Finite Group Databasebeta

← C2×#10595324 #11918876

Subgroups — C2×#10595324 #11918876

Order 1152.

3317 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64364C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3C2×C3×#942C211yesmaximal, characteristic, complemented
4C22×C3×#215C211yesmaximal, characteristic, complemented
5C2×#63951C212yesmaximal, complemented
6C2×#63950C212yesmaximal, complemented
7#10595324C2116yesmaximal, direct product factor
8C2×#63941C212yesmaximal, complemented
9C2×#63940C212yesmaximal, complemented
10C2×#63830C211yesmaximal, characteristic, complemented
11C2×#63829C211yesmaximal, characteristic, complemented
12C2×#63817C211yesmaximal, characteristic, complemented
13C2×#5778—31nomaximal
14C2×#5762—31nomaximal
15C22×C32×Q8C2211yescharacteristic, complemented
16#64364—24no—
17#64364C2218yescomplemented
18C2×#3832—21no—
19C2×#3832C2212yescomplemented
20C2×Q8×C3⋊D3—21no—
21C2×Q8×C3⋊D3C2212yescomplemented
22C2×#3828—22no—
23C2×#3828C2211yescharacteristic
24C2×#3828C2211yescharacteristic, complemented
25C2×C3×#235C2211yescharacteristic
26C22×C3×D12C2211yescharacteristic
27C2×D3×#67—22no—
28#64307—24no—
29#64307C2218yescomplemented
30C2×#3802C2212yes—
31C2×D3×D12—21no—
32C2×#3796C2212yes—
33C2×#3795—21no—
34C2×C3×#216C2212yescomplemented
35C3×#942C2218yescomplemented
36C2×C3×#215C2212yescomplemented
37C2×C3×#215C2212yescomplemented
38C2×C3×#215C2212yescomplemented
39C2×C3×#215C2218yescomplemented
40C2×C3×#208C2211yescharacteristic, complemented
41C22×C3×C3⋊C8C2211yescharacteristic, complemented
42#63951C22116yescomplemented
43#63950C22116yescomplemented
44#63941C22116yescomplemented
45#63940C22116yescomplemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48#63830C2218yescomplemented
49#63829C2218yescomplemented
50C2×#3716C2212yescomplemented
51C2×#3716C2211yescharacteristic, complemented
52C2×#3714C2212yescomplemented
53C2×#3714C2211yescharacteristic, complemented
54C2×#3712C2212yescomplemented
55#63817C2218yescomplemented
56C2×#3710C2212yescomplemented
57C2×#1009—31no—
58C2×#1007—31no—
59C2×#1007—31no—
60C2×#1007—61no—
61C2×#1004—31no—
62C2×C3×#137—31no—
63C22×C3×SD16—31no—
64C2×#950—31no—
65C2×#942D311yescharacteristic, complemented
66C22×#215D311yescharacteristic, complemented
67C2×#932—31no—
68#5778—316no—
69C2×#919—32no—
70C2×#918—32no—
71#5762—316no—
72C2×#916—32no—
73C2×#915—32no—
74C2×#914—32no—
75C2×#914—32no—
76C2×D3×SD16—32no—
77C2×D3×SD16—32no—
78C2×#908—31no—
79C2×#907—31no—
80C2×#904—31no—
81C2×#901—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×#638—21no—
91C2×#638D412yes—
92#3832—28no—
93#3832—24no—
94#3832C2318yescomplemented
95Q8×C3⋊D3—24no—
96Q8×C3⋊D3—28no—
97Q8×C3⋊D3C2318yescomplemented
98#3828—22no—
99#3828—216no—
100#3828D414yes—
101#3828C2314yes—
102#3828C2314yescomplemented
103C2×C4⋊(C3⋊D3)—22no—
104C2×C4⋊(C3⋊D3)D411yescharacteristic
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3—22no—
107C2×C4×C3⋊D3—21no—
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3C2312yes—
110C2×#634—22no—
111C2×#634D411yescharacteristic
112C2×#634C2311yescharacteristic
113C2×C3×#67—21no—
114C3×#235—22no—
115C3×#235C2314yes—
116C2×C3×D12—21no—
117C2×C3×D12—22no—
118C2×C3×D12C2312yes—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2314yes—
121C2×C3×C4×D3—21no—
122C2×C3×Dic6C2311yescharacteristic
123D3×#67—216no—
124C2×#626—22no—
125C2×#625—22no—
126C2×D3×Dic3—22no—
127#3802—24no—
128#3802C2318yes—
129D3×D12—28no—
130#3796—24no—
131#3796C2318yes—
132#3795—28no—
133C3×#216C2318yescomplemented
134C3×#215C2318yescomplemented
135C3×#215C2318yescomplemented
136C3×#215C2318yescomplemented
137C3×#208C2314yescomplemented
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2312yes—
141C2×C3×C3⋊C8C2314yescomplemented
142#3719C2314yescomplemented
143#3717C2314yescomplemented
144#3716C2314yescomplemented
145#3716C2318yescomplemented
146#3714C2314yescomplemented
147#3714C2318yescomplemented
148#3712C2318yescomplemented
149#3710C2318yescomplemented
150C2×#577—91noSylow
151C2×C3×#41—31no—
152C22×C3×Q8—21no—
153C22×C3×Q8C2×D311yescharacteristic, complemented
154C22×C3×Q8C2×D311yescharacteristic, complemented
155C22×C3×D4—31no—
156C22×#67—62no—
157#1009—38no—
158#1009—64no—
159#1007—38no—
160#1007—38no—
161#1007—68no—
162#1007—64no—
163#1007—64no—
164#1007—68no—
165C2×#239—32no—
166C2×#239—32no—
167C2×#239—32no—
168C2×#239—62no—
169C2×#239—61no—
170C2×#239—61no—
171C2×#239—62no—
172C2×D3×Q8—32no—
173C2×D3×Q8—32no—
174C2×D3×Q8—62no—
175C2×D3×Q8—61no—
176C2×D3×Q8—61no—
177C2×D3×Q8—62no—
178#1004—38no—
179#1004—64no—
180C2×#237—32no—
181C2×#237—61no—
182C2×D3×D4—32no—
183C2×D3×D4—32no—
184C2×D3×D4—61no—
185C2×D3×D4—62no—
186C2×#235—31no—
187C2×#235—31no—
188C2×#235—31no—
189C2×#235—31no—
190C2×#235—61no—
191C2×#235—61no—
192C2×#235—61no—
193C2×#235—62no—
194C2×#235—62no—
195C2×#235—64no—
196C2×#235C2×D311yescharacteristic
197C22×D12—61no—
198C22×D12C2×D311yescharacteristic
199C3×#137—38no—
200C2×C3×Q16—32no—
201C2×C3×SD16—32no—
202C2×C3×SD16—32no—
203C2×C3×SD16—32no—
204C2×C3×SD16—38no—
205C2×C3×M16—31no—
206C22×C3×C8—31no—
207#950—38no—
208C2×#216—31no—
209C2×#216C2×D312yescomplemented
210#942C2×D318yescomplemented
211C2×#215—31no—
212C2×#215C2×D312yescomplemented
213C2×#215C2×D312yescomplemented
214C2×#215C2×D312yescomplemented
215C2×#215C2×D318yescomplemented
216C2×#214—31no—
217C2×#214—32no—
218#932—38no—
219C2×#213—31no—
220C2×#213—32no—
221C2×#208C2×D311yescharacteristic, complemented
222C22×C3⋊C8C2×D311yescharacteristic, complemented
223#919—316no—
224#918—316no—
225#916—316no—
226#915—316no—
227#914—316no—
228#914—316no—
229D3×SD16—316no—
230D3×SD16—316no—
231#908—38no—
232#907—38no—
233C2×Dic12—31no—
234#904—38no—
235C2×D24—31no—
236C2×D24—32no—
237C2×#204—31no—
238C2×#204—32no—
239C2×#204—31no—
240#901—38no—
241C2×ΓL(1,𝔽25)—32no—
242C2×ΓL(1,𝔽25)—32no—
243C2×D3×C8—32no—
244C2×D3×C8—32no—
245C23×C32C2×D411yescharacteristic
246C22×C3⋊D3—21no—
247C22×C3⋊D3C2×D412yes—
248C22×C3×D3—21no—
249C22×C3×D3—22no—
250C22×C3×D3—24no—
251C22×C3×D3—82no—
252C2×D32—28no—
253C2×D32—84no—
254C32×Q8—22no—
255C32×Q8—24no—
256C32×Q8C2414yes—
257C2×C32×C4—22no—
258C2×C32×C4—24no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2×D412yes—
261C2×C32×C4C2411yescharacteristic
262C2×C32×C4C2412yes—
263#638—24no—
264#638C2×D418yes—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C2×D412yes—
267C4⋊(C3⋊D3)—28no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)C2×D414yes—
270C4⋊(C3⋊D3)C2412yes—
271C4×C3⋊D3—28no—
272C4×C3⋊D3—24no—
273C4×C3⋊D3—28no—
274C4×C3⋊D3C2×D414yes—
275C4×C3⋊D3C2414yes—
276#634—21no—
277#634—28no—
278#634C2×D414yes—
279#634C2412yes—
280C3×#67—24no—
281C2×C3×Dic3—21no—
282C3×D12—24no—
283C3×D12—22no—
284C3×D12—21no—
285C3×D12C2414yes—
286C3×D12C2412yes—
287C3×C4×D3—24no—
288C3×Dic6—21no—
289C3×Dic6C2412yes—
290#626—28no—
291#625—28no—
292D3×Dic3—28no—
293C3×C3⋊C8C2412yes—
294C3×C3⋊C8C2414yes—
295C3×C3⋊C8C2412yes—
296C2×2−1+4—91no—
297C2×H(5,𝔽2)—91no—
298#577—916no—
299C2×#137—31no—
300C2×#137—92no—
301C2×AGL(1,ℤ/8)—91no—
302C2×AGL(1,ℤ/8)—92no—
303C2×#135—91no—
304C2×#135—92no—
305C22×SD16—31no—
306C22×SD16—92no—
307C2×#131—91no—
308C24×C3—61no—
309C23×D3—21no—
310C23×D3—62no—
311C23×D3—62no—
312C3×#41—34no—
313C3×#41—62no—
314C2×C3×Q8—22no—
315C2×C3×Q8—24no—
316C2×C3×Q8—21no—
317C2×C3×Q8—21no—
318C2×C3×Q8—22no—
319C2×C3×Q8—22no—
320C2×C3×Q8—22no—
321C2×C3×Q8—24no—
322C2×C3×Q8—31no—
323C2×C3×Q8C22×D312yes—
324C2×C3×Q8C22×D312yes—
325C2×C3×Q8C22×D314yescomplemented
326C2×C3×Q8C22×D314yescomplemented
327C2×C3×D4—31no—
328C2×C3×D4—32no—
329C2×C3×D4—34no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4—62no—
333C22×C3×C4—22no—
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—61no—
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C2×#67—21no—
341C2×#67—32no—
342C2×#67—32no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—62no—
346C2×#67—62no—
347C2×#67—616no—
348C2×#67—62no—
349C2×#67—61no—
350C2×#67—61no—
351C22×Dic3—62no—
352#239—38no—
353#239—38no—
354#239—38no—
355#239—68no—
356#239—64no—
357#239—64no—
358#239—64no—
359#239—68no—
360#239—68no—
361#239—68no—
362#239—616no—
363D3×Q8—38no—
364D3×Q8—38no—
365D3×Q8—68no—
366D3×Q8—68no—
367D3×Q8—68no—
368D3×Q8—64no—
369D3×Q8—64no—
370D3×Q8—68no—
371D3×Q8—616no—
372#237—38no—
373#237—64no—
374#237—68no—
375D3×D4—38no—
376D3×D4—38no—
377D3×D4—68no—
378D3×D4—64no—
379D3×D4—64no—
380D3×D4—616no—
381#235—22no—
382#235—34no—
383#235—34no—
384#235—34no—
385#235—34no—
386#235—34no—
387#235—34no—
388#235—64no—
389#235—64no—
390#235—64no—
391#235—68no—
392#235—616no—
393#235—616no—
394#235—632no—
395#235—64no—
396#235—62no—
397#235—62no—
398#235C22×D314yes—
399C2×D12—21no—
400C2×D12—22no—
401C2×D12—31no—
402C2×D12—31no—
403C2×D12—31no—
404C2×D12—31no—
405C2×D12—61no—
406C2×D12—61no—
407C2×D12—68no—
408C2×D12—62no—
409C2×D12—62no—
410C2×D12—64no—
411C2×D12—62no—
412C2×D12C22×D312yes—
413C2×D12C22×D311yescharacteristic
414C2×D12C22×D314yes—
415C2×C4×D3—21no—
416C2×C4×D3—32no—
417C2×C4×D3—32no—
418C2×C4×D3—62no—
419C2×C4×D3—62no—
420C2×C4×D3—62no—
421C2×C4×D3—62no—
422C2×C4×D3—62no—
423C2×C4×D3—62no—
424C2×C4×D3—64no—
425C2×C4×D3—64no—
426C2×C4×D3—62no—
427C2×C4×D3—61no—
428C2×C4×D3—61no—
429C2×Dic6—31no—
430C2×Dic6—31no—
431C2×Dic6—31no—
432C2×Dic6—31no—
433C2×Dic6—61no—
434C2×Dic6—61no—
435C2×Dic6—62no—
436C2×Dic6—62no—
437C2×Dic6—64no—
438C2×Dic6C22×D311yescharacteristic
439C3×Q16—38no—
440C3×SD16—38no—
441C3×SD16—38no—
442C3×SD16—38no—
443C3×M16—34no—
444C2×C3×C8—31no—
445C2×C3×C8—32no—
446C2×C3×C8—31no—
447C2×C3×C8—34no—
448#216—34no—
449#216C22×D318yescomplemented
450#215—34no—
451#215C22×D318yescomplemented
452#215C22×D318yescomplemented
453#215C22×D318yescomplemented
454#214—34no—
455#214—38no—
456#213—34no—
457#213—38no—
458#208C22×D314yescomplemented
459C2×C3⋊C8C22×D311yescharacteristic
460C2×C3⋊C8C22×D312yes—
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D314yescomplemented
463Dic12—34no—
464D24—34no—
465D24—38no—
466#204—34no—
467#204—38no—
468#204—34no—
469ΓL(1,𝔽25)—38no—
470ΓL(1,𝔽25)—38no—
471D3×C8—38no—
472D3×C8—38no—
473C22×C32—22no—
474C22×C32C22×D412yes—
475C22×C32C22×D411yescharacteristic
476C2×C3⋊D3—22no—
477C2×C3⋊D3—24no—
478C2×C3⋊D3—42no—
479C2×C3⋊D3C22×D414yes—
480C2×C3×D3—24no—
481C2×C3×D3—22no—
482C2×C3×D3—42no—
483C2×C3×D3—44no—
484C2×C3×D3—84no—
485D32—88no—
486C32×C4—24no—
487C32×C4C22×D411yescharacteristic
488C32×C4C22×D412yes—
489C32×C4C2511yescharacteristic
490C3⋊Dic3—22no—
491C3⋊Dic3C22×D414yes—
492C3×Dic3—22no—
4932−1+4—98no—
4942−1+4—184no—
495H(5,𝔽2)—98no—
496H(5,𝔽2)—184no—
497C2×#41—31no—
498C2×#41—91no—
499C2×#41—92no—
500C2×#41—92no—
501C2×#41—91no—
502C2×#41—182no—
503C2×#41—181no—
504C2×#41—181no—
505C22×Q8—92no—
506C22×Q8—181no—
507C22×Q8D3211yescharacteristic, complemented
508C22×D4—31no—
509C22×D4—92no—
510C22×D4—181no—
511C22×D4—182no—
512#137—38no—
513#137—916no—
514AGL(1,ℤ/8)—98no—
515AGL(1,ℤ/8)—916no—
516#135—98no—
517#135—916no—
518C2×Q16—32no—
519C2×Q16—91no—
520C2×SD16—32no—
521C2×SD16—32no—
522C2×SD16—32no—
523C2×SD16—38no—
524C2×SD16—91no—
525C2×SD16—92no—
526C2×SD16—91no—
527C2×SD16—916no—
528C2×D8—91no—
529C2×D8—92no—
530#131—98no—
531C2×M16—31no—
532C2×M16—92no—
533C22×C8—31no—
534C22×C8—92no—
535C23×C3—21no—
536C23×C3—62no—
537C23×C3—61no—
538C23×C3—64no—
539C23×C3—242no—
540C23×C3D3×D411yescharacteristic
541C23×C3D3×D411yescharacteristic
542C22×D3—21no—
543C22×D3—22no—
544C22×D3—24no—
545C22×D3—32no—
546C22×D3—32no—
547C22×D3—62no—
548C22×D3—68no—
549C22×D3—68no—
550C22×D3—62no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—82no—
554C22×D3—244no—
555C22×D3—244no—
556C3×Q8—24no—
557C3×Q8—28no—
558C3×Q8—22no—
559C3×Q8—22no—
560C3×Q8—24no—
561C3×Q8—24no—
562C3×Q8—24no—
563C3×Q8—32no—
564C3×Q8—61no—
565C3×Q8C23×D314yes—
566C3×Q8C23×D314yes—
567C3×D4—32no—
568C3×D4—34no—
569C3×D4—64no—
570C3×D4—61no—
571C3×D4—62no—
572C3×D4—64no—
573C2×C3×C4—24no—
574C2×C3×C4—28no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—24no—
578C2×C3×C4—24no—
579C2×C3×C4—21no—
580C2×C3×C4—22no—
581C2×C3×C4—21no—
582C2×C3×C4—22no—
583C2×C3×C4—61no—
584C2×C3×C4—64no—
585C2×C3×C4D3×D411yescharacteristic
586C2×C3×C4D3×D411yescharacteristic
587C2×C3×C4D3×D412yes—
588C2×C3×C4D3×D412yes—
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D312yes—
592C2×C3×C4C23×D312yes—
593#67—24no—
594#67—38no—
595#67—38no—
596#67—68no—
597#67—68no—
598#67—68no—
599#67—68no—
600#67—68no—
601#67—64no—
602#67—64no—
603C2×Dic3—21no—
604C2×Dic3—32no—
605C2×Dic3—32no—
606C2×Dic3—62no—
607C2×Dic3—68no—
608C2×Dic3—62no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611D12—24no—
612D12—22no—
613D12—21no—
614D12—34no—
615D12—34no—
616D12—32no—
617D12—32no—
618D12—64no—
619D12—62no—
620D12—68no—
621D12—68no—
622D12—616no—
623D12—62no—
624D12—68no—
625D12—61no—
626D12—61no—
627D12C23×D314yes—
628D12C23×D312yes—
629C4×D3—24no—
630C4×D3—34no—
631C4×D3—34no—
632C4×D3—34no—
633C4×D3—34no—
634C4×D3—64no—
635C4×D3—64no—
636C4×D3—68no—
637C4×D3—68no—
638C4×D3—68no—
639C4×D3—68no—
640C4×D3—68no—
641C4×D3—616no—
642C4×D3—616no—
643C4×D3—68no—
644C4×D3—64no—
645C4×D3—64no—
646Dic6—21no—
647Dic6—34no—
648Dic6—34no—
649Dic6—32no—
650Dic6—32no—
651Dic6—64no—
652Dic6—62no—
653Dic6—68no—
654Dic6—68no—
655Dic6—616no—
656Dic6—62no—
657Dic6—61no—
658Dic6—61no—
659Dic6C23×D312yes—
660C3×C8—32no—
661C3×C8—34no—
662C3×C8—32no—
663C3⋊C8C23×D312yes—
664C3⋊C8C23×D314yes—
665C3⋊C8C23×D312yes—
666C2×C32—22no—
667C2×C32#57712yescomplemented
668C2×C32C23×D411yescharacteristic
669C3⋊D3—24no—
670C3⋊D3—42no—
671C3×D3—42no—
672C3×D3—44no—
673C24—61no—
674C24—182no—
675#41—34no—
676#41—62no—
677#41—94no—
678#41—94no—
679#41—98no—
680#41—98no—
681#41—94no—
682#41—1816no—
683#41—188no—
684#41—184no—
685#41—184no—
686#41—188no—
687#41—182no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—31no—
691C2×Q8—91no—
692C2×Q8—98no—
693C2×Q8—91no—
694C2×Q8—182no—
695C2×Q8—184no—
696C2×Q8—188no—
697C2×Q8C2×D3212yes—
698C2×Q8C2×D3214yescomplemented
699C2×D4—32no—
700C2×D4—31no—
701C2×D4—34no—
702C2×D4—61no—
703C2×D4—61no—
704C2×D4—62no—
705C2×D4—98no—
706C2×D4—92no—
707C2×D4—91no—
708C2×D4—91no—
709C2×D4—182no—
710C2×D4—188no—
711C2×D4—182no—
712C2×D4—184no—
713C2×D4—182no—
714C2×D4—1816no—
715C2×D4—181no—
716C22×C4—21no—
717C22×C4—61no—
718C22×C4—92no—
719C22×C4—182no—
720C22×C4—182no—
721C22×C4—182no—
722C22×C4—181no—
723C22×C4C2×D3211yescharacteristic
724Q16—38no—
725Q16—94no—
726SD16—38no—
727SD16—38no—
728SD16—38no—
729SD16—94no—
730SD16—98no—
731SD16—94no—
732D8—94no—
733D8—98no—
734M16—34no—
735M16—98no—
736C2×C8—31no—
737C2×C8—31no—
738C2×C8—34no—
739C2×C8—32no—
740C2×C8—98no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—22no—
744C22×C3—21no—
745C22×C3—42no—
746C22×C3—64no—
747C22×C3—62no—
748C22×C3—122no—
749C22×C3—124no—
750C22×C3—244no—
751C22×C3C2×D3×D412yes—
752C22×C3C2×D3×D412yes—
753C22×C3C2×D3×D411yescharacteristic
754C22×C3C2×D3×D411yescharacteristic
755C2×D3—22no—
756C2×D3—24no—
757C2×D3—34no—
758C2×D3—34no—
759C2×D3—44no—
760C2×D3—42no—
761C2×D3—64no—
762C2×D3—64no—
763C2×D3—64no—
764C2×D3—64no—
765C2×D3—62no—
766C2×D3—62no—
767C2×D3—84no—
768C2×D3—124no—
769C2×D3—124no—
770C2×D3—122no—
771C2×D3—122no—
772C2×D3—248no—
773C2×D3—248no—
774C3×C4—28no—
775C3×C4—24no—
776C3×C4—24no—
777C3×C4—22no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—62no—
781C3×C4C2×D3×D411yescharacteristic
782C3×C4C2×D3×D412yes—
783C3×C4C2×D3×D412yes—
784C3×C4C2×D3×D411yescharacteristic
785C3×C4C24×D311yescharacteristic
786C3×C4C24×D311yescharacteristic
787Dic3—22no—
788Dic3—34no—
789Dic3—34no—
790Dic3—64no—
791Dic3—64no—
792Dic3—62no—
793Dic3—62no—
794C32C2×#57711yescharacteristic, complemented, Sylow
795C23—61no—
796C23—62no—
797C23—64no—
798C23—92no—
799C23—188no—
800C23—181no—
801C23—242no—
802C23—724no—
803C23#381111yescharacteristic
804Q8—22no—
805Q8—24no—
806Q8—32no—
807Q8—61no—
808Q8—94no—
809Q8—92no—
810Q8—188no—
811Q8—181no—
812Q8C22×D3214yes—
813D4—34no—
814D4—32no—
815D4—64no—
816D4—64no—
817D4—62no—
818D4—61no—
819D4—98no—
820D4—94no—
821D4—92no—
822D4—188no—
823D4—188no—
824D4—188no—
825D4—184no—
826D4—181no—
827C2×C4—24no—
828C2×C4—22no—
829C2×C4—61no—
830C2×C4—64no—
831C2×C4—92no—
832C2×C4—94no—
833C2×C4—94no—
834C2×C4—188no—
835C2×C4—188no—
836C2×C4—188no—
837C2×C4—181no—
838C2×C4—184no—
839C2×C4#381112yes—
840C2×C4#381111yescharacteristic
841C2×C4C22×D3212yes—
842C2×C4C22×D3211yescharacteristic
843C8—32no—
844C8—32no—
845C8—34no—
846C2×C3—22no—
847C2×C3—22no—
848C2×C3—21no—
849C2×C3—22no—
850C2×C3—42no—
851C2×C3—122no—
852C2×C3—124no—
853C2×C3#576212yescomplemented
854C2×C3#577812yescomplemented
855C2×C3C22×D3×D411yescharacteristic
856C2×C3C22×D3×D411yescharacteristic
857D3—44no—
858D3—42no—
859D3—64no—
860D3—64no—
861D3—124no—
862D3—124no—
863D3—122no—
864D3—122no—
865C22—22no—
866C22—62no—
867C22—64no—
868C22—94no—
869C22—124no—
870C22—122no—
871C22—184no—
872C22—182no—
873C22—244no—
874C22—362no—
875C22—728no—
876C22C2×#381112yes—
877C22C2×#381111yescharacteristic
878C4—24no—
879C4—62no—
880C4—94no—
881C4—182no—
882C4C2×#381112yes—
883C4C2×#381111yescharacteristic
884C4C23×D3211yescharacteristic
885C3—21no—
886C3C2×#576211yescharacteristic, complemented
887C3C2×#577811yescharacteristic, complemented
888C2—22no—
889C2—124no—
890C2—122no—
891C2—184no—
892C2—362no—
893C2#1059532412yesdirect product factor
894C2C22×#381111yescharacteristic
subgroupG/H
centerC22C2×#3811
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×#64364C2semidirect
2. C2×#64307C2semidirect
3. C2×C3×#942C2semidirect
4. C22×C3×#215C2semidirect
5. C2×#63951C2semidirect
6. C2×#63950C2semidirect
7. #10595324C2direct (N × H)
8. C2×#63941C2semidirect
9. C2×#63940C2semidirect
10. C2×#63830C2semidirect
11. C2×#63829C2semidirect
12. C2×#63817C2semidirect
15. C22×C32×Q8C22semidirect
17. #64364C22semidirect
19. C2×#3832C22semidirect
21. C2×Q8×C3⋊D3C22semidirect
24. C2×#3828C22semidirect
29. #64307C22semidirect
34. C2×C3×#216C22semidirect
35. C3×#942C22semidirect
36. C2×C3×#215C22semidirect
37. C2×C3×#215C22semidirect
38. C2×C3×#215C22semidirect
39. C2×C3×#215C22semidirect
40. C2×C3×#208C22semidirect
41. C22×C3×C3⋊C8C22semidirect
42. #63951C22semidirect
43. #63950C22semidirect
44. #63941C22semidirect
45. #63940C22semidirect
46. C2×#3719C22semidirect
47. C2×#3717C22semidirect
48. #63830C22semidirect
49. #63829C22semidirect
50. C2×#3716C22semidirect
51. C2×#3716C22semidirect
52. C2×#3714C22semidirect
53. C2×#3714C22semidirect
54. C2×#3712C22semidirect
55. #63817C22semidirect
56. C2×#3710C22semidirect
65. C2×#942D3semidirect
66. C22×#215D3semidirect
87. C2×C32×Q8C23semidirect
94. #3832C23semidirect
97. Q8×C3⋊D3C23semidirect
102. #3828C23semidirect
133. C3×#216C23semidirect
134. C3×#215C23semidirect
135. C3×#215C23semidirect
136. C3×#215C23semidirect
137. C3×#208C23semidirect
141. C2×C3×C3⋊C8C23semidirect
142. #3719C23semidirect
143. #3717C23semidirect
144. #3716C23semidirect
145. #3716C23semidirect
146. #3714C23semidirect
147. #3714C23semidirect
148. #3712C23semidirect
149. #3710C23semidirect
153. C22×C3×Q8C2×D3semidirect
154. C22×C3×Q8C2×D3semidirect
209. C2×#216C2×D3semidirect
210. #942C2×D3semidirect
212. C2×#215C2×D3semidirect
213. C2×#215C2×D3semidirect
214. C2×#215C2×D3semidirect
215. C2×#215C2×D3semidirect
221. C2×#208C2×D3semidirect
222. C22×C3⋊C8C2×D3semidirect
325. C2×C3×Q8C22×D3semidirect
326. C2×C3×Q8C22×D3semidirect
449. #216C22×D3semidirect
451. #215C22×D3semidirect
452. #215C22×D3semidirect
453. #215C22×D3semidirect
458. #208C22×D3semidirect
462. C2×C3⋊C8C22×D3semidirect
507. C22×Q8D32semidirect
667. C2×C32#577semidirect
698. C2×Q8C2×D32semidirect
794. C32C2×#577semidirect
853. C2×C3#5762semidirect
854. C2×C3#5778semidirect
886. C3C2×#5762semidirect
887. C3C2×#5778semidirect
893. C2#10595324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643642
C2×#643072
C2×C3×#9422
C22×C3×#2152
C2×#639512
C2×#639502
#105953242
C2×#639412
C2×#639402
C2×#638302
C2×#638292
C2×#638172
C2×#57783
C2×#57623