Finite Group Databasebeta

← C2×#10595115 #11918879

Subgroups — C2×#10595115 #11918879

Order 1152.

3369 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3C22×C3×#214C211yesmaximal, characteristic, complemented
4C2×C3×#932C211yesmaximal, characteristic, complemented
5#10595115C2116yesmaximal, direct product factor
6C2×#63937C212yesmaximal, complemented
7C2×#63936C212yesmaximal, complemented
8C2×#63931C212yesmaximal, complemented
9C2×#63930C212yesmaximal, complemented
10C2×#63833C211yesmaximal, characteristic, complemented
11C2×#63829C211yesmaximal, characteristic, complemented
12C2×#63817C211yesmaximal, characteristic, complemented
13C2×#5775—31nomaximal
14C2×#5762—31nomaximal
15C22×C32×D4C2211yescharacteristic
16C22×#638—22no—
17#64361—24no—
18#64361C2218yescomplemented
19C2×#3830—21no—
20C2×#3830C2212yes—
21C2×D4×C3⋊D3—21no—
22C2×D4×C3⋊D3C2212yes—
23C2×#3828C2211yescharacteristic
24C2×#3828C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic, complemented
26C22×C3×Dic6C2211yescharacteristic, complemented
27C2×#3804—22no—
28C2×#3799—21no—
29C2×#3797C2212yescomplemented
30#64297—24no—
31#64297C2218yescomplemented
32C2×#3796C2212yescomplemented
33C2×D3×Dic6—21no—
34C2×C3×#214C2212yescomplemented
35C2×C3×#214C2212yescomplemented
36C2×C3×#214C2212yescomplemented
37C2×C3×#214C2218yescomplemented
38C3×#932C2218yescomplemented
39C2×C3×#213C2212yescomplemented
40C2×C3×#208C2211yescharacteristic, complemented
41C22×C3×C3⋊C8C2211yescharacteristic, complemented
42#63937C22116yescomplemented
43#63936C22116yescomplemented
44#63931C22116yescomplemented
45#63930C22116yescomplemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3719C2212yescomplemented
48#63833C2218yescomplemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3717C2212yescomplemented
51#63829C2218yescomplemented
52C2×#3716C2211yescharacteristic, complemented
53C2×#3714C2211yescharacteristic, complemented
54C2×#3712C2212yescomplemented
55#63817C2218yescomplemented
56C2×#3710C2212yescomplemented
57C2×#1010—31no—
58C2×#1007—31no—
59C2×#1004—31no—
60C2×#1004—31no—
61C2×#1004—61no—
62C2×C3×AGL(1,ℤ/8)—31no—
63C22×C3×SD16—31no—
64C2×#950—31no—
65C2×#942—31no—
66C22×#214D311yescharacteristic, complemented
67C2×#932D311yescharacteristic, complemented
68#5775—316no—
69#5762—316no—
70C2×#916—32no—
71C2×#915—32no—
72C2×#915—32no—
73C2×#914—32no—
74C2×D3×SD16—32no—
75C2×D3×SD16—32no—
76C2×#912—32no—
77C2×#911—32no—
78C2×#909—31no—
79C2×#907—31no—
80C2×#904—31no—
81C2×#901—31no—
82C24×C32—21no—
83C23×C3⋊D3—22no—
84C2×C32×D4—21no—
85C2×C32×D4—22no—
86C2×C32×D4C2312yes—
87C2×C32×D4C2314yes—
88C22×C32×C4C2311yescharacteristic
89C2×#638—21no—
90C2×#638—22no—
91C2×#638—216no—
92C2×#638—22no—
93C2×#638D412yes—
94C22×C3⋊Dic3—22no—
95#3830—24no—
96#3830—28no—
97#3830C2318yes—
98D4×C3⋊D3—28no—
99D4×C3⋊D3—24no—
100D4×C3⋊D3C2318yes—
101#3828—22no—
102#3828D414yes—
103#3828C2314yes—
104#3828C2314yes—
105C2×C4⋊(C3⋊D3)D411yescharacteristic
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4×C3⋊D3—21no—
108C2×C4×C3⋊D3C2312yes—
109C2×#634D411yescharacteristic
110C2×#634C2311yescharacteristic
111C2×C3×#67—21no—
112C22×C3×Dic3—21no—
113C3×#235—22no—
114C3×#235C2314yescomplemented
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×Dic6—21no—
118C2×C3×Dic6—22no—
119C2×C3×Dic6C2312yes—
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2314yescomplemented
122C2×#627—22no—
123C2×#626—22no—
124C2×#624—22no—
125#3804—216no—
126C2×D3×Dic3—22no—
127#3799—28no—
128#3797—24no—
129#3797C2318yescomplemented
130#3796—24no—
131#3796C2318yescomplemented
132D3×Dic6—28no—
133C3×#214C2318yescomplemented
134C3×#214C2318yescomplemented
135C3×#214C2318yescomplemented
136C3×#213C2318yescomplemented
137C3×#208C2314yescomplemented
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2312yes—
141C2×C3×C3⋊C8C2314yescomplemented
142#3719C2314yescomplemented
143#3719C2318yescomplemented
144#3717C2314yescomplemented
145#3717C2318yescomplemented
146#3716C2314yescomplemented
147#3714C2314yescomplemented
148#3712C2318yescomplemented
149#3710C2318yescomplemented
150C2×#577—91noSylow
151C2×C3×#41—31no—
152C22×C3×Q8—31no—
153C22×C3×D4—21no—
154C22×C3×D4C2×D311yescharacteristic
155C22×C3×D4C2×D311yescharacteristic
156C22×#67—62no—
157C22×#67—62no—
158C22×#67—64no—
159#1010—38no—
160#1010—64no—
161#1007—38no—
162#1007—64no—
163C2×#239—32no—
164C2×#239—61no—
165C2×D3×Q8—32no—
166C2×D3×Q8—32no—
167C2×D3×Q8—61no—
168#1004—38no—
169#1004—38no—
170#1004—68no—
171#1004—64no—
172#1004—64no—
173#1004—68no—
174C2×#237—32no—
175C2×#237—32no—
176C2×#237—32no—
177C2×#237—62no—
178C2×#237—61no—
179C2×#237—61no—
180C2×#237—62no—
181C2×#237—62no—
182C2×D3×D4—32no—
183C2×D3×D4—32no—
184C2×D3×D4—62no—
185C2×D3×D4—61no—
186C2×D3×D4—61no—
187C2×D3×D4—62no—
188C2×#235—31no—
189C2×#235—31no—
190C2×#235—31no—
191C2×#235—31no—
192C2×#235—61no—
193C2×#235—61no—
194C2×#235—61no—
195C2×#235—62no—
196C2×#235C2×D311yescharacteristic, complemented
197C22×Dic6—61no—
198C22×Dic6C2×D311yescharacteristic, complemented
199C3×AGL(1,ℤ/8)—38no—
200C2×C3×SD16—32no—
201C2×C3×SD16—32no—
202C2×C3×SD16—38no—
203C2×C3×SD16—32no—
204C2×C3×D8—32no—
205C2×C3×M16—31no—
206C22×C3×C8—31no—
207#950—38no—
208C2×#216—31no—
209C2×#216—32no—
210#942—38no—
211C2×#215—31no—
212C2×#215—32no—
213C2×#214—31no—
214C2×#214C2×D312yescomplemented
215C2×#214C2×D312yescomplemented
216C2×#214C2×D312yescomplemented
217C2×#214C2×D318yescomplemented
218#932C2×D318yescomplemented
219C2×#213—31no—
220C2×#213C2×D312yescomplemented
221C2×#208C2×D311yescharacteristic, complemented
222C22×C3⋊C8C2×D311yescharacteristic, complemented
223#916—316no—
224#915—316no—
225#915—316no—
226#914—316no—
227D3×SD16—316no—
228D3×SD16—316no—
229#912—316no—
230#911—316no—
231#909—38no—
232#907—38no—
233C2×Dic12—31no—
234C2×Dic12—32no—
235#904—38no—
236C2×D24—31no—
237C2×#204—31no—
238C2×#204—31no—
239C2×#204—32no—
240#901—38no—
241C2×ΓL(1,𝔽25)—32no—
242C2×ΓL(1,𝔽25)—32no—
243C2×D3×C8—32no—
244C2×D3×C8—32no—
245C23×C32—22no—
246C23×C32—24no—
247C23×C32—82no—
248C23×C32C2×D411yescharacteristic
249C22×C3⋊D3—21no—
250C22×C3⋊D3—28no—
251C22×C3⋊D3—84no—
252C22×C3⋊D3C2×D412yes—
253C22×C3×D3—21no—
254C32×D4—22no—
255C32×D4—24no—
256C32×D4C2414yes—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2×D412yes—
259C2×C32×C4C2411yescharacteristic
260C2×C32×C4C2412yes—
261#638—24no—
262#638—28no—
263#638—28no—
264#638C2×D418yes—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—28no—
267C2×C3⋊Dic3C2×D412yes—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)C2×D414yes—
270C4⋊(C3⋊D3)C2412yes—
271C4×C3⋊D3—24no—
272C4×C3⋊D3C2×D414yes—
273C4×C3⋊D3C2414yes—
274#634—21no—
275#634C2×D414yes—
276#634C2412yes—
277C3×#67—24no—
278C2×C3×Dic3—22no—
279C2×C3×Dic3—24no—
280C2×C3×Dic3—21no—
281C3×D12—21no—
282C3×D12C2412yes—
283C3×C4×D3—24no—
284C3×Dic6—24no—
285C3×Dic6—22no—
286C3×Dic6—21no—
287C3×Dic6C2414yes—
288C3×Dic6C2412yes—
289#627—28no—
290#626—28no—
291#624—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—91no—
300C2×#137—92no—
301C2×AGL(1,ℤ/8)—31no—
302C2×AGL(1,ℤ/8)—92no—
303C2×#135—91no—
304C2×#135—92no—
305C22×SD16—31no—
306C22×SD16—92no—
307C2×#131—91no—
308C24×C3—22no—
309C24×C3—21no—
310C24×C3—21no—
311C23×D3—62no—
312C23×D3—62no—
313C23×D3—64no—
314C3×#41—34no—
315C3×#41—62no—
316C2×C3×Q8—31no—
317C2×C3×Q8—32no—
318C2×C3×Q8—34no—
319C2×C3×Q8—61no—
320C2×C3×Q8—62no—
321C2×C3×D4—22no—
322C2×C3×D4—24no—
323C2×C3×D4—21no—
324C2×C3×D4—21no—
325C2×C3×D4—22no—
326C2×C3×D4—22no—
327C2×C3×D4—22no—
328C2×C3×D4—24no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C2×C3×D4C22×D312yes—
332C2×C3×D4C22×D314yes—
333C2×C3×D4C22×D312yes—
334C2×C3×D4C22×D314yes—
335C22×C3×C4—21no—
336C22×C3×C4—61no—
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—616no—
349C2×#67—62no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67—64no—
353C2×#67—64no—
354C2×#67—632no—
355C2×#67—61no—
356C2×#67—61no—
357C22×Dic3—21no—
358C22×Dic3—62no—
359C22×Dic3—62no—
360C22×Dic3—62no—
361C22×Dic3—64no—
362#239—38no—
363#239—68no—
364#239—64no—
365D3×Q8—38no—
366D3×Q8—38no—
367D3×Q8—64no—
368D3×Q8—64no—
369D3×Q8—68no—
370#237—38no—
371#237—38no—
372#237—38no—
373#237—68no—
374#237—64no—
375#237—68no—
376#237—68no—
377#237—64no—
378#237—64no—
379#237—616no—
380#237—68no—
381#237—616no—
382D3×D4—38no—
383D3×D4—38no—
384D3×D4—68no—
385D3×D4—64no—
386D3×D4—64no—
387D3×D4—68no—
388D3×D4—68no—
389D3×D4—68no—
390D3×D4—616no—
391#235—22no—
392#235—34no—
393#235—34no—
394#235—34no—
395#235—34no—
396#235—34no—
397#235—34no—
398#235—64no—
399#235—64no—
400#235—64no—
401#235—68no—
402#235—616no—
403#235—64no—
404#235—62no—
405#235—62no—
406#235C22×D314yescomplemented
407C2×D12—31no—
408C2×D12—31no—
409C2×D12—31no—
410C2×D12—31no—
411C2×D12—61no—
412C2×D12—61no—
413C2×D12—62no—
414C2×D12C22×D311yescharacteristic
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—61no—
424C2×C4×D3—61no—
425C2×Dic6—21no—
426C2×Dic6—22no—
427C2×Dic6—31no—
428C2×Dic6—31no—
429C2×Dic6—31no—
430C2×Dic6—31no—
431C2×Dic6—61no—
432C2×Dic6—61no—
433C2×Dic6—68no—
434C2×Dic6—62no—
435C2×Dic6—62no—
436C2×Dic6C22×D312yes—
437C2×Dic6C22×D311yescharacteristic
438C2×Dic6C22×D314yescomplemented
439C3×SD16—38no—
440C3×SD16—38no—
441C3×SD16—38no—
442C3×D8—38no—
443C3×M16—34no—
444C2×C3×C8—31no—
445C2×C3×C8—32no—
446C2×C3×C8—31no—
447C2×C3×C8—34no—
448#216—34no—
449#216—38no—
450#215—34no—
451#215—38no—
452#214—34no—
453#214C22×D318yescomplemented
454#214C22×D318yescomplemented
455#214C22×D318yescomplemented
456#213—34no—
457#213C22×D318yescomplemented
458#208C22×D314yescomplemented
459C2×C3⋊C8C22×D311yescharacteristic
460C2×C3⋊C8C22×D312yes—
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D314yescomplemented
463Dic12—34no—
464Dic12—38no—
465D24—34no—
466#204—34no—
467#204—34no—
468#204—38no—
469ΓL(1,𝔽25)—38no—
470ΓL(1,𝔽25)—38no—
471D3×C8—38no—
472D3×C8—38no—
473C22×C32—24no—
474C22×C32—22no—
475C22×C32—44no—
476C22×C32—84no—
477C22×C32C22×D412yes—
478C22×C32C22×D411yescharacteristic
479C2×C3⋊D3—22no—
480C2×C3⋊D3—24no—
481C2×C3⋊D3—42no—
482C2×C3⋊D3—88no—
483C2×C3⋊D3C22×D414yes—
484C2×C3×D3—22no—
485C2×C3×D3—42no—
486C32×C4C22×D411yescharacteristic
487C32×C4C22×D412yes—
488C32×C4C2511yescharacteristic
489C3⋊Dic3—22no—
490C3⋊Dic3C22×D414yes—
491C3×Dic3—24no—
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—31no—
506C22×Q8—92no—
507C22×Q8—181no—
508C22×D4—92no—
509C22×D4—181no—
510C22×D4—182no—
511C22×D4D3211yescharacteristic
512#137—98no—
513#137—916no—
514AGL(1,ℤ/8)—38no—
515AGL(1,ℤ/8)—916no—
516#135—98no—
517#135—916no—
518C2×Q16—91no—
519C2×Q16—92no—
520C2×SD16—32no—
521C2×SD16—32no—
522C2×SD16—38no—
523C2×SD16—32no—
524C2×SD16—91no—
525C2×SD16—91no—
526C2×SD16—92no—
527C2×SD16—916no—
528C2×D8—32no—
529C2×D8—91no—
530#131—98no—
531C2×M16—31no—
532C2×M16—92no—
533C22×C8—31no—
534C22×C8—92no—
535C23×C3—24no—
536C23×C3—28no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—24no—
540C23×C3—24no—
541C23×C3—21no—
542C23×C3—61no—
543C23×C3—82no—
544C23×C3—82no—
545C23×C3—84no—
546C23×C3D3×D411yescharacteristic
547C23×C3D3×D411yescharacteristic
548C22×D3—21no—
549C22×D3—32no—
550C22×D3—32no—
551C22×D3—62no—
552C22×D3—68no—
553C22×D3—68no—
554C22×D3—62no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—616no—
558C22×D3—244no—
559C22×D3—244no—
560C22×D3—248no—
561C3×Q8—32no—
562C3×Q8—34no—
563C3×Q8—61no—
564C3×Q8—62no—
565C3×Q8—64no—
566C3×D4—28no—
567C3×D4—24no—
568C3×D4—24no—
569C3×D4—22no—
570C3×D4—22no—
571C3×D4—24no—
572C3×D4—24no—
573C3×D4—32no—
574C3×D4—64no—
575C3×D4—61no—
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—61no—
583C2×C3×C4—62no—
584C2×C3×C4—64no—
585C2×C3×C4—64no—
586C2×C3×C4D3×D411yescharacteristic
587C2×C3×C4D3×D412yes—
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4D3×D412yes—
590C2×C3×C4C23×D311yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D312yes—
593C2×C3×C4C23×D312yes—
594#67—24no—
595#67—38no—
596#67—38no—
597#67—68no—
598#67—68no—
599#67—68no—
600#67—68no—
601#67—68no—
602#67—68no—
603#67—68no—
604#67—616no—
605#67—616no—
606#67—64no—
607#67—64no—
608C2×Dic3—22no—
609C2×Dic3—24no—
610C2×Dic3—21no—
611C2×Dic3—32no—
612C2×Dic3—32no—
613C2×Dic3—62no—
614C2×Dic3—68no—
615C2×Dic3—68no—
616C2×Dic3—68no—
617C2×Dic3—62no—
618C2×Dic3—616no—
619C2×Dic3—61no—
620C2×Dic3—61no—
621D12—21no—
622D12—34no—
623D12—34no—
624D12—32no—
625D12—32no—
626D12—64no—
627D12—62no—
628D12—62no—
629D12—68no—
630D12—61no—
631D12—61no—
632D12C23×D312yes—
633C4×D3—24no—
634C4×D3—34no—
635C4×D3—34no—
636C4×D3—34no—
637C4×D3—34no—
638C4×D3—64no—
639C4×D3—64no—
640C4×D3—68no—
641C4×D3—68no—
642C4×D3—68no—
643C4×D3—68no—
644C4×D3—64no—
645C4×D3—64no—
646Dic6—24no—
647Dic6—22no—
648Dic6—21no—
649Dic6—34no—
650Dic6—34no—
651Dic6—32no—
652Dic6—32no—
653Dic6—64no—
654Dic6—62no—
655Dic6—68no—
656Dic6—68no—
657Dic6—62no—
658Dic6—61no—
659Dic6—61no—
660Dic6C23×D314yes—
661Dic6C23×D312yes—
662C3×C8—32no—
663C3×C8—34no—
664C3×C8—32no—
665C3⋊C8C23×D312yes—
666C3⋊C8C23×D314yes—
667C3⋊C8C23×D312yes—
668C2×C32—22no—
669C2×C32—44no—
670C2×C32#57712yescomplemented
671C2×C32C23×D411yescharacteristic
672C3⋊D3—24no—
673C3⋊D3—42no—
674C3×D3—42no—
675C24—21no—
676C24—182no—
677#41—34no—
678#41—62no—
679#41—94no—
680#41—94no—
681#41—98no—
682#41—98no—
683#41—94no—
684#41—1816no—
685#41—188no—
686#41—184no—
687#41—184no—
688#41—188no—
689#41—182no—
690C2×Q8—32no—
691C2×Q8—31no—
692C2×Q8—34no—
693C2×Q8—61no—
694C2×Q8—62no—
695C2×Q8—91no—
696C2×Q8—98no—
697C2×Q8—91no—
698C2×Q8—182no—
699C2×Q8—188no—
700C2×Q8—184no—
701C2×D4—21no—
702C2×D4—22no—
703C2×D4—31no—
704C2×D4—61no—
705C2×D4—92no—
706C2×D4—98no—
707C2×D4—91no—
708C2×D4—91no—
709C2×D4—182no—
710C2×D4—184no—
711C2×D4—182no—
712C2×D4—188no—
713C2×D4—1816no—
714C2×D4—182no—
715C2×D4—181no—
716C2×D4C2×D3212yes—
717C2×D4C2×D3214yes—
718C22×C4—61no—
719C22×C4—61no—
720C22×C4—92no—
721C22×C4—182no—
722C22×C4—182no—
723C22×C4—182no—
724C22×C4—181no—
725C22×C4C2×D3211yescharacteristic
726Q16—94no—
727Q16—98no—
728SD16—38no—
729SD16—38no—
730SD16—38no—
731SD16—94no—
732SD16—94no—
733SD16—98no—
734D8—38no—
735D8—94no—
736M16—34no—
737M16—98no—
738C2×C8—31no—
739C2×C8—31no—
740C2×C8—34no—
741C2×C8—32no—
742C2×C8—98no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—28no—
746C22×C3—24no—
747C22×C3—24no—
748C22×C3—22no—
749C22×C3—21no—
750C22×C3—42no—
751C22×C3—48no—
752C22×C3—44no—
753C22×C3—44no—
754C22×C3—62no—
755C22×C3—84no—
756C22×C3—84no—
757C22×C3—88no—
758C22×C3—122no—
759C22×C3C2×D3×D412yes—
760C22×C3C2×D3×D412yes—
761C22×C3C2×D3×D411yescharacteristic
762C22×C3C2×D3×D411yescharacteristic
763C2×D3—22no—
764C2×D3—34no—
765C2×D3—34no—
766C2×D3—42no—
767C2×D3—64no—
768C2×D3—64no—
769C2×D3—64no—
770C2×D3—64no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—124no—
774C2×D3—124no—
775C2×D3—122no—
776C2×D3—122no—
777C2×D3—248no—
778C2×D3—248no—
779C2×D3—2416no—
780C3×C4—22no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—62no—
784C3×C4—64no—
785C3×C4C2×D3×D412yes—
786C3×C4C2×D3×D411yescharacteristic
787C3×C4C2×D3×D411yescharacteristic
788C3×C4C2×D3×D412yes—
789C3×C4C24×D311yescharacteristic
790C3×C4C24×D311yescharacteristic
791Dic3—24no—
792Dic3—22no—
793Dic3—34no—
794Dic3—34no—
795Dic3—64no—
796Dic3—64no—
797Dic3—62no—
798Dic3—62no—
799C32C2×#57711yescharacteristic, complemented, Sylow
800C23—22no—
801C23—24no—
802C23—61no—
803C23—82no—
804C23—92no—
805C23—188no—
806C23—181no—
807C23—724no—
808C23#381111yescharacteristic
809Q8—34no—
810Q8—32no—
811Q8—64no—
812Q8—62no—
813Q8—61no—
814Q8—94no—
815Q8—92no—
816Q8—188no—
817Q8—181no—
818D4—24no—
819D4—22no—
820D4—32no—
821D4—64no—
822D4—61no—
823D4—98no—
824D4—94no—
825D4—92no—
826D4—188no—
827D4—188no—
828D4—188no—
829D4—184no—
830D4—181no—
831D4C22×D3214yes—
832C2×C4—64no—
833C2×C4—61no—
834C2×C4—62no—
835C2×C4—64no—
836C2×C4—92no—
837C2×C4—94no—
838C2×C4—94no—
839C2×C4—188no—
840C2×C4—188no—
841C2×C4—188no—
842C2×C4—181no—
843C2×C4—184no—
844C2×C4#381112yes—
845C2×C4#381111yescharacteristic
846C2×C4C22×D3212yes—
847C2×C4C22×D3211yescharacteristic
848C8—32no—
849C8—32no—
850C8—34no—
851C2×C3—22no—
852C2×C3—22no—
853C2×C3—22no—
854C2×C3—21no—
855C2×C3—42no—
856C2×C3—48no—
857C2×C3—44no—
858C2×C3—44no—
859C2×C3—122no—
860C2×C3#576212yescomplemented
861C2×C3#577512yescomplemented
862C2×C3C22×D3×D411yescharacteristic
863C2×C3C22×D3×D411yescharacteristic
864D3—42no—
865D3—64no—
866D3—64no—
867D3—124no—
868D3—124no—
869D3—122no—
870D3—122no—
871C22—22no—
872C22—24no—
873C22—44no—
874C22—62no—
875C22—84no—
876C22—94no—
877C22—122no—
878C22—184no—
879C22—182no—
880C22—362no—
881C22—728no—
882C22C2×#381112yes—
883C22C2×#381111yescharacteristic
884C4—62no—
885C4—64no—
886C4—94no—
887C4—182no—
888C4C2×#381112yes—
889C4C2×#381111yescharacteristic
890C4C23×D3211yescharacteristic
891C3—21no—
892C3C2×#576211yescharacteristic, complemented
893C3C2×#577511yescharacteristic, complemented
894C2—22no—
895C2—44no—
896C2—122no—
897C2—184no—
898C2—362no—
899C2#1059511512yesdirect product factor
900C2C22×#381111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32C2×#577
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×#64361C2semidirect
2. C2×#64297C2semidirect
3. C22×C3×#214C2semidirect
4. C2×C3×#932C2semidirect
5. #10595115C2direct (N × H)
6. C2×#63937C2semidirect
7. C2×#63936C2semidirect
8. C2×#63931C2semidirect
9. C2×#63930C2semidirect
10. C2×#63833C2semidirect
11. C2×#63829C2semidirect
12. C2×#63817C2semidirect
18. #64361C22semidirect
25. C2×C3×#235C22semidirect
26. C22×C3×Dic6C22semidirect
29. C2×#3797C22semidirect
31. #64297C22semidirect
32. C2×#3796C22semidirect
34. C2×C3×#214C22semidirect
35. C2×C3×#214C22semidirect
36. C2×C3×#214C22semidirect
37. C2×C3×#214C22semidirect
38. C3×#932C22semidirect
39. C2×C3×#213C22semidirect
40. C2×C3×#208C22semidirect
41. C22×C3×C3⋊C8C22semidirect
42. #63937C22semidirect
43. #63936C22semidirect
44. #63931C22semidirect
45. #63930C22semidirect
46. C2×#3719C22semidirect
47. C2×#3719C22semidirect
48. #63833C22semidirect
49. C2×#3717C22semidirect
50. C2×#3717C22semidirect
51. #63829C22semidirect
52. C2×#3716C22semidirect
53. C2×#3714C22semidirect
54. C2×#3712C22semidirect
55. #63817C22semidirect
56. C2×#3710C22semidirect
66. C22×#214D3semidirect
67. C2×#932D3semidirect
114. C3×#235C23semidirect
121. C2×C3×Dic6C23semidirect
129. #3797C23semidirect
131. #3796C23semidirect
133. C3×#214C23semidirect
134. C3×#214C23semidirect
135. C3×#214C23semidirect
136. C3×#213C23semidirect
137. C3×#208C23semidirect
141. C2×C3×C3⋊C8C23semidirect
142. #3719C23semidirect
143. #3719C23semidirect
144. #3717C23semidirect
145. #3717C23semidirect
146. #3716C23semidirect
147. #3714C23semidirect
148. #3712C23semidirect
149. #3710C23semidirect
196. C2×#235C2×D3semidirect
198. C22×Dic6C2×D3semidirect
214. C2×#214C2×D3semidirect
215. C2×#214C2×D3semidirect
216. C2×#214C2×D3semidirect
217. C2×#214C2×D3semidirect
218. #932C2×D3semidirect
220. C2×#213C2×D3semidirect
221. C2×#208C2×D3semidirect
222. C22×C3⋊C8C2×D3semidirect
406. #235C22×D3semidirect
438. C2×Dic6C22×D3semidirect
453. #214C22×D3semidirect
454. #214C22×D3semidirect
455. #214C22×D3semidirect
457. #213C22×D3semidirect
458. #208C22×D3semidirect
462. C2×C3⋊C8C22×D3semidirect
670. C2×C32#577semidirect
799. C32C2×#577semidirect
860. C2×C3#5762semidirect
861. C2×C3#5775semidirect
892. C3C2×#5762semidirect
893. C3C2×#5775semidirect
899. C2#10595115direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643612
C2×#642972
C22×C3×#2142
C2×C3×#9322
#105951152
C2×#639372
C2×#639362
C2×#639312
C2×#639302
C2×#638332
C2×#638292
C2×#638172
C2×#57753
C2×#57623