Finite Group Databasebeta

← #11909315

Subgroups — #11909315

Order 1152.

2359 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C3×#5727C211yesmaximal, characteristic, complemented
3C3×#5726C211yesmaximal, characteristic, complemented
4#10595424C212yesmaximal, complemented
5D3×#946C212yesmaximal, complemented
6#10595409C212yesmaximal, complemented
7#10595380C212yesmaximal, complemented
8#10594653C214yesmaximal, complemented
9#10594630C212yesmaximal, complemented
10#10594537C212yesmaximal, complemented
11#10594494C212yesmaximal, complemented
12#10594455C214yesmaximal, complemented
13#10594359C212yesmaximal, complemented
14C4×#3802C211yesmaximal, characteristic, complemented
15#10593895C211yesmaximal, characteristic, complemented
16#10593879C211yesmaximal, characteristic, complemented
17#10593875C211yesmaximal, characteristic, complemented
18#86751—31nomaximal
19#86686—31nomaximal
20C2×C3×#239C2212yescomplemented
21C2×C3×D3×Q8C2212yescomplemented
22C2×#3802C2211yescharacteristic
23C2×C4×D32C2212yes—
24C2×#3795C2212yes—
25C32×C4⋊Q8C2211yescharacteristic, complemented
26#64155C2212yes—
27Q8×C3⋊Dic3C2212yescomplemented
28#64106C2212yes—
29#64101C2212yes—
30#64099C2212yescomplemented
31#64096C2212yescomplemented
32C42×C3⋊D3C2211yescharacteristic
33#64078C2211yescharacteristic, complemented
34C3×#946C2212yescomplemented
35C3×#946C2212yescomplemented
36C3×#896C2214yescomplemented
37C3×#895C2212yes—
38C3×#894C2214yescomplemented
39C3×#893C2212yes—
40C3×D3×C4⋊C4C2212yescomplemented
41C3×#888C2212yescomplemented
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic
44C3×C4×D12C2211yescharacteristic, complemented
45C3×C4×Dic6C2211yescharacteristic, complemented
46#63922C2214yes—
47#63921C2212yes—
48D3×(C2×D3)⋊C4C2214yes—
49#63916C2211yescharacteristic
50#63908C2214yes—
51#63908C2212yescomplemented
52#63904C2214yes—
53C4×#626C2212yes—
54#63902C2212yes—
55C4×#625C2212yes—
56C4×#625C2214yescomplemented
57#63900C2211yescharacteristic
58#63898C2211yescharacteristic
59#63898C2211yescharacteristic
60#63891C2214yes—
61#63891C2214yescomplemented
62D3×C4⋊Dic3C2212yescomplemented
63#63888C2214yes—
64#63887C2214yescomplemented
65#63884C2214yescomplemented
66#63879C2214yescomplemented
67#63878C2214yescomplemented
68D3×Dic3⋊C4C2214yescomplemented
69#63872C2211yescharacteristic, complemented
70#63871C2211yescharacteristic
71#63863C2211yescharacteristic, complemented
72#63863C2214yescomplemented
73#63862C2214yescomplemented
74#63862C2212yescomplemented
75#63861C2214yescomplemented
76#63860C2212yes—
77#63857C2212yescomplemented
78#63856C2212yescomplemented
79#63856C2214yescomplemented
80#63855C2212yescomplemented
81#63853C2212yes—
82#63845C2214yescomplemented
83#63844C2212yescomplemented
84#63841C2212yescomplemented
85C3×D4×Q8—31no—
86C3×#547—31no—
87#5831—32no—
88#5828—32no—
89#5817—32no—
90C2×#946—32no—
91#5733—32no—
92#5730—32no—
93#5728—31no—
94#5728—31no—
95#5728—61no—
96#5727D311yescharacteristic, complemented
97#5726D311yescharacteristic, complemented
98#5660—34no—
99#5659—34no—
100#5645—34no—
101#5642—32no—
102#5639—32no—
103#5637—34no—
104#5627—32no—
105D3×C22⋊Q8—32no—
106#5612—32no—
107#5603—32no—
108#5584—31no—
109#5580—31no—
110#5557—31no—
111#5555—31no—
112#5554—32no—
113#5551—31no—
114#5546—32no—
115C4×D3×D4—31no—
116C4×D3×D4—31no—
117#5542—31no—
118#5511—32no—
119#5504—32no—
120C22×D32C2312yes—
121C2×C32×Q8C2312yes—
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×#634C2312yes—
126C3×#239—44no—
127C3×D3×Q8—44no—
128C2×C3×D12C2311yescharacteristic
129C2×C3×D12C2311yescharacteristic
130C2×C3×D12C2314yes—
131C2×C3×D12C2311yescharacteristic
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2312yes—
134C2×C3×C4×D3C2312yes—
135C2×C3×C4×D3C2314yes—
136C2×C3×C4×D3C2314yes—
137C2×C3×Dic6C2311yescharacteristic
138C2×C3×Dic6C2314yes—
139C2×#626C2312yes—
140C2×#625C2314yes—
141C2×#625C2312yes—
142C2×#624C2312yes—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2312yes—
145C2×D3×Dic3C2312yes—
146#3802—24no—
147C4×D32—44no—
148#3795—28no—
149C32×C4⋊C4C2312yes—
150C32×C4⋊C4C2312yes—
151C32×C42C2311yescharacteristic
152#3752C2314yes—
153C4⋊(C3⋊Dic3)C2312yes—
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2314yes—
156#3750C2314yes—
157C4×C3⋊Dic3C2311yescharacteristic
158C4×C3⋊Dic3C2311yescharacteristic
159C4×C3⋊Dic3C2311yescharacteristic
160C4×C3⋊Dic3C2314yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×(C2×D3)⋊C4C2312yes—
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2312yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2311yescharacteristic
169C3×C4⋊Dic3C2311yescharacteristic
170C3×Dic3⋊C4C2314yes—
171C3×Dic3⋊C4C2314yes—
172C3×Dic3⋊C4C2312yes—
173C3×C4×Dic3C2312yes—
174#3724C2314yes—
175#3724C2312yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2312yes—
180#3722C2312yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2312yes—
188(C2×D3)⋊Dic3C2312yes—
189Dic32C2314yes—
190#3520—91noSylow
191C2×C3×#41—32no—
192C22×C3×Q8—32no—
193C2×#239C2×D312yescomplemented
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—21no—
202C3×C4⋊Q8—32no—
203C3×C4⋊Q8C2×D311yescharacteristic, complemented
204C3×C4⋊Q8C2×D311yescharacteristic, complemented
205C3×#123—34no—
206C3×C22⋊Q8—32no—
207C3×C22⋊Q8—32no—
208C3×C22⋊Q8—34no—
209C3×#121—32no—
210C3×C4×Q8—31no—
211C3×C4×D4—32no—
212C3×C4×D4—31no—
213C3×C4×D4—31no—
214C3×C4×D4—31no—
215C2×C3×C4⋊C4—32no—
216#947—34no—
217#947—31no—
218#946—32no—
219#946—32no—
220#946—34no—
221#946—32no—
222#946—34no—
223#946—31no—
224#946—34no—
225#946—62no—
226#946C2×D312yescomplemented
227#946C2×D312yescomplemented
228Q8×Dic3—32no—
229Q8×Dic3—32no—
230Q8×Dic3—62no—
231#938—34no—
232#938—32no—
233#938—31no—
234#937—34no—
235#936—34no—
236#936—31no—
237#936—32no—
238#935—34no—
239D4×Dic3—31no—
240D4×Dic3—31no—
241#930—34no—
242#930—32no—
243C4×#67—34no—
244C4×#67—32no—
245C4×#67—32no—
246C4×#67—34no—
247C4×#67—34no—
248C4×#67—34no—
249C4×#67—32no—
250C2×(C2×D3)⋊C4—34no—
251#926—32no—
252#926—32no—
253C2×C4⋊Dic3—32no—
254#924—34no—
255#924—32no—
256#924—32no—
257C2×Dic3⋊C4—34no—
258#898—34no—
259#898—34no—
260#898—32no—
261#897—32no—
262#897—31no—
263#897—32no—
264#897—32no—
265#897—62no—
266#896—34no—
267#896C2×D314yescomplemented
268#895—31no—
269#895C2×D312yes—
270#894—34no—
271#894—32no—
272#894C2×D314yescomplemented
273#893—31no—
274#893—31no—
275#893—34no—
276#893C2×D312yes—
277#892—32no—
278#892—32no—
279#892—32no—
280#892—34no—
281#892—62no—
282D3×C4⋊C4—32no—
283D3×C4⋊C4—34no—
284D3×C4⋊C4—31no—
285D3×C4⋊C4—31no—
286D3×C4⋊C4C2×D312yescomplemented
287#890—32no—
288#890—32no—
289#890—31no—
290#890—31no—
291#890—34no—
292#890—62no—
293#889—34no—
294#888C2×D312yescomplemented
295#887—32no—
296#887—32no—
297#887—32no—
298#887—62no—
299#886—34no—
300#886—34no—
301#883—34no—
302#883—34no—
303#883—32no—
304#882—34no—
305#67⋊C4—34no—
306#67⋊C4—32no—
307#67⋊C4—32no—
308D3×C22⋊C4—34no—
309D3×C22⋊C4—32no—
310D3×C22⋊C4—32no—
311#879—34no—
312#879—34no—
313#879—32no—
314#878—34no—
315#877—34no—
316#875—32no—
317C4×D12—32no—
318C4×D12C2×D311yescharacteristic
319C4×D12C2×D311yescharacteristic
320C4×D12C2×D311yescharacteristic, complemented
321#872—32no—
322C42×D3—31no—
323C42×D3—31no—
324C42×D3—61no—
325#869—31no—
326#869—31no—
327#869—61no—
328C4×Dic6—32no—
329C4×Dic6C2×D311yescharacteristic, complemented
330C22×C3⋊D3C2411yescharacteristic
331C22×C3×D3C2412yes—
332C22×C3×D3C2412yes—
333C22×C3×D3C2412yes—
334C2×D32—24no—
335C2×D32—24no—
336C2×D32—42no—
337C32×Q8—24no—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2414yes—
340C2×C32×C4C2411yescharacteristic
341C2×C32×C4C2411yescharacteristic
342C2×C3⋊Dic3C2414yes—
343C2×C3⋊Dic3C2411yescharacteristic
344C2×C3⋊Dic3C2411yescharacteristic
345C2×C3⋊Dic3C2411yescharacteristic
346C4×C3⋊D3—22no—
347C4×C3⋊D3—22no—
348C4×C3⋊D3—22no—
349#634—24no—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C3×D12—22no—
356C3×D12—22no—
357C3×D12—44no—
358C3×D12#4114yescomplemented
359C3×C4×D3—24no—
360C3×C4×D3—24no—
361C3×C4×D3—24no—
362C3×C4×D3—44no—
363C3×C4×D3—44no—
364C3×Dic6—22no—
365C3×Dic6—44no—
366#626—24no—
367#625—28no—
368#625—24no—
369#624—42no—
370D3×Dic3—28no—
371D3×Dic3—42no—
372D3×Dic3—42no—
373#556—91no—
374#554—92no—
375#552—92no—
376#551—94no—
377D4×Q8—31no—
378#548—92no—
379#547—31no—
380#547—91no—
381#546—92no—
382#542—92no—
383#539—94no—
384#533—91no—
385#529—91no—
386#525—92no—
387C2×C22⋊Q8—92no—
388#520—92no—
389C2×C4×D4—91no—
390C23×D3—32no—
391C23×D3—32no—
392C3×#41—124no—
393C2×C3×Q8—22no—
394C2×C3×Q8—31no—
395C2×C3×Q8—34no—
396C2×C3×Q8—124no—
397C2×C3×Q8C22×D312yes—
398C2×C3×Q8C22×D312yes—
399C2×C3×D4—31no—
400C2×C3×D4—31no—
401C2×C3×D4—31no—
402C2×C3×D4—34no—
403C22×C3×C4—32no—
404C22×C3×C4—32no—
405C22×C3×C4—32no—
406C22×C3×C4—34no—
407C22×C3×C4—34no—
408C2×#67—34no—
409C2×#67—32no—
410C2×#67—32no—
411C2×#67—34no—
412C2×#67—32no—
413C22×Dic3—34no—
414C22×Dic3—32no—
415C22×Dic3—32no—
416#239—44no—
417D3×Q8—44no—
418#237—68no—
419D3×D4—64no—
420D3×D4—64no—
421#235—68no—
422C2×D12—32no—
423C2×D12C22×D311yescharacteristic
424C2×D12C22×D311yescharacteristic
425C2×D12C22×D314yes—
426C2×D12C22×D311yescharacteristic
427C2×C4×D3—34no—
428C2×C4×D3—31no—
429C2×C4×D3—31no—
430C2×C4×D3—31no—
431C2×C4×D3—31no—
432C2×C4×D3—31no—
433C2×C4×D3—31no—
434C2×C4×D3—32no—
435C2×C4×D3—32no—
436C2×C4×D3—32no—
437C2×C4×D3—32no—
438C2×C4×D3—61no—
439C2×C4×D3—61no—
440C2×C4×D3—61no—
441C2×C4×D3—124no—
442C2×C4×D3—124no—
443C2×C4×D3C22×D312yes—
444C2×C4×D3C22×D312yes—
445C2×C4×D3C22×D312yes—
446C2×C4×D3C22×D314yes—
447C2×C4×D3C22×D314yes—
448C2×Dic6—32no—
449C2×Dic6—32no—
450C2×Dic6—62no—
451C2×Dic6C22×D311yescharacteristic
452C2×Dic6C22×D314yes—
453C3×C4⋊C4—22no—
454C3×C4⋊C4—22no—
455C3×C4⋊C4—31no—
456C3×C4⋊C4—34no—
457C3×C4⋊C4—31no—
458C3×C4⋊C4—31no—
459C3×C4⋊C4—34no—
460C3×C4⋊C4—31no—
461C3×C4⋊C4—32no—
462C3×C4⋊C4C22×D312yes—
463C3×C4⋊C4C22×D312yes—
464C3×C4⋊C4C22×D312yes—
465C3×C4⋊C4C22×D312yes—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—32no—
469C3×C22⋊C4—32no—
470C3×C22⋊C4—32no—
471C3×C42—21no—
472C3×C42—32no—
473C3×C42C22×D311yescharacteristic
474C3×C42C22×D311yescharacteristic
475#217—32no—
476#217—34no—
477#217—32no—
478#217—34no—
479#217—32no—
480#217—32no—
481#217—34no—
482#217—32no—
483(C2×D3)⋊C4—32no—
484(C2×D3)⋊C4—32no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—34no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—32no—
494(C2×D3)⋊C4—32no—
495(C2×D3)⋊C4—64no—
496(C2×D3)⋊C4C22×D312yes—
497(C2×D3)⋊C4C22×D312yes—
498(C2×D3)⋊C4C22×D312yes—
499(C2×D3)⋊C4C22×D314yes—
500(C2×D3)⋊C4C22×D314yes—
501C4⋊Dic3—32no—
502C4⋊Dic3—32no—
503C4⋊Dic3—32no—
504C4⋊Dic3—32no—
505C4⋊Dic3—34no—
506C4⋊Dic3—34no—
507C4⋊Dic3—32no—
508C4⋊Dic3—32no—
509C4⋊Dic3—32no—
510C4⋊Dic3—34no—
511C4⋊Dic3—62no—
512C4⋊Dic3—62no—
513C4⋊Dic3—64no—
514C4⋊Dic3C22×D311yescharacteristic
515C4⋊Dic3C22×D311yescharacteristic
516C4⋊Dic3C22×D311yescharacteristic
517C4⋊Dic3C22×D311yescharacteristic
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—32no—
522Dic3⋊C4—32no—
523Dic3⋊C4—34no—
524Dic3⋊C4—32no—
525Dic3⋊C4—34no—
526Dic3⋊C4—32no—
527Dic3⋊C4—32no—
528Dic3⋊C4—64no—
529Dic3⋊C4C22×D312yes—
530Dic3⋊C4C22×D314yes—
531Dic3⋊C4C22×D314yes—
532C4×Dic3—31no—
533C4×Dic3—31no—
534C4×Dic3—31no—
535C4×Dic3—31no—
536C4×Dic3—31no—
537C4×Dic3—31no—
538C4×Dic3—34no—
539C4×Dic3—34no—
540C4×Dic3—34no—
541C4×Dic3—34no—
542C4×Dic3—61no—
543C4×Dic3—61no—
544C4×Dic3—61no—
545C4×Dic3—64no—
546C4×Dic3C22×D312yes—
547C22×C32C2511yescharacteristic
548C2×C3⋊D3—21no—
549C2×C3⋊D3—21no—
550C2×C3⋊D32−1+412yes—
551C2×C3×D3—22no—
552C2×C3×D3—22no—
553C2×C3×D3—22no—
554C2×C3×D3—22no—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C2×C3×D3—22no—
559C2×C3×D3C2×#4114yes—
560D32—48no—
561C32×C4—21no—
562C32×C4—24no—
563C32×C4C2×#4112yes—
564C32×C4H(5,𝔽2)12yes—
565C3⋊Dic3—21no—
566C3⋊Dic3—24no—
567C3⋊Dic3—21no—
568C3⋊Dic3—21no—
569C3×Dic3—22no—
570C3×Dic3—22no—
571C3×Dic3—22no—
572C3×Dic3—22no—
573C3×Dic3—22no—
574C2×#41—32no—
575C2×#41—92no—
576C22×Q8—32no—
577C22×D4—91no—
578C23×C4—92no—
579C4⋊Q8—32no—
580C4⋊Q8—91no—
581C4⋊Q8D3211yescharacteristic, complemented
582#126—92no—
583#126—94no—
584#126—94no—
585#125—91no—
586#125—94no—
587#125—92no—
588#124—92no—
589#124—91no—
590#124—94no—
591#123—34no—
592#123—94no—
593#123—94no—
594#123—92no—
595#123—94no—
596C22⋊Q8—32no—
597C22⋊Q8—32no—
598C22⋊Q8—34no—
599C22⋊Q8—94no—
600C22⋊Q8—92no—
601C22⋊Q8—91no—
602C22⋊Q8—94no—
603C22⋊Q8—92no—
604C22⋊Q8—94no—
605C22⋊Q8—92no—
606C22⋊Q8—92no—
607#121—32no—
608#121—91no—
609#121—92no—
610#121—94no—
611#120—94no—
612C4×Q8—31no—
613C4×Q8—92no—
614C4×Q8—92no—
615C4×Q8—92no—
616C4×D4—32no—
617C4×D4—31no—
618C4×D4—31no—
619C4×D4—31no—
620C4×D4—92no—
621C4×D4—92no—
622C4×D4—94no—
623C4×D4—94no—
624C4×D4—91no—
625C4×D4—91no—
626C4×D4—92no—
627C4×D4—94no—
628#117—92no—
629#117—94no—
630#117—92no—
631#117—92no—
632C2×C4⋊C4—32no—
633C2×C4⋊C4—91no—
634C2×C4⋊C4—94no—
635C2×C4⋊C4—92no—
636C2×C22⋊C4—92no—
637C2×C22⋊C4—94no—
638C2×C42—91no—
639C23×C3—32no—
640C23×C3—32no—
641C23×C3—32no—
642C22×D3—31no—
643C22×D3—31no—
644C22×D3—61no—
645C22×D3—64no—
646C22×D3—64no—
647C22×D3—64no—
648C22×D3—64no—
649C22×D3—122no—
650C22×D3—122no—
651C22×D3C23×D312yes—
652C22×D3C23×D312yes—
653C22×D3C23×D312yes—
654C3×Q8—24no—
655C3×Q8—24no—
656C3×Q8—44no—
657C3×Q8—62no—
658C3×Q8—124no—
659C3×D4—34no—
660C3×D4—62no—
661C3×D4—62no—
662C3×D4—124no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—24no—
667C2×C3×C4—32no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—32no—
672C2×C3×C4—64no—
673C2×C3×C4—64no—
674C2×C3×C4—64no—
675C2×C3×C4—124no—
676C2×C3×C4—124no—
677C2×C3×C4C23×D314yes—
678C2×C3×C4C23×D314yes—
679C2×C3×C4C23×D311yescharacteristic
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685#67—64no—
686#67—64no—
687#67—68no—
688#67—68no—
689#67—64no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—34no—
696C2×Dic3—31no—
697C2×Dic3—34no—
698C2×Dic3—61no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—64no—
702C2×Dic3—68no—
703C2×Dic3—122no—
704C2×Dic3—122no—
705C2×Dic3C23×D312yes—
706C2×Dic3C23×D312yes—
707C2×Dic3C23×D312yes—
708C2×Dic3C23×D312yes—
709C2×Dic3C23×D312yes—
710D12—22no—
711D12—22no—
712D12—44no—
713D12—64no—
714D12#23914yescomplemented
715C4×D3—24no—
716C4×D3—24no—
717C4×D3—24no—
718C4×D3—44no—
719C4×D3—44no—
720C4×D3—62no—
721C4×D3—62no—
722C4×D3—64no—
723C4×D3—68no—
724C4×D3—62no—
725C4×D3—62no—
726C4×D3—62no—
727C4×D3—62no—
728C4×D3—122no—
729C4×D3—122no—
730C4×D3—122no—
731C4×D3—122no—
732C4×D3—122no—
733C4×D3—122no—
734Dic6—22no—
735Dic6—44no—
736Dic6—64no—
737Dic6—64no—
738Dic6—124no—
739C2×C32C22×#4111yescharacteristic
740C2×C32C2×H(5,𝔽2)11yescharacteristic
741C2×C32C2×2−1+411yescharacteristic
742C3⋊D3—22no—
743C3×D3—24no—
744C3×D3—42no—
745C3×D3—42no—
746C24—92no—
747#41—124no—
748#41—188no—
749C2×Q8—31no—
750C2×Q8—34no—
751C2×Q8—92no—
752C2×Q8—124no—
753C2×Q8C2×D3212yes—
754C2×D4—31no—
755C2×D4—31no—
756C2×D4—31no—
757C2×D4—34no—
758C2×D4—92no—
759C2×D4—94no—
760C2×D4—92no—
761C2×D4—184no—
762C22×C4—32no—
763C22×C4—32no—
764C22×C4—32no—
765C22×C4—34no—
766C22×C4—34no—
767C22×C4—92no—
768C22×C4—94no—
769C22×C4—92no—
770C22×C4—92no—
771C22×C4—91no—
772C22×C4—91no—
773C22×C4—91no—
774C22×C4—364no—
775C4⋊C4—31no—
776C4⋊C4—34no—
777C4⋊C4—31no—
778C4⋊C4—31no—
779C4⋊C4—31no—
780C4⋊C4—34no—
781C4⋊C4—32no—
782C4⋊C4—92no—
783C4⋊C4—92no—
784C4⋊C4—94no—
785C4⋊C4—94no—
786C4⋊C4—92no—
787C4⋊C4—92no—
788C4⋊C4—92no—
789C4⋊C4—94no—
790C4⋊C4—92no—
791C4⋊C4—94no—
792C4⋊C4C2×D3212yes—
793C4⋊C4C2×D3212yes—
794C22⋊C4—32no—
795C22⋊C4—32no—
796C22⋊C4—34no—
797C22⋊C4—34no—
798C22⋊C4—32no—
799C22⋊C4—92no—
800C22⋊C4—92no—
801C22⋊C4—92no—
802C22⋊C4—94no—
803C22⋊C4—92no—
804C22⋊C4—92no—
805C22⋊C4—94no—
806C22⋊C4—92no—
807C22⋊C4—94no—
808C22⋊C4—94no—
809C42—32no—
810C42—94no—
811C42—91no—
812C42—91no—
813C42—91no—
814C42—94no—
815C42C2×D3211yescharacteristic
816C22×C3—21no—
817C22×C3—34no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3—62no—
826C22×C3C24×D311yescharacteristic
827C22×C3C24×D311yescharacteristic
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—32no—
837C2×D3—32no—
838C2×D3—62no—
839C2×D3—61no—
840C2×D3—61no—
841C2×D3—61no—
842C2×D3—61no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—128no—
846C2×D3—128no—
847C2×D3C2×#23914yes—
848C3×C4—22no—
849C3×C4—24no—
850C3×C4—24no—
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—22no—
854C3×C4—22no—
855C3×C4—44no—
856C3×C4—62no—
857C3×C4—62no—
858C3×C4—62no—
859C3×C4—62no—
860C3×C4—62no—
861C3×C4#100412yes—
862C3×C4#100412yes—
863C3×C4C2×#23912yes—
864C3×C4D3×#4112yes—
865Dic3—22no—
866Dic3—22no—
867Dic3—22no—
868Dic3—22no—
869Dic3—22no—
870Dic3—62no—
871Dic3—61no—
872Dic3—61no—
873Dic3—64no—
874Dic3—61no—
875Dic3—64no—
876Dic3—61no—
877Dic3—61no—
878Dic3—61no—
879Dic3—124no—
880Dic3—121no—
881Dic3—121no—
882C32#352011yescharacteristic, complemented, Sylow
883C23—32no—
884C23—32no—
885C23—32no—
886C23—91no—
887C23—184no—
888C23—184no—
889C23—362no—
890Q8—24no—
891Q8—62no—
892Q8—124no—
893Q8—184no—
894D4—34no—
895D4—62no—
896D4—62no—
897D4—124no—
898D4—184no—
899D4—184no—
900D4—188no—
901C2×C4—32no—
902C2×C4—32no—
903C2×C4—32no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—64no—
907C2×C4—64no—
908C2×C4—64no—
909C2×C4—91no—
910C2×C4—94no—
911C2×C4—91no—
912C2×C4—91no—
913C2×C4—124no—
914C2×C4—124no—
915C2×C4—182no—
916C2×C4—188no—
917C2×C4—182no—
918C2×C4—182no—
919C2×C4—362no—
920C2×C4—362no—
921C2×C4—362no—
922C2×C4C22×D3211yescharacteristic
923C2×C4C22×D3214yes—
924C2×C4C22×D3211yescharacteristic
925C2×C4C22×D3211yescharacteristic
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—64no—
930C2×C3—122no—
931C2×C3—122no—
932C2×C3C2×#100411yescharacteristic
933C2×C3C2×#100411yescharacteristic
934C2×C3C22×#23911yescharacteristic
935C2×C3C2×D3×#4111yescharacteristic
936C2×C3D3×2−1+411yescharacteristic
937C2×C3D3×2−1+411yescharacteristic
938D3—24no—
939D3—42no—
940D3—42no—
941D3—62no—
942D3—62no—
943D3—122no—
944C22—34no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—62no—
951C22—62no—
952C22—62no—
953C22—92no—
954C22—181no—
955C22—181no—
956C22—368no—
957C22C23×D3211yescharacteristic
958C4—24no—
959C4—21no—
960C4—62no—
961C4—62no—
962C4—62no—
963C4—62no—
964C4—62no—
965C4—181no—
966C4—181no—
967C4—184no—
968C4—181no—
969C4#6431312yes—
970C4D3×#23912yes—
971C3—21no—
972C3#8668611yescharacteristic, complemented
973C3#8675111yescharacteristic, complemented
974C2—64no—
975C2—122no—
976C2—122no—
977C2—182no—
978C2C2×#6431311yescharacteristic
979C2C2×D3×#23911yescharacteristic
980C2#1059668711yescharacteristic
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. #10596199C2semidirect
2. C3×#5727C2semidirect
3. C3×#5726C2semidirect
4. #10595424C2semidirect
5. D3×#946C2semidirect
6. #10595409C2semidirect
7. #10595380C2semidirect
8. #10594653C2semidirect
9. #10594630C2semidirect
10. #10594537C2semidirect
11. #10594494C2semidirect
12. #10594455C2semidirect
13. #10594359C2semidirect
14. C4×#3802C2semidirect
15. #10593895C2semidirect
16. #10593879C2semidirect
17. #10593875C2semidirect
20. C2×C3×#239C22semidirect
21. C2×C3×D3×Q8C22semidirect
25. C32×C4⋊Q8C22semidirect
27. Q8×C3⋊Dic3C22semidirect
30. #64099C22semidirect
31. #64096C22semidirect
33. #64078C22semidirect
34. C3×#946C22semidirect
35. C3×#946C22semidirect
36. C3×#896C22semidirect
38. C3×#894C22semidirect
40. C3×D3×C4⋊C4C22semidirect
41. C3×#888C22semidirect
44. C3×C4×D12C22semidirect
45. C3×C4×Dic6C22semidirect
51. #63908C22semidirect
56. C4×#625C22semidirect
61. #63891C22semidirect
62. D3×C4⋊Dic3C22semidirect
64. #63887C22semidirect
65. #63884C22semidirect
66. #63879C22semidirect
67. #63878C22semidirect
68. D3×Dic3⋊C4C22semidirect
69. #63872C22semidirect
71. #63863C22semidirect
72. #63863C22semidirect
73. #63862C22semidirect
74. #63862C22semidirect
75. #63861C22semidirect
77. #63857C22semidirect
78. #63856C22semidirect
79. #63856C22semidirect
80. #63855C22semidirect
82. #63845C22semidirect
83. #63844C22semidirect
84. #63841C22semidirect
96. #5727D3semidirect
97. #5726D3semidirect
193. C2×#239C2×D3semidirect
194. C2×D3×Q8C2×D3semidirect
203. C3×C4⋊Q8C2×D3semidirect
204. C3×C4⋊Q8C2×D3semidirect
226. #946C2×D3semidirect
227. #946C2×D3semidirect
267. #896C2×D3semidirect
272. #894C2×D3semidirect
286. D3×C4⋊C4C2×D3semidirect
294. #888C2×D3semidirect
320. C4×D12C2×D3semidirect
329. C4×Dic6C2×D3semidirect
358. C3×D12#41semidirect
581. C4⋊Q8D32semidirect
714. D12#239semidirect
882. C32#3520semidirect
972. C3#86686semidirect
973. C3#86751semidirect

Maximal subgroups

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

subgroupindex
#105961992
C3×#57272
C3×#57262
#105954242
D3×#9462
#105954092
#105953802
#105946532
#105946302
#105945372
#105944942
#105944552
#105943592
C4×#38022
#105938952
#105938792
#105938752
#867513
#866863