Finite Group Databasebeta

← C2×#10595457 #11918884

Subgroups — C2×#10595457 #11918884

Order 1152.

3069 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×#64308C211yesmaximal, characteristic, complemented
3C2×#64158C211yesmaximal, characteristic, complemented
4C2×C3×#950C211yesmaximal, characteristic, complemented
5#10595457C2116yesmaximal, direct product factor
6C2×#63948C212yesmaximal, complemented
7C2×D3×#215C212yesmaximal, complemented
8C2×#63935C212yesmaximal, complemented
9C2×#63925C212yesmaximal, complemented
10C22×#3717C211yesmaximal, characteristic, complemented
11C2×#63827C211yesmaximal, characteristic, complemented
12C2×#63814C211yesmaximal, characteristic, complemented
13C2×#5837—31nomaximal
14C2×#5770—31nomaximal
15C2×C32×#41C2211yescharacteristic, complemented
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#1010—24no—
18C3×#1010C2218yescomplemented
19C2×C3×D3×Q8C2212yescomplemented
20C2×C3×#237—22no—
21C2×C3×#237C2212yescomplemented
22C2×C3×#235—21no—
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2211yescharacteristic
25C22×C3×Dic6—21no—
26C22×C3×Dic6C2211yescharacteristic, complemented
27C2×#3811—22no—
28#64308—24no—
29#64308C2218yescomplemented
30C2×D3×D12—21no—
31C2×D3×D12C2212yes—
32C2×#3799—21no—
33C2×#3799C2212yes—
34#64158C2218yescomplemented
35C2×#3755C2212yescomplemented
36C2×#3753C2212yescomplemented
37C2×#3748C2211yescharacteristic, complemented
38C3×#950C2218yescomplemented
39C2×C3×#216C2211yescharacteristic, complemented
40C2×C3×#215C2211yescharacteristic, complemented
41C2×C3×#214C2211yescharacteristic, complemented
42C2×C3×#213C2211yescharacteristic, complemented
43C22×C3×C3⋊C8C2211yescharacteristic, complemented
44#63948C22116yescomplemented
45D3×#215C22116yescomplemented
46#63935C22116yescomplemented
47#63925C22116yescomplemented
48C2×#3718C2212yescomplemented
49C2×#3717C2212yescomplemented
50C2×#3717C2212yescomplemented
51C2×#3717C2218yescomplemented
52#63827C2218yescomplemented
53C2×#3715C2212yescomplemented
54C2×#3711C2212yescomplemented
55#63814C2218yescomplemented
56C2×D3×C3⋊C8C2212yescomplemented
57C2×C3×2−1+4—31no—
58C2×#1010D311yescharacteristic, complemented
59C2×#1009—31no—
60C2×#1009—31no—
61C2×C3×#135—31no—
62#5837—316no—
63C2×#951—31no—
64C2×#950—32no—
65C2×#950D311yescharacteristic, complemented
66C2×#949—31no—
67C2×#949—31no—
68C2×#949—32no—
69C2×#949—61no—
70C2×#948—31no—
71C2×#942—31no—
72C2×#942—32no—
73C22×#215—32no—
74C22×#215—31no—
75#5770—316no—
76C2×#918—32no—
77C2×#916—32no—
78C2×D3×SD16—32no—
79C2×#911—32no—
80C22×#204—31no—
81C2×#901—31no—
82C23×C3⋊D3—21no—
83C22×D32—22no—
84C32×#41—22no—
85C32×#41C2314yescomplemented
86C2×C32×Q8C2311yescharacteristic
87C2×C32×D4—21no—
88C2×C32×D4C2311yescharacteristic
89C22×C32×C4—21no—
90C22×C32×C4C2311yescharacteristic
91C2×C4⋊(C3⋊D3)—21no—
92C2×C4⋊(C3⋊D3)—22no—
93C2×C4⋊(C3⋊D3)C2312yes—
94C2×C4⋊(C3⋊D3)C2314yes—
95C2×C3×#67—21no—
96C2×C3×#67—22no—
97C2×C3×#67D412yes—
98C22×C3×Dic3—21no—
99C22×C3×Dic3—22no—
100C3×D3×Q8—24no—
101C3×D3×Q8C2318yescomplemented
102C3×#237—216no—
103C3×#237—24no—
104C3×#237C2318yescomplemented
105C3×#235—22no—
106C3×#235—28no—
107C3×#235D414yes—
108C3×#235C2314yes—
109C3×#235C2314yes—
110C2×C3×D12D411yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2312yes—
115C2×C3×Dic6—21no—
116C2×C3×Dic6—22no—
117C2×C3×Dic6—22no—
118C2×C3×Dic6—28no—
119C2×C3×Dic6D411yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2312yes—
122C2×C3×Dic6C2314yescomplemented
123#3811—216no—
124C2×#626—22no—
125C2×#626—22no—
126C2×#624—22no—
127D3×D12—28no—
128D3×D12—24no—
129D3×D12C2318yes—
130#3799—24no—
131#3799—28no—
132#3799C2318yes—
133#3755C2318yescomplemented
134#3753C2318yescomplemented
135#3748C2314yescomplemented
136C2×C3⋊(C3⋊C8)C2312yes—
137C3×#216C2314yescomplemented
138C3×#215C2314yescomplemented
139C3×#214C2314yescomplemented
140C3×#213C2314yescomplemented
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2314yescomplemented
144#3718C2318yescomplemented
145#3717C2318yescomplemented
146#3717C2318yescomplemented
147#3715C2318yescomplemented
148#3711C2318yescomplemented
149D3×C3⋊C8C2318yescomplemented
150C2×#577—91noSylow
151C3×2−1+4—38no—
152C3×2−1+4—64no—
153C2×C3×#41—21no—
154C2×C3×#41—31no—
155C2×C3×#41—32no—
156C2×C3×#41—31no—
157C2×C3×#41—61no—
158C2×C3×#41—62no—
159C2×C3×#41C2×D311yescharacteristic, complemented
160C2×C3×#41C2×D311yescharacteristic, complemented
161C22×C3×Q8—32no—
162C22×C3×Q8—31no—
163C22×C3×Q8—61no—
164#1010—24no—
165#1010C2×D318yescomplemented
166#1009—38no—
167#1009—38no—
168#1009—64no—
169#1009—64no—
170C2×#239—32no—
171C2×#239—61no—
172C2×D3×Q8C2×D312yescomplemented
173C2×#237—22no—
174C2×#237C2×D312yescomplemented
175C2×D3×D4—32no—
176C2×D3×D4—61no—
177C2×D3×D4—62no—
178C2×D3×D4—62no—
179C2×#235—21no—
180C2×#235—32no—
181C2×#235—61no—
182C2×#235C2×D311yescharacteristic
183C2×#235C2×D311yescharacteristic
184C22×D12—31no—
185C22×D12—31no—
186C22×D12—32no—
187C22×D12—61no—
188C22×D12—61no—
189C22×Dic6—21no—
190C22×Dic6C2×D311yescharacteristic, complemented
191C3×#135—38no—
192C2×C3×Q16—31no—
193C2×C3×SD16—31no—
194C2×C3×SD16—31no—
195C2×C3×D8—31no—
196C22×C3×C8—31no—
197#951—38no—
198#950—316no—
199#950C2×D318yescomplemented
200#949—38no—
201#949—38no—
202#949—316no—
203#949—68no—
204#948—38no—
205C2×#216—32no—
206C2×#216—32no—
207C2×#216C2×D311yescharacteristic, complemented
208#942—38no—
209#942—316no—
210C2×#215—32no—
211C2×#215—32no—
212C2×#215—32no—
213C2×#215—316no—
214C2×#215—32no—
215C2×#215—32no—
216C2×#215—38no—
217C2×#215—62no—
218C2×#215C2×D311yescharacteristic, complemented
219C2×#214—32no—
220C2×#214C2×D311yescharacteristic, complemented
221C2×#213—32no—
222C2×#213—32no—
223C2×#213—62no—
224C2×#213C2×D311yescharacteristic, complemented
225C2×#208—31no—
226C2×#208—31no—
227C2×#208—32no—
228C2×#208—61no—
229C22×C3⋊C8—32no—
230C22×C3⋊C8C2×D311yescharacteristic, complemented
231#918—316no—
232#916—316no—
233D3×SD16—316no—
234#911—316no—
235C2×#204—32no—
236C2×#204—32no—
237C2×#204—38no—
238#901—38no—
239C2×ΓL(1,𝔽25)—32no—
240C2×D3×C8—32no—
241C23×C32—21no—
242C23×C32C2×D411yescharacteristic
243C22×C3⋊D3—22no—
244C22×C3⋊D3—24no—
245C22×C3⋊D3—82no—
246C22×C3×D3—21no—
247C22×C3×D3C2×D412yes—
248C2×D32—28no—
249C2×D32—84no—
250C32×Q8—21no—
251C32×Q8C2412yes—
252C32×D4—24no—
253C32×D4—21no—
254C32×D4C2412yes—
255C2×C32×C4—21no—
256C2×C32×C4—24no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D412yes—
259C2×C32×C4C2411yescharacteristic
260C2×C32×C4C2412yes—
261C4⋊(C3⋊D3)—22no—
262C4⋊(C3⋊D3)—24no—
263C4⋊(C3⋊D3)C2414yes—
264C3×#67—24no—
265C3×#67—28no—
266C3×#67C2×D418yes—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3—24no—
270C2×C3×Dic3—28no—
271C2×C3×Dic3C2×D412yes—
272C3×D12—21no—
273C3×D12C2×D414yes—
274C3×D12C2412yes—
275C3×C4×D3—28no—
276C3×C4×D3—24no—
277C3×C4×D3C2×D414yes—
278C3×C4×D3C2414yes—
279C3×Dic6—21no—
280C3×Dic6—24no—
281C3×Dic6—22no—
282C3×Dic6—28no—
283C3×Dic6C2×D414yes—
284C3×Dic6C2414yes—
285C3×Dic6C2412yes—
286#626—28no—
287#626—28no—
288#624—28no—
289C3⋊(C3⋊C8)C2414yes—
290C3×C3⋊C8C2412yes—
291C3×C3⋊C8C2412yes—
292C2×2−1+4—31no—
293C2×H(5,𝔽2)—91no—
294#577—916no—
295C2×#137—92no—
296C2×#137—91no—
297C2×AGL(1,ℤ/8)—92no—
298C2×AGL(1,ℤ/8)—91no—
299C2×#135—31no—
300C2×#135—92no—
301C22×SD16—91no—
302C22×SD16—92no—
303C2×#131—91no—
304C23×D3—62no—
305C23×D3—61no—
306C23×D3—61no—
307C23×D3—62no—
308C23×D3—121no—
309C3×#41—22no—
310C3×#41—22no—
311C3×#41—24no—
312C3×#41—34no—
313C3×#41—34no—
314C3×#41—38no—
315C3×#41—34no—
316C3×#41—42no—
317C3×#41—68no—
318C3×#41—64no—
319C3×#41—616no—
320C3×#41—62no—
321C3×#41C22×D314yescomplemented
322C3×#41C22×D314yescomplemented
323C2×C3×Q8—21no—
324C2×C3×Q8—31no—
325C2×C3×Q8—38no—
326C2×C3×Q8—32no—
327C2×C3×Q8—34no—
328C2×C3×Q8—31no—
329C2×C3×Q8—62no—
330C2×C3×Q8—68no—
331C2×C3×Q8—64no—
332C2×C3×Q8—61no—
333C2×C3×Q8—62no—
334C2×C3×Q8C22×D311yescharacteristic
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×D4—21no—
337C2×C3×D4—21no—
338C2×C3×D4—21no—
339C2×C3×D4—32no—
340C2×C3×D4—31no—
341C2×C3×D4—31no—
342C2×C3×D4—41no—
343C2×C3×D4—62no—
344C2×C3×D4—61no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—21no—
350C22×C3×C4—32no—
351C22×C3×C4—41no—
352C22×C3×C4—62no—
353C22×C3×C4—62no—
354C22×C3×C4—61no—
355C22×C3×C4—61no—
356C22×C3×C4C22×D311yescharacteristic
357C22×C3×C4C22×D311yescharacteristic
358C2×#67—21no—
359C2×#67—22no—
360C2×#67—62no—
361C2×#67—62no—
362C2×#67#6712yes—
363C22×Dic3—21no—
364C22×Dic3—22no—
365#239—38no—
366#239—68no—
367#239—64no—
368D3×Q8—24no—
369D3×Q8C22×D318yescomplemented
370#237—216no—
371#237—24no—
372#237C22×D318yescomplemented
373D3×D4—38no—
374D3×D4—68no—
375D3×D4—616no—
376D3×D4—616no—
377D3×D4—64no—
378#235—22no—
379#235—28no—
380#235—38no—
381#235—64no—
382#235—68no—
383#235#6714yes—
384#235C22×D314yes—
385#235C22×D314yes—
386C2×D12—32no—
387C2×D12—34no—
388C2×D12—32no—
389C2×D12—34no—
390C2×D12—38no—
391C2×D12—62no—
392C2×D12—64no—
393C2×D12—64no—
394C2×D12—62no—
395C2×D12—62no—
396C2×D12—61no—
397C2×D12—62no—
398C2×D12—61no—
399C2×D12—62no—
400C2×D12—68no—
401C2×D12—121no—
402C2×D12—122no—
403C2×D12#6711yescharacteristic
404C2×D12C22×D311yescharacteristic
405C2×C4×D3—22no—
406C2×C4×D3—21no—
407C2×C4×D3—62no—
408C2×C4×D3—62no—
409C2×C4×D3C22×D312yes—
410C2×Dic6—21no—
411C2×Dic6—22no—
412C2×Dic6—22no—
413C2×Dic6—28no—
414C2×Dic6#6711yescharacteristic
415C2×Dic6C22×D312yes—
416C2×Dic6C22×D311yescharacteristic
417C2×Dic6C22×D314yescomplemented
418C3×Q16—34no—
419C3×SD16—34no—
420C3×SD16—34no—
421C3×D8—34no—
422C2×C3×C8—31no—
423C2×C3×C8—31no—
424C2×C3×C8—34no—
425#216—38no—
426#216—38no—
427#216C22×D314yescomplemented
428#215—38no—
429#215—38no—
430#215—38no—
431#215—38no—
432#215—38no—
433#215—68no—
434#215C22×D314yescomplemented
435#214—38no—
436#214C22×D314yescomplemented
437#213—38no—
438#213—38no—
439#213—68no—
440#213C22×D314yescomplemented
441#208—34no—
442#208—34no—
443#208—38no—
444#208—64no—
445C2×C3⋊C8—32no—
446C2×C3⋊C8—32no—
447C2×C3⋊C8—38no—
448C2×C3⋊C8—62no—
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451C2×C3⋊C8C22×D314yescomplemented
452#204—38no—
453#204—38no—
454ΓL(1,𝔽25)—38no—
455D3×C8—38no—
456C22×C32—22no—
457C22×C32—22no—
458C22×C32—42no—
459C22×C32C22×D412yes—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—24no—
462C2×C3⋊D3—44no—
463C2×C3⋊D3—84no—
464C2×C3×D3—24no—
465C2×C3×D3—22no—
466C2×C3×D3—42no—
467C2×C3×D3C22×D414yes—
468D32—88no—
469C32×C4—22no—
470C32×C4C22×D411yescharacteristic
471C32×C4C22×D412yes—
472C32×C4C2511yescharacteristic
473C3×Dic3—22no—
474C3×Dic3—24no—
475C3×Dic3C22×D414yes—
4762−1+4—38no—
4772−1+4—64no—
478H(5,𝔽2)—98no—
479H(5,𝔽2)—184no—
480C2×#41—31no—
481C2×#41—32no—
482C2×#41—31no—
483C2×#41—61no—
484C2×#41—62no—
485C2×#41—92no—
486C2×#41—181no—
487C2×#41D3211yescharacteristic, complemented
488C22×Q8—32no—
489C22×Q8—31no—
490C22×Q8—61no—
491C22×D4—92no—
492C22×D4—91no—
493C22×D4—181no—
494C22×D4—182no—
495#137—916no—
496#137—98no—
497AGL(1,ℤ/8)—916no—
498AGL(1,ℤ/8)—98no—
499#135—38no—
500#135—916no—
501C2×Q16—31no—
502C2×Q16—92no—
503C2×SD16—31no—
504C2×SD16—31no—
505C2×SD16—92no—
506C2×SD16—92no—
507C2×SD16—98no—
508C2×SD16—916no—
509C2×SD16—92no—
510C2×SD16—92no—
511C2×D8—31no—
512C2×D8—92no—
513#131—98no—
514C2×M16—92no—
515C2×M16—91no—
516C22×C8—31no—
517C22×C8—92no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—32no—
522C23×C3—41no—
523C23×C3—61no—
524C23×C3D3×D411yescharacteristic
525C23×C3C2×#6711yescharacteristic
526C22×D3—21no—
527C22×D3—68no—
528C22×D3—62no—
529C22×D3—62no—
530C22×D3—64no—
531C22×D3—64no—
532C22×D3—68no—
533C22×D3—122no—
534C22×D3—124no—
535C22×D3—244no—
536C22×D3—244no—
537C22×D3—242no—
538C22×D3—242no—
539C22×D3—244no—
540C22×D3C2×#6712yes—
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—22no—
544C3×Q8—34no—
545C3×Q8—34no—
546C3×Q8—32no—
547C3×Q8—41no—
548C3×Q8—68no—
549C3×Q8—62no—
550C3×Q8—64no—
551C3×Q8—61no—
552C3×Q8C23×D312yes—
553C3×Q8C23×D312yes—
554C3×D4—24no—
555C3×D4—24no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—22no—
559C3×D4—38no—
560C3×D4—34no—
561C3×D4—32no—
562C3×D4—41no—
563C3×D4—44no—
564C3×D4—68no—
565C3×D4—64no—
566C3×D4—61no—
567C3×D4C23×D312yes—
568C3×D4C23×D312yes—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—24no—
572C2×C3×C4—24no—
573C2×C3×C4—21no—
574C2×C3×C4—22no—
575C2×C3×C4—21no—
576C2×C3×C4—22no—
577C2×C3×C4—32no—
578C2×C3×C4—34no—
579C2×C3×C4—34no—
580C2×C3×C4—44no—
581C2×C3×C4—41no—
582C2×C3×C4—68no—
583C2×C3×C4—68no—
584C2×C3×C4—62no—
585C2×C3×C4—64no—
586C2×C3×C4—61no—
587C2×C3×C4—64no—
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4D3×D412yes—
590C2×C3×C4C2×#6711yescharacteristic
591C2×C3×C4C2×#6712yes—
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C23×D312yes—
594C2×C3×C4C23×D311yescharacteristic
595C2×C3×C4C23×D312yes—
596#67—24no—
597#67—28no—
598#67—68no—
599#67—68no—
600#67C2×#6718yes—
601C2×Dic3—21no—
602C2×Dic3—22no—
603C2×Dic3—24no—
604C2×Dic3—28no—
605C2×Dic3C2×#6712yes—
606D12—21no—
607D12—34no—
608D12—34no—
609D12—64no—
610D12—68no—
611D12—68no—
612D12—62no—
613D12—64no—
614D12—64no—
615D12—62no—
616D12—124no—
617D12—122no—
618D12C2×#6714yes—
619D12C23×D312yes—
620C4×D3—28no—
621C4×D3—24no—
622C4×D3—68no—
623C4×D3—68no—
624C4×D3C2×#6714yes—
625C4×D3C23×D314yes—
626Dic6—21no—
627Dic6—24no—
628Dic6—22no—
629Dic6—28no—
630Dic6C2×#6714yes—
631Dic6C23×D314yes—
632Dic6C23×D312yes—
633C3×C8—32no—
634C3×C8—32no—
635C3⋊C8—34no—
636C3⋊C8—34no—
637C3⋊C8—64no—
638C3⋊C8C23×D312yes—
639C3⋊C8C23×D312yes—
640C2×C32—22no—
641C2×C32—42no—
642C2×C32#57712yescomplemented
643C2×C32C23×D411yescharacteristic
644C3⋊D3—44no—
645C3×D3—24no—
646C3×D3—42no—
647C24—182no—
648C24—181no—
649#41—22no—
650#41—34no—
651#41—34no—
652#41—38no—
653#41—34no—
654#41—68no—
655#41—64no—
656#41—616no—
657#41—62no—
658#41—98no—
659#41—184no—
660#41—188no—
661#41C2×D3214yescomplemented
662C2×Q8—31no—
663C2×Q8—38no—
664C2×Q8—31no—
665C2×Q8—32no—
666C2×Q8—34no—
667C2×Q8—62no—
668C2×Q8—68no—
669C2×Q8—64no—
670C2×Q8—61no—
671C2×Q8—62no—
672C2×Q8C2×D3211yescharacteristic
673C2×D4—21no—
674C2×D4—32no—
675C2×D4—31no—
676C2×D4—31no—
677C2×D4—62no—
678C2×D4—61no—
679C2×D4—98no—
680C2×D4—92no—
681C2×D4—94no—
682C2×D4—184no—
683C2×D4—182no—
684C2×D4—188no—
685C2×D4—182no—
686C2×D4—1816no—
687C2×D4—181no—
688C2×D4—182no—
689C2×D4C2×D3211yescharacteristic
690C22×C4—21no—
691C22×C4—32no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—61no—
695C22×C4—61no—
696C22×C4—182no—
697C22×C4C2×D3211yescharacteristic
698Q16—34no—
699Q16—98no—
700SD16—34no—
701SD16—34no—
702SD16—98no—
703SD16—98no—
704SD16—98no—
705SD16—98no—
706D8—34no—
707D8—98no—
708M16—98no—
709M16—94no—
710C2×C8—31no—
711C2×C8—31no—
712C2×C8—34no—
713C2×C8—98no—
714C2×C8—92no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—22no—
718C22×C3—22no—
719C22×C3—22no—
720C22×C3—21no—
721C22×C3—34no—
722C22×C3—42no—
723C22×C3—42no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3—64no—
727C22×C3—62no—
728C22×C3—82no—
729C22×C3—122no—
730C22×C3C2×D3×D412yes—
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C22×#6712yes—
733C22×C3C22×#6711yescharacteristic
734C2×D3—24no—
735C2×D3—22no—
736C2×D3—42no—
737C2×D3—64no—
738C2×D3—64no—
739C2×D3—124no—
740C2×D3—124no—
741C2×D3—124no—
742C2×D3—244no—
743C2×D3—248no—
744C2×D3—248no—
745C2×D3—244no—
746C2×D3—244no—
747C2×D3—248no—
748C2×D3C22×#6714yes—
749C3×C4—22no—
750C3×C4—22no—
751C3×C4—22no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—34no—
755C3×C4—42no—
756C3×C4—64no—
757C3×C4—62no—
758C3×C4C2×D3×D411yescharacteristic
759C3×C4C2×D3×D412yes—
760C3×C4C22×#6712yes—
761C3×C4C22×#6711yescharacteristic
762C3×C4C24×D311yescharacteristic
763C3×C4C24×D311yescharacteristic
764Dic3—22no—
765Dic3—24no—
766Dic3C22×#6714yes—
767C32C2×#57711yescharacteristic, complemented, Sylow
768C23—21no—
769C23—32no—
770C23—61no—
771C23—188no—
772C23—182no—
773C23—184no—
774C23—722no—
775C23—724no—
776C23D3×#6711yescharacteristic
777Q8—21no—
778Q8—34no—
779Q8—32no—
780Q8—34no—
781Q8—68no—
782Q8—64no—
783Q8—62no—
784Q8—61no—
785Q8C22×D3212yes—
786D4—24no—
787D4—21no—
788D4—38no—
789D4—34no—
790D4—32no—
791D4—68no—
792D4—64no—
793D4—61no—
794D4—94no—
795D4—188no—
796D4—188no—
797D4—184no—
798D4—182no—
799D4C22×D3212yes—
800C2×C4—21no—
801C2×C4—24no—
802C2×C4—32no—
803C2×C4—34no—
804C2×C4—34no—
805C2×C4—68no—
806C2×C4—68no—
807C2×C4—64no—
808C2×C4—62no—
809C2×C4—61no—
810C2×C4—64no—
811C2×C4—188no—
812C2×C4D3×#6712yes—
813C2×C4D3×#6711yescharacteristic
814C2×C4C22×D3212yes—
815C2×C4C22×D3211yescharacteristic
816C8—32no—
817C8—32no—
818C8—94no—
819C2×C3—22no—
820C2×C3—22no—
821C2×C3—21no—
822C2×C3—22no—
823C2×C3—42no—
824C2×C3—42no—
825C2×C3—42no—
826C2×C3—64no—
827C2×C3—82no—
828C2×C3—122no—
829C2×C3#577012yescomplemented
830C2×C3#583712yescomplemented
831C2×C3C22×D3×D411yescharacteristic
832C2×C3C23×#6711yescharacteristic
833D3—24no—
834D3—42no—
835D3—124no—
836D3—124no—
837D3—244no—
838C22—22no—
839C22—22no—
840C22—34no—
841C22—42no—
842C22—64no—
843C22—62no—
844C22—122no—
845C22—184no—
846C22—364no—
847C22—724no—
848C22—728no—
849C22C2×D3×#6712yes—
850C22C2×D3×#6711yescharacteristic
851C4—22no—
852C4—34no—
853C4—64no—
854C4—62no—
855C4C2×D3×#6712yes—
856C4C2×D3×#6711yescharacteristic
857C4C23×D3211yescharacteristic
858C3—21no—
859C3C2×#577011yescharacteristic, complemented
860C3C2×#583711yescharacteristic, complemented
861C2—22no—
862C2—42no—
863C2—64no—
864C2—122no—
865C2—364no—
866C2#1059545712yesdirect product factor
867C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#577
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×C3×#1010C2semidirect
2. C2×#64308C2semidirect
3. C2×#64158C2semidirect
4. C2×C3×#950C2semidirect
5. #10595457C2direct (N × H)
6. C2×#63948C2semidirect
7. C2×D3×#215C2semidirect
8. C2×#63935C2semidirect
9. C2×#63925C2semidirect
10. C22×#3717C2semidirect
11. C2×#63827C2semidirect
12. C2×#63814C2semidirect
15. C2×C32×#41C22semidirect
18. C3×#1010C22semidirect
19. C2×C3×D3×Q8C22semidirect
21. C2×C3×#237C22semidirect
26. C22×C3×Dic6C22semidirect
29. #64308C22semidirect
34. #64158C22semidirect
35. C2×#3755C22semidirect
36. C2×#3753C22semidirect
37. C2×#3748C22semidirect
38. C3×#950C22semidirect
39. C2×C3×#216C22semidirect
40. C2×C3×#215C22semidirect
41. C2×C3×#214C22semidirect
42. C2×C3×#213C22semidirect
43. C22×C3×C3⋊C8C22semidirect
44. #63948C22semidirect
45. D3×#215C22semidirect
46. #63935C22semidirect
47. #63925C22semidirect
48. C2×#3718C22semidirect
49. C2×#3717C22semidirect
50. C2×#3717C22semidirect
51. C2×#3717C22semidirect
52. #63827C22semidirect
53. C2×#3715C22semidirect
54. C2×#3711C22semidirect
55. #63814C22semidirect
56. C2×D3×C3⋊C8C22semidirect
58. C2×#1010D3semidirect
65. C2×#950D3semidirect
85. C32×#41C23semidirect
101. C3×D3×Q8C23semidirect
104. C3×#237C23semidirect
122. C2×C3×Dic6C23semidirect
133. #3755C23semidirect
134. #3753C23semidirect
135. #3748C23semidirect
137. C3×#216C23semidirect
138. C3×#215C23semidirect
139. C3×#214C23semidirect
140. C3×#213C23semidirect
143. C2×C3×C3⋊C8C23semidirect
144. #3718C23semidirect
145. #3717C23semidirect
146. #3717C23semidirect
147. #3715C23semidirect
148. #3711C23semidirect
149. D3×C3⋊C8C23semidirect
159. C2×C3×#41C2×D3semidirect
160. C2×C3×#41C2×D3semidirect
165. #1010C2×D3semidirect
172. C2×D3×Q8C2×D3semidirect
174. C2×#237C2×D3semidirect
190. C22×Dic6C2×D3semidirect
199. #950C2×D3semidirect
207. C2×#216C2×D3semidirect
218. C2×#215C2×D3semidirect
220. C2×#214C2×D3semidirect
224. C2×#213C2×D3semidirect
230. C22×C3⋊C8C2×D3semidirect
321. C3×#41C22×D3semidirect
322. C3×#41C22×D3semidirect
369. D3×Q8C22×D3semidirect
372. #237C22×D3semidirect
417. C2×Dic6C22×D3semidirect
427. #216C22×D3semidirect
434. #215C22×D3semidirect
436. #214C22×D3semidirect
440. #213C22×D3semidirect
451. C2×C3⋊C8C22×D3semidirect
487. C2×#41D32semidirect
642. C2×C32#577semidirect
661. #41C2×D32semidirect
767. C32C2×#577semidirect
829. C2×C3#5770semidirect
830. C2×C3#5837semidirect
859. C3C2×#5770semidirect
860. C3C2×#5837semidirect
866. C2#10595457direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×#643082
C2×#641582
C2×C3×#9502
#105954572
C2×#639482
C2×D3×#2152
C2×#639352
C2×#639252
C22×#37172
C2×#638272
C2×#638142
C2×#58373
C2×#57703