Finite Group Databasebeta

← C2×#10595462 #11918885

Subgroups — C2×#10595462 #11918885

Order 1152.

3317 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3C2×C3×#950C211yesmaximal, characteristic, complemented
4C2×C3×#949C211yesmaximal, characteristic, complemented
5#10595462C2116yesmaximal, direct product factor
6C2×#63951C212yesmaximal, complemented
7C2×#63940C212yesmaximal, complemented
8C2×#63936C212yesmaximal, complemented
9C2×#63927C212yesmaximal, complemented
10C2×#63831C211yesmaximal, characteristic, complemented
11C22×#3716C211yesmaximal, characteristic, complemented
12C2×#63817C211yesmaximal, characteristic, complemented
13C2×#5775—31nomaximal
14C2×#5770—31nomaximal
15C2×C32×#41C2211yescharacteristic, complemented
16#64367—24no—
17#64367C2218yescomplemented
18C2×Q8×C3⋊D3C2212yescomplemented
19C2×#3830—22no—
20C2×#3830C2212yescomplemented
21C2×#3828—21no—
22C2×#3828C2211yescharacteristic
23C22×#634—21no—
24C22×#634C2211yescharacteristic, complemented
25C2×C3×#235C2211yescharacteristic
26C22×C3×D12C2211yescharacteristic
27C2×D3×#67—22no—
28#64307—24no—
29#64307C2218yescomplemented
30C2×#3802C2212yes—
31C2×D3×D12—21no—
32C2×#3796C2212yes—
33C2×#3795—21no—
34C3×#950C2218yescomplemented
35C3×#949C2218yescomplemented
36C2×C3×#216C2211yescharacteristic, complemented
37C2×C3×#215C2212yescomplemented
38C2×C3×#215C2211yescharacteristic, complemented
39C2×C3×#214C2211yescharacteristic, complemented
40C2×C3×#213C2211yescharacteristic, complemented
41C2×C3×#213C2212yescomplemented
42C2×C3×#208C2211yescharacteristic, complemented
43C22×C3×C3⋊C8C2211yescharacteristic, complemented
44#63951C22116yescomplemented
45#63940C22116yescomplemented
46#63936C22116yescomplemented
47#63927C22116yescomplemented
48C2×#3719C2212yescomplemented
49#63831C2218yescomplemented
50C2×#3716C2212yescomplemented
51C2×#3716C2212yescomplemented
52C2×#3716C2212yescomplemented
53C2×#3716C2218yescomplemented
54C2×#3712C2212yescomplemented
55#63817C2218yescomplemented
56C2×#3710C2212yescomplemented
57C2×#1010—31no—
58C2×#1010—31no—
59C2×#1010—61no—
60C2×#1009—31no—
61C2×#1004—31no—
62C2×C3×AGL(1,ℤ/8)—31no—
63C2×C3×#135—31no—
64C2×#951—31no—
65C2×#950D311yescharacteristic, complemented
66C2×#949D311yescharacteristic, complemented
67C22×#214—31no—
68#5775—316no—
69#5770—316no—
70C2×#918—32no—
71C2×#916—32no—
72C2×#915—32no—
73C2×D3×SD16—32no—
74C2×D3×SD16—32no—
75C2×#912—32no—
76C2×#911—32no—
77C2×#911—32no—
78C2×#909—31no—
79C2×#907—31no—
80C22×#204—31no—
81C2×#901—31no—
82C23×C3×D3—21no—
83C22×D32—22no—
84C32×#41—22no—
85C32×#41C2314yescomplemented
86C2×C32×Q8C2311yescharacteristic
87C2×C32×D4—21no—
88C2×C32×D4C2311yescharacteristic
89C22×C32×C4—21no—
90C22×C32×C4C2311yescharacteristic
91C2×#638—22no—
92C2×#638D412yes—
93C22×C3⋊Dic3—21no—
94C22×C3⋊Dic3—22no—
95Q8×C3⋊D3—24no—
96Q8×C3⋊D3C2318yescomplemented
97#3830—216no—
98#3830—24no—
99#3830C2318yescomplemented
100#3828—28no—
101#3828D414yes—
102#3828C2314yes—
103C2×C4⋊(C3⋊D3)D411yescharacteristic
104C2×C4×C3⋊D3—22no—
105C2×C4×C3⋊D3C2312yes—
106C2×#634—21no—
107C2×#634—22no—
108C2×#634—22no—
109C2×#634—28no—
110C2×#634D411yescharacteristic
111C2×#634C2312yes—
112C2×#634C2314yescomplemented
113C2×C3×#67—21no—
114C3×#235—22no—
115C3×#235C2314yes—
116C2×C3×D12—21no—
117C2×C3×D12—22no—
118C2×C3×D12C2312yes—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2314yes—
121C2×C3×C4×D3—21no—
122C2×C3×Dic6C2311yescharacteristic
123D3×#67—216no—
124C2×#626—22no—
125C2×#625—22no—
126C2×D3×Dic3—22no—
127#3802—24no—
128#3802C2318yes—
129D3×D12—28no—
130#3796—24no—
131#3796C2318yes—
132#3795—28no—
133C3×#216C2314yescomplemented
134C3×#215C2318yescomplemented
135C3×#215C2314yescomplemented
136C3×#214C2314yescomplemented
137C3×#213C2318yescomplemented
138C3×#213C2314yescomplemented
139C3×#208C2314yescomplemented
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2312yes—
143C2×C3×C3⋊C8C2314yescomplemented
144#3719C2318yescomplemented
145#3716C2318yescomplemented
146#3716C2318yescomplemented
147#3716C2318yescomplemented
148#3712C2318yescomplemented
149#3710C2318yescomplemented
150C2×#577—91noSylow
151C2×C3×#41—21no—
152C2×C3×#41—31no—
153C2×C3×#41C2×D311yescharacteristic, complemented
154C2×C3×#41C2×D311yescharacteristic, complemented
155C22×C3×D4—31no—
156C22×#67—62no—
157#1010—38no—
158#1010—38no—
159#1010—68no—
160#1010—64no—
161#1010—64no—
162#1010—68no—
163#1009—38no—
164#1009—64no—
165C2×#239—32no—
166C2×D3×Q8—32no—
167C2×D3×Q8—32no—
168C2×D3×Q8—62no—
169#1004—38no—
170#1004—64no—
171C2×#237—32no—
172C2×#237—32no—
173C2×#237—32no—
174C2×#237—62no—
175C2×#237—61no—
176C2×#237—62no—
177C2×#237—62no—
178C2×#237—64no—
179C2×D3×D4—32no—
180C2×D3×D4—32no—
181C2×D3×D4—61no—
182C2×D3×D4—62no—
183C2×#235—31no—
184C2×#235—31no—
185C2×#235—61no—
186C2×#235—61no—
187C2×#235—61no—
188C2×#235—61no—
189C2×#235—62no—
190C2×#235C2×D311yescharacteristic
191C22×D12—61no—
192C22×D12C2×D311yescharacteristic
193C22×Dic6—31no—
194C22×Dic6—31no—
195C22×Dic6—61no—
196C22×Dic6—61no—
197C22×Dic6—61no—
198C22×Dic6—62no—
199C3×AGL(1,ℤ/8)—38no—
200C3×#135—38no—
201C2×C3×Q16—31no—
202C2×C3×SD16—31no—
203C2×C3×SD16—32no—
204C2×C3×SD16—31no—
205C2×C3×D8—31no—
206C2×C3×D8—32no—
207C2×C3×M16—31no—
208C22×C3×C8—31no—
209#951—38no—
210#950C2×D318yescomplemented
211#949C2×D318yescomplemented
212C2×#216—32no—
213C2×#216C2×D311yescharacteristic, complemented
214C2×#215C2×D311yescharacteristic, complemented
215C2×#215C2×D312yescomplemented
216C2×#214—32no—
217C2×#214—32no—
218C2×#214—32no—
219C2×#214—38no—
220C2×#214C2×D311yescharacteristic, complemented
221C2×#213C2×D311yescharacteristic, complemented
222C2×#213C2×D312yescomplemented
223C2×#208C2×D311yescharacteristic, complemented
224C22×C3⋊C8C2×D311yescharacteristic, complemented
225#918—316no—
226#916—316no—
227#915—316no—
228D3×SD16—316no—
229D3×SD16—316no—
230#912—316no—
231#911—316no—
232#911—316no—
233#909—38no—
234#907—38no—
235C2×Dic12—32no—
236C2×#204—32no—
237C2×#204—32no—
238C2×#204—38no—
239C2×#204—32no—
240#901—38no—
241C2×ΓL(1,𝔽25)—32no—
242C2×ΓL(1,𝔽25)—32no—
243C2×D3×C8—32no—
244C2×D3×C8—32no—
245C23×C32—21no—
246C23×C32C2×D411yescharacteristic
247C22×C3⋊D3C2×D412yes—
248C22×C3×D3—21no—
249C22×C3×D3—22no—
250C22×C3×D3—24no—
251C22×C3×D3—82no—
252C2×D32—28no—
253C2×D32—84no—
254C32×Q8—21no—
255C32×Q8C2412yes—
256C32×D4—24no—
257C32×D4—21no—
258C32×D4C2412yes—
259C2×C32×C4—21no—
260C2×C32×C4—24no—
261C2×C32×C4C2×D411yescharacteristic
262C2×C32×C4C2×D412yes—
263C2×C32×C4C2411yescharacteristic
264C2×C32×C4C2412yes—
265#638—28no—
266#638C2×D418yes—
267C2×C3⋊Dic3—22no—
268C2×C3⋊Dic3—24no—
269C2×C3⋊Dic3—28no—
270C2×C3⋊Dic3C2×D412yes—
271C4⋊(C3⋊D3)C2×D414yes—
272C4×C3⋊D3—28no—
273C4×C3⋊D3C2×D414yes—
274C4×C3⋊D3C2414yes—
275#634—24no—
276#634—22no—
277#634—28no—
278#634C2×D414yes—
279#634C2414yes—
280C3×#67—24no—
281C2×C3×Dic3—21no—
282C3×D12—24no—
283C3×D12—22no—
284C3×D12—21no—
285C3×D12C2414yes—
286C3×D12C2412yes—
287C3×C4×D3—24no—
288C3×Dic6—21no—
289C3×Dic6C2412yes—
290#626—28no—
291#625—28no—
292D3×Dic3—28no—
293C3×C3⋊C8C2412yes—
294C3×C3⋊C8C2414yes—
295C3×C3⋊C8C2412yes—
296C2×2−1+4—91no—
297C2×H(5,𝔽2)—91no—
298#577—916no—
299C2×#137—91no—
300C2×#137—92no—
301C2×AGL(1,ℤ/8)—31no—
302C2×AGL(1,ℤ/8)—92no—
303C2×#135—31no—
304C2×#135—92no—
305C22×SD16—91no—
306C22×SD16—92no—
307C2×#131—91no—
308C24×C3—61no—
309C23×D3—21no—
310C23×D3—62no—
311C23×D3—62no—
312C3×#41—24no—
313C3×#41—22no—
314C3×#41—22no—
315C3×#41—24no—
316C3×#41—34no—
317C3×#41—62no—
318C3×#41C22×D314yescomplemented
319C3×#41C22×D314yescomplemented
320C2×C3×Q8—21no—
321C2×C3×Q8—31no—
322C2×C3×Q8C22×D311yescharacteristic
323C2×C3×Q8C22×D311yescharacteristic
324C2×C3×D4—22no—
325C2×C3×D4—21no—
326C2×C3×D4—21no—
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—32no—
330C2×C3×D4—34no—
331C2×C3×D4—61no—
332C2×C3×D4—61no—
333C2×C3×D4—62no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—22no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—61no—
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C2×#67—21no—
344C2×#67—32no—
345C2×#67—32no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—62no—
350C2×#67—616no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67—64no—
354C22×Dic3—62no—
355C22×Dic3—62no—
356C22×Dic3—62no—
357C22×Dic3—64no—
358C22×Dic3—62no—
359C22×Dic3—61no—
360C22×Dic3—61no—
361#239—38no—
362#239—64no—
363D3×Q8—38no—
364D3×Q8—38no—
365D3×Q8—68no—
366D3×Q8—64no—
367D3×Q8—64no—
368D3×Q8—68no—
369#237—38no—
370#237—38no—
371#237—38no—
372#237—68no—
373#237—64no—
374#237—68no—
375#237—64no—
376#237—64no—
377#237—616no—
378#237—616no—
379#237—68no—
380#237—632no—
381D3×D4—38no—
382D3×D4—38no—
383D3×D4—68no—
384D3×D4—64no—
385D3×D4—64no—
386D3×D4—616no—
387#235—22no—
388#235—34no—
389#235—34no—
390#235—34no—
391#235—34no—
392#235—64no—
393#235—64no—
394#235—68no—
395#235—68no—
396#235—68no—
397#235—616no—
398#235C22×D314yes—
399C2×D12—21no—
400C2×D12—22no—
401C2×D12—31no—
402C2×D12—31no—
403C2×D12—61no—
404C2×D12—68no—
405C2×D12—62no—
406C2×D12C22×D312yes—
407C2×D12C22×D311yescharacteristic
408C2×D12C22×D314yes—
409C2×C4×D3—21no—
410C2×C4×D3—32no—
411C2×C4×D3—32no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—62no—
416C2×C4×D3—64no—
417C2×Dic6—31no—
418C2×Dic6—31no—
419C2×Dic6—32no—
420C2×Dic6—34no—
421C2×Dic6—32no—
422C2×Dic6—34no—
423C2×Dic6—61no—
424C2×Dic6—62no—
425C2×Dic6—64no—
426C2×Dic6—68no—
427C2×Dic6—68no—
428C2×Dic6—62no—
429C2×Dic6—62no—
430C2×Dic6—62no—
431C2×Dic6—64no—
432C2×Dic6—616no—
433C2×Dic6—64no—
434C2×Dic6—61no—
435C2×Dic6—61no—
436C2×Dic6—62no—
437C2×Dic6—62no—
438C2×Dic6C22×D311yescharacteristic
439C3×Q16—34no—
440C3×SD16—34no—
441C3×SD16—38no—
442C3×SD16—34no—
443C3×D8—34no—
444C3×D8—38no—
445C3×M16—34no—
446C2×C3×C8—31no—
447C2×C3×C8—32no—
448C2×C3×C8—31no—
449C2×C3×C8—34no—
450#216—38no—
451#216C22×D314yescomplemented
452#215C22×D314yescomplemented
453#215C22×D318yescomplemented
454#214—38no—
455#214—38no—
456#214—38no—
457#214C22×D314yescomplemented
458#213C22×D314yescomplemented
459#213C22×D318yescomplemented
460#208C22×D314yescomplemented
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D312yes—
463C2×C3⋊C8C22×D311yescharacteristic
464C2×C3⋊C8C22×D314yescomplemented
465Dic12—38no—
466#204—38no—
467#204—38no—
468#204—38no—
469ΓL(1,𝔽25)—38no—
470ΓL(1,𝔽25)—38no—
471D3×C8—38no—
472D3×C8—38no—
473C22×C32—22no—
474C22×C32—22no—
475C22×C32—42no—
476C22×C32C22×D412yes—
477C22×C32C22×D411yescharacteristic
478C2×C3⋊D3—24no—
479C2×C3⋊D3C22×D414yes—
480C2×C3×D3—24no—
481C2×C3×D3—22no—
482C2×C3×D3—42no—
483C2×C3×D3—44no—
484C2×C3×D3—84no—
485D32—88no—
486C32×C4—22no—
487C32×C4C22×D411yescharacteristic
488C32×C4C22×D412yes—
489C32×C4C2511yescharacteristic
490C3⋊Dic3—24no—
491C3⋊Dic3C22×D414yes—
492C3×Dic3—22no—
4932−1+4—98no—
4942−1+4—184no—
495H(5,𝔽2)—98no—
496H(5,𝔽2)—184no—
497C2×#41—31no—
498C2×#41—91no—
499C2×#41—92no—
500C2×#41—92no—
501C2×#41—181no—
502C2×#41—181no—
503C2×#41—182no—
504C2×#41D3211yescharacteristic, complemented
505C22×Q8—92no—
506C22×Q8—91no—
507C22×Q8—181no—
508C22×D4—31no—
509C22×D4—92no—
510C22×D4—181no—
511C22×D4—182no—
512#137—98no—
513#137—916no—
514AGL(1,ℤ/8)—38no—
515AGL(1,ℤ/8)—916no—
516#135—38no—
517#135—916no—
518C2×Q16—31no—
519C2×Q16—92no—
520C2×SD16—31no—
521C2×SD16—32no—
522C2×SD16—31no—
523C2×SD16—92no—
524C2×SD16—92no—
525C2×SD16—92no—
526C2×SD16—98no—
527C2×SD16—916no—
528C2×D8—31no—
529C2×D8—32no—
530#131—98no—
531C2×M16—31no—
532C2×M16—92no—
533C22×C8—31no—
534C22×C8—92no—
535C23×C3—22no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—21no—
539C23×C3—62no—
540C23×C3—61no—
541C23×C3—64no—
542C23×C3—242no—
543C23×C3D3×D411yescharacteristic
544C23×C3D3×D411yescharacteristic
545C22×D3—21no—
546C22×D3—22no—
547C22×D3—24no—
548C22×D3—32no—
549C22×D3—32no—
550C22×D3—62no—
551C22×D3—68no—
552C22×D3—68no—
553C22×D3—82no—
554C22×D3—244no—
555C22×D3—244no—
556C3×Q8—22no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—22no—
560C3×Q8—32no—
561C3×Q8—61no—
562C3×Q8C23×D312yes—
563C3×Q8C23×D312yes—
564C3×D4—28no—
565C3×D4—22no—
566C3×D4—24no—
567C3×D4—24no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—22no—
571C3×D4—32no—
572C3×D4—34no—
573C3×D4—64no—
574C3×D4—61no—
575C3×D4—62no—
576C3×D4—64no—
577C3×D4C23×D312yes—
578C3×D4C23×D312yes—
579C2×C3×C4—22no—
580C2×C3×C4—28no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—24no—
584C2×C3×C4—24no—
585C2×C3×C4—21no—
586C2×C3×C4—22no—
587C2×C3×C4—21no—
588C2×C3×C4—22no—
589C2×C3×C4—61no—
590C2×C3×C4—64no—
591C2×C3×C4D3×D411yescharacteristic
592C2×C3×C4D3×D411yescharacteristic
593C2×C3×C4D3×D412yes—
594C2×C3×C4D3×D412yes—
595C2×C3×C4C23×D311yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597C2×C3×C4C23×D312yes—
598C2×C3×C4C23×D312yes—
599#67—24no—
600#67—38no—
601#67—38no—
602#67—68no—
603#67—68no—
604#67—68no—
605#67—68no—
606#67—68no—
607#67—68no—
608#67—616no—
609C2×Dic3—21no—
610C2×Dic3—32no—
611C2×Dic3—32no—
612C2×Dic3—62no—
613C2×Dic3—68no—
614C2×Dic3—68no—
615C2×Dic3—68no—
616C2×Dic3—64no—
617C2×Dic3—616no—
618C2×Dic3—68no—
619C2×Dic3—62no—
620C2×Dic3—62no—
621C2×Dic3—64no—
622C2×Dic3—64no—
623D12—24no—
624D12—22no—
625D12—21no—
626D12—34no—
627D12—34no—
628D12—64no—
629D12—68no—
630D12C23×D314yes—
631D12C23×D312yes—
632C4×D3—24no—
633C4×D3—34no—
634C4×D3—34no—
635C4×D3—34no—
636C4×D3—34no—
637C4×D3—64no—
638C4×D3—64no—
639C4×D3—68no—
640C4×D3—68no—
641C4×D3—68no—
642C4×D3—616no—
643Dic6—21no—
644Dic6—34no—
645Dic6—34no—
646Dic6—34no—
647Dic6—34no—
648Dic6—64no—
649Dic6—64no—
650Dic6—68no—
651Dic6—68no—
652Dic6—68no—
653Dic6—616no—
654Dic6—64no—
655Dic6—64no—
656Dic6—64no—
657Dic6—62no—
658Dic6—62no—
659Dic6C23×D312yes—
660C3×C8—32no—
661C3×C8—34no—
662C3×C8—32no—
663C3⋊C8C23×D312yes—
664C3⋊C8C23×D314yes—
665C3⋊C8C23×D312yes—
666C2×C32—22no—
667C2×C32—42no—
668C2×C32#57712yescomplemented
669C2×C32C23×D411yescharacteristic
670C3⋊D3—24no—
671C3×D3—42no—
672C3×D3—44no—
673C24—61no—
674C24—182no—
675#41—22no—
676#41—34no—
677#41—62no—
678#41—94no—
679#41—94no—
680#41—98no—
681#41—98no—
682#41—188no—
683#41—188no—
684#41—184no—
685#41—184no—
686#41—1816no—
687#41C2×D3214yescomplemented
688C2×Q8—31no—
689C2×Q8—91no—
690C2×Q8—98no—
691C2×Q8—92no—
692C2×Q8—94no—
693C2×Q8—182no—
694C2×Q8—188no—
695C2×Q8—184no—
696C2×Q8—181no—
697C2×Q8—182no—
698C2×Q8C2×D3211yescharacteristic
699C2×D4—21no—
700C2×D4—32no—
701C2×D4—31no—
702C2×D4—34no—
703C2×D4—61no—
704C2×D4—61no—
705C2×D4—62no—
706C2×D4—98no—
707C2×D4—92no—
708C2×D4—91no—
709C2×D4—188no—
710C2×D4—182no—
711C2×D4—184no—
712C2×D4—182no—
713C2×D4—1816no—
714C2×D4—182no—
715C2×D4C2×D3211yescharacteristic
716C22×C4—21no—
717C22×C4—61no—
718C22×C4—92no—
719C22×C4—182no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—181no—
723C22×C4C2×D3211yescharacteristic
724Q16—34no—
725Q16—98no—
726SD16—34no—
727SD16—38no—
728SD16—34no—
729SD16—98no—
730SD16—98no—
731SD16—98no—
732D8—34no—
733D8—38no—
734M16—34no—
735M16—98no—
736C2×C8—31no—
737C2×C8—31no—
738C2×C8—34no—
739C2×C8—32no—
740C2×C8—98no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—24no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—21no—
748C22×C3—42no—
749C22×C3—44no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—64no—
753C22×C3—62no—
754C22×C3—124no—
755C22×C3—122no—
756C22×C3—244no—
757C22×C3C2×D3×D412yes—
758C22×C3C2×D3×D412yes—
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C2×D3—22no—
762C2×D3—24no—
763C2×D3—34no—
764C2×D3—34no—
765C2×D3—42no—
766C2×D3—44no—
767C2×D3—64no—
768C2×D3—64no—
769C2×D3—64no—
770C2×D3—84no—
771C2×D3—124no—
772C2×D3—248no—
773C2×D3—248no—
774C3×C4—24no—
775C3×C4—22no—
776C3×C4—22no—
777C3×C4—22no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—62no—
781C3×C4C2×D3×D411yescharacteristic
782C3×C4C2×D3×D412yes—
783C3×C4C2×D3×D412yes—
784C3×C4C2×D3×D411yescharacteristic
785C3×C4C24×D311yescharacteristic
786C3×C4C24×D311yescharacteristic
787Dic3—22no—
788Dic3—34no—
789Dic3—34no—
790Dic3—64no—
791Dic3—68no—
792Dic3—64no—
793Dic3—64no—
794C32C2×#57711yescharacteristic, complemented, Sylow
795C23—21no—
796C23—61no—
797C23—62no—
798C23—64no—
799C23—92no—
800C23—188no—
801C23—242no—
802C23—724no—
803C23#381111yescharacteristic
804Q8—21no—
805Q8—32no—
806Q8—61no—
807Q8—94no—
808Q8—94no—
809Q8—188no—
810Q8—184no—
811Q8—182no—
812Q8C22×D3212yes—
813D4—24no—
814D4—21no—
815D4—34no—
816D4—32no—
817D4—64no—
818D4—64no—
819D4—62no—
820D4—61no—
821D4—98no—
822D4—94no—
823D4—188no—
824D4—188no—
825D4—188no—
826D4C22×D3212yes—
827C2×C4—21no—
828C2×C4—24no—
829C2×C4—61no—
830C2×C4—64no—
831C2×C4—92no—
832C2×C4—94no—
833C2×C4—94no—
834C2×C4—188no—
835C2×C4—188no—
836C2×C4—188no—
837C2×C4—184no—
838C2×C4—182no—
839C2×C4#381112yes—
840C2×C4#381111yescharacteristic
841C2×C4C22×D3212yes—
842C2×C4C22×D3211yescharacteristic
843C8—32no—
844C8—32no—
845C8—34no—
846C2×C3—22no—
847C2×C3—22no—
848C2×C3—21no—
849C2×C3—22no—
850C2×C3—42no—
851C2×C3—44no—
852C2×C3—42no—
853C2×C3—42no—
854C2×C3—124no—
855C2×C3—122no—
856C2×C3#577012yescomplemented
857C2×C3#577512yescomplemented
858C2×C3C22×D3×D411yescharacteristic
859C2×C3C22×D3×D411yescharacteristic
860D3—42no—
861D3—44no—
862D3—64no—
863D3—64no—
864D3—124no—
865C22—22no—
866C22—22no—
867C22—42no—
868C22—62no—
869C22—64no—
870C22—94no—
871C22—124no—
872C22—122no—
873C22—184no—
874C22—244no—
875C22—728no—
876C22C2×#381112yes—
877C22C2×#381111yescharacteristic
878C4—22no—
879C4—62no—
880C4—94no—
881C4—184no—
882C4C2×#381112yes—
883C4C2×#381111yescharacteristic
884C4C23×D3211yescharacteristic
885C3—21no—
886C3C2×#577011yescharacteristic, complemented
887C3C2×#577511yescharacteristic, complemented
888C2—22no—
889C2—42no—
890C2—124no—
891C2—122no—
892C2—184no—
893C2#1059546212yesdirect product factor
894C2C22×#381111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64367C2semidirect
2. C2×#64307C2semidirect
3. C2×C3×#950C2semidirect
4. C2×C3×#949C2semidirect
5. #10595462C2direct (N × H)
6. C2×#63951C2semidirect
7. C2×#63940C2semidirect
8. C2×#63936C2semidirect
9. C2×#63927C2semidirect
10. C2×#63831C2semidirect
11. C22×#3716C2semidirect
12. C2×#63817C2semidirect
15. C2×C32×#41C22semidirect
17. #64367C22semidirect
18. C2×Q8×C3⋊D3C22semidirect
20. C2×#3830C22semidirect
24. C22×#634C22semidirect
29. #64307C22semidirect
34. C3×#950C22semidirect
35. C3×#949C22semidirect
36. C2×C3×#216C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#215C22semidirect
39. C2×C3×#214C22semidirect
40. C2×C3×#213C22semidirect
41. C2×C3×#213C22semidirect
42. C2×C3×#208C22semidirect
43. C22×C3×C3⋊C8C22semidirect
44. #63951C22semidirect
45. #63940C22semidirect
46. #63936C22semidirect
47. #63927C22semidirect
48. C2×#3719C22semidirect
49. #63831C22semidirect
50. C2×#3716C22semidirect
51. C2×#3716C22semidirect
52. C2×#3716C22semidirect
53. C2×#3716C22semidirect
54. C2×#3712C22semidirect
55. #63817C22semidirect
56. C2×#3710C22semidirect
65. C2×#950D3semidirect
66. C2×#949D3semidirect
85. C32×#41C23semidirect
96. Q8×C3⋊D3C23semidirect
99. #3830C23semidirect
112. C2×#634C23semidirect
133. C3×#216C23semidirect
134. C3×#215C23semidirect
135. C3×#215C23semidirect
136. C3×#214C23semidirect
137. C3×#213C23semidirect
138. C3×#213C23semidirect
139. C3×#208C23semidirect
143. C2×C3×C3⋊C8C23semidirect
144. #3719C23semidirect
145. #3716C23semidirect
146. #3716C23semidirect
147. #3716C23semidirect
148. #3712C23semidirect
149. #3710C23semidirect
153. C2×C3×#41C2×D3semidirect
154. C2×C3×#41C2×D3semidirect
210. #950C2×D3semidirect
211. #949C2×D3semidirect
213. C2×#216C2×D3semidirect
214. C2×#215C2×D3semidirect
215. C2×#215C2×D3semidirect
220. C2×#214C2×D3semidirect
221. C2×#213C2×D3semidirect
222. C2×#213C2×D3semidirect
223. C2×#208C2×D3semidirect
224. C22×C3⋊C8C2×D3semidirect
318. C3×#41C22×D3semidirect
319. C3×#41C22×D3semidirect
451. #216C22×D3semidirect
452. #215C22×D3semidirect
453. #215C22×D3semidirect
457. #214C22×D3semidirect
458. #213C22×D3semidirect
459. #213C22×D3semidirect
460. #208C22×D3semidirect
464. C2×C3⋊C8C22×D3semidirect
504. C2×#41D32semidirect
668. C2×C32#577semidirect
687. #41C2×D32semidirect
794. C32C2×#577semidirect
856. C2×C3#5770semidirect
857. C2×C3#5775semidirect
886. C3C2×#5770semidirect
887. C3C2×#5775semidirect
893. C2#10595462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643672
C2×#643072
C2×C3×#9502
C2×C3×#9492
#105954622
C2×#639512
C2×#639402
C2×#639362
C2×#639272
C2×#638312
C22×#37162
C2×#638172
C2×#57753
C2×#57703