Finite Group Databasebeta

← C2×#10594721 #11918945

Subgroups — C2×#10594721 #11918945

Order 1152.

2945 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C2×#64118C211yesmaximal, characteristic, complemented
4C2×C3×#909C211yesmaximal, characteristic, complemented
5C2×C3×#907C211yesmaximal, characteristic, complemented
6C22×#3719C211yesmaximal, characteristic, complemented
7C2×#63829C211yesmaximal, characteristic, complemented
8#10594721C2116yesmaximal, direct product factor
9C2×#63806C212yesmaximal, complemented
10C2×#63801C212yesmaximal, complemented
11C2×#63800C212yesmaximal, complemented
12C2×D3×Dic12C212yesmaximal, complemented
13C2×#5779—31nomaximal
14C2×#5753—31nomaximal
15C2×#3828C2211yescharacteristic
16C22×#634C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic
18C2×C3×#235C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×#3805—22no—
21C2×#3804—22no—
22C2×#3799C2212yes—
23C2×#3797—21no—
24#64298—24no—
25#64298C2218yescomplemented
26#64297—24no—
27#64297C2218yescomplemented
28C2×#3796—21no—
29C2×#3795—21no—
30C2×#3795C2212yes—
31C2×D3×Dic6—21no—
32C2×D3×Dic6C2212yes—
33C2×D3×Dic6C2212yes—
34C2×C32×M16C2211yescharacteristic
35#64118C2218yescomplemented
36C2×#3746C2212yes—
37C2×#3744C2212yes—
38C22×C3×C3⋊C8C2211yescharacteristic
39C3×#909C2218yescomplemented
40C3×#907C2218yescomplemented
41C2×C3×Dic12C2212yes—
42C2×C3×#204C2212yes—
43C2×C3×ΓL(1,𝔽25)C2212yes—
44C2×C3×D3×C8C2212yes—
45C2×#3719C2211yescharacteristic
46C2×#3719C2212yes—
47C2×#3719C2212yes—
48C2×#3719C2218yescomplemented
49C2×#3717C2211yescharacteristic
50#63829C2218yescomplemented
51C2×#3716C2211yescharacteristic
52C2×#3714C2211yescharacteristic
53#63806C22116yescomplemented
54#63801C22116yescomplemented
55#63800C22116yescomplemented
56D3×Dic12C22116yescomplemented
57C2×#1010—31no—
58C2×#1010—31no—
59C2×#1010—31no—
60C2×#1007—31no—
61C2×C3×#137—31no—
62C2×C3×#131—31no—
63C2×#950—31no—
64C22×#216—31no—
65#5779—316no—
66C2×#918—32no—
67C2×D3×Q16—32no—
68C2×#916—32no—
69C2×#915—32no—
70#5753—316no—
71C2×#909—31no—
72C2×#909—31no—
73C2×#909—32no—
74C2×#909—32no—
75C2×#909—61no—
76C2×#909D311yescharacteristic, complemented
77C2×#907D311yescharacteristic, complemented
78C22×Dic12—31no—
79C22×Dic12—32no—
80C2×#904—31no—
81C2×#904—32no—
82C22×C32×C4C2311yescharacteristic
83C2×#638—21no—
84C22×C3⋊Dic3—21no—
85#3828—22no—
86#3828C2314yes—
87C2×C4⋊(C3⋊D3)C2311yescharacteristic
88C2×C4×C3⋊D3—21no—
89C2×#634—21no—
90C2×#634—22no—
91C2×#634C2311yescharacteristic
92C2×#634C2312yes—
93C2×#634C2314yes—
94C2×C3×#67—21no—
95C2×C3×#67D412yes—
96C22×C3×Dic3—21no—
97C3×#235—22no—
98C3×#235D414yes—
99C3×#235C2314yes—
100C3×#235C2314yes—
101C2×C3×D12D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2312yes—
105C2×C3×Dic6—21no—
106C2×C3×Dic6—22no—
107C2×C3×Dic6D411yescharacteristic
108C2×C3×Dic6C2312yes—
109C2×C3×Dic6C2311yescharacteristic
110C2×C3×Dic6C2314yes—
111C2×#627—22no—
112C2×#627—22no—
113C2×#626—22no—
114C2×#625—22no—
115C2×#624—22no—
116#3805—216no—
117#3804—216no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121#3799—24no—
122#3799C2318yes—
123#3797—28no—
124#3796—28no—
125#3795—28no—
126#3795—24no—
127#3795C2318yes—
128D3×Dic6—24no—
129D3×Dic6—24no—
130D3×Dic6—28no—
131D3×Dic6C2318yes—
132D3×Dic6C2318yes—
133C32×M16C2314yes—
134C2×C32×C8C2312yes—
135#3746C2318yes—
136#3744C2318yes—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2314yes—
140C3×Dic12C2318yes—
141C3×#204C2318yes—
142C3×ΓL(1,𝔽25)C2318yes—
143C3×D3×C8C2318yes—
144#3719C2314yes—
145#3719C2318yes—
146#3719C2318yes—
147#3717C2314yes—
148#3716C2314yes—
149#3714C2314yes—
150C2×#578—91noSylow
151C2×C3×#41—31no—
152C2×C3×#41—31no—
153C22×C3×Q8—31no—
154#1010—38no—
155#1010—38no—
156#1010—38no—
157#1010—64no—
158#1010—64no—
159#1010—64no—
160#1007—38no—
161#1007—64no—
162C2×#239—32no—
163C2×#239—61no—
164C2×D3×Q8—32no—
165C2×D3×Q8—32no—
166C2×D3×Q8—61no—
167C2×D3×Q8—61no—
168C2×D3×Q8—61no—
169C2×#237—32no—
170C2×#237—61no—
171C2×#237—61no—
172C2×#237—62no—
173C2×#237—62no—
174C2×#237—62no—
175C2×#235—31no—
176C2×#235—31no—
177C2×#235—32no—
178C2×#235—32no—
179C2×#235—61no—
180C2×#235—62no—
181C2×#235—61no—
182C2×#235C2×D311yescharacteristic
183C2×#235C2×D311yescharacteristic
184C22×Dic6—31no—
185C22×Dic6—31no—
186C22×Dic6—32no—
187C22×Dic6—32no—
188C22×Dic6—61no—
189C22×Dic6—61no—
190C22×Dic6C2×D311yescharacteristic
191C3×#137—38no—
192C2×C3×Q16—32no—
193C2×C3×SD16—32no—
194C3×#131—38no—
195C2×C3×M16—21no—
196C2×C3×M16—32no—
197C2×C3×M16C2×D311yescharacteristic
198C2×C3×M16C2×D311yescharacteristic
199C22×C3×C8—31no—
200C22×C3×C8—32no—
201#950—38no—
202C2×#216—32no—
203C2×#216—32no—
204C2×#216—31no—
205C2×#216—38no—
206C2×#215—31no—
207C2×#214—31no—
208C2×#213—31no—
209C22×C3⋊C8C2×D311yescharacteristic
210#918—316no—
211D3×Q16—316no—
212#916—316no—
213#915—316no—
214#909—38no—
215#909—38no—
216#909—316no—
217#909—316no—
218#909—68no—
219#909C2×D318yescomplemented
220#907C2×D318yescomplemented
221C2×Dic12—31no—
222C2×Dic12—32no—
223C2×Dic12—32no—
224C2×Dic12—38no—
225C2×Dic12—32no—
226C2×Dic12—32no—
227C2×Dic12—316no—
228C2×Dic12—62no—
229C2×Dic12C2×D312yes—
230#904—38no—
231#904—316no—
232C2×D24—31no—
233C2×#204—31no—
234C2×#204—31no—
235C2×#204—32no—
236C2×#204—32no—
237C2×#204—62no—
238C2×#204C2×D312yes—
239C2×ΓL(1,𝔽25)C2×D312yes—
240C2×D3×C8C2×D312yes—
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D412yes—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D412yes—
247C2×C32×C4C2411yescharacteristic
248C2×C32×C4C2412yes—
249#638—24no—
250C2×C3⋊Dic3—22no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—24no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)C2412yes—
255C4×C3⋊D3—24no—
256#634—21no—
257#634—24no—
258#634—22no—
259#634C2412yes—
260#634C2414yes—
261C3×#67—24no—
262C3×#67C2×D418yes—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—22no—
265C2×C3×Dic3—24no—
266C2×C3×Dic3C2×D412yes—
267C3×D12—21no—
268C3×D12C2×D414yes—
269C3×D12C2412yes—
270C3×C4×D3—24no—
271C3×C4×D3C2×D414yes—
272C3×C4×D3C2414yes—
273C3×Dic6—21no—
274C3×Dic6—22no—
275C3×Dic6—24no—
276C3×Dic6C2×D414yes—
277C3×Dic6C2412yes—
278C3×Dic6C2414yes—
279#627—28no—
280#627—28no—
281#626—28no—
282#625—28no—
283#624—28no—
284D3×Dic3—28no—
285D3×Dic3—28no—
286D3×Dic3—28no—
287C32×C8C2414yes—
288C3×C3⋊C8C2412yes—
289C3×C3⋊C8C2412yes—
290C2×2−1+4—91no—
291C2×2−1+4—91no—
292#578—916no—
293C2×#137—31no—
294C2×#137—92no—
295C2×#137—92no—
296C2×#137—91no—
297C2×#135—92no—
298C2×#135—91no—
299C22×Q16—92no—
300C22×Q16—91no—
301C2×#131—31no—
302C3×#41—34no—
303C3×#41—34no—
304C3×#41—34no—
305C3×#41—62no—
306C2×C3×Q8—31no—
307C2×C3×Q8—31no—
308C2×C3×Q8—32no—
309C2×C3×Q8—34no—
310C2×C3×Q8—61no—
311C2×C3×Q8—62no—
312C2×C3×D4—32no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—61no—
316C22×C3×C4—21no—
317C22×C3×C4—32no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C2×#67—21no—
323C2×#67—62no—
324C2×#67—62no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—62no—
328C2×#67—121no—
329C2×#67D1212yes—
330C22×Dic3—21no—
331C22×Dic3—62no—
332C22×Dic3—62no—
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3—62no—
336C22×Dic3—121no—
337#239—38no—
338#239—68no—
339#239—64no—
340D3×Q8—38no—
341D3×Q8—38no—
342D3×Q8—68no—
343D3×Q8—68no—
344D3×Q8—64no—
345D3×Q8—64no—
346D3×Q8—68no—
347#237—38no—
348#237—68no—
349#237—68no—
350#237—616no—
351#237—616no—
352#237—616no—
353#237—64no—
354#235—22no—
355#235—34no—
356#235—34no—
357#235—38no—
358#235—38no—
359#235—64no—
360#235—64no—
361#235—64no—
362#235—62no—
363#235—62no—
364#235—616no—
365#235—68no—
366#235—122no—
367#235D1214yes—
368#235C22×D314yes—
369#235C22×D314yes—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—61no—
373C2×D12—62no—
374C2×D12D1211yescharacteristic
375C2×D12C22×D311yescharacteristic
376C2×C4×D3—21no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—62no—
384C2×C4×D3—121no—
385C2×C4×D3C22×D312yes—
386C2×Dic6—21no—
387C2×Dic6—22no—
388C2×Dic6—31no—
389C2×Dic6—32no—
390C2×Dic6—32no—
391C2×Dic6—34no—
392C2×Dic6—31no—
393C2×Dic6—34no—
394C2×Dic6—38no—
395C2×Dic6—38no—
396C2×Dic6—62no—
397C2×Dic6—61no—
398C2×Dic6—64no—
399C2×Dic6—64no—
400C2×Dic6—64no—
401C2×Dic6—62no—
402C2×Dic6—62no—
403C2×Dic6—61no—
404C2×Dic6—62no—
405C2×Dic6—61no—
406C2×Dic6—62no—
407C2×Dic6—62no—
408C2×Dic6—62no—
409C2×Dic6—68no—
410C2×Dic6—121no—
411C2×Dic6—122no—
412C2×Dic6D1211yescharacteristic
413C2×Dic6C22×D311yescharacteristic
414C2×Dic6C22×D312yes—
415C2×Dic6C22×D314yes—
416C3×Q16—38no—
417C3×SD16—38no—
418C3×M16—24no—
419C3×M16—38no—
420C3×M16C22×D314yes—
421C3×M16C22×D314yes—
422C2×C3×C8—22no—
423C2×C3×C8—31no—
424C2×C3×C8—31no—
425C2×C3×C8—34no—
426C2×C3×C8—38no—
427C2×C3×C8C22×D312yes—
428C2×C3×C8C22×D312yes—
429#216—38no—
430#216—38no—
431#216—34no—
432#215—34no—
433#214—34no—
434#213—34no—
435C2×C3⋊C8C22×D311yescharacteristic
436C2×C3⋊C8C22×D311yescharacteristic
437C2×C3⋊C8C22×D314yes—
438Dic12—34no—
439Dic12—38no—
440Dic12—38no—
441Dic12—38no—
442Dic12—38no—
443Dic12—68no—
444Dic12C22×D318yes—
445D24—34no—
446#204—34no—
447#204—34no—
448#204—38no—
449#204—38no—
450#204—68no—
451#204C22×D318yes—
452ΓL(1,𝔽25)C22×D318yes—
453D3×C8C22×D318yes—
454C22×C32—22no—
455C22×C32C22×D412yes—
456C22×C32C22×D411yescharacteristic
457C2×C3⋊D3—22no—
458C2×C3⋊D3—42no—
459C2×C3×D3—24no—
460C2×C3×D3—22no—
461C2×C3×D3—42no—
462C2×C3×D3C22×D414yes—
463C32×C4C22×D411yescharacteristic
464C32×C4C22×D412yes—
465C32×C4C2511yescharacteristic
466C3⋊Dic3—24no—
467C3⋊Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—24no—
470C3×Dic3C22×D414yes—
4712−1+4—98no—
4722−1+4—98no—
4732−1+4—184no—
4742−1+4—184no—
475C2×#41—31no—
476C2×#41—31no—
477C2×#41—92no—
478C2×#41—92no—
479C2×#41—91no—
480C2×#41—182no—
481C2×#41—181no—
482C2×#41—182no—
483C2×#41—181no—
484C22×Q8—31no—
485C22×Q8—92no—
486C22×Q8—92no—
487C22×Q8—91no—
488C22×Q8—181no—
489C22×Q8—181no—
490#137—38no—
491#137—916no—
492#137—916no—
493#137—98no—
494#135—916no—
495#135—98no—
496C2×Q16—32no—
497C2×Q16—916no—
498C2×Q16—92no—
499C2×Q16—91no—
500C2×Q16—92no—
501C2×Q16—98no—
502C2×Q16—92no—
503C2×SD16—32no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—92no—
507C2×D8—91no—
508#131—38no—
509C2×M16—32no—
510C2×M16D3211yescharacteristic
511C22×C8—31no—
512C22×C8—32no—
513C23×C3—21no—
514C23×C3—32no—
515C23×C3—61no—
516C23×C3C2×D1211yescharacteristic
517C23×C3D3×D411yescharacteristic
518C22×D3—21no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—121no—
522C22×D3C2×D1212yes—
523C3×Q8—34no—
524C3×Q8—32no—
525C3×Q8—34no—
526C3×Q8—61no—
527C3×Q8—62no—
528C3×Q8—64no—
529C3×D4—38no—
530C3×D4—34no—
531C3×D4—32no—
532C3×D4—64no—
533C3×D4—61no—
534C2×C3×C4—21no—
535C2×C3×C4—22no—
536C2×C3×C4—21no—
537C2×C3×C4—22no—
538C2×C3×C4—32no—
539C2×C3×C4—34no—
540C2×C3×C4—34no—
541C2×C3×C4—61no—
542C2×C3×C4—62no—
543C2×C3×C4—64no—
544C2×C3×C4—64no—
545C2×C3×C4C2×D1211yescharacteristic
546C2×C3×C4C2×D1212yes—
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4D3×D412yes—
549C2×C3×C4C23×D311yescharacteristic
550C2×C3×C4C23×D312yes—
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D312yes—
553#67—24no—
554#67—68no—
555#67—68no—
556#67—64no—
557#67—64no—
558#67—68no—
559#67—124no—
560#67C2×D1218yes—
561C2×Dic3—22no—
562C2×Dic3—24no—
563C2×Dic3—21no—
564C2×Dic3—68no—
565C2×Dic3—68no—
566C2×Dic3—61no—
567C2×Dic3—62no—
568C2×Dic3—64no—
569C2×Dic3—62no—
570C2×Dic3—61no—
571C2×Dic3—64no—
572C2×Dic3—68no—
573C2×Dic3—124no—
574C2×Dic3—122no—
575C2×Dic3—121no—
576C2×Dic3C2×D1212yes—
577D12—21no—
578D12—32no—
579D12—32no—
580D12—62no—
581D12—68no—
582D12—61no—
583D12—61no—
584D12—121no—
585D12C2×D1214yes—
586D12C23×D312yes—
587C4×D3—24no—
588C4×D3—68no—
589C4×D3—68no—
590C4×D3—68no—
591C4×D3—68no—
592C4×D3—64no—
593C4×D3—64no—
594C4×D3—68no—
595C4×D3—124no—
596C4×D3C2×D1214yes—
597C4×D3C23×D314yes—
598Dic6—22no—
599Dic6—24no—
600Dic6—21no—
601Dic6—32no—
602Dic6—34no—
603Dic6—34no—
604Dic6—32no—
605Dic6—64no—
606Dic6—62no—
607Dic6—68no—
608Dic6—68no—
609Dic6—64no—
610Dic6—62no—
611Dic6—61no—
612Dic6—61no—
613Dic6—62no—
614Dic6—64no—
615Dic6—68no—
616Dic6—68no—
617Dic6—122no—
618Dic6—124no—
619Dic6—121no—
620Dic6C2×D1214yes—
621Dic6C23×D312yes—
622Dic6C23×D314yes—
623C3×C8—24no—
624C3×C8—32no—
625C3×C8—32no—
626C3×C8C23×D314yes—
627C3×C8C23×D314yes—
628C3⋊C8C23×D312yes—
629C3⋊C8C23×D312yes—
630C2×C32—22no—
631C2×C32#57812yescomplemented
632C2×C32C23×D411yescharacteristic
633C3⋊D3—42no—
634C3×D3—24no—
635C3×D3—42no—
636#41—34no—
637#41—34no—
638#41—34no—
639#41—62no—
640#41—98no—
641#41—98no—
642#41—94no—
643#41—184no—
644#41—184no—
645#41—1816no—
646#41—188no—
647#41—1816no—
648#41—188no—
649#41—182no—
650C2×Q8—31no—
651C2×Q8—32no—
652C2×Q8—31no—
653C2×Q8—34no—
654C2×Q8—61no—
655C2×Q8—62no—
656C2×Q8—98no—
657C2×Q8—98no—
658C2×Q8—91no—
659C2×Q8—92no—
660C2×Q8—94no—
661C2×Q8—182no—
662C2×Q8—182no—
663C2×Q8—184no—
664C2×Q8—184no—
665C2×Q8—188no—
666C2×Q8—188no—
667C2×Q8—181no—
668C2×Q8—182no—
669C2×D4—32no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—61no—
673C2×D4—91no—
674C2×D4—182no—
675C2×D4—182no—
676C2×D4—181no—
677C22×C4—32no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—182no—
681C22×C4—182no—
682C22×C4—182no—
683C22×C4—182no—
684C22×C4—181no—
685C22×C4—181no—
686C22×C4C2×D3211yescharacteristic
687Q16—38no—
688Q16—98no—
689Q16—94no—
690Q16—98no—
691Q16—98no—
692SD16—38no—
693SD16—94no—
694SD16—94no—
695SD16—98no—
696D8—94no—
697M16—38no—
698M16C2×D3214yes—
699C2×C8—31no—
700C2×C8—31no—
701C2×C8—34no—
702C2×C8—38no—
703C2×C8C2×D3212yes—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—21no—
708C22×C3—34no—
709C22×C3—42no—
710C22×C3—64no—
711C22×C3—62no—
712C22×C3—122no—
713C22×C3C22×D1212yes—
714C22×C3C22×D1211yescharacteristic
715C22×C3C2×D3×D412yes—
716C22×C3C2×D3×D411yescharacteristic
717C2×D3—24no—
718C2×D3—22no—
719C2×D3—42no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—122no—
723C2×D3—122no—
724C2×D3—122no—
725C2×D3—242no—
726C2×D3C22×D1214yes—
727C3×C4—21no—
728C3×C4—22no—
729C3×C4—21no—
730C3×C4—34no—
731C3×C4—62no—
732C3×C4—64no—
733C3×C4C22×D1211yescharacteristic
734C3×C4C22×D1212yes—
735C3×C4C2×D3×D411yescharacteristic
736C3×C4C2×D3×D412yes—
737C3×C4C24×D311yescharacteristic
738C3×C4C24×D311yescharacteristic
739Dic3—24no—
740Dic3—22no—
741Dic3—62no—
742Dic3—64no—
743Dic3—62no—
744Dic3—64no—
745Dic3—124no—
746Dic3—122no—
747Dic3C22×D1214yes—
748C32C2×#57811yescharacteristic, complemented, Sylow
749C23—32no—
750C23—61no—
751C23—181no—
752C23D3×D1211yescharacteristic
753Q8—34no—
754Q8—34no—
755Q8—32no—
756Q8—62no—
757Q8—64no—
758Q8—61no—
759Q8—92no—
760Q8—94no—
761Q8—188no—
762Q8—188no—
763Q8—181no—
764Q8—182no—
765Q8—184no—
766D4—38no—
767D4—34no—
768D4—32no—
769D4—64no—
770D4—61no—
771D4—92no—
772D4—188no—
773D4—188no—
774D4—184no—
775D4—181no—
776C2×C4—32no—
777C2×C4—34no—
778C2×C4—34no—
779C2×C4—64no—
780C2×C4—61no—
781C2×C4—62no—
782C2×C4—64no—
783C2×C4—188no—
784C2×C4—188no—
785C2×C4—188no—
786C2×C4—188no—
787C2×C4—184no—
788C2×C4—182no—
789C2×C4—181no—
790C2×C4—184no—
791C2×C4D3×D1212yes—
792C2×C4D3×D1211yescharacteristic
793C2×C4C22×D3212yes—
794C2×C4C22×D3211yescharacteristic
795C8—32no—
796C8—32no—
797C8C22×D3214yes—
798C2×C3—22no—
799C2×C3—22no—
800C2×C3—21no—
801C2×C3—22no—
802C2×C3—42no—
803C2×C3—64no—
804C2×C3—122no—
805C2×C3#575312yescomplemented
806C2×C3#577912yescomplemented
807C2×C3C23×D1211yescharacteristic
808C2×C3C22×D3×D411yescharacteristic
809D3—24no—
810D3—42no—
811D3—122no—
812D3—122no—
813D3—242no—
814C22—22no—
815C22—34no—
816C22—64no—
817C22—62no—
818C22—122no—
819C22—182no—
820C22—362no—
821C22C2×D3×D1212yes—
822C22C2×D3×D1211yescharacteristic
823C4—34no—
824C4—62no—
825C4—64no—
826C4—184no—
827C4—182no—
828C4C2×D3×D1211yescharacteristic
829C4C2×D3×D1212yes—
830C4C23×D3211yescharacteristic
831C3—21no—
832C3C2×#575311yescharacteristic, complemented
833C3C2×#577911yescharacteristic, complemented
834C2—22no—
835C2—64no—
836C2—122no—
837C2—362no—
838C2#1059472112yesdirect product factor
839C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32C2×#578
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×#64298C2semidirect
2. C2×#64297C2semidirect
3. C2×#64118C2semidirect
4. C2×C3×#909C2semidirect
5. C2×C3×#907C2semidirect
6. C22×#3719C2semidirect
7. C2×#63829C2semidirect
8. #10594721C2direct (N × H)
9. C2×#63806C2semidirect
10. C2×#63801C2semidirect
11. C2×#63800C2semidirect
12. C2×D3×Dic12C2semidirect
25. #64298C22semidirect
27. #64297C22semidirect
35. #64118C22semidirect
39. C3×#909C22semidirect
40. C3×#907C22semidirect
48. C2×#3719C22semidirect
50. #63829C22semidirect
53. #63806C22semidirect
54. #63801C22semidirect
55. #63800C22semidirect
56. D3×Dic12C22semidirect
76. C2×#909D3semidirect
77. C2×#907D3semidirect
219. #909C2×D3semidirect
220. #907C2×D3semidirect
631. C2×C32#578semidirect
748. C32C2×#578semidirect
805. C2×C3#5753semidirect
806. C2×C3#5779semidirect
832. C3C2×#5753semidirect
833. C3C2×#5779semidirect
838. C2#10594721direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642982
C2×#642972
C2×#641182
C2×C3×#9092
C2×C3×#9072
C22×#37192
C2×#638292
#105947212
C2×#638062
C2×#638012
C2×#638002
C2×D3×Dic122
C2×#57793
C2×#57533