Finite Group Databasebeta

← #11906189

Subgroups — #11906189

Order 1152.

2311 conjugacy classes of subgroups.

The subgroup lattice has 975 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596049C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C3×Q8×D12C211yesmaximal, characteristic, complemented
4D3×#946C212yesmaximal, complemented
5#10595400C212yesmaximal, complemented
6#10594635C214yesmaximal, complemented
7D3×#897C212yesmaximal, complemented
8#10594535C214yesmaximal, complemented
9#10594532C212yesmaximal, complemented
10#10593996C212yesmaximal
11C4×#3802C211yesmaximal, characteristic
12#10593956C211yesmaximal, characteristic, complemented
13#10593956C212yesmaximal, complemented
14#10593941C212yesmaximal, complemented
15#10593904C211yesmaximal, characteristic, complemented
16#10593866C211yesmaximal, characteristic, complemented
17#10593855C212yesmaximal, complemented
18#86948—31nomaximal
19#86761—31nomaximal
20C2×C3×D3×Q8C2212yescomplemented
21C2×#3802C2211yescharacteristic
22C2×C4×D32C2212yes—
23C2×D3×Dic6C2212yescomplemented
24C32×C4×Q8C2211yescharacteristic, complemented
25#64155C2211yescharacteristic
26#64153C2211yescharacteristic, complemented
27#64106C2211yescharacteristic
28#64105C2212yes—
29#64098C2212yescomplemented
30#64097C2211yescharacteristic, complemented
31#64081C2212yes—
32C42×C3⋊D3C2211yescharacteristic
33C4×#634C2211yescharacteristic, complemented
34C4×#634C2212yescomplemented
35C3×#946C2212yescomplemented
36C3×#897C2212yescomplemented
37C3×#897C2214yescomplemented
38C3×#896C2214yescomplemented
39C3×D3×C4⋊C4C2212yescomplemented
40C3×C4×D12C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2212yes—
44C3×#870C2212yescomplemented
45C3×#869C2212yescomplemented
46C3×#869C2211yescharacteristic, complemented
47C3×#869C2211yescharacteristic, complemented
48#63921C2212yes—
49D3×(C2×D3)⋊C4C2214yes—
50D3×(C2×D3)⋊C4C2214yes—
51#63919C2212yescomplemented
52#63902C2212yes—
53C4×#625C2212yes—
54#63900C2211yescharacteristic
55#63899C2214yescomplemented
56#63898C2212yes—
57#63898C2211yescharacteristic
58#63898C2212yes—
59#63898C2211yescharacteristic
60#63896C2214yescomplemented
61#63895C2214yes—
62#63893C2214yescomplemented
63D3×C4⋊Dic3C2214yescomplemented
64D3×C4⋊Dic3C2212yescomplemented
65#63888C2214yes—
66#63887C2214yescomplemented
67#63887C2214yescomplemented
68#63887C2214yescomplemented
69#63879C2214yes—
70#63879C2214yes—
71D3×Dic3⋊C4C2214yescomplemented
72#63872C2212yescomplemented
73#63872C2212yescomplemented
74#63871C2212yes—
75#63871C2212yes—
76#63857C2212yescomplemented
77#63857C2214yescomplemented
78#63856C2212yescomplemented
79#63851C2214yescomplemented
80#63849C2212yes—
81#63847C2214yescomplemented
82#63843C2212yescomplemented
83#63843C2212yescomplemented
84#63839C2214yescomplemented
85C3×#554—31no—
86C3×D4×Q8—31no—
87Q8×#67—32no—
88C2×#946—32no—
89#5730—31no—
90#5730—32no—
91#5729—32no—
92#5728—31no—
93#5728—31no—
94#5727—31no—
95#5690—32no—
96#5689—32no—
97#5636—34no—
98#5635—34no—
99#5635—32no—
100#5634—34no—
101#5634—34no—
102#5632—32no—
103D3×C22⋊Q8—32no—
104D3×C22⋊Q8—32no—
105#5579D311yescharacteristic, complemented
106#5578—31no—
107#5578—31no—
108#5578—61no—
109Q8×D12D311yescharacteristic, complemented
110#5545—32no—
111#5545—32no—
112C4×D3×D4—31no—
113C4×D3×D4—31no—
114#5543—32no—
115#5543—31no—
116#5539—32no—
117D4×Dic6—31no—
118#5511—32no—
119C2×#897—32no—
120C22×D32C2312yes—
121C2×C32×Q8C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×#634C2311yescharacteristic
126C2×#634C2312yes—
127C3×D3×Q8—44no—
128C2×C3×D12C2311yescharacteristic
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2314yes—
133C2×C3×C4×D3C2314yes—
134C2×C3×Dic6C2312yes—
135C2×C3×Dic6C2312yes—
136C2×C3×Dic6C2314yes—
137C2×#627C2314yes—
138C2×#625C2312yes—
139C2×#624C2312yes—
140C2×D3×Dic3C2314yes—
141C2×D3×Dic3C2312yes—
142C2×D3×Dic3C2312yes—
143C2×D3×Dic3C2314yes—
144#3802Q818yescomplemented
145C4×D32—44no—
146D3×Dic6—44no—
147C32×C4⋊C4C2311yescharacteristic
148C32×C4⋊C4C2312yes—
149C32×C42C2311yescharacteristic
150C32×C42C2312yes—
151#3752C2312yes—
152#3752C2312yes—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C4⋊(C3⋊Dic3)C2312yes—
155#3750C2312yes—
156#3750C2312yes—
157#3750C2312yes—
158#3750C2312yes—
159#3750C2312yes—
160C4×C3⋊Dic3C2311yescharacteristic
161C4×C3⋊Dic3C2312yes—
162C4×C3⋊Dic3C2311yescharacteristic
163C4×C3⋊Dic3C2311yescharacteristic
164C3×(C2×D3)⋊C4C2312yes—
165C3×(C2×D3)⋊C4C2314yes—
166C3×(C2×D3)⋊C4C2314yes—
167C3×(C2×D3)⋊C4C2312yes—
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2312yes—
170C3×C4⋊Dic3C2314yes—
171C3×C4⋊Dic3C2312yes—
172C3×C4⋊Dic3C2312yes—
173C3×C4⋊Dic3C2311yescharacteristic
174C3×C4⋊Dic3C2311yescharacteristic
175C3×Dic3⋊C4C2314yes—
176C3×Dic3⋊C4C2314yes—
177#3724C2312yes—
178#3724C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183#3722C2314yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2312yes—
188Dic32C2314yes—
189#3501—91noSylow
190C22×C3×Q8—32no—
191C2×D3×Q8—32no—
192C2×D3×Q8C2×D312yescomplemented
193C2×D3×D4—31no—
194C2×D3×D4—31no—
195C22×C4×D3—32no—
196C22×C4×D3—32no—
197C22×Dic6—32no—
198C3×C4⋊Q8—31no—
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8—32no—
201C3×#125—32no—
202C3×C22⋊Q8—32no—
203C3×C22⋊Q8—34no—
204C3×C22⋊Q8—34no—
205C3×C22⋊Q8—32no—
206C3×C4×Q8—21no—
207C3×C4×Q8C2×D311yescharacteristic, complemented
208C3×C4×Q8C2×D311yescharacteristic, complemented
209C3×C4×D4—31no—
210C3×C4×D4—32no—
211C3×C4×D4—31no—
212C3×C4×D4—32no—
213C2×C3×C4⋊C4—32no—
214#946—31no—
215#946—31no—
216#946—32no—
217#946—34no—
218#946—34no—
219#946—34no—
220#946—32no—
221#946—32no—
222#946—34no—
223#946—61no—
224#946C2×D312yescomplemented
225Q8×Dic3—32no—
226Q8×Dic3—32no—
227#944—31no—
228#944—31no—
229#944—34no—
230#944—61no—
231D4×Dic3—32no—
232D4×Dic3—31no—
233D4×Dic3—32no—
234D4×Dic3—31no—
235C4×#67—32no—
236C4×#67—32no—
237C4×#67—34no—
238C4×#67—34no—
239C2×(C2×D3)⋊C4—34no—
240C2×(C2×D3)⋊C4—34no—
241C2×C4⋊Dic3—34no—
242C2×C4⋊Dic3—32no—
243#924—32no—
244#924—34no—
245#924—32no—
246#924—34no—
247C2×Dic3⋊C4—34no—
248#897—32no—
249#897—34no—
250#897—32no—
251#897—32no—
252#897—31no—
253#897—31no—
254#897—34no—
255#897—34no—
256#897—61no—
257#897C2×D314yescomplemented
258#897C2×D312yescomplemented
259#896—34no—
260#896—34no—
261#896—32no—
262#896—32no—
263#896—34no—
264#896—34no—
265#896—34no—
266#896—62no—
267#896C2×D314yescomplemented
268#893—31no—
269#893—32no—
270#893—32no—
271#893—31no—
272#892—32no—
273#892—32no—
274D3×C4⋊C4—34no—
275D3×C4⋊C4—34no—
276D3×C4⋊C4—32no—
277D3×C4⋊C4—31no—
278D3×C4⋊C4—31no—
279D3×C4⋊C4C2×D312yescomplemented
280#890—32no—
281#890—32no—
282#890—32no—
283#890—32no—
284#889—32no—
285#889—32no—
286#889—34no—
287#889—34no—
288#889—62no—
289#888—34no—
290#888—31no—
291#888—31no—
292#888—32no—
293#888—32no—
294#888—61no—
295#887—32no—
296#887—32no—
297#67⋊C4—34no—
298#67⋊C4—34no—
299#67⋊C4—32no—
300#67⋊C4—32no—
301D3×C22⋊C4—34no—
302D3×C22⋊C4—34no—
303D3×C22⋊C4—32no—
304D3×C22⋊C4—32no—
305#878—34no—
306#878—34no—
307#878—34no—
308#878—34no—
309#878—34no—
310#878—34no—
311C4×D12C2×D312yes—
312C4×D12C2×D311yescharacteristic
313C4×D12C2×D311yescharacteristic
314C4×D12C2×D312yes—
315#872—32no—
316#872—32no—
317#872—62no—
318C42×D3—31no—
319C42×D3—31no—
320C42×D3—61no—
321#870C2×D312yescomplemented
322#869C2×D312yescomplemented
323#869C2×D311yescharacteristic, complemented
324#869C2×D311yescharacteristic, complemented
325C4×Dic6—32no—
326C4×Dic6—31no—
327C4×Dic6—31no—
328C4×Dic6—32no—
329C4×Dic6—61no—
330C4×Dic6—62no—
331C22×C3⋊D3C2411yescharacteristic
332C22×C3×D3C2412yes—
333C22×C3×D3C2412yes—
334C2×D32—42no—
335C2×D32—42no—
336C2×D32C2×Q818yescomplemented
337C32×Q8—22no—
338C2×C32×C4C2412yes—
339C2×C32×C4C2412yes—
340C2×C32×C4C2411yescharacteristic
341C2×C32×C4C2411yescharacteristic
342C2×C32×C4C2411yescharacteristic
343C2×C3⋊Dic3C2411yescharacteristic
344C2×C3⋊Dic3C2412yes—
345C2×C3⋊Dic3C2412yes—
346C2×C3⋊Dic3C2411yescharacteristic
347C2×C3⋊Dic3C2411yescharacteristic
348C4×C3⋊D3—22no—
349C4×C3⋊D3—41no—
350C4×C3⋊D3C2×Q814yescomplemented
351#634—22no—
352#634—42no—
353C2×C3×Dic3C2414yes—
354C2×C3×Dic3C2414yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2412yes—
357C3×D12C2×Q814yescomplemented
358C3×D12C2×Q814yescomplemented
359C3×C4×D3—24no—
360C3×C4×D3—24no—
361C3×C4×D3—44no—
362C3×C4×D3—44no—
363C3×Dic6—24no—
364C3×Dic6—42no—
365C3×Dic6—44no—
366#627—44no—
367#625C2×Q818yescomplemented
368#624—42no—
369D3×Dic3—44no—
370D3×Dic3—42no—
371D3×Dic3—42no—
372D3×Dic3—44no—
373#554—31no—
374#554—92no—
375#554—92no—
376#554—91no—
377#554—92no—
378#554—94no—
379D4×Q8—31no—
380D4×Q8—91no—
381D4×Q8—92no—
382#544—92no—
383#543—94no—
384#533—91no—
385#533—91no—
386C2×C22⋊Q8—92no—
387C2×C22⋊Q8—92no—
388#518—92no—
389C2×C4×D4—91no—
390C23×D3—32no—
391C23×D3—32no—
392C2×C3×Q8—21no—
393C2×C3×Q8—32no—
394C2×C3×Q8—34no—
395C2×C3×Q8—32no—
396C2×C3×Q8—124no—
397C2×C3×Q8C22×D311yescharacteristic
398C2×C3×Q8C22×D311yescharacteristic
399C2×C3×D4—31no—
400C2×C3×D4—31no—
401C22×C3×C4—32no—
402C22×C3×C4—32no—
403C22×C3×C4—34no—
404C22×C3×C4—34no—
405C2×#67—32no—
406C2×#67—32no—
407C22×Dic3—32no—
408C22×Dic3—34no—
409C22×Dic3—32no—
410C22×Dic3—34no—
411D3×Q8—44no—
412D3×Q8—124no—
413D3×D4—38no—
414D3×D4—38no—
415C2×D12C22×D311yescharacteristic
416C2×D12C22×D311yescharacteristic
417C2×C4×D3—31no—
418C2×C4×D3—31no—
419C2×C4×D3—31no—
420C2×C4×D3—31no—
421C2×C4×D3—34no—
422C2×C4×D3—34no—
423C2×C4×D3—32no—
424C2×C4×D3—32no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—32no—
428C2×C4×D3—32no—
429C2×C4×D3—61no—
430C2×C4×D3—61no—
431C2×C4×D3—61no—
432C2×C4×D3—124no—
433C2×C4×D3—124no—
434C2×C4×D3C22×D312yes—
435C2×C4×D3C22×D312yes—
436C2×C4×D3C22×D314yes—
437C2×C4×D3C22×D314yes—
438C2×Dic6—31no—
439C2×Dic6—31no—
440C2×Dic6—32no—
441C2×Dic6—32no—
442C2×Dic6—34no—
443C2×Dic6—34no—
444C2×Dic6—62no—
445C2×Dic6—61no—
446C2×Dic6—124no—
447C2×Dic6C22×D312yes—
448C2×Dic6C22×D312yes—
449C2×Dic6C22×D314yes—
450C3×C4⋊C4—21no—
451C3×C4⋊C4—22no—
452C3×C4⋊C4—32no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4—31no—
455C3×C4⋊C4—32no—
456C3×C4⋊C4—34no—
457C3×C4⋊C4—34no—
458C3×C4⋊C4—34no—
459C3×C4⋊C4—31no—
460C3×C4⋊C4—32no—
461C3×C4⋊C4C22×D311yescharacteristic
462C3×C4⋊C4C22×D311yescharacteristic
463C3×C4⋊C4C22×D312yes—
464C3×C4⋊C4C22×D312yes—
465C3×C22⋊C4—34no—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—32no—
468C3×C22⋊C4—32no—
469C3×C42—21no—
470C3×C42—22no—
471C3×C42C22×D311yescharacteristic
472C3×C42C22×D311yescharacteristic
473C3×C42C22×D312yes—
474C3×C42C22×D312yes—
475#217—32no—
476#217—32no—
477#217—34no—
478#217—34no—
479(C2×D3)⋊C4—32no—
480(C2×D3)⋊C4—32no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—32no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—62no—
490(C2×D3)⋊C4—62no—
491(C2×D3)⋊C4C22×D312yes—
492(C2×D3)⋊C4C22×D312yes—
493(C2×D3)⋊C4C22×D314yes—
494(C2×D3)⋊C4C22×D314yes—
495C4⋊Dic3—32no—
496C4⋊Dic3—31no—
497C4⋊Dic3—31no—
498C4⋊Dic3—32no—
499C4⋊Dic3—34no—
500C4⋊Dic3—34no—
501C4⋊Dic3—34no—
502C4⋊Dic3—34no—
503C4⋊Dic3—61no—
504C4⋊Dic3—62no—
505C4⋊Dic3C22×D312yes—
506C4⋊Dic3C22×D311yescharacteristic
507C4⋊Dic3C22×D312yes—
508C4⋊Dic3C22×D312yes—
509C4⋊Dic3C22×D314yes—
510C4⋊Dic3C22×D312yes—
511C4⋊Dic3C22×D311yescharacteristic
512Dic3⋊C4—32no—
513Dic3⋊C4—32no—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—32no—
517Dic3⋊C4—32no—
518Dic3⋊C4—32no—
519Dic3⋊C4—32no—
520Dic3⋊C4—32no—
521Dic3⋊C4—32no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—34no—
526Dic3⋊C4—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—32no—
529Dic3⋊C4—32no—
530Dic3⋊C4—62no—
531Dic3⋊C4—62no—
532Dic3⋊C4—62no—
533Dic3⋊C4—62no—
534Dic3⋊C4—62no—
535Dic3⋊C4C22×D314yes—
536Dic3⋊C4C22×D314yes—
537C4×Dic3—31no—
538C4×Dic3—31no—
539C4×Dic3—32no—
540C4×Dic3—32no—
541C4×Dic3—31no—
542C4×Dic3—31no—
543C4×Dic3—31no—
544C4×Dic3—31no—
545C4×Dic3—34no—
546C4×Dic3—34no—
547C4×Dic3—61no—
548C4×Dic3—62no—
549C4×Dic3—61no—
550C4×Dic3—61no—
551C22×C32C2511yescharacteristic
552C2×C3⋊D3—21no—
553C2×C3⋊D3—21no—
554C2×C3⋊D3C22×Q812yes—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3C22×Q814yes—
560C2×C3×D3C22×Q814yes—
561D32—48no—
562C32×C4—22no—
563C32×C4—21no—
564C32×C4—22no—
565C32×C4C22×Q812yes—
566C32×C4H(5,𝔽2)12yes—
567C3⋊Dic3—21no—
568C3⋊Dic3—21no—
569C3⋊Dic3—22no—
570C3⋊Dic3—22no—
571C3⋊Dic3C22×Q812yes—
572C3×Dic3—22no—
573C3×Dic3—22no—
574C3×Dic3—24no—
575C3×Dic3—24no—
576C22×Q8—32no—
577C22×Q8—92no—
578C22×D4—91no—
579C23×C4—92no—
580C4⋊Q8—31no—
581C4⋊Q8—31no—
582C4⋊Q8—32no—
583C4⋊Q8—92no—
584C4⋊Q8—94no—
585C4⋊Q8—91no—
586C4⋊Q8—91no—
587#125—32no—
588#125—92no—
589#125—94no—
590#125—92no—
591#125—92no—
592C22⋊Q8—32no—
593C22⋊Q8—32no—
594C22⋊Q8—34no—
595C22⋊Q8—34no—
596C22⋊Q8—94no—
597C22⋊Q8—94no—
598C22⋊Q8—94no—
599C22⋊Q8—94no—
600C22⋊Q8—94no—
601C22⋊Q8—94no—
602C22⋊Q8—94no—
603C22⋊Q8—92no—
604C22⋊Q8—94no—
605C22⋊Q8—94no—
606C22⋊Q8—92no—
607C22⋊Q8—94no—
608C22⋊Q8—92no—
609C22⋊Q8—92no—
610C22⋊Q8—91no—
611C22⋊Q8—91no—
612C22⋊Q8—92no—
613C4×Q8—92no—
614C4×Q8—92no—
615C4×Q8—91no—
616C4×Q8—92no—
617C4×Q8D3211yescharacteristic, complemented
618C4×D4—31no—
619C4×D4—31no—
620C4×D4—32no—
621C4×D4—32no—
622C4×D4—92no—
623C4×D4—94no—
624C4×D4—94no—
625C4×D4—91no—
626C4×D4—91no—
627C4×D4—92no—
628C4×D4—92no—
629C4×D4—92no—
630#117—92no—
631#117—92no—
632C2×C4⋊C4—32no—
633C2×C4⋊C4—91no—
634C2×C4⋊C4—94no—
635C2×C4⋊C4—92no—
636C2×C4⋊C4—94no—
637C2×C22⋊C4—92no—
638C2×C22⋊C4—94no—
639C2×C22⋊C4—94no—
640C2×C42—91no—
641C23×C3—32no—
642C23×C3—32no—
643C22×D3—31no—
644C22×D3—31no—
645C22×D3—38no—
646C22×D3—38no—
647C22×D3—61no—
648C22×D3—122no—
649C22×D3—122no—
650C22×D3—122no—
651C22×D3—122no—
652C22×D3C23×D312yes—
653C22×D3C23×D312yes—
654C3×Q8—22no—
655C3×Q8—22no—
656C3×Q8—42no—
657C3×Q8—64no—
658C3×Q8—122no—
659C3×Q8—124no—
660C3×D4—34no—
661C3×D4—34no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—34no—
668C2×C3×C4—34no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—64no—
672C2×C3×C4—64no—
673C2×C3×C4—124no—
674C2×C3×C4—124no—
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D312yes—
678C2×C3×C4C23×D312yes—
679C2×C3×C4C23×D312yes—
680C2×C3×C4C23×D312yes—
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685#67—38no—
686#67—38no—
687C2×Dic3—31no—
688C2×Dic3—31no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—32no—
694C2×Dic3—32no—
695C2×Dic3—32no—
696C2×Dic3—32no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—62no—
701C2×Dic3—62no—
702C2×Dic3—124no—
703C2×Dic3—122no—
704C2×Dic3—122no—
705C2×Dic3—124no—
706C2×Dic3C23×D314yes—
707C2×Dic3C23×D314yes—
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710D12D3×Q814yescomplemented
711D12D3×Q814yescomplemented
712C4×D3—24no—
713C4×D3—24no—
714C4×D3—34no—
715C4×D3—34no—
716C4×D3—44no—
717C4×D3—44no—
718C4×D3—64no—
719C4×D3—62no—
720C4×D3—62no—
721C4×D3—122no—
722C4×D3—122no—
723C4×D3—122no—
724C4×D3—121no—
725C4×D3—121no—
726C4×D3—122no—
727C4×D3—124no—
728C4×D3—122no—
729C4×D3—122no—
730C4×D3—124no—
731Dic6—24no—
732Dic6—42no—
733Dic6—44no—
734Dic6—62no—
735Dic6—62no—
736Dic6—122no—
737Dic6—124no—
738Dic6—124no—
739Dic6—122no—
740Dic6—122no—
741Dic6—124no—
742C2×C32C23×Q811yescharacteristic
743C2×C32C2×H(5,𝔽2)11yescharacteristic
744C2×C32#58511yescharacteristic
745C3⋊D3—22no—
746C3×D3—24no—
747C3×D3—24no—
748C24—92no—
749C2×Q8—32no—
750C2×Q8—32no—
751C2×Q8—34no—
752C2×Q8—94no—
753C2×Q8—91no—
754C2×Q8—92no—
755C2×Q8—124no—
756C2×Q8—364no—
757C2×Q8C2×D3211yescharacteristic
758C2×D4—31no—
759C2×D4—31no—
760C2×D4—98no—
761C2×D4—92no—
762C22×C4—32no—
763C22×C4—32no—
764C22×C4—34no—
765C22×C4—34no—
766C22×C4—92no—
767C22×C4—94no—
768C22×C4—94no—
769C22×C4—92no—
770C22×C4—92no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—91no—
774C22×C4—364no—
775C4⋊C4—32no—
776C4⋊C4—34no—
777C4⋊C4—31no—
778C4⋊C4—31no—
779C4⋊C4—34no—
780C4⋊C4—34no—
781C4⋊C4—32no—
782C4⋊C4—32no—
783C4⋊C4—32no—
784C4⋊C4—94no—
785C4⋊C4—92no—
786C4⋊C4—94no—
787C4⋊C4—94no—
788C4⋊C4—94no—
789C4⋊C4—94no—
790C4⋊C4—92no—
791C4⋊C4—92no—
792C4⋊C4—91no—
793C4⋊C4—92no—
794C4⋊C4—92no—
795C4⋊C4—92no—
796C4⋊C4—92no—
797C4⋊C4C2×D3211yescharacteristic
798C4⋊C4C2×D3212yes—
799C22⋊C4—34no—
800C22⋊C4—34no—
801C22⋊C4—32no—
802C22⋊C4—32no—
803C22⋊C4—94no—
804C22⋊C4—94no—
805C22⋊C4—94no—
806C22⋊C4—92no—
807C22⋊C4—92no—
808C22⋊C4—92no—
809C22⋊C4—92no—
810C42—94no—
811C42—91no—
812C42—91no—
813C42—91no—
814C42—92no—
815C42C2×D3211yescharacteristic
816C42C2×D3212yes—
817C22×C3—21no—
818C22×C3—34no—
819C22×C3—34no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3C24×D311yescharacteristic
825C22×C3C24×D311yescharacteristic
826C2×D3—22no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—32no—
831C2×D3—32no—
832C2×D3—62no—
833C2×D3—61no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—121no—
838C2×D3—121no—
839C2×D3—128no—
840C2×D3—128no—
841C2×D3C2×D3×Q814yes—
842C2×D3C2×D3×Q814yes—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—21no—
846C3×C4—22no—
847C3×C4—22no—
848C3×C4—21no—
849C3×C4—22no—
850C3×C4—22no—
851C3×C4—42no—
852C3×C4—41no—
853C3×C4—42no—
854C3×C4—62no—
855C3×C4—64no—
856C3×C4—62no—
857C3×C4—64no—
858C3×C4#100412yes—
859C3×C4C2×D3×Q812yes—
860C3×C4C2×D3×Q812yes—
861C3×C4#100912yes—
862Dic3—24no—
863Dic3—22no—
864Dic3—22no—
865Dic3—24no—
866Dic3—32no—
867Dic3—32no—
868Dic3—62no—
869Dic3—62no—
870Dic3—62no—
871Dic3—61no—
872Dic3—62no—
873Dic3—61no—
874Dic3—61no—
875Dic3—62no—
876Dic3—61no—
877Dic3—62no—
878Dic3—122no—
879Dic3—122no—
880Dic3—121no—
881C32#350111yescharacteristic, complemented, Sylow
882C23—32no—
883C23—32no—
884C23—98no—
885C23—91no—
886C23—362no—
887C23—362no—
888Q8—22no—
889Q8—64no—
890Q8—124no—
891Q8—122no—
892Q8—182no—
893Q8—362no—
894Q8—364no—
895D4—34no—
896D4—34no—
897D4—98no—
898C2×C4—34no—
899C2×C4—34no—
900C2×C4—32no—
901C2×C4—32no—
902C2×C4—64no—
903C2×C4—64no—
904C2×C4—91no—
905C2×C4—94no—
906C2×C4—91no—
907C2×C4—91no—
908C2×C4—92no—
909C2×C4—92no—
910C2×C4—124no—
911C2×C4—124no—
912C2×C4—182no—
913C2×C4—361no—
914C2×C4—362no—
915C2×C4—362no—
916C2×C4—362no—
917C2×C4—364no—
918C2×C4—364no—
919C2×C4C22×D3211yescharacteristic
920C2×C4C22×D3212yes—
921C2×C4C22×D3212yes—
922C2×C4C22×D3211yescharacteristic
923C2×C4C22×D3211yescharacteristic
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—64no—
928C2×C3—64no—
929C2×C3C2×#100411yescharacteristic
930C2×C3C22×D3×Q811yescharacteristic
931C2×C3C22×D3×Q811yescharacteristic
932C2×C3C2×#100911yescharacteristic
933C2×C3#596611yescharacteristic
934C2×C3#596811yescharacteristic
935D3—24no—
936D3—24no—
937D3—62no—
938D3—62no—
939D3—122no—
940C22—34no—
941C22—34no—
942C22—62no—
943C22—62no—
944C22—62no—
945C22—62no—
946C22—92no—
947C22—181no—
948C22—181no—
949C22—368no—
950C22C23×D3211yescharacteristic
951C4—22no—
952C4—22no—
953C4—21no—
954C4—62no—
955C4—62no—
956C4—64no—
957C4—64no—
958C4—92no—
959C4—181no—
960C4—182no—
961C4—182no—
962C4—181no—
963C4#6430712yes—
964C4D32×Q812yes—
965C3—21no—
966C3#8676111yescharacteristic, complemented
967C3#8694811yescharacteristic, complemented
968C2—64no—
969C2—64no—
970C2—182no—
971C2C2×#6430711yescharacteristic
972C2C2×D32×Q811yescharacteristic
973C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC2×#3802C22
hypercenterC4×Q8D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596049C2semidirect
2. C3×#5579C2semidirect
3. C3×Q8×D12C2semidirect
4. D3×#946C2semidirect
5. #10595400C2semidirect
6. #10594635C2semidirect
7. D3×#897C2semidirect
8. #10594535C2semidirect
9. #10594532C2semidirect
12. #10593956C2semidirect
13. #10593956C2semidirect
14. #10593941C2semidirect
15. #10593904C2semidirect
16. #10593866C2semidirect
17. #10593855C2semidirect
20. C2×C3×D3×Q8C22semidirect
23. C2×D3×Dic6C22semidirect
24. C32×C4×Q8C22semidirect
26. #64153C22semidirect
29. #64098C22semidirect
30. #64097C22semidirect
33. C4×#634C22semidirect
34. C4×#634C22semidirect
35. C3×#946C22semidirect
36. C3×#897C22semidirect
37. C3×#897C22semidirect
38. C3×#896C22semidirect
39. C3×D3×C4⋊C4C22semidirect
44. C3×#870C22semidirect
45. C3×#869C22semidirect
46. C3×#869C22semidirect
47. C3×#869C22semidirect
51. #63919C22semidirect
55. #63899C22semidirect
60. #63896C22semidirect
62. #63893C22semidirect
63. D3×C4⋊Dic3C22semidirect
64. D3×C4⋊Dic3C22semidirect
66. #63887C22semidirect
67. #63887C22semidirect
68. #63887C22semidirect
71. D3×Dic3⋊C4C22semidirect
72. #63872C22semidirect
73. #63872C22semidirect
76. #63857C22semidirect
77. #63857C22semidirect
78. #63856C22semidirect
79. #63851C22semidirect
81. #63847C22semidirect
82. #63843C22semidirect
83. #63843C22semidirect
84. #63839C22semidirect
105. #5579D3semidirect
109. Q8×D12D3semidirect
144. #3802Q8semidirect
192. C2×D3×Q8C2×D3semidirect
207. C3×C4×Q8C2×D3semidirect
208. C3×C4×Q8C2×D3semidirect
224. #946C2×D3semidirect
257. #897C2×D3semidirect
258. #897C2×D3semidirect
267. #896C2×D3semidirect
279. D3×C4⋊C4C2×D3semidirect
321. #870C2×D3semidirect
322. #869C2×D3semidirect
323. #869C2×D3semidirect
324. #869C2×D3semidirect
336. C2×D32C2×Q8semidirect
350. C4×C3⋊D3C2×Q8semidirect
357. C3×D12C2×Q8semidirect
358. C3×D12C2×Q8semidirect
367. #625C2×Q8semidirect
617. C4×Q8D32semidirect
710. D12D3×Q8semidirect
711. D12D3×Q8semidirect
881. C32#3501semidirect
966. C3#86761semidirect
967. C3#86948semidirect

Maximal subgroups

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

subgroupindex
#105960492
C3×#55792
C3×Q8×D122
D3×#9462
#105954002
#105946352
D3×#8972
#105945352
#105945322
#105939962
C4×#38022
#105939562
#105939412
#105939042
#105938662
#105938552
#869483
#867613