Finite Group Databasebeta

← C2×#10594677 #11918883

Subgroups — C2×#10594677 #11918883

Order 1152.

3053 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C2×#64113C211yesmaximal, characteristic, complemented
4C22×C3×#204C211yesmaximal, characteristic, complemented
5C2×C3×#901C211yesmaximal, characteristic, complemented
6C2×#63833C211yesmaximal, characteristic, complemented
7C2×#63830C211yesmaximal, characteristic, complemented
8C2×#63806C212yesmaximal, complemented
9C2×#63800C212yesmaximal, complemented
10#10594677C2116yesmaximal, direct product factor
11C2×#63794C212yesmaximal, complemented
12C2×D3×#204C212yesmaximal, complemented
13C2×#5762—31nomaximal
14C2×#5751—31nomaximal
15C2×#3828C2211yescharacteristic
16C2×#3828C2211yescharacteristic, complemented
17C2×C3×#235C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic, complemented
20C2×D3×#67—22no—
21C2×#3804—22no—
22#64307—24no—
23#64307C2218yescomplemented
24C2×#3802—21no—
25C2×D3×D12C2212yes—
26C2×#3799C2212yescomplemented
27C2×#3797—21no—
28#64297—24no—
29#64297C2218yescomplemented
30C2×#3796—21no—
31C2×#3796—21no—
32C2×#3795C2212yes—
33C2×D3×Dic6C2212yescomplemented
34C22×C32×C8C2211yescharacteristic, complemented
35C2×#3746C2211yescharacteristic, complemented
36#64113C2218yescomplemented
37C2×#3745C2211yescharacteristic, complemented
38C2×#3744C2211yescharacteristic, complemented
39C2×#3744C2211yescharacteristic, complemented
40C2×C3×#208C2211yescharacteristic, complemented
41C2×C3×#204C2212yescomplemented
42C2×C3×#204C2212yescomplemented
43C2×C3×#204C2218yescomplemented
44C3×#901C2218yescomplemented
45C2×C3×ΓL(1,𝔽25)C2212yescomplemented
46C2×C3×D3×C8C2212yescomplemented
47C2×#3719C2212yescomplemented
48#63833C2218yescomplemented
49C2×#3717C2212yescomplemented
50#63830C2218yescomplemented
51C2×#3716C2212yescomplemented
52C2×#3714C2212yescomplemented
53#63806C22116yescomplemented
54#63800C22116yescomplemented
55#63794C22116yescomplemented
56D3×#204C22116yescomplemented
57C2×#1010—31no—
58C2×#1009—31no—
59C2×#1007—31no—
60C2×#1004—31no—
61C22×C3×SD16—31no—
62C2×C3×#131—31no—
63C2×#942—31no—
64C2×#932—31no—
65#5762—316no—
66C2×#916—32no—
67C2×#915—32no—
68C2×#914—32no—
69C2×D3×SD16—32no—
70#5751—316no—
71C2×#909—31no—
72C2×#909—32no—
73C2×#908—31no—
74C2×#908—32no—
75C2×#904—31no—
76C2×#904—31no—
77C2×#904—32no—
78C2×#904—61no—
79C22×#204—32no—
80C22×#204D311yescharacteristic, complemented
81C2×#901D311yescharacteristic, complemented
82C23×C3×D3—21no—
83C22×D32—22no—
84C22×C32×C4C2311yescharacteristic
85C2×#638—21no—
86C2×#638—21no—
87#3828—22no—
88#3828—22no—
89#3828C2314yes—
90#3828C2314yescomplemented
91C2×C4⋊(C3⋊D3)C2311yescharacteristic
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×C4×C3⋊D3—21no—
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67D412yes—
98C22×C3×Dic3—21no—
99C3×#235D414yes—
100C3×#235C2314yes—
101C2×C3×D12—21no—
102C2×C3×D12—22no—
103C2×C3×D12D411yescharacteristic
104C2×C3×D12C2312yes—
105C2×C3×D12C2314yes—
106C2×C3×C4×D3C2312yes—
107C2×C3×Dic6—21no—
108C2×C3×Dic6—22no—
109C2×C3×Dic6D411yescharacteristic
110C2×C3×Dic6C2312yes—
111C2×C3×Dic6C2314yescomplemented
112D3×#67—216no—
113C2×#627—22no—
114C2×#626—22no—
115C2×#626—22no—
116C2×#625—22no—
117C2×#624—22no—
118#3804—216no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121#3802—28no—
122D3×D12—24no—
123D3×D12C2318yes—
124#3799—24no—
125#3799C2318yescomplemented
126#3797—28no—
127#3796—28no—
128#3796—28no—
129#3795—24no—
130#3795C2318yes—
131D3×Dic6—24no—
132D3×Dic6C2318yescomplemented
133C2×C32×C8C2311yescharacteristic
134C2×C32×C8C2311yescharacteristic
135C2×C32×C8C2314yescomplemented
136#3746C2314yescomplemented
137#3745C2314yescomplemented
138#3744C2314yescomplemented
139#3744C2314yescomplemented
140C3×#208C2314yescomplemented
141C2×C3×C3⋊C8C2312yes—
142C3×#204C2318yescomplemented
143C3×#204C2318yescomplemented
144C3×ΓL(1,𝔽25)C2318yescomplemented
145C3×D3×C8C2318yescomplemented
146#3719C2318yescomplemented
147#3717C2318yescomplemented
148#3716C2318yescomplemented
149#3714C2318yescomplemented
150C2×#577—91noSylow
151C2×C3×#41—31no—
152C22×C3×Q8—31no—
153C22×C3×D4—31no—
154C22×#67—62no—
155#1010—38no—
156#1010—64no—
157#1009—38no—
158#1009—64no—
159#1007—38no—
160#1007—64no—
161C2×#239—32no—
162C2×#239—61no—
163C2×#239—61no—
164C2×D3×Q8—32no—
165C2×D3×Q8—61no—
166C2×D3×Q8—61no—
167#1004—38no—
168#1004—64no—
169C2×#237—32no—
170C2×#237—61no—
171C2×#237—62no—
172C2×#237—61no—
173C2×D3×D4—32no—
174C2×D3×D4—61no—
175C2×D3×D4—62no—
176C2×D3×D4—61no—
177C2×#235—31no—
178C2×#235—31no—
179C2×#235—31no—
180C2×#235—31no—
181C2×#235—32no—
182C2×#235—32no—
183C2×#235—61no—
184C2×#235—61no—
185C2×#235—62no—
186C2×#235C2×D311yescharacteristic
187C22×D12—32no—
188C22×D12C2×D311yescharacteristic
189C22×Dic6—32no—
190C22×Dic6C2×D311yescharacteristic, complemented
191C2×C3×SD16—32no—
192C2×C3×SD16—32no—
193C2×C3×SD16—38no—
194C3×#131—38no—
195C2×C3×M16—31no—
196C2×C3×M16—32no—
197C22×C3×C8—21no—
198C22×C3×C8—32no—
199C22×C3×C8C2×D311yescharacteristic, complemented
200C22×C3×C8C2×D311yescharacteristic, complemented
201C2×#216—32no—
202#942—38no—
203C2×#215—32no—
204C2×#214—32no—
205#932—38no—
206C2×#213—32no—
207C2×#208C2×D311yescharacteristic, complemented
208#916—316no—
209#915—316no—
210#914—316no—
211D3×SD16—316no—
212#909—38no—
213#909—316no—
214#908—38no—
215#908—316no—
216C2×Dic12—32no—
217C2×Dic12—31no—
218C2×Dic12—31no—
219C2×Dic12—61no—
220#904—38no—
221#904—38no—
222#904—316no—
223#904—68no—
224C2×D24—32no—
225C2×D24—31no—
226C2×D24—31no—
227C2×D24—61no—
228C2×#204—32no—
229C2×#204—32no—
230C2×#204—31no—
231C2×#204—31no—
232C2×#204—31no—
233C2×#204—31no—
234C2×#204—316no—
235C2×#204—61no—
236C2×#204—61no—
237C2×#204C2×D312yescomplemented
238C2×#204C2×D312yescomplemented
239C2×#204C2×D318yescomplemented
240#901C2×D318yescomplemented
241C2×ΓL(1,𝔽25)C2×D312yescomplemented
242C2×D3×C8C2×D312yescomplemented
243C23×C32C2×D411yescharacteristic
244C22×C3⋊D3—21no—
245C22×C3⋊D3—21no—
246C22×C3×D3—22no—
247C22×C3×D3—24no—
248C22×C3×D3—82no—
249C22×C3×D3C2×D412yes—
250C2×D32—28no—
251C2×D32—84no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D412yes—
254C2×C32×C4C2411yescharacteristic
255C2×C32×C4C2412yes—
256#638—24no—
257#638—24no—
258C2×C3⋊Dic3—21no—
259C2×C3⋊Dic3—21no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)C2412yes—
263C4⋊(C3⋊D3)C2412yes—
264C4×C3⋊D3—24no—
265C4×C3⋊D3—24no—
266#634—21no—
267#634—21no—
268#634C2412yes—
269#634C2412yes—
270C3×#67C2×D418yes—
271C2×C3×Dic3—22no—
272C2×C3×Dic3—24no—
273C2×C3×Dic3C2×D412yes—
274C3×D12—22no—
275C3×D12—24no—
276C3×D12C2×D414yes—
277C3×D12C2414yes—
278C3×C4×D3C2×D414yes—
279C3×C4×D3C2414yes—
280C3×Dic6—22no—
281C3×Dic6—24no—
282C3×Dic6C2×D414yes—
283C3×Dic6C2414yes—
284#627—28no—
285#626—28no—
286#626—28no—
287#625—28no—
288#624—28no—
289D3×Dic3—28no—
290D3×Dic3—28no—
291C32×C8C2412yes—
292C32×C8C2412yes—
293C3×C3⋊C8C2414yes—
294C2×2−1+4—91no—
295C2×H(5,𝔽2)—91no—
296#577—916no—
297C2×#137—92no—
298C2×#137—91no—
299C2×AGL(1,ℤ/8)—92no—
300C2×AGL(1,ℤ/8)—91no—
301C2×#135—92no—
302C2×#135—91no—
303C22×SD16—31no—
304C22×SD16—92no—
305C2×#131—31no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—62no—
309C23×D3—62no—
310C3×#41—34no—
311C3×#41—34no—
312C2×C3×Q8—31no—
313C2×C3×Q8—32no—
314C2×C3×Q8—34no—
315C2×C3×Q8—61no—
316C2×C3×Q8—62no—
317C2×C3×D4—32no—
318C2×C3×D4—31no—
319C2×C3×D4—32no—
320C2×C3×D4—34no—
321C2×C3×D4—61no—
322C2×C3×D4—62no—
323C22×C3×C4—21no—
324C22×C3×C4—32no—
325C22×C3×C4—61no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C2×#67—62no—
329C2×#67—62no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—62no—
335C2×#67—616no—
336C2×#67—62no—
337C2×#67—121no—
338C2×#67—121no—
339C2×#67D1212yes—
340C22×Dic3—21no—
341C22×Dic3—62no—
342C22×Dic3—62no—
343#239—38no—
344#239—68no—
345#239—68no—
346#239—64no—
347D3×Q8—38no—
348D3×Q8—68no—
349D3×Q8—64no—
350D3×Q8—68no—
351#237—38no—
352#237—68no—
353#237—616no—
354#237—64no—
355#237—68no—
356D3×D4—38no—
357D3×D4—68no—
358D3×D4—616no—
359D3×D4—68no—
360D3×D4—64no—
361#235—34no—
362#235—34no—
363#235—34no—
364#235—34no—
365#235—38no—
366#235—38no—
367#235—64no—
368#235—64no—
369#235—64no—
370#235—64no—
371#235—62no—
372#235—62no—
373#235—62no—
374#235—62no—
375#235—616no—
376#235—122no—
377#235—122no—
378#235D1214yes—
379#235C22×D314yes—
380C2×D12—21no—
381C2×D12—22no—
382C2×D12—31no—
383C2×D12—31no—
384C2×D12—31no—
385C2×D12—31no—
386C2×D12—38no—
387C2×D12—61no—
388C2×D12—61no—
389C2×D12—64no—
390C2×D12—62no—
391C2×D12—62no—
392C2×D12D1211yescharacteristic
393C2×D12C22×D312yes—
394C2×D12C22×D314yes—
395C2×C4×D3—62no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C2×C4×D3—61no—
399C2×C4×D3—61no—
400C2×C4×D3—61no—
401C2×C4×D3—61no—
402C2×C4×D3—62no—
403C2×C4×D3—121no—
404C2×C4×D3—121no—
405C2×C4×D3C22×D312yes—
406C2×Dic6—21no—
407C2×Dic6—22no—
408C2×Dic6—31no—
409C2×Dic6—31no—
410C2×Dic6—31no—
411C2×Dic6—31no—
412C2×Dic6—38no—
413C2×Dic6—61no—
414C2×Dic6—61no—
415C2×Dic6—64no—
416C2×Dic6—62no—
417C2×Dic6—62no—
418C2×Dic6D1211yescharacteristic
419C2×Dic6C22×D312yes—
420C2×Dic6C22×D314yescomplemented
421C3×SD16—38no—
422C3×SD16—38no—
423C3×M16—34no—
424C3×M16—38no—
425C2×C3×C8—21no—
426C2×C3×C8—21no—
427C2×C3×C8—24no—
428C2×C3×C8—32no—
429C2×C3×C8—38no—
430C2×C3×C8C22×D311yescharacteristic
431C2×C3×C8C22×D311yescharacteristic
432C2×C3×C8C22×D311yescharacteristic
433C2×C3×C8C22×D311yescharacteristic
434C2×C3×C8C22×D314yescomplemented
435C2×C3×C8C22×D314yescomplemented
436#216—38no—
437#215—38no—
438#214—38no—
439#213—38no—
440#208C22×D314yescomplemented
441C2×C3⋊C8C22×D312yes—
442Dic12—38no—
443Dic12—34no—
444Dic12—34no—
445Dic12—64no—
446D24—38no—
447D24—34no—
448D24—34no—
449D24—64no—
450#204—38no—
451#204—38no—
452#204—34no—
453#204—34no—
454#204—34no—
455#204—34no—
456#204—64no—
457#204—64no—
458#204C22×D318yescomplemented
459#204C22×D318yescomplemented
460ΓL(1,𝔽25)C22×D318yescomplemented
461D3×C8C22×D318yescomplemented
462C22×C32—22no—
463C22×C32C22×D412yes—
464C22×C32C22×D411yescharacteristic
465C2×C3⋊D3—22no—
466C2×C3⋊D3—22no—
467C2×C3⋊D3—42no—
468C2×C3⋊D3—42no—
469C2×C3×D3—24no—
470C2×C3×D3—24no—
471C2×C3×D3—44no—
472C2×C3×D3—84no—
473C2×C3×D3C22×D414yes—
474D32—88no—
475C32×C4C22×D412yes—
476C32×C4C22×D411yescharacteristic
477C32×C4C2511yescharacteristic
478C3⋊Dic3—22no—
479C3⋊Dic3—22no—
480C3×Dic3—24no—
481C3×Dic3C22×D414yes—
4822−1+4—98no—
4832−1+4—184no—
484H(5,𝔽2)—98no—
485H(5,𝔽2)—184no—
486C2×#41—31no—
487C2×#41—92no—
488C2×#41—92no—
489C2×#41—91no—
490C2×#41—91no—
491C2×#41—182no—
492C2×#41—181no—
493C2×#41—181no—
494C22×Q8—31no—
495C22×Q8—92no—
496C22×Q8—181no—
497C22×D4—31no—
498C22×D4—92no—
499C22×D4—181no—
500C22×D4—182no—
501#137—916no—
502#137—98no—
503AGL(1,ℤ/8)—916no—
504AGL(1,ℤ/8)—98no—
505#135—916no—
506#135—98no—
507C2×Q16—92no—
508C2×Q16—91no—
509C2×SD16—32no—
510C2×SD16—32no—
511C2×SD16—38no—
512C2×SD16—916no—
513C2×SD16—92no—
514C2×SD16—92no—
515C2×SD16—91no—
516C2×SD16—91no—
517C2×D8—92no—
518C2×D8—91no—
519#131—38no—
520C2×M16—31no—
521C2×M16—32no—
522C22×C8—32no—
523C22×C8D3211yescharacteristic, complemented
524C23×C3—21no—
525C23×C3—32no—
526C23×C3—62no—
527C23×C3—64no—
528C23×C3—242no—
529C23×C3C2×D1211yescharacteristic
530C23×C3D3×D411yescharacteristic
531C22×D3—22no—
532C22×D3—24no—
533C22×D3—68no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—68no—
539C22×D3—82no—
540C22×D3—121no—
541C22×D3—121no—
542C22×D3—244no—
543C22×D3—244no—
544C22×D3C2×D1212yes—
545C3×Q8—34no—
546C3×Q8—34no—
547C3×Q8—62no—
548C3×Q8—64no—
549C3×D4—38no—
550C3×D4—34no—
551C3×D4—34no—
552C3×D4—62no—
553C3×D4—64no—
554C2×C3×C4—21no—
555C2×C3×C4—22no—
556C2×C3×C4—21no—
557C2×C3×C4—22no—
558C2×C3×C4—32no—
559C2×C3×C4—34no—
560C2×C3×C4—34no—
561C2×C3×C4—62no—
562C2×C3×C4—64no—
563C2×C3×C4C2×D1211yescharacteristic
564C2×C3×C4C2×D1212yes—
565C2×C3×C4D3×D411yescharacteristic
566C2×C3×C4D3×D412yes—
567C2×C3×C4C23×D311yescharacteristic
568C2×C3×C4C23×D312yes—
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D312yes—
571#67—68no—
572#67—68no—
573#67—64no—
574#67—64no—
575#67—64no—
576#67—64no—
577#67—68no—
578#67—68no—
579#67—124no—
580#67—124no—
581#67C2×D1218yes—
582C2×Dic3—22no—
583C2×Dic3—24no—
584C2×Dic3—68no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—68no—
590C2×Dic3—121no—
591C2×Dic3—121no—
592C2×Dic3C2×D1212yes—
593D12—22no—
594D12—24no—
595D12—32no—
596D12—32no—
597D12—32no—
598D12—32no—
599D12—62no—
600D12—62no—
601D12—68no—
602D12—68no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—121no—
608D12—121no—
609D12C2×D1214yes—
610D12C23×D314yes—
611C4×D3—68no—
612C4×D3—68no—
613C4×D3—68no—
614C4×D3—64no—
615C4×D3—64no—
616C4×D3—64no—
617C4×D3—64no—
618C4×D3—68no—
619C4×D3—124no—
620C4×D3—124no—
621C4×D3C2×D1214yes—
622C4×D3C23×D314yes—
623Dic6—22no—
624Dic6—24no—
625Dic6—32no—
626Dic6—32no—
627Dic6—32no—
628Dic6—32no—
629Dic6—62no—
630Dic6—62no—
631Dic6—68no—
632Dic6—61no—
633Dic6—61no—
634Dic6—61no—
635Dic6—61no—
636Dic6—68no—
637Dic6—121no—
638Dic6—121no—
639Dic6C2×D1214yes—
640Dic6C23×D314yes—
641C3×C8—22no—
642C3×C8—22no—
643C3×C8—34no—
644C3×C8C23×D312yes—
645C3×C8C23×D312yes—
646C3×C8C23×D312yes—
647C3×C8C23×D312yes—
648C3⋊C8C23×D314yes—
649C2×C32—22no—
650C2×C32#57712yescomplemented
651C2×C32C23×D411yescharacteristic
652C3⋊D3—42no—
653C3⋊D3—42no—
654C3×D3—24no—
655C3×D3—44no—
656C24—61no—
657C24—182no—
658#41—34no—
659#41—34no—
660#41—98no—
661#41—98no—
662#41—94no—
663#41—94no—
664#41—184no—
665#41—184no—
666#41—1816no—
667#41—188no—
668#41—188no—
669#41—182no—
670#41—182no—
671C2×Q8—31no—
672C2×Q8—32no—
673C2×Q8—34no—
674C2×Q8—61no—
675C2×Q8—62no—
676C2×Q8—98no—
677C2×Q8—91no—
678C2×Q8—91no—
679C2×Q8—182no—
680C2×Q8—184no—
681C2×Q8—188no—
682C2×D4—32no—
683C2×D4—32no—
684C2×D4—34no—
685C2×D4—31no—
686C2×D4—61no—
687C2×D4—62no—
688C2×D4—98no—
689C2×D4—91no—
690C2×D4—91no—
691C2×D4—184no—
692C2×D4—182no—
693C2×D4—182no—
694C2×D4—188no—
695C2×D4—1816no—
696C2×D4—182no—
697C2×D4—181no—
698C2×D4—181no—
699C22×C4—32no—
700C22×C4—61no—
701C22×C4—182no—
702C22×C4—182no—
703C22×C4—182no—
704C22×C4—181no—
705C22×C4—181no—
706C22×C4C2×D3211yescharacteristic
707Q16—98no—
708Q16—94no—
709SD16—38no—
710SD16—38no—
711SD16—98no—
712SD16—98no—
713SD16—94no—
714SD16—94no—
715D8—98no—
716D8—94no—
717M16—34no—
718M16—38no—
719C2×C8—32no—
720C2×C8—38no—
721C2×C8C2×D3211yescharacteristic
722C2×C8C2×D3211yescharacteristic
723C2×C8C2×D3214yescomplemented
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—34no—
729C22×C3—42no—
730C22×C3—64no—
731C22×C3—64no—
732C22×C3—124no—
733C22×C3—244no—
734C22×C3C22×D1212yes—
735C22×C3C22×D1211yescharacteristic
736C22×C3C2×D3×D412yes—
737C22×C3C2×D3×D411yescharacteristic
738C2×D3—24no—
739C2×D3—24no—
740C2×D3—44no—
741C2×D3—62no—
742C2×D3—62no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—84no—
746C2×D3—122no—
747C2×D3—122no—
748C2×D3—122no—
749C2×D3—122no—
750C2×D3—122no—
751C2×D3—122no—
752C2×D3—242no—
753C2×D3—242no—
754C2×D3—248no—
755C2×D3—248no—
756C2×D3C22×D1214yes—
757C3×C4—21no—
758C3×C4—22no—
759C3×C4—21no—
760C3×C4—34no—
761C3×C4—64no—
762C3×C4C22×D1211yescharacteristic
763C3×C4C22×D1212yes—
764C3×C4C2×D3×D411yescharacteristic
765C3×C4C2×D3×D412yes—
766C3×C4C24×D311yescharacteristic
767C3×C4C24×D311yescharacteristic
768Dic3—24no—
769Dic3—62no—
770Dic3—62no—
771Dic3—62no—
772Dic3—62no—
773Dic3—122no—
774Dic3—122no—
775Dic3C22×D1214yes—
776C32C2×#57711yescharacteristic, complemented, Sylow
777C23—32no—
778C23—62no—
779C23—64no—
780C23—188no—
781C23—181no—
782C23—181no—
783C23—242no—
784C23—724no—
785C23D3×D1211yescharacteristic
786Q8—34no—
787Q8—34no—
788Q8—62no—
789Q8—64no—
790Q8—92no—
791Q8—92no—
792Q8—188no—
793Q8—181no—
794Q8—181no—
795D4—38no—
796D4—34no—
797D4—34no—
798D4—62no—
799D4—64no—
800D4—92no—
801D4—92no—
802D4—188no—
803D4—188no—
804D4—188no—
805D4—184no—
806D4—184no—
807D4—181no—
808D4—181no—
809C2×C4—32no—
810C2×C4—34no—
811C2×C4—34no—
812C2×C4—64no—
813C2×C4—62no—
814C2×C4—188no—
815C2×C4—188no—
816C2×C4—188no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—184no—
820C2×C4—184no—
821C2×C4D3×D1212yes—
822C2×C4D3×D1211yescharacteristic
823C2×C4C22×D3212yes—
824C2×C4C22×D3211yescharacteristic
825C8—34no—
826C8C22×D3212yes—
827C8C22×D3212yes—
828C2×C3—22no—
829C2×C3—22no—
830C2×C3—21no—
831C2×C3—22no—
832C2×C3—42no—
833C2×C3—64no—
834C2×C3—124no—
835C2×C3#575112yescomplemented
836C2×C3#576212yescomplemented
837C2×C3C23×D1211yescharacteristic
838C2×C3C22×D3×D411yescharacteristic
839D3—24no—
840D3—44no—
841D3—122no—
842D3—122no—
843D3—122no—
844D3—122no—
845D3—242no—
846D3—242no—
847C22—22no—
848C22—34no—
849C22—64no—
850C22—64no—
851C22—124no—
852C22—182no—
853C22—182no—
854C22—244no—
855C22—362no—
856C22—362no—
857C22—728no—
858C22C2×D3×D1212yes—
859C22C2×D3×D1211yescharacteristic
860C4—34no—
861C4—64no—
862C4—182no—
863C4—182no—
864C4C2×D3×D1211yescharacteristic
865C4C2×D3×D1212yes—
866C4C23×D3211yescharacteristic
867C3—21no—
868C3C2×#575111yescharacteristic, complemented
869C3C2×#576211yescharacteristic, complemented
870C2—22no—
871C2—64no—
872C2—124no—
873C2—362no—
874C2—362no—
875C2#1059467712yesdirect product factor
876C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C2×#64297C2semidirect
3. C2×#64113C2semidirect
4. C22×C3×#204C2semidirect
5. C2×C3×#901C2semidirect
6. C2×#63833C2semidirect
7. C2×#63830C2semidirect
8. C2×#63806C2semidirect
9. C2×#63800C2semidirect
10. #10594677C2direct (N × H)
11. C2×#63794C2semidirect
12. C2×D3×#204C2semidirect
16. C2×#3828C22semidirect
19. C22×C3×Dic6C22semidirect
23. #64307C22semidirect
26. C2×#3799C22semidirect
29. #64297C22semidirect
33. C2×D3×Dic6C22semidirect
34. C22×C32×C8C22semidirect
35. C2×#3746C22semidirect
36. #64113C22semidirect
37. C2×#3745C22semidirect
38. C2×#3744C22semidirect
39. C2×#3744C22semidirect
40. C2×C3×#208C22semidirect
41. C2×C3×#204C22semidirect
42. C2×C3×#204C22semidirect
43. C2×C3×#204C22semidirect
44. C3×#901C22semidirect
45. C2×C3×ΓL(1,𝔽25)C22semidirect
46. C2×C3×D3×C8C22semidirect
47. C2×#3719C22semidirect
48. #63833C22semidirect
49. C2×#3717C22semidirect
50. #63830C22semidirect
51. C2×#3716C22semidirect
52. C2×#3714C22semidirect
53. #63806C22semidirect
54. #63800C22semidirect
55. #63794C22semidirect
56. D3×#204C22semidirect
80. C22×#204D3semidirect
81. C2×#901D3semidirect
90. #3828C23semidirect
111. C2×C3×Dic6C23semidirect
125. #3799C23semidirect
132. D3×Dic6C23semidirect
135. C2×C32×C8C23semidirect
136. #3746C23semidirect
137. #3745C23semidirect
138. #3744C23semidirect
139. #3744C23semidirect
140. C3×#208C23semidirect
142. C3×#204C23semidirect
143. C3×#204C23semidirect
144. C3×ΓL(1,𝔽25)C23semidirect
145. C3×D3×C8C23semidirect
146. #3719C23semidirect
147. #3717C23semidirect
148. #3716C23semidirect
149. #3714C23semidirect
190. C22×Dic6C2×D3semidirect
199. C22×C3×C8C2×D3semidirect
200. C22×C3×C8C2×D3semidirect
207. C2×#208C2×D3semidirect
237. C2×#204C2×D3semidirect
238. C2×#204C2×D3semidirect
239. C2×#204C2×D3semidirect
240. #901C2×D3semidirect
241. C2×ΓL(1,𝔽25)C2×D3semidirect
242. C2×D3×C8C2×D3semidirect
420. C2×Dic6C22×D3semidirect
434. C2×C3×C8C22×D3semidirect
435. C2×C3×C8C22×D3semidirect
440. #208C22×D3semidirect
458. #204C22×D3semidirect
459. #204C22×D3semidirect
460. ΓL(1,𝔽25)C22×D3semidirect
461. D3×C8C22×D3semidirect
523. C22×C8D32semidirect
650. C2×C32#577semidirect
723. C2×C8C2×D32semidirect
776. C32C2×#577semidirect
835. C2×C3#5751semidirect
836. C2×C3#5762semidirect
868. C3C2×#5751semidirect
869. C3C2×#5762semidirect
875. C2#10594677direct (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×#642972
C2×#641132
C22×C3×#2042
C2×C3×#9012
C2×#638332
C2×#638302
C2×#638062
C2×#638002
#105946772
C2×#637942
C2×D3×#2042
C2×#57623
C2×#57513