Finite Group Databasebeta

← #11903778

Subgroups — #11903778

Order 1152.

2291 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic
2C3×#5517C212yesmaximal, complemented
3#10595050C211yesmaximal, characteristic, complemented
4C2×C4×#627C211yesmaximal, characteristic, complemented
5#10594954C212yesmaximal
6#10594484C211yesmaximal, characteristic, complemented
7#10594470C212yesmaximal, complemented
8#10594379C211yesmaximal, characteristic, complemented
9#10594324C211yesmaximal, characteristic, complemented
10#10594318C212yesmaximal, complemented
11#10594313C211yesmaximal, characteristic, complemented
12#10594168C212yesmaximal, complemented
13#10594141C214yesmaximal, complemented
14#10594072C212yesmaximal, complemented
15#10593935C214yesmaximal, complemented
16C4×#3797C212yesmaximal, complemented
17#10593882C212yesmaximal, complemented
18#86277—32nomaximal
19C2×#3828C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C2×#3797C2212yes—
22C32×#117C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24#64102C2211yescharacteristic
25#64102C2211yescharacteristic
26#64096C2211yescharacteristic
27#64096C2211yescharacteristic
28#64090C2212yes—
29#64090C2212yes—
30#64081C2212yes—
31C42×C3⋊D3C2212yes—
32C3×#926C2212yes—
33C2×C3×C4×Dic3C2212yes—
34C3×#890C2212yes—
35C3×#890C2212yes—
36C3×#888C2212yes—
37C3×#888C2212yes—
38C3×#878C2214yes—
39C3×#878C2214yes—
40C3×C4×Dic6C2214yes—
41C3×C4×Dic6C2214yes—
42#63982C2212yes—
43#63982C2212yes—
44C2×#3724C2211yescharacteristic
45C2×Dic3⋊Dic3C2212yes—
46#63952C2214yes—
47#63952C2214yes—
48#63919C2211yescharacteristic
49#63919C2212yes—
50#63919C2211yescharacteristic
51C4×#627C2211yescharacteristic
52C4×#627C2212yes—
53C4×#627C2211yescharacteristic
54C4×#627C2211yescharacteristic
55C4×#627C2212yes—
56C4×#627C2211yescharacteristic
57C4×#627C2212yes—
58C4×#627C2212yes—
59#63900C2212yes—
60#63895C2214yes—
61#63895C2214yes—
62#63894C2212yes—
63#63894C2212yes—
64#63888C2214yes—
65#63888C2214yes—
66#63883C2214yes—
67C4×#624C2214yes—
68#63874C2214yes—
69#63873C2212yes—
70#63872C2212yes—
71#63871C2214yes—
72#63870C2214yes—
73#63865C2212yes—
74#63865C2212yes—
75#63847C2214yes—
76#63847C2214yes—
77#63844C2212yes—
78#63844C2212yes—
79#63843C2214yes—
80#63839C2214yes—
81#63839C2214yes—
82#63838C2212yes—
83#63838C2212yes—
84C3×#533—32no—
85#5730—32no—
86#5727—32no—
87#5722—32no—
88#5721—32no—
89#5690—32no—
90#5690—32no—
91#5685—32no—
92#5685—32no—
93#5636—34no—
94#5636—34no—
95#5635—34no—
96#5632—34no—
97#5578—34no—
98#5578—34no—
99#5578—34no—
100C4×D3×Q8—34no—
101#5522—32no—
102#5522—32no—
103#5522—61no—
104#5517—32no—
105#5517D312yescomplemented
106C4×#235—32no—
107C2×C4×Dic6—32no—
108C22×C32×C4C2311yescharacteristic
109C2×#638C2312yes—
110C22×C3⋊Dic3C2311yescharacteristic
111C22×C3⋊Dic3C2311yescharacteristic
112#3828Q818yescomplemented
113C2×C4⋊(C3⋊D3)C2311yescharacteristic
114C2×C4×C3⋊D3C2312yes—
115C2×C4×C3⋊D3C2312yes—
116C2×C4×C3⋊D3C2312yes—
117C2×#634C2311yescharacteristic
118C22×C3×Dic3C2312yes—
119C22×C3×Dic3C2312yes—
120C2×C3×Dic6C2314yes—
121C2×C3×Dic6C2314yes—
122C2×#627—24no—
123C2×#627C2312yes—
124C2×#627C2312yes—
125C2×#627C2311yescharacteristic
126C2×#627C2312yes—
127C2×#627C2311yescharacteristic
128C2×#624C2314yes—
129C2×#624C2314yes—
130#3797—28no—
131C32×C4⋊C4C2311yescharacteristic
132C32×C4⋊C4C2311yescharacteristic
133C32×C22⋊C4C2312yes—
134C32×C42C2312yes—
135#3752C2312yes—
136#3752C2312yes—
137#3750C2312yes—
138#3750C2312yes—
139C4×C3⋊Dic3C2311yescharacteristic
140C4×C3⋊Dic3C2312yes—
141C4×C3⋊Dic3C2312yes—
142C4×C3⋊Dic3C2311yescharacteristic
143C4×C3⋊Dic3C2311yescharacteristic
144C4×C3⋊Dic3C2311yescharacteristic
145C3×#217C2314yes—
146C3×C4⋊Dic3C2314yes—
147C3×C4⋊Dic3C2314yes—
148C3×C4⋊Dic3C2312yes—
149C3×C4⋊Dic3C2312yes—
150C3×Dic3⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×C4×Dic3C2312yes—
155C3×C4×Dic3C2312yes—
156C3×C4×Dic3C2312yes—
157C3×C4×Dic3C2312yes—
158C3×C4×Dic3C2314yes—
159#3724C2311yescharacteristic
160#3724C2312yes—
161#3724C2314yes—
162#3724C2314yes—
163#3724C2312yes—
164#3724C2312yes—
165#3724C2311yescharacteristic
166Dic3⋊Dic3C2312yes—
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2312yes—
169Dic3⋊Dic3C2314yes—
170Dic3⋊Dic3C2312yes—
171Dic3⋊Dic3C2312yes—
172#3722C2314yes—
173#3722C2314yes—
174Dic32C2314yes—
175Dic32C2314yes—
176Q8×#41—91noSylow
177C2×D3×Q8—34no—
178C2×#235—32no—
179C2×#235—61no—
180C22×Dic6—32no—
181C3×C4⋊Q8—32no—
182C3×C4⋊Q8—32no—
183C3×#125—32no—
184C3×#125—32no—
185C3×C22⋊Q8—34no—
186C3×C22⋊Q8—34no—
187C3×C4×Q8—34no—
188C3×C4×Q8—34no—
189C3×#117—21no—
190C3×#117—32no—
191C3×#117C2×D312yes—
192C2×C3×C42—32no—
193#946—34no—
194#946—34no—
195#946—34no—
196Q8×Dic3—34no—
197#944—34no—
198#944—34no—
199#944—34no—
200C4×#67—34no—
201C4×#67—34no—
202#926C2×D312yes—
203C2×C4⋊Dic3—32no—
204C2×Dic3⋊C4—32no—
205C2×Dic3⋊C4—32no—
206C2×C4×Dic3—32no—
207C2×C4×Dic3—61no—
208C2×C4×Dic3C2×D312yes—
209#897—34no—
210#897—34no—
211#897—34no—
212#896—34no—
213#896—34no—
214#896—34no—
215#896—34no—
216#896—34no—
217#896—34no—
218#893—32no—
219#893—32no—
220#893—32no—
221#893—32no—
222#893—61no—
223#893—61no—
224D3×C4⋊C4—34no—
225D3×C4⋊C4—34no—
226D3×C4⋊C4—34no—
227#890—32no—
228#890—32no—
229#890C2×D312yes—
230#890C2×D312yes—
231#889—34no—
232#889—34no—
233#889—34no—
234#889—34no—
235#889—34no—
236#889—34no—
237#888—34no—
238#888—34no—
239#888—34no—
240#888—32no—
241#888—32no—
242#888C2×D312yes—
243#888C2×D312yes—
244#887—34no—
245#887—32no—
246#887—32no—
247#887—34no—
248#887—34no—
249#887—32no—
250#887—32no—
251#887—61no—
252#887—61no—
253#67⋊C4—34no—
254#67⋊C4—34no—
255#67⋊C4—34no—
256#67⋊C4—34no—
257#67⋊C4—62no—
258#67⋊C4—62no—
259#878—34no—
260#878—34no—
261#878C2×D314yes—
262#878C2×D314yes—
263C4×D12—32no—
264C4×D12—32no—
265#872—34no—
266#872—34no—
267#872—34no—
268#872—62no—
269C42×D3—34no—
270C42×D3—34no—
271C42×D3—34no—
272C42×D3—62no—
273C4×Dic6—32no—
274C4×Dic6—32no—
275C4×Dic6—32no—
276C4×Dic6—32no—
277C4×Dic6—32no—
278C4×Dic6—32no—
279C4×Dic6—32no—
280C4×Dic6—32no—
281C4×Dic6—32no—
282C4×Dic6—32no—
283C4×Dic6—34no—
284C4×Dic6—34no—
285C4×Dic6C2×D314yes—
286C4×Dic6C2×D314yes—
287C23×C32C2411yescharacteristic
288C22×C3⋊D3C2412yes—
289C2×C32×C4C2×Q814yescomplemented
290C2×C32×C4C2412yes—
291C2×C32×C4C2412yes—
292C2×C32×C4C2411yescharacteristic
293C2×C32×C4C2411yescharacteristic
294#638C2×Q818yescomplemented
295C2×C3⋊Dic3—22no—
296C2×C3⋊Dic3—41no—
297C2×C3⋊Dic3C2411yescharacteristic
298C2×C3⋊Dic3C2411yescharacteristic
299C2×C3⋊Dic3C2411yescharacteristic
300C2×C3⋊Dic3C2412yes—
301C2×C3⋊Dic3C2411yescharacteristic
302C4⋊(C3⋊D3)C2×Q814yescomplemented
303C4×C3⋊D3—24no—
304C4×C3⋊D3—42no—
305C4×C3⋊D3C2×Q818yescomplemented
306#634C2×Q814yescomplemented
307C2×C3×Dic3—24no—
308C2×C3×Dic3—42no—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2414yes—
311C2×C3×Dic3C2414yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2412yes—
314C2×C3×Dic3C2412yes—
315C3×Dic6—28no—
316C3×Dic6—44no—
317#627—24no—
318#627—22no—
319#627—24no—
320#627—42no—
321#627#4114yescomplemented
322#624—28no—
323#624—44no—
324Q82—91no—
325#557—91no—
326#557—92no—
327#554—94no—
328#554—92no—
329#554—91no—
330#554—92no—
331D4×Q8—92no—
332D4×Q8—91no—
333#533—32no—
334#533—91no—
335#533—94no—
336#533—92no—
337C4×#41—92no—
338C4×#41—91no—
339C2×C4×Q8—91no—
340C2×C4×Q8—92no—
341C2×C3×Q8—34no—
342C2×C3×Q8—34no—
343C22×C3×C4—21no—
344C22×C3×C4—32no—
345C22×C3×C4—32no—
346C22×C3×C4C22×D312yes—
347C2×#67—34no—
348C2×#67—62no—
349C22×Dic3—32no—
350C22×Dic3—32no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3C22×D312yes—
354C22×Dic3C22×D312yes—
355D3×Q8—616no—
356#235—316no—
357#235—68no—
358C2×D12—32no—
359C2×D12—61no—
360C2×C4×D3—34no—
361C2×C4×D3—34no—
362C2×C4×D3—34no—
363C2×C4×D3—34no—
364C2×C4×D3—34no—
365C2×C4×D3—34no—
366C2×C4×D3—34no—
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×Dic6—32no—
371C2×Dic6—32no—
372C2×Dic6—32no—
373C2×Dic6—32no—
374C2×Dic6—32no—
375C2×Dic6—34no—
376C2×Dic6—34no—
377C2×Dic6—61no—
378C2×Dic6—68no—
379C2×Dic6C22×D314yes—
380C2×Dic6C22×D314yes—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—32no—
384C3×C4⋊C4—32no—
385C3×C4⋊C4—34no—
386C3×C4⋊C4—34no—
387C3×C4⋊C4—34no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4C22×D312yes—
392C3×C4⋊C4C22×D312yes—
393C3×C22⋊C4—22no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4C22×D314yes—
396C3×C42—22no—
397C3×C42—32no—
398C3×C42—32no—
399C3×C42—32no—
400C3×C42—34no—
401C3×C42—32no—
402C3×C42C22×D314yes—
403#217C22×D314yes—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—34no—
408(C2×D3)⋊C4—34no—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412C4⋊Dic3—32no—
413C4⋊Dic3—32no—
414C4⋊Dic3—32no—
415C4⋊Dic3—32no—
416C4⋊Dic3—34no—
417C4⋊Dic3—34no—
418C4⋊Dic3C22×D312yes—
419C4⋊Dic3C22×D312yes—
420C4⋊Dic3C22×D314yes—
421C4⋊Dic3C22×D314yes—
422Dic3⋊C4—34no—
423Dic3⋊C4—34no—
424Dic3⋊C4—32no—
425Dic3⋊C4—32no—
426Dic3⋊C4—32no—
427Dic3⋊C4—32no—
428Dic3⋊C4—32no—
429Dic3⋊C4—32no—
430Dic3⋊C4—32no—
431Dic3⋊C4—32no—
432Dic3⋊C4—34no—
433Dic3⋊C4—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—34no—
440Dic3⋊C4—62no—
441Dic3⋊C4—62no—
442Dic3⋊C4C22×D314yes—
443Dic3⋊C4C22×D314yes—
444Dic3⋊C4C22×D314yes—
445Dic3⋊C4C22×D314yes—
446C4×Dic3—32no—
447C4×Dic3—32no—
448C4×Dic3—32no—
449C4×Dic3—32no—
450C4×Dic3—34no—
451C4×Dic3—34no—
452C4×Dic3—34no—
453C4×Dic3—34no—
454C4×Dic3—34no—
455C4×Dic3—34no—
456C4×Dic3—61no—
457C4×Dic3—62no—
458C4×Dic3—62no—
459C4×Dic3—61no—
460C4×Dic3—61no—
461C4×Dic3—61no—
462C4×Dic3C22×D312yes—
463C4×Dic3C22×D314yes—
464C4×Dic3C22×D312yes—
465C4×Dic3C22×D312yes—
466C4×Dic3C22×D312yes—
467C22×C32—21no—
468C22×C32—21no—
469C22×C32C22×Q812yes—
470C22×C32C2511yescharacteristic
471C2×C3⋊D3—22no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3C22×Q814yes—
474C32×C4—22no—
475C32×C4—22no—
476C32×C4C22×Q812yes—
477C32×C4C22×Q812yes—
478C3⋊Dic3—21no—
479C3⋊Dic3—21no—
480C3⋊Dic3—21no—
481C3⋊Dic3C22×Q814yes—
482C3⋊Dic3C2×#4112yes—
483C3×Dic3—24no—
484C3×Dic3—22no—
485C3×Dic3—22no—
486C3×Dic3—24no—
487C3×Dic3—22no—
488C3×Dic3C2×#4114yes—
489C2×#41—91no—
490C22×Q8—91no—
491C22×Q8—92no—
492C4⋊Q8—32no—
493C4⋊Q8—32no—
494C4⋊Q8—91no—
495C4⋊Q8—92no—
496C4⋊Q8—91no—
497C4⋊Q8—94no—
498C4⋊Q8—94no—
499C4⋊Q8—92no—
500#125—32no—
501#125—32no—
502#125—94no—
503#125—94no—
504#125—94no—
505#125—92no—
506C22⋊Q8—34no—
507C22⋊Q8—34no—
508C22⋊Q8—92no—
509C22⋊Q8—92no—
510C22⋊Q8—92no—
511C22⋊Q8—92no—
512C22⋊Q8—94no—
513C22⋊Q8—94no—
514C22⋊Q8—94no—
515C22⋊Q8—94no—
516C22⋊Q8—94no—
517C4×Q8—34no—
518C4×Q8—34no—
519C4×Q8—91no—
520C4×Q8—92no—
521C4×Q8—91no—
522C4×Q8—92no—
523C4×Q8—91no—
524C4×Q8—91no—
525C4×Q8—92no—
526C4×Q8—92no—
527C4×Q8—92no—
528C4×Q8—92no—
529C4×Q8—92no—
530C4×Q8—92no—
531C4×Q8—94no—
532C4×Q8—91no—
533C4×Q8—91no—
534C4×D4—92no—
535C4×D4—92no—
536C4×D4—94no—
537C4×D4—94no—
538C4×D4—91no—
539C4×D4—91no—
540C4×D4—92no—
541C4×D4—92no—
542#117—32no—
543#117—94no—
544#117—92no—
545#117D3211yescharacteristic
546C2×C4⋊C4—94no—
547C2×C4⋊C4—92no—
548C2×C4⋊C4—91no—
549C2×C4⋊C4—92no—
550C2×C42—32no—
551C2×C42—94no—
552C2×C42—91no—
553C2×C42—92no—
554C23×C3—21no—
555C23×C3C23×D312yes—
556C22×D3—34no—
557C22×D3—62no—
558C3×Q8—68no—
559C3×Q8—124no—
560C2×C3×C4—21no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—21no—
564C2×C3×C4—24no—
565C2×C3×C4—32no—
566C2×C3×C4—32no—
567C2×C3×C4—34no—
568C2×C3×C4—34no—
569C2×C3×C4—32no—
570C2×C3×C4—32no—
571C2×C3×C4—64no—
572C2×C3×C4—122no—
573C2×C3×C4D3×Q818yescomplemented
574C2×C3×C4C23×D314yes—
575C2×C3×C4C23×D314yes—
576C2×C3×C4C23×D312yes—
577C2×C3×C4C23×D312yes—
578#67—316no—
579#67—68no—
580C2×Dic3—24no—
581C2×Dic3—34no—
582C2×Dic3—32no—
583C2×Dic3—32no—
584C2×Dic3—32no—
585C2×Dic3—32no—
586C2×Dic3—42no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—62no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—64no—
593C2×Dic3—122no—
594C2×Dic3—122no—
595C2×Dic3—122no—
596C2×Dic3C23×D312yes—
597C2×Dic3C23×D314yes—
598C2×Dic3C23×D314yes—
599C2×Dic3C23×D312yes—
600C2×Dic3C23×D312yes—
601C2×Dic3C23×D312yes—
602D12—38no—
603D12—64no—
604C4×D3—316no—
605C4×D3—68no—
606C4×D3—68no—
607C4×D3—68no—
608C4×D3—68no—
609C4×D3—124no—
610C4×D3—124no—
611C4×D3—124no—
612C4×D3—124no—
613C4×D3—124no—
614Dic6—28no—
615Dic6—38no—
616Dic6—38no—
617Dic6—44no—
618Dic6—64no—
619Dic6—64no—
620Dic6—68no—
621Dic6—64no—
622Dic6—64no—
623Dic6—124no—
624C2×C32—22no—
625C2×C32C23×Q811yescharacteristic
626C2×C32C22×#4111yescharacteristic
627C2×C32#58511yescharacteristic
628C3⋊D3—24no—
629#41—98no—
630C2×Q8—34no—
631C2×Q8—34no—
632C2×Q8—91no—
633C2×Q8—92no—
634C2×Q8—91no—
635C2×Q8—92no—
636C2×Q8—92no—
637C2×Q8—91no—
638C2×Q8—184no—
639C2×Q8—188no—
640C2×D4—92no—
641C2×D4—91no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—94no—
645C22×C4—94no—
646C22×C4—92no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—92no—
650C22×C4—92no—
651C22×C4C2×D3211yescharacteristic
652C4⋊C4—34no—
653C4⋊C4—34no—
654C4⋊C4—34no—
655C4⋊C4—32no—
656C4⋊C4—32no—
657C4⋊C4—34no—
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—91no—
661C4⋊C4—92no—
662C4⋊C4—92no—
663C4⋊C4—92no—
664C4⋊C4—92no—
665C4⋊C4—94no—
666C4⋊C4—91no—
667C4⋊C4—92no—
668C4⋊C4—92no—
669C4⋊C4—94no—
670C4⋊C4—94no—
671C4⋊C4—92no—
672C4⋊C4—94no—
673C4⋊C4—92no—
674C4⋊C4—92no—
675C4⋊C4C2×D3211yescharacteristic
676C4⋊C4C2×D3211yescharacteristic
677C22⋊C4—34no—
678C22⋊C4—94no—
679C22⋊C4—94no—
680C22⋊C4—92no—
681C22⋊C4—92no—
682C22⋊C4C2×D3212yes—
683C42—32no—
684C42—32no—
685C42—32no—
686C42—32no—
687C42—34no—
688C42—94no—
689C42—94no—
690C42—92no—
691C42—91no—
692C42—92no—
693C42—91no—
694C42—91no—
695C42—91no—
696C42C2×D3212yes—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—21no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3C2×D3×Q814yes—
704C22×C3C24×D312yes—
705C2×D3—38no—
706C2×D3—64no—
707C2×D3—64no—
708C2×D3—64no—
709C2×D3—122no—
710C2×D3—122no—
711C3×C4—24no—
712C3×C4—24no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—34no—
716C3×C4—42no—
717C3×C4—42no—
718C3×C4—62no—
719C3×C4—64no—
720C3×C4—64no—
721C3×C4—62no—
722C3×C4—62no—
723C3×C4C2×D3×Q814yes—
724C3×C4C2×D3×Q814yes—
725Dic3—24no—
726Dic3—22no—
727Dic3—22no—
728Dic3—24no—
729Dic3—22no—
730Dic3—38no—
731Dic3—34no—
732Dic3—64no—
733Dic3—62no—
734Dic3—62no—
735Dic3—62no—
736Dic3—62no—
737Dic3—62no—
738Dic3—121no—
739Dic3—121no—
740Dic3D3×#4114yes—
741C32Q8×#4111yescharacteristic, complemented, Sylow
742C23—92no—
743C23C22×D3211yescharacteristic
744Q8—68no—
745Q8—94no—
746Q8—94no—
747Q8—124no—
748Q8—184no—
749Q8—182no—
750Q8—184no—
751Q8—362no—
752D4—98no—
753D4—94no—
754C2×C4—32no—
755C2×C4—32no—
756C2×C4—32no—
757C2×C4—32no—
758C2×C4—34no—
759C2×C4—34no—
760C2×C4—64no—
761C2×C4—92no—
762C2×C4—91no—
763C2×C4—98no—
764C2×C4—91no—
765C2×C4—91no—
766C2×C4—91no—
767C2×C4—122no—
768C2×C4—184no—
769C2×C4—188no—
770C2×C4—182no—
771C2×C4—362no—
772C2×C4—364no—
773C2×C4—361no—
774C2×C4#379714yescomplemented
775C2×C4C22×D3212yes—
776C2×C4C22×D3212yes—
777C2×C4C22×D3211yescharacteristic
778C2×C4C22×D3211yescharacteristic
779C2×C3—24no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—42no—
784C2×C3C22×D3×Q812yes—
785C2×C3C2×D3×#4112yes—
786C2×C3#596412yes—
787D3—68no—
788D3—124no—
789C22—21no—
790C22—21no—
791C22—94no—
792C22—182no—
793C22—182no—
794C22C2×#379712yes—
795C22C23×D3211yescharacteristic
796C4—22no—
797C4—22no—
798C4—34no—
799C4—62no—
800C4—64no—
801C4—62no—
802C4—62no—
803C4—64no—
804C4—94no—
805C4—92no—
806C4—181no—
807C4—181no—
808C4—181no—
809C4C2×#379712yes—
810C4C2×#379712yes—
811C3—21no—
812C3#8627712yescomplemented
813C2—22no—
814C2—184no—
815C2C22×#379711yescharacteristic
816C2D32×#4111yescharacteristic
817C2#1059669511yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC32×#117C22
prime radicalC2×#3828C22
hypercenter#117D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5517C2semidirect
3. #10595050C2semidirect
4. C2×C4×#627C2semidirect
6. #10594484C2semidirect
7. #10594470C2semidirect
8. #10594379C2semidirect
9. #10594324C2semidirect
10. #10594318C2semidirect
11. #10594313C2semidirect
12. #10594168C2semidirect
13. #10594141C2semidirect
14. #10594072C2semidirect
15. #10593935C2semidirect
16. C4×#3797C2semidirect
17. #10593882C2semidirect
105. #5517D3semidirect
112. #3828Q8semidirect
289. C2×C32×C4C2×Q8semidirect
294. #638C2×Q8semidirect
302. C4⋊(C3⋊D3)C2×Q8semidirect
305. C4×C3⋊D3C2×Q8semidirect
306. #634C2×Q8semidirect
321. #627#41semidirect
573. C2×C3×C4D3×Q8semidirect
741. C32Q8×#41semidirect
774. C2×C4#3797semidirect
812. C3#86277semidirect

Maximal subgroups

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

subgroupindex
#105959932
C3×#55172
#105950502
C2×C4×#6272
#105949542
#105944842
#105944702
#105943792
#105943242
#105943182
#105943132
#105941682
#105941412
#105940722
#105939352
C4×#37972
#105938822
#862773