Finite Group Databasebeta

← C2×#10595328 #11918936

Subgroups — C2×#10595328 #11918936

Order 1152.

2945 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3C22×#3756C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5C2×#63947C212yesmaximal, complemented
6C2×#63946C212yesmaximal, complemented
7#10595328C2116yesmaximal, direct product factor
8C2×#63943C212yesmaximal, complemented
9C2×D3×#216C212yesmaximal, complemented
10C2×#63831C211yesmaximal, characteristic, complemented
11C2×#63822C211yesmaximal, characteristic, complemented
12C2×#63815C211yesmaximal, characteristic, complemented
13C2×#5838—31nomaximal
14C2×#5779—31nomaximal
15C22×C32×Q8C2211yescharacteristic
16C22×#634C2211yescharacteristic
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
26C2×C3×#235C2211yescharacteristic
27C2×#3805—22no—
28#64298—24no—
29#64298C2218yescomplemented
30C2×#3795—21no—
31C2×#3795C2212yes—
32C2×D3×Dic6—21no—
33C2×D3×Dic6C2212yes—
34C2×#3756C2212yes—
35C2×#3756C2212yes—
36C2×#3756C2218yescomplemented
37C22×C3⋊(C3⋊C8)C2211yescharacteristic
38C2×C3×#216C2212yes—
39C3×#942C2218yescomplemented
40C2×C3×#215C2212yes—
41C2×C3×#208C2211yescharacteristic
42#63947C22116yescomplemented
43#63946C22116yescomplemented
44#63943C22116yescomplemented
45D3×#216C22116yescomplemented
46C2×#3719C2212yes—
47C2×#3718C2211yescharacteristic
48#63831C2218yescomplemented
49C2×#3716C2212yes—
50C2×#3715C2211yescharacteristic
51C2×#3715C2211yescharacteristic
52#63822C2218yescomplemented
53C2×#3713C2211yescharacteristic
54C2×#3711C2212yes—
55#63815C2218yescomplemented
56C2×D3×C3⋊C8C2212yes—
57C2×C3×2−1+4—31no—
58C2×#1010—31no—
59C2×#1010—31no—
60C2×#1007D311yescharacteristic, complemented
61C2×C3×#137—31no—
62#5838—316no—
63C2×#951—32no—
64C2×#951—31no—
65C2×#950—31no—
66C2×#950—31no—
67C2×#950—32no—
68C2×#948—31no—
69C22×#216—31no—
70C22×#216—31no—
71C22×#216—32no—
72C22×#216—61no—
73C2×#942—32no—
74C2×#942D311yescharacteristic, complemented
75#5779—316no—
76C2×#918—32no—
77C2×D3×Q16—32no—
78C2×#916—32no—
79C2×#915—32no—
80C2×#909—31no—
81C2×#907—31no—
82C2×C32×Q8—21no—
83C2×C32×Q8—22no—
84C2×C32×Q8C2312yes—
85C2×C32×Q8C2314yes—
86C22×C32×C4—21no—
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3—21no—
89C2×#634—21no—
90C2×#634—22no—
91C2×#634C2312yes—
92C2×#634C2314yes—
93C2×C3×#67—21no—
94C2×C3×#67—21no—
95C2×C3×#67D412yes—
96C3×#239—28no—
97C3×#239—24no—
98C3×#239C2318yes—
99C3×D3×Q8—24no—
100C3×D3×Q8—28no—
101C3×D3×Q8C2318yes—
102C3×#235—22no—
103C3×#235—22no—
104C3×#235—216no—
105C3×#235D414yes—
106C3×#235C2314yes—
107C3×#235C2314yes—
108C3×#235C2314yes—
109C2×C3×D12—22no—
110C2×C3×D12D411yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3C2312yes—
118C2×C3×Dic6—22no—
119C2×C3×Dic6D411yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C2×#627—22no—
123C2×#625—22no—
124#3805—216no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127#3795—28no—
128#3795—24no—
129#3795C2318yes—
130D3×Dic6—24no—
131D3×Dic6—28no—
132D3×Dic6C2318yes—
133#3756C2318yes—
134#3756C2318yes—
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2314yes—
137C2×C3⋊(C3⋊C8)C2311yescharacteristic
138C3×#216C2318yes—
139C3×#215C2318yes—
140C3×#208C2314yes—
141C2×C3×C3⋊C8C2312yes—
142#3719C2318yes—
143#3718C2314yes—
144#3716C2318yes—
145#3715C2314yes—
146#3715C2314yes—
147#3713C2314yes—
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—31no—
157C2×C3×#41—62no—
158C2×C3×#41—61no—
159C22×C3×Q8—21no—
160C22×C3×Q8—32no—
161C22×C3×Q8—61no—
162C22×C3×Q8C2×D311yescharacteristic
163C22×C3×Q8C2×D311yescharacteristic
164#1010—38no—
165#1010—38no—
166#1010—64no—
167#1010—64no—
168#1007—24no—
169#1007C2×D318yescomplemented
170C2×#239—21no—
171C2×#239C2×D312yes—
172C2×D3×Q8—21no—
173C2×D3×Q8—32no—
174C2×D3×Q8—61no—
175C2×D3×Q8C2×D312yes—
176C2×#237—32no—
177C2×#237—61no—
178C2×#237—62no—
179C2×#237—62no—
180C2×#235—22no—
181C2×#235—32no—
182C2×#235—61no—
183C2×#235C2×D311yescharacteristic
184C2×#235C2×D311yescharacteristic
185C2×#235C2×D311yescharacteristic
186C22×Dic6—31no—
187C22×Dic6—31no—
188C22×Dic6—32no—
189C22×Dic6—61no—
190C22×Dic6—61no—
191C3×#137—38no—
192C2×C3×Q16—32no—
193C2×C3×SD16—32no—
194C2×C3×M16—31no—
195#951—316no—
196#951—38no—
197#950—38no—
198#950—38no—
199#950—316no—
200#948—38no—
201C2×#216—32no—
202C2×#216—32no—
203C2×#216—38no—
204C2×#216—32no—
205C2×#216—32no—
206C2×#216—38no—
207C2×#216—31no—
208C2×#216—31no—
209C2×#216—316no—
210C2×#216—32no—
211C2×#216—62no—
212C2×#216—62no—
213C2×#216—68no—
214C2×#216C2×D312yes—
215#942—316no—
216#942C2×D318yescomplemented
217C2×#215—31no—
218C2×#215—31no—
219C2×#215C2×D312yes—
220C2×#214—31no—
221C2×#214—31no—
222C2×#214—32no—
223C2×#213—31no—
224C2×#213—31no—
225C2×#208—32no—
226C2×#208C2×D311yescharacteristic
227C22×C3⋊C8—31no—
228C22×C3⋊C8—31no—
229C22×C3⋊C8—32no—
230C22×C3⋊C8—61no—
231#918—316no—
232D3×Q16—316no—
233#916—316no—
234#915—316no—
235#909—38no—
236#907—38no—
237C2×Dic12—32no—
238C2×#204—32no—
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—
254C2×C3⋊Dic3—22no—
255C2×C3⋊Dic3—24no—
256#634—22no—
257#634—24no—
258#634C2414yes—
259C3×#67—24no—
260C3×#67—24no—
261C3×#67C2×D418yes—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D412yes—
265C3×D12—28no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12C2×D414yes—
269C3×D12C2412yes—
270C3×D12C2412yes—
271C3×C4×D3—28no—
272C3×C4×D3—24no—
273C3×C4×D3—24no—
274C3×C4×D3—28no—
275C3×C4×D3C2×D414yes—
276C3×C4×D3C2414yes—
277C3×Dic6—21no—
278C3×Dic6—21no—
279C3×Dic6—28no—
280C3×Dic6C2×D414yes—
281C3×Dic6C2412yes—
282C3×Dic6C2412yes—
283#627—28no—
284#625—28no—
285D3×Dic3—28no—
286D3×Dic3—28no—
287C3⋊(C3⋊C8)C2412yes—
288C3⋊(C3⋊C8)C2412yes—
289C3×C3⋊C8C2414yes—
290C2×2−1+4—31no—
291C2×2−1+4—91no—
292#578—916no—
293C2×#137—31no—
294C2×#137—91no—
295C2×#137—92no—
296C2×#137—92no—
297C2×#135—92no—
298C2×#135—91no—
299C22×Q16—92no—
300C22×Q16—91no—
301C2×#131—91no—
302C3×#41—34no—
303C3×#41—34no—
304C3×#41—38no—
305C3×#41—34no—
306C3×#41—34no—
307C3×#41—616no—
308C3×#41—64no—
309C3×#41—68no—
310C3×#41—62no—
311C3×#41—62no—
312C2×C3×Q8—21no—
313C2×C3×Q8—22no—
314C2×C3×Q8—21no—
315C2×C3×Q8—22no—
316C2×C3×Q8—22no—
317C2×C3×Q8—24no—
318C2×C3×Q8—31no—
319C2×C3×Q8—38no—
320C2×C3×Q8—31no—
321C2×C3×Q8—31no—
322C2×C3×Q8—41no—
323C2×C3×Q8—42no—
324C2×C3×Q8—62no—
325C2×C3×Q8—64no—
326C2×C3×Q8—68no—
327C2×C3×Q8C22×D312yes—
328C2×C3×Q8C22×D314yes—
329C2×C3×Q8C22×D312yes—
330C2×C3×Q8C22×D314yes—
331C2×C3×D4—32no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—62no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—32no—
342C22×C3×C4—41no—
343C22×C3×C4—62no—
344C22×C3×C4—62no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C2×#67—21no—
350C2×#67—21no—
351C2×#67—62no—
352C2×#67—62no—
353C2×#67#6712yes—
354C22×Dic3—62no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—62no—
358C22×Dic3—121no—
359#239—28no—
360#239—24no—
361#239C22×D318yes—
362D3×Q8—24no—
363D3×Q8—28no—
364D3×Q8—38no—
365D3×Q8—68no—
366D3×Q8—64no—
367D3×Q8C22×D318yes—
368#237—38no—
369#237—68no—
370#237—616no—
371#237—616no—
372#237—64no—
373#235—22no—
374#235—22no—
375#235—216no—
376#235—38no—
377#235—64no—
378#235—68no—
379#235#6714yes—
380#235C22×D314yes—
381#235C22×D314yes—
382#235C22×D314yes—
383C2×D12—22no—
384C2×D12#6711yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×D12C22×D311yescharacteristic
387C2×C4×D3—22no—
388C2×C4×D3—21no—
389C2×C4×D3—21no—
390C2×C4×D3—22no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×C4×D3C22×D312yes—
394C2×Dic6—22no—
395C2×Dic6—32no—
396C2×Dic6—34no—
397C2×Dic6—32no—
398C2×Dic6—34no—
399C2×Dic6—38no—
400C2×Dic6—62no—
401C2×Dic6—64no—
402C2×Dic6—64no—
403C2×Dic6—62no—
404C2×Dic6—61no—
405C2×Dic6—62no—
406C2×Dic6—61no—
407C2×Dic6—62no—
408C2×Dic6—62no—
409C2×Dic6—68no—
410C2×Dic6—121no—
411C2×Dic6—122no—
412C2×Dic6#6711yescharacteristic
413C2×Dic6C22×D311yescharacteristic
414C2×Dic6C22×D311yescharacteristic
415C3×Q16—38no—
416C3×SD16—38no—
417C3×M16—34no—
418C2×C3×C8—32no—
419#216—38no—
420#216—38no—
421#216—38no—
422#216—38no—
423#216—34no—
424#216—34no—
425#216—38no—
426#216—68no—
427#216—68no—
428#216C22×D318yes—
429#215—34no—
430#215—34no—
431#215C22×D318yes—
432#214—34no—
433#214—34no—
434#214—38no—
435#213—34no—
436#213—34no—
437#208—38no—
438#208C22×D314yes—
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—34no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—34no—
445C2×C3⋊C8—38no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—61no—
448C2×C3⋊C8—64no—
449C2×C3⋊C8C22×D312yes—
450Dic12—38no—
451#204—38no—
452ΓL(1,𝔽25)—38no—
453D3×C8—38no—
454C22×C32—22no—
455C22×C32C22×D412yes—
456C22×C32C22×D411yescharacteristic
457C2×C3×D3—24no—
458C2×C3×D3—22no—
459C2×C3×D3—22no—
460C2×C3×D3—42no—
461C2×C3×D3—42no—
462C2×C3×D3C22×D414yes—
463C32×C4—24no—
464C32×C4C22×D411yescharacteristic
465C32×C4C22×D412yes—
466C32×C4C2511yescharacteristic
467C3⋊Dic3—24no—
468C3×Dic3—22no—
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—31no—
479C2×#41—62no—
480C2×#41—61no—
481C2×#41—92no—
482C2×#41—181no—
483C2×#41—182no—
484C22×Q8—32no—
485C22×Q8—61no—
486C22×Q8—92no—
487C22×Q8—91no—
488C22×Q8—181no—
489C22×Q8D3211yescharacteristic
490#137—38no—
491#137—98no—
492#137—916no—
493#137—916no—
494#135—916no—
495#135—98no—
496C2×Q16—32no—
497C2×Q16—92no—
498C2×Q16—916no—
499C2×Q16—91no—
500C2×Q16—92no—
501C2×Q16—92no—
502C2×Q16—98no—
503C2×SD16—32no—
504C2×SD16—92no—
505C2×SD16—91no—
506C2×SD16—91no—
507C2×D8—91no—
508#131—98no—
509C2×M16—31no—
510C2×M16—92no—
511C22×C8—92no—
512C22×C8—91no—
513C23×C3—21no—
514C23×C3—32no—
515C23×C3—61no—
516C23×C3—61no—
517C23×C3D3×D411yescharacteristic
518C23×C3C2×#6711yescharacteristic
519C22×D3—21no—
520C22×D3—21no—
521C22×D3C2×#6712yes—
522C3×Q8—22no—
523C3×Q8—24no—
524C3×Q8—22no—
525C3×Q8—24no—
526C3×Q8—24no—
527C3×Q8—34no—
528C3×Q8—32no—
529C3×Q8—32no—
530C3×Q8—42no—
531C3×Q8—44no—
532C3×Q8—68no—
533C3×Q8—61no—
534C3×Q8—61no—
535C3×Q8C23×D314yes—
536C3×Q8C23×D314yes—
537C3×D4—38no—
538C3×D4—34no—
539C3×D4—32no—
540C3×D4—32no—
541C3×D4—68no—
542C3×D4—64no—
543C3×D4—64no—
544C3×D4—61no—
545C3×D4—61no—
546C2×C3×C4—22no—
547C2×C3×C4—24no—
548C2×C3×C4—22no—
549C2×C3×C4—24no—
550C2×C3×C4—22no—
551C2×C3×C4—21no—
552C2×C3×C4—22no—
553C2×C3×C4—21no—
554C2×C3×C4—32no—
555C2×C3×C4—34no—
556C2×C3×C4—34no—
557C2×C3×C4—44no—
558C2×C3×C4—42no—
559C2×C3×C4—68no—
560C2×C3×C4—68no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—64no—
564C2×C3×C4—64no—
565C2×C3×C4D3×D411yescharacteristic
566C2×C3×C4D3×D412yes—
567C2×C3×C4C2×#6711yescharacteristic
568C2×C3×C4C2×#6712yes—
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D312yes—
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D312yes—
573#67—24no—
574#67—24no—
575#67—68no—
576#67—68no—
577#67C2×#6718yes—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—68no—
581C2×Dic3—62no—
582C2×Dic3—64no—
583C2×Dic3—62no—
584C2×Dic3—64no—
585C2×Dic3—68no—
586C2×Dic3—124no—
587C2×Dic3—122no—
588C2×Dic3C2×#6712yes—
589D12—28no—
590D12—21no—
591D12—21no—
592D12C2×#6714yes—
593D12C23×D312yes—
594D12C23×D312yes—
595C4×D3—28no—
596C4×D3—24no—
597C4×D3—24no—
598C4×D3—28no—
599C4×D3—68no—
600C4×D3—68no—
601C4×D3C2×#6714yes—
602C4×D3C23×D314yes—
603Dic6—21no—
604Dic6—21no—
605Dic6—28no—
606Dic6—34no—
607Dic6—34no—
608Dic6—64no—
609Dic6—68no—
610Dic6—62no—
611Dic6—64no—
612Dic6—64no—
613Dic6—62no—
614Dic6—68no—
615Dic6—122no—
616Dic6—124no—
617Dic6C2×#6714yes—
618Dic6C23×D312yes—
619Dic6C23×D312yes—
620C3×C8—34no—
621C3⋊C8—32no—
622C3⋊C8—32no—
623C3⋊C8—32no—
624C3⋊C8—32no—
625C3⋊C8—62no—
626C3⋊C8—62no—
627C3⋊C8C23×D314yes—
628C2×C32—22no—
629C2×C32#57812yescomplemented
630C2×C32C23×D411yescharacteristic
631C3×D3—24no—
632C3×D3—42no—
633C3×D3—42no—
634#41—34no—
635#41—34no—
636#41—38no—
637#41—34no—
638#41—34no—
639#41—616no—
640#41—64no—
641#41—68no—
642#41—62no—
643#41—62no—
644#41—98no—
645#41—184no—
646#41—188no—
647#41—1816no—
648C2×Q8—21no—
649C2×Q8—22no—
650C2×Q8—31no—
651C2×Q8—38no—
652C2×Q8—31no—
653C2×Q8—31no—
654C2×Q8—62no—
655C2×Q8—64no—
656C2×Q8—68no—
657C2×Q8—98no—
658C2×Q8—92no—
659C2×Q8—94no—
660C2×Q8—182no—
661C2×Q8—184no—
662C2×Q8—188no—
663C2×Q8—181no—
664C2×Q8—182no—
665C2×Q8C2×D3212yes—
666C2×Q8C2×D3214yes—
667C2×D4—32no—
668C2×D4—31no—
669C2×D4—31no—
670C2×D4—31no—
671C2×D4—62no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—182no—
675C22×C4—21no—
676C22×C4—32no—
677C22×C4—62no—
678C22×C4—62no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—182no—
682C22×C4—182no—
683C22×C4—181no—
684C22×C4C2×D3211yescharacteristic
685Q16—38no—
686Q16—98no—
687Q16—94no—
688Q16—98no—
689Q16—98no—
690SD16—38no—
691SD16—98no—
692SD16—94no—
693SD16—94no—
694D8—94no—
695M16—34no—
696M16—98no—
697C2×C8—32no—
698C2×C8—98no—
699C2×C8—91no—
700C2×C8—91no—
701C2×C8—94no—
702C22×C3—24no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—21no—
707C22×C3—34no—
708C22×C3—64no—
709C22×C3—62no—
710C22×C3—62no—
711C22×C3—122no—
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—22no—
720C2×D3—42no—
721C2×D3—42no—
722C2×D3C22×#6714yes—
723C3×C4—24no—
724C3×C4—24no—
725C3×C4—21no—
726C3×C4—22no—
727C3×C4—21no—
728C3×C4—34no—
729C3×C4—44no—
730C3×C4—62no—
731C3×C4—62no—
732C3×C4C2×D3×D411yescharacteristic
733C3×C4C2×D3×D412yes—
734C3×C4C22×#6711yescharacteristic
735C3×C4C22×#6712yes—
736C3×C4C24×D311yescharacteristic
737C3×C4C24×D311yescharacteristic
738Dic3—22no—
739Dic3—22no—
740Dic3—64no—
741Dic3—64no—
742Dic3—124no—
743Dic3C22×#6714yes—
744C32C2×#57811yescharacteristic, complemented, Sylow
745C23—32no—
746C23—61no—
747C23—61no—
748C23D3×#6711yescharacteristic
749Q8—22no—
750Q8—24no—
751Q8—34no—
752Q8—32no—
753Q8—32no—
754Q8—68no—
755Q8—61no—
756Q8—61no—
757Q8—94no—
758Q8—188no—
759Q8—182no—
760Q8—184no—
761Q8C22×D3214yes—
762D4—38no—
763D4—34no—
764D4—32no—
765D4—32no—
766D4—68no—
767D4—64no—
768D4—64no—
769D4—61no—
770D4—61no—
771D4—188no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—32no—
775C2×C4—34no—
776C2×C4—34no—
777C2×C4—68no—
778C2×C4—68no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—64no—
782C2×C4—64no—
783C2×C4—188no—
784C2×C4—188no—
785C2×C4—184no—
786C2×C4—182no—
787C2×C4D3×#6712yes—
788C2×C4D3×#6711yescharacteristic
789C2×C4C22×D3212yes—
790C2×C4C22×D3211yescharacteristic
791C8—34no—
792C8—92no—
793C8—92no—
794C2×C3—24no—
795C2×C3—22no—
796C2×C3—22no—
797C2×C3—22no—
798C2×C3—21no—
799C2×C3—64no—
800C2×C3—122no—
801C2×C3—122no—
802C2×C3#577912yescomplemented
803C2×C3#583812yescomplemented
804C2×C3C22×D3×D411yescharacteristic
805C2×C3C23×#6711yescharacteristic
806D3—24no—
807D3—42no—
808D3—42no—
809C22—22no—
810C22—34no—
811C22—64no—
812C22—62no—
813C22—62no—
814C22—122no—
815C22—122no—
816C22C2×D3×#6712yes—
817C22C2×D3×#6711yescharacteristic
818C4—24no—
819C4—34no—
820C4—62no—
821C4—62no—
822C4—184no—
823C4C2×D3×#6711yescharacteristic
824C4C2×D3×#6712yes—
825C4C23×D3211yescharacteristic
826C3—21no—
827C3C2×#577911yescharacteristic, complemented
828C3C2×#583811yescharacteristic, complemented
829C2—22no—
830C2—64no—
831C2—122no—
832C2—122no—
833C2#1059532812yesdirect product factor
834C2C22×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×#64298C2semidirect
3. C22×#3756C2semidirect
4. C2×C3×#942C2semidirect
5. C2×#63947C2semidirect
6. C2×#63946C2semidirect
7. #10595328C2direct (N × H)
8. C2×#63943C2semidirect
9. C2×D3×#216C2semidirect
10. C2×#63831C2semidirect
11. C2×#63822C2semidirect
12. C2×#63815C2semidirect
18. C3×#1007C22semidirect
29. #64298C22semidirect
36. C2×#3756C22semidirect
39. C3×#942C22semidirect
42. #63947C22semidirect
43. #63946C22semidirect
44. #63943C22semidirect
45. D3×#216C22semidirect
48. #63831C22semidirect
52. #63822C22semidirect
55. #63815C22semidirect
60. C2×#1007D3semidirect
74. C2×#942D3semidirect
169. #1007C2×D3semidirect
216. #942C2×D3semidirect
629. C2×C32#578semidirect
744. C32C2×#578semidirect
802. C2×C3#5779semidirect
803. C2×C3#5838semidirect
827. C3C2×#5779semidirect
828. C3C2×#5838semidirect
833. C2#10595328direct (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×#642982
C22×#37562
C2×C3×#9422
C2×#639472
C2×#639462
#105953282
C2×#639432
C2×D3×#2162
C2×#638312
C2×#638222
C2×#638152
C2×#58383
C2×#57793