidirect
353. C2×C3×Q8C22×D3semidirect
354. C2×C3×Q8C22×D3semidirect
400. #239C22×D3semidirect
438. C2×D12C22×D3semidirect
473. #216C22×D3semidirect
478. #215C22×D3semidirect
488. #208C22×D3semidirect
537. C22×Q8D32semidirect
706. C2×C32#575semidirect
740. C2×Q8C2×D32semidirect
848. C32C2×#575semidirect
918. C2×C3#5777semidirect
919. C2×C3#5822semidirect
954. C3C2×#5777semidirect
955. C3C2×#5822semidirect
962. C2#10595317direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C2×D3×#2352
C2×#641512
C2×C3×#9422
C2×#639492
C2×#639472
C2×#639432
#105953172
C2×#639392
C2×#638302
C2×#638232
C2×D3×#2082
C2×#58223
C2×#57773