Finite Group Databasebeta

← C2×#10595319 #11918875

Subgroups — C2×#10595319 #11918875

Order 1152.

3069 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C2×#64308C211yesmaximal, characteristic, complemented
3C22×#3755C211yesmaximal, characteristic, complemented
4C2×C3×#942C211yesmaximal, characteristic, complemented
5C2×#63949C212yesmaximal, complemented
6C2×#63948C212yesmaximal, complemented
7#10595319C2116yesmaximal, direct product factor
8C2×#63939C212yesmaximal, complemented
9C2×D3×#215C212yesmaximal, complemented
10C2×#63825C211yesmaximal, characteristic, complemented
11C2×#63822C211yesmaximal, characteristic, complemented
12C2×#63815C211yesmaximal, characteristic, complemented
13C2×#5837—31nomaximal
14C2×#5778—31nomaximal
15C22×C32×Q8C2211yescharacteristic, complemented
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×#1007—24no—
18C3×#1007C2218yescomplemented
19C2×C3×#239—21no—
20C2×C3×#239C2212yescomplemented
21C2×C3×D3×Q8—21no—
22C2×C3×D3×Q8C2212yescomplemented
23C2×C3×#235—22no—
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic
26C2×C3×#235C2211yescharacteristic, complemented
27C2×#3811—22no—
28#64308—24no—
29#64308C2218yescomplemented
30C2×D3×D12—21no—
31C2×D3×D12C2212yes—
32C2×#3799—21no—
33C2×#3799C2212yes—
34C2×#3755C2212yescomplemented
35C2×#3755C2212yescomplemented
36C2×#3755C2218yescomplemented
37C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
38C2×C3×#216C2212yescomplemented
39C3×#942C2218yescomplemented
40C2×C3×#215C2212yescomplemented
41C2×C3×#208C2211yescharacteristic, complemented
42#63949C22116yescomplemented
43#63948C22116yescomplemented
44#63939C22116yescomplemented
45D3×#215C22116yescomplemented
46C2×#3718C2211yescharacteristic, complemented
47C2×#3717C2212yescomplemented
48C2×#3715C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50#63825C2218yescomplemented
51C2×#3714C2212yescomplemented
52#63822C2218yescomplemented
53C2×#3713C2211yescharacteristic, complemented
54C2×#3711C2212yescomplemented
55#63815C2218yescomplemented
56C2×D3×C3⋊C8C2212yescomplemented
57C2×C3×2−1+4—31no—
58C2×#1009—31no—
59C2×#1009—31no—
60C2×#1007D311yescharacteristic, complemented
61C2×C3×#137—31no—
62#5837—316no—
63C2×#950—31no—
64C2×#950—31no—
65C2×#950—32no—
66C2×#949—32no—
67C2×#949—31no—
68C2×#948—31no—
69C2×#942—32no—
70C2×#942D311yescharacteristic, complemented
71C22×#215—31no—
72C22×#215—31no—
73C22×#215—32no—
74C22×#215—61no—
75#5778—316no—
76C2×#919—32no—
77C2×#918—32no—
78C2×#914—32no—
79C2×D3×SD16—32no—
80C2×#908—31no—
81C2×#907—31no—
82C23×C3⋊D3—21no—
83C22×D32—22no—
84C2×C32×Q8—21no—
85C2×C32×Q8—22no—
86C2×C32×Q8C2312yes—
87C2×C32×Q8C2314yescomplemented
88C22×C32×C4—21no—
89C22×C32×C4C2311yescharacteristic
90C2×C4⋊(C3⋊D3)—21no—
91C2×C4⋊(C3⋊D3)—22no—
92C2×C4⋊(C3⋊D3)C2312yes—
93C2×C4⋊(C3⋊D3)C2314yes—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×#67D412yes—
97C3×#239—28no—
98C3×#239—24no—
99C3×#239C2318yescomplemented
100C3×D3×Q8—24no—
101C3×D3×Q8—28no—
102C3×D3×Q8C2318yescomplemented
103C3×#235—22no—
104C3×#235—22no—
105C3×#235—216no—
106C3×#235D414yes—
107C3×#235C2314yes—
108C3×#235C2314yes—
109C3×#235C2314yescomplemented
110C2×C3×D12—22no—
111C2×C3×D12D411yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—22no—
118C2×C3×C4×D3C2312yes—
119C2×C3×Dic6—22no—
120C2×C3×Dic6D411yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
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#3755C2318yescomplemented
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137C2×C3⋊(C3⋊C8)C2314yescomplemented
138C3×#216C2318yescomplemented
139C3×#215C2318yescomplemented
140C3×#208C2314yescomplemented
141C2×C3×C3⋊C8C2312yes—
142#3718C2314yescomplemented
143#3717C2318yescomplemented
144#3715C2314yescomplemented
145#3715C2314yescomplemented
146#3714C2318yescomplemented
147#3713C2314yescomplemented
148#3711C2318yescomplemented
149D3×C3⋊C8C2318yescomplemented
150C2×#577—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, complemented
163C22×C3×Q8C2×D311yescharacteristic, complemented
164#1009—38no—
165#1009—38no—
166#1009—64no—
167#1009—64no—
168#1007—24no—
169#1007C2×D318yescomplemented
170C2×#239—21no—
171C2×#239—32no—
172C2×#239—61no—
173C2×#239C2×D312yescomplemented
174C2×D3×Q8—21no—
175C2×D3×Q8C2×D312yescomplemented
176C2×D3×D4—32no—
177C2×D3×D4—61no—
178C2×D3×D4—62no—
179C2×D3×D4—62no—
180C2×#235—22no—
181C2×#235—32no—
182C2×#235—61no—
183C2×#235C2×D311yescharacteristic
184C2×#235C2×D311yescharacteristic
185C2×#235C2×D311yescharacteristic, complemented
186C22×D12—31no—
187C22×D12—31no—
188C22×D12—32no—
189C22×D12—61no—
190C22×D12—61no—
191C3×#137—38no—
192C2×C3×Q16—32no—
193C2×C3×SD16—32no—
194C2×C3×M16—31no—
195#950—38no—
196#950—38no—
197#950—316no—
198#949—316no—
199#949—38no—
200#948—38no—
201C2×#216—31no—
202C2×#216—31no—
203C2×#216C2×D312yescomplemented
204#942—316no—
205#942C2×D318yescomplemented
206C2×#215—32no—
207C2×#215—32no—
208C2×#215—32no—
209C2×#215—32no—
210C2×#215—38no—
211C2×#215—38no—
212C2×#215—31no—
213C2×#215—31no—
214C2×#215—316no—
215C2×#215—32no—
216C2×#215—62no—
217C2×#215—62no—
218C2×#215—68no—
219C2×#215C2×D312yescomplemented
220C2×#214—31no—
221C2×#214—31no—
222C2×#213—31no—
223C2×#213—31no—
224C2×#213—32no—
225C2×#208—32no—
226C2×#208C2×D311yescharacteristic, complemented
227C22×C3⋊C8—31no—
228C22×C3⋊C8—31no—
229C22×C3⋊C8—32no—
230C22×C3⋊C8—61no—
231#919—316no—
232#918—316no—
233#914—316no—
234D3×SD16—316no—
235#908—38no—
236#907—38no—
237C2×D24—32no—
238C2×#204—32no—
239C2×ΓL(1,𝔽25)—32no—
240C2×D3×C8—32no—
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—22no—
243C22×C3⋊D3—24no—
244C22×C3⋊D3—82no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3C2×D412yes—
248C2×D32—28no—
249C2×D32—84no—
250C32×Q8—22no—
251C32×Q8—24no—
252C32×Q8C2414yes—
253C2×C32×C4—22no—
254C2×C32×C4—24no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2×D412yes—
257C2×C32×C4C2411yescharacteristic
258C2×C32×C4C2412yes—
259C4⋊(C3⋊D3)—22no—
260C4⋊(C3⋊D3)—24no—
261C4⋊(C3⋊D3)C2414yes—
262C3×#67—24no—
263C3×#67—24no—
264C3×#67C2×D418yes—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D412yes—
268C3×D12—28no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12C2×D414yes—
272C3×D12C2412yes—
273C3×D12C2412yes—
274C3×C4×D3—28no—
275C3×C4×D3—24no—
276C3×C4×D3—24no—
277C3×C4×D3—28no—
278C3×C4×D3C2×D414yes—
279C3×C4×D3C2414yes—
280C3×Dic6—21no—
281C3×Dic6—21no—
282C3×Dic6—28no—
283C3×Dic6C2×D414yes—
284C3×Dic6C2412yes—
285C3×Dic6C2412yes—
286#626—28no—
287#626—28no—
288#624—28no—
289C3⋊(C3⋊C8)C2412yes—
290C3⋊(C3⋊C8)C2412yes—
291C3×C3⋊C8C2414yes—
292C2×2−1+4—31no—
293C2×H(5,𝔽2)—91no—
294#577—916no—
295C2×#137—31no—
296C2×#137—92no—
297C2×AGL(1,ℤ/8)—91no—
298C2×AGL(1,ℤ/8)—92no—
299C2×#135—92no—
300C2×#135—91no—
301C22×SD16—92no—
302C22×SD16—91no—
303C2×#131—91no—
304C23×D3—62no—
305C23×D3—61no—
306C23×D3—61no—
307C23×D3—62no—
308C23×D3—121no—
309C3×#41—34no—
310C3×#41—34no—
311C3×#41—38no—
312C3×#41—34no—
313C3×#41—34no—
314C3×#41—616no—
315C3×#41—64no—
316C3×#41—68no—
317C3×#41—62no—
318C3×#41—62no—
319C2×C3×Q8—21no—
320C2×C3×Q8—22no—
321C2×C3×Q8—21no—
322C2×C3×Q8—22no—
323C2×C3×Q8—22no—
324C2×C3×Q8—24no—
325C2×C3×Q8—31no—
326C2×C3×Q8—38no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×Q8—41no—
330C2×C3×Q8—42no—
331C2×C3×Q8—62no—
332C2×C3×Q8—64no—
333C2×C3×Q8—68no—
334C2×C3×Q8C22×D312yes—
335C2×C3×Q8C22×D312yes—
336C2×C3×Q8C22×D314yescomplemented
337C2×C3×Q8C22×D314yescomplemented
338C2×C3×D4—32no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—31no—
342C2×C3×D4—62no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—32no—
349C22×C3×C4—41no—
350C22×C3×C4—62no—
351C22×C3×C4—62no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4C22×D311yescharacteristic
355C22×C3×C4C22×D311yescharacteristic
356C2×#67—21no—
357C2×#67—21no—
358C2×#67—62no—
359C2×#67—62no—
360C2×#67#6712yes—
361#239—28no—
362#239—24no—
363#239—38no—
364#239—68no—
365#239—64no—
366#239C22×D318yescomplemented
367D3×Q8—24no—
368D3×Q8—28no—
369D3×Q8C22×D318yescomplemented
370D3×D4—38no—
371D3×D4—68no—
372D3×D4—616no—
373D3×D4—616no—
374D3×D4—64no—
375#235—22no—
376#235—22no—
377#235—216no—
378#235—38no—
379#235—64no—
380#235—68no—
381#235#6714yes—
382#235C22×D314yes—
383#235C22×D314yes—
384#235C22×D314yescomplemented
385C2×D12—22no—
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×D12C22×D311yescharacteristic
406C2×C4×D3—22no—
407C2×C4×D3—21no—
408C2×C4×D3—21no—
409C2×C4×D3—22no—
410C2×C4×D3—62no—
411C2×C4×D3—62no—
412C2×C4×D3C22×D312yes—
413C2×Dic6—22no—
414C2×Dic6#6711yescharacteristic
415C2×Dic6C22×D311yescharacteristic
416C2×Dic6C22×D311yescharacteristic
417C3×Q16—38no—
418C3×SD16—38no—
419C3×M16—34no—
420C2×C3×C8—32no—
421#216—34no—
422#216—34no—
423#216C22×D318yescomplemented
424#215—38no—
425#215—38no—
426#215—38no—
427#215—38no—
428#215—34no—
429#215—34no—
430#215—38no—
431#215—68no—
432#215—68no—
433#215C22×D318yescomplemented
434#214—34no—
435#214—34no—
436#213—34no—
437#213—34no—
438#213—38no—
439#208—38no—
440#208C22×D314yescomplemented
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—34no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—34no—
447C2×C3⋊C8—38no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8—64no—
451C2×C3⋊C8C22×D312yes—
452D24—38no—
453#204—38no—
454ΓL(1,𝔽25)—38no—
455D3×C8—38no—
456C22×C32—22no—
457C22×C32C22×D412yes—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—24no—
460C2×C3⋊D3—44no—
461C2×C3⋊D3—84no—
462C2×C3×D3—24no—
463C2×C3×D3—22no—
464C2×C3×D3—22no—
465C2×C3×D3—42no—
466C2×C3×D3—42no—
467C2×C3×D3C22×D414yes—
468D32—88no—
469C32×C4—24no—
470C32×C4C22×D411yescharacteristic
471C32×C4C22×D412yes—
472C32×C4C2511yescharacteristic
473C3×Dic3—22no—
474C3×Dic3—22no—
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—31no—
484C2×#41—62no—
485C2×#41—61no—
486C2×#41—92no—
487C2×#41—181no—
488C22×Q8—32no—
489C22×Q8—61no—
490C22×Q8D3211yescharacteristic, complemented
491C22×D4—92no—
492C22×D4—91no—
493C22×D4—181no—
494C22×D4—182no—
495#137—38no—
496#137—916no—
497AGL(1,ℤ/8)—98no—
498AGL(1,ℤ/8)—916no—
499#135—916no—
500#135—98no—
501C2×Q16—32no—
502C2×Q16—91no—
503C2×SD16—32no—
504C2×SD16—92no—
505C2×SD16—916no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—92no—
509C2×SD16—92no—
510C2×SD16—98no—
511C2×D8—92no—
512C2×D8—91no—
513#131—98no—
514C2×M16—31no—
515C2×M16—92no—
516C22×C8—92no—
517C22×C8—91no—
518C23×C3—21no—
519C23×C3—32no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3D3×D411yescharacteristic
523C23×C3C2×#6711yescharacteristic
524C22×D3—21no—
525C22×D3—21no—
526C22×D3—68no—
527C22×D3—62no—
528C22×D3—62no—
529C22×D3—64no—
530C22×D3—64no—
531C22×D3—68no—
532C22×D3—122no—
533C22×D3—124no—
534C22×D3—244no—
535C22×D3—244no—
536C22×D3—242no—
537C22×D3—242no—
538C22×D3—244no—
539C22×D3C2×#6712yes—
540C3×Q8—22no—
541C3×Q8—24no—
542C3×Q8—22no—
543C3×Q8—24no—
544C3×Q8—24no—
545C3×Q8—34no—
546C3×Q8—32no—
547C3×Q8—32no—
548C3×Q8—42no—
549C3×Q8—44no—
550C3×Q8—68no—
551C3×Q8—61no—
552C3×Q8—61no—
553C3×Q8C23×D314yes—
554C3×Q8C23×D314yes—
555C3×D4—38no—
556C3×D4—34no—
557C3×D4—32no—
558C3×D4—32no—
559C3×D4—68no—
560C3×D4—64no—
561C3×D4—64no—
562C3×D4—61no—
563C3×D4—61no—
564C2×C3×C4—22no—
565C2×C3×C4—24no—
566C2×C3×C4—22no—
567C2×C3×C4—24no—
568C2×C3×C4—22no—
569C2×C3×C4—21no—
570C2×C3×C4—22no—
571C2×C3×C4—21no—
572C2×C3×C4—32no—
573C2×C3×C4—34no—
574C2×C3×C4—34no—
575C2×C3×C4—44no—
576C2×C3×C4—42no—
577C2×C3×C4—68no—
578C2×C3×C4—68no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—64no—
582C2×C3×C4—64no—
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4D3×D412yes—
585C2×C3×C4C2×#6711yescharacteristic
586C2×C3×C4C2×#6712yes—
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D312yes—
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D312yes—
591#67—24no—
592#67—24no—
593#67—68no—
594#67—68no—
595#67C2×#6718yes—
596C2×Dic3—21no—
597C2×Dic3—21no—
598C2×Dic3C2×#6712yes—
599D12—28no—
600D12—21no—
601D12—21no—
602D12—34no—
603D12—34no—
604D12—64no—
605D12—68no—
606D12—68no—
607D12—62no—
608D12—64no—
609D12—64no—
610D12—62no—
611D12—122no—
612D12—124no—
613D12C2×#6714yes—
614D12C23×D312yes—
615D12C23×D312yes—
616C4×D3—28no—
617C4×D3—24no—
618C4×D3—24no—
619C4×D3—28no—
620C4×D3—68no—
621C4×D3—68no—
622C4×D3C2×#6714yes—
623C4×D3C23×D314yes—
624Dic6—21no—
625Dic6—21no—
626Dic6—28no—
627Dic6C2×#6714yes—
628Dic6C23×D312yes—
629Dic6C23×D312yes—
630C3×C8—34no—
631C3⋊C8—32no—
632C3⋊C8—32no—
633C3⋊C8—32no—
634C3⋊C8—32no—
635C3⋊C8—62no—
636C3⋊C8—62no—
637C3⋊C8C23×D314yes—
638C2×C32—22no—
639C2×C32#57712yescomplemented
640C2×C32C23×D411yescharacteristic
641C3⋊D3—44no—
642C3×D3—24no—
643C3×D3—42no—
644C3×D3—42no—
645C24—182no—
646C24—181no—
647#41—34no—
648#41—34no—
649#41—38no—
650#41—34no—
651#41—34no—
652#41—616no—
653#41—64no—
654#41—68no—
655#41—62no—
656#41—62no—
657#41—98no—
658#41—184no—
659#41—188no—
660C2×Q8—21no—
661C2×Q8—22no—
662C2×Q8—31no—
663C2×Q8—38no—
664C2×Q8—31no—
665C2×Q8—31no—
666C2×Q8—62no—
667C2×Q8—64no—
668C2×Q8—68no—
669C2×Q8C2×D3212yes—
670C2×Q8C2×D3214yescomplemented
671C2×D4—32no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—62no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—98no—
679C2×D4—92no—
680C2×D4—94no—
681C2×D4—184no—
682C2×D4—182no—
683C2×D4—188no—
684C2×D4—182no—
685C2×D4—1816no—
686C2×D4—181no—
687C2×D4—182no—
688C22×C4—21no—
689C22×C4—32no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—61no—
693C22×C4—61no—
694C22×C4—182no—
695C22×C4C2×D3211yescharacteristic
696Q16—38no—
697Q16—94no—
698SD16—38no—
699SD16—98no—
700SD16—94no—
701SD16—94no—
702SD16—98no—
703SD16—98no—
704D8—98no—
705D8—94no—
706M16—34no—
707M16—98no—
708C2×C8—32no—
709C2×C8—98no—
710C2×C8—91no—
711C2×C8—91no—
712C2×C8—94no—
713C22×C3—24no—
714C22×C3—22no—
715C22×C3—22no—
716C22×C3—22no—
717C22×C3—21no—
718C22×C3—34no—
719C22×C3—64no—
720C22×C3—62no—
721C22×C3—62no—
722C22×C3—122no—
723C22×C3—122no—
724C22×C3C2×D3×D412yes—
725C22×C3C2×D3×D411yescharacteristic
726C22×C3C22×#6712yes—
727C22×C3C22×#6711yescharacteristic
728C2×D3—24no—
729C2×D3—22no—
730C2×D3—22no—
731C2×D3—42no—
732C2×D3—42no—
733C2×D3—64no—
734C2×D3—64no—
735C2×D3—124no—
736C2×D3—124no—
737C2×D3—124no—
738C2×D3—244no—
739C2×D3—248no—
740C2×D3—248no—
741C2×D3—244no—
742C2×D3—244no—
743C2×D3—248no—
744C2×D3C22×#6714yes—
745C3×C4—24no—
746C3×C4—24no—
747C3×C4—21no—
748C3×C4—22no—
749C3×C4—21no—
750C3×C4—34no—
751C3×C4—44no—
752C3×C4—62no—
753C3×C4—62no—
754C3×C4C2×D3×D411yescharacteristic
755C3×C4C2×D3×D412yes—
756C3×C4C22×#6711yescharacteristic
757C3×C4C22×#6712yes—
758C3×C4C24×D311yescharacteristic
759C3×C4C24×D311yescharacteristic
760Dic3—22no—
761Dic3—22no—
762Dic3C22×#6714yes—
763C32C2×#57711yescharacteristic, complemented, Sylow
764C23—32no—
765C23—61no—
766C23—61no—
767C23—188no—
768C23—182no—
769C23—184no—
770C23—722no—
771C23—724no—
772C23D3×#6711yescharacteristic
773Q8—22no—
774Q8—24no—
775Q8—34no—
776Q8—32no—
777Q8—32no—
778Q8—68no—
779Q8—61no—
780Q8—61no—
781Q8C22×D3214yes—
782D4—38no—
783D4—34no—
784D4—32no—
785D4—32no—
786D4—68no—
787D4—64no—
788D4—64no—
789D4—61no—
790D4—61no—
791D4—94no—
792D4—188no—
793D4—188no—
794D4—182no—
795D4—184no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—32no—
799C2×C4—34no—
800C2×C4—34no—
801C2×C4—68no—
802C2×C4—68no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—64no—
806C2×C4—64no—
807C2×C4—188no—
808C2×C4D3×#6712yes—
809C2×C4D3×#6711yescharacteristic
810C2×C4C22×D3212yes—
811C2×C4C22×D3211yescharacteristic
812C8—34no—
813C8—92no—
814C8—92no—
815C2×C3—24no—
816C2×C3—22no—
817C2×C3—22no—
818C2×C3—21no—
819C2×C3—22no—
820C2×C3—64no—
821C2×C3—122no—
822C2×C3—122no—
823C2×C3#577812yescomplemented
824C2×C3#583712yescomplemented
825C2×C3C22×D3×D411yescharacteristic
826C2×C3C23×#6711yescharacteristic
827D3—24no—
828D3—42no—
829D3—42no—
830D3—124no—
831D3—124no—
832D3—244no—
833C22—22no—
834C22—34no—
835C22—64no—
836C22—62no—
837C22—62no—
838C22—122no—
839C22—122no—
840C22—184no—
841C22—364no—
842C22—724no—
843C22—728no—
844C22C2×D3×#6712yes—
845C22C2×D3×#6711yescharacteristic
846C4—24no—
847C4—34no—
848C4—62no—
849C4—62no—
850C4C2×D3×#6711yescharacteristic
851C4C2×D3×#6712yes—
852C4C23×D3211yescharacteristic
853C3—21no—
854C3C2×#577811yescharacteristic, complemented
855C3C2×#583711yescharacteristic, complemented
856C2—22no—
857C2—64no—
858C2—122no—
859C2—122no—
860C2—364no—
861C2#1059531912yesdirect product factor
862C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
hypercenterC22×Q8D32
hypocenterC32C2×#577
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×#64308C2semidirect
3. C22×#3755C2semidirect
4. C2×C3×#942C2semidirect
5. C2×#63949C2semidirect
6. C2×#63948C2semidirect
7. #10595319C2direct (N × H)
8. C2×#63939C2semidirect
9. C2×D3×#215C2semidirect
10. C2×#63825C2semidirect
11. C2×#63822C2semidirect
12. C2×#63815C2semidirect
15. C22×C32×Q8C22semidirect
18. C3×#1007C22semidirect
20. C2×C3×#239C22semidirect
22. C2×C3×D3×Q8C22semidirect
26. C2×C3×#235C22semidirect
29. #64308C22semidirect
34. C2×#3755C22semidirect
35. C2×#3755C22semidirect
36. C2×#3755C22semidirect
37. C22×C3⋊(C3⋊C8)C22semidirect
38. C2×C3×#216C22semidirect
39. C3×#942C22semidirect
40. C2×C3×#215C22semidirect
41. C2×C3×#208C22semidirect
42. #63949C22semidirect
43. #63948C22semidirect
44. #63939C22semidirect
45. D3×#215C22semidirect
46. C2×#3718C22semidirect
47. C2×#3717C22semidirect
48. C2×#3715C22semidirect
49. C2×#3715C22semidirect
50. #63825C22semidirect
51. C2×#3714C22semidirect
52. #63822C22semidirect
53. C2×#3713C22semidirect
54. C2×#3711C22semidirect
55. #63815C22semidirect
56. C2×D3×C3⋊C8C22semidirect
60. C2×#1007D3semidirect
70. C2×#942D3semidirect
87. C2×C32×Q8C23semidirect
99. C3×#239C23semidirect
102. C3×D3×Q8C23semidirect
109. C3×#235C23semidirect
133. #3755C23semidirect
134. #3755C23semidirect
137. C2×C3⋊(C3⋊C8)C23semidirect
138. C3×#216C23semidirect
139. C3×#215C23semidirect
140. C3×#208C23semidirect
142. #3718C23semidirect
143. #3717C23semidirect
144. #3715C23semidirect
145. #3715C23semidirect
146. #3714C23semidirect
147. #3713C23semidirect
148. #3711C23semidirect
149. D3×C3⋊C8C23semidirect
162. C22×C3×Q8C2×D3semidirect
163. C22×C3×Q8C2×D3semidirect
169. #1007C2×D3semidirect
173. C2×#239C2×D3semidirect
175. C2×D3×Q8C2×D3semidirect
185. C2×#235C2×D3semidirect
203. C2×#216C2×D3semidirect
205. #942C2×D3semidirect
219. C2×#215C2×D3semidirect
226. C2×#208C2×D3semidirect
336. C2×C3×Q8C22×D3semidirect
337. C2×C3×Q8C22×D3semidirect
366. #239C22×D3semidirect
369. D3×Q8C22×D3semidirect
384. #235C22×D3semidirect
423. #216C22×D3semidirect
433. #215C22×D3semidirect
440. #208C22×D3semidirect
490. C22×Q8D32semidirect
639. C2×C32#577semidirect
670. C2×Q8C2×D32semidirect
763. C32C2×#577semidirect
823. C2×C3#5778semidirect
824. C2×C3#5837semidirect
854. C3C2×#5778semidirect
855. C3C2×#5837semidirect
861. C2#10595319direct (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×#643082
C22×#37552
C2×C3×#9422
C2×#639492
C2×#639482
#105953192
C2×#639392
C2×D3×#2152
C2×#638252
C2×#638222
C2×#638152
C2×#58373
C2×#57783