Finite Group Databasebeta

← C2×#10594713 #11918892

Subgroups — C2×#10594713 #11918892

Order 1152.

3049 conjugacy classes of subgroups.

The subgroup lattice has 865 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3C2×#64118C211yesmaximal, characteristic, complemented
4C2×C3×#908C211yesmaximal, characteristic, complemented
5C2×C3×#907C211yesmaximal, characteristic, complemented
6C2×#63829C211yesmaximal, characteristic, complemented
7C22×#3716C211yesmaximal, characteristic, complemented
8#10594713C2116yesmaximal, direct product factor
9C2×#63807C212yesmaximal, complemented
10C2×#63800C212yesmaximal, complemented
11C2×#63795C212yesmaximal, complemented
12C2×D3×#204C212yesmaximal, complemented
13C2×#5775—31nomaximal
14C2×#5751—31nomaximal
15C2×#3828C2211yescharacteristic
16C22×#634C2211yescharacteristic, complemented
17C2×C3×#235C2211yescharacteristic
18C2×C3×#235C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic
20C2×D3×#67—22no—
21C2×#3805—22no—
22#64307—24no—
23#64307C2218yescomplemented
24C2×#3802—21no—
25C2×D3×D12C2212yes—
26#64298—24no—
27#64298C2218yescomplemented
28C2×#3796—21no—
29C2×#3795—21no—
30C2×#3795C2212yes—
31C2×#3795C2212yescomplemented
32C2×D3×Dic6—21no—
33C2×D3×Dic6C2212yescomplemented
34C2×C32×M16C2211yescharacteristic, complemented
35#64118C2218yescomplemented
36C2×#3746C2212yescomplemented
37C2×#3744C2212yescomplemented
38C22×C3×C3⋊C8C2211yescharacteristic, complemented
39C3×#908C2218yescomplemented
40C3×#907C2218yescomplemented
41C2×C3×D24C2212yescomplemented
42C2×C3×#204C2212yescomplemented
43C2×C3×ΓL(1,𝔽25)C2212yescomplemented
44C2×C3×D3×C8C2212yescomplemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic, complemented
47#63829C2218yescomplemented
48C2×#3716C2212yescomplemented
49C2×#3716C2212yescomplemented
50C2×#3716C2211yescharacteristic, complemented
51C2×#3716C2218yescomplemented
52C2×#3714C2211yescharacteristic, complemented
53#63807C22116yescomplemented
54#63800C22116yescomplemented
55#63795C22116yescomplemented
56D3×#204C22116yescomplemented
57C2×#1010—31no—
58C2×#1010—31no—
59C2×#1009—31no—
60C2×#1004—31no—
61C2×C3×AGL(1,ℤ/8)—31no—
62C2×C3×#131—31no—
63C2×#950—31no—
64C22×#214—31no—
65#5775—316no—
66C2×#915—32no—
67C2×D3×SD16—32no—
68C2×#912—32no—
69C2×#911—32no—
70#5751—316no—
71C2×#909—31no—
72C2×#909—31no—
73C2×#909—32no—
74C2×#909—61no—
75C2×#908—32no—
76C2×#908D311yescharacteristic, complemented
77C2×#907D311yescharacteristic, complemented
78C2×#904—31no—
79C2×#904—32no—
80C22×#204—31no—
81C22×#204—32no—
82C23×C3×D3—21no—
83C22×D32—22no—
84C22×C32×C4C2311yescharacteristic
85C2×#638—21no—
86C22×C3⋊Dic3—21no—
87#3828—22no—
88#3828C2314yes—
89C2×C4⋊(C3⋊D3)C2311yescharacteristic
90C2×C4×C3⋊D3—21no—
91C2×#634—21no—
92C2×#634—22no—
93C2×#634C2312yes—
94C2×#634C2311yescharacteristic
95C2×#634C2314yescomplemented
96C2×C3×#67—21no—
97C2×C3×#67D412yes—
98C3×#235—22no—
99C3×#235D414yes—
100C3×#235C2314yes—
101C3×#235C2314yescomplemented
102C2×C3×D12—21no—
103C2×C3×D12—22no—
104C2×C3×D12D411yescharacteristic
105C2×C3×D12C2312yes—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2314yes—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2312yes—
110C2×C3×Dic6D411yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112D3×#67—216no—
113C2×#627—22no—
114C2×#626—22no—
115C2×#625—22no—
116C2×#625—22no—
117#3805—216no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121#3802—28no—
122D3×D12—24no—
123D3×D12C2318yes—
124#3796—28no—
125#3795—28no—
126#3795—24no—
127#3795—24no—
128#3795C2318yes—
129#3795C2318yescomplemented
130D3×Dic6—24no—
131D3×Dic6—28no—
132D3×Dic6C2318yescomplemented
133C32×M16C2314yescomplemented
134C2×C32×C8C2312yes—
135#3746C2318yescomplemented
136#3744C2318yescomplemented
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2314yescomplemented
140C3×D24C2318yescomplemented
141C3×#204C2318yescomplemented
142C3×ΓL(1,𝔽25)C2318yescomplemented
143C3×D3×C8C2318yescomplemented
144#3719C2314yescomplemented
145#3717C2314yescomplemented
146#3716C2318yescomplemented
147#3716C2318yescomplemented
148#3716C2314yescomplemented
149#3714C2314yescomplemented
150C2×#577—91noSylow
151C2×C3×#41—31no—
152C2×C3×#41—31no—
153C22×C3×D4—31no—
154C22×#67—62no—
155#1010—38no—
156#1010—38no—
157#1010—64no—
158#1010—64no—
159#1009—38no—
160#1009—64no—
161C2×#239—61no—
162C2×D3×Q8—32no—
163C2×D3×Q8—61no—
164#1004—38no—
165#1004—64no—
166C2×#237—32no—
167C2×#237—32no—
168C2×#237—61no—
169C2×#237—62no—
170C2×#237—62no—
171C2×#237—61no—
172C2×D3×D4—32no—
173C2×D3×D4—61no—
174C2×D3×D4—62no—
175C2×D3×D4—61no—
176C2×#235—31no—
177C2×#235—31no—
178C2×#235—32no—
179C2×#235—32no—
180C2×#235—61no—
181C2×#235—61no—
182C2×#235C2×D311yescharacteristic
183C2×#235C2×D311yescharacteristic, complemented
184C22×D12—32no—
185C22×D12C2×D311yescharacteristic
186C22×Dic6—31no—
187C22×Dic6—31no—
188C22×Dic6—32no—
189C22×Dic6—61no—
190C22×Dic6—61no—
191C3×AGL(1,ℤ/8)—38no—
192C2×C3×SD16—32no—
193C2×C3×D8—32no—
194C3×#131—38no—
195C2×C3×M16—21no—
196C2×C3×M16—32no—
197C2×C3×M16C2×D311yescharacteristic, complemented
198C2×C3×M16C2×D311yescharacteristic, complemented
199C22×C3×C8—31no—
200C22×C3×C8—32no—
201#950—38no—
202C2×#216—31no—
203C2×#215—31no—
204C2×#214—32no—
205C2×#214—31no—
206C2×#214—32no—
207C2×#214—38no—
208C2×#213—31no—
209C22×C3⋊C8C2×D311yescharacteristic, complemented
210#915—316no—
211D3×SD16—316no—
212#912—316no—
213#911—316no—
214#909—38no—
215#909—38no—
216#909—316no—
217#909—68no—
218#908—316no—
219#908C2×D318yescomplemented
220#907C2×D318yescomplemented
221C2×Dic12—31no—
222C2×Dic12—32no—
223C2×Dic12—32no—
224C2×Dic12—62no—
225#904—38no—
226#904—316no—
227C2×D24—31no—
228C2×D24C2×D312yescomplemented
229C2×#204—32no—
230C2×#204—32no—
231C2×#204—38no—
232C2×#204—31no—
233C2×#204—31no—
234C2×#204—32no—
235C2×#204—32no—
236C2×#204—316no—
237C2×#204—62no—
238C2×#204C2×D312yescomplemented
239C2×ΓL(1,𝔽25)C2×D312yescomplemented
240C2×D3×C8C2×D312yescomplemented
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3—22no—
244C22×C3×D3—21no—
245C22×C3×D3—24no—
246C22×C3×D3—82no—
247C22×C3×D3C2×D412yes—
248C2×D32—28no—
249C2×D32—84no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D412yes—
252C2×C32×C4C2411yescharacteristic
253C2×C32×C4C2412yes—
254#638—24no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—22no—
257C2×C3⋊Dic3—24no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)C2412yes—
260C4×C3⋊D3—24no—
261#634—22no—
262#634—24no—
263#634—21no—
264#634C2414yes—
265#634C2412yes—
266C3×#67—24no—
267C3×#67C2×D418yes—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D412yes—
270C3×D12—21no—
271C3×D12—22no—
272C3×D12—24no—
273C3×D12C2×D414yes—
274C3×D12C2412yes—
275C3×D12C2414yes—
276C3×C4×D3—24no—
277C3×C4×D3C2×D414yes—
278C3×C4×D3C2414yes—
279C3×Dic6—21no—
280C3×Dic6C2×D414yes—
281C3×Dic6C2412yes—
282#627—28no—
283#626—28no—
284#625—28no—
285#625—28no—
286D3×Dic3—28no—
287D3×Dic3—28no—
288D3×Dic3—28no—
289C32×C8C2414yes—
290C3×C3⋊C8C2412yes—
291C3×C3⋊C8C2412yes—
292C2×2−1+4—91no—
293C2×H(5,𝔽2)—91no—
294#577—916no—
295C2×#137—92no—
296C2×#137—91no—
297C2×AGL(1,ℤ/8)—31no—
298C2×AGL(1,ℤ/8)—92no—
299C2×#135—92no—
300C2×#135—91no—
301C22×SD16—92no—
302C22×SD16—91no—
303C2×#131—31no—
304C24×C3—61no—
305C23×D3—21no—
306C23×D3—62no—
307C23×D3—62no—
308C3×#41—34no—
309C3×#41—34no—
310C3×#41—34no—
311C3×#41—62no—
312C2×C3×Q8—31no—
313C2×C3×Q8—31no—
314C2×C3×D4—32no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—32no—
318C2×C3×D4—34no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—62no—
322C22×C3×C4—21no—
323C22×C3×C4—32no—
324C22×C3×C4—61no—
325C22×C3×C4C22×D311yescharacteristic
326C22×C3×C4C22×D311yescharacteristic
327C2×#67—21no—
328C2×#67—62no—
329C2×#67—62no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—62no—
333C2×#67—62no—
334C2×#67—616no—
335C2×#67—62no—
336C2×#67—121no—
337C2×#67D1212yes—
338C22×Dic3—62no—
339C22×Dic3—61no—
340C22×Dic3—61no—
341C22×Dic3—62no—
342C22×Dic3—62no—
343C22×Dic3—121no—
344#239—68no—
345D3×Q8—38no—
346D3×Q8—68no—
347D3×Q8—64no—
348#237—38no—
349#237—38no—
350#237—68no—
351#237—616no—
352#237—616no—
353#237—64no—
354#237—64no—
355#237—68no—
356D3×D4—38no—
357D3×D4—68no—
358D3×D4—616no—
359D3×D4—68no—
360D3×D4—64no—
361#235—22no—
362#235—34no—
363#235—34no—
364#235—38no—
365#235—38no—
366#235—64no—
367#235—64no—
368#235—64no—
369#235—62no—
370#235—62no—
371#235—68no—
372#235—122no—
373#235D1214yes—
374#235C22×D314yes—
375#235C22×D314yescomplemented
376C2×D12—21no—
377C2×D12—22no—
378C2×D12—31no—
379C2×D12—31no—
380C2×D12—38no—
381C2×D12—61no—
382C2×D12—64no—
383C2×D12—62no—
384C2×D12D1211yescharacteristic
385C2×D12C22×D312yes—
386C2×D12C22×D314yes—
387C2×D12C22×D311yescharacteristic
388C2×C4×D3—21no—
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—61no—
393C2×C4×D3—61no—
394C2×C4×D3—121no—
395C2×C4×D3C22×D312yes—
396C2×Dic6—32no—
397C2×Dic6—34no—
398C2×Dic6—31no—
399C2×Dic6—32no—
400C2×Dic6—31no—
401C2×Dic6—34no—
402C2×Dic6—38no—
403C2×Dic6—62no—
404C2×Dic6—61no—
405C2×Dic6—64no—
406C2×Dic6—64no—
407C2×Dic6—62no—
408C2×Dic6—61no—
409C2×Dic6—62no—
410C2×Dic6—61no—
411C2×Dic6—62no—
412C2×Dic6—62no—
413C2×Dic6—68no—
414C2×Dic6—121no—
415C2×Dic6—122no—
416C2×Dic6D1211yescharacteristic
417C2×Dic6C22×D311yescharacteristic
418C3×SD16—38no—
419C3×D8—38no—
420C3×M16—24no—
421C3×M16—38no—
422C3×M16C22×D314yescomplemented
423C3×M16C22×D314yescomplemented
424C2×C3×C8—22no—
425C2×C3×C8—31no—
426C2×C3×C8—31no—
427C2×C3×C8—34no—
428C2×C3×C8—38no—
429C2×C3×C8C22×D312yes—
430C2×C3×C8C22×D312yes—
431#216—34no—
432#215—34no—
433#214—38no—
434#214—34no—
435#214—38no—
436#213—34no—
437C2×C3⋊C8C22×D311yescharacteristic
438C2×C3⋊C8C22×D311yescharacteristic
439C2×C3⋊C8C22×D314yescomplemented
440Dic12—34no—
441Dic12—38no—
442Dic12—38no—
443Dic12—68no—
444D24—34no—
445D24C22×D318yescomplemented
446#204—38no—
447#204—38no—
448#204—34no—
449#204—34no—
450#204—38no—
451#204—38no—
452#204—68no—
453#204C22×D318yescomplemented
454ΓL(1,𝔽25)C22×D318yescomplemented
455D3×C8C22×D318yescomplemented
456C22×C32—22no—
457C22×C32C22×D412yes—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—22no—
460C2×C3⋊D3—42no—
461C2×C3×D3—24no—
462C2×C3×D3—22no—
463C2×C3×D3—24no—
464C2×C3×D3—44no—
465C2×C3×D3—42no—
466C2×C3×D3—84no—
467C2×C3×D3C22×D414yes—
468D32—88no—
469C32×C4C22×D411yescharacteristic
470C32×C4C22×D412yes—
471C32×C4C2511yescharacteristic
472C3⋊Dic3—22no—
473C3⋊Dic3—24no—
474C3×Dic3—22no—
475C3×Dic3C22×D414yes—
4762−1+4—98no—
4772−1+4—184no—
478H(5,𝔽2)—98no—
479H(5,𝔽2)—184no—
480C2×#41—31no—
481C2×#41—31no—
482C2×#41—92no—
483C2×#41—92no—
484C2×#41—91no—
485C2×#41—181no—
486C2×#41—182no—
487C2×#41—181no—
488C22×Q8—92no—
489C22×Q8—91no—
490C22×Q8—181no—
491C22×D4—31no—
492C22×D4—92no—
493C22×D4—181no—
494C22×D4—182no—
495#137—916no—
496#137—98no—
497AGL(1,ℤ/8)—38no—
498AGL(1,ℤ/8)—916no—
499#135—916no—
500#135—98no—
501C2×Q16—91no—
502C2×Q16—92no—
503C2×SD16—32no—
504C2×SD16—916no—
505C2×SD16—92no—
506C2×SD16—92no—
507C2×SD16—98no—
508C2×SD16—91no—
509C2×SD16—91no—
510C2×SD16—92no—
511C2×D8—32no—
512C2×D8—91no—
513#131—38no—
514C2×M16—32no—
515C2×M16D3211yescharacteristic, complemented
516C22×C8—31no—
517C22×C8—32no—
518C23×C3—21no—
519C23×C3—32no—
520C23×C3—61no—
521C23×C3—62no—
522C23×C3—64no—
523C23×C3—242no—
524C23×C3C2×D1211yescharacteristic
525C23×C3D3×D411yescharacteristic
526C22×D3—21no—
527C22×D3—22no—
528C22×D3—24no—
529C22×D3—68no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—68no—
533C22×D3—82no—
534C22×D3—121no—
535C22×D3—244no—
536C22×D3—244no—
537C22×D3C2×D1212yes—
538C3×Q8—34no—
539C3×Q8—32no—
540C3×Q8—61no—
541C3×D4—38no—
542C3×D4—34no—
543C3×D4—32no—
544C3×D4—34no—
545C3×D4—64no—
546C3×D4—62no—
547C3×D4—64no—
548C3×D4—61no—
549C2×C3×C4—21no—
550C2×C3×C4—22no—
551C2×C3×C4—21no—
552C2×C3×C4—22no—
553C2×C3×C4—32no—
554C2×C3×C4—34no—
555C2×C3×C4—34no—
556C2×C3×C4—61no—
557C2×C3×C4—64no—
558C2×C3×C4C2×D1211yescharacteristic
559C2×C3×C4C2×D1212yes—
560C2×C3×C4D3×D411yescharacteristic
561C2×C3×C4D3×D412yes—
562C2×C3×C4C23×D311yescharacteristic
563C2×C3×C4C23×D312yes—
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D312yes—
566#67—24no—
567#67—68no—
568#67—68no—
569#67—64no—
570#67—64no—
571#67—68no—
572#67—68no—
573#67—68no—
574#67—124no—
575#67C2×D1218yes—
576C2×Dic3—21no—
577C2×Dic3—68no—
578C2×Dic3—62no—
579C2×Dic3—64no—
580C2×Dic3—61no—
581C2×Dic3—62no—
582C2×Dic3—64no—
583C2×Dic3—61no—
584C2×Dic3—68no—
585C2×Dic3—68no—
586C2×Dic3—124no—
587C2×Dic3—122no—
588C2×Dic3—121no—
589C2×Dic3C2×D1212yes—
590D12—22no—
591D12—24no—
592D12—21no—
593D12—32no—
594D12—32no—
595D12—62no—
596D12—68no—
597D12—61no—
598D12—61no—
599D12—121no—
600D12C2×D1214yes—
601D12C23×D314yes—
602D12C23×D312yes—
603C4×D3—24no—
604C4×D3—68no—
605C4×D3—68no—
606C4×D3—68no—
607C4×D3—64no—
608C4×D3—64no—
609C4×D3—124no—
610C4×D3C2×D1214yes—
611C4×D3C23×D314yes—
612Dic6—21no—
613Dic6—34no—
614Dic6—32no—
615Dic6—34no—
616Dic6—32no—
617Dic6—64no—
618Dic6—62no—
619Dic6—68no—
620Dic6—64no—
621Dic6—62no—
622Dic6—61no—
623Dic6—62no—
624Dic6—64no—
625Dic6—61no—
626Dic6—68no—
627Dic6—122no—
628Dic6—124no—
629Dic6—121no—
630Dic6C2×D1214yes—
631Dic6C23×D312yes—
632C3×C8—24no—
633C3×C8—32no—
634C3×C8—32no—
635C3×C8C23×D314yes—
636C3×C8C23×D314yes—
637C3⋊C8C23×D312yes—
638C3⋊C8C23×D312yes—
639C2×C32—22no—
640C2×C32#57712yescomplemented
641C2×C32C23×D411yescharacteristic
642C3⋊D3—42no—
643C3×D3—24no—
644C3×D3—44no—
645C3×D3—42no—
646C24—61no—
647C24—182no—
648#41—34no—
649#41—34no—
650#41—34no—
651#41—62no—
652#41—98no—
653#41—98no—
654#41—94no—
655#41—184no—
656#41—184no—
657#41—188no—
658#41—1816no—
659#41—188no—
660#41—182no—
661C2×Q8—31no—
662C2×Q8—31no—
663C2×Q8—98no—
664C2×Q8—92no—
665C2×Q8—94no—
666C2×Q8—91no—
667C2×Q8—182no—
668C2×Q8—184no—
669C2×Q8—188no—
670C2×Q8—181no—
671C2×Q8—182no—
672C2×D4—32no—
673C2×D4—31no—
674C2×D4—32no—
675C2×D4—34no—
676C2×D4—31no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—62no—
680C2×D4—98no—
681C2×D4—91no—
682C2×D4—184no—
683C2×D4—182no—
684C2×D4—188no—
685C2×D4—1816no—
686C2×D4—182no—
687C2×D4—182no—
688C2×D4—181no—
689C22×C4—32no—
690C22×C4—61no—
691C22×C4—182no—
692C22×C4—182no—
693C22×C4—182no—
694C22×C4—181no—
695C22×C4—181no—
696C22×C4C2×D3211yescharacteristic
697Q16—94no—
698Q16—98no—
699SD16—38no—
700SD16—98no—
701SD16—98no—
702SD16—94no—
703SD16—94no—
704SD16—98no—
705D8—38no—
706D8—94no—
707M16—38no—
708M16C2×D3214yescomplemented
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—34no—
712C2×C8—38no—
713C2×C8C2×D3212yes—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—21no—
718C22×C3—34no—
719C22×C3—42no—
720C22×C3—64no—
721C22×C3—62no—
722C22×C3—64no—
723C22×C3—124no—
724C22×C3—122no—
725C22×C3—244no—
726C22×C3C22×D1212yes—
727C22×C3C22×D1211yescharacteristic
728C22×C3C2×D3×D412yes—
729C22×C3C2×D3×D411yescharacteristic
730C2×D3—24no—
731C2×D3—22no—
732C2×D3—24no—
733C2×D3—44no—
734C2×D3—42no—
735C2×D3—62no—
736C2×D3—62no—
737C2×D3—84no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3—122no—
741C2×D3—242no—
742C2×D3—248no—
743C2×D3—248no—
744C2×D3C22×D1214yes—
745C3×C4—21no—
746C3×C4—22no—
747C3×C4—21no—
748C3×C4—34no—
749C3×C4—62no—
750C3×C4C22×D1211yescharacteristic
751C3×C4C22×D1212yes—
752C3×C4C2×D3×D411yescharacteristic
753C3×C4C2×D3×D412yes—
754C3×C4C24×D311yescharacteristic
755C3×C4C24×D311yescharacteristic
756Dic3—22no—
757Dic3—64no—
758Dic3—62no—
759Dic3—64no—
760Dic3—62no—
761Dic3—124no—
762Dic3—122no—
763Dic3C22×D1214yes—
764C32C2×#57711yescharacteristic, complemented, Sylow
765C23—32no—
766C23—61no—
767C23—62no—
768C23—64no—
769C23—188no—
770C23—181no—
771C23—242no—
772C23—724no—
773C23D3×D1211yescharacteristic
774Q8—34no—
775Q8—32no—
776Q8—61no—
777Q8—94no—
778Q8—92no—
779Q8—188no—
780Q8—182no—
781Q8—184no—
782Q8—181no—
783D4—38no—
784D4—34no—
785D4—32no—
786D4—34no—
787D4—64no—
788D4—62no—
789D4—64no—
790D4—61no—
791D4—92no—
792D4—188no—
793D4—188no—
794D4—188no—
795D4—184no—
796D4—181no—
797C2×C4—32no—
798C2×C4—34no—
799C2×C4—34no—
800C2×C4—61no—
801C2×C4—64no—
802C2×C4—188no—
803C2×C4—188no—
804C2×C4—188no—
805C2×C4—184no—
806C2×C4—181no—
807C2×C4—182no—
808C2×C4—184no—
809C2×C4D3×D1212yes—
810C2×C4D3×D1211yescharacteristic
811C2×C4C22×D3212yes—
812C2×C4C22×D3211yescharacteristic
813C8—32no—
814C8—32no—
815C8C22×D3214yes—
816C2×C3—22no—
817C2×C3—22no—
818C2×C3—21no—
819C2×C3—22no—
820C2×C3—42no—
821C2×C3—64no—
822C2×C3—124no—
823C2×C3—122no—
824C2×C3#575112yescomplemented
825C2×C3#577512yescomplemented
826C2×C3C23×D1211yescharacteristic
827C2×C3C22×D3×D411yescharacteristic
828D3—24no—
829D3—44no—
830D3—42no—
831D3—122no—
832D3—122no—
833D3—242no—
834C22—22no—
835C22—34no—
836C22—64no—
837C22—62no—
838C22—64no—
839C22—124no—
840C22—122no—
841C22—182no—
842C22—244no—
843C22—362no—
844C22—728no—
845C22C2×D3×D1212yes—
846C22C2×D3×D1211yescharacteristic
847C4—34no—
848C4—62no—
849C4—182no—
850C4—184no—
851C4C2×D3×D1211yescharacteristic
852C4C2×D3×D1212yes—
853C4C23×D3211yescharacteristic
854C3—21no—
855C3C2×#575111yescharacteristic, complemented
856C3C2×#577511yescharacteristic, complemented
857C2—22no—
858C2—64no—
859C2—124no—
860C2—122no—
861C2—362no—
862C2#1059471312yesdirect product factor
863C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C2×#64298C2semidirect
3. C2×#64118C2semidirect
4. C2×C3×#908C2semidirect
5. C2×C3×#907C2semidirect
6. C2×#63829C2semidirect
7. C22×#3716C2semidirect
8. #10594713C2direct (N × H)
9. C2×#63807C2semidirect
10. C2×#63800C2semidirect
11. C2×#63795C2semidirect
12. C2×D3×#204C2semidirect
16. C22×#634C22semidirect
18. C2×C3×#235C22semidirect
23. #64307C22semidirect
27. #64298C22semidirect
31. C2×#3795C22semidirect
33. C2×D3×Dic6C22semidirect
34. C2×C32×M16C22semidirect
35. #64118C22semidirect
36. C2×#3746C22semidirect
37. C2×#3744C22semidirect
38. C22×C3×C3⋊C8C22semidirect
39. C3×#908C22semidirect
40. C3×#907C22semidirect
41. C2×C3×D24C22semidirect
42. C2×C3×#204C22semidirect
43. C2×C3×ΓL(1,𝔽25)C22semidirect
44. C2×C3×D3×C8C22semidirect
45. C2×#3719C22semidirect
46. C2×#3717C22semidirect
47. #63829C22semidirect
48. C2×#3716C22semidirect
49. C2×#3716C22semidirect
50. C2×#3716C22semidirect
51. C2×#3716C22semidirect
52. C2×#3714C22semidirect
53. #63807C22semidirect
54. #63800C22semidirect
55. #63795C22semidirect
56. D3×#204C22semidirect
76. C2×#908D3semidirect
77. C2×#907D3semidirect
95. C2×#634C23semidirect
101. C3×#235C23semidirect
129. #3795C23semidirect
132. D3×Dic6C23semidirect
133. C32×M16C23semidirect
135. #3746C23semidirect
136. #3744C23semidirect
139. C2×C3×C3⋊C8C23semidirect
140. C3×D24C23semidirect
141. C3×#204C23semidirect
142. C3×ΓL(1,𝔽25)C23semidirect
143. C3×D3×C8C23semidirect
144. #3719C23semidirect
145. #3717C23semidirect
146. #3716C23semidirect
147. #3716C23semidirect
148. #3716C23semidirect
149. #3714C23semidirect
183. C2×#235C2×D3semidirect
197. C2×C3×M16C2×D3semidirect
198. C2×C3×M16C2×D3semidirect
209. C22×C3⋊C8C2×D3semidirect
219. #908C2×D3semidirect
220. #907C2×D3semidirect
228. C2×D24C2×D3semidirect
238. C2×#204C2×D3semidirect
239. C2×ΓL(1,𝔽25)C2×D3semidirect
240. C2×D3×C8C2×D3semidirect
375. #235C22×D3semidirect
422. C3×M16C22×D3semidirect
423. C3×M16C22×D3semidirect
439. C2×C3⋊C8C22×D3semidirect
445. D24C22×D3semidirect
453. #204C22×D3semidirect
454. ΓL(1,𝔽25)C22×D3semidirect
455. D3×C8C22×D3semidirect
515. C2×M16D32semidirect
640. C2×C32#577semidirect
708. M16C2×D32semidirect
764. C32C2×#577semidirect
824. C2×C3#5751semidirect
825. C2×C3#5775semidirect
855. C3C2×#5751semidirect
856. C3C2×#5775semidirect
862. C2#10594713direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643072
C2×#642982
C2×#641182
C2×C3×#9082
C2×C3×#9072
C2×#638292
C22×#37162
#105947132
C2×#638072
C2×#638002
C2×#637952
C2×D3×#2042
C2×#57753
C2×#57513