Finite Group Databasebeta

← #11858197

Subgroups — #11858197

Order 1152.

1881 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596756C211yesmaximal, characteristic
2#10594954C211yesmaximal, characteristic, complemented
3#10594780C211yesmaximal, characteristic, complemented
4C3×#5236C211yesmaximal, characteristic, complemented
5C2×C3×#837C211yesmaximal, characteristic, complemented
6#10591672C214yesmaximal, complemented
7#10591671C214yesmaximal, complemented
8#10591113C211yesmaximal, characteristic, complemented
9C2×#63570C211yesmaximal, characteristic, complemented
10#78992—31nomaximal
11#78983—31nomaximal
12C2×C32×#41C2211yescharacteristic
13#64367—21no—
14#64367C412yescomplemented
15#64366—21no—
16#64366C412yescomplemented
17#41×C3⋊D3—22no—
18#41×C3⋊D3C2214yes—
19#64364C412yescomplemented
20#64361—22no—
21#64361C412yescomplemented
22C2×#3828—22no—
23C2×#3828C2211yescharacteristic
24C2×#3828C2211yescharacteristic
25C3×#926C2211yescharacteristic, complemented
26C2×C3×C4×Dic3C2211yescharacteristic, complemented
27C2×C3×#208C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29#63952—22no—
30#63894—21no—
31C4×#624C2212yescomplemented
32#63874C2212yescomplemented
33#63844—21no—
34#63818C2214yescomplemented
35#63817—22no—
36#63817—22no—
37C3×#837C2212yescomplemented
38C3×#837C2212yescomplemented
39C3×#837C2214yescomplemented
40#63570C2212yescomplemented
41#63570C2212yescomplemented
42#63570C2214yescomplemented
43#5964—31no—
44#5964—31no—
45#5964—61no—
46#5745—31no—
47#5745—31no—
48#5522—31no—
49C4×#235—31no—
50C3×#421—31no—
51C2×C3×#104—31no—
52#5236D311yescharacteristic, complemented
53C2×#837D311yescharacteristic, complemented
54#5139—31no—
55C2×#825—31no—
56#5005—31no—
57C2×#805—31no—
58#4821—34no—
59#4821—34no—
60D3×#104—34no—
61D3×#104—34no—
62C32×#41—21no—
63C32×#41—21no—
64C32×#41C2×C412yescomplemented
65C32×#41C2312yes—
66C2×C32×Q8C2×C411yescharacteristic, complemented
67C2×C32×D4—21no—
68C2×C32×D4C2×C411yescharacteristic, complemented
69C22×C32×C4—21no—
70C22×C32×C4C2311yescharacteristic
71C2×#638—21no—
72C2×#638—24no—
73C2×#638D412yes—
74#3832—22no—
75#3832C2×C414yescomplemented
76Q8×C3⋊D3—22no—
77Q8×C3⋊D3C2×C414yescomplemented
78#3830—24no—
79#3830—24no—
80#3830—22no—
81#3830C2×C414yescomplemented
82D4×C3⋊D3—24no—
83D4×C3⋊D3—24no—
84D4×C3⋊D3—22no—
85D4×C3⋊D3C2×C414yescomplemented
86#3828—21no—
87#3828—21no—
88#3828—24no—
89#3828—22no—
90#3828—24no—
91#3828—22no—
92#3828C2×C412yes—
93#3828C2×C412yes—
94#3828C2×C412yescomplemented
95#3828D412yes—
96#3828D412yes—
97#3828C2312yes—
98C2×C4⋊(C3⋊D3)—22no—
99C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
100C2×C4⋊(C3⋊D3)D411yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—24no—
103C2×C4×C3⋊D3C2312yes—
104C2×#634—22no—
105C2×#634C2×C411yescharacteristic, complemented
106C2×#634D411yescharacteristic
107C22×C3×Dic3—21no—
108C2×#624—22no—
109C3×#217—21no—
110C3×C4⋊Dic3—21no—
111C3×C4×Dic3—21no—
112C3×C4×Dic3C2311yescharacteristic
113C3×C4×Dic3C2311yescharacteristic
114C3×C4×Dic3C2312yes—
115C3×#208—21no—
116C3×#208—21no—
117C3×#208C2312yes—
118C3×#208C2312yes—
119C2×C3×C3⋊C8—21no—
120C2×C3×C3⋊C8—21no—
121#3724—22no—
122#3722—22no—
123Dic32—22no—
124#3712—24no—
125#3710—24no—
126#2901—91noSylow
127C2×C3×#41—21no—
128C2×C3×#41C2×D311yescharacteristic
129C2×C3×#41C2×D311yescharacteristic
130#1010—32no—
131#1010—32no—
132#1010—62no—
133#1010—61no—
134#1010—61no—
135#1010—62no—
136#1009—32no—
137#1009—32no—
138#1009—62no—
139#1009—61no—
140#1009—61no—
141#1009—62no—
142D3×#41—34no—
143D3×#41—34no—
144D3×#41—64no—
145D3×#41—62no—
146D3×#41—62no—
147D3×#41—64no—
148#1007—32no—
149#1007—32no—
150#1007—62no—
151#1004—32no—
152#1004—32no—
153#1004—62no—
154#1004—62no—
155#1004—62no—
156#1004—64no—
157C2×#235—31no—
158C2×#235—31no—
159C2×#235—31no—
160C2×#235—31no—
161C2×#235—61no—
162C2×#235—61no—
163C2×#235—62no—
164C2×#235—62no—
165C2×#235—64no—
166C2×C3×M16—31no—
167C2×C3×M16—31no—
168C3×#117—31no—
169C2×C3×C42—31no—
170C4×#67—62no—
171#926C2×D311yescharacteristic, complemented
172C2×C4×Dic3C2×D311yescharacteristic, complemented
173C2×#208C2×D311yescharacteristic, complemented
174C2×#208C2×D311yescharacteristic, complemented
175#907—62no—
176#907—62no—
177D3×M16—34no—
178D3×M16—34no—
179#901—62no—
180#901—62no—
181#893—61no—
182#887—61no—
183#67⋊C4—62no—
184C4×D12—61no—
185#872—32no—
186#872—32no—
187C42×D3—32no—
188C42×D3—32no—
189C4×Dic6—61no—
190C3×#104—32no—
191C3×#104—32no—
192C3×#104—34no—
193#837C2×D312yescomplemented
194#837C2×D312yescomplemented
195#837C2×D314yescomplemented
196#825—32no—
197#825—32no—
198#825—34no—
199#805—32no—
200#805—32no—
201#805—34no—
202C23×C32—21no—
203C23×C32C2×D411yescharacteristic
204C22×C3⋊D3—21no—
205C22×C3⋊D3—24no—
206C22×C3⋊D3C2×D412yes—
207C32×Q8—21no—
208C32×Q8C22×C412yes—
209C32×D4—22no—
210C32×D4—22no—
211C32×D4—21no—
212C32×D4C22×C412yes—
213C2×C32×C4—21no—
214C2×C32×C4—22no—
215C2×C32×C4—22no—
216C2×C32×C4C22×C411yescharacteristic
217C2×C32×C4C22×C411yescharacteristic
218C2×C32×C4C2×D411yescharacteristic
219C2×C32×C4C2×D411yescharacteristic
220C2×C32×C4C2×D411yescharacteristic
221C2×C32×C4C2411yescharacteristic
222#638—22no—
223#638—22no—
224#638—24no—
225#638—24no—
226#638C22⋊C414yes—
227#638C22⋊C414yes—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—24no—
230C2×C3⋊Dic3C2×D412yes—
231C4⋊(C3⋊D3)—24no—
232C4⋊(C3⋊D3)—21no—
233C4⋊(C3⋊D3)C22⋊C412yes—
234C4⋊(C3⋊D3)C22⋊C412yes—
235C4⋊(C3⋊D3)C22×C412yes—
236C4×C3⋊D3—24no—
237C4×C3⋊D3—22no—
238C4×C3⋊D3—22no—
239C4×C3⋊D3—24no—
240C4×C3⋊D3C22×C414yes—
241C4×C3⋊D3C2×D414yes—
242#634—21no—
243#634—24no—
244#634C22⋊C412yes—
245#634C22⋊C412yes—
246#634C22×C412yes—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—22no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—42no—
251#624—44no—
252C3×C3⋊C8—22no—
253C3×C3⋊C8—22no—
254#585—91no—
255#568—91no—
256C4×#41—91no—
257#421—31no—
258#421—94no—
259#421—91no—
260C2×#104—31no—
261C2×#104—94no—
262C2×#104—91no—
263C3×#41—22no—
264C3×#41—22no—
265C3×#41—21no—
266C3×#41—21no—
267C3×#41—21no—
268C3×#41—21no—
269C3×#41—22no—
270C3×#41—22no—
271C3×#41C4×D312yescomplemented
272C3×#41C4×D312yescomplemented
273C3×#41C22×D312yes—
274C3×#41C22×D312yes—
275C2×C3×Q8—21no—
276C2×C3×Q8C4×D311yescharacteristic, complemented
277C2×C3×Q8C4×D311yescharacteristic, complemented
278C2×C3×D4—22no—
279C2×C3×D4—21no—
280C2×C3×D4—21no—
281C2×C3×D4—21no—
282C2×C3×D4C4×D311yescharacteristic, complemented
283C2×C3×D4C4×D311yescharacteristic, complemented
284C22×C3×C4—22no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—61no—
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C2×#67—32no—
292C2×#67—32no—
293C2×#67—62no—
294C2×#67—64no—
295C2×#67—64no—
296C2×#67—68no—
297C2×#67—62no—
298C2×#67—61no—
299C2×#67—61no—
300C22×Dic3—21no—
301#239—34no—
302#239—34no—
303#239—64no—
304#239—62no—
305#239—62no—
306#239—64no—
307D3×Q8—34no—
308D3×Q8—34no—
309D3×Q8—64no—
310D3×Q8—62no—
311D3×Q8—62no—
312D3×Q8—64no—
313#237—34no—
314#237—34no—
315#237—64no—
316#237—62no—
317#237—62no—
318#237—64no—
319#237—64no—
320#237—64no—
321#237—64no—
322#237—68no—
323#237—68no—
324#237—64no—
325D3×D4—34no—
326D3×D4—34no—
327D3×D4—64no—
328D3×D4—62no—
329D3×D4—62no—
330D3×D4—64no—
331D3×D4—64no—
332D3×D4—64no—
333D3×D4—64no—
334D3×D4—64no—
335D3×D4—68no—
336D3×D4—68no—
337#235—32no—
338#235—32no—
339#235—32no—
340#235—32no—
341#235—32no—
342#235—32no—
343#235—32no—
344#235—32no—
345#235—32no—
346#235—32no—
347#235—32no—
348#235—32no—
349#235—62no—
350#235—62no—
351#235—62no—
352#235—62no—
353#235—62no—
354#235—62no—
355#235—62no—
356#235—62no—
357#235—64no—
358#235—64no—
359#235—62no—
360#235—62no—
361#235—64no—
362#235—64no—
363#235—62no—
364#235—68no—
365#235—68no—
366#235—64no—
367#235—64no—
368#235—62no—
369#235—61no—
370#235—61no—
371#235—61no—
372#235—61no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—62no—
380C2×D12—62no—
381C2×D12—64no—
382C2×C4×D3—32no—
383C2×C4×D3—32no—
384C2×C4×D3—62no—
385C2×C4×D3—64no—
386C2×C4×D3—64no—
387C2×C4×D3—68no—
388C2×C4×D3—62no—
389C2×C4×D3—61no—
390C2×C4×D3—61no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C2×Dic6—31no—
394C2×Dic6—31no—
395C2×Dic6—31no—
396C2×Dic6—31no—
397C2×Dic6—61no—
398C2×Dic6—61no—
399C2×Dic6—62no—
400C2×Dic6—62no—
401C2×Dic6—64no—
402C3×M16—32no—
403C3×M16—32no—
404C3×M16—61no—
405C3×M16—61no—
406C2×C3×C8—61no—
407C2×C3×C8—61no—
408C3×C4⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C42—31no—
411C3×C42—32no—
412C3×C42—31no—
413C3×C42—61no—
414#217—21no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—62no—
417C4⋊Dic3—21no—
418Dic3⋊C4—62no—
419Dic3⋊C4—62no—
420C4×Dic3—21no—
421C4×Dic3—62no—
422C4×Dic3—62no—
423C4×Dic3C22×D311yescharacteristic
424C4×Dic3C22×D312yes—
425C4×Dic3C22×D311yescharacteristic
426#208—21no—
427#208—21no—
428#208C22×D312yes—
429#208C22×D312yes—
430C2×C3⋊C8—21no—
431C2×C3⋊C8—21no—
432ΓL(1,𝔽25)—64no—
433ΓL(1,𝔽25)—64no—
434D3×C8—64no—
435D3×C8—64no—
436C22×C32—22no—
437C22×C32—41no—
438C22×C32—81no—
439C22×C32C2×C22⋊C411yescharacteristic
440C22×C32C2×C22⋊C411yescharacteristic
441C22×C32C22×D411yescharacteristic
442C2×C3⋊D3—22no—
443C2×C3⋊D3—42no—
444C2×C3⋊D3—84no—
445C2×C3⋊D3—81no—
446C2×C3⋊D3C2×C22⋊C414yes—
447C32×C4—22no—
448C32×C4C2×C22⋊C411yescharacteristic
449C32×C4C2×C22⋊C411yescharacteristic
450C32×C4C23×C411yescharacteristic
451C32×C4C22×D411yescharacteristic
452C3⋊Dic3—22no—
453C3⋊Dic3C2×C22⋊C414yes—
454C3×Dic3—22no—
455C3×Dic3—42no—
456C3×Dic3—41no—
4572−1+4—92no—
4582−1+4—92no—
4592−1+4—181no—
460H(5,𝔽2)—92no—
461H(5,𝔽2)—92no—
462H(5,𝔽2)—182no—
463H(5,𝔽2)—181no—
464C2×#41—91no—
465C2×#41—94no—
466C2×#41—91no—
467C2×#41—182no—
468C2×#41—182no—
469C2×#41D3211yescharacteristic
470#131—182no—
471#131—182no—
472C2×M16—31no—
473C2×M16—31no—
474C2×M16—94no—
475C4×Q8—181no—
476C4×D4—181no—
477C4×D4—182no—
478#117—31no—
479#117—92no—
480C2×C42—31no—
481C2×C42—92no—
482#104—32no—
483#104—32no—
484#104—34no—
485#104—92no—
486#104—92no—
487#104—94no—
488C23×C3—22no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3D3×D411yescharacteristic
493C23×C3D3×D411yescharacteristic
494C22×D3—32no—
495C22×D3—32no—
496C22×D3—62no—
497C22×D3—64no—
498C22×D3—64no—
499C22×D3—68no—
500C22×D3—62no—
501C22×D3—61no—
502C22×D3—61no—
503C3×Q8—22no—
504C3×Q8—21no—
505C3×Q8—21no—
506C3×Q8—22no—
507C3×Q8C2×C4×D312yes—
508C3×Q8C2×C4×D312yes—
509C3×D4—24no—
510C3×D4—24no—
511C3×D4—22no—
512C3×D4—22no—
513C3×D4—22no—
514C3×D4—22no—
515C3×D4—22no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—22no—
519C3×D4C2×C4×D312yes—
520C3×D4C2×C4×D312yes—
521C2×C3×C4—24no—
522C2×C3×C4—24no—
523C2×C3×C4—22no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—61no—
537C2×C3×C4—62no—
538C2×C3×C4—61no—
539C2×C3×C4—122no—
540C2×C3×C4C2×C4×D311yescharacteristic
541C2×C3×C4C2×C4×D311yescharacteristic
542C2×C3×C4C2×C4×D311yescharacteristic
543C2×C3×C4C2×C4×D311yescharacteristic
544C2×C3×C4D3×D411yescharacteristic
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4D3×D411yescharacteristic
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C23×D311yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552#67—34no—
553#67—34no—
554#67—34no—
555#67—34no—
556#67—64no—
557#67—64no—
558#67—64no—
559#67—64no—
560#67—64no—
561#67—64no—
562#67—64no—
563#67—68no—
564#67—68no—
565#67—64no—
566#67—62no—
567#67—62no—
568#67—62no—
569#67—62no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—22no—
573C2×Dic3—32no—
574C2×Dic3—32no—
575C2×Dic3—42no—
576C2×Dic3—62no—
577C2×Dic3—64no—
578C2×Dic3—64no—
579C2×Dic3—68no—
580C2×Dic3—62no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583D12—32no—
584D12—32no—
585D12—32no—
586D12—32no—
587D12—32no—
588D12—32no—
589D12—62no—
590D12—62no—
591D12—62no—
592D12—64no—
593D12—64no—
594D12—62no—
595D12—68no—
596D12—61no—
597D12—61no—
598C4×D3—34no—
599C4×D3—34no—
600C4×D3—34no—
601C4×D3—34no—
602C4×D3—64no—
603C4×D3—64no—
604C4×D3—64no—
605C4×D3—64no—
606C4×D3—64no—
607C4×D3—64no—
608C4×D3—64no—
609C4×D3—68no—
610C4×D3—68no—
611C4×D3—64no—
612C4×D3—62no—
613C4×D3—62no—
614C4×D3—62no—
615C4×D3—62no—
616C4×D3—124no—
617C4×D3—124no—
618Dic6—32no—
619Dic6—32no—
620Dic6—32no—
621Dic6—32no—
622Dic6—32no—
623Dic6—32no—
624Dic6—62no—
625Dic6—62no—
626Dic6—62no—
627Dic6—64no—
628Dic6—64no—
629Dic6—62no—
630Dic6—68no—
631Dic6—61no—
632Dic6—61no—
633C3×C8—62no—
634C3×C8—62no—
635C3⋊C8—22no—
636C3⋊C8—22no—
637C2×C32—21no—
638C2×C32—21no—
639C2×C32—21no—
640C2×C32—42no—
641C2×C32C22×C22⋊C411yescharacteristic
642C3⋊D3—24no—
643C3⋊D3—42no—
644#41—21no—
645#41—21no—
646#41—92no—
647#41—92no—
648#41—92no—
649#41—92no—
650#41—94no—
651#41—94no—
652#41—92no—
653#41—92no—
654#41—184no—
655#41—184no—
656#41—182no—
657#41—182no—
658#41—184no—
659#41—184no—
660#41—182no—
661#41—182no—
662#41—181no—
663#41—181no—
664#41#62412yescomplemented
665#41C2×D3212yes—
666C2×Q8—91no—
667C2×Q8—94no—
668C2×Q8—91no—
669C2×Q8—182no—
670C2×Q8—182no—
671C2×Q8#62411yescharacteristic, complemented
672C2×D4—21no—
673C2×D4—92no—
674C2×D4—94no—
675C2×D4—91no—
676C2×D4—91no—
677C2×D4—182no—
678C2×D4—184no—
679C2×D4—182no—
680C2×D4—184no—
681C2×D4—184no—
682C2×D4—181no—
683C2×D4#62411yescharacteristic, complemented
684C22×C4—21no—
685C22×C4—61no—
686C22×C4—92no—
687C22×C4—184no—
688C22×C4—182no—
689C22×C4—181no—
690C22×C4C2×D3211yescharacteristic
691M16—32no—
692M16—32no—
693M16—61no—
694M16—61no—
695M16—184no—
696C2×C8—61no—
697C2×C8—61no—
698C2×C8—184no—
699C4⋊C4—61no—
700C4⋊C4—182no—
701C22⋊C4—61no—
702C22⋊C4—182no—
703C42—31no—
704C42—31no—
705C42—32no—
706C42—61no—
707C42—182no—
708C22×C3—24no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—82no—
720C22×C3D3×C22⋊C411yescharacteristic
721C22×C3D3×C22⋊C411yescharacteristic
722C22×C3D3×C22⋊C411yescharacteristic
723C22×C3D3×C22⋊C411yescharacteristic
724C22×C3C2×D3×D411yescharacteristic
725C22×C3C2×D3×D411yescharacteristic
726C2×D3—34no—
727C2×D3—34no—
728C2×D3—64no—
729C2×D3—64no—
730C2×D3—62no—
731C2×D3—62no—
732C2×D3—122no—
733C2×D3—122no—
734C2×D3—242no—
735C2×D3—244no—
736C2×D3—244no—
737C2×D3—241no—
738C2×D3—241no—
739C2×D3—242no—
740C2×D3—248no—
741C3×C4—24no—
742C3×C4—22no—
743C3×C4—22no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—62no—
749C3×C4—122no—
750C3×C4—121no—
751C3×C4D3×C22⋊C411yescharacteristic
752C3×C4D3×C22⋊C411yescharacteristic
753C3×C4D3×C22⋊C411yescharacteristic
754C3×C4D3×C22⋊C411yescharacteristic
755C3×C4C22×C4×D311yescharacteristic
756C3×C4C22×C4×D311yescharacteristic
757C3×C4C2×D3×D411yescharacteristic
758C3×C4C2×D3×D411yescharacteristic
759Dic3—22no—
760Dic3—34no—
761Dic3—34no—
762Dic3—42no—
763Dic3—41no—
764Dic3—64no—
765Dic3—64no—
766Dic3—62no—
767Dic3—62no—
768C32#290111yescharacteristic, complemented, Sylow
769C23—21no—
770C23—92no—
771C23—184no—
772C23—181no—
773C23#381111yescharacteristic
774Q8—21no—
775Q8—92no—
776Q8—92no—
777Q8—92no—
778Q8—184no—
779Q8—181no—
780Q8C2×#62412yes—
781D4—22no—
782D4—22no—
783D4—21no—
784D4—94no—
785D4—94no—
786D4—92no—
787D4—92no—
788D4—92no—
789D4—184no—
790D4—184no—
791D4—184no—
792D4—182no—
793D4—182no—
794D4—181no—
795D4C2×#62412yes—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—62no—
802C2×C4—92no—
803C2×C4—94no—
804C2×C4—94no—
805C2×C4—122no—
806C2×C4—184no—
807C2×C4—184no—
808C2×C4—184no—
809C2×C4—181no—
810C2×C4—182no—
811C2×C4—182no—
812C2×C4—364no—
813C2×C4C2×#62411yescharacteristic
814C2×C4C2×#62411yescharacteristic
815C2×C4#381111yescharacteristic
816C2×C4#381111yescharacteristic
817C2×C4#381111yescharacteristic
818C2×C4C22×D3211yescharacteristic
819C8—62no—
820C8—62no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—41no—
829C2×C3—41no—
830C2×C3—41no—
831C2×C3—44no—
832C2×C3—42no—
833C2×C3—42no—
834C2×C3C2×D3×C22⋊C411yescharacteristic
835C2×C3C2×D3×C22⋊C411yescharacteristic
836D3—64no—
837D3—64no—
838D3—124no—
839D3—124no—
840D3—122no—
841D3—122no—
842C22—22no—
843C22—41no—
844C22—81no—
845C22—94no—
846C22—182no—
847C22—362no—
848C22—721no—
849C22—724no—
850C22#6397411yescharacteristic
851C22#6397411yescharacteristic
852C22C2×#381111yescharacteristic
853C4—22no—
854C4—62no—
855C4—94no—
856C4—121no—
857C4—122no—
858C4—182no—
859C4#6397411yescharacteristic
860C4#6397411yescharacteristic
861C4C22×#62411yescharacteristic
862C4C2×#381111yescharacteristic
863C3—21no—
864C3#7898311yescharacteristic, complemented
865C3#7899211yescharacteristic, complemented
866C2—21no—
867C2—21no—
868C2—21no—
869C2—42no—
870C2—184no—
871C2—362no—
872C2C2×#6397411yescharacteristic
subgroupG/H
centerC4C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C22×C22⋊C4
prime radical#10596756C2
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2901
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594954C2semidirect
3. #10594780C2semidirect
4. C3×#5236C2semidirect
5. C2×C3×#837C2semidirect
6. #10591672C2semidirect
7. #10591671C2semidirect
8. #10591113C2semidirect
9. C2×#63570C2semidirect
14. #64367C4semidirect
16. #64366C4semidirect
19. #64364C4semidirect
21. #64361C4semidirect
25. C3×#926C22semidirect
26. C2×C3×C4×Dic3C22semidirect
27. C2×C3×#208C22semidirect
28. C2×C3×#208C22semidirect
31. C4×#624C22semidirect
32. #63874C22semidirect
34. #63818C22semidirect
37. C3×#837C22semidirect
38. C3×#837C22semidirect
39. C3×#837C22semidirect
40. #63570C22semidirect
41. #63570C22semidirect
42. #63570C22semidirect
52. #5236D3semidirect
53. C2×#837D3semidirect
64. C32×#41C2×C4semidirect
66. C2×C32×Q8C2×C4semidirect
68. C2×C32×D4C2×C4semidirect
75. #3832C2×C4semidirect
77. Q8×C3⋊D3C2×C4semidirect
81. #3830C2×C4semidirect
85. D4×C3⋊D3C2×C4semidirect
94. #3828C2×C4semidirect
99. C2×C4⋊(C3⋊D3)C2×C4semidirect
105. C2×#634C2×C4semidirect
171. #926C2×D3semidirect
172. C2×C4×Dic3C2×D3semidirect
173. C2×#208C2×D3semidirect
174. C2×#208C2×D3semidirect
193. #837C2×D3semidirect
194. #837C2×D3semidirect
195. #837C2×D3semidirect
271. C3×#41C4×D3semidirect
272. C3×#41C4×D3semidirect
276. C2×C3×Q8C4×D3semidirect
277. C2×C3×Q8C4×D3semidirect
282. C2×C3×D4C4×D3semidirect
283. C2×C3×D4C4×D3semidirect
664. #41#624semidirect
671. C2×Q8#624semidirect
683. C2×D4#624semidirect
768. C32#2901semidirect
864. C3#78983semidirect
865. C3#78992semidirect

Maximal subgroups

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

subgroupindex
#105967562
#105949542
#105947802
C3×#52362
C2×C3×#8372
#105916722
#105916712
#105911132
C2×#635702
#789923
#789833