Finite Group Databasebeta

← C2×#10595327 #11918938

Subgroups — C2×#10595327 #11918938

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×C3×#1007C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C2×#64151C211yesmaximal, characteristic, complemented
4C22×C3×#216C211yesmaximal, characteristic, complemented
5C2×#63949C212yesmaximal, complemented
6C2×#63948C212yesmaximal, complemented
7#10595327C2116yesmaximal, direct product factor
8C2×#63943C212yesmaximal, complemented
9C2×D3×#216C212yesmaximal, complemented
10C2×#63829C211yesmaximal, characteristic, complemented
11C2×#63827C211yesmaximal, characteristic, complemented
12C2×#63814C211yesmaximal, characteristic, complemented
13C2×#5838—31nomaximal
14C2×#5766—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C2×#3828C2211yescharacteristic
17C3×#1007—24no—
18C3×#1007C2218yescomplemented
19C2×C3×#239—21no—
20C2×C3×#239C2212yes—
21C2×C3×D3×Q8—21no—
22C2×C3×D3×Q8C2212yes—
23C2×C3×#235—22no—
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C2×#3804—22no—
28C2×#3799C2212yes—
29C2×#3797—21no—
30#64297—24no—
31#64297C2218yescomplemented
32C2×#3796—21no—
33C2×D3×Dic6C2212yes—
34C2×#3756C2212yes—
35#64151C2218yescomplemented
36C2×#3755C2212yes—
37C2×#3748C2211yescharacteristic
38C2×C3×#216C2212yes—
39C2×C3×#216C2212yes—
40C2×C3×#216C2218yescomplemented
41C22×C3×C3⋊C8C2211yescharacteristic
42#63949C22116yescomplemented
43#63948C22116yescomplemented
44#63943C22116yescomplemented
45D3×#216C22116yescomplemented
46C2×#3719C2211yescharacteristic
47C2×#3718C2212yes—
48C2×#3717C2211yescharacteristic
49#63829C2218yescomplemented
50C2×#3716C2211yescharacteristic
51#63827C2218yescomplemented
52C2×#3715C2212yes—
53C2×#3714C2211yescharacteristic
54C2×#3711C2212yes—
55#63814C2218yescomplemented
56C2×D3×C3⋊C8C2212yes—
57C2×C3×2−1+4—31no—
58C2×#1010—31no—
59C2×#1007—31no—
60C2×#1007D311yescharacteristic, complemented
61C22×C3×Q16—31no—
62#5838—316no—
63C2×#951—31no—
64C2×#951—32no—
65C2×#950—32no—
66C2×#950—31no—
67C2×#948—31no—
68C22×#216—32no—
69C22×#216D311yescharacteristic, complemented
70C2×#942—31no—
71C2×#942—31no—
72C2×#942—31no—
73C2×#942—32no—
74C2×#942—61no—
75#5766—316no—
76C2×#919—32no—
77C2×#918—32no—
78C2×#918—32no—
79C2×D3×Q16—32no—
80C2×#904—31no—
81C2×#901—31no—
82C2×C32×Q8—21no—
83C2×C32×Q8—22no—
84C2×C32×Q8C2312yes—
85C2×C32×Q8C2314yes—
86C22×C32×C4—21no—
87C22×C32×C4C2311yescharacteristic
88C2×#638—21no—
89#3828—22no—
90#3828C2314yes—
91C2×C4⋊(C3⋊D3)C2311yescharacteristic
92C2×C4×C3⋊D3—21no—
93C2×#634C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67D412yes—
96C22×C3×Dic3—21no—
97C3×#239—28no—
98C3×#239—24no—
99C3×#239C2318yes—
100C3×D3×Q8—24no—
101C3×D3×Q8—28no—
102C3×D3×Q8C2318yes—
103C3×#235—22no—
104C3×#235—216no—
105C3×#235D414yes—
106C3×#235C2314yes—
107C3×#235C2314yes—
108C2×C3×D12—22no—
109C2×C3×D12D411yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3C2312yes—
115C2×C3×Dic6—21no—
116C2×C3×Dic6—22no—
117C2×C3×Dic6—22no—
118C2×C3×Dic6D411yescharacteristic
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—24no—
128#3799C2318yes—
129#3797—28no—
130#3796—28no—
131D3×Dic6—24no—
132D3×Dic6C2318yes—
133#3756C2318yes—
134#3755C2318yes—
135#3748C2314yes—
136C2×C3⋊(C3⋊C8)C2312yes—
137C3×#216C2318yes—
138C3×#216C2318yes—
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2314yes—
142#3719C2314yes—
143#3718C2318yes—
144#3717C2314yes—
145#3716C2314yes—
146#3715C2318yes—
147#3714C2314yes—
148#3711C2318yes—
149D3×C3⋊C8C2318yes—
150C2×#578—91noSylow
151C3×2−1+4—38no—
152C3×2−1+4—64no—
153C2×C3×#41—31no—
154C2×C3×#41—32no—
155C2×C3×#41—31no—
156C2×C3×#41—62no—
157C2×C3×#41—61no—
158C22×C3×Q8—21no—
159C22×C3×Q8—32no—
160C22×C3×Q8—31no—
161C22×C3×Q8—61no—
162C22×C3×Q8C2×D311yescharacteristic
163C22×C3×Q8C2×D311yescharacteristic
164#1010—38no—
165#1010—64no—
166#1007—24no—
167#1007—38no—
168#1007—64no—
169#1007C2×D318yescomplemented
170C2×#239—21no—
171C2×#239—32no—
172C2×#239—61no—
173C2×#239C2×D312yes—
174C2×D3×Q8—21no—
175C2×D3×Q8—32no—
176C2×D3×Q8—61no—
177C2×D3×Q8—61no—
178C2×D3×Q8C2×D312yes—
179C2×#237—61no—
180C2×#237—62no—
181C2×#235—22no—
182C2×#235—31no—
183C2×#235—31no—
184C2×#235—32no—
185C2×#235—61no—
186C2×#235—62no—
187C2×#235C2×D311yescharacteristic
188C2×#235C2×D311yescharacteristic
189C22×Dic6—32no—
190C22×Dic6C2×D311yescharacteristic
191C2×C3×Q16—32no—
192C2×C3×Q16—32no—
193C2×C3×Q16—38no—
194C22×C3×C8—31no—
195#951—38no—
196#951—316no—
197#950—316no—
198#950—38no—
199#948—38no—
200C2×#216—32no—
201C2×#216—32no—
202C2×#216—32no—
203C2×#216—32no—
204C2×#216—316no—
205C2×#216—31no—
206C2×#216—62no—
207C2×#216C2×D312yes—
208C2×#216C2×D312yes—
209C2×#216C2×D318yescomplemented
210#942—38no—
211#942—38no—
212#942—38no—
213#942—316no—
214#942—68no—
215C2×#215—32no—
216C2×#215—32no—
217C2×#215—32no—
218C2×#215—31no—
219C2×#215—62no—
220C2×#214—32no—
221C2×#214—31no—
222C2×#213—31no—
223C2×#208—31no—
224C2×#208—31no—
225C2×#208—32no—
226C2×#208—61no—
227C22×C3⋊C8—32no—
228C22×C3⋊C8C2×D311yescharacteristic
229#919—316no—
230#918—316no—
231#918—316no—
232D3×Q16—316no—
233C2×Dic12—31no—
234#904—38no—
235C2×D24—31no—
236C2×#204—31no—
237C2×#204—31no—
238#901—38no—
239C2×ΓL(1,𝔽25)—32no—
240C2×D3×C8—32no—
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D412yes—
245C32×Q8—22no—
246C32×Q8—24no—
247C32×Q8C2414yes—
248C2×C32×C4—22no—
249C2×C32×C4—24no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2×D412yes—
252C2×C32×C4C2411yescharacteristic
253C2×C32×C4C2412yes—
254#638—24no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)C2412yes—
258C4×C3⋊D3—24no—
259#634—21no—
260#634C2412yes—
261C3×#67—24no—
262C3×#67C2×D418yes—
263C2×C3×Dic3—22no—
264C2×C3×Dic3—24no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D412yes—
267C3×D12—28no—
268C3×D12—21no—
269C3×D12C2×D414yes—
270C3×D12C2412yes—
271C3×C4×D3—28no—
272C3×C4×D3—24no—
273C3×C4×D3—28no—
274C3×C4×D3C2×D414yes—
275C3×C4×D3C2414yes—
276C3×Dic6—22no—
277C3×Dic6—24no—
278C3×Dic6—21no—
279C3×Dic6—28no—
280C3×Dic6C2×D414yes—
281C3×Dic6C2414yes—
282C3×Dic6C2412yes—
283#627—28no—
284#626—28no—
285#624—28no—
286D3×Dic3—28no—
287C3⋊(C3⋊C8)C2414yes—
288C3×C3⋊C8C2412yes—
289C3×C3⋊C8C2412yes—
290C2×2−1+4—31no—
291C2×2−1+4—91no—
292#578—916no—
293C2×#137—92no—
294C2×#137—92no—
295C2×#137—91no—
296C2×#137—91no—
297C2×#135—91no—
298C2×#135—92no—
299C22×Q16—31no—
300C22×Q16—92no—
301C2×#131—91no—
302C3×#41—34no—
303C3×#41—34no—
304C3×#41—38no—
305C3×#41—34no—
306C3×#41—616no—
307C3×#41—64no—
308C3×#41—68no—
309C3×#41—62no—
310C2×C3×Q8—21no—
311C2×C3×Q8—22no—
312C2×C3×Q8—21no—
313C2×C3×Q8—22no—
314C2×C3×Q8—22no—
315C2×C3×Q8—24no—
316C2×C3×Q8—31no—
317C2×C3×Q8—38no—
318C2×C3×Q8—31no—
319C2×C3×Q8—32no—
320C2×C3×Q8—34no—
321C2×C3×Q8—41no—
322C2×C3×Q8—42no—
323C2×C3×Q8—62no—
324C2×C3×Q8—64no—
325C2×C3×Q8—68no—
326C2×C3×Q8—61no—
327C2×C3×Q8—62no—
328C2×C3×Q8C22×D312yes—
329C2×C3×Q8C22×D312yes—
330C2×C3×Q8C22×D314yes—
331C2×C3×Q8C22×D314yes—
332C2×C3×D4—32no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—62no—
336C2×C3×D4—61no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—32no—
341C22×C3×C4—41no—
342C22×C3×C4—62no—
343C22×C3×C4—62no—
344C22×C3×C4—61no—
345C22×C3×C4—61no—
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C2×#67—21no—
349C2×#67—62no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—121no—
353C2×#67#6712yes—
354C22×Dic3—21no—
355C22×Dic3—62no—
356#239—28no—
357#239—24no—
358#239—38no—
359#239—68no—
360#239—64no—
361#239C22×D318yes—
362D3×Q8—24no—
363D3×Q8—28no—
364D3×Q8—38no—
365D3×Q8—68no—
366D3×Q8—64no—
367D3×Q8—68no—
368D3×Q8C22×D318yes—
369#237—68no—
370#237—616no—
371#235—22no—
372#235—216no—
373#235—34no—
374#235—34no—
375#235—38no—
376#235—64no—
377#235—64no—
378#235—62no—
379#235—62no—
380#235—616no—
381#235—122no—
382#235#6714yes—
383#235C22×D314yes—
384#235C22×D314yes—
385C2×D12—22no—
386C2×D12—31no—
387C2×D12—31no—
388C2×D12—61no—
389C2×D12—62no—
390C2×D12#6711yescharacteristic
391C2×D12C22×D311yescharacteristic
392C2×C4×D3—22no—
393C2×C4×D3—21no—
394C2×C4×D3—22no—
395C2×C4×D3—62no—
396C2×C4×D3—62no—
397C2×C4×D3—61no—
398C2×C4×D3—61no—
399C2×C4×D3—62no—
400C2×C4×D3—121no—
401C2×C4×D3C22×D312yes—
402C2×Dic6—21no—
403C2×Dic6—22no—
404C2×Dic6—22no—
405C2×Dic6—31no—
406C2×Dic6—31no—
407C2×Dic6—38no—
408C2×Dic6—61no—
409C2×Dic6—64no—
410C2×Dic6—62no—
411C2×Dic6—62no—
412C2×Dic6#6711yescharacteristic
413C2×Dic6C22×D311yescharacteristic
414C2×Dic6C22×D312yes—
415C2×Dic6C22×D314yes—
416C3×Q16—38no—
417C3×Q16—38no—
418C2×C3×C8—31no—
419C2×C3×C8—31no—
420C2×C3×C8—34no—
421#216—38no—
422#216—38no—
423#216—38no—
424#216—38no—
425#216—34no—
426#216—68no—
427#216C22×D318yes—
428#216C22×D318yes—
429#215—38no—
430#215—38no—
431#215—38no—
432#215—34no—
433#215—68no—
434#214—38no—
435#214—34no—
436#213—34no—
437#208—34no—
438#208—34no—
439#208—38no—
440#208—64no—
441C2×C3⋊C8—32no—
442C2×C3⋊C8—32no—
443C2×C3⋊C8—38no—
444C2×C3⋊C8—62no—
445C2×C3⋊C8C22×D311yescharacteristic
446C2×C3⋊C8C22×D311yescharacteristic
447C2×C3⋊C8C22×D314yes—
448Dic12—34no—
449D24—34no—
450#204—34no—
451#204—34no—
452ΓL(1,𝔽25)—38no—
453D3×C8—38no—
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×C4—24no—
464C32×C4C22×D411yescharacteristic
465C32×C4C22×D412yes—
466C32×C4C2511yescharacteristic
467C3⋊Dic3—22no—
468C3×Dic3—24no—
469C3×Dic3—22no—
470C3×Dic3C22×D414yes—
4712−1+4—38no—
4722−1+4—64no—
4732−1+4—98no—
4742−1+4—184no—
475C2×#41—31no—
476C2×#41—32no—
477C2×#41—31no—
478C2×#41—62no—
479C2×#41—61no—
480C2×#41—92no—
481C2×#41—91no—
482C2×#41—182no—
483C2×#41—181no—
484C22×Q8—32no—
485C22×Q8—31no—
486C22×Q8—61no—
487C22×Q8—92no—
488C22×Q8—181no—
489C22×Q8D3211yescharacteristic
490#137—916no—
491#137—916no—
492#137—98no—
493#137—98no—
494#135—98no—
495#135—916no—
496C2×Q16—32no—
497C2×Q16—32no—
498C2×Q16—38no—
499C2×Q16—91no—
500C2×Q16—916no—
501C2×Q16—92no—
502C2×Q16—92no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—92no—
506C2×SD16—92no—
507C2×D8—91no—
508#131—98no—
509C2×M16—92no—
510C2×M16—91no—
511C22×C8—31no—
512C22×C8—92no—
513C23×C3—21no—
514C23×C3—32no—
515C23×C3—61no—
516C23×C3D3×D411yescharacteristic
517C23×C3C2×#6711yescharacteristic
518C22×D3—21no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—121no—
522C22×D3C2×#6712yes—
523C3×Q8—22no—
524C3×Q8—24no—
525C3×Q8—22no—
526C3×Q8—24no—
527C3×Q8—24no—
528C3×Q8—34no—
529C3×Q8—32no—
530C3×Q8—34no—
531C3×Q8—42no—
532C3×Q8—44no—
533C3×Q8—68no—
534C3×Q8—61no—
535C3×Q8—62no—
536C3×Q8—64no—
537C3×Q8C23×D314yes—
538C3×Q8C23×D314yes—
539C3×D4—38no—
540C3×D4—34no—
541C3×D4—32no—
542C3×D4—68no—
543C3×D4—64no—
544C3×D4—61no—
545C2×C3×C4—22no—
546C2×C3×C4—24no—
547C2×C3×C4—22no—
548C2×C3×C4—24no—
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—44no—
557C2×C3×C4—42no—
558C2×C3×C4—68no—
559C2×C3×C4—68no—
560C2×C3×C4—61no—
561C2×C3×C4—62no—
562C2×C3×C4—64no—
563C2×C3×C4—64no—
564C2×C3×C4D3×D411yescharacteristic
565C2×C3×C4D3×D412yes—
566C2×C3×C4C2×#6711yescharacteristic
567C2×C3×C4C2×#6712yes—
568C2×C3×C4C23×D311yescharacteristic
569C2×C3×C4C23×D312yes—
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D312yes—
572#67—24no—
573#67—68no—
574#67—64no—
575#67—64no—
576#67—124no—
577#67C2×#6718yes—
578C2×Dic3—22no—
579C2×Dic3—24no—
580C2×Dic3—21no—
581C2×Dic3—68no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—121no—
585C2×Dic3C2×#6712yes—
586D12—28no—
587D12—21no—
588D12—32no—
589D12—32no—
590D12—62no—
591D12—68no—
592D12—61no—
593D12—61no—
594D12—121no—
595D12C2×#6714yes—
596D12C23×D312yes—
597C4×D3—28no—
598C4×D3—24no—
599C4×D3—28no—
600C4×D3—68no—
601C4×D3—68no—
602C4×D3—64no—
603C4×D3—64no—
604C4×D3—68no—
605C4×D3—124no—
606C4×D3C2×#6714yes—
607C4×D3C23×D314yes—
608Dic6—22no—
609Dic6—24no—
610Dic6—21no—
611Dic6—28no—
612Dic6—32no—
613Dic6—32no—
614Dic6—62no—
615Dic6—68no—
616Dic6—61no—
617Dic6—61no—
618Dic6—68no—
619Dic6—121no—
620Dic6C2×#6714yes—
621Dic6C23×D312yes—
622Dic6C23×D314yes—
623C3×C8—32no—
624C3×C8—32no—
625C3⋊C8—34no—
626C3⋊C8—34no—
627C3⋊C8—64no—
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—38no—
639#41—34no—
640#41—616no—
641#41—64no—
642#41—68no—
643#41—62no—
644#41—98no—
645#41—94no—
646#41—184no—
647#41—1816no—
648#41—188no—
649#41—182no—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—31no—
653C2×Q8—38no—
654C2×Q8—32no—
655C2×Q8—31no—
656C2×Q8—34no—
657C2×Q8—62no—
658C2×Q8—64no—
659C2×Q8—68no—
660C2×Q8—61no—
661C2×Q8—62no—
662C2×Q8—98no—
663C2×Q8—91no—
664C2×Q8—182no—
665C2×Q8—184no—
666C2×Q8—188no—
667C2×Q8C2×D3212yes—
668C2×Q8C2×D3214yes—
669C2×D4—32no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—62no—
673C2×D4—61no—
674C2×D4—91no—
675C2×D4—182no—
676C2×D4—181no—
677C22×C4—21no—
678C22×C4—32no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—182no—
684C22×C4—182no—
685C22×C4—181no—
686C22×C4C2×D3211yescharacteristic
687Q16—38no—
688Q16—38no—
689Q16—94no—
690Q16—98no—
691Q16—98no—
692SD16—94no—
693SD16—94no—
694SD16—98no—
695SD16—98no—
696D8—94no—
697M16—98no—
698M16—94no—
699C2×C8—31no—
700C2×C8—31no—
701C2×C8—34no—
702C2×C8—98no—
703C2×C8—92no—
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×C3C2×D3×D412yes—
714C22×C3C2×D3×D411yescharacteristic
715C22×C3C22×#6712yes—
716C22×C3C22×#6711yescharacteristic
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×#6714yes—
727C3×C4—24no—
728C3×C4—24no—
729C3×C4—21no—
730C3×C4—22no—
731C3×C4—21no—
732C3×C4—34no—
733C3×C4—44no—
734C3×C4—62no—
735C3×C4—64no—
736C3×C4C2×D3×D411yescharacteristic
737C3×C4C2×D3×D412yes—
738C3×C4C22×#6711yescharacteristic
739C3×C4C22×#6712yes—
740C3×C4C24×D311yescharacteristic
741C3×C4C24×D311yescharacteristic
742Dic3—24no—
743Dic3—22no—
744Dic3—62no—
745Dic3—62no—
746Dic3—122no—
747Dic3C22×#6714yes—
748C32C2×#57811yescharacteristic, complemented, Sylow
749C23—32no—
750C23—61no—
751C23—181no—
752C23D3×#6711yescharacteristic
753Q8—22no—
754Q8—24no—
755Q8—34no—
756Q8—34no—
757Q8—32no—
758Q8—68no—
759Q8—61no—
760Q8—62no—
761Q8—64no—
762Q8—92no—
763Q8—188no—
764Q8—181no—
765Q8C22×D3214yes—
766D4—38no—
767D4—34no—
768D4—32no—
769D4—68no—
770D4—64no—
771D4—61no—
772D4—92no—
773D4—188no—
774D4—184no—
775D4—181no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—32no—
779C2×C4—34no—
780C2×C4—34no—
781C2×C4—68no—
782C2×C4—68no—
783C2×C4—64no—
784C2×C4—61no—
785C2×C4—62no—
786C2×C4—64no—
787C2×C4—188no—
788C2×C4—188no—
789C2×C4—181no—
790C2×C4—184no—
791C2×C4D3×#6712yes—
792C2×C4D3×#6711yescharacteristic
793C2×C4C22×D3212yes—
794C2×C4C22×D3211yescharacteristic
795C8—32no—
796C8—32no—
797C8—94no—
798C2×C3—22no—
799C2×C3—22no—
800C2×C3—21no—
801C2×C3—22no—
802C2×C3—42no—
803C2×C3—64no—
804C2×C3—122no—
805C2×C3#576612yescomplemented
806C2×C3#583812yescomplemented
807C2×C3C22×D3×D411yescharacteristic
808C2×C3C23×#6711yescharacteristic
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×#6712yes—
822C22C2×D3×#6711yescharacteristic
823C4—24no—
824C4—34no—
825C4—62no—
826C4—64no—
827C4—182no—
828C4C2×D3×#6711yescharacteristic
829C4C2×D3×#6712yes—
830C4C23×D3211yescharacteristic
831C3—21no—
832C3C2×#576611yescharacteristic, complemented
833C3C2×#583811yescharacteristic, complemented
834C2—22no—
835C2—64no—
836C2—122no—
837C2—362no—
838C2#1059532712yesdirect product factor
839C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
hypercenterC22×Q8D32
hypocenterC32C2×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×#64297C2semidirect
3. C2×#64151C2semidirect
4. C22×C3×#216C2semidirect
5. C2×#63949C2semidirect
6. C2×#63948C2semidirect
7. #10595327C2direct (N × H)
8. C2×#63943C2semidirect
9. C2×D3×#216C2semidirect
10. C2×#63829C2semidirect
11. C2×#63827C2semidirect
12. C2×#63814C2semidirect
18. C3×#1007C22semidirect
31. #64297C22semidirect
35. #64151C22semidirect
40. C2×C3×#216C22semidirect
42. #63949C22semidirect
43. #63948C22semidirect
44. #63943C22semidirect
45. D3×#216C22semidirect
49. #63829C22semidirect
51. #63827C22semidirect
55. #63814C22semidirect
60. C2×#1007D3semidirect
69. C22×#216D3semidirect
169. #1007C2×D3semidirect
209. C2×#216C2×D3semidirect
631. C2×C32#578semidirect
748. C32C2×#578semidirect
805. C2×C3#5766semidirect
806. C2×C3#5838semidirect
832. C3C2×#5766semidirect
833. C3C2×#5838semidirect
838. C2#10595327direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×#642972
C2×#641512
C22×C3×#2162
C2×#639492
C2×#639482
#105953272
C2×#639432
C2×D3×#2162
C2×#638292
C2×#638272
C2×#638142
C2×#58383
C2×#57663