Finite Group Databasebeta

← #11909314

Subgroups — #11909314

Order 1152.

2388 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic, complemented
3C3×#5726C211yesmaximal, characteristic, complemented
4#10595429C212yesmaximal, complemented
5#10595424C212yesmaximal, complemented
6#10595414C212yesmaximal, complemented
7#10595344C212yesmaximal, complemented
8#10594644C214yesmaximal, complemented
9#10594633C212yesmaximal, complemented
10#10594532C212yesmaximal, complemented
11#10594498C212yesmaximal, complemented
12#10594490C214yesmaximal, complemented
13#10594327C212yesmaximal, complemented
14C4×D3×D12C211yesmaximal, characteristic, complemented
15#10593974C211yesmaximal, characteristic, complemented
16#10593869C211yesmaximal, characteristic, complemented
17#10593863C211yesmaximal, characteristic, complemented
18#86686—31nomaximal
19#86285—31nomaximal
20C2×Q8×C3⋊D3C2212yescomplemented
21C2×C3×#239C2212yescomplemented
22C2×D3×D12C2211yescharacteristic
23C2×C4×D32C2212yes—
24C2×#3799C2212yes—
25C32×C4⋊Q8C2211yescharacteristic, complemented
26#64155C2212yescomplemented
27#64105C2214yescomplemented
28#64102C2212yes—
29#64097C2212yescomplemented
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C4×#634C2211yescharacteristic, complemented
32C3×#946C2212yes—
33C3×#946C2212yescomplemented
34C3×Q8×Dic3C2212yescomplemented
35C3×#897C2212yes—
36C3×#895C2212yes—
37C3×#894C2214yescomplemented
38C3×#892C2212yes—
39C3×D3×C4⋊C4C2212yescomplemented
40C3×#890C2212yescomplemented
41C3×#887C2212yescomplemented
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic, complemented
44C3×C42×D3C2211yescharacteristic
45C3×#869C2211yescharacteristic, complemented
46#63922C2214yes—
47#63921C2214yes—
48D3×(C2×D3)⋊C4C2212yes—
49#63916C2214yes—
50#63916C2212yescomplemented
51#63908C2211yescharacteristic
52#63905C2212yes—
53#63904C2214yescomplemented
54C4×#626C2212yes—
55C4×#626C2214yescomplemented
56C4×#625C2212yes—
57#63900C2212yescomplemented
58#63896C2214yes—
59#63896C2214yescomplemented
60#63894C2211yescharacteristic
61Dic3×D12C2211yescharacteristic
62D3×C4⋊Dic3C2211yescharacteristic
63#63884C2214yescomplemented
64#63883C2214yescomplemented
65#63880C2212yes—
66#63879C2214yes—
67#63869C2211yescharacteristic, complemented
68#63863C2212yes—
69#63860C2214yescomplemented
70#63860C2211yescharacteristic, complemented
71#63859C2214yescomplemented
72#63859C2212yescomplemented
73#63858C2214yescomplemented
74#63857C2211yescharacteristic
75#63857C2212yescomplemented
76#63857C2214yescomplemented
77#63856C2212yescomplemented
78#63855C2212yescomplemented
79#63854C2214yes—
80#63854C2214yescomplemented
81#63847C2214yescomplemented
82#63843C2212yescomplemented
83#63841C2212yescomplemented
84#63836C2214yescomplemented
85C3×#547—31no—
86C3×#533—31no—
87#5831—32no—
88#5828—32no—
89#5732—31no—
90#5728D311yescharacteristic, complemented
91#5727—31no—
92#5727—31no—
93#5727—61no—
94#5726—31no—
95#5726D311yescharacteristic, complemented
96#5692—34no—
97#5660—34no—
98#5659—34no—
99#5639—32no—
100#5635—32no—
101#5630—32no—
102#5627—32no—
103D3×C22⋊Q8—32no—
104D3×C22⋊Q8—32no—
105#5612—32no—
106#5603—32no—
107#5582—32no—
108#5581—32no—
109#5576—32no—
110#5574—32no—
111#5557—31no—
112#5551—31no—
113C4×D3×D4—31no—
114#5542—31no—
115#5527—34no—
116#5511—32no—
117#5504—32no—
118#5479—31no—
119C2×C4×D12—31no—
120C22×D32C2312yes—
121C2×C32×Q8C2312yes—
122Q8×C3⋊D3—44no—
123C2×C4⋊(C3⋊D3)C2311yescharacteristic
124C2×C4×C3⋊D3C2312yes—
125C2×C4×C3⋊D3C2314yes—
126C2×#634C2311yescharacteristic
127C2×#634C2314yes—
128C3×#239—44no—
129C2×C3×D12C2311yescharacteristic
130C2×C3×D12C2311yescharacteristic
131C2×C3×D12C2314yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2314yes—
138C2×C3×Dic6C2312yes—
139C2×#626C2314yes—
140C2×#626C2312yes—
141C2×#625C2312yes—
142C2×#624C2314yes—
143C2×#624C2312yes—
144C2×D3×Dic3C2312yes—
145C2×D3×Dic3C2312yes—
146D3×D12—24no—
147C4×D32—44no—
148#3799—28no—
149C32×C4⋊C4C2312yes—
150C32×C4⋊C4C2312yes—
151C32×C42C2311yescharacteristic
152#3752C2312yes—
153#3752C2314yes—
154C4⋊(C3⋊Dic3)C2311yescharacteristic
155C4⋊(C3⋊Dic3)C2311yescharacteristic
156#3750C2312yes—
157#3750C2314yes—
158C4×C3⋊Dic3C2312yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×(C2×D3)⋊C4C2314yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2314yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2314yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2314yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2311yescharacteristic
174#3724C2312yes—
175#3724C2314yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2312yes—
180#3722C2312yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2312yes—
186(C2×D3)⋊Dic3C2312yes—
187(C2×D3)⋊Dic3C2314yes—
188(C2×D3)⋊Dic3C2312yes—
189Dic32C2314yes—
190#3520—91noSylow
191C2×C3×#41—32no—
192C2×#239—32no—
193C2×#239C2×D312yescomplemented
194C2×D3×Q8—32no—
195C2×D3×Q8—32no—
196C2×D3×Q8—62no—
197C2×D3×D4—31no—
198C2×#235—32no—
199C22×D12—31no—
200C22×C4×D3—32no—
201C22×C4×D3—32no—
202C3×C4⋊Q8—21no—
203C3×C4⋊Q8—31no—
204C3×C4⋊Q8C2×D311yescharacteristic, complemented
205C3×C4⋊Q8C2×D311yescharacteristic, complemented
206C3×#125—32no—
207C3×#123—34no—
208C3×C22⋊Q8—32no—
209C3×C22⋊Q8—32no—
210C3×C22⋊Q8—32no—
211C3×#121—32no—
212C3×C4×Q8—32no—
213C3×C4×Q8—32no—
214C3×C4×D4—31no—
215C3×C4×D4—31no—
216C3×#117—32no—
217C2×C3×C4⋊C4—32no—
218C2×C3×C42—31no—
219#947—32no—
220#946—32no—
221#946—32no—
222#946—32no—
223#946—62no—
224#946C2×D312yes—
225#946C2×D312yescomplemented
226Q8×Dic3—32no—
227Q8×Dic3C2×D312yescomplemented
228#938—31no—
229#938—34no—
230#938—32no—
231#937—34no—
232#936—32no—
233#936—34no—
234#936—31no—
235#935—34no—
236D4×Dic3—31no—
237#930—31no—
238#929—32no—
239C4×#67—32no—
240C4×#67—32no—
241C4×#67—34no—
242C4×#67—34no—
243C4×#67—32no—
244C4×#67—34no—
245C2×(C2×D3)⋊C4—32no—
246#926—32no—
247#926—32no—
248C2×C4⋊Dic3—31no—
249#924—32no—
250#924—34no—
251#924—31no—
252#924—32no—
253#898—34no—
254#897—34no—
255#897—32no—
256#897—31no—
257#897C2×D312yes—
258#896—34no—
259#896—34no—
260#896—34no—
261#896—34no—
262#896—64no—
263#895—34no—
264#895—32no—
265#895C2×D312yes—
266#894—34no—
267#894—34no—
268#894—34no—
269#894C2×D314yescomplemented
270#893—34no—
271#893—32no—
272#893—32no—
273#893—31no—
274#893—62no—
275#892—32no—
276#892—34no—
277#892C2×D312yes—
278D3×C4⋊C4—31no—
279D3×C4⋊C4—32no—
280D3×C4⋊C4—32no—
281D3×C4⋊C4—34no—
282D3×C4⋊C4—34no—
283D3×C4⋊C4C2×D312yescomplemented
284#890—31no—
285#890C2×D312yescomplemented
286#889—34no—
287#889—34no—
288#888—32no—
289#888—32no—
290#888—62no—
291#887—32no—
292#887C2×D312yescomplemented
293#883—32no—
294#883—34no—
295#883—34no—
296#882—34no—
297#67⋊C4—34no—
298#67⋊C4—32no—
299D3×C22⋊C4—32no—
300D3×C22⋊C4—34no—
301D3×C22⋊C4—34no—
302#879—34no—
303#879—34no—
304#879—32no—
305#878—34no—
306#878—34no—
307#876—32no—
308#876—34no—
309#875—31no—
310#875—34no—
311C4×D12—31no—
312C4×D12—32no—
313C4×D12—34no—
314C4×D12—31no—
315C4×D12—31no—
316C4×D12—32no—
317C4×D12—31no—
318C4×D12—61no—
319C4×D12C2×D311yescharacteristic
320C4×D12C2×D311yescharacteristic, complemented
321#872—32no—
322#872—34no—
323C42×D3C2×D311yescharacteristic
324#870—31no—
325#869C2×D311yescharacteristic, complemented
326C4×Dic6—31no—
327C4×Dic6—31no—
328C4×Dic6—61no—
329C22×C3⋊D3C2412yes—
330C22×C3×D3C2412yes—
331C22×C3×D3C2412yes—
332C22×C3×D3C2411yescharacteristic
333C2×D32—24no—
334C2×D32—24no—
335C2×D32—42no—
336C32×Q8—24no—
337C2×C32×C4C2414yes—
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C3⋊Dic3C2412yes—
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2412yes—
344C4⋊(C3⋊D3)#4114yescomplemented
345C4×C3⋊D3—24no—
346C4×C3⋊D3—44no—
347#634—22no—
348#634—44no—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2411yescharacteristic
352C2×C3×Dic3C2411yescharacteristic
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2412yes—
355C3×D12—22no—
356C3×D12—22no—
357C3×D12—44no—
358C3×C4×D3—22no—
359C3×C4×D3—24no—
360C3×C4×D3—22no—
361C3×C4×D3—22no—
362C3×C4×D3—24no—
363C3×C4×D3—44no—
364C3×Dic6—24no—
365#626—28no—
366#626—24no—
367#625—24no—
368#624—28no—
369#624—42no—
370D3×Dic3—42no—
371D3×Dic3—42no—
372#556—91no—
373#554—92no—
374#552—92no—
375#551—94no—
376D4×Q8—91no—
377#548—92no—
378#547—31no—
379#547—91no—
380#546—92no—
381#542—92no—
382#539—94no—
383#533—31no—
384#529—91no—
385#525—92no—
386C2×C22⋊Q8—92no—
387#520—92no—
388C2×C4×D4—91no—
389C23×D3—32no—
390C23×D3—32no—
391C3×#41—124no—
392C2×C3×Q8—22no—
393C2×C3×Q8—32no—
394C2×C3×Q8C22×D312yes—
395C2×C3×Q8C22×D312yes—
396C2×C3×D4—31no—
397C2×C3×D4—31no—
398C2×C3×D4—34no—
399C22×C3×C4—32no—
400C22×C3×C4—32no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—34no—
405C2×#67—32no—
406C2×#67—32no—
407C2×#67—32no—
408C2×#67—34no—
409C22×Dic3—32no—
410C22×Dic3—32no—
411#239—44no—
412#239—68no—
413D3×Q8—124no—
414D3×Q8—124no—
415D3×Q8—128no—
416D3×D4—64no—
417#235—68no—
418C2×D12—31no—
419C2×D12—31no—
420C2×D12—32no—
421C2×D12—34no—
422C2×D12—61no—
423C2×D12—64no—
424C2×D12C22×D311yescharacteristic
425C2×D12C22×D311yescharacteristic
426C2×D12C22×D314yes—
427C2×C4×D3—32no—
428C2×C4×D3—32no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—32no—
432C2×C4×D3—32no—
433C2×C4×D3—34no—
434C2×C4×D3—34no—
435C2×C4×D3—32no—
436C2×C4×D3—32no—
437C2×C4×D3—62no—
438C2×C4×D3—64no—
439C2×C4×D3—124no—
440C2×C4×D3—124no—
441C2×C4×D3C22×D311yescharacteristic
442C2×C4×D3C22×D311yescharacteristic
443C2×C4×D3C22×D311yescharacteristic
444C2×C4×D3C22×D312yes—
445C2×C4×D3C22×D312yes—
446C2×C4×D3C22×D314yes—
447C2×Dic6—31no—
448C2×Dic6—31no—
449C2×Dic6—34no—
450C2×Dic6—34no—
451C2×Dic6—61no—
452C2×Dic6—64no—
453C2×Dic6C22×D312yes—
454C3×C4⋊C4—22no—
455C3×C4⋊C4—22no—
456C3×C4⋊C4—31no—
457C3×C4⋊C4—34no—
458C3×C4⋊C4—34no—
459C3×C4⋊C4—31no—
460C3×C4⋊C4—32no—
461C3×C4⋊C4—34no—
462C3×C4⋊C4—32no—
463C3×C4⋊C4C22×D312yes—
464C3×C4⋊C4C22×D312yes—
465C3×C4⋊C4C22×D312yes—
466C3×C4⋊C4C22×D312yes—
467C3×C22⋊C4—34no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—32no—
470C3×C22⋊C4—32no—
471C3×C42—21no—
472C3×C42—31no—
473C3×C42—31no—
474C3×C42—34no—
475C3×C42—31no—
476C3×C42C22×D311yescharacteristic
477C3×C42C22×D311yescharacteristic
478#217—32no—
479#217—34no—
480#217—32no—
481#217—34no—
482#217—32no—
483#217—32no—
484#217—34no—
485#217—32no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—32no—
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—34no—
495(C2×D3)⋊C4—32no—
496(C2×D3)⋊C4—32no—
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—32no—
499(C2×D3)⋊C4—32no—
500(C2×D3)⋊C4—62no—
501(C2×D3)⋊C4—64no—
502(C2×D3)⋊C4C22×D312yes—
503(C2×D3)⋊C4C22×D312yes—
504(C2×D3)⋊C4C22×D314yes—
505(C2×D3)⋊C4C22×D314yes—
506C4⋊Dic3—31no—
507C4⋊Dic3—31no—
508C4⋊Dic3—31no—
509C4⋊Dic3—31no—
510C4⋊Dic3—32no—
511C4⋊Dic3—34no—
512C4⋊Dic3—32no—
513C4⋊Dic3—32no—
514C4⋊Dic3—61no—
515C4⋊Dic3—61no—
516C4⋊Dic3C22×D312yes—
517C4⋊Dic3C22×D312yes—
518C4⋊Dic3C22×D311yescharacteristic
519C4⋊Dic3C22×D311yescharacteristic
520C4⋊Dic3C22×D314yes—
521Dic3⋊C4—32no—
522Dic3⋊C4—32no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—32no—
526Dic3⋊C4—32no—
527Dic3⋊C4—32no—
528Dic3⋊C4—34no—
529Dic3⋊C4—34no—
530Dic3⋊C4—32no—
531Dic3⋊C4—34no—
532Dic3⋊C4—32no—
533Dic3⋊C4—62no—
534Dic3⋊C4—64no—
535Dic3⋊C4C22×D314yes—
536Dic3⋊C4C22×D314yes—
537C4×Dic3—32no—
538C4×Dic3—32no—
539C4×Dic3—34no—
540C4×Dic3—34no—
541C4×Dic3—62no—
542C4×Dic3C22×D311yescharacteristic
543C4×Dic3C22×D311yescharacteristic
544C4×Dic3C22×D311yescharacteristic
545C4×Dic3C22×D314yes—
546C22×C32C2511yescharacteristic
547C2×C3⋊D3—22no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3C2×#4114yes—
550C2×C3×D3—21no—
551C2×C3×D3—21no—
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×D32−1+412yes—
559D32—48no—
560C32×C4—24no—
561C32×C4—21no—
562C32×C4C2×#4112yes—
563C32×C4H(5,𝔽2)12yes—
564C3⋊Dic3—22no—
565C3⋊Dic3—22no—
566C3⋊Dic3—22no—
567C3×Dic3—22no—
568C3×Dic3—24no—
569C3×Dic3—21no—
570C3×Dic3—21no—
571C3×Dic3—22no—
572C3×Dic3—21no—
573C2×#41—32no—
574C2×#41—92no—
575C22×Q8—92no—
576C22×D4—91no—
577C23×C4—92no—
578C4⋊Q8—31no—
579C4⋊Q8—92no—
580C4⋊Q8D3211yescharacteristic, complemented
581#126—92no—
582#126—94no—
583#126—94no—
584#125—32no—
585#125—91no—
586#125—94no—
587#124—91no—
588#124—94no—
589#124—92no—
590#123—34no—
591#123—94no—
592#123—94no—
593#123—92no—
594#123—94no—
595C22⋊Q8—32no—
596C22⋊Q8—32no—
597C22⋊Q8—32no—
598C22⋊Q8—94no—
599C22⋊Q8—94no—
600C22⋊Q8—91no—
601C22⋊Q8—92no—
602C22⋊Q8—94no—
603C22⋊Q8—92no—
604C22⋊Q8—92no—
605C22⋊Q8—94no—
606#121—32no—
607#121—92no—
608#121—94no—
609#121—91no—
610#120—94no—
611C4×Q8—32no—
612C4×Q8—32no—
613C4×Q8—92no—
614C4×Q8—91no—
615C4×D4—31no—
616C4×D4—31no—
617C4×D4—92no—
618C4×D4—91no—
619C4×D4—92no—
620C4×D4—94no—
621C4×D4—91no—
622C4×D4—94no—
623C4×D4—94no—
624C4×D4—92no—
625C4×D4—92no—
626C4×D4—91no—
627#117—32no—
628#117—94no—
629#117—92no—
630#117—92no—
631C2×C4⋊C4—32no—
632C2×C4⋊C4—94no—
633C2×C4⋊C4—92no—
634C2×C4⋊C4—91no—
635C2×C22⋊C4—94no—
636C2×C22⋊C4—92no—
637C2×C42—31no—
638C23×C3—31no—
639C23×C3—32no—
640C23×C3—32no—
641C22×D3—32no—
642C22×D3—32no—
643C22×D3—62no—
644C22×D3—64no—
645C22×D3—64no—
646C22×D3—64no—
647C22×D3—64no—
648C22×D3—122no—
649C22×D3—122no—
650C22×D3C23×D312yes—
651C22×D3C23×D312yes—
652C22×D3C23×D311yescharacteristic
653C3×Q8—24no—
654C3×Q8—24no—
655C3×Q8—44no—
656C3×Q8—64no—
657C3×D4—62no—
658C3×D4—62no—
659C3×D4—124no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—24no—
664C2×C3×C4—32no—
665C2×C3×C4—34no—
666C2×C3×C4—32no—
667C2×C3×C4—31no—
668C2×C3×C4—31no—
669C2×C3×C4—31no—
670C2×C3×C4—62no—
671C2×C3×C4—62no—
672C2×C3×C4—62no—
673C2×C3×C4—64no—
674C2×C3×C4—64no—
675C2×C3×C4—124no—
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D314yes—
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D314yes—
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684#67—68no—
685#67—64no—
686#67—64no—
687#67—64no—
688C2×Dic3—32no—
689C2×Dic3—32no—
690C2×Dic3—32no—
691C2×Dic3—32no—
692C2×Dic3—32no—
693C2×Dic3—32no—
694C2×Dic3—62no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—122no—
698C2×Dic3—122no—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D314yes—
701C2×Dic3C23×D311yescharacteristic
702C2×Dic3C23×D311yescharacteristic
703C2×Dic3C23×D311yescharacteristic
704C2×Dic3C23×D312yes—
705D12—22no—
706D12—22no—
707D12—34no—
708D12—34no—
709D12—44no—
710D12—64no—
711D12—64no—
712D12—68no—
713C4×D3—22no—
714C4×D3—24no—
715C4×D3—22no—
716C4×D3—24no—
717C4×D3—22no—
718C4×D3—44no—
719C4×D3—68no—
720C4×D3—68no—
721C4×D3—64no—
722C4×D3—64no—
723C4×D3—124no—
724C4×D3—122no—
725C4×D3—122no—
726C4×D3—124no—
727C4×D3—124no—
728C4×D3—128no—
729C4×D3—122no—
730C4×D3—122no—
731Dic6—24no—
732Dic6—64no—
733Dic6—62no—
734Dic6—62no—
735Dic6—124no—
736Dic6—124no—
737Dic6—128no—
738C2×C32C22×#4111yescharacteristic
739C2×C32C2×H(5,𝔽2)11yescharacteristic
740C2×C32C2×2−1+411yescharacteristic
741C3⋊D3—24no—
742C3×D3—22no—
743C3×D3—42no—
744C3×D3—42no—
745C24—92no—
746#41—124no—
747#41—188no—
748C2×Q8—32no—
749C2×Q8—91no—
750C2×Q8—94no—
751C2×Q8—364no—
752C2×Q8C2×D3212yes—
753C2×D4—31no—
754C2×D4—31no—
755C2×D4—34no—
756C2×D4—94no—
757C2×D4—92no—
758C2×D4—92no—
759C2×D4—91no—
760C2×D4—184no—
761C22×C4—31no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—32no—
765C22×C4—32no—
766C22×C4—34no—
767C22×C4—94no—
768C22×C4—92no—
769C22×C4—92no—
770C22×C4—92no—
771C22×C4—92no—
772C22×C4—94no—
773C22×C4—364no—
774C4⋊C4—31no—
775C4⋊C4—34no—
776C4⋊C4—31no—
777C4⋊C4—32no—
778C4⋊C4—34no—
779C4⋊C4—32no—
780C4⋊C4—34no—
781C4⋊C4—92no—
782C4⋊C4—92no—
783C4⋊C4—94no—
784C4⋊C4—94no—
785C4⋊C4—92no—
786C4⋊C4—92no—
787C4⋊C4—91no—
788C4⋊C4—91no—
789C4⋊C4—94no—
790C4⋊C4—92no—
791C4⋊C4C2×D3212yes—
792C4⋊C4C2×D3212yes—
793C22⋊C4—34no—
794C22⋊C4—32no—
795C22⋊C4—34no—
796C22⋊C4—32no—
797C22⋊C4—92no—
798C22⋊C4—92no—
799C22⋊C4—92no—
800C22⋊C4—94no—
801C22⋊C4—92no—
802C22⋊C4—92no—
803C22⋊C4—94no—
804C22⋊C4—92no—
805C22⋊C4—94no—
806C22⋊C4—92no—
807C22⋊C4—94no—
808C42—31no—
809C42—31no—
810C42—31no—
811C42—34no—
812C42—94no—
813C42—92no—
814C42C2×D3211yescharacteristic
815C22×C3—21no—
816C22×C3—32no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3—62no—
824C22×C3—62no—
825C22×C3C24×D311yescharacteristic
826C22×C3C24×D311yescharacteristic
827C2×D3—21no—
828C2×D3—21no—
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—34no—
836C2×D3—34no—
837C2×D3—64no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—122no—
843C2×D3—122no—
844C2×D3—128no—
845C2×D3—128no—
846C2×D3#100712yes—
847C3×C4—24no—
848C3×C4—21no—
849C3×C4—24no—
850C3×C4—21no—
851C3×C4—22no—
852C3×C4—22no—
853C3×C4—44no—
854C3×C4—41no—
855C3×C4—61no—
856C3×C4—62no—
857C3×C4—64no—
858C3×C4—61no—
859C3×C4—62no—
860C3×C4—61no—
861C3×C4#100412yes—
862C3×C4D3×#4112yes—
863C3×C4D3×#4112yes—
864C3×C4#100912yes—
865Dic3—22no—
866Dic3—21no—
867Dic3—24no—
868Dic3—22no—
869Dic3—21no—
870Dic3—21no—
871Dic3—64no—
872Dic3—62no—
873Dic3—62no—
874Dic3—62no—
875Dic3—62no—
876Dic3—62no—
877Dic3—62no—
878Dic3—122no—
879Dic3—122no—
880C32#352011yescharacteristic, complemented, Sylow
881C23—31no—
882C23—32no—
883C23—32no—
884C23—92no—
885C23—184no—
886C23—184no—
887C23—362no—
888Q8—24no—
889Q8—64no—
890Q8—182no—
891Q8—364no—
892D4—62no—
893D4—62no—
894D4—94no—
895D4—124no—
896D4—184no—
897D4—188no—
898D4—184no—
899C2×C4—31no—
900C2×C4—31no—
901C2×C4—31no—
902C2×C4—34no—
903C2×C4—32no—
904C2×C4—32no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—64no—
908C2×C4—62no—
909C2×C4—64no—
910C2×C4—92no—
911C2×C4—92no—
912C2×C4—92no—
913C2×C4—124no—
914C2×C4—188no—
915C2×C4—184no—
916C2×C4—364no—
917C2×C4—362no—
918C2×C4—362no—
919C2×C4—362no—
920C2×C4C22×D3211yescharacteristic
921C2×C4C22×D3214yes—
922C2×C4C22×D3211yescharacteristic
923C2×C4C22×D3211yescharacteristic
924C2×C3—21no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—62no—
928C2×C3—122no—
929C2×C3—122no—
930C2×C3C2×#100411yescharacteristic
931C2×C3C2×#100711yescharacteristic
932C2×C3C2×D3×#4111yescharacteristic
933C2×C3C2×D3×#4111yescharacteristic
934C2×C3C2×#100911yescharacteristic
935C2×C3D3×2−1+411yescharacteristic
936D3—22no—
937D3—42no—
938D3—42no—
939D3—64no—
940D3—64no—
941D3—124no—
942C22—32no—
943C22—61no—
944C22—61no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—62no—
949C22—62no—
950C22—62no—
951C22—94no—
952C22—182no—
953C22—182no—
954C22—368no—
955C22C23×D3211yescharacteristic
956C4—24no—
957C4—21no—
958C4—62no—
959C4—61no—
960C4—62no—
961C4—61no—
962C4—64no—
963C4—61no—
964C4—182no—
965C4—182no—
966C4—182no—
967C4#6431412yes—
968C4#6431912yes—
969C3—21no—
970C3#8628511yescharacteristic, complemented
971C3#8668611yescharacteristic, complemented
972C2—62no—
973C2—122no—
974C2—122no—
975C2—184no—
976C2C2×#6431411yescharacteristic
977C2C2×#6431911yescharacteristic
978C2D3×#100711yescharacteristic
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. #10596198C2semidirect
2. C3×#5728C2semidirect
3. C3×#5726C2semidirect
4. #10595429C2semidirect
5. #10595424C2semidirect
6. #10595414C2semidirect
7. #10595344C2semidirect
8. #10594644C2semidirect
9. #10594633C2semidirect
10. #10594532C2semidirect
11. #10594498C2semidirect
12. #10594490C2semidirect
13. #10594327C2semidirect
14. C4×D3×D12C2semidirect
15. #10593974C2semidirect
16. #10593869C2semidirect
17. #10593863C2semidirect
20. C2×Q8×C3⋊D3C22semidirect
21. C2×C3×#239C22semidirect
25. C32×C4⋊Q8C22semidirect
26. #64155C22semidirect
27. #64105C22semidirect
29. #64097C22semidirect
31. C4×#634C22semidirect
33. C3×#946C22semidirect
34. C3×Q8×Dic3C22semidirect
37. C3×#894C22semidirect
39. C3×D3×C4⋊C4C22semidirect
40. C3×#890C22semidirect
41. C3×#887C22semidirect
43. C3×C4×D12C22semidirect
45. C3×#869C22semidirect
50. #63916C22semidirect
53. #63904C22semidirect
55. C4×#626C22semidirect
57. #63900C22semidirect
59. #63896C22semidirect
63. #63884C22semidirect
64. #63883C22semidirect
67. #63869C22semidirect
69. #63860C22semidirect
70. #63860C22semidirect
71. #63859C22semidirect
72. #63859C22semidirect
73. #63858C22semidirect
75. #63857C22semidirect
76. #63857C22semidirect
77. #63856C22semidirect
78. #63855C22semidirect
80. #63854C22semidirect
81. #63847C22semidirect
82. #63843C22semidirect
83. #63841C22semidirect
84. #63836C22semidirect
90. #5728D3semidirect
95. #5726D3semidirect
193. C2×#239C2×D3semidirect
204. C3×C4⋊Q8C2×D3semidirect
205. C3×C4⋊Q8C2×D3semidirect
225. #946C2×D3semidirect
227. Q8×Dic3C2×D3semidirect
269. #894C2×D3semidirect
283. D3×C4⋊C4C2×D3semidirect
285. #890C2×D3semidirect
292. #887C2×D3semidirect
320. C4×D12C2×D3semidirect
325. #869C2×D3semidirect
344. C4⋊(C3⋊D3)#41semidirect
580. C4⋊Q8D32semidirect
880. C32#3520semidirect
970. C3#86285semidirect
971. C3#86686semidirect

Maximal subgroups

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

subgroupindex
#105961982
C3×#57282
C3×#57262
#105954292
#105954242
#105954142
#105953442
#105946442
#105946332
#105945322
#105944982
#105944902
#105943272
C4×D3×D122
#105939742
#105938692
#105938632
#866863
#862853