Finite Group Databasebeta

← C2×#10595096 #11918815

Subgroups — C2×#10595096 #11918815

Order 1152.

3173 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3C2×#64141C211yesmaximal, characteristic, complemented
4C22×C3×#213C211yesmaximal, characteristic, complemented
5C2×#63933C212yesmaximal, complemented
6C2×#63932C212yesmaximal, complemented
7#10595096C2116yesmaximal, direct product factor
8C2×#63925C212yesmaximal, complemented
9C2×D3×#213C212yesmaximal, complemented
10C2×#63829C211yesmaximal, characteristic, complemented
11C2×#63823C211yesmaximal, characteristic, complemented
12C2×#63814C211yesmaximal, characteristic, complemented
13C2×#5835—31nomaximal
14C2×#5757—31nomaximal
15C22×C32×D4C2211yescharacteristic, complemented
16C2×#3828C2211yescharacteristic, complemented
17C22×C3×#67—22no—
18C3×#1004—24no—
19C3×#1004C2218yescomplemented
20C2×C3×#237—21no—
21C2×C3×#237C2212yescomplemented
22C2×C3×D3×D4—21no—
23C2×C3×D3×D4C2212yescomplemented
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic, complemented
27C2×D3×#67—22no—
28#64307—24no—
29#64307C2218yescomplemented
30C2×#3802—21no—
31C2×D3×D12C2212yescomplemented
32C2×#3796—21no—
33C2×#3795C2212yescomplemented
34C2×#3754C2212yescomplemented
35#64141C2218yescomplemented
36C2×#3753C2212yescomplemented
37C2×#3748C2211yescharacteristic, complemented
38C2×C3×#213C2212yescomplemented
39C2×C3×#213C2212yescomplemented
40C2×C3×#213C2218yescomplemented
41C22×C3×C3⋊C8C2211yescharacteristic, complemented
42#63933C22116yescomplemented
43#63932C22116yescomplemented
44#63925C22116yescomplemented
45D3×#213C22116yescomplemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48#63829C2218yescomplemented
49C2×#3716C2211yescharacteristic, complemented
50C2×#3715C2212yescomplemented
51C2×#3714C2211yescharacteristic, complemented
52#63823C2218yescomplemented
53C2×#3713C2212yescomplemented
54C2×#3711C2212yescomplemented
55#63814C2218yescomplemented
56C2×D3×C3⋊C8C2212yescomplemented
57C2×C3×H(5,𝔽2)—31no—
58C2×#1009—31no—
59C2×#1004—31no—
60C2×#1004D311yescharacteristic, complemented
61C22×C3×D8—31no—
62#5835—316no—
63C2×#950—32no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#949—32no—
67C2×#948—31no—
68C2×#932—31no—
69C2×#932—31no—
70C2×#932—31no—
71C2×#932—32no—
72C2×#932—61no—
73C22×#213—32no—
74C22×#213D311yescharacteristic, complemented
75#5757—316no—
76C2×#912—32no—
77C2×#911—32no—
78C2×#911—32no—
79C2×D3×D8—32no—
80C2×#904—31no—
81C2×#901—31no—
82C24×C32—21no—
83C23×C3×D3—21no—
84C23×C3×D3—22no—
85C22×D32—22no—
86C2×C32×D4—21no—
87C2×C32×D4—22no—
88C2×C32×D4C2312yes—
89C2×C32×D4C2314yescomplemented
90C22×C32×C4C2311yescharacteristic
91C2×#638—21no—
92#3828—22no—
93#3828C2314yescomplemented
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—22no—
99C2×C3×#67—216no—
100C2×C3×#67—22no—
101C2×C3×#67D412yes—
102C22×C3×Dic3—22no—
103C3×#237—24no—
104C3×#237—28no—
105C3×#237C2318yescomplemented
106C3×D3×D4—28no—
107C3×D3×D4—24no—
108C3×D3×D4C2318yescomplemented
109C3×#235—22no—
110C3×#235D414yes—
111C3×#235C2314yes—
112C3×#235C2314yescomplemented
113C2×C3×D12—21no—
114C2×C3×D12—22no—
115C2×C3×D12D411yescharacteristic
116C2×C3×D12C2312yes—
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2314yescomplemented
119C2×C3×C4×D3—21no—
120C2×C3×C4×D3C2312yes—
121C2×C3×Dic6D411yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
123D3×#67—216no—
124C2×#626—22no—
125C2×#625—22no—
126C2×D3×Dic3—22no—
127#3802—28no—
128D3×D12—24no—
129D3×D12C2318yescomplemented
130#3796—28no—
131#3795—24no—
132#3795C2318yescomplemented
133#3754C2318yescomplemented
134#3753C2318yescomplemented
135#3748C2314yescomplemented
136C2×C3⋊(C3⋊C8)C2312yes—
137C3×#213C2318yescomplemented
138C3×#213C2318yescomplemented
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2314yescomplemented
142#3719C2314yescomplemented
143#3717C2314yescomplemented
144#3716C2314yescomplemented
145#3715C2318yescomplemented
146#3714C2314yescomplemented
147#3713C2318yescomplemented
148#3711C2318yescomplemented
149D3×C3⋊C8C2318yescomplemented
150C2×#576—91noSylow
151C3×H(5,𝔽2)—38no—
152C3×H(5,𝔽2)—64no—
153C2×C3×#41—31no—
154C2×C3×#41—32no—
155C2×C3×#41—31no—
156C2×C3×#41—61no—
157C22×C3×D4—21no—
158C22×C3×D4—32no—
159C22×C3×D4—31no—
160C22×C3×D4—61no—
161C22×C3×D4—62no—
162C22×C3×D4C2×D311yescharacteristic, complemented
163C22×C3×D4C2×D311yescharacteristic, complemented
164C22×#67—22no—
165C22×#67—62no—
166#1009—38no—
167#1009—64no—
168C2×#239—61no—
169#1004—24no—
170#1004—38no—
171#1004—64no—
172#1004C2×D318yescomplemented
173C2×#237—21no—
174C2×#237—32no—
175C2×#237—61no—
176C2×#237C2×D312yescomplemented
177C2×D3×D4—21no—
178C2×D3×D4—32no—
179C2×D3×D4—61no—
180C2×D3×D4—62no—
181C2×D3×D4—61no—
182C2×D3×D4C2×D312yescomplemented
183C2×#235—31no—
184C2×#235—31no—
185C2×#235—32no—
186C2×#235—61no—
187C2×#235C2×D311yescharacteristic
188C2×#235C2×D311yescharacteristic, complemented
189C22×D12—32no—
190C22×D12C2×D311yescharacteristic, complemented
191C2×C3×D8—32no—
192C2×C3×D8—32no—
193C2×C3×D8—38no—
194C22×C3×C8—31no—
195#950—316no—
196#950—38no—
197#949—38no—
198#949—316no—
199#948—38no—
200C2×#216—31no—
201C2×#215—32no—
202C2×#215—31no—
203C2×#214—32no—
204C2×#214—32no—
205C2×#214—32no—
206C2×#214—31no—
207C2×#214—62no—
208#932—38no—
209#932—38no—
210#932—38no—
211#932—316no—
212#932—68no—
213C2×#213—32no—
214C2×#213—32no—
215C2×#213—32no—
216C2×#213—32no—
217C2×#213—316no—
218C2×#213—31no—
219C2×#213—62no—
220C2×#213C2×D312yescomplemented
221C2×#213C2×D312yescomplemented
222C2×#213C2×D318yescomplemented
223C2×#208—31no—
224C2×#208—31no—
225C2×#208—32no—
226C2×#208—61no—
227C22×C3⋊C8—32no—
228C22×C3⋊C8C2×D311yescharacteristic, complemented
229#912—316no—
230#911—316no—
231#911—316no—
232D3×D8—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×C32—22no—
242C23×C32—24no—
243C23×C32—82no—
244C23×C32C2×D411yescharacteristic
245C22×C3⋊D3—21no—
246C22×C3×D3—22no—
247C22×C3×D3—21no—
248C22×C3×D3—24no—
249C22×C3×D3—28no—
250C22×C3×D3—84no—
251C22×C3×D3—82no—
252C22×C3×D3C2×D412yes—
253C2×D32—28no—
254C2×D32—84no—
255C32×D4—22no—
256C32×D4—24no—
257C32×D4C2414yes—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D412yes—
260C2×C32×C4C2411yescharacteristic
261C2×C32×C4C2412yes—
262#638—24no—
263C2×C3⋊Dic3—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)C2412yes—
266C4×C3⋊D3—24no—
267#634—21no—
268#634C2412yes—
269C3×#67—24no—
270C3×#67—28no—
271C3×#67—28no—
272C3×#67C2×D418yes—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—28no—
275C2×C3×Dic3C2×D412yes—
276C3×D12—22no—
277C3×D12—24no—
278C3×D12—21no—
279C3×D12C2×D414yes—
280C3×D12C2412yes—
281C3×D12C2414yes—
282C3×C4×D3—24no—
283C3×C4×D3C2×D414yes—
284C3×C4×D3C2414yes—
285C3×Dic6—21no—
286C3×Dic6C2×D414yes—
287C3×Dic6C2412yes—
288#626—28no—
289#625—28no—
290D3×Dic3—28no—
291C3⋊(C3⋊C8)C2414yes—
292C3×C3⋊C8C2412yes—
293C3×C3⋊C8C2412yes—
294C2×H(5,𝔽2)—31no—
295C2×H(5,𝔽2)—91no—
296#576—916no—
297C2×AGL(1,ℤ/8)—92no—
298C2×AGL(1,ℤ/8)—92no—
299C2×AGL(1,ℤ/8)—91no—
300C2×AGL(1,ℤ/8)—91no—
301C2×#135—91no—
302C2×#135—92no—
303C22×D8—31no—
304C22×D8—92no—
305C2×#131—91no—
306C24×C3—21no—
307C24×C3—21no—
308C24×C3—41no—
309C24×C3—62no—
310C24×C3—61no—
311C23×D3—21no—
312C23×D3—22no—
313C23×D3—62no—
314C23×D3—62no—
315C3×#41—34no—
316C3×#41—34no—
317C3×#41—38no—
318C3×#41—34no—
319C3×#41—64no—
320C3×#41—68no—
321C3×#41—62no—
322C2×C3×Q8—31no—
323C2×C3×Q8—31no—
324C2×C3×D4—21no—
325C2×C3×D4—22no—
326C2×C3×D4—21no—
327C2×C3×D4—22no—
328C2×C3×D4—22no—
329C2×C3×D4—24no—
330C2×C3×D4—32no—
331C2×C3×D4—38no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—32no—
335C2×C3×D4—34no—
336C2×C3×D4—41no—
337C2×C3×D4—42no—
338C2×C3×D4—64no—
339C2×C3×D4—62no—
340C2×C3×D4—68no—
341C2×C3×D4—616no—
342C2×C3×D4—62no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—62no—
346C2×C3×D4C22×D312yes—
347C2×C3×D4C22×D312yes—
348C2×C3×D4C22×D314yescomplemented
349C2×C3×D4C22×D314yescomplemented
350C22×C3×C4—21no—
351C22×C3×C4—32no—
352C22×C3×C4—62no—
353C22×C3×C4—61no—
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C2×#67—21no—
357C2×#67—22no—
358C2×#67—216no—
359C2×#67—22no—
360C2×#67—62no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—62no—
364C2×#67—616no—
365C2×#67—62no—
366C2×#67—121no—
367C2×#67#6712yes—
368C22×Dic3—22no—
369C22×Dic3—62no—
370#239—68no—
371#237—24no—
372#237—28no—
373#237—38no—
374#237—64no—
375#237—68no—
376#237C22×D318yescomplemented
377D3×D4—28no—
378D3×D4—24no—
379D3×D4—38no—
380D3×D4—68no—
381D3×D4—616no—
382D3×D4—68no—
383D3×D4—64no—
384D3×D4C22×D318yescomplemented
385#235—22no—
386#235—34no—
387#235—34no—
388#235—38no—
389#235—64no—
390#235—64no—
391#235—62no—
392#235—62no—
393#235—122no—
394#235#6714yes—
395#235C22×D314yes—
396#235C22×D314yescomplemented
397C2×D12—21no—
398C2×D12—22no—
399C2×D12—31no—
400C2×D12—31no—
401C2×D12—38no—
402C2×D12—61no—
403C2×D12—64no—
404C2×D12—62no—
405C2×D12#6711yescharacteristic
406C2×D12C22×D311yescharacteristic
407C2×D12C22×D312yes—
408C2×D12C22×D314yescomplemented
409C2×C4×D3—21no—
410C2×C4×D3—62no—
411C2×C4×D3—61no—
412C2×C4×D3—61no—
413C2×C4×D3—121no—
414C2×C4×D3C22×D312yes—
415C2×Dic6—31no—
416C2×Dic6—31no—
417C2×Dic6—61no—
418C2×Dic6#6711yescharacteristic
419C2×Dic6C22×D311yescharacteristic
420C3×D8—38no—
421C3×D8—38no—
422C2×C3×C8—31no—
423C2×C3×C8—31no—
424C2×C3×C8—34no—
425#216—34no—
426#215—38no—
427#215—34no—
428#214—38no—
429#214—38no—
430#214—38no—
431#214—34no—
432#214—68no—
433#213—38no—
434#213—38no—
435#213—38no—
436#213—38no—
437#213—34no—
438#213—68no—
439#213C22×D318yescomplemented
440#213C22×D318yescomplemented
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
452Dic12—34no—
453D24—34no—
454#204—34no—
455#204—34no—
456ΓL(1,𝔽25)—38no—
457D3×C8—38no—
458C22×C32—22no—
459C22×C32—24no—
460C22×C32—44no—
461C22×C32—84no—
462C22×C32C22×D412yes—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—22no—
465C2×C3⋊D3—42no—
466C2×C3×D3—24no—
467C2×C3×D3—24no—
468C2×C3×D3—22no—
469C2×C3×D3—44no—
470C2×C3×D3—42no—
471C2×C3×D3—88no—
472C2×C3×D3—84no—
473C2×C3×D3C22×D414yes—
474D32—88no—
475C32×C4C22×D411yescharacteristic
476C32×C4C22×D412yes—
477C32×C4C2511yescharacteristic
478C3⋊Dic3—22no—
479C3×Dic3—22no—
480C3×Dic3C22×D414yes—
481H(5,𝔽2)—38no—
482H(5,𝔽2)—64no—
483H(5,𝔽2)—98no—
484H(5,𝔽2)—184no—
485C2×#41—31no—
486C2×#41—32no—
487C2×#41—31no—
488C2×#41—61no—
489C2×#41—92no—
490C2×#41—91no—
491C2×#41—181no—
492C22×D4—32no—
493C22×D4—31no—
494C22×D4—61no—
495C22×D4—62no—
496C22×D4—92no—
497C22×D4—181no—
498C22×D4—182no—
499C22×D4D3211yescharacteristic, complemented
500AGL(1,ℤ/8)—916no—
501AGL(1,ℤ/8)—916no—
502AGL(1,ℤ/8)—98no—
503AGL(1,ℤ/8)—98no—
504#135—98no—
505#135—916no—
506C2×Q16—91no—
507C2×SD16—91no—
508C2×SD16—91no—
509C2×SD16—92no—
510C2×SD16—92no—
511C2×D8—32no—
512C2×D8—32no—
513C2×D8—38no—
514C2×D8—91no—
515C2×D8—916no—
516C2×D8—92no—
517C2×D8—92no—
518#131—98no—
519C2×M16—92no—
520C2×M16—91no—
521C22×C8—31no—
522C22×C8—92no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—24no—
526C23×C3—24no—
527C23×C3—21no—
528C23×C3—32no—
529C23×C3—42no—
530C23×C3—44no—
531C23×C3—68no—
532C23×C3—61no—
533C23×C3—62no—
534C23×C3—64no—
535C23×C3—82no—
536C23×C3—82no—
537C23×C3—84no—
538C23×C3—242no—
539C23×C3—244no—
540C23×C3D3×D411yescharacteristic
541C23×C3C2×#6711yescharacteristic
542C22×D3—22no—
543C22×D3—21no—
544C22×D3—24no—
545C22×D3—28no—
546C22×D3—68no—
547C22×D3—61no—
548C22×D3—61no—
549C22×D3—68no—
550C22×D3—84no—
551C22×D3—82no—
552C22×D3—121no—
553C22×D3—244no—
554C22×D3—244no—
555C22×D3C2×#6712yes—
556C3×Q8—34no—
557C3×Q8—32no—
558C3×Q8—61no—
559C3×D4—22no—
560C3×D4—24no—
561C3×D4—22no—
562C3×D4—24no—
563C3×D4—24no—
564C3×D4—38no—
565C3×D4—34no—
566C3×D4—32no—
567C3×D4—34no—
568C3×D4—42no—
569C3×D4—44no—
570C3×D4—68no—
571C3×D4—68no—
572C3×D4—64no—
573C3×D4—61no—
574C3×D4—62no—
575C3×D4—64no—
576C3×D4C23×D314yes—
577C3×D4C23×D314yes—
578C2×C3×C4—21no—
579C2×C3×C4—22no—
580C2×C3×C4—21no—
581C2×C3×C4—22no—
582C2×C3×C4—32no—
583C2×C3×C4—34no—
584C2×C3×C4—34no—
585C2×C3×C4—68no—
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—28no—
599#67—68no—
600#67—64no—
601#67—64no—
602#67—68no—
603#67—68no—
604#67—124no—
605#67C2×#6718yes—
606C2×Dic3—21no—
607C2×Dic3—28no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—68no—
611C2×Dic3—121no—
612C2×Dic3C2×#6712yes—
613D12—22no—
614D12—24no—
615D12—21no—
616D12—32no—
617D12—32no—
618D12—62no—
619D12—68no—
620D12—61no—
621D12—61no—
622D12—121no—
623D12C2×#6714yes—
624D12C23×D312yes—
625D12C23×D314yes—
626C4×D3—24no—
627C4×D3—68no—
628C4×D3—64no—
629C4×D3—64no—
630C4×D3—124no—
631C4×D3C2×#6714yes—
632C4×D3C23×D314yes—
633Dic6—21no—
634Dic6—32no—
635Dic6—32no—
636Dic6—62no—
637Dic6—61no—
638Dic6—61no—
639Dic6—121no—
640Dic6C2×#6714yes—
641Dic6C23×D312yes—
642C3×C8—32no—
643C3×C8—32no—
644C3⋊C8—34no—
645C3⋊C8—34no—
646C3⋊C8—64no—
647C3⋊C8C23×D312yes—
648C3⋊C8C23×D312yes—
649C2×C32—22no—
650C2×C32—44no—
651C2×C32#57612yescomplemented
652C2×C32C23×D411yescharacteristic
653C3⋊D3—42no—
654C3×D3—24no—
655C3×D3—44no—
656C3×D3—42no—
657C24—21no—
658C24—62no—
659C24—61no—
660C24—182no—
661#41—34no—
662#41—34no—
663#41—38no—
664#41—34no—
665#41—64no—
666#41—68no—
667#41—62no—
668#41—98no—
669#41—94no—
670#41—184no—
671#41—188no—
672#41—182no—
673C2×Q8—31no—
674C2×Q8—31no—
675C2×Q8—91no—
676C2×D4—21no—
677C2×D4—22no—
678C2×D4—32no—
679C2×D4—38no—
680C2×D4—32no—
681C2×D4—34no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—64no—
685C2×D4—62no—
686C2×D4—68no—
687C2×D4—616no—
688C2×D4—62no—
689C2×D4—61no—
690C2×D4—61no—
691C2×D4—62no—
692C2×D4—98no—
693C2×D4—91no—
694C2×D4—184no—
695C2×D4—182no—
696C2×D4—188no—
697C2×D4—1816no—
698C2×D4—182no—
699C2×D4—181no—
700C2×D4C2×D3212yes—
701C2×D4C2×D3214yescomplemented
702C22×C4—32no—
703C22×C4—62no—
704C22×C4—61no—
705C22×C4—182no—
706C22×C4—181no—
707C22×C4C2×D3211yescharacteristic
708Q16—94no—
709SD16—94no—
710SD16—94no—
711SD16—98no—
712SD16—98no—
713D8—38no—
714D8—38no—
715D8—94no—
716D8—98no—
717D8—98no—
718M16—98no—
719M16—94no—
720C2×C8—31no—
721C2×C8—31no—
722C2×C8—34no—
723C2×C8—98no—
724C2×C8—92no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—24no—
728C22×C3—24no—
729C22×C3—22no—
730C22×C3—21no—
731C22×C3—34no—
732C22×C3—42no—
733C22×C3—44no—
734C22×C3—44no—
735C22×C3—44no—
736C22×C3—64no—
737C22×C3—62no—
738C22×C3—64no—
739C22×C3—84no—
740C22×C3—84no—
741C22×C3—84no—
742C22×C3—88no—
743C22×C3—122no—
744C22×C3—124no—
745C22×C3—244no—
746C22×C3—248no—
747C22×C3C2×D3×D412yes—
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C22×#6712yes—
750C22×C3C22×#6711yescharacteristic
751C2×D3—24no—
752C2×D3—24no—
753C2×D3—22no—
754C2×D3—44no—
755C2×D3—42no—
756C2×D3—62no—
757C2×D3—62no—
758C2×D3—88no—
759C2×D3—84no—
760C2×D3—122no—
761C2×D3—122no—
762C2×D3—122no—
763C2×D3—242no—
764C2×D3—248no—
765C2×D3—248no—
766C2×D3C22×#6714yes—
767C3×C4—21no—
768C3×C4—22no—
769C3×C4—21no—
770C3×C4—34no—
771C3×C4—62no—
772C3×C4C2×D3×D411yescharacteristic
773C3×C4C2×D3×D412yes—
774C3×C4C22×#6711yescharacteristic
775C3×C4C22×#6712yes—
776C3×C4C24×D311yescharacteristic
777C3×C4C24×D311yescharacteristic
778Dic3—22no—
779Dic3—62no—
780Dic3—62no—
781Dic3—122no—
782Dic3C22×#6714yes—
783C32C2×#57611yescharacteristic, complemented, Sylow
784C23—22no—
785C23—24no—
786C23—32no—
787C23—68no—
788C23—61no—
789C23—62no—
790C23—64no—
791C23—82no—
792C23—188no—
793C23—181no—
794C23—242no—
795C23—244no—
796C23—724no—
797C23D3×#6711yescharacteristic
798Q8—34no—
799Q8—32no—
800Q8—61no—
801Q8—92no—
802Q8—181no—
803D4—22no—
804D4—24no—
805D4—38no—
806D4—34no—
807D4—34no—
808D4—32no—
809D4—68no—
810D4—68no—
811D4—64no—
812D4—61no—
813D4—62no—
814D4—64no—
815D4—92no—
816D4—188no—
817D4—188no—
818D4—184no—
819D4—181no—
820D4C22×D3214yes—
821C2×C4—32no—
822C2×C4—34no—
823C2×C4—34no—
824C2×C4—68no—
825C2×C4—61no—
826C2×C4—64no—
827C2×C4—188no—
828C2×C4—181no—
829C2×C4—184no—
830C2×C4D3×#6712yes—
831C2×C4D3×#6711yescharacteristic
832C2×C4C22×D3212yes—
833C2×C4C22×D3211yescharacteristic
834C8—32no—
835C8—32no—
836C8—94no—
837C2×C3—22no—
838C2×C3—22no—
839C2×C3—22no—
840C2×C3—21no—
841C2×C3—42no—
842C2×C3—44no—
843C2×C3—44no—
844C2×C3—64no—
845C2×C3—84no—
846C2×C3—122no—
847C2×C3—124no—
848C2×C3#575712yescomplemented
849C2×C3#583512yescomplemented
850C2×C3C22×D3×D411yescharacteristic
851C2×C3C23×#6711yescharacteristic
852D3—24no—
853D3—44no—
854D3—42no—
855D3—122no—
856D3—122no—
857D3—242no—
858C22—22no—
859C22—24no—
860C22—34no—
861C22—44no—
862C22—64no—
863C22—62no—
864C22—64no—
865C22—84no—
866C22—122no—
867C22—124no—
868C22—182no—
869C22—244no—
870C22—248no—
871C22—362no—
872C22—728no—
873C22C2×D3×#6712yes—
874C22C2×D3×#6711yescharacteristic
875C4—34no—
876C4—62no—
877C4—182no—
878C4C2×D3×#6711yescharacteristic
879C4C2×D3×#6712yes—
880C4C23×D3211yescharacteristic
881C3—21no—
882C3C2×#575711yescharacteristic, complemented
883C3C2×#583511yescharacteristic, complemented
884C2—22no—
885C2—44no—
886C2—64no—
887C2—122no—
888C2—124no—
889C2—362no—
890C2#1059509612yesdirect product factor
891C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32C2×#576
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C2×#64307C2semidirect
3. C2×#64141C2semidirect
4. C22×C3×#213C2semidirect
5. C2×#63933C2semidirect
6. C2×#63932C2semidirect
7. #10595096C2direct (N × H)
8. C2×#63925C2semidirect
9. C2×D3×#213C2semidirect
10. C2×#63829C2semidirect
11. C2×#63823C2semidirect
12. C2×#63814C2semidirect
15. C22×C32×D4C22semidirect
16. C2×#3828C22semidirect
19. C3×#1004C22semidirect
21. C2×C3×#237C22semidirect
23. C2×C3×D3×D4C22semidirect
25. C2×C3×#235C22semidirect
26. C22×C3×D12C22semidirect
29. #64307C22semidirect
31. C2×D3×D12C22semidirect
33. C2×#3795C22semidirect
34. C2×#3754C22semidirect
35. #64141C22semidirect
36. C2×#3753C22semidirect
37. C2×#3748C22semidirect
38. C2×C3×#213C22semidirect
39. C2×C3×#213C22semidirect
40. C2×C3×#213C22semidirect
41. C22×C3×C3⋊C8C22semidirect
42. #63933C22semidirect
43. #63932C22semidirect
44. #63925C22semidirect
45. D3×#213C22semidirect
46. C2×#3719C22semidirect
47. C2×#3717C22semidirect
48. #63829C22semidirect
49. C2×#3716C22semidirect
50. C2×#3715C22semidirect
51. C2×#3714C22semidirect
52. #63823C22semidirect
53. C2×#3713C22semidirect
54. C2×#3711C22semidirect
55. #63814C22semidirect
56. C2×D3×C3⋊C8C22semidirect
60. C2×#1004D3semidirect
74. C22×#213D3semidirect
89. C2×C32×D4C23semidirect
93. #3828C23semidirect
105. C3×#237C23semidirect
108. C3×D3×D4C23semidirect
112. C3×#235C23semidirect
118. C2×C3×D12C23semidirect
129. D3×D12C23semidirect
132. #3795C23semidirect
133. #3754C23semidirect
134. #3753C23semidirect
135. #3748C23semidirect
137. C3×#213C23semidirect
138. C3×#213C23semidirect
141. C2×C3×C3⋊C8C23semidirect
142. #3719C23semidirect
143. #3717C23semidirect
144. #3716C23semidirect
145. #3715C23semidirect
146. #3714C23semidirect
147. #3713C23semidirect
148. #3711C23semidirect
149. D3×C3⋊C8C23semidirect
162. C22×C3×D4C2×D3semidirect
163. C22×C3×D4C2×D3semidirect
172. #1004C2×D3semidirect
176. C2×#237C2×D3semidirect
182. C2×D3×D4C2×D3semidirect
188. C2×#235C2×D3semidirect
190. C22×D12C2×D3semidirect
220. C2×#213C2×D3semidirect
221. C2×#213C2×D3semidirect
222. C2×#213C2×D3semidirect
228. C22×C3⋊C8C2×D3semidirect
348. C2×C3×D4C22×D3semidirect
349. C2×C3×D4C22×D3semidirect
376. #237C22×D3semidirect
384. D3×D4C22×D3semidirect
396. #235C22×D3semidirect
408. C2×D12C22×D3semidirect
439. #213C22×D3semidirect
440. #213C22×D3semidirect
451. C2×C3⋊C8C22×D3semidirect
499. C22×D4D32semidirect
651. C2×C32#576semidirect
701. C2×D4C2×D32semidirect
783. C32C2×#576semidirect
848. C2×C3#5757semidirect
849. C2×C3#5835semidirect
882. C3C2×#5757semidirect
883. C3C2×#5835semidirect
890. C2#10595096direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×#643072
C2×#641412
C22×C3×#2132
C2×#639332
C2×#639322
#105950962
C2×#639252
C2×D3×#2132
C2×#638292
C2×#638232
C2×#638142
C2×#58353
C2×#57573