Finite Group Databasebeta

← C2×#10595472 #11918943

Subgroups — C2×#10595472 #11918943

Order 1152.

3213 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C2×C3×#951C211yesmaximal, characteristic, complemented
4C2×C3×#950C211yesmaximal, characteristic, complemented
5#10595472C2116yesmaximal, direct product factor
6C2×#63951C212yesmaximal, complemented
7C2×#63944C212yesmaximal, complemented
8C2×#63936C212yesmaximal, complemented
9C2×#63931C212yesmaximal, complemented
10C22×#3719C211yesmaximal, characteristic, complemented
11C2×#63831C211yesmaximal, characteristic, complemented
12C2×#63817C211yesmaximal, characteristic, complemented
13C2×#5779—31nomaximal
14C2×#5771—31nomaximal
15C2×C32×#41C2211yescharacteristic
16#64367—24no—
17#64367C2218yescomplemented
18C2×Q8×C3⋊D3C2212yes—
19C2×#3830—22no—
20C2×#3830C2212yes—
21C2×#3828—21no—
22C2×#3828C2211yescharacteristic
23C22×#634—21no—
24C22×#634C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C2×#3804—22no—
28C2×#3799—21no—
29C2×#3797C2212yes—
30#64297—24no—
31#64297C2218yescomplemented
32C2×#3796C2212yes—
33C2×D3×Dic6—21no—
34C3×#951C2218yescomplemented
35C3×#950C2218yescomplemented
36C2×C3×#216C2211yescharacteristic
37C2×C3×#216C2212yes—
38C2×C3×#215C2211yescharacteristic
39C2×C3×#214C2211yescharacteristic
40C2×C3×#214C2212yes—
41C2×C3×#213C2211yescharacteristic
42C2×C3×#208C2211yescharacteristic
43C22×C3×C3⋊C8C2211yescharacteristic
44#63951C22116yescomplemented
45#63944C22116yescomplemented
46#63936C22116yescomplemented
47#63931C22116yescomplemented
48C2×#3719C2212yes—
49C2×#3719C2212yes—
50C2×#3719C2212yes—
51C2×#3719C2218yescomplemented
52#63831C2218yescomplemented
53C2×#3716C2212yes—
54C2×#3712C2212yes—
55#63817C2218yescomplemented
56C2×#3710C2212yes—
57C2×#1010—31no—
58C2×#1010—31no—
59C2×#1010—31no—
60C2×#1010—61no—
61C2×#1007—31no—
62C2×C3×#137—31no—
63C2×C3×#135—31no—
64C2×#951—31no—
65C2×#951D311yescharacteristic, complemented
66C2×#950D311yescharacteristic, complemented
67C22×#216—31no—
68#5779—316no—
69#5771—316no—
70C2×#918—32no—
71C2×D3×Q16—32no—
72C2×D3×Q16—32no—
73C2×#916—32no—
74C2×#915—32no—
75C2×#915—32no—
76C2×#915—32no—
77C2×#912—32no—
78C2×#909—31no—
79C2×#907—31no—
80C22×Dic12—31no—
81C2×#901—31no—
82C32×#41—22no—
83C32×#41C2314yes—
84C2×C32×Q8C2311yescharacteristic
85C2×C32×D4—21no—
86C2×C32×D4C2311yescharacteristic
87C22×C32×C4—21no—
88C22×C32×C4C2311yescharacteristic
89C2×#638—22no—
90C2×#638D412yes—
91C22×C3⋊Dic3—21no—
92C22×C3⋊Dic3—22no—
93Q8×C3⋊D3—24no—
94Q8×C3⋊D3C2318yes—
95#3830—216no—
96#3830—24no—
97#3830C2318yes—
98#3828—28no—
99#3828D414yes—
100#3828C2314yes—
101C2×C4⋊(C3⋊D3)D411yescharacteristic
102C2×C4×C3⋊D3—22no—
103C2×C4×C3⋊D3C2312yes—
104C2×#634—21no—
105C2×#634—22no—
106C2×#634—22no—
107C2×#634—28no—
108C2×#634D411yescharacteristic
109C2×#634C2312yes—
110C2×#634C2314yes—
111C2×C3×#67—21no—
112C22×C3×Dic3—21no—
113C3×#235—22no—
114C3×#235C2314yes—
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×Dic6—21no—
118C2×C3×Dic6—22no—
119C2×C3×Dic6C2312yes—
120C2×C3×Dic6C2314yes—
121C2×C3×Dic6C2311yescharacteristic
122C2×#627—22no—
123C2×#626—22no—
124C2×#624—22no—
125#3804—216no—
126C2×D3×Dic3—22no—
127#3799—28no—
128#3797—24no—
129#3797C2318yes—
130#3796—24no—
131#3796C2318yes—
132D3×Dic6—28no—
133C3×#216C2314yes—
134C3×#216C2318yes—
135C3×#215C2314yes—
136C3×#214C2314yes—
137C3×#214C2318yes—
138C3×#213C2314yes—
139C3×#208C2314yes—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2314yes—
143C2×C3×C3⋊C8C2312yes—
144#3719C2318yes—
145#3719C2318yes—
146#3719C2318yes—
147#3716C2318yes—
148#3712C2318yes—
149#3710C2318yes—
150C2×#578—91noSylow
151C2×C3×#41—21no—
152C2×C3×#41—31no—
153C2×C3×#41C2×D311yescharacteristic
154C2×C3×#41C2×D311yescharacteristic
155C22×C3×Q8—31no—
156#1010—38no—
157#1010—38no—
158#1010—38no—
159#1010—68no—
160#1010—64no—
161#1010—64no—
162#1010—64no—
163#1010—68no—
164#1007—38no—
165#1007—64no—
166C2×#239—32no—
167C2×#239—61no—
168C2×D3×Q8—32no—
169C2×D3×Q8—32no—
170C2×D3×Q8—32no—
171C2×D3×Q8—32no—
172C2×D3×Q8—62no—
173C2×D3×Q8—61no—
174C2×#237—32no—
175C2×#237—32no—
176C2×#237—32no—
177C2×#237—62no—
178C2×#237—62no—
179C2×#237—62no—
180C2×#237—62no—
181C2×#237—64no—
182C2×#235—31no—
183C2×#235—31no—
184C2×#235—61no—
185C2×#235—61no—
186C2×#235—61no—
187C2×#235—61no—
188C2×#235—62no—
189C2×#235—62no—
190C2×#235C2×D311yescharacteristic
191C22×Dic6—31no—
192C22×Dic6—31no—
193C22×Dic6—61no—
194C22×Dic6—61no—
195C22×Dic6—61no—
196C22×Dic6—61no—
197C22×Dic6—62no—
198C22×Dic6C2×D311yescharacteristic
199C3×#137—38no—
200C3×#135—38no—
201C2×C3×Q16—31no—
202C2×C3×Q16—32no—
203C2×C3×SD16—31no—
204C2×C3×SD16—31no—
205C2×C3×SD16—32no—
206C2×C3×D8—31no—
207C2×C3×M16—31no—
208C22×C3×C8—31no—
209#951—38no—
210#951C2×D318yescomplemented
211#950C2×D318yescomplemented
212C2×#216—32no—
213C2×#216—32no—
214C2×#216—32no—
215C2×#216—38no—
216C2×#216C2×D312yes—
217C2×#216C2×D311yescharacteristic
218C2×#215C2×D311yescharacteristic
219C2×#214—32no—
220C2×#214C2×D312yes—
221C2×#214C2×D311yescharacteristic
222C2×#213C2×D311yescharacteristic
223C2×#208C2×D311yescharacteristic
224C22×C3⋊C8C2×D311yescharacteristic
225#918—316no—
226D3×Q16—316no—
227D3×Q16—316no—
228#916—316no—
229#915—316no—
230#915—316no—
231#915—316no—
232#912—316no—
233#909—38no—
234#907—38no—
235C2×Dic12—32no—
236C2×Dic12—32no—
237C2×Dic12—32no—
238C2×Dic12—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—
249C32×Q8—21no—
250C32×Q8C2412yes—
251C32×D4—24no—
252C32×D4—21no—
253C32×D4C2412yes—
254C2×C32×C4—21no—
255C2×C32×C4—24no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D412yes—
258C2×C32×C4C2411yescharacteristic
259C2×C32×C4C2412yes—
260#638—28no—
261#638C2×D418yes—
262C2×C3⋊Dic3—22no—
263C2×C3⋊Dic3—24no—
264C2×C3⋊Dic3—28no—
265C2×C3⋊Dic3C2×D412yes—
266C4⋊(C3⋊D3)C2×D414yes—
267C4×C3⋊D3—28no—
268C4×C3⋊D3C2×D414yes—
269C4×C3⋊D3C2414yes—
270#634—24no—
271#634—22no—
272#634—28no—
273#634C2×D414yes—
274#634C2414yes—
275C3×#67—24no—
276C2×C3×Dic3—22no—
277C2×C3×Dic3—24no—
278C2×C3×Dic3—21no—
279C3×D12—21no—
280C3×D12C2412yes—
281C3×C4×D3—24no—
282C3×Dic6—24no—
283C3×Dic6—22no—
284C3×Dic6—21no—
285C3×Dic6C2414yes—
286C3×Dic6C2412yes—
287#627—28no—
288#626—28no—
289#624—28no—
290D3×Dic3—28no—
291C3×C3⋊C8C2412yes—
292C3×C3⋊C8C2414yes—
293C3×C3⋊C8C2412yes—
294C2×2−1+4—91no—
295C2×2−1+4—91no—
296#578—916no—
297C2×#137—31no—
298C2×#137—91no—
299C2×#137—92no—
300C2×#137—92no—
301C2×#135—31no—
302C2×#135—92no—
303C22×Q16—91no—
304C22×Q16—92no—
305C2×#131—91no—
306C3×#41—24no—
307C3×#41—22no—
308C3×#41—22no—
309C3×#41—24no—
310C3×#41—34no—
311C3×#41—62no—
312C3×#41C22×D314yes—
313C3×#41C22×D314yes—
314C2×C3×Q8—21no—
315C2×C3×Q8—31no—
316C2×C3×Q8—32no—
317C2×C3×Q8—34no—
318C2×C3×Q8—61no—
319C2×C3×Q8—62no—
320C2×C3×Q8C22×D311yescharacteristic
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×D4—22no—
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—21no—
326C2×C3×D4—31no—
327C2×C3×D4—61no—
328C2×C3×D4C22×D311yescharacteristic
329C2×C3×D4C22×D311yescharacteristic
330C22×C3×C4—22no—
331C22×C3×C4—21no—
332C22×C3×C4—21no—
333C22×C3×C4—21no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C2×#67—21no—
339C2×#67—32no—
340C2×#67—32no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—64no—
346C22×Dic3—21no—
347C22×Dic3—62no—
348C22×Dic3—62no—
349C22×Dic3—62no—
350C22×Dic3—64no—
351C22×Dic3—62no—
352C22×Dic3—61no—
353C22×Dic3—61no—
354#239—38no—
355#239—68no—
356#239—64no—
357D3×Q8—38no—
358D3×Q8—38no—
359D3×Q8—38no—
360D3×Q8—38no—
361D3×Q8—68no—
362D3×Q8—64no—
363D3×Q8—64no—
364D3×Q8—68no—
365D3×Q8—64no—
366D3×Q8—64no—
367D3×Q8—68no—
368#237—38no—
369#237—38no—
370#237—38no—
371#237—68no—
372#237—64no—
373#237—64no—
374#237—64no—
375#237—616no—
376#237—616no—
377#237—616no—
378#237—68no—
379#237—632no—
380#235—22no—
381#235—34no—
382#235—34no—
383#235—34no—
384#235—34no—
385#235—64no—
386#235—64no—
387#235—68no—
388#235—68no—
389#235—68no—
390#235—616no—
391#235—616no—
392#235C22×D314yes—
393C2×D12—31no—
394C2×D12—31no—
395C2×D12—61no—
396C2×D12—62no—
397C2×D12C22×D311yescharacteristic
398C2×C4×D3—21no—
399C2×C4×D3—32no—
400C2×C4×D3—32no—
401C2×C4×D3—62no—
402C2×C4×D3—62no—
403C2×C4×D3—62no—
404C2×C4×D3—62no—
405C2×C4×D3—62no—
406C2×C4×D3—62no—
407C2×C4×D3—64no—
408C2×Dic6—21no—
409C2×Dic6—22no—
410C2×Dic6—31no—
411C2×Dic6—31no—
412C2×Dic6—32no—
413C2×Dic6—32no—
414C2×Dic6—34no—
415C2×Dic6—34no—
416C2×Dic6—61no—
417C2×Dic6—62no—
418C2×Dic6—64no—
419C2×Dic6—68no—
420C2×Dic6—68no—
421C2×Dic6—68no—
422C2×Dic6—62no—
423C2×Dic6—62no—
424C2×Dic6—62no—
425C2×Dic6—62no—
426C2×Dic6—62no—
427C2×Dic6—64no—
428C2×Dic6—616no—
429C2×Dic6—64no—
430C2×Dic6—61no—
431C2×Dic6—61no—
432C2×Dic6—62no—
433C2×Dic6—62no—
434C2×Dic6C22×D312yes—
435C2×Dic6C22×D311yescharacteristic
436C2×Dic6C22×D314yes—
437C3×Q16—34no—
438C3×Q16—38no—
439C3×SD16—34no—
440C3×SD16—34no—
441C3×SD16—38no—
442C3×D8—34no—
443C3×M16—34no—
444C2×C3×C8—31no—
445C2×C3×C8—32no—
446C2×C3×C8—31no—
447C2×C3×C8—34no—
448#216—38no—
449#216—38no—
450#216—38no—
451#216C22×D318yes—
452#216C22×D314yes—
453#215C22×D314yes—
454#214—38no—
455#214C22×D318yes—
456#214C22×D314yes—
457#213C22×D314yes—
458#208C22×D314yes—
459C2×C3⋊C8C22×D311yescharacteristic
460C2×C3⋊C8C22×D312yes—
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D314yes—
463Dic12—38no—
464Dic12—38no—
465Dic12—38no—
466#204—38no—
467ΓL(1,𝔽25)—38no—
468ΓL(1,𝔽25)—38no—
469D3×C8—38no—
470D3×C8—38no—
471C22×C32—22no—
472C22×C32—22no—
473C22×C32—42no—
474C22×C32C22×D412yes—
475C22×C32C22×D411yescharacteristic
476C2×C3⋊D3—24no—
477C2×C3⋊D3C22×D414yes—
478C2×C3×D3—22no—
479C2×C3×D3—42no—
480C32×C4—22no—
481C32×C4C22×D411yescharacteristic
482C32×C4C22×D412yes—
483C32×C4C2511yescharacteristic
484C3⋊Dic3—24no—
485C3⋊Dic3C22×D414yes—
486C3×Dic3—24no—
487C3×Dic3—22no—
4882−1+4—98no—
4892−1+4—98no—
4902−1+4—184no—
4912−1+4—184no—
492C2×#41—31no—
493C2×#41—91no—
494C2×#41—92no—
495C2×#41—92no—
496C2×#41—181no—
497C2×#41—182no—
498C2×#41—181no—
499C2×#41—182no—
500C2×#41D3211yescharacteristic
501C22×Q8—31no—
502C22×Q8—92no—
503C22×Q8—92no—
504C22×Q8—91no—
505C22×Q8—181no—
506C22×Q8—181no—
507#137—38no—
508#137—98no—
509#137—916no—
510#137—916no—
511#135—38no—
512#135—916no—
513C2×Q16—31no—
514C2×Q16—32no—
515C2×Q16—92no—
516C2×Q16—92no—
517C2×Q16—92no—
518C2×Q16—98no—
519C2×Q16—916no—
520C2×SD16—31no—
521C2×SD16—31no—
522C2×SD16—32no—
523C2×SD16—92no—
524C2×D8—31no—
525#131—98no—
526C2×M16—31no—
527C2×M16—92no—
528C22×C8—31no—
529C22×C8—92no—
530C23×C3—22no—
531C23×C3—21no—
532C23×C3—21no—
533C23×C3—21no—
534C23×C3—61no—
535C23×C3D3×D411yescharacteristic
536C23×C3D3×D411yescharacteristic
537C22×D3—21no—
538C22×D3—32no—
539C22×D3—32no—
540C22×D3—62no—
541C3×Q8—22no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—22no—
545C3×Q8—32no—
546C3×Q8—34no—
547C3×Q8—61no—
548C3×Q8—62no—
549C3×Q8—64no—
550C3×Q8C23×D312yes—
551C3×Q8C23×D312yes—
552C3×D4—28no—
553C3×D4—22no—
554C3×D4—24no—
555C3×D4—24no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—22no—
559C3×D4—32no—
560C3×D4—64no—
561C3×D4—61no—
562C3×D4C23×D312yes—
563C3×D4C23×D312yes—
564C2×C3×C4—22no—
565C2×C3×C4—28no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—24no—
569C2×C3×C4—24no—
570C2×C3×C4—21no—
571C2×C3×C4—22no—
572C2×C3×C4—21no—
573C2×C3×C4—22no—
574C2×C3×C4—61no—
575C2×C3×C4—62no—
576C2×C3×C4—64no—
577C2×C3×C4—64no—
578C2×C3×C4D3×D411yescharacteristic
579C2×C3×C4D3×D412yes—
580C2×C3×C4D3×D411yescharacteristic
581C2×C3×C4D3×D412yes—
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D312yes—
585C2×C3×C4C23×D312yes—
586#67—24no—
587#67—38no—
588#67—38no—
589#67—68no—
590#67—68no—
591#67—68no—
592#67—68no—
593#67—616no—
594C2×Dic3—22no—
595C2×Dic3—24no—
596C2×Dic3—21no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—62no—
600C2×Dic3—68no—
601C2×Dic3—68no—
602C2×Dic3—68no—
603C2×Dic3—64no—
604C2×Dic3—616no—
605C2×Dic3—68no—
606C2×Dic3—62no—
607C2×Dic3—62no—
608C2×Dic3—64no—
609C2×Dic3—64no—
610D12—21no—
611D12—34no—
612D12—34no—
613D12—64no—
614D12—68no—
615D12C23×D312yes—
616C4×D3—24no—
617C4×D3—34no—
618C4×D3—34no—
619C4×D3—34no—
620C4×D3—34no—
621C4×D3—64no—
622C4×D3—64no—
623C4×D3—68no—
624C4×D3—68no—
625C4×D3—68no—
626C4×D3—68no—
627C4×D3—68no—
628C4×D3—616no—
629Dic6—24no—
630Dic6—22no—
631Dic6—21no—
632Dic6—34no—
633Dic6—34no—
634Dic6—34no—
635Dic6—34no—
636Dic6—64no—
637Dic6—64no—
638Dic6—68no—
639Dic6—68no—
640Dic6—68no—
641Dic6—68no—
642Dic6—68no—
643Dic6—616no—
644Dic6—64no—
645Dic6—64no—
646Dic6—64no—
647Dic6—62no—
648Dic6—62no—
649Dic6C23×D314yes—
650Dic6C23×D312yes—
651C3×C8—32no—
652C3×C8—34no—
653C3×C8—32no—
654C3⋊C8C23×D312yes—
655C3⋊C8C23×D314yes—
656C3⋊C8C23×D312yes—
657C2×C32—22no—
658C2×C32—42no—
659C2×C32#57812yescomplemented
660C2×C32C23×D411yescharacteristic
661C3⋊D3—24no—
662C3×D3—42no—
663#41—22no—
664#41—34no—
665#41—62no—
666#41—94no—
667#41—94no—
668#41—98no—
669#41—98no—
670#41—188no—
671#41—1816no—
672#41—188no—
673#41—184no—
674#41—184no—
675#41—1816no—
676#41C2×D3214yes—
677C2×Q8—32no—
678C2×Q8—31no—
679C2×Q8—34no—
680C2×Q8—61no—
681C2×Q8—62no—
682C2×Q8—91no—
683C2×Q8—98no—
684C2×Q8—98no—
685C2×Q8—92no—
686C2×Q8—94no—
687C2×Q8—182no—
688C2×Q8—188no—
689C2×Q8—182no—
690C2×Q8—188no—
691C2×Q8—184no—
692C2×Q8—184no—
693C2×Q8—181no—
694C2×Q8—182no—
695C2×Q8C2×D3211yescharacteristic
696C2×D4—21no—
697C2×D4—31no—
698C2×D4—61no—
699C2×D4—92no—
700C2×D4—91no—
701C2×D4—182no—
702C2×D4—182no—
703C2×D4C2×D3211yescharacteristic
704C22×C4—21no—
705C22×C4—61no—
706C22×C4—61no—
707C22×C4—92no—
708C22×C4—182no—
709C22×C4—182no—
710C22×C4—182no—
711C22×C4—182no—
712C22×C4—181no—
713C22×C4C2×D3211yescharacteristic
714Q16—34no—
715Q16—38no—
716Q16—98no—
717Q16—98no—
718Q16—98no—
719SD16—34no—
720SD16—34no—
721SD16—38no—
722SD16—98no—
723D8—34no—
724M16—34no—
725M16—98no—
726C2×C8—31no—
727C2×C8—31no—
728C2×C8—34no—
729C2×C8—32no—
730C2×C8—98no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—24no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—21no—
738C22×C3—42no—
739C22×C3—44no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—62no—
743C22×C3—122no—
744C22×C3C2×D3×D412yes—
745C22×C3C2×D3×D412yes—
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C2×D3×D411yescharacteristic
748C2×D3—22no—
749C2×D3—34no—
750C2×D3—34no—
751C2×D3—42no—
752C2×D3—64no—
753C2×D3—64no—
754C2×D3—64no—
755C2×D3—124no—
756C3×C4—24no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—62no—
763C3×C4—64no—
764C3×C4C2×D3×D412yes—
765C3×C4C2×D3×D411yescharacteristic
766C3×C4C2×D3×D411yescharacteristic
767C3×C4C2×D3×D412yes—
768C3×C4C24×D311yescharacteristic
769C3×C4C24×D311yescharacteristic
770Dic3—24no—
771Dic3—22no—
772Dic3—34no—
773Dic3—34no—
774Dic3—64no—
775Dic3—68no—
776Dic3—64no—
777Dic3—64no—
778C32C2×#57811yescharacteristic, complemented, Sylow
779C23—21no—
780C23—61no—
781C23—92no—
782C23#381111yescharacteristic
783Q8—21no—
784Q8—34no—
785Q8—32no—
786Q8—64no—
787Q8—62no—
788Q8—61no—
789Q8—94no—
790Q8—94no—
791Q8—188no—
792Q8—188no—
793Q8—184no—
794Q8—182no—
795Q8C22×D3212yes—
796D4—24no—
797D4—21no—
798D4—32no—
799D4—64no—
800D4—61no—
801D4—98no—
802D4—94no—
803D4—188no—
804D4—188no—
805D4C22×D3212yes—
806C2×C4—21no—
807C2×C4—24no—
808C2×C4—64no—
809C2×C4—61no—
810C2×C4—62no—
811C2×C4—64no—
812C2×C4—92no—
813C2×C4—94no—
814C2×C4—94no—
815C2×C4—188no—
816C2×C4—188no—
817C2×C4—188no—
818C2×C4—188no—
819C2×C4—184no—
820C2×C4—182no—
821C2×C4#381112yes—
822C2×C4#381111yescharacteristic
823C2×C4C22×D3212yes—
824C2×C4C22×D3211yescharacteristic
825C8—32no—
826C8—32no—
827C8—34no—
828C2×C3—22no—
829C2×C3—22no—
830C2×C3—21no—
831C2×C3—22no—
832C2×C3—42no—
833C2×C3—44no—
834C2×C3—42no—
835C2×C3—42no—
836C2×C3—122no—
837C2×C3#577112yescomplemented
838C2×C3#577912yescomplemented
839C2×C3C22×D3×D411yescharacteristic
840C2×C3C22×D3×D411yescharacteristic
841D3—42no—
842D3—64no—
843D3—64no—
844D3—124no—
845C22—22no—
846C22—22no—
847C22—42no—
848C22—62no—
849C22—94no—
850C22—122no—
851C22—184no—
852C22C2×#381112yes—
853C22C2×#381111yescharacteristic
854C4—22no—
855C4—62no—
856C4—64no—
857C4—94no—
858C4—184no—
859C4C2×#381112yes—
860C4C2×#381111yescharacteristic
861C4C23×D3211yescharacteristic
862C3—21no—
863C3C2×#577111yescharacteristic, complemented
864C3C2×#577911yescharacteristic, complemented
865C2—22no—
866C2—42no—
867C2—122no—
868C2—184no—
869C2#1059547212yesdirect product factor
870C2C22×#381111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#578
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×#64297C2semidirect
3. C2×C3×#951C2semidirect
4. C2×C3×#950C2semidirect
5. #10595472C2direct (N × H)
6. C2×#63951C2semidirect
7. C2×#63944C2semidirect
8. C2×#63936C2semidirect
9. C2×#63931C2semidirect
10. C22×#3719C2semidirect
11. C2×#63831C2semidirect
12. C2×#63817C2semidirect
17. #64367C22semidirect
31. #64297C22semidirect
34. C3×#951C22semidirect
35. C3×#950C22semidirect
44. #63951C22semidirect
45. #63944C22semidirect
46. #63936C22semidirect
47. #63931C22semidirect
51. C2×#3719C22semidirect
52. #63831C22semidirect
55. #63817C22semidirect
65. C2×#951D3semidirect
66. C2×#950D3semidirect
210. #951C2×D3semidirect
211. #950C2×D3semidirect
659. C2×C32#578semidirect
778. C32C2×#578semidirect
837. C2×C3#5771semidirect
838. C2×C3#5779semidirect
863. C3C2×#5771semidirect
864. C3C2×#5779semidirect
869. C2#10595472direct (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×#642972
C2×C3×#9512
C2×C3×#9502
#105954722
C2×#639512
C2×#639442
C2×#639362
C2×#639312
C22×#37192
C2×#638312
C2×#638172
C2×#57793
C2×#57713