Finite Group Databasebeta

← #11858157

Subgroups — #11858157

Order 1152.

1709 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic
2C3⋊D3×#117C211yesmaximal, characteristic, complemented
3C2×#63818C211yesmaximal, characteristic, complemented
4C3×#5005C212yesmaximal, complemented
5#10591110C212yesmaximal, complemented
6#10590394C214yesmaximal, complemented
7#10590393C214yesmaximal, complemented
8D3×#421—32nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C3×#235C2212yes—
11C2×#3811—21no—
12C2×#3805—21no—
13#64306—21no—
14#64306—21no—
15#64306—21no—
16#64306—21no—
17#64306C412yescomplemented
18#64306C412yescomplemented
19#64306C2212yes—
20#64306C2212yes—
21C2×#3802C411yescharacteristic, complemented
22C2×C4×D32—21no—
23C2×#3798—21no—
24C2×#3797C411yescharacteristic, complemented
25C2×#3796C412yescomplemented
26C32×#117C2211yescharacteristic, complemented
27#64135C2211yescharacteristic, complemented
28#64101—21no—
29C4⋊C4×C3⋊D3—21no—
30C22⋊C4×C3⋊D3—21no—
31#64086—21no—
32#64081C2212yescomplemented
33C42×C3⋊D3C2212yescomplemented
34C2×C3×#208C2212yescomplemented
35C2×#3712—21no—
36#63818—21no—
37#63818—21no—
38#63818C2212yescomplemented
39#63818C2212yescomplemented
40C2×#3710—21no—
41C3×#805C2218yescomplemented
42#63568C2218yescomplemented
43C2×D3×#41—32no—
44C2×D3×M16—32no—
45D3×#117—32no—
46D3×#117—61no—
47C3×#421—32no—
48#5236—32no—
49#5139—32no—
50#5005D312yescomplemented
51#4821—38no—
52D3×#104—38no—
53C23×C3⋊D3D411yescharacteristic
54C22×D32—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3D411yescharacteristic
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3C2×C411yescharacteristic
59C2×C4×C3⋊D3C2×C411yescharacteristic
60C2×C4×C3⋊D3C2×C411yescharacteristic
61C2×C4×C3⋊D3C2×C411yescharacteristic
62C2×C4×C3⋊D3D411yescharacteristic
63C2×C4×C3⋊D3D411yescharacteristic
64C2×C4×C3⋊D3D411yescharacteristic
65C2×C4×C3⋊D3D411yescharacteristic
66C2×C4×C3⋊D3D411yescharacteristic
67C2×C4×C3⋊D3D411yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C4×C3⋊D3C2311yescharacteristic
70C2×C3×#67—22no—
71C3×#235—22no—
72C3×#235—22no—
73C3×#235C2×C414yescomplemented
74C3×#235C2314yes—
75C2×C3×D12C2×C412yescomplemented
76C2×C3×C4×D3—22no—
77C2×C3×Dic6C2×C412yescomplemented
78#3811—22no—
79#3811—22no—
80#3811—22no—
81#3811—22no—
82C2×#627—21no—
83C2×#626—22no—
84C2×#625—21no—
85C2×#624—21no—
86#3805—22no—
87#3805—22no—
88#3805—22no—
89#3805—22no—
90C2×D3×Dic3—22no—
91#3802—21no—
92#3802—21no—
93#3802C2×C412yes—
94#3802C2×C412yescomplemented
95C4×D32—22no—
96C4×D32—22no—
97C4×D32—22no—
98C4×D32—22no—
99#3798—22no—
100#3798—22no—
101#3798—22no—
102#3798—22no—
103#3797—21no—
104#3797—21no—
105#3797C2×C412yes—
106#3797C2×C412yescomplemented
107#3796—22no—
108#3796—22no—
109#3796C2×C414yes—
110#3796C2×C414yescomplemented
111C32×C4⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C42C2312yescomplemented
114#3757—21no—
115#3752—22no—
116C4⋊(C3⋊Dic3)—21no—
117#3750—22no—
118C4×C3⋊Dic3—22no—
119C4×C3⋊Dic3C2312yescomplemented
120C3×#208—22no—
121C3×#208C2314yescomplemented
122C2×C3×C3⋊C8—22no—
123#3712—22no—
124#3712—22no—
125#3710—22no—
126#3710—22no—
127C2×#421—91noSylow
128C2×C3×#41—32no—
129D3×#41—34no—
130D3×#41—34no—
131D3×#41—34no—
132D3×#41—34no—
133D3×#41—62no—
134D3×#41—62no—
135D3×#41—62no—
136D3×#41—62no—
137C2×#239—32no—
138C2×D3×Q8—32no—
139C2×#237—32no—
140C2×#237—62no—
141C2×D3×D4—32no—
142C2×D3×D4—62no—
143C2×#235—62no—
144C2×#235C2×D312yes—
145C22×C4×D3—32no—
146C22×C4×D3—61no—
147C22×C4×D3—62no—
148C2×C3×M16—32no—
149C3×#117—21no—
150C3×#117C2×D312yescomplemented
151#926—32no—
152#926—61no—
153C2×#208C2×D312yescomplemented
154D3×M16—34no—
155D3×M16—34no—
156D3×M16—62no—
157D3×M16—62no—
158C2×ΓL(1,𝔽25)—62no—
159C2×D3×C8—62no—
160#892—62no—
161#892—62no—
162D3×C4⋊C4—62no—
163D3×C4⋊C4—62no—
164D3×C22⋊C4—62no—
165D3×C22⋊C4—62no—
166#877—62no—
167#877—62no—
168#872—34no—
169#872—62no—
170C42×D3—34no—
171C42×D3—62no—
172C3×#104—38no—
173#837—38no—
174#825—38no—
175#805C2×D318yescomplemented
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—42no—
178C22×C3⋊D3C22⋊C411yescharacteristic
179C22×C3⋊D3C22⋊C411yescharacteristic
180C22×C3⋊D3C22⋊C411yescharacteristic
181C22×C3⋊D3C22⋊C411yescharacteristic
182C22×C3⋊D3C2×D411yescharacteristic
183C22×C3⋊D3C2×D411yescharacteristic
184C22×C3×D3—22no—
185C2×D32—22no—
186C2×D32—22no—
187C2×D32—44no—
188C2×C32×C4—22no—
189C2×C32×C4C22×C411yescharacteristic
190C2×C32×C4C22×C411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2411yescharacteristic
195C2×C3⋊Dic3—22no—
196C2×C3⋊Dic3C22⋊C411yescharacteristic
197C2×C3⋊Dic3C22⋊C411yescharacteristic
198C2×C3⋊Dic3C22⋊C411yescharacteristic
199C2×C3⋊Dic3C22⋊C411yescharacteristic
200C2×C3⋊Dic3C2×D411yescharacteristic
201C2×C3⋊Dic3C2×D411yescharacteristic
202C4×C3⋊D3—44no—
203C4×C3⋊D3C22⋊C411yescharacteristic
204C4×C3⋊D3C22⋊C411yescharacteristic
205C4×C3⋊D3C22⋊C411yescharacteristic
206C4×C3⋊D3C22⋊C411yescharacteristic
207C4×C3⋊D3C22⋊C411yescharacteristic
208C4×C3⋊D3C22⋊C411yescharacteristic
209C4×C3⋊D3C22⋊C411yescharacteristic
210C4×C3⋊D3C22⋊C411yescharacteristic
211C4×C3⋊D3C22×C411yescharacteristic
212C4×C3⋊D3C22×C411yescharacteristic
213C4×C3⋊D3C22×C411yescharacteristic
214C4×C3⋊D3C22×C411yescharacteristic
215C4×C3⋊D3C2×D411yescharacteristic
216C4×C3⋊D3C2×D411yescharacteristic
217C4×C3⋊D3C2×D411yescharacteristic
218C4×C3⋊D3C2×D411yescharacteristic
219C3×#67—24no—
220C3×#67—24no—
221C2×C3×Dic3—22no—
222C3×D12—22no—
223C3×D12C22×C414yes—
224C3×C4×D3—24no—
225C3×C4×D3—24no—
226C3×Dic6—22no—
227C3×Dic6C22×C414yes—
228#627—22no—
229#627—22no—
230#626—24no—
231#626—24no—
232#625—22no—
233#625—22no—
234#624—22no—
235#624—22no—
236D3×Dic3—24no—
237D3×Dic3—24no—
238C3×C3⋊C8—24no—
239C22×#41—91no—
240C22×M16—91no—
241C2×#117—91no—
242#421—32no—
243#421—94no—
244#421—92no—
245C2×#104—94no—
246C23×D3—32no—
247C23×D3—61no—
248C23×D3—62no—
249C3×#41—34no—
250C3×#41—34no—
251C3×#41—62no—
252C3×#41—62no—
253C2×C3×Q8—32no—
254C2×C3×D4—32no—
255C2×C3×D4—62no—
256C22×C3×C4—21no—
257C22×C3×C4—62no—
258C22×C3×C4C22×D312yes—
259C2×#67—22no—
260C2×#67—62no—
261C2×#67—62no—
262C22×Dic3—32no—
263C22×Dic3—61no—
264C22×Dic3—62no—
265#239—34no—
266#239—34no—
267#239—62no—
268#239—62no—
269D3×Q8—34no—
270D3×Q8—34no—
271D3×Q8—62no—
272D3×Q8—62no—
273#237—34no—
274#237—34no—
275#237—62no—
276#237—62no—
277#237—64no—
278#237—64no—
279#237—64no—
280#237—64no—
281D3×D4—34no—
282D3×D4—34no—
283D3×D4—62no—
284D3×D4—62no—
285D3×D4—64no—
286D3×D4—64no—
287D3×D4—64no—
288D3×D4—64no—
289#235—22no—
290#235—22no—
291#235—64no—
292#235—64no—
293#235—64no—
294#235—64no—
295#235C4×D314yescomplemented
296#235C22×D314yes—
297C2×D12—62no—
298C2×D12C4×D312yescomplemented
299C2×C4×D3—22no—
300C2×C4×D3—32no—
301C2×C4×D3—32no—
302C2×C4×D3—32no—
303C2×C4×D3—32no—
304C2×C4×D3—32no—
305C2×C4×D3—32no—
306C2×C4×D3—32no—
307C2×C4×D3—32no—
308C2×C4×D3—32no—
309C2×C4×D3—32no—
310C2×C4×D3—32no—
311C2×C4×D3—32no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—64no—
325C2×C4×D3—64no—
326C2×C4×D3—64no—
327C2×C4×D3—64no—
328C2×C4×D3—62no—
329C2×C4×D3—62no—
330C2×C4×D3—64no—
331C2×C4×D3—64no—
332C2×Dic6—62no—
333C2×Dic6C4×D312yescomplemented
334C3×M16—34no—
335C3×M16—62no—
336C2×C3×C8—62no—
337C3×C4⋊C4—22no—
338C3×C4⋊C4—22no—
339C3×C22⋊C4—22no—
340C3×C22⋊C4—22no—
341C3×C42—22no—
342C3×C42C22×D314yescomplemented
343#217—62no—
344#217—62no—
345(C2×D3)⋊C4—64no—
346(C2×D3)⋊C4—64no—
347C4⋊Dic3—62no—
348C4⋊Dic3—62no—
349Dic3⋊C4—64no—
350Dic3⋊C4—64no—
351C4×Dic3—34no—
352C4×Dic3—62no—
353C4×Dic3—64no—
354C4×Dic3—64no—
355#208—22no—
356#208C22×D314yescomplemented
357C2×C3⋊C8—22no—
358ΓL(1,𝔽25)—64no—
359ΓL(1,𝔽25)—64no—
360D3×C8—64no—
361D3×C8—64no—
362C22×C32—41no—
363C22×C32C2×C22⋊C411yescharacteristic
364C22×C32C2×C22⋊C411yescharacteristic
365C22×C32C22×D411yescharacteristic
366C2×C3⋊D3—22no—
367C2×C3⋊D3—22no—
368C2×C3⋊D3—22no—
369C2×C3⋊D3—41no—
370C2×C3⋊D3—41no—
371C2×C3⋊D3—41no—
372C2×C3⋊D3C2×C22⋊C411yescharacteristic
373C2×C3⋊D3C2×C22⋊C411yescharacteristic
374C2×C3⋊D3C2×C22⋊C411yescharacteristic
375C2×C3⋊D3C2×C22⋊C411yescharacteristic
376C2×C3×D3—24no—
377C2×C3×D3—44no—
378D32—44no—
379D32—44no—
380C32×C4—42no—
381C32×C4C2×C22⋊C411yescharacteristic
382C32×C4C2×C22⋊C411yescharacteristic
383C32×C4C23×C411yescharacteristic
384C32×C4C22×D411yescharacteristic
385C3⋊Dic3—42no—
386C3⋊Dic3C2×C22⋊C411yescharacteristic
387C3⋊Dic3C2×C22⋊C411yescharacteristic
388C3⋊Dic3C2×C22⋊C411yescharacteristic
389C3⋊Dic3C2×C22⋊C411yescharacteristic
390C3×Dic3—24no—
391C2×#41—32no—
392C2×#41—92no—
393C2×#41—92no—
394C2×#41—92no—
395C2×#41—92no—
396C2×#41—92no—
397C2×#41—181no—
398C2×#41—181no—
399C2×#41—181no—
400C2×#41—181no—
401C2×#41—181no—
402C2×#41—181no—
403C22×Q8—91no—
404C22×D4—91no—
405C22×D4—181no—
406C23×C4—91no—
407C23×C4—181no—
408C2×M16—32no—
409C2×M16—92no—
410C2×M16—92no—
411C2×M16—181no—
412C2×M16—181no—
413C2×M16—181no—
414C22×C8—181no—
415#117—91no—
416#117—92no—
417#117—181no—
418#117—181no—
419#117D3211yescharacteristic, complemented
420C2×C4⋊C4—181no—
421C2×C22⋊C4—181no—
422C2×C42—92no—
423#104—38no—
424#104—98no—
425C23×C3—21no—
426C23×C3—62no—
427C23×C3D3×D412yes—
428C22×D3—22no—
429C22×D3—32no—
430C22×D3—32no—
431C22×D3—32no—
432C22×D3—32no—
433C22×D3—32no—
434C22×D3—32no—
435C22×D3—61no—
436C22×D3—61no—
437C22×D3—61no—
438C22×D3—61no—
439C22×D3—61no—
440C22×D3—61no—
441C22×D3—64no—
442C22×D3—64no—
443C22×D3—128no—
444C22×D3—124no—
445C22×D3—124no—
446C3×Q8—34no—
447C3×Q8—62no—
448C3×D4—34no—
449C3×D4—64no—
450C3×D4—64no—
451C3×D4—62no—
452C2×C3×C4—24no—
453C2×C3×C4—24no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—62no—
461C2×C3×C4—64no—
462C2×C3×C4—64no—
463C2×C3×C4C2×C4×D312yes—
464C2×C3×C4C2×C4×D312yes—
465C2×C3×C4D3×D412yes—
466C2×C3×C4D3×D412yes—
467C2×C3×C4D3×D412yes—
468C2×C3×C4C23×D312yes—
469#67—24no—
470#67—24no—
471#67—64no—
472#67—64no—
473#67—64no—
474#67—64no—
475C2×Dic3—22no—
476C2×Dic3—32no—
477C2×Dic3—32no—
478C2×Dic3—32no—
479C2×Dic3—32no—
480C2×Dic3—32no—
481C2×Dic3—32no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—61no—
485C2×Dic3—61no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—64no—
489C2×Dic3—64no—
490C2×Dic3—64no—
491C2×Dic3—64no—
492D12—22no—
493D12—64no—
494D12—64no—
495D12C2×C4×D314yes—
496C4×D3—24no—
497C4×D3—24no—
498C4×D3—32no—
499C4×D3—32no—
500C4×D3—32no—
501C4×D3—32no—
502C4×D3—32no—
503C4×D3—32no—
504C4×D3—32no—
505C4×D3—32no—
506C4×D3—32no—
507C4×D3—32no—
508C4×D3—32no—
509C4×D3—32no—
510C4×D3—32no—
511C4×D3—32no—
512C4×D3—32no—
513C4×D3—32no—
514C4×D3—61no—
515C4×D3—61no—
516C4×D3—61no—
517C4×D3—61no—
518C4×D3—61no—
519C4×D3—61no—
520C4×D3—61no—
521C4×D3—61no—
522C4×D3—61no—
523C4×D3—61no—
524C4×D3—61no—
525C4×D3—61no—
526C4×D3—61no—
527C4×D3—61no—
528C4×D3—61no—
529C4×D3—61no—
530C4×D3—64no—
531C4×D3—64no—
532C4×D3—64no—
533C4×D3—64no—
534C4×D3—128no—
535C4×D3—128no—
536Dic6—22no—
537Dic6—64no—
538Dic6—64no—
539Dic6C2×C4×D314yes—
540C3×C8—64no—
541C3⋊C8—24no—
542C2×C32—21no—
543C2×C32—21no—
544C2×C32—21no—
545C2×C32C22×C22⋊C411yescharacteristic
546C3⋊D3—21no—
547C3⋊D3—21no—
548C3⋊D3—21no—
549C3⋊D3#42112yescomplemented
550C3×D3—44no—
551C24—91no—
552C24—181no—
553#41—34no—
554#41—34no—
555#41—62no—
556#41—62no—
557#41—94no—
558#41—94no—
559#41—182no—
560#41—182no—
561#41—182no—
562#41—182no—
563#41—182no—
564#41—182no—
565#41—182no—
566#41—182no—
567#41—182no—
568#41—182no—
569C2×Q8—32no—
570C2×Q8—92no—
571C2×Q8—92no—
572C2×Q8—181no—
573C2×Q8—181no—
574C2×Q8—181no—
575C2×D4—32no—
576C2×D4—62no—
577C2×D4—92no—
578C2×D4—92no—
579C2×D4—182no—
580C2×D4—181no—
581C2×D4—181no—
582C2×D4—181no—
583C2×D4—182no—
584C2×D4—182no—
585C2×D4—182no—
586C2×D4—182no—
587C22×C4—62no—
588C22×C4—91no—
589C22×C4—91no—
590C22×C4—91no—
591C22×C4—91no—
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—91no—
597C22×C4—91no—
598C22×C4—91no—
599C22×C4—91no—
600C22×C4—91no—
601C22×C4—182no—
602C22×C4—182no—
603C22×C4—182no—
604C22×C4—182no—
605C22×C4—182no—
606C22×C4—181no—
607C22×C4—182no—
608C22×C4C2×D3211yescharacteristic
609M16—34no—
610M16—62no—
611M16—182no—
612M16—182no—
613C2×C8—62no—
614C2×C8—182no—
615C2×C8—182no—
616C4⋊C4—21no—
617C4⋊C4—182no—
618C4⋊C4—181no—
619C22⋊C4—21no—
620C22⋊C4—182no—
621C22⋊C4—181no—
622C42—92no—
623C42—182no—
624C42C2×D3212yescomplemented
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—42no—
629C22×C3—42no—
630C22×C3—64no—
631C22×C3—124no—
632C22×C3D3×C22⋊C412yes—
633C22×C3D3×C22⋊C412yes—
634C22×C3C2×D3×D412yes—
635C2×D3—24no—
636C2×D3—32no—
637C2×D3—32no—
638C2×D3—32no—
639C2×D3—32no—
640C2×D3—44no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—64no—
646C2×D3—64no—
647C2×D3—64no—
648C2×D3—64no—
649C2×D3—122no—
650C2×D3—122no—
651C2×D3—128no—
652C2×D3—128no—
653C2×D3—122no—
654C2×D3—122no—
655C2×D3—122no—
656C2×D3—122no—
657C2×D3—122no—
658C2×D3—122no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—44no—
664C3×C4—44no—
665C3×C4—64no—
666C3×C4D3×C22⋊C412yes—
667C3×C4D3×C22⋊C412yes—
668C3×C4C22×C4×D312yes—
669C3×C4C2×D3×D412yes—
670Dic3—24no—
671Dic3—32no—
672Dic3—32no—
673Dic3—32no—
674Dic3—32no—
675Dic3—61no—
676Dic3—61no—
677Dic3—61no—
678Dic3—61no—
679Dic3—124no—
680Dic3—124no—
681C32C2×#42111yescharacteristic, complemented, Sylow
682C23—62no—
683C23—91no—
684C23—91no—
685C23—91no—
686C23—91no—
687C23—91no—
688C23—91no—
689C23—182no—
690C23—182no—
691C23—362no—
692C23—364no—
693C23#381111yescharacteristic
694Q8—34no—
695Q8—62no—
696Q8—182no—
697Q8—182no—
698D4—34no—
699D4—64no—
700D4—64no—
701D4—62no—
702D4—184no—
703D4—184no—
704D4—182no—
705D4—182no—
706C2×C4—22no—
707C2×C4—62no—
708C2×C4—64no—
709C2×C4—64no—
710C2×C4—91no—
711C2×C4—91no—
712C2×C4—91no—
713C2×C4—91no—
714C2×C4—91no—
715C2×C4—91no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—91no—
721C2×C4—91no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—91no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—91no—
729C2×C4—91no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—182no—
733C2×C4—182no—
734C2×C4—184no—
735C2×C4—184no—
736C2×C4—182no—
737C2×C4—364no—
738C2×C4C4×D3211yescharacteristic
739C2×C4C4×D3211yescharacteristic
740C2×C4#380211yescharacteristic
741C2×C4#380211yescharacteristic
742C2×C4#381111yescharacteristic
743C2×C4C22×D3211yescharacteristic
744C8—64no—
745C2×C3—22no—
746C2×C3—22no—
747C2×C3—22no—
748C2×C3—22no—
749C2×C3—21no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3—124no—
753C2×C3C2×D3×C22⋊C412yes—
754D3—34no—
755D3—44no—
756D3—62no—
757D3—62no—
758D3—62no—
759D3—62no—
760D3—62no—
761D3—121no—
762D3—121no—
763C22—41no—
764C22—64no—
765C22—91no—
766C22—91no—
767C22—91no—
768C22—91no—
769C22—124no—
770C22—182no—
771C22—182no—
772C22—182no—
773C22—361no—
774C22—361no—
775C22—361no—
776C22—364no—
777C22—364no—
778C22#6392111yescharacteristic
779C22#6392111yescharacteristic
780C22C2×#381111yescharacteristic
781C4—42no—
782C4—64no—
783C4—91no—
784C4—91no—
785C4—91no—
786C4—91no—
787C4—362no—
788C4#6392111yescharacteristic
789C4#6392111yescharacteristic
790C4C2×C4×D3211yescharacteristic
791C4C2×#380211yescharacteristic
792C3—21no—
793C3D3×#42112yescomplemented
794C2—21no—
795C2—21no—
796C2—21no—
797C2—92no—
798C2—124no—
799C2—181no—
800C2—181no—
801C2—181no—
802C2C2×#6392111yescharacteristic
subgroupG/H
centerC4C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC2×C32C22×C22⋊C4
prime radicalC2×#64306C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32C2×#421
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3⋊D3×#117C2semidirect
3. C2×#63818C2semidirect
4. C3×#5005C2semidirect
5. #10591110C2semidirect
6. #10590394C2semidirect
7. #10590393C2semidirect
17. #64306C4semidirect
18. #64306C4semidirect
21. C2×#3802C4semidirect
24. C2×#3797C4semidirect
25. C2×#3796C4semidirect
26. C32×#117C22semidirect
27. #64135C22semidirect
32. #64081C22semidirect
33. C42×C3⋊D3C22semidirect
34. C2×C3×#208C22semidirect
38. #63818C22semidirect
39. #63818C22semidirect
41. C3×#805C22semidirect
42. #63568C22semidirect
50. #5005D3semidirect
73. C3×#235C2×C4semidirect
75. C2×C3×D12C2×C4semidirect
77. C2×C3×Dic6C2×C4semidirect
94. #3802C2×C4semidirect
106. #3797C2×C4semidirect
110. #3796C2×C4semidirect
113. C32×C42C23semidirect
119. C4×C3⋊Dic3C23semidirect
121. C3×#208C23semidirect
150. C3×#117C2×D3semidirect
153. C2×#208C2×D3semidirect
175. #805C2×D3semidirect
295. #235C4×D3semidirect
298. C2×D12C4×D3semidirect
333. C2×Dic6C4×D3semidirect
342. C3×C42C22×D3semidirect
356. #208C22×D3semidirect
419. #117D32semidirect
549. C3⋊D3#421semidirect
624. C42C2×D32semidirect
681. C32C2×#421semidirect
793. C3D3×#421semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C3⋊D3×#1172
C2×#638182
C3×#50052
#105911102
#105903942
#105903932
D3×#4213