Finite Group Databasebeta

← #11910306

Subgroups — #11910306

Order 1152.

2209 conjugacy classes of subgroups.

The subgroup lattice has 1246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C3×#5646C212yesmaximal, complemented
3#10595429C211yesmaximal, characteristic, complemented
4#10595365C211yesmaximal, characteristic, complemented
5#10595345C212yesmaximal, complemented
6#10595079C211yesmaximal, characteristic
7#10594972C212yesmaximal, complemented
8#10594925C211yesmaximal, characteristic, complemented
9#10594656C211yesmaximal, characteristic, complemented
10#10594656C211yesmaximal, characteristic, complemented
11#10594624C211yesmaximal, characteristic, complemented
12#10594504C212yesmaximal, complemented
13#10594503C212yesmaximal, complemented
14#10594482C211yesmaximal, characteristic, complemented
15#10594399C211yesmaximal, characteristic, complemented
16#10594374C211yesmaximal, characteristic, complemented
17#10594339C212yesmaximal, complemented
18#10594288C211yesmaximal, characteristic
19#10594260C211yesmaximal, characteristic
20#10594176C212yesmaximal, complemented
21#10594154C211yesmaximal, characteristic, complemented
22#10594154C211yesmaximal, characteristic, complemented
23#10594044C212yesmaximal, complemented
24D3×#563—32nomaximal
25C2×Q8×C3⋊D3C2211yescharacteristic
26C22×C4×C3⋊D3C2211yescharacteristic
27C2×#3811C2211yescharacteristic
28C2×C4×D32C2211yescharacteristic
29C2×#3797C2211yescharacteristic
30C2×#3797C2211yescharacteristic
31C32×C22⋊Q8C2211yescharacteristic, complemented
32#64155C2211yescharacteristic, complemented
33#64133C2211yescharacteristic, complemented
34#64106C2211yescharacteristic, complemented
35#64105C2211yescharacteristic, complemented
36#64105C2211yescharacteristic, complemented
37C4⋊C4×C3⋊D3C2211yescharacteristic
38C4⋊C4×C3⋊D3C2211yescharacteristic
39C4⋊C4×C3⋊D3C2211yescharacteristic
40C22⋊C4×C3⋊D3C2211yescharacteristic
41C22⋊C4×C3⋊D3C2211yescharacteristic
42#64087C2211yescharacteristic, complemented
43#64087C2211yescharacteristic, complemented
44C3×#946C2212yescomplemented
45C3×#944C2212yescomplemented
46C3×#929C2212yes—
47C3×#924C2212yescomplemented
48C3×#898C2212yescomplemented
49C3×#898C2212yescomplemented
50C3×#896C2212yescomplemented
51C3×#890C2212yescomplemented
52C3×#889C2212yescomplemented
53C3×#888C2212yescomplemented
54C3×#885C2212yes—
55C3×#883C2212yes—
56C3×#879C2212yescomplemented
57C3×#879C2212yescomplemented
58#63982C2212yescomplemented
59#63974C2211yescharacteristic
60#63974C2211yescharacteristic
61#63974C2211yescharacteristic
62#63969C2212yes—
63#63962C2212yes—
64#63959C2212yes—
65#63956C2212yescomplemented
66#63956C2212yescomplemented
67#63921C2211yescharacteristic
68#63921C2211yescharacteristic
69#63921C2211yescharacteristic
70#63921C2211yescharacteristic
71#63921C2211yescharacteristic
72#63918C2212yescomplemented
73#63907C2212yes—
74#63900C2211yescharacteristic
75#63900C2211yescharacteristic
76#63900C2211yescharacteristic
77#63900C2211yescharacteristic
78#63896C2212yescomplemented
79#63896C2212yescomplemented
80#63893C2212yescomplemented
81#63890C2212yes—
82#63887C2212yescomplemented
83#63883C2211yescharacteristic
84#63883C2211yescharacteristic
85#63883C2211yescharacteristic
86#63883C2211yescharacteristic
87#63883C2211yescharacteristic
88#63883C2211yescharacteristic
89#63883C2211yescharacteristic
90#63883C2211yescharacteristic
91#63883C2211yescharacteristic
92C4×#624C2211yescharacteristic
93C4×#624C2211yescharacteristic
94C4×#624C2211yescharacteristic
95#63871C2212yescomplemented
96#63869C2212yescomplemented
97#63868C2212yescomplemented
98#63868C2212yescomplemented
99#63867C2212yescomplemented
100#63866C2212yescomplemented
101#63865C2212yescomplemented
102#63861C2212yescomplemented
103#63861C2212yescomplemented
104#63859C2212yescomplemented
105#63859C2212yescomplemented
106#63858C2212yescomplemented
107#63858C2212yescomplemented
108#63857C2212yescomplemented
109#63853C2212yes—
110#63853C2212yes—
111#63852C2212yes—
112#63851C2212yescomplemented
113#63850C2212yes—
114#63848C2212yescomplemented
115#63848C2212yescomplemented
116#63847C2212yescomplemented
117#63847C2212yescomplemented
118#63846C2212yescomplemented
119#63845C2212yescomplemented
120#63840C2212yescomplemented
121#63840C2212yescomplemented
122#63839C2212yescomplemented
123#63839C2212yescomplemented
124C3×#563—32no—
125#5735—32no—
126#5735—32no—
127D3×C4⋊Q8—32no—
128D3×C4⋊Q8—32no—
129#5712—32no—
130#5712—32no—
131#5712—32no—
132#5712—32no—
133D3×#126—32no—
134D3×#126—32no—
135D3×#126—32no—
136D3×#126—32no—
137#5699—32no—
138#5699—32no—
139D3×#125—32no—
140D3×#125—32no—
141D3×#124—32no—
142#5672—32no—
143D3×#123—32no—
144D3×#123—32no—
145#5651—32no—
146#5651—32no—
147#5646—32no—
148#5646—32no—
149#5646—32no—
150#5646D312yescomplemented
151D3×C22⋊Q8—32no—
152D3×C22⋊Q8—32no—
153D3×C22⋊Q8—32no—
154D3×C22⋊Q8—32no—
155D3×C22⋊Q8—61no—
156C23×C3⋊D3C2311yescharacteristic
157C22×D32C2311yescharacteristic
158C2×C32×Q8C2311yescharacteristic
159C22×C32×C4C2311yescharacteristic
160C22×C3⋊Dic3C2311yescharacteristic
161Q8×C3⋊D3—42no—
162C2×C4×C3⋊D3—42no—
163C2×C4×C3⋊D3C2311yescharacteristic
164C2×C4×C3⋊D3C2311yescharacteristic
165C2×C4×C3⋊D3C2311yescharacteristic
166C2×C4×C3⋊D3C2311yescharacteristic
167C2×C4×C3⋊D3C2311yescharacteristic
168C2×C4×C3⋊D3C2311yescharacteristic
169C2×C4×C3⋊D3C2311yescharacteristic
170C2×C4×C3⋊D3C2311yescharacteristic
171C2×#634C2311yescharacteristic
172C2×#634C2311yescharacteristic
173C2×#634C2311yescharacteristic
174C2×C3×#67C2312yes—
175C2×C3×C4×D3C2312yes—
176C2×C3×Dic6C2312yes—
177C2×C3×Dic6C2312yes—
178#3811—42no—
179C2×#627C2312yes—
180C2×#627C2312yes—
181C2×#626C2312yes—
182C2×#624C2311yescharacteristic
183C2×#624C2311yescharacteristic
184C2×#624C2311yescharacteristic
185C2×#624C2311yescharacteristic
186C2×#624C2311yescharacteristic
187C2×#624C2311yescharacteristic
188C2×#624C2311yescharacteristic
189C2×D3×Dic3C2312yes—
190C4×D32—42no—
191#3797—42no—
192#3797—42no—
193C32×C4⋊C4C2311yescharacteristic
194C32×C4⋊C4C2311yescharacteristic
195C32×C4⋊C4C2311yescharacteristic
196C32×C22⋊C4C2311yescharacteristic
197C32×C22⋊C4C2311yescharacteristic
198#3757C2311yescharacteristic
199#3757C2311yescharacteristic
200#3752C2311yescharacteristic
201#3752C2311yescharacteristic
202#3752C2311yescharacteristic
203#3752C2311yescharacteristic
204C4⋊(C3⋊Dic3)C2311yescharacteristic
205C4⋊(C3⋊Dic3)C2311yescharacteristic
206C4⋊(C3⋊Dic3)C2311yescharacteristic
207#3750C2311yescharacteristic
208#3750C2311yescharacteristic
209#3750C2311yescharacteristic
210#3750C2311yescharacteristic
211#3750C2311yescharacteristic
212#3750C2311yescharacteristic
213C3×#217C2312yes—
214C3×#217C2312yes—
215C3×#217C2312yes—
216C3×(C2×D3)⋊C4C2312yes—
217C3×(C2×D3)⋊C4C2312yes—
218C3×(C2×D3)⋊C4C2312yes—
219C3×(C2×D3)⋊C4C2312yes—
220C3×(C2×D3)⋊C4C2312yes—
221C3×C4⋊Dic3C2312yes—
222C3×C4⋊Dic3C2312yes—
223C3×C4⋊Dic3C2312yes—
224C3×C4⋊Dic3C2312yes—
225C3×Dic3⋊C4C2312yes—
226C3×Dic3⋊C4C2312yes—
227C3×Dic3⋊C4C2312yes—
228C3×Dic3⋊C4C2312yes—
229C3×Dic3⋊C4C2312yes—
230C3×Dic3⋊C4C2312yes—
231C3×Dic3⋊C4C2312yes—
232C3×Dic3⋊C4C2312yes—
233C3×Dic3⋊C4C2312yes—
234C3×C4×Dic3C2312yes—
235C3×C4×Dic3C2312yes—
236C3×C4×Dic3C2312yes—
237#3724C2312yes—
238#3724C2312yes—
239#3724C2312yes—
240#3724C2312yes—
241Dic3⋊Dic3C2312yes—
242Dic3⋊Dic3C2312yes—
243Dic3⋊Dic3C2312yes—
244Dic3⋊Dic3C2312yes—
245Dic3⋊Dic3C2312yes—
246Dic3⋊Dic3C2312yes—
247Dic3⋊Dic3C2312yes—
248Dic3⋊Dic3C2312yes—
249Dic3⋊Dic3C2312yes—
250#3722C2312yes—
251#3722C2312yes—
252#3722C2312yes—
253(C2×D3)⋊Dic3C2312yes—
254(C2×D3)⋊Dic3C2312yes—
255(C2×D3)⋊Dic3C2312yes—
256(C2×D3)⋊Dic3C2312yes—
257(C2×D3)⋊Dic3C2312yes—
258Dic32C2312yes—
259Dic32C2312yes—
260Dic32C2312yes—
261C2×#563—91noSylow
262C2×D3×Q8—32no—
263C2×D3×Q8—32no—
264C2×D3×Q8—32no—
265C2×D3×Q8—61no—
266C2×D3×D4—32no—
267C22×C4×D3—32no—
268C22×C4×D3—32no—
269C22×C4×D3—61no—
270C3×C4⋊Q8—32no—
271C3×C4⋊Q8—32no—
272C3×#126—32no—
273C3×#126—32no—
274C3×#126—32no—
275C3×#126—32no—
276C3×#125—32no—
277C3×#125—32no—
278C3×#124—32no—
279C3×#123—32no—
280C3×#123—32no—
281C3×C22⋊Q8—21no—
282C3×C22⋊Q8—32no—
283C3×C22⋊Q8—32no—
284C3×C22⋊Q8—32no—
285C3×C22⋊Q8C2×D312yescomplemented
286#947—32no—
287#946—32no—
288#946—32no—
289#946—32no—
290#946—61no—
291#946C2×D312yescomplemented
292#944—32no—
293#944—32no—
294#944—32no—
295#944C2×D312yescomplemented
296#936—32no—
297#935—32no—
298#935—32no—
299#929—32no—
300#929C2×D312yes—
301#924—32no—
302#924—32no—
303#924—32no—
304#924—61no—
305#924C2×D312yescomplemented
306#898—32no—
307#898—32no—
308#898—32no—
309#898—32no—
310#898—32no—
311#898—32no—
312#898—32no—
313#898—32no—
314#898—32no—
315#898—32no—
316#898C2×D312yescomplemented
317#898C2×D312yescomplemented
318#897—32no—
319#897—32no—
320#897—32no—
321#897—32no—
322#897—61no—
323#896—32no—
324#896—32no—
325#896—32no—
326#896—32no—
327#896—32no—
328#896—32no—
329#896—32no—
330#896—61no—
331#896—61no—
332#896C2×D312yescomplemented
333#894—32no—
334#894—32no—
335#894—32no—
336#894—32no—
337D3×C4⋊C4—32no—
338D3×C4⋊C4—32no—
339D3×C4⋊C4—32no—
340D3×C4⋊C4—32no—
341D3×C4⋊C4—32no—
342D3×C4⋊C4—32no—
343D3×C4⋊C4—32no—
344D3×C4⋊C4—32no—
345D3×C4⋊C4—32no—
346D3×C4⋊C4—32no—
347D3×C4⋊C4—32no—
348D3×C4⋊C4—32no—
349D3×C4⋊C4—32no—
350D3×C4⋊C4—32no—
351D3×C4⋊C4—32no—
352D3×C4⋊C4—32no—
353D3×C4⋊C4—61no—
354D3×C4⋊C4—61no—
355D3×C4⋊C4—61no—
356#890—32no—
357#890—32no—
358#890—32no—
359#890C2×D312yescomplemented
360#889—32no—
361#889—32no—
362#889—32no—
363#889—32no—
364#889—32no—
365#889—32no—
366#889—32no—
367#889C2×D312yescomplemented
368#888—32no—
369#888—32no—
370#888—32no—
371#888—32no—
372#888—32no—
373#888—32no—
374#888—32no—
375#888C2×D312yescomplemented
376#886—32no—
377#886—32no—
378#885—32no—
379#885—32no—
380#885—32no—
381#885C2×D312yes—
382#883—32no—
383#883—32no—
384#883—32no—
385#883C2×D312yes—
386D3×C22⋊C4—32no—
387D3×C22⋊C4—32no—
388D3×C22⋊C4—32no—
389D3×C22⋊C4—32no—
390D3×C22⋊C4—32no—
391D3×C22⋊C4—32no—
392D3×C22⋊C4—32no—
393D3×C22⋊C4—32no—
394D3×C22⋊C4—32no—
395D3×C22⋊C4—32no—
396D3×C22⋊C4—61no—
397D3×C22⋊C4—61no—
398#879—32no—
399#879—32no—
400#879—32no—
401#879—32no—
402#879—32no—
403#879—32no—
404#879—32no—
405#879—32no—
406#879—32no—
407#879—32no—
408#879C2×D312yescomplemented
409#879C2×D312yescomplemented
410#878—32no—
411#878—32no—
412#878—32no—
413#878—32no—
414#878—32no—
415#878—32no—
416#878—32no—
417#878—32no—
418#878—61no—
419#878—61no—
420#876—32no—
421#876—32no—
422#876—32no—
423#876—32no—
424#875—32no—
425C42×D3—32no—
426C42×D3—32no—
427C42×D3—32no—
428#870—32no—
429#870—32no—
430#869—32no—
431#869—32no—
432C23×C32C2411yescharacteristic
433C22×C3⋊D3—22no—
434C22×C3⋊D3—22no—
435C22×C3⋊D3—22no—
436C22×C3⋊D3C2411yescharacteristic
437C22×C3⋊D3C2411yescharacteristic
438C22×C3×D3C2412yes—
439C2×D32—22no—
440C2×D32—22no—
441C2×D32—22no—
442C32×Q8—41no—
443C2×C32×C4—41no—
444C2×C32×C4C2411yescharacteristic
445C2×C32×C4C2411yescharacteristic
446C2×C32×C4C2411yescharacteristic
447C2×C32×C4C2411yescharacteristic
448C2×C32×C4C2411yescharacteristic
449C2×C32×C4C2411yescharacteristic
450C2×C3⋊Dic3—41no—
451C2×C3⋊Dic3C2411yescharacteristic
452C2×C3⋊Dic3C2411yescharacteristic
453C2×C3⋊Dic3C2411yescharacteristic
454C2×C3⋊Dic3C2411yescharacteristic
455C2×C3⋊Dic3C2411yescharacteristic
456C2×C3⋊Dic3C2411yescharacteristic
457C4×C3⋊D3—22no—
458C4×C3⋊D3—22no—
459C4×C3⋊D3—22no—
460C4×C3⋊D3—22no—
461C4×C3⋊D3—22no—
462C4×C3⋊D3—22no—
463C4×C3⋊D3—41no—
464C4×C3⋊D3—41no—
465#634—41no—
466#634—41no—
467#634—41no—
468C3×#67—42no—
469C2×C3×Dic3C2412yes—
470C2×C3×Dic3C2412yes—
471C2×C3×Dic3C2412yes—
472C2×C3×Dic3C2412yes—
473C2×C3×Dic3C2412yes—
474C2×C3×Dic3C2412yes—
475C2×C3×Dic3C2412yes—
476C3×C4×D3—42no—
477C3×Dic6—42no—
478C3×Dic6—42no—
479#627—42no—
480#627—42no—
481#626—42no—
482#624—22no—
483#624—22no—
484#624—22no—
485#624—22no—
486#624—22no—
487#624—22no—
488#624—22no—
489D3×Dic3—42no—
490#563—32no—
491#563—92no—
492#563—92no—
493#563—92no—
494#563—92no—
495#563—92no—
496#563—92no—
497#563—92no—
498C2×C4⋊Q8—91no—
499C2×C4⋊Q8—91no—
500C2×#126—91no—
501C2×#126—91no—
502C2×#126—91no—
503C2×#126—91no—
504C2×#125—91no—
505C2×#125—91no—
506C2×#124—91no—
507C2×#123—91no—
508C2×#123—91no—
509C2×C22⋊Q8—91no—
510C2×C22⋊Q8—91no—
511C2×C22⋊Q8—91no—
512C2×C22⋊Q8—91no—
513C23×D3—32no—
514C23×D3—32no—
515C23×D3—61no—
516C2×C3×Q8—21no—
517C2×C3×Q8—32no—
518C2×C3×Q8—32no—
519C2×C3×Q8C22×D312yes—
520C2×C3×D4—32no—
521C22×C3×C4—21no—
522C22×C3×C4—32no—
523C22×C3×C4C22×D312yes—
524C2×#67—32no—
525C2×#67C22×D312yes—
526C22×Dic3—32no—
527C22×Dic3—32no—
528C22×Dic3—61no—
529D3×Q8—124no—
530D3×Q8—124no—
531D3×Q8—124no—
532D3×Q8—124no—
533D3×D4—124no—
534C2×D12—32no—
535C2×C4×D3—32no—
536C2×C4×D3—32no—
537C2×C4×D3—32no—
538C2×C4×D3—32no—
539C2×C4×D3—32no—
540C2×C4×D3—32no—
541C2×C4×D3—32no—
542C2×C4×D3—32no—
543C2×C4×D3—32no—
544C2×C4×D3—32no—
545C2×C4×D3—32no—
546C2×C4×D3—32no—
547C2×C4×D3—32no—
548C2×C4×D3—32no—
549C2×C4×D3—32no—
550C2×C4×D3—32no—
551C2×C4×D3—61no—
552C2×C4×D3—61no—
553C2×C4×D3—61no—
554C2×C4×D3—61no—
555C2×C4×D3—61no—
556C2×C4×D3—61no—
557C2×C4×D3—61no—
558C2×C4×D3—61no—
559C2×C4×D3—124no—
560C2×C4×D3—124no—
561C2×C4×D3—124no—
562C2×C4×D3C22×D312yes—
563C2×Dic6—32no—
564C2×Dic6—32no—
565C2×Dic6—32no—
566C2×Dic6—32no—
567C2×Dic6—32no—
568C2×Dic6—32no—
569C2×Dic6—32no—
570C2×Dic6—61no—
571C2×Dic6—61no—
572C2×Dic6—61no—
573C2×Dic6C22×D312yes—
574C2×Dic6C22×D312yes—
575C3×C4⋊C4—21no—
576C3×C4⋊C4—21no—
577C3×C4⋊C4—21no—
578C3×C4⋊C4—32no—
579C3×C4⋊C4—32no—
580C3×C4⋊C4—32no—
581C3×C4⋊C4—32no—
582C3×C4⋊C4—32no—
583C3×C4⋊C4—32no—
584C3×C4⋊C4—32no—
585C3×C4⋊C4—32no—
586C3×C4⋊C4—32no—
587C3×C4⋊C4—32no—
588C3×C4⋊C4—32no—
589C3×C4⋊C4—32no—
590C3×C4⋊C4—32no—
591C3×C4⋊C4C22×D312yes—
592C3×C4⋊C4C22×D312yes—
593C3×C4⋊C4C22×D312yes—
594C3×C22⋊C4—21no—
595C3×C22⋊C4—21no—
596C3×C22⋊C4—32no—
597C3×C22⋊C4—32no—
598C3×C22⋊C4—32no—
599C3×C22⋊C4—32no—
600C3×C22⋊C4—32no—
601C3×C22⋊C4—32no—
602C3×C22⋊C4—32no—
603C3×C22⋊C4—32no—
604C3×C22⋊C4C22×D312yes—
605C3×C22⋊C4C22×D312yes—
606C3×C42—32no—
607C3×C42—32no—
608C3×C42—32no—
609#217—32no—
610#217—32no—
611#217—32no—
612#217—32no—
613#217—32no—
614#217—32no—
615#217—32no—
616#217—61no—
617#217—61no—
618#217C22×D312yes—
619#217C22×D312yes—
620#217C22×D312yes—
621(C2×D3)⋊C4—32no—
622(C2×D3)⋊C4—32no—
623(C2×D3)⋊C4—32no—
624(C2×D3)⋊C4—32no—
625(C2×D3)⋊C4—32no—
626(C2×D3)⋊C4—32no—
627(C2×D3)⋊C4—32no—
628(C2×D3)⋊C4—32no—
629(C2×D3)⋊C4—32no—
630(C2×D3)⋊C4—32no—
631(C2×D3)⋊C4—32no—
632(C2×D3)⋊C4—32no—
633(C2×D3)⋊C4—32no—
634(C2×D3)⋊C4—32no—
635(C2×D3)⋊C4—32no—
636(C2×D3)⋊C4—61no—
637(C2×D3)⋊C4—61no—
638(C2×D3)⋊C4—61no—
639(C2×D3)⋊C4—61no—
640(C2×D3)⋊C4C22×D312yes—
641(C2×D3)⋊C4C22×D312yes—
642(C2×D3)⋊C4C22×D312yes—
643(C2×D3)⋊C4C22×D312yes—
644(C2×D3)⋊C4C22×D312yes—
645C4⋊Dic3—32no—
646C4⋊Dic3—32no—
647C4⋊Dic3—32no—
648C4⋊Dic3—32no—
649C4⋊Dic3—32no—
650C4⋊Dic3—32no—
651C4⋊Dic3—32no—
652C4⋊Dic3—32no—
653C4⋊Dic3—32no—
654C4⋊Dic3—32no—
655C4⋊Dic3—32no—
656C4⋊Dic3—32no—
657C4⋊Dic3—61no—
658C4⋊Dic3—61no—
659C4⋊Dic3—61no—
660C4⋊Dic3C22×D312yes—
661C4⋊Dic3C22×D312yes—
662C4⋊Dic3C22×D312yes—
663C4⋊Dic3C22×D312yes—
664Dic3⋊C4—32no—
665Dic3⋊C4—32no—
666Dic3⋊C4—32no—
667Dic3⋊C4—32no—
668Dic3⋊C4—32no—
669Dic3⋊C4—32no—
670Dic3⋊C4—32no—
671Dic3⋊C4—32no—
672Dic3⋊C4—32no—
673Dic3⋊C4—32no—
674Dic3⋊C4—32no—
675Dic3⋊C4—32no—
676Dic3⋊C4—32no—
677Dic3⋊C4—32no—
678Dic3⋊C4—32no—
679Dic3⋊C4—32no—
680Dic3⋊C4—32no—
681Dic3⋊C4—32no—
682Dic3⋊C4—32no—
683Dic3⋊C4—32no—
684Dic3⋊C4—32no—
685Dic3⋊C4—32no—
686Dic3⋊C4—32no—
687Dic3⋊C4—61no—
688Dic3⋊C4—61no—
689Dic3⋊C4—61no—
690Dic3⋊C4—61no—
691Dic3⋊C4—61no—
692Dic3⋊C4—61no—
693Dic3⋊C4C22×D312yes—
694Dic3⋊C4C22×D312yes—
695Dic3⋊C4C22×D312yes—
696Dic3⋊C4C22×D312yes—
697Dic3⋊C4C22×D312yes—
698Dic3⋊C4C22×D312yes—
699Dic3⋊C4C22×D312yes—
700Dic3⋊C4C22×D312yes—
701Dic3⋊C4C22×D312yes—
702C4×Dic3—32no—
703C4×Dic3—32no—
704C4×Dic3—32no—
705C4×Dic3—32no—
706C4×Dic3—32no—
707C4×Dic3—32no—
708C4×Dic3C22×D312yes—
709C4×Dic3C22×D312yes—
710C4×Dic3C22×D312yes—
711C22×C32—21no—
712C22×C32—21no—
713C22×C32—21no—
714C22×C32C2511yescharacteristic
715C2×C3⋊D3—21no—
716C2×C3⋊D3—21no—
717C2×C3⋊D3—21no—
718C2×C3⋊D3—44no—
719C2×C3⋊D3H(5,𝔽2)12yes—
720C2×C3⋊D32−1+412yes—
721C2×C3⋊D32−1+412yes—
722C2×C3×D3—22no—
723C2×C3×D3—22no—
724C2×C3×D3—22no—
725D32—44no—
726C32×C4—21no—
727C32×C4—21no—
728C32×C4—21no—
729C32×C4—21no—
730C32×C4—21no—
731C32×C4—21no—
732C3⋊Dic3—21no—
733C3⋊Dic3—21no—
734C3⋊Dic3—21no—
735C3⋊Dic3—21no—
736C3⋊Dic3—21no—
737C3⋊Dic3—21no—
738C3×Dic3—22no—
739C3×Dic3—22no—
740C3×Dic3—22no—
741C3×Dic3—22no—
742C3×Dic3—22no—
743C3×Dic3—22no—
744C3×Dic3—22no—
745C22×Q8—91no—
746C22×Q8—91no—
747C22×Q8—91no—
748C22×D4—91no—
749C23×C4—91no—
750C23×C4—91no—
751C4⋊Q8—32no—
752C4⋊Q8—32no—
753C4⋊Q8—92no—
754C4⋊Q8—92no—
755C4⋊Q8—92no—
756C4⋊Q8—92no—
757C4⋊Q8—92no—
758C4⋊Q8—92no—
759#126—32no—
760#126—32no—
761#126—32no—
762#126—32no—
763#126—92no—
764#126—92no—
765#126—92no—
766#126—92no—
767#126—92no—
768#126—92no—
769#126—92no—
770#126—92no—
771#126—92no—
772#126—92no—
773#126—92no—
774#126—92no—
775#125—32no—
776#125—32no—
777#125—92no—
778#125—92no—
779#125—92no—
780#125—92no—
781#125—92no—
782#125—92no—
783#124—32no—
784#124—92no—
785#124—92no—
786#124—92no—
787#123—32no—
788#123—32no—
789#123—92no—
790#123—92no—
791#123—92no—
792#123—92no—
793#123—92no—
794#123—92no—
795C22⋊Q8—32no—
796C22⋊Q8—32no—
797C22⋊Q8—32no—
798C22⋊Q8—92no—
799C22⋊Q8—92no—
800C22⋊Q8—92no—
801C22⋊Q8—92no—
802C22⋊Q8—92no—
803C22⋊Q8—92no—
804C22⋊Q8—92no—
805C22⋊Q8—92no—
806C22⋊Q8—92no—
807C22⋊Q8—91no—
808C22⋊Q8—91no—
809C22⋊Q8—91no—
810C22⋊Q8—91no—
811C22⋊Q8—91no—
812C22⋊Q8—91no—
813C22⋊Q8—91no—
814C22⋊Q8D3211yescharacteristic, complemented
815C2×C4⋊C4—91no—
816C2×C4⋊C4—91no—
817C2×C4⋊C4—91no—
818C2×C4⋊C4—91no—
819C2×C4⋊C4—91no—
820C2×C4⋊C4—91no—
821C2×C4⋊C4—91no—
822C2×C4⋊C4—91no—
823C2×C4⋊C4—91no—
824C2×C4⋊C4—91no—
825C2×C4⋊C4—91no—
826C2×C4⋊C4—91no—
827C2×C4⋊C4—91no—
828C2×C4⋊C4—91no—
829C2×C4⋊C4—91no—
830C2×C4⋊C4—91no—
831C2×C22⋊C4—91no—
832C2×C22⋊C4—91no—
833C2×C22⋊C4—91no—
834C2×C22⋊C4—91no—
835C2×C22⋊C4—91no—
836C2×C22⋊C4—91no—
837C2×C22⋊C4—91no—
838C2×C22⋊C4—91no—
839C2×C22⋊C4—91no—
840C2×C22⋊C4—91no—
841C2×C42—91no—
842C2×C42—91no—
843C2×C42—91no—
844C23×C3—21no—
845C23×C3—32no—
846C23×C3C23×D312yes—
847C22×D3—32no—
848C22×D3—32no—
849C22×D3—61no—
850C22×D3—61no—
851C22×D3—64no—
852C22×D3—64no—
853C22×D3—64no—
854C22×D3—64no—
855C22×D3—64no—
856C22×D3—64no—
857C22×D3—64no—
858C22×D3—122no—
859C22×D3—122no—
860C22×D3C23×D312yes—
861C3×Q8—42no—
862C3×Q8—42no—
863C3×Q8—122no—
864C3×Q8—122no—
865C3×D4—122no—
866C2×C3×C4—21no—
867C2×C3×C4—21no—
868C2×C3×C4—21no—
869C2×C3×C4—21no—
870C2×C3×C4—21no—
871C2×C3×C4—21no—
872C2×C3×C4—32no—
873C2×C3×C4—32no—
874C2×C3×C4—32no—
875C2×C3×C4—32no—
876C2×C3×C4—32no—
877C2×C3×C4—32no—
878C2×C3×C4—32no—
879C2×C3×C4—42no—
880C2×C3×C4—42no—
881C2×C3×C4—122no—
882C2×C3×C4C23×D312yes—
883C2×C3×C4C23×D312yes—
884C2×C3×C4C23×D312yes—
885C2×C3×C4C23×D312yes—
886C2×C3×C4C23×D312yes—
887C2×C3×C4C23×D312yes—
888#67—42no—
889#67—122no—
890C2×Dic3—32no—
891C2×Dic3—32no—
892C2×Dic3—32no—
893C2×Dic3—32no—
894C2×Dic3—32no—
895C2×Dic3—32no—
896C2×Dic3—61no—
897C2×Dic3—61no—
898C2×Dic3—61no—
899C2×Dic3—61no—
900C2×Dic3—61no—
901C2×Dic3—61no—
902C2×Dic3—122no—
903C2×Dic3—122no—
904C2×Dic3—122no—
905C2×Dic3C23×D312yes—
906C2×Dic3C23×D312yes—
907C2×Dic3C23×D312yes—
908C2×Dic3C23×D312yes—
909C2×Dic3C23×D312yes—
910C2×Dic3C23×D312yes—
911C2×Dic3C23×D312yes—
912D12—122no—
913C4×D3—42no—
914C4×D3—64no—
915C4×D3—64no—
916C4×D3—64no—
917C4×D3—64no—
918C4×D3—64no—
919C4×D3—64no—
920C4×D3—64no—
921C4×D3—64no—
922C4×D3—64no—
923C4×D3—64no—
924C4×D3—64no—
925C4×D3—64no—
926C4×D3—64no—
927C4×D3—64no—
928C4×D3—122no—
929C4×D3—122no—
930C4×D3—122no—
931C4×D3—122no—
932C4×D3—122no—
933C4×D3—122no—
934C4×D3—122no—
935C4×D3—122no—
936C4×D3—122no—
937C4×D3—122no—
938Dic6—42no—
939Dic6—42no—
940Dic6—122no—
941Dic6—122no—
942Dic6—122no—
943Dic6—122no—
944Dic6—122no—
945Dic6—122no—
946Dic6—122no—
947Dic6—122no—
948Dic6—122no—
949Dic6—122no—
950C2×C32—41no—
951C2×C32C2×H(5,𝔽2)11yescharacteristic
952C2×C32C2×2−1+411yescharacteristic
953C2×C32C2×2−1+411yescharacteristic
954C3⋊D3—41no—
955C3⋊D3#56314yescomplemented
956C3×D3—42no—
957C24—91no—
958C24—91no—
959C2×Q8—32no—
960C2×Q8—32no—
961C2×Q8—92no—
962C2×Q8—92no—
963C2×Q8—91no—
964C2×Q8—91no—
965C2×Q8—91no—
966C2×Q8—362no—
967C2×Q8—362no—
968C2×Q8—362no—
969C2×Q8C2×D3211yescharacteristic
970C2×D4—32no—
971C2×D4—92no—
972C2×D4—362no—
973C22×C4—32no—
974C22×C4—91no—
975C22×C4—91no—
976C22×C4—91no—
977C22×C4—91no—
978C22×C4—91no—
979C22×C4—91no—
980C22×C4—91no—
981C22×C4—92no—
982C22×C4—91no—
983C22×C4—91no—
984C22×C4—91no—
985C22×C4—91no—
986C22×C4—91no—
987C22×C4—91no—
988C22×C4—91no—
989C22×C4—91no—
990C22×C4—91no—
991C22×C4—362no—
992C22×C4—362no—
993C22×C4C2×D3211yescharacteristic
994C4⋊C4—32no—
995C4⋊C4—32no—
996C4⋊C4—32no—
997C4⋊C4—32no—
998C4⋊C4—32no—
999C4⋊C4—32no—
1000C4⋊C4—32no—
1001C4⋊C4—32no—
1002C4⋊C4—32no—
1003C4⋊C4—32no—
1004C4⋊C4—32no—
1005C4⋊C4—32no—
1006C4⋊C4—32no—
1007C4⋊C4—92no—
1008C4⋊C4—92no—
1009C4⋊C4—92no—
1010C4⋊C4—92no—
1011C4⋊C4—92no—
1012C4⋊C4—92no—
1013C4⋊C4—92no—
1014C4⋊C4—92no—
1015C4⋊C4—92no—
1016C4⋊C4—92no—
1017C4⋊C4—92no—
1018C4⋊C4—92no—
1019C4⋊C4—92no—
1020C4⋊C4—91no—
1021C4⋊C4—91no—
1022C4⋊C4—91no—
1023C4⋊C4—91no—
1024C4⋊C4—91no—
1025C4⋊C4—91no—
1026C4⋊C4—91no—
1027C4⋊C4—91no—
1028C4⋊C4—91no—
1029C4⋊C4C2×D3211yescharacteristic
1030C4⋊C4C2×D3211yescharacteristic
1031C4⋊C4C2×D3211yescharacteristic
1032C22⋊C4—32no—
1033C22⋊C4—32no—
1034C22⋊C4—32no—
1035C22⋊C4—32no—
1036C22⋊C4—32no—
1037C22⋊C4—32no—
1038C22⋊C4—32no—
1039C22⋊C4—32no—
1040C22⋊C4—92no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—92no—
1044C22⋊C4—92no—
1045C22⋊C4—92no—
1046C22⋊C4—92no—
1047C22⋊C4—92no—
1048C22⋊C4—91no—
1049C22⋊C4—91no—
1050C22⋊C4—91no—
1051C22⋊C4—91no—
1052C22⋊C4—91no—
1053C22⋊C4—91no—
1054C22⋊C4C2×D3211yescharacteristic
1055C22⋊C4C2×D3211yescharacteristic
1056C42—32no—
1057C42—32no—
1058C42—32no—
1059C42—92no—
1060C42—92no—
1061C42—92no—
1062C22×C3—22no—
1063C22×C3—22no—
1064C22×C3—22no—
1065C22×C3—22no—
1066C22×C3—21no—
1067C22×C3—41no—
1068C22×C3—41no—
1069C22×C3—62no—
1070C22×C3—62no—
1071C22×C3—62no—
1072C22×C3C24×D312yes—
1073C2×D3—22no—
1074C2×D3—22no—
1075C2×D3—22no—
1076C2×D3—34no—
1077C2×D3—34no—
1078C2×D3—34no—
1079C2×D3—62no—
1080C2×D3—62no—
1081C2×D3—62no—
1082C2×D3—62no—
1083C2×D3—62no—
1084C2×D3—62no—
1085C2×D3—62no—
1086C2×D3—121no—
1087C2×D3—121no—
1088C2×D3—128no—
1089C2×D3—128no—
1090C2×D3—128no—
1091C3×C4—22no—
1092C3×C4—22no—
1093C3×C4—22no—
1094C3×C4—22no—
1095C3×C4—22no—
1096C3×C4—22no—
1097C3×C4—22no—
1098C3×C4—41no—
1099C3×C4—41no—
1100C3×C4—41no—
1101C3×C4—41no—
1102C3×C4—41no—
1103C3×C4—62no—
1104C3×C4—62no—
1105C3×C4—62no—
1106C3×C4—62no—
1107C3×C4—62no—
1108C3×C4—62no—
1109C3×C4—62no—
1110Dic3—22no—
1111Dic3—22no—
1112Dic3—22no—
1113Dic3—22no—
1114Dic3—22no—
1115Dic3—22no—
1116Dic3—22no—
1117Dic3—62no—
1118Dic3—62no—
1119Dic3—62no—
1120Dic3—62no—
1121Dic3—62no—
1122Dic3—62no—
1123Dic3—62no—
1124Dic3—121no—
1125Dic3—121no—
1126Dic3—121no—
1127Dic3—121no—
1128Dic3—121no—
1129C32C2×#56311yescharacteristic, complemented, Sylow
1130C23—32no—
1131C23—91no—
1132C23—91no—
1133C23—182no—
1134C23—182no—
1135C23—182no—
1136C23—182no—
1137C23—182no—
1138C23—182no—
1139C23C22×D3211yescharacteristic
1140Q8—41no—
1141Q8—122no—
1142Q8—122no—
1143Q8—361no—
1144Q8—361no—
1145Q8—361no—
1146Q8—362no—
1147Q8—362no—
1148D4—122no—
1149D4—362no—
1150C2×C4—32no—
1151C2×C4—32no—
1152C2×C4—32no—
1153C2×C4—32no—
1154C2×C4—32no—
1155C2×C4—32no—
1156C2×C4—32no—
1157C2×C4—41no—
1158C2×C4—91no—
1159C2×C4—91no—
1160C2×C4—91no—
1161C2×C4—91no—
1162C2×C4—91no—
1163C2×C4—91no—
1164C2×C4—122no—
1165C2×C4—182no—
1166C2×C4—182no—
1167C2×C4—182no—
1168C2×C4—182no—
1169C2×C4—182no—
1170C2×C4—182no—
1171C2×C4—182no—
1172C2×C4—182no—
1173C2×C4—182no—
1174C2×C4—182no—
1175C2×C4—182no—
1176C2×C4—182no—
1177C2×C4—182no—
1178C2×C4—361no—
1179C2×C4—361no—
1180C2×C4—362no—
1181C2×C4—361no—
1182C2×C4C22×D3211yescharacteristic
1183C2×C4C22×D3211yescharacteristic
1184C2×C4C22×D3211yescharacteristic
1185C2×C4C22×D3211yescharacteristic
1186C2×C4C22×D3211yescharacteristic
1187C2×C4C22×D3211yescharacteristic
1188C2×C3—21no—
1189C2×C3—21no—
1190C2×C3—21no—
1191C2×C3—42no—
1192C2×C3—42no—
1193C2×C3—122no—
1194C2×C3D3×H(5,𝔽2)12yes—
1195C2×C3D3×2−1+412yes—
1196C2×C3D3×2−1+412yes—
1197D3—38no—
1198D3—42no—
1199D3—64no—
1200D3—122no—
1201D3—122no—
1202C22—21no—
1203C22—21no—
1204C22—21no—
1205C22—62no—
1206C22—62no—
1207C22—62no—
1208C22—92no—
1209C22—92no—
1210C22—92no—
1211C22—181no—
1212C22—181no—
1213C22—181no—
1214C22—364no—
1215C22—364no—
1216C22C23×D3211yescharacteristic
1217C4—21no—
1218C4—21no—
1219C4—21no—
1220C4—21no—
1221C4—21no—
1222C4—21no—
1223C4—62no—
1224C4—62no—
1225C4—62no—
1226C4—62no—
1227C4—62no—
1228C4—62no—
1229C4—62no—
1230C4—181no—
1231C4—181no—
1232C4—181no—
1233C4—181no—
1234C4—181no—
1235C4—181no—
1236C3—21no—
1237C3D3×#56312yescomplemented
1238C2—41no—
1239C2—94no—
1240C2—122no—
1241C2—361no—
1242C2#1059667511yescharacteristic
1243C2#1059668711yescharacteristic
1244C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
prime radicalC2×#3811C22
hypercenterC22⋊Q8D32
hypocenterC32C2×#563
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×C22⋊Q8C2semidirect
2. C3×#5646C2semidirect
3. #10595429C2semidirect
4. #10595365C2semidirect
5. #10595345C2semidirect
7. #10594972C2semidirect
8. #10594925C2semidirect
9. #10594656C2semidirect
10. #10594656C2semidirect
11. #10594624C2semidirect
12. #10594504C2semidirect
13. #10594503C2semidirect
14. #10594482C2semidirect
15. #10594399C2semidirect
16. #10594374C2semidirect
17. #10594339C2semidirect
20. #10594176C2semidirect
21. #10594154C2semidirect
22. #10594154C2semidirect
23. #10594044C2semidirect
31. C32×C22⋊Q8C22semidirect
32. #64155C22semidirect
33. #64133C22semidirect
34. #64106C22semidirect
35. #64105C22semidirect
36. #64105C22semidirect
42. #64087C22semidirect
43. #64087C22semidirect
44. C3×#946C22semidirect
45. C3×#944C22semidirect
47. C3×#924C22semidirect
48. C3×#898C22semidirect
49. C3×#898C22semidirect
50. C3×#896C22semidirect
51. C3×#890C22semidirect
52. C3×#889C22semidirect
53. C3×#888C22semidirect
56. C3×#879C22semidirect
57. C3×#879C22semidirect
58. #63982C22semidirect
65. #63956C22semidirect
66. #63956C22semidirect
72. #63918C22semidirect
78. #63896C22semidirect
79. #63896C22semidirect
80. #63893C22semidirect
82. #63887C22semidirect
95. #63871C22semidirect
96. #63869C22semidirect
97. #63868C22semidirect
98. #63868C22semidirect
99. #63867C22semidirect
100. #63866C22semidirect
101. #63865C22semidirect
102. #63861C22semidirect
103. #63861C22semidirect
104. #63859C22semidirect
105. #63859C22semidirect
106. #63858C22semidirect
107. #63858C22semidirect
108. #63857C22semidirect
112. #63851C22semidirect
114. #63848C22semidirect
115. #63848C22semidirect
116. #63847C22semidirect
117. #63847C22semidirect
118. #63846C22semidirect
119. #63845C22semidirect
120. #63840C22semidirect
121. #63840C22semidirect
122. #63839C22semidirect
123. #63839C22semidirect
150. #5646D3semidirect
285. C3×C22⋊Q8C2×D3semidirect
291. #946C2×D3semidirect
295. #944C2×D3semidirect
305. #924C2×D3semidirect
316. #898C2×D3semidirect
317. #898C2×D3semidirect
332. #896C2×D3semidirect
359. #890C2×D3semidirect
367. #889C2×D3semidirect
375. #888C2×D3semidirect
408. #879C2×D3semidirect
409. #879C2×D3semidirect
814. C22⋊Q8D32semidirect
955. C3⋊D3#563semidirect
1129. C32C2×#563semidirect
1237. C3D3×#563semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C22⋊Q82
C3×#56462
#105954292
#105953652
#105953452
#105950792
#105949722
#105949252
#105946562
#105946242
#105945042
#105945032
#105944822
#105943992
#105943742
#105943392
#105942882
#105942602
#105941762
#105941542
#105940442
D3×#5633