Finite Group Databasebeta

← #11909308

Subgroups — #11909308

Order 1152.

2394 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596197C211yesmaximal, characteristic, complemented
2C3×#5732C211yesmaximal, characteristic, complemented
3C3×#5728C211yesmaximal, characteristic, complemented
4#10595431C212yesmaximal, complemented
5#10595395C212yesmaximal, complemented
6#10595371C212yesmaximal, complemented
7#10595353C212yesmaximal, complemented
8#10594643C214yesmaximal, complemented
9#10594631C212yesmaximal, complemented
10#10594627C212yesmaximal, complemented
11#10594481C214yesmaximal, complemented
12#10594337C212yesmaximal, complemented
13#10594329C212yesmaximal, complemented
14C4×D3×D12C211yesmaximal, characteristic, complemented
15#10593903C211yesmaximal, characteristic, complemented
16#10593870C211yesmaximal, characteristic, complemented
17#10593869C211yesmaximal, characteristic, complemented
18#86990—31nomaximal
19#86285—31nomaximal
20C2×#3832C2212yes—
21C2×D3×D12C2211yescharacteristic
22C2×C4×D32C2212yes—
23C2×#3799C2212yescomplemented
24C2×#3797C2212yescomplemented
25C32×C4⋊Q8C2211yescharacteristic, complemented
26#64155C2212yescomplemented
27#64104C2212yescomplemented
28#64103C2214yescomplemented
29C4⋊C4×C3⋊D3C2212yescomplemented
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
32C3×#947C2212yes—
33C3×#946C2212yes—
34C3×Q8×Dic3C2212yescomplemented
35C3×Q8×Dic3C2212yescomplemented
36C3×#898C2214yescomplemented
37C3×#897C2212yes—
38C3×#897C2212yescomplemented
39C3×#892C2212yes—
40C3×#892C2212yescomplemented
41C3×#890C2212yescomplemented
42C3×#887C2212yescomplemented
43C3×C4×D12C2211yescharacteristic
44C3×C42×D3C2211yescharacteristic
45C3×#869C2211yescharacteristic, complemented
46C3×C4×Dic6C2211yescharacteristic, complemented
47#63923C2214yes—
48#63921C2214yes—
49D3×(C2×D3)⋊C4C2212yes—
50#63918C2212yescomplemented
51#63916C2212yes—
52#63910C2214yes—
53#63909C2211yescharacteristic
54C4×#626C2212yes—
55C4×#626C2212yes—
56#63900C2212yescomplemented
57#63900C2214yescomplemented
58#63899C2214yes—
59#63899C2214yescomplemented
60#63895C2214yescomplemented
61#63895C2214yescomplemented
62#63894C2211yescharacteristic
63#63894C2212yes—
64#63894C2214yescomplemented
65#63894C2214yescomplemented
66Dic3×D12C2211yescharacteristic
67#63890C2214yescomplemented
68D3×C4⋊Dic3C2211yescharacteristic
69#63880C2214yes—
70#63880C2212yes—
71#63874C2214yescomplemented
72#63874C2212yescomplemented
73#63871C2212yescomplemented
74#63869C2211yescharacteristic, complemented
75#63868C2212yescomplemented
76#63867C2214yescomplemented
77#63864C2211yescharacteristic, complemented
78#63859C2214yescomplemented
79#63856C2211yescharacteristic
80#63856C2212yescomplemented
81#63854C2214yescomplemented
82#63853C2214yes—
83#63852C2214yescomplemented
84#63850C2212yes—
85C3×#556—31no—
86C3×#533—31no—
87#5732D311yescharacteristic, complemented
88#5728D311yescharacteristic, complemented
89#5727—31no—
90#5726—31no—
91#5726—31no—
92#5726—31no—
93#5726—61no—
94#5707—34no—
95#5705—34no—
96#5692—34no—
97#5682—32no—
98#5676—32no—
99#5635—32no—
100#5633—32no—
101#5630—32no—
102#5627—32no—
103D3×C22⋊Q8—32no—
104D3×C22⋊Q8—32no—
105#5582—32no—
106#5581—32no—
107#5580—31no—
108#5579—32no—
109#5576—32no—
110Q8×D12—31no—
111#5574—32no—
112#5574—32no—
113#5551—31no—
114C4×D3×D4—31no—
115#5529—32no—
116#5527—34no—
117#5524—32no—
118#5479—31no—
119C2×C4×D12—31no—
120C22×D32C2312yes—
121C2×C32×Q8C2312yes—
122#3832—28no—
123C2×C4⋊(C3⋊D3)C2311yescharacteristic
124C2×C4⋊(C3⋊D3)C2314yes—
125C2×C4⋊(C3⋊D3)C2311yescharacteristic
126C2×C4×C3⋊D3C2312yes—
127C2×C4×C3⋊D3C2312yes—
128C2×C4×C3⋊D3C2314yes—
129C2×C3×D12C2311yescharacteristic
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×Dic6C2312yes—
135C2×C3×Dic6C2311yescharacteristic
136C2×#627C2314yes—
137C2×#626C2312yes—
138C2×#626C2312yes—
139C2×#626C2314yes—
140C2×#624C2314yes—
141C2×#624C2314yes—
142C2×#624C2312yes—
143C2×D3×Dic3C2312yes—
144C2×D3×Dic3C2312yes—
145D3×D12—24no—
146C4×D32—44no—
147#3799—44no—
148#3797—44no—
149C32×C4⋊C4C2312yes—
150C32×C4⋊C4C2312yes—
151C32×C42C2311yescharacteristic
152#3752C2312yes—
153#3752C2312yes—
154#3752C2314yes—
155C4⋊(C3⋊Dic3)C2311yescharacteristic
156C4⋊(C3⋊Dic3)C2311yescharacteristic
157#3750C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2314yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2314yes—
164C3×C4⋊Dic3C2311yescharacteristic
165C3×C4⋊Dic3C2314yes—
166C3×C4⋊Dic3C2311yescharacteristic
167C3×C4⋊Dic3C2312yes—
168C3×Dic3⋊C4C2314yes—
169C3×Dic3⋊C4C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2314yes—
172C3×C4×Dic3C2311yescharacteristic
173C3×C4×Dic3C2314yes—
174C3×C4×Dic3C2311yescharacteristic
175C3×C4×Dic3C2312yes—
176#3724C2312yes—
177#3724C2314yes—
178#3724C2312yes—
179Dic3⋊Dic3C2312yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2312yes—
182#3722C2312yes—
183#3722C2314yes—
184#3722C2312yes—
185#3722C2312yes—
186#3722C2312yes—
187(C2×D3)⋊Dic3C2312yes—
188(C2×D3)⋊Dic3C2312yes—
189(C2×D3)⋊Dic3C2314yes—
190#3520—91noSylow
191C2×#239—32no—
192C2×#239—32no—
193C2×#239—32no—
194C2×#239—62no—
195C2×D3×Q8—32no—
196C2×D3×Q8—32no—
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×#126—34no—
207C3×#125—32no—
208C3×#124—32no—
209C3×C22⋊Q8—32no—
210C3×C22⋊Q8—32no—
211C3×C22⋊Q8—32no—
212C3×C4×Q8—32no—
213C3×C4×Q8—32no—
214C3×C4×Q8—32no—
215C3×C4×Q8—31no—
216C3×C4×D4—31no—
217C3×#117—32no—
218C3×#117—32no—
219C2×C3×C42—31no—
220#947—31no—
221#947C2×D312yes—
222#946—32no—
223#946—32no—
224#946—32no—
225#946—31no—
226#946—32no—
227#946—62no—
228#946C2×D312yes—
229Q8×Dic3C2×D312yescomplemented
230Q8×Dic3C2×D312yescomplemented
231#938—32no—
232D4×Dic3—31no—
233#930—31no—
234#929—32no—
235C4×#67—32no—
236C4×#67—32no—
237C2×(C2×D3)⋊C4—32no—
238C2×C4⋊Dic3—31no—
239#924—31no—
240#924—32no—
241#898—32no—
242#898C2×D314yescomplemented
243#897—32no—
244#897—34no—
245#897—34no—
246#897C2×D312yes—
247#897C2×D312yescomplemented
248#896—34no—
249#896—34no—
250#896—34no—
251#896—34no—
252#895—32no—
253#895—31no—
254#895—32no—
255#895—32no—
256#895—34no—
257#895—62no—
258#894—32no—
259#894—34no—
260#894—34no—
261#894—34no—
262#894—34no—
263#894—34no—
264#894—64no—
265#893—34no—
266#893—34no—
267#893—32no—
268#893—31no—
269#892C2×D312yes—
270#892C2×D312yescomplemented
271D3×C4⋊C4—31no—
272D3×C4⋊C4—32no—
273D3×C4⋊C4—32no—
274D3×C4⋊C4—32no—
275D3×C4⋊C4—34no—
276D3×C4⋊C4—34no—
277D3×C4⋊C4—32no—
278D3×C4⋊C4—62no—
279#890—31no—
280#890C2×D312yescomplemented
281#889—34no—
282#888—32no—
283#887C2×D312yescomplemented
284#886—34no—
285#885—34no—
286#884—34no—
287#883—34no—
288#883—34no—
289#882—34no—
290#882—34no—
291#67⋊C4—34no—
292#67⋊C4—32no—
293D3×C22⋊C4—32no—
294D3×C22⋊C4—34no—
295D3×C22⋊C4—34no—
296#879—34no—
297#878—34no—
298#878—34no—
299#876—34no—
300#876—32no—
301#875—31no—
302#875—34no—
303C4×D12—31no—
304C4×D12—32no—
305C4×D12—32no—
306C4×D12—31no—
307C4×D12—31no—
308C4×D12—31no—
309C4×D12—31no—
310C4×D12—32no—
311C4×D12—34no—
312C4×D12—32no—
313C4×D12—34no—
314C4×D12—31no—
315C4×D12—34no—
316C4×D12—61no—
317C4×D12—61no—
318C4×D12C2×D311yescharacteristic
319#872—32no—
320#872—34no—
321#872—32no—
322#872—34no—
323C42×D3C2×D311yescharacteristic
324#870—31no—
325#870—34no—
326#869—32no—
327#869C2×D311yescharacteristic, complemented
328C4×Dic6C2×D311yescharacteristic, complemented
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—
343C4⋊(C3⋊D3)—28no—
344C4⋊(C3⋊D3)—22no—
345C4⋊(C3⋊D3)#4114yescomplemented
346C4×C3⋊D3—28no—
347C4×C3⋊D3—24no—
348C4×C3⋊D3—24no—
349C2×C3×Dic3C2411yescharacteristic
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2414yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2411yescharacteristic
355C2×C3×Dic3C2412yes—
356C3×D12—22no—
357C3×C4×D3—22no—
358C3×C4×D3—22no—
359C3×C4×D3—24no—
360C3×C4×D3—22no—
361C3×Dic6—22no—
362C3×Dic6—24no—
363#627—44no—
364#626—24no—
365#626—24no—
366#626—44no—
367#624—44no—
368#624—44no—
369#624—42no—
370D3×Dic3—42no—
371D3×Dic3—42no—
372#556—31no—
373#554—92no—
374#552—92no—
375#551—94no—
376D4×Q8—91no—
377#548—92no—
378#547—91no—
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—
391C2×C3×Q8—22no—
392C2×C3×Q8—32no—
393C2×C3×Q8—31no—
394C2×C3×Q8C22×D312yes—
395C2×C3×Q8C22×D312yes—
396C2×C3×D4—31no—
397C22×C3×C4—32no—
398C22×C3×C4—31no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C2×#67—32no—
402C2×#67—32no—
403C2×#67—34no—
404C22×Dic3—32no—
405C22×Dic3—32no—
406#239—68no—
407#239—68no—
408#239—128no—
409#239—124no—
410D3×Q8—124no—
411D3×Q8—124no—
412D3×D4—64no—
413#235—124no—
414C2×D12—31no—
415C2×D12—31no—
416C2×D12—32no—
417C2×D12—32no—
418C2×D12—31no—
419C2×D12—34no—
420C2×D12—34no—
421C2×D12—31no—
422C2×D12—34no—
423C2×D12—61no—
424C2×D12—61no—
425C2×D12—64no—
426C2×D12—64no—
427C2×D12C22×D311yescharacteristic
428C2×C4×D3—32no—
429C2×C4×D3—32no—
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—32no—
433C2×C4×D3—32no—
434C2×C4×D3—32no—
435C2×C4×D3—32no—
436C2×C4×D3—32no—
437C2×C4×D3—34no—
438C2×C4×D3—32no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—62no—
443C2×C4×D3—62no—
444C2×C4×D3—64no—
445C2×C4×D3—124no—
446C2×C4×D3—124no—
447C2×C4×D3C22×D311yescharacteristic
448C2×C4×D3C22×D311yescharacteristic
449C2×C4×D3C22×D311yescharacteristic
450C2×C4×D3C22×D312yes—
451C2×Dic6—34no—
452C2×Dic6—34no—
453C2×Dic6C22×D311yescharacteristic
454C2×Dic6C22×D312yes—
455C3×C4⋊C4—22no—
456C3×C4⋊C4—22no—
457C3×C4⋊C4—32no—
458C3×C4⋊C4—34no—
459C3×C4⋊C4—31no—
460C3×C4⋊C4—31no—
461C3×C4⋊C4—34no—
462C3×C4⋊C4—34no—
463C3×C4⋊C4—32no—
464C3×C4⋊C4—32no—
465C3×C4⋊C4C22×D312yes—
466C3×C4⋊C4C22×D312yes—
467C3×C4⋊C4C22×D312yes—
468C3×C4⋊C4C22×D312yes—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—34no—
471C3×C22⋊C4—34no—
472C3×C22⋊C4—32no—
473C3×C42—21no—
474C3×C42—32no—
475C3×C42—34no—
476C3×C42—31no—
477C3×C42—31no—
478C3×C42—34no—
479C3×C42—31no—
480C3×C42C22×D311yescharacteristic
481C3×C42C22×D311yescharacteristic
482#217—32no—
483#217—34no—
484#217—32no—
485(C2×D3)⋊C4—32no—
486(C2×D3)⋊C4—32no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—32no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—34no—
494(C2×D3)⋊C4—32no—
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—34no—
501(C2×D3)⋊C4—32no—
502(C2×D3)⋊C4—32no—
503(C2×D3)⋊C4—32no—
504(C2×D3)⋊C4—62no—
505(C2×D3)⋊C4—62no—
506(C2×D3)⋊C4—64no—
507(C2×D3)⋊C4C22×D312yes—
508(C2×D3)⋊C4C22×D314yes—
509(C2×D3)⋊C4C22×D314yes—
510(C2×D3)⋊C4C22×D314yes—
511C4⋊Dic3—31no—
512C4⋊Dic3—31no—
513C4⋊Dic3—31no—
514C4⋊Dic3—31no—
515C4⋊Dic3—34no—
516C4⋊Dic3—32no—
517C4⋊Dic3—32no—
518C4⋊Dic3—61no—
519C4⋊Dic3—61no—
520C4⋊Dic3C22×D311yescharacteristic
521C4⋊Dic3C22×D312yes—
522C4⋊Dic3C22×D312yes—
523C4⋊Dic3C22×D311yescharacteristic
524C4⋊Dic3C22×D314yes—
525C4⋊Dic3C22×D314yes—
526Dic3⋊C4—34no—
527Dic3⋊C4—34no—
528Dic3⋊C4—32no—
529Dic3⋊C4—32no—
530Dic3⋊C4—34no—
531Dic3⋊C4—32no—
532Dic3⋊C4—32no—
533Dic3⋊C4—32no—
534Dic3⋊C4—32no—
535Dic3⋊C4—34no—
536Dic3⋊C4—34no—
537Dic3⋊C4—64no—
538Dic3⋊C4C22×D312yes—
539Dic3⋊C4C22×D314yes—
540C4×Dic3C22×D312yes—
541C4×Dic3C22×D311yescharacteristic
542C4×Dic3C22×D311yescharacteristic
543C4×Dic3C22×D311yescharacteristic
544C4×Dic3C22×D314yes—
545C4×Dic3C22×D314yes—
546C22×C32C2511yescharacteristic
547C2×C3⋊D3—22no—
548C2×C3⋊D3—22no—
549C2×C3⋊D3—22no—
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3C2×#4114yes—
553C2×C3×D3—21no—
554C2×C3×D3—21no—
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—21no—
567C3×Dic3—21no—
568C3×Dic3—22no—
569C3×Dic3—24no—
570C3×Dic3—22no—
571C3×Dic3—22no—
572C3×Dic3—21no—
573C2×#41—92no—
574C2×#41—92no—
575C22×Q8—92no—
576C22×D4—91no—
577C23×C4—92no—
578C4⋊Q8—31no—
579C4⋊Q8—92no—
580C4⋊Q8D3211yescharacteristic, complemented
581#126—34no—
582#126—94no—
583#126—92no—
584#125—32no—
585#125—91no—
586#125—94no—
587#124—32no—
588#124—94no—
589#124—91no—
590#123—94no—
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—94no—
601C22⋊Q8—94no—
602C22⋊Q8—92no—
603C22⋊Q8—91no—
604C22⋊Q8—92no—
605C22⋊Q8—92no—
606#121—94no—
607#121—91no—
608#121—92no—
609#121—92no—
610#120—94no—
611C4×Q8—32no—
612C4×Q8—32no—
613C4×Q8—32no—
614C4×Q8—31no—
615C4×D4—31no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—91no—
619C4×D4—94no—
620C4×D4—92no—
621C4×D4—94no—
622C4×D4—92no—
623C4×D4—92no—
624C4×D4—91no—
625C4×D4—91no—
626C4×D4—91no—
627#117—32no—
628#117—32no—
629#117—92no—
630#117—94no—
631C2×C4⋊C4—94no—
632C2×C4⋊C4—92no—
633C2×C4⋊C4—91no—
634C2×C4⋊C4—92no—
635C2×C22⋊C4—94no—
636C2×C22⋊C4—92no—
637C2×C42—31no—
638C23×C3—31no—
639C23×C3—32no—
640C22×D3—32no—
641C22×D3—32no—
642C22×D3—32no—
643C22×D3—32no—
644C22×D3—62no—
645C22×D3—62no—
646C22×D3—64no—
647C22×D3—64no—
648C22×D3—64no—
649C22×D3—64no—
650C22×D3—122no—
651C22×D3—122no—
652C22×D3C23×D312yes—
653C22×D3C23×D311yescharacteristic
654C3×Q8—24no—
655C3×Q8—24no—
656C3×Q8—44no—
657C3×Q8—62no—
658C3×Q8—64no—
659C3×D4—62no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—24no—
663C2×C3×C4—21no—
664C2×C3×C4—32no—
665C2×C3×C4—31no—
666C2×C3×C4—31no—
667C2×C3×C4—31no—
668C2×C3×C4—34no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—62no—
672C2×C3×C4—62no—
673C2×C3×C4—62no—
674C2×C3×C4—64no—
675C2×C3×C4C23×D314yes—
676C2×C3×C4C23×D314yes—
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D311yescharacteristic
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683#67—64no—
684#67—64no—
685#67—124no—
686C2×Dic3—32no—
687C2×Dic3—32no—
688C2×Dic3—32no—
689C2×Dic3—32no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—122no—
693C2×Dic3—122no—
694C2×Dic3C23×D311yescharacteristic
695C2×Dic3C23×D312yes—
696C2×Dic3C23×D311yescharacteristic
697C2×Dic3C23×D312yes—
698C2×Dic3C23×D311yescharacteristic
699C2×Dic3C23×D314yes—
700C2×Dic3C23×D312yes—
701D12—22no—
702D12—34no—
703D12—34no—
704D12—64no—
705D12—68no—
706D12—68no—
707D12—64no—
708D12—64no—
709D12—62no—
710D12—62no—
711D12—122no—
712D12—128no—
713D12—124no—
714C4×D3—22no—
715C4×D3—22no—
716C4×D3—22no—
717C4×D3—24no—
718C4×D3—68no—
719C4×D3—68no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—64no—
723C4×D3—64no—
724C4×D3—124no—
725C4×D3—124no—
726C4×D3—128no—
727C4×D3—122no—
728C4×D3—122no—
729C4×D3—124no—
730C4×D3—124no—
731C4×D3—124no—
732C4×D3—124no—
733C4×D3—122no—
734C4×D3—122no—
735Dic6—24no—
736Dic6—22no—
737Dic6—124no—
738Dic6—124no—
739C2×C32C22×#4111yescharacteristic
740C2×C32C2×H(5,𝔽2)11yescharacteristic
741C2×C32C2×2−1+411yescharacteristic
742C3⋊D3—24no—
743C3⋊D3—42no—
744C3×D3—22no—
745C3×D3—42no—
746C24—92no—
747#41—188no—
748#41—364no—
749C2×Q8—31no—
750C2×Q8—32no—
751C2×Q8—94no—
752C2×Q8—364no—
753C2×Q8C2×D3212yes—
754C2×D4—31no—
755C2×D4—92no—
756C2×D4—92no—
757C2×D4—94no—
758C2×D4—91no—
759C2×D4—94no—
760C2×D4—91no—
761C2×D4—184no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—31no—
765C22×C4—32no—
766C22×C4—94no—
767C22×C4—92no—
768C22×C4—94no—
769C22×C4—92no—
770C22×C4—92no—
771C22×C4—94no—
772C22×C4—92no—
773C22×C4—92no—
774C22×C4—364no—
775C4⋊C4—31no—
776C4⋊C4—32no—
777C4⋊C4—34no—
778C4⋊C4—34no—
779C4⋊C4—31no—
780C4⋊C4—32no—
781C4⋊C4—34no—
782C4⋊C4—32no—
783C4⋊C4—92no—
784C4⋊C4—94no—
785C4⋊C4—92no—
786C4⋊C4—92no—
787C4⋊C4—94no—
788C4⋊C4—92no—
789C4⋊C4—91no—
790C4⋊C4—91no—
791C4⋊C4—94no—
792C4⋊C4C2×D3212yes—
793C4⋊C4C2×D3212yes—
794C22⋊C4—34no—
795C22⋊C4—32no—
796C22⋊C4—34no—
797C22⋊C4—34no—
798C22⋊C4—92no—
799C22⋊C4—94no—
800C22⋊C4—92no—
801C22⋊C4—92no—
802C22⋊C4—92no—
803C22⋊C4—92no—
804C22⋊C4—92no—
805C22⋊C4—94no—
806C22⋊C4—92no—
807C22⋊C4—94no—
808C22⋊C4—92no—
809C42—31no—
810C42—31no—
811C42—31no—
812C42—34no—
813C42—34no—
814C42—32no—
815C42C2×D3211yescharacteristic
816C22×C3—21no—
817C22×C3—32no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—62no—
821C22×C3—62no—
822C22×C3—62no—
823C22×C3C24×D311yescharacteristic
824C22×C3C24×D311yescharacteristic
825C2×D3—21no—
826C2×D3—21no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—34no—
831C2×D3—34no—
832C2×D3—64no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—122no—
844C2×D3—122no—
845C2×D3—122no—
846C2×D3—122no—
847C2×D3—122no—
848C2×D3—128no—
849C2×D3—128no—
850C2×D3#100712yes—
851C3×C4—21no—
852C3×C4—24no—
853C3×C4—24no—
854C3×C4—21no—
855C3×C4—22no—
856C3×C4—22no—
857C3×C4—44no—
858C3×C4—41no—
859C3×C4—62no—
860C3×C4—61no—
861C3×C4—62no—
862C3×C4—64no—
863C3×C4—62no—
864C3×C4—61no—
865C3×C4—61no—
866C3×C4D3×#4112yes—
867C3×C4D3×#4112yes—
868C3×C4#100912yes—
869C3×C4#100912yes—
870Dic3—21no—
871Dic3—21no—
872Dic3—22no—
873Dic3—24no—
874Dic3—22no—
875Dic3—21no—
876Dic3—22no—
877Dic3—62no—
878Dic3—62no—
879Dic3—62no—
880Dic3—62no—
881Dic3—122no—
882Dic3—122no—
883C32#352011yescharacteristic, complemented, Sylow
884C23—31no—
885C23—32no—
886C23—92no—
887C23—92no—
888C23—184no—
889C23—184no—
890C23—362no—
891Q8—24no—
892Q8—62no—
893Q8—64no—
894Q8—364no—
895D4—62no—
896D4—94no—
897D4—188no—
898D4—184no—
899D4—184no—
900D4—182no—
901D4—364no—
902C2×C4—31no—
903C2×C4—32no—
904C2×C4—32no—
905C2×C4—31no—
906C2×C4—31no—
907C2×C4—32no—
908C2×C4—34no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—64no—
913C2×C4—92no—
914C2×C4—92no—
915C2×C4—188no—
916C2×C4—184no—
917C2×C4—184no—
918C2×C4—362no—
919C2×C4—364no—
920C2×C4—364no—
921C2×C4—362no—
922C2×C4—362no—
923C2×C4C22×D3214yes—
924C2×C4C22×D3211yescharacteristic
925C2×C4C22×D3211yescharacteristic
926C2×C4C22×D3211yescharacteristic
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—62no—
931C2×C3—122no—
932C2×C3C2×#100711yescharacteristic
933C2×C3C2×D3×#4111yescharacteristic
934C2×C3C2×D3×#4111yescharacteristic
935C2×C3C2×#100911yescharacteristic
936C2×C3C2×#100911yescharacteristic
937C2×C3D3×2−1+411yescharacteristic
938D3—22no—
939D3—42no—
940D3—64no—
941D3—64no—
942D3—124no—
943D3—122no—
944D3—122no—
945D3—242no—
946C22—32no—
947C22—61no—
948C22—61no—
949C22—62no—
950C22—62no—
951C22—62no—
952C22—94no—
953C22—182no—
954C22—182no—
955C22—182no—
956C22—182no—
957C22—182no—
958C22—368no—
959C22C23×D3211yescharacteristic
960C4—24no—
961C4—21no—
962C4—61no—
963C4—62no—
964C4—61no—
965C4—64no—
966C4—62no—
967C4—61no—
968C4—62no—
969C4—182no—
970C4—182no—
971C4#6431212yes—
972C4#6432012yes—
973C3—21no—
974C3#8628511yescharacteristic, complemented
975C3#8699011yescharacteristic, complemented
976C2—62no—
977C2—122no—
978C2—184no—
979C2—362no—
980C2C2×#6431211yescharacteristic
981C2C2×#6432011yescharacteristic
982C2D3×#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. #10596197C2semidirect
2. C3×#5732C2semidirect
3. C3×#5728C2semidirect
4. #10595431C2semidirect
5. #10595395C2semidirect
6. #10595371C2semidirect
7. #10595353C2semidirect
8. #10594643C2semidirect
9. #10594631C2semidirect
10. #10594627C2semidirect
11. #10594481C2semidirect
12. #10594337C2semidirect
13. #10594329C2semidirect
14. C4×D3×D12C2semidirect
15. #10593903C2semidirect
16. #10593870C2semidirect
17. #10593869C2semidirect
23. C2×#3799C22semidirect
24. C2×#3797C22semidirect
25. C32×C4⋊Q8C22semidirect
26. #64155C22semidirect
27. #64104C22semidirect
28. #64103C22semidirect
29. C4⋊C4×C3⋊D3C22semidirect
31. C4×C4⋊(C3⋊D3)C22semidirect
34. C3×Q8×Dic3C22semidirect
35. C3×Q8×Dic3C22semidirect
36. C3×#898C22semidirect
38. C3×#897C22semidirect
40. C3×#892C22semidirect
41. C3×#890C22semidirect
42. C3×#887C22semidirect
45. C3×#869C22semidirect
46. C3×C4×Dic6C22semidirect
50. #63918C22semidirect
56. #63900C22semidirect
57. #63900C22semidirect
59. #63899C22semidirect
60. #63895C22semidirect
61. #63895C22semidirect
64. #63894C22semidirect
65. #63894C22semidirect
67. #63890C22semidirect
71. #63874C22semidirect
72. #63874C22semidirect
73. #63871C22semidirect
74. #63869C22semidirect
75. #63868C22semidirect
76. #63867C22semidirect
77. #63864C22semidirect
78. #63859C22semidirect
80. #63856C22semidirect
81. #63854C22semidirect
83. #63852C22semidirect
87. #5732D3semidirect
88. #5728D3semidirect
204. C3×C4⋊Q8C2×D3semidirect
205. C3×C4⋊Q8C2×D3semidirect
229. Q8×Dic3C2×D3semidirect
230. Q8×Dic3C2×D3semidirect
242. #898C2×D3semidirect
247. #897C2×D3semidirect
270. #892C2×D3semidirect
280. #890C2×D3semidirect
283. #887C2×D3semidirect
327. #869C2×D3semidirect
328. C4×Dic6C2×D3semidirect
345. C4⋊(C3⋊D3)#41semidirect
580. C4⋊Q8D32semidirect
883. C32#3520semidirect
974. C3#86285semidirect
975. C3#86990semidirect

Maximal subgroups

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

subgroupindex
#105961972
C3×#57322
C3×#57282
#105954312
#105953952
#105953712
#105953532
#105946432
#105946312
#105946272
#105944812
#105943372
#105943292
C4×D3×D122
#105939032
#105938702
#105938692
#869903
#862853