Finite Group Databasebeta

← #11909318

Subgroups — #11909318

Order 1152.

2365 conjugacy classes of subgroups.

The subgroup lattice has 999 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596051C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C3×Q8×D12C211yesmaximal, characteristic, complemented
4D3×#946C212yesmaximal, complemented
5#10595402C212yesmaximal, complemented
6#10594654C214yesmaximal, complemented
7#10594627C212yesmaximal, complemented
8#10594456C212yesmaximal, complemented
9#10594439C214yesmaximal, complemented
10#10594005C212yesmaximal, complemented
11C4×#3802C211yesmaximal, characteristic, complemented
12#10593958C212yesmaximal, complemented
13#10593955C212yesmaximal, complemented
14#10593896C211yesmaximal, characteristic, complemented
15#10593889C212yesmaximal, complemented
16#10593869C211yesmaximal, characteristic, complemented
17#10593866C211yesmaximal, characteristic, complemented
18#86990—31nomaximal
19#86751—31nomaximal
20C2×C3×D3×Q8C2212yescomplemented
21C2×#3802C2211yescharacteristic
22C2×C4×D32C2212yes—
23C2×#3799C2212yescomplemented
24C2×#3796C2212yes—
25C32×C4×Q8C2211yescharacteristic, complemented
26#64156C2211yescharacteristic, complemented
27#64155C2211yescharacteristic
28#64107C2212yescomplemented
29#64104C2211yescharacteristic
30#64103C2212yes—
31#64099C2211yescharacteristic, complemented
32C4×C4⋊(C3⋊D3)C2212yes—
33C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
34#64081C2212yescomplemented
35C42×C3⋊D3C2211yescharacteristic
36C3×#946C2212yescomplemented
37C3×#898C2214yescomplemented
38C3×#897C2212yescomplemented
39C3×#897C2214yescomplemented
40C3×#892C2212yescomplemented
41C3×#875C2212yes—
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2212yes—
44C3×C4×D12C2211yescharacteristic
45C3×#869C2211yescharacteristic, complemented
46C3×#869C2211yescharacteristic, complemented
47C3×#869C2212yescomplemented
48C3×C4×Dic6C2212yescomplemented
49#63923C2214yes—
50#63921C2212yes—
51D3×(C2×D3)⋊C4C2214yes—
52#63916C2212yes—
53#63909C2212yescomplemented
54#63907C2214yescomplemented
55#63906C2214yes—
56#63904C2214yescomplemented
57#63902C2212yes—
58C4×#625C2212yes—
59#63900C2211yescharacteristic
60#63900C2212yescomplemented
61#63898C2211yescharacteristic
62#63898C2211yescharacteristic
63#63894C2214yes—
64#63891C2214yes—
65#63890C2214yescomplemented
66#63890C2214yescomplemented
67D3×C4⋊Dic3C2212yescomplemented
68#63888C2214yes—
69#63888C2214yescomplemented
70#63887C2214yescomplemented
71#63880C2214yescomplemented
72#63877C2214yescomplemented
73D3×Dic3⋊C4C2214yescomplemented
74#63872C2212yescomplemented
75#63871C2212yes—
76#63871C2212yes—
77#63871C2212yescomplemented
78#63869C2214yescomplemented
79#63858C2214yescomplemented
80#63856C2212yescomplemented
81#63854C2214yescomplemented
82#63849C2212yes—
83#63843C2212yescomplemented
84#63843C2212yescomplemented
85C3×#556—31no—
86C3×D4×Q8—31no—
87#5817—32no—
88C2×#946—32no—
89#5733—32no—
90#5730—32no—
91#5728—31no—
92#5728—31no—
93#5726—31no—
94#5726—31no—
95#5707—34no—
96#5705—34no—
97#5682—32no—
98#5676—32no—
99#5645—34no—
100#5642—32no—
101#5637—34no—
102#5633—32no—
103#5627—32no—
104D3×C22⋊Q8—32no—
105#5584D311yescharacteristic, complemented
106#5580—31no—
107#5580—31no—
108#5580—61no—
109#5579—32no—
110Q8×D12D311yescharacteristic, complemented
111#5574—32no—
112#5555—31no—
113#5554—32no—
114#5551—31no—
115#5546—32no—
116C4×D3×D4—31no—
117C4×D3×D4—31no—
118#5529—32no—
119#5524—32no—
120C22×D32C2312yes—
121C2×C32×Q8C2311yescharacteristic
122C2×C4⋊(C3⋊D3)C2311yescharacteristic
123C2×C4⋊(C3⋊D3)C2312yes—
124C2×C4×C3⋊D3C2312yes—
125C2×C4×C3⋊D3C2311yescharacteristic
126C2×C4×C3⋊D3C2311yescharacteristic
127C2×C4×C3⋊D3C2311yescharacteristic
128C3×D3×Q8—44no—
129C2×C3×D12C2311yescharacteristic
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2314yes—
134C2×C3×Dic6C2312yes—
135C2×C3×Dic6C2312yes—
136C2×C3×Dic6C2314yes—
137C2×#626C2314yes—
138C2×#626C2314yes—
139C2×#625C2312yes—
140C2×#624C2314yes—
141C2×#624C2312yes—
142C2×D3×Dic3C2314yes—
143C2×D3×Dic3C2312yes—
144C2×D3×Dic3C2312yes—
145#3802—24no—
146C4×D32—44no—
147#3799—44no—
148#3796—28no—
149C32×C4⋊C4C2311yescharacteristic
150C32×C4⋊C4C2312yes—
151C32×C42C2311yescharacteristic
152C32×C42C2312yes—
153#3752C2312yes—
154#3752C2312yes—
155#3752C2312yes—
156#3752C2312yes—
157#3752C2312yes—
158C4⋊(C3⋊Dic3)C2312yes—
159C4⋊(C3⋊Dic3)C2311yescharacteristic
160#3750C2312yes—
161#3750C2312yes—
162C4×C3⋊Dic3C2311yescharacteristic
163C4×C3⋊Dic3C2311yescharacteristic
164C4×C3⋊Dic3C2311yescharacteristic
165C3×(C2×D3)⋊C4C2314yes—
166C3×(C2×D3)⋊C4C2314yes—
167C3×(C2×D3)⋊C4C2312yes—
168C3×(C2×D3)⋊C4C2312yes—
169C3×(C2×D3)⋊C4C2314yes—
170C3×C4⋊Dic3C2312yes—
171C3×C4⋊Dic3C2312yes—
172C3×C4⋊Dic3C2314yes—
173C3×C4⋊Dic3C2312yes—
174C3×C4⋊Dic3C2312yes—
175C3×C4⋊Dic3C2311yescharacteristic
176C3×C4⋊Dic3C2311yescharacteristic
177C3×Dic3⋊C4C2314yes—
178C3×C4×Dic3C2314yes—
179#3724C2314yes—
180#3724C2312yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183Dic3⋊Dic3C2314yes—
184#3722C2314yes—
185#3722C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2312yes—
188(C2×D3)⋊Dic3C2312yes—
189Dic32C2314yes—
190#3520—91noSylow
191C22×C3×Q8—32no—
192C2×#239—32no—
193C2×#239—32no—
194C2×D3×Q8C2×D312yescomplemented
195C2×#237—32no—
196C2×D3×D4—31no—
197C2×D3×D4—31no—
198C2×#235—32no—
199C22×C4×D3—32no—
200C22×C4×D3—32no—
201C3×C4⋊Q8—31no—
202C3×C4⋊Q8—31no—
203C3×C4⋊Q8—32no—
204C3×#126—34no—
205C3×#124—32no—
206C3×C22⋊Q8—32no—
207C3×C22⋊Q8—34no—
208C3×C22⋊Q8—32no—
209C3×C4×Q8—21no—
210C3×C4×Q8—32no—
211C3×C4×Q8C2×D311yescharacteristic, complemented
212C3×C4×Q8C2×D311yescharacteristic, complemented
213C3×C4×D4—31no—
214C3×C4×D4—31no—
215C3×C4×D4—32no—
216C3×#117—32no—
217#947—31no—
218#947—31no—
219#947—34no—
220#947—61no—
221#946—31no—
222#946—31no—
223#946—32no—
224#946—34no—
225#946—32no—
226#946—32no—
227#946—32no—
228#946—34no—
229#946—34no—
230#946—61no—
231#946C2×D312yescomplemented
232Q8×Dic3—32no—
233Q8×Dic3—32no—
234#938—32no—
235D4×Dic3—31no—
236D4×Dic3—31no—
237#930—34no—
238#930—32no—
239C4×#67—32no—
240C4×#67—32no—
241C4×#67—34no—
242C2×(C2×D3)⋊C4—34no—
243C2×C4⋊Dic3—32no—
244#924—32no—
245C2×Dic3⋊C4—34no—
246#898—32no—
247#898—32no—
248#898—34no—
249#898—62no—
250#898C2×D314yescomplemented
251#897—32no—
252#897—32no—
253#897—32no—
254#897C2×D314yescomplemented
255#897C2×D312yescomplemented
256#896—34no—
257#896—34no—
258#895—32no—
259#895—32no—
260#895—31no—
261#895—31no—
262#895—61no—
263#894—32no—
264#894—32no—
265#894—34no—
266#894—34no—
267#894—34no—
268#894—62no—
269#893—31no—
270#893—31no—
271#893—34no—
272#893—34no—
273#892—32no—
274#892—32no—
275#892C2×D312yescomplemented
276D3×C4⋊C4—34no—
277D3×C4⋊C4—32no—
278D3×C4⋊C4—32no—
279D3×C4⋊C4—31no—
280D3×C4⋊C4—31no—
281D3×C4⋊C4—32no—
282#890—31no—
283#890—31no—
284#890—32no—
285#890—32no—
286#890—34no—
287#890—61no—
288#887—32no—
289#887—32no—
290#886—34no—
291#886—34no—
292#886—34no—
293#885—34no—
294#884—34no—
295#883—34no—
296#883—34no—
297#882—34no—
298#882—34no—
299#67⋊C4—32no—
300#67⋊C4—32no—
301#67⋊C4—34no—
302D3×C22⋊C4—34no—
303D3×C22⋊C4—32no—
304D3×C22⋊C4—32no—
305#879—34no—
306#878—34no—
307#877—34no—
308#875C2×D312yes—
309C4×D12—32no—
310C4×D12—32no—
311C4×D12—31no—
312C4×D12—31no—
313C4×D12—34no—
314C4×D12—34no—
315C4×D12—62no—
316C4×D12—61no—
317C4×D12C2×D312yes—
318C4×D12C2×D311yescharacteristic
319C4×D12C2×D311yescharacteristic
320#872—32no—
321#872—32no—
322#872—34no—
323#872—62no—
324C42×D3—31no—
325C42×D3—31no—
326C42×D3—61no—
327#870—34no—
328#869C2×D312yescomplemented
329#869C2×D311yescharacteristic, complemented
330#869C2×D311yescharacteristic, complemented
331C4×Dic6C2×D312yescomplemented
332C22×C3⋊D3C2412yes—
333C22×C3⋊D3C2411yescharacteristic
334C22×C3×D3C2412yes—
335C22×C3×D3C2412yes—
336C2×D32—24no—
337C2×D32—24no—
338C2×D32—42no—
339C32×Q8—22no—
340C2×C32×C4C2412yes—
341C2×C32×C4C2412yes—
342C2×C32×C4C2411yescharacteristic
343C2×C32×C4C2411yescharacteristic
344C2×C32×C4C2411yescharacteristic
345C2×C3⋊Dic3C2411yescharacteristic
346C2×C3⋊Dic3C2412yes—
347C2×C3⋊Dic3C2411yescharacteristic
348C2×C3⋊Dic3C2411yescharacteristic
349C4⋊(C3⋊D3)—24no—
350C4⋊(C3⋊D3)—22no—
351C4×C3⋊D3—22no—
352C4×C3⋊D3—24no—
353C4×C3⋊D3—22no—
354C4×C3⋊D3—22no—
355C2×C3×Dic3C2414yes—
356C2×C3×Dic3C2414yes—
357C2×C3×Dic3C2412yes—
358C2×C3×Dic3C2412yes—
359C3×D12—22no—
360C3×D12#4114yescomplemented
361C3×C4×D3—24no—
362C3×C4×D3—24no—
363C3×C4×D3—44no—
364C3×Dic6—24no—
365C3×Dic6—24no—
366C3×Dic6—44no—
367#626—28no—
368#626—44no—
369#625—24no—
370#624—44no—
371#624—42no—
372D3×Dic3—28no—
373D3×Dic3—42no—
374D3×Dic3—42no—
375#556—31no—
376#554—92no—
377#552—92no—
378#551—94no—
379D4×Q8—31no—
380#548—92no—
381#547—91no—
382#547—91no—
383#546—92no—
384#542—92no—
385#539—94no—
386#533—91no—
387#529—91no—
388#525—92no—
389C2×C22⋊Q8—92no—
390#520—92no—
391C2×C4×D4—91no—
392C23×D3—32no—
393C23×D3—32no—
394C2×C3×Q8—21no—
395C2×C3×Q8—32no—
396C2×C3×Q8—32no—
397C2×C3×Q8—34no—
398C2×C3×Q8—124no—
399C2×C3×Q8C22×D311yescharacteristic
400C2×C3×Q8C22×D311yescharacteristic
401C2×C3×D4—31no—
402C2×C3×D4—31no—
403C22×C3×C4—32no—
404C22×C3×C4—32no—
405C22×C3×C4—34no—
406C2×#67—32no—
407C2×#67—32no—
408C2×#67—34no—
409C2×#67—34no—
410C22×Dic3—34no—
411C22×Dic3—32no—
412C22×Dic3—32no—
413#239—68no—
414#239—124no—
415D3×Q8—44no—
416#237—68no—
417D3×D4—64no—
418D3×D4—64no—
419#235—124no—
420C2×D12—34no—
421C2×D12—32no—
422C2×D12—32no—
423C2×D12—31no—
424C2×D12—31no—
425C2×D12—34no—
426C2×D12—62no—
427C2×D12—61no—
428C2×D12C22×D311yescharacteristic
429C2×D12C22×D311yescharacteristic
430C2×C4×D3—34no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—31no—
435C2×C4×D3—31no—
436C2×C4×D3—31no—
437C2×C4×D3—32no—
438C2×C4×D3—32no—
439C2×C4×D3—32no—
440C2×C4×D3—32no—
441C2×C4×D3—32no—
442C2×C4×D3—34no—
443C2×C4×D3—32no—
444C2×C4×D3—34no—
445C2×C4×D3—61no—
446C2×C4×D3—61no—
447C2×C4×D3—61no—
448C2×C4×D3—62no—
449C2×C4×D3—124no—
450C2×C4×D3—124no—
451C2×C4×D3C22×D312yes—
452C2×C4×D3C22×D312yes—
453C2×C4×D3C22×D314yes—
454C2×Dic6C22×D312yes—
455C2×Dic6C22×D312yes—
456C2×Dic6C22×D314yes—
457C3×C4⋊C4—21no—
458C3×C4⋊C4—22no—
459C3×C4⋊C4—32no—
460C3×C4⋊C4—32no—
461C3×C4⋊C4—32no—
462C3×C4⋊C4—32no—
463C3×C4⋊C4—34no—
464C3×C4⋊C4—31no—
465C3×C4⋊C4—34no—
466C3×C4⋊C4—31no—
467C3×C4⋊C4C22×D311yescharacteristic
468C3×C4⋊C4C22×D311yescharacteristic
469C3×C4⋊C4C22×D312yes—
470C3×C4⋊C4C22×D312yes—
471C3×C22⋊C4—34no—
472C3×C22⋊C4—34no—
473C3×C22⋊C4—34no—
474C3×C22⋊C4—32no—
475C3×C22⋊C4—32no—
476C3×C42—21no—
477C3×C42—22no—
478C3×C42—34no—
479C3×C42C22×D312yes—
480C3×C42C22×D311yescharacteristic
481C3×C42C22×D311yescharacteristic
482C3×C42C22×D312yes—
483#217—32no—
484#217—34no—
485#217—32no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—32no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—32no—
496(C2×D3)⋊C4—32no—
497(C2×D3)⋊C4—32no—
498(C2×D3)⋊C4—32no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—62no—
504(C2×D3)⋊C4—62no—
505(C2×D3)⋊C4—62no—
506(C2×D3)⋊C4—62no—
507(C2×D3)⋊C4—62no—
508(C2×D3)⋊C4C22×D314yes—
509(C2×D3)⋊C4C22×D312yes—
510(C2×D3)⋊C4C22×D312yes—
511(C2×D3)⋊C4C22×D314yes—
512(C2×D3)⋊C4C22×D314yes—
513C4⋊Dic3—32no—
514C4⋊Dic3—32no—
515C4⋊Dic3—31no—
516C4⋊Dic3—31no—
517C4⋊Dic3—34no—
518C4⋊Dic3—34no—
519C4⋊Dic3—34no—
520C4⋊Dic3—62no—
521C4⋊Dic3—61no—
522C4⋊Dic3C22×D311yescharacteristic
523C4⋊Dic3C22×D311yescharacteristic
524C4⋊Dic3C22×D312yes—
525C4⋊Dic3C22×D314yes—
526C4⋊Dic3C22×D312yes—
527C4⋊Dic3C22×D312yes—
528C4⋊Dic3C22×D312yes—
529Dic3⋊C4—32no—
530Dic3⋊C4—32no—
531Dic3⋊C4—32no—
532Dic3⋊C4—32no—
533Dic3⋊C4—32no—
534Dic3⋊C4—34no—
535Dic3⋊C4—34no—
536Dic3⋊C4—34no—
537Dic3⋊C4—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4—32no—
540Dic3⋊C4—62no—
541Dic3⋊C4—62no—
542Dic3⋊C4C22×D314yes—
543C4×Dic3—31no—
544C4×Dic3—31no—
545C4×Dic3—31no—
546C4×Dic3—31no—
547C4×Dic3—31no—
548C4×Dic3—31no—
549C4×Dic3—34no—
550C4×Dic3—34no—
551C4×Dic3—61no—
552C4×Dic3—61no—
553C4×Dic3—61no—
554C4×Dic3C22×D314yes—
555C22×C32C2511yescharacteristic
556C2×C3⋊D3—21no—
557C2×C3⋊D3—21no—
558C2×C3⋊D3—22no—
559C2×C3⋊D3—22no—
560C2×C3⋊D3—22no—
561C2×C3⋊D32−1+412yes—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3C2×#4114yes—
568D32—48no—
569C32×C4—22no—
570C32×C4—21no—
571C32×C4—22no—
572C32×C4C2×#4112yes—
573C32×C4H(5,𝔽2)12yes—
574C3⋊Dic3—22no—
575C3⋊Dic3—21no—
576C3⋊Dic3—21no—
577C3⋊Dic3—21no—
578C3×Dic3—24no—
579C3×Dic3—22no—
580C3×Dic3—22no—
581C3×Dic3—24no—
582C2×#41—92no—
583C2×#41—92no—
584C22×Q8—32no—
585C22×D4—91no—
586C23×C4—92no—
587C4⋊Q8—31no—
588C4⋊Q8—31no—
589C4⋊Q8—32no—
590#126—34no—
591#126—94no—
592#126—92no—
593#125—94no—
594#125—92no—
595#125—91no—
596#124—32no—
597#124—94no—
598#124—91no—
599#123—94no—
600#123—94no—
601#123—94no—
602#123—94no—
603#123—92no—
604C22⋊Q8—32no—
605C22⋊Q8—32no—
606C22⋊Q8—34no—
607C22⋊Q8—94no—
608C22⋊Q8—92no—
609C22⋊Q8—94no—
610C22⋊Q8—92no—
611C22⋊Q8—94no—
612C22⋊Q8—92no—
613C22⋊Q8—92no—
614C22⋊Q8—91no—
615#121—94no—
616#121—92no—
617#121—92no—
618#121—91no—
619#120—94no—
620C4×Q8—32no—
621C4×Q8—92no—
622C4×Q8—92no—
623C4×Q8D3211yescharacteristic, complemented
624C4×D4—31no—
625C4×D4—31no—
626C4×D4—32no—
627C4×D4—94no—
628C4×D4—94no—
629C4×D4—92no—
630C4×D4—94no—
631C4×D4—91no—
632C4×D4—91no—
633C4×D4—92no—
634C4×D4—92no—
635C4×D4—91no—
636#117—32no—
637#117—94no—
638#117—92no—
639#117—92no—
640C2×C4⋊C4—91no—
641C2×C4⋊C4—92no—
642C2×C4⋊C4—94no—
643C2×C4⋊C4—92no—
644C2×C22⋊C4—92no—
645C2×C22⋊C4—94no—
646C2×C42—91no—
647C23×C3—32no—
648C23×C3—32no—
649C22×D3—31no—
650C22×D3—31no—
651C22×D3—32no—
652C22×D3—32no—
653C22×D3—61no—
654C22×D3—62no—
655C22×D3—64no—
656C22×D3—64no—
657C22×D3—64no—
658C22×D3—64no—
659C22×D3—122no—
660C22×D3—122no—
661C22×D3C23×D312yes—
662C22×D3C23×D312yes—
663C3×Q8—22no—
664C3×Q8—22no—
665C3×Q8—42no—
666C3×Q8—64no—
667C3×Q8—64no—
668C3×Q8—124no—
669C3×D4—34no—
670C3×D4—62no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—34no—
677C2×C3×C4—34no—
678C2×C3×C4—32no—
679C2×C3×C4—32no—
680C2×C3×C4—64no—
681C2×C3×C4—64no—
682C2×C3×C4—124no—
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D312yes—
686C2×C3×C4C23×D312yes—
687C2×C3×C4C23×D312yes—
688C2×C3×C4C23×D312yes—
689C2×C3×C4C23×D311yescharacteristic
690C2×C3×C4C23×D311yescharacteristic
691C2×C3×C4C23×D311yescharacteristic
692C2×C3×C4C23×D311yescharacteristic
693#67—68no—
694#67—64no—
695#67—64no—
696#67—124no—
697C2×Dic3—31no—
698C2×Dic3—31no—
699C2×Dic3—31no—
700C2×Dic3—31no—
701C2×Dic3—31no—
702C2×Dic3—31no—
703C2×Dic3—32no—
704C2×Dic3—32no—
705C2×Dic3—61no—
706C2×Dic3—61no—
707C2×Dic3—61no—
708C2×Dic3—62no—
709C2×Dic3—68no—
710C2×Dic3—122no—
711C2×Dic3—122no—
712C2×Dic3C23×D314yes—
713C2×Dic3C23×D314yes—
714C2×Dic3C23×D312yes—
715C2×Dic3C23×D312yes—
716D12—22no—
717D12—64no—
718D12—64no—
719D12—68no—
720D12—62no—
721D12—62no—
722D12—122no—
723D12—124no—
724D12—124no—
725D12#23914yescomplemented
726C4×D3—24no—
727C4×D3—24no—
728C4×D3—44no—
729C4×D3—62no—
730C4×D3—62no—
731C4×D3—68no—
732C4×D3—62no—
733C4×D3—62no—
734C4×D3—64no—
735C4×D3—62no—
736C4×D3—64no—
737C4×D3—62no—
738C4×D3—122no—
739C4×D3—122no—
740C4×D3—124no—
741C4×D3—122no—
742C4×D3—122no—
743C4×D3—122no—
744C4×D3—124no—
745C4×D3—124no—
746C4×D3—122no—
747C4×D3—122no—
748Dic6—24no—
749Dic6—24no—
750Dic6—44no—
751C2×C32C22×#4111yescharacteristic
752C2×C32C2×H(5,𝔽2)11yescharacteristic
753C2×C32C2×2−1+411yescharacteristic
754C3⋊D3—22no—
755C3⋊D3—42no—
756C3×D3—24no—
757C3×D3—42no—
758C24—92no—
759#41—188no—
760#41—364no—
761C2×Q8—32no—
762C2×Q8—32no—
763C2×Q8—34no—
764C2×Q8—124no—
765C2×Q8C2×D3211yescharacteristic
766C2×D4—31no—
767C2×D4—31no—
768C2×D4—94no—
769C2×D4—94no—
770C2×D4—92no—
771C2×D4—92no—
772C2×D4—91no—
773C2×D4—184no—
774C22×C4—32no—
775C22×C4—32no—
776C22×C4—34no—
777C22×C4—92no—
778C22×C4—94no—
779C22×C4—94no—
780C22×C4—92no—
781C22×C4—92no—
782C22×C4—91no—
783C22×C4—91no—
784C22×C4—91no—
785C22×C4—92no—
786C22×C4—364no—
787C4⋊C4—31no—
788C4⋊C4—32no—
789C4⋊C4—31no—
790C4⋊C4—32no—
791C4⋊C4—34no—
792C4⋊C4—32no—
793C4⋊C4—32no—
794C4⋊C4—34no—
795C4⋊C4—94no—
796C4⋊C4—92no—
797C4⋊C4—94no—
798C4⋊C4—94no—
799C4⋊C4—94no—
800C4⋊C4—92no—
801C4⋊C4—91no—
802C4⋊C4—92no—
803C4⋊C4—92no—
804C4⋊C4C2×D3211yescharacteristic
805C4⋊C4C2×D3212yes—
806C22⋊C4—32no—
807C22⋊C4—32no—
808C22⋊C4—34no—
809C22⋊C4—34no—
810C22⋊C4—34no—
811C22⋊C4—94no—
812C22⋊C4—94no—
813C22⋊C4—92no—
814C22⋊C4—92no—
815C22⋊C4—94no—
816C22⋊C4—92no—
817C22⋊C4—92no—
818C22⋊C4—92no—
819C22⋊C4—92no—
820C22⋊C4—92no—
821C42—34no—
822C42—94no—
823C42—91no—
824C42—91no—
825C42—91no—
826C42C2×D3211yescharacteristic
827C42C2×D3212yes—
828C22×C3—21no—
829C22×C3—34no—
830C22×C3—62no—
831C22×C3—62no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—62no—
835C22×C3C24×D311yescharacteristic
836C22×C3C24×D311yescharacteristic
837C2×D3—22no—
838C2×D3—22no—
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—32no—
843C2×D3—32no—
844C2×D3—62no—
845C2×D3—61no—
846C2×D3—61no—
847C2×D3—61no—
848C2×D3—61no—
849C2×D3—62no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—121no—
856C2×D3—121no—
857C2×D3—122no—
858C2×D3—122no—
859C2×D3—122no—
860C2×D3—128no—
861C2×D3—128no—
862C2×D3C2×#23914yes—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—21no—
866C3×C4—21no—
867C3×C4—22no—
868C3×C4—22no—
869C3×C4—22no—
870C3×C4—22no—
871C3×C4—41no—
872C3×C4—42no—
873C3×C4—42no—
874C3×C4—62no—
875C3×C4—64no—
876C3×C4—62no—
877C3×C4—64no—
878C3×C4#100412yes—
879C3×C4C2×#23912yes—
880C3×C4D3×#4112yes—
881C3×C4#100912yes—
882Dic3—24no—
883Dic3—22no—
884Dic3—24no—
885Dic3—22no—
886Dic3—61no—
887Dic3—62no—
888Dic3—61no—
889Dic3—62no—
890Dic3—61no—
891Dic3—61no—
892Dic3—61no—
893Dic3—61no—
894Dic3—121no—
895Dic3—122no—
896Dic3—121no—
897Dic3—121no—
898C32#352011yescharacteristic, complemented, Sylow
899C23—32no—
900C23—32no—
901C23—91no—
902C23—92no—
903C23—184no—
904C23—184no—
905C23—362no—
906Q8—22no—
907Q8—64no—
908Q8—64no—
909Q8—124no—
910D4—34no—
911D4—62no—
912D4—184no—
913D4—188no—
914D4—184no—
915D4—182no—
916D4—364no—
917C2×C4—32no—
918C2×C4—34no—
919C2×C4—34no—
920C2×C4—32no—
921C2×C4—64no—
922C2×C4—64no—
923C2×C4—91no—
924C2×C4—91no—
925C2×C4—91no—
926C2×C4—92no—
927C2×C4—124no—
928C2×C4—182no—
929C2×C4—188no—
930C2×C4—182no—
931C2×C4—182no—
932C2×C4—184no—
933C2×C4—362no—
934C2×C4—364no—
935C2×C4—362no—
936C2×C4—362no—
937C2×C4C22×D3212yes—
938C2×C4C22×D3211yescharacteristic
939C2×C4C22×D3212yes—
940C2×C4C22×D3211yescharacteristic
941C2×C4C22×D3211yescharacteristic
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—64no—
946C2×C3—122no—
947C2×C3C2×#100411yescharacteristic
948C2×C3C22×#23911yescharacteristic
949C2×C3C2×D3×#4111yescharacteristic
950C2×C3C2×#100911yescharacteristic
951C2×C3D3×2−1+411yescharacteristic
952C2×C3D3×2−1+411yescharacteristic
953D3—24no—
954D3—42no—
955D3—62no—
956D3—62no—
957D3—122no—
958D3—122no—
959D3—122no—
960D3—242no—
961C22—34no—
962C22—62no—
963C22—62no—
964C22—62no—
965C22—62no—
966C22—62no—
967C22—92no—
968C22—181no—
969C22—181no—
970C22—182no—
971C22—182no—
972C22—182no—
973C22—368no—
974C22C23×D3211yescharacteristic
975C4—22no—
976C4—21no—
977C4—22no—
978C4—62no—
979C4—62no—
980C4—64no—
981C4—64no—
982C4—181no—
983C4—182no—
984C4—181no—
985C4—181no—
986C4#6430712yes—
987C4D3×#23912yes—
988C3—21no—
989C3#8675111yescharacteristic, complemented
990C3#8699011yescharacteristic, complemented
991C2—64no—
992C2—122no—
993C2—182no—
994C2—362no—
995C2C2×#6430711yescharacteristic
996C2C2×D3×#23911yescharacteristic
997C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3520
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596051C2semidirect
2. C3×#5584C2semidirect
3. C3×Q8×D12C2semidirect
4. D3×#946C2semidirect
5. #10595402C2semidirect
6. #10594654C2semidirect
7. #10594627C2semidirect
8. #10594456C2semidirect
9. #10594439C2semidirect
10. #10594005C2semidirect
11. C4×#3802C2semidirect
12. #10593958C2semidirect
13. #10593955C2semidirect
14. #10593896C2semidirect
15. #10593889C2semidirect
16. #10593869C2semidirect
17. #10593866C2semidirect
20. C2×C3×D3×Q8C22semidirect
23. C2×#3799C22semidirect
25. C32×C4×Q8C22semidirect
26. #64156C22semidirect
28. #64107C22semidirect
31. #64099C22semidirect
33. C4×C4⋊(C3⋊D3)C22semidirect
34. #64081C22semidirect
36. C3×#946C22semidirect
37. C3×#898C22semidirect
38. C3×#897C22semidirect
39. C3×#897C22semidirect
40. C3×#892C22semidirect
45. C3×#869C22semidirect
46. C3×#869C22semidirect
47. C3×#869C22semidirect
48. C3×C4×Dic6C22semidirect
53. #63909C22semidirect
54. #63907C22semidirect
56. #63904C22semidirect
60. #63900C22semidirect
65. #63890C22semidirect
66. #63890C22semidirect
67. D3×C4⋊Dic3C22semidirect
69. #63888C22semidirect
70. #63887C22semidirect
71. #63880C22semidirect
72. #63877C22semidirect
73. D3×Dic3⋊C4C22semidirect
74. #63872C22semidirect
77. #63871C22semidirect
78. #63869C22semidirect
79. #63858C22semidirect
80. #63856C22semidirect
81. #63854C22semidirect
83. #63843C22semidirect
84. #63843C22semidirect
105. #5584D3semidirect
110. Q8×D12D3semidirect
194. C2×D3×Q8C2×D3semidirect
211. C3×C4×Q8C2×D3semidirect
212. C3×C4×Q8C2×D3semidirect
231. #946C2×D3semidirect
250. #898C2×D3semidirect
254. #897C2×D3semidirect
255. #897C2×D3semidirect
275. #892C2×D3semidirect
328. #869C2×D3semidirect
329. #869C2×D3semidirect
330. #869C2×D3semidirect
331. C4×Dic6C2×D3semidirect
360. C3×D12#41semidirect
623. C4×Q8D32semidirect
725. D12#239semidirect
898. C32#3520semidirect
989. C3#86751semidirect
990. C3#86990semidirect

Maximal subgroups

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

subgroupindex
#105960512
C3×#55842
C3×Q8×D122
D3×#9462
#105954022
#105946542
#105946272
#105944562
#105944392
#105940052
C4×#38022
#105939582
#105939552
#105938962
#105938892
#105938692
#105938662
#869903
#867513