Finite Group Databasebeta

← #11918413

Subgroups — #11918413

Order 1152.

2033 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596095C211yesmaximal, characteristic, complemented
2C3×#5640C212yesmaximal, complemented
3#10595439C211yesmaximal, characteristic, complemented
4#10595384C212yesmaximal, complemented
5#10595352C211yesmaximal, characteristic, complemented
6#10595085C212yesmaximal, complemented
7#10595033C211yesmaximal, characteristic, complemented
8#10594963C211yesmaximal, characteristic, complemented
9#10594655C212yesmaximal, complemented
10#10594653C212yesmaximal, complemented
11#10594640C212yesmaximal, complemented
12#10594589C211yesmaximal, characteristic, complemented
13#10594565C212yesmaximal, complemented
14#10594507C211yesmaximal, characteristic, complemented
15#10594332C212yesmaximal, complemented
16#10594306C212yesmaximal, complemented
17#10594301C212yesmaximal, complemented
18#10594152C212yesmaximal, complemented
19#10594138C212yesmaximal, complemented
20#86548—32nomaximal
21C32×C22⋊Q8C2211yescharacteristic, complemented
22#64156C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24#64139C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
26#64107C2212yescomplemented
27#64102C2211yescharacteristic
28#64101C2212yescomplemented
29#64099C2211yescharacteristic, complemented
30#64095C2212yescomplemented
31#64090C2212yescomplemented
32C3×#947C2212yes—
33C3×#944C2212yescomplemented
34C3×#929C2212yescomplemented
35C3×C4×#67C2212yescomplemented
36C3×#898C2212yescomplemented
37C3×#896C2212yescomplemented
38C3×#896C2212yescomplemented
39C3×#894C2212yes—
40C3×#892C2212yescomplemented
41C3×#887C2212yescomplemented
42C3×#885C2212yescomplemented
43C3×#885C2212yescomplemented
44C3×#884C2212yes—
45C3×#879C2212yescomplemented
46#63983C2212yescomplemented
47#63982C2211yescharacteristic, complemented
48#63982C2211yescharacteristic, complemented
49#63980C2211yescharacteristic
50#63980C2211yescharacteristic
51#67⋊Dic3C2212yescomplemented
52#63971C2212yes—
53#63962C2212yescomplemented
54#63958C2212yes—
55#63953C2212yescomplemented
56#63923C2212yes—
57#63922C2212yes—
58#63922C2212yes—
59#63921C2212yescomplemented
60D3×(C2×D3)⋊C4C2212yescomplemented
61D3×(C2×D3)⋊C4C2212yescomplemented
62#63918C2212yescomplemented
63C4×#627C2211yescharacteristic, complemented
64C4×#627C2212yescomplemented
65#63915C2211yescharacteristic
66#63915C2211yescharacteristic
67#63907C2212yes—
68#63905C2212yes—
69#63904C2212yes—
70C4×#626C2212yes—
71#63902C2211yescharacteristic
72C4×#625C2211yescharacteristic
73#63899C2212yescomplemented
74#63897C2212yes—
75#63893C2212yescomplemented
76#63893C2212yescomplemented
77Dic3×D12C2212yes—
78#63891C2212yes—
79#63890C2212yes—
80#63888C2212yescomplemented
81#63888C2212yescomplemented
82#63878C2212yescomplemented
83#63878C2212yescomplemented
84#63871C2212yescomplemented
85#63870C2211yescharacteristic, complemented
86#63870C2211yescharacteristic, complemented
87#63868C2212yescomplemented
88#63868C2212yescomplemented
89#63868C2212yescomplemented
90#63863C2212yes—
91#63862C2212yescomplemented
92#63862C2212yescomplemented
93#63862C2212yescomplemented
94#63861C2212yescomplemented
95#63861C2212yescomplemented
96#63861C2212yescomplemented
97#63859C2212yescomplemented
98#63856C2212yescomplemented
99#63855C2212yescomplemented
100#63853C2212yes—
101#63852C2212yes—
102#63852C2212yes—
103#63852C2212yes—
104Dic3×Dic6C2212yescomplemented
105#63839C2212yescomplemented
106#63838C2211yescharacteristic, complemented
107#63836C2212yescomplemented
108C3×#542—32no—
109#5735—32no—
110#5732—32no—
111#5712—32no—
112#5710—32no—
113#5710—32no—
114#5705—32no—
115#5683—32no—
116#5682—32no—
117#5678—32no—
118#5678—32no—
119#5671—32no—
120#5669—32no—
121#5659—32no—
122#5658—32no—
123#5657—32no—
124#5649—32no—
125#5646—32no—
126#5641—32no—
127#5640D312yescomplemented
128#5637—32no—
129#5637—32no—
130#5624—32no—
131#5624—61no—
132#5617—32no—
133#5613—32no—
134#5584—32no—
135#5568—32no—
136#5560—32no—
137#5538—32no—
138#5533—32no—
139#5527—32no—
140C22×D32C2312yes—
141C2×C32×Q8C2311yescharacteristic
142C22×C32×C4C2311yescharacteristic
143C2×#638C2312yes—
144C22×C3⋊Dic3C2311yescharacteristic
145C22×C3⋊Dic3C2311yescharacteristic
146C2×C4⋊(C3⋊D3)C2311yescharacteristic
147C2×C4×C3⋊D3C2312yes—
148C2×C3×#67C2312yes—
149C2×C3×#67C2312yes—
150C2×C3×D12C2312yes—
151C2×C3×C4×D3C2312yes—
152C2×C3×C4×D3C2312yes—
153C2×C3×Dic6C2312yes—
154C2×C3×Dic6C2312yes—
155C2×#627C2311yescharacteristic
156C2×#627C2311yescharacteristic
157C2×#627C2312yes—
158C2×#626C2312yes—
159C2×#626C2312yes—
160C2×#625C2311yescharacteristic
161C2×#625C2311yescharacteristic
162C2×#624C2312yes—
163C2×D3×Dic3C2312yes—
164C2×D3×Dic3C2312yes—
165C32×C4⋊C4C2312yes—
166C32×C4⋊C4C2311yescharacteristic
167C32×C22⋊C4C2312yes—
168#3752C2312yes—
169#3752C2312yes—
170#3752C2312yes—
171#3752C2312yes—
172C4⋊(C3⋊Dic3)C2312yes—
173C4⋊(C3⋊Dic3)C2312yes—
174C4⋊(C3⋊Dic3)C2311yescharacteristic
175#3750C2312yes—
176C4×C3⋊Dic3C2312yes—
177C4×C3⋊Dic3C2311yescharacteristic
178C4×C3⋊Dic3C2311yescharacteristic
179C4×C3⋊Dic3C2311yescharacteristic
180C4×C3⋊Dic3C2311yescharacteristic
181C3×#217C2312yes—
182C3×#217C2312yes—
183C3×(C2×D3)⋊C4C2312yes—
184C3×(C2×D3)⋊C4C2312yes—
185C3×(C2×D3)⋊C4C2312yes—
186C3×(C2×D3)⋊C4C2312yes—
187C3×(C2×D3)⋊C4C2312yes—
188C3×(C2×D3)⋊C4C2312yes—
189C3×(C2×D3)⋊C4C2312yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×C4⋊Dic3C2312yes—
192C3×Dic3⋊C4C2312yes—
193C3×Dic3⋊C4C2312yes—
194C3×Dic3⋊C4C2312yes—
195C3×Dic3⋊C4C2312yes—
196C3×Dic3⋊C4C2312yes—
197C3×Dic3⋊C4C2312yes—
198C3×C4×Dic3C2312yes—
199C3×C4×Dic3C2312yes—
200C3×C4×Dic3C2312yes—
201C3×C4×Dic3C2312yes—
202#3724C2311yescharacteristic
203#3724C2312yes—
204#3724C2311yescharacteristic
205#3724C2311yescharacteristic
206#3724C2311yescharacteristic
207Dic3⋊Dic3C2312yes—
208Dic3⋊Dic3C2312yes—
209Dic3⋊Dic3C2312yes—
210Dic3⋊Dic3C2312yes—
211Dic3⋊Dic3C2312yes—
212Dic3⋊Dic3C2312yes—
213#3722C2312yes—
214#3722C2312yes—
215#3722C2312yes—
216#3722C2312yes—
217(C2×D3)⋊Dic3C2312yes—
218(C2×D3)⋊Dic3C2312yes—
219(C2×D3)⋊Dic3C2312yes—
220(C2×D3)⋊Dic3C2312yes—
221(C2×D3)⋊Dic3C2312yes—
222(C2×D3)⋊Dic3C2312yes—
223(C2×D3)⋊Dic3C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225Dic32C2312yes—
226Dic32C2312yes—
227#3568—91noSylow
228C3×C4⋊Q8—32no—
229C3×#126—32no—
230C3×#126—32no—
231C3×#124—32no—
232C3×#124—32no—
233C3×#124—32no—
234C3×#123—32no—
235C3×#123—32no—
236C3×C22⋊Q8—21no—
237C3×C22⋊Q8—32no—
238C3×C22⋊Q8—32no—
239C3×C22⋊Q8C2×D312yescomplemented
240C3×#121—32no—
241C3×C4×Q8—32no—
242C3×C4×D4—32no—
243C3×#117—32no—
244#947—32no—
245#947—32no—
246#947—32no—
247#947—61no—
248#947C2×D312yes—
249#946—32no—
250#946—32no—
251#946—32no—
252#946—32no—
253Q8×Dic3—32no—
254Q8×Dic3—32no—
255Q8×Dic3—61no—
256#944—32no—
257#944C2×D312yescomplemented
258#939—32no—
259#939—32no—
260#939—32no—
261#938—32no—
262#937—32no—
263#937—32no—
264#937—32no—
265#937—32no—
266#936—32no—
267#935—32no—
268D4×Dic3—32no—
269D4×Dic3—32no—
270#930—32no—
271#930—61no—
272#929—32no—
273#929C2×D312yescomplemented
274C4×#67—32no—
275C4×#67—32no—
276C4×#67—32no—
277C4×#67C2×D312yescomplemented
278C2×(C2×D3)⋊C4—32no—
279C2×(C2×D3)⋊C4—32no—
280#926—32no—
281#924—32no—
282C2×C4×Dic3—32no—
283C2×C4×Dic3—61no—
284#898—32no—
285#898—32no—
286#898—32no—
287#898—32no—
288#898—32no—
289#898—32no—
290#898—32no—
291#898—32no—
292#898—32no—
293#898—32no—
294#898—32no—
295#898—62no—
296#898C2×D312yescomplemented
297#897—32no—
298#897—32no—
299#897—32no—
300#896—32no—
301#896—32no—
302#896—32no—
303#896C2×D312yescomplemented
304#896C2×D312yescomplemented
305#894—32no—
306#894—32no—
307#894—32no—
308#894—32no—
309#894C2×D312yes—
310#893—32no—
311#893—32no—
312#893—61no—
313#892—32no—
314#892—32no—
315#892—32no—
316#892—32no—
317#892—32no—
318#892—62no—
319#892C2×D312yescomplemented
320#890—32no—
321#890—61no—
322#889—32no—
323#889—32no—
324#888—32no—
325#888—32no—
326#887—32no—
327#887C2×D312yescomplemented
328#886—32no—
329#886—32no—
330#886—32no—
331#886—32no—
332#886—32no—
333#886—62no—
334#885—32no—
335#885—32no—
336#885—32no—
337#885—32no—
338#885—32no—
339#885—32no—
340#885—32no—
341#885—32no—
342#885C2×D312yescomplemented
343#885C2×D312yescomplemented
344#884—32no—
345#884—32no—
346#884C2×D312yes—
347#883—32no—
348#883—32no—
349#883—32no—
350#882—32no—
351#882—32no—
352#882—32no—
353#882—32no—
354#67⋊C4—32no—
355#67⋊C4—32no—
356#67⋊C4—32no—
357#67⋊C4—32no—
358#67⋊C4—62no—
359D3×C22⋊C4—32no—
360D3×C22⋊C4—32no—
361D3×C22⋊C4—32no—
362D3×C22⋊C4—32no—
363#879—32no—
364#879—32no—
365#879—32no—
366#879—32no—
367#879—32no—
368#879—32no—
369#879—32no—
370#879C2×D312yescomplemented
371#878—32no—
372#878—32no—
373#878—32no—
374#878—32no—
375#878—32no—
376#877—32no—
377#877—32no—
378#876—32no—
379#876—32no—
380#876—32no—
381#876—32no—
382#875—32no—
383#875—32no—
384#875—32no—
385C4×D12—32no—
386C4×D12—32no—
387#872—32no—
388#872—32no—
389#869—32no—
390C4×Dic6—32no—
391C4×Dic6—32no—
392C4×Dic6—32no—
393C4×Dic6—32no—
394C23×C32C2411yescharacteristic
395C22×C3⋊D3C2412yes—
396C22×C3×D3C2412yes—
397C22×C3×D3C2412yes—
398C2×D32—42no—
399C2×D32—42no—
400C2×D32—42no—
401C32×Q8—41no—
402C2×C32×C4—41no—
403C2×C32×C4C2411yescharacteristic
404C2×C32×C4C2412yes—
405C2×C32×C4C2412yes—
406C2×C32×C4C2411yescharacteristic
407#638—42no—
408C2×C3⋊Dic3—41no—
409C2×C3⋊Dic3—41no—
410C2×C3⋊Dic3C2411yescharacteristic
411C2×C3⋊Dic3C2412yes—
412C2×C3⋊Dic3C2411yescharacteristic
413C2×C3⋊Dic3C2411yescharacteristic
414C2×C3⋊Dic3C2411yescharacteristic
415C4⋊(C3⋊D3)—41no—
416C4×C3⋊D3—42no—
417C3×#67—42no—
418C3×#67—42no—
419C2×C3×Dic3C2412yes—
420C2×C3×Dic3C2412yes—
421C2×C3×Dic3C2412yes—
422C2×C3×Dic3C2412yes—
423C2×C3×Dic3C2412yes—
424C2×C3×Dic3C2412yes—
425C3×D12—42no—
426C3×C4×D3—42no—
427C3×C4×D3—42no—
428C3×Dic6—42no—
429C3×Dic6—42no—
430#627—42no—
431#627—41no—
432#627—41no—
433#626—42no—
434#626—42no—
435#625—41no—
436#625—41no—
437#624—42no—
438D3×Dic3—42no—
439D3×Dic3—42no—
440#563—91no—
441#563—91no—
442#563—91no—
443H(3,𝔽4)—91no—
444#556—92no—
445#556—92no—
446#556—92no—
447#551—92no—
448#551—92no—
449#551—92no—
450#542—32no—
451#542—92no—
452#542—92no—
453#538—92no—
454#538—92no—
455#538—92no—
456#529—91no—
457#529—91no—
458#529—91no—
459C23×D3—32no—
460C23×D3—32no—
461C2×C3×Q8—21no—
462C2×C3×Q8—32no—
463C2×C3×Q8—32no—
464C2×C3×Q8C22×D312yes—
465C2×C3×D4—32no—
466C2×C3×D4—32no—
467C2×C3×D4—32no—
468C22×C3×C4—21no—
469C22×C3×C4—32no—
470C22×C3×C4—32no—
471C22×C3×C4C22×D312yes—
472C2×#67—32no—
473C2×#67—32no—
474C2×#67—32no—
475C2×#67—32no—
476C2×#67—32no—
477C2×#67—32no—
478C2×#67—62no—
479C2×#67C22×D312yes—
480C2×#67C22×D312yes—
481C22×Dic3—32no—
482C22×Dic3—32no—
483C22×Dic3—32no—
484C22×Dic3—32no—
485C22×Dic3—61no—
486C22×Dic3—61no—
487C2×D12—32no—
488C2×D12—32no—
489C2×D12—32no—
490C2×D12—61no—
491C2×D12C22×D312yes—
492C2×C4×D3—32no—
493C2×C4×D3—32no—
494C2×C4×D3—32no—
495C2×C4×D3—32no—
496C2×C4×D3—32no—
497C2×C4×D3—32no—
498C2×C4×D3—62no—
499C2×C4×D3C22×D312yes—
500C2×C4×D3C22×D312yes—
501C2×Dic6—32no—
502C2×Dic6—32no—
503C2×Dic6—32no—
504C2×Dic6—32no—
505C2×Dic6C22×D312yes—
506C2×Dic6C22×D312yes—
507C3×C4⋊C4—21no—
508C3×C4⋊C4—22no—
509C3×C4⋊C4—32no—
510C3×C4⋊C4—32no—
511C3×C4⋊C4—32no—
512C3×C4⋊C4—32no—
513C3×C4⋊C4—32no—
514C3×C4⋊C4—32no—
515C3×C4⋊C4—32no—
516C3×C4⋊C4C22×D312yes—
517C3×C4⋊C4C22×D312yes—
518C3×C4⋊C4C22×D312yes—
519C3×C22⋊C4—22no—
520C3×C22⋊C4—32no—
521C3×C22⋊C4—32no—
522C3×C22⋊C4—32no—
523C3×C22⋊C4—32no—
524C3×C22⋊C4—32no—
525C3×C22⋊C4—32no—
526C3×C22⋊C4—32no—
527C3×C22⋊C4—32no—
528C3×C22⋊C4—32no—
529C3×C22⋊C4—32no—
530C3×C22⋊C4C22×D312yes—
531C3×C22⋊C4C22×D312yes—
532C3×C42—32no—
533C3×C42—32no—
534C3×C42—32no—
535C3×C42—32no—
536#217—32no—
537#217—32no—
538#217—32no—
539#217—32no—
540#217—32no—
541#217—32no—
542#217—32no—
543#217—32no—
544#217C22×D312yes—
545#217C22×D312yes—
546(C2×D3)⋊C4—32no—
547(C2×D3)⋊C4—32no—
548(C2×D3)⋊C4—32no—
549(C2×D3)⋊C4—32no—
550(C2×D3)⋊C4—32no—
551(C2×D3)⋊C4—32no—
552(C2×D3)⋊C4—32no—
553(C2×D3)⋊C4—32no—
554(C2×D3)⋊C4—32no—
555(C2×D3)⋊C4—32no—
556(C2×D3)⋊C4—32no—
557(C2×D3)⋊C4—32no—
558(C2×D3)⋊C4—32no—
559(C2×D3)⋊C4—32no—
560(C2×D3)⋊C4—32no—
561(C2×D3)⋊C4—32no—
562(C2×D3)⋊C4—32no—
563(C2×D3)⋊C4—32no—
564(C2×D3)⋊C4—32no—
565(C2×D3)⋊C4—32no—
566(C2×D3)⋊C4—32no—
567(C2×D3)⋊C4—32no—
568(C2×D3)⋊C4—32no—
569(C2×D3)⋊C4—32no—
570(C2×D3)⋊C4—62no—
571(C2×D3)⋊C4—62no—
572(C2×D3)⋊C4—62no—
573(C2×D3)⋊C4—62no—
574(C2×D3)⋊C4C22×D312yes—
575(C2×D3)⋊C4C22×D312yes—
576(C2×D3)⋊C4C22×D312yes—
577(C2×D3)⋊C4C22×D312yes—
578(C2×D3)⋊C4C22×D312yes—
579(C2×D3)⋊C4C22×D312yes—
580(C2×D3)⋊C4C22×D312yes—
581(C2×D3)⋊C4C22×D312yes—
582C4⋊Dic3—32no—
583C4⋊Dic3—32no—
584C4⋊Dic3—32no—
585C4⋊Dic3—32no—
586C4⋊Dic3—32no—
587C4⋊Dic3—32no—
588C4⋊Dic3—32no—
589C4⋊Dic3—32no—
590C4⋊Dic3—32no—
591C4⋊Dic3—32no—
592C4⋊Dic3—32no—
593C4⋊Dic3—62no—
594C4⋊Dic3—62no—
595C4⋊Dic3—61no—
596C4⋊Dic3C22×D312yes—
597Dic3⋊C4—32no—
598Dic3⋊C4—32no—
599Dic3⋊C4—32no—
600Dic3⋊C4—32no—
601Dic3⋊C4—32no—
602Dic3⋊C4—32no—
603Dic3⋊C4—32no—
604Dic3⋊C4—32no—
605Dic3⋊C4—32no—
606Dic3⋊C4—32no—
607Dic3⋊C4—32no—
608Dic3⋊C4—32no—
609Dic3⋊C4—32no—
610Dic3⋊C4—32no—
611Dic3⋊C4—62no—
612Dic3⋊C4C22×D312yes—
613Dic3⋊C4C22×D312yes—
614Dic3⋊C4C22×D312yes—
615Dic3⋊C4C22×D312yes—
616Dic3⋊C4C22×D312yes—
617Dic3⋊C4C22×D312yes—
618C4×Dic3—32no—
619C4×Dic3—32no—
620C4×Dic3—32no—
621C4×Dic3—32no—
622C4×Dic3—32no—
623C4×Dic3—32no—
624C4×Dic3—32no—
625C4×Dic3—32no—
626C4×Dic3—32no—
627C4×Dic3—32no—
628C4×Dic3—62no—
629C4×Dic3—61no—
630C4×Dic3—61no—
631C4×Dic3—61no—
632C4×Dic3—61no—
633C4×Dic3C22×D312yes—
634C4×Dic3C22×D312yes—
635C4×Dic3C22×D312yes—
636C4×Dic3C22×D312yes—
637C22×C32—21no—
638C22×C32—21no—
639C22×C32—21no—
640C22×C32C2511yescharacteristic
641C2×C3⋊D3—22no—
642C2×C3⋊D3—22no—
643C2×C3⋊D3—22no—
644C2×C3×D3—22no—
645C2×C3×D3—22no—
646C2×C3×D3—22no—
647C2×C3×D3—22no—
648C2×C3×D3—22no—
649C2×C3×D3—22no—
650D32—84no—
651C32×C4—21no—
652C32×C4—22no—
653C32×C4—22no—
654C32×C4—21no—
655C3⋊Dic3—21no—
656C3⋊Dic3—21no—
657C3⋊Dic3—22no—
658C3⋊Dic3—21no—
659C3⋊Dic3—21no—
660C3×Dic3—22no—
661C3×Dic3—22no—
662C3×Dic3—22no—
663C3×Dic3—22no—
664C3×Dic3—22no—
665C3×Dic3—22no—
666C4⋊Q8—32no—
667C4⋊Q8—92no—
668C4⋊Q8—92no—
669#126—32no—
670#126—32no—
671#126—92no—
672#126—92no—
673#126—92no—
674#126—92no—
675#126—92no—
676#126—92no—
677#126—92no—
678#126—92no—
679#126—92no—
680#126—92no—
681#126—92no—
682#125—91no—
683#125—91no—
684#125—91no—
685#124—32no—
686#124—32no—
687#124—32no—
688#124—92no—
689#124—92no—
690#124—92no—
691#124—91no—
692#124—91no—
693#124—92no—
694#124—92no—
695#124—92no—
696#124—91no—
697#123—32no—
698#123—32no—
699#123—92no—
700#123—92no—
701#123—92no—
702#123—92no—
703#123—92no—
704#123—92no—
705#123—92no—
706C22⋊Q8—32no—
707C22⋊Q8—32no—
708C22⋊Q8—91no—
709C22⋊Q8—91no—
710C22⋊Q8—92no—
711C22⋊Q8—92no—
712C22⋊Q8—92no—
713C22⋊Q8—92no—
714C22⋊Q8—92no—
715C22⋊Q8—92no—
716C22⋊Q8—92no—
717C22⋊Q8D3211yescharacteristic, complemented
718#121—32no—
719#121—92no—
720#121—92no—
721#121—91no—
722#121—91no—
723#121—91no—
724#120—92no—
725#120—92no—
726#120—92no—
727#120—92no—
728C4×Q8—32no—
729C4×Q8—91no—
730C4×Q8—92no—
731C4×Q8—92no—
732C4×Q8—91no—
733C4×Q8—91no—
734C4×D4—32no—
735C4×D4—92no—
736C4×D4—92no—
737C4×D4—91no—
738C4×D4—92no—
739C4×D4—92no—
740C4×D4—91no—
741C4×D4—91no—
742C4×D4—92no—
743#117—32no—
744#117—92no—
745#117—92no—
746#117—92no—
747#117—92no—
748#117—92no—
749C2×C22⋊C4—92no—
750C2×C22⋊C4—92no—
751C2×C22⋊C4—92no—
752C2×C42—91no—
753C23×C3—21no—
754C23×C3—32no—
755C23×C3—32no—
756C23×C3C23×D312yes—
757C22×D3—32no—
758C22×D3—32no—
759C22×D3—62no—
760C22×D3—122no—
761C22×D3—122no—
762C22×D3—122no—
763C22×D3—122no—
764C22×D3—122no—
765C22×D3—122no—
766C22×D3C23×D312yes—
767C22×D3C23×D312yes—
768C3×Q8—42no—
769C3×Q8—42no—
770C3×Q8—122no—
771C3×Q8—122no—
772C3×D4—122no—
773C3×D4—122no—
774C3×D4—122no—
775C2×C3×C4—21no—
776C2×C3×C4—21no—
777C2×C3×C4—22no—
778C2×C3×C4—22no—
779C2×C3×C4—32no—
780C2×C3×C4—32no—
781C2×C3×C4—32no—
782C2×C3×C4—32no—
783C2×C3×C4—32no—
784C2×C3×C4—32no—
785C2×C3×C4—42no—
786C2×C3×C4—42no—
787C2×C3×C4—122no—
788C2×C3×C4—122no—
789C2×C3×C4C23×D312yes—
790C2×C3×C4C23×D312yes—
791C2×C3×C4C23×D312yes—
792C2×C3×C4C23×D312yes—
793C2×C3×C4C23×D312yes—
794C2×C3×C4C23×D312yes—
795#67—42no—
796#67—42no—
797#67—122no—
798#67—122no—
799#67—122no—
800#67—122no—
801#67—122no—
802#67—122no—
803#67—124no—
804C2×Dic3—32no—
805C2×Dic3—32no—
806C2×Dic3—32no—
807C2×Dic3—32no—
808C2×Dic3—32no—
809C2×Dic3—32no—
810C2×Dic3—61no—
811C2×Dic3—61no—
812C2×Dic3—61no—
813C2×Dic3—61no—
814C2×Dic3—62no—
815C2×Dic3—122no—
816C2×Dic3—122no—
817C2×Dic3—122no—
818C2×Dic3—122no—
819C2×Dic3—122no—
820C2×Dic3—122no—
821C2×Dic3C23×D312yes—
822C2×Dic3C23×D312yes—
823C2×Dic3C23×D312yes—
824C2×Dic3C23×D312yes—
825C2×Dic3C23×D312yes—
826C2×Dic3C23×D312yes—
827D12—42no—
828D12—122no—
829D12—122no—
830D12—122no—
831D12—122no—
832C4×D3—42no—
833C4×D3—42no—
834C4×D3—122no—
835C4×D3—122no—
836C4×D3—122no—
837C4×D3—122no—
838C4×D3—124no—
839C4×D3—122no—
840C4×D3—122no—
841Dic6—42no—
842Dic6—42no—
843Dic6—122no—
844Dic6—122no—
845Dic6—122no—
846Dic6—122no—
847C2×C32—41no—
848C2×C32#58511yescharacteristic
849C2×C32#58511yescharacteristic
850C2×C32#58511yescharacteristic
851C3⋊D3—42no—
852C3×D3—42no—
853C3×D3—42no—
854C24—92no—
855C2×Q8—32no—
856C2×Q8—32no—
857C2×Q8—92no—
858C2×Q8—91no—
859C2×Q8—91no—
860C2×Q8C2×D3211yescharacteristic
861C2×D4—32no—
862C2×D4—32no—
863C2×D4—32no—
864C2×D4—92no—
865C2×D4—92no—
866C2×D4—91no—
867C2×D4—91no—
868C2×D4—92no—
869C2×D4—91no—
870C22×C4—32no—
871C22×C4—32no—
872C22×C4—92no—
873C22×C4—92no—
874C22×C4—92no—
875C22×C4—91no—
876C22×C4—91no—
877C22×C4—92no—
878C22×C4C2×D3211yescharacteristic
879C4⋊C4—32no—
880C4⋊C4—32no—
881C4⋊C4—32no—
882C4⋊C4—32no—
883C4⋊C4—32no—
884C4⋊C4—32no—
885C4⋊C4—32no—
886C4⋊C4—92no—
887C4⋊C4—92no—
888C4⋊C4—92no—
889C4⋊C4—92no—
890C4⋊C4—91no—
891C4⋊C4—91no—
892C4⋊C4—92no—
893C4⋊C4—91no—
894C4⋊C4—91no—
895C4⋊C4—92no—
896C4⋊C4—92no—
897C4⋊C4—92no—
898C4⋊C4—92no—
899C4⋊C4—92no—
900C4⋊C4—91no—
901C4⋊C4C2×D3212yes—
902C4⋊C4C2×D3211yescharacteristic
903C22⋊C4—32no—
904C22⋊C4—32no—
905C22⋊C4—32no—
906C22⋊C4—32no—
907C22⋊C4—32no—
908C22⋊C4—32no—
909C22⋊C4—32no—
910C22⋊C4—32no—
911C22⋊C4—32no—
912C22⋊C4—32no—
913C22⋊C4—92no—
914C22⋊C4—92no—
915C22⋊C4—92no—
916C22⋊C4—92no—
917C22⋊C4—92no—
918C22⋊C4—92no—
919C22⋊C4—92no—
920C22⋊C4—92no—
921C22⋊C4—92no—
922C22⋊C4—92no—
923C22⋊C4—92no—
924C22⋊C4—92no—
925C22⋊C4—92no—
926C22⋊C4—92no—
927C22⋊C4—92no—
928C22⋊C4—92no—
929C22⋊C4C2×D3212yes—
930C42—32no—
931C42—32no—
932C42—32no—
933C42—32no—
934C42—92no—
935C42—92no—
936C42—91no—
937C42—91no—
938C42—91no—
939C42—91no—
940C42—92no—
941C22×C3—22no—
942C22×C3—22no—
943C22×C3—22no—
944C22×C3—22no—
945C22×C3—21no—
946C22×C3—41no—
947C22×C3—41no—
948C22×C3—62no—
949C22×C3—62no—
950C22×C3—62no—
951C22×C3—62no—
952C22×C3—62no—
953C22×C3—62no—
954C22×C3C24×D312yes—
955C2×D3—22no—
956C2×D3—22no—
957C2×D3—22no—
958C2×D3—22no—
959C2×D3—22no—
960C2×D3—22no—
961C2×D3—62no—
962C2×D3—62no—
963C2×D3—62no—
964C2×D3—62no—
965C2×D3—62no—
966C2×D3—62no—
967C2×D3—122no—
968C2×D3—122no—
969C2×D3—122no—
970C2×D3—244no—
971C2×D3—244no—
972C3×C4—22no—
973C3×C4—22no—
974C3×C4—22no—
975C3×C4—22no—
976C3×C4—22no—
977C3×C4—22no—
978C3×C4—22no—
979C3×C4—42no—
980C3×C4—41no—
981C3×C4—42no—
982C3×C4—62no—
983C3×C4—62no—
984C3×C4—62no—
985C3×C4—62no—
986C3×C4—62no—
987C3×C4—62no—
988Dic3—22no—
989Dic3—22no—
990Dic3—22no—
991Dic3—22no—
992Dic3—22no—
993Dic3—22no—
994Dic3—62no—
995Dic3—62no—
996Dic3—62no—
997Dic3—62no—
998Dic3—62no—
999Dic3—62no—
1000Dic3—62no—
1001Dic3—121no—
1002Dic3—121no—
1003Dic3—121no—
1004Dic3—122no—
1005C32#356811yescharacteristic, complemented, Sylow
1006C23—32no—
1007C23—32no—
1008C23—92no—
1009C23—362no—
1010C23—362no—
1011C23—362no—
1012C23C22×D3211yescharacteristic
1013Q8—41no—
1014Q8—122no—
1015Q8—122no—
1016Q8—362no—
1017Q8—361no—
1018Q8—361no—
1019D4—122no—
1020D4—122no—
1021D4—122no—
1022D4—361no—
1023D4—362no—
1024D4—362no—
1025D4—362no—
1026D4—361no—
1027D4—361no—
1028C2×C4—32no—
1029C2×C4—32no—
1030C2×C4—32no—
1031C2×C4—32no—
1032C2×C4—32no—
1033C2×C4—32no—
1034C2×C4—41no—
1035C2×C4—91no—
1036C2×C4—91no—
1037C2×C4—92no—
1038C2×C4—91no—
1039C2×C4—91no—
1040C2×C4—122no—
1041C2×C4—122no—
1042C2×C4—362no—
1043C2×C4—362no—
1044C2×C4—362no—
1045C2×C4—362no—
1046C2×C4—361no—
1047C2×C4—361no—
1048C2×C4C22×D3211yescharacteristic
1049C2×C4C22×D3212yes—
1050C2×C4C22×D3212yes—
1051C2×C4C22×D3211yescharacteristic
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—42no—
1056C2×C3—42no—
1057C2×C3—122no—
1058C2×C3—122no—
1059C2×C3#596412yes—
1060C2×C3#596612yes—
1061C2×C3#596812yes—
1062D3—42no—
1063D3—42no—
1064D3—122no—
1065D3—122no—
1066D3—242no—
1067C22—21no—
1068C22—21no—
1069C22—21no—
1070C22—62no—
1071C22—62no—
1072C22—62no—
1073C22—62no—
1074C22—62no—
1075C22—62no—
1076C22—182no—
1077C22—182no—
1078C22—182no—
1079C22—724no—
1080C22C23×D3211yescharacteristic
1081C4—21no—
1082C4—21no—
1083C4—22no—
1084C4—22no—
1085C4—62no—
1086C4—62no—
1087C4—62no—
1088C4—62no—
1089C4—62no—
1090C4—62no—
1091C4—181no—
1092C4—182no—
1093C4—181no—
1094C4—181no—
1095C4—181no—
1096C3—21no—
1097C3#8654812yescomplemented
1098C2—41no—
1099C2—122no—
1100C2—122no—
1101C2—362no—
1102C2#1059667911yescharacteristic
1103C2#1059668911yescharacteristic
1104C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
hypercenterC22⋊Q8D32
hypocenterC32#3568
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596095C2semidirect
2. C3×#5640C2semidirect
3. #10595439C2semidirect
4. #10595384C2semidirect
5. #10595352C2semidirect
6. #10595085C2semidirect
7. #10595033C2semidirect
8. #10594963C2semidirect
9. #10594655C2semidirect
10. #10594653C2semidirect
11. #10594640C2semidirect
12. #10594589C2semidirect
13. #10594565C2semidirect
14. #10594507C2semidirect
15. #10594332C2semidirect
16. #10594306C2semidirect
17. #10594301C2semidirect
18. #10594152C2semidirect
19. #10594138C2semidirect
21. C32×C22⋊Q8C22semidirect
23. Q8×C3⋊Dic3C22semidirect
25. C2×C4×C3⋊Dic3C22semidirect
26. #64107C22semidirect
28. #64101C22semidirect
29. #64099C22semidirect
30. #64095C22semidirect
31. #64090C22semidirect
33. C3×#944C22semidirect
34. C3×#929C22semidirect
35. C3×C4×#67C22semidirect
36. C3×#898C22semidirect
37. C3×#896C22semidirect
38. C3×#896C22semidirect
40. C3×#892C22semidirect
41. C3×#887C22semidirect
42. C3×#885C22semidirect
43. C3×#885C22semidirect
45. C3×#879C22semidirect
46. #63983C22semidirect
47. #63982C22semidirect
48. #63982C22semidirect
51. #67⋊Dic3C22semidirect
53. #63962C22semidirect
55. #63953C22semidirect
59. #63921C22semidirect
60. D3×(C2×D3)⋊C4C22semidirect
61. D3×(C2×D3)⋊C4C22semidirect
62. #63918C22semidirect
63. C4×#627C22semidirect
64. C4×#627C22semidirect
73. #63899C22semidirect
75. #63893C22semidirect
76. #63893C22semidirect
80. #63888C22semidirect
81. #63888C22semidirect
82. #63878C22semidirect
83. #63878C22semidirect
84. #63871C22semidirect
85. #63870C22semidirect
86. #63870C22semidirect
87. #63868C22semidirect
88. #63868C22semidirect
89. #63868C22semidirect
91. #63862C22semidirect
92. #63862C22semidirect
93. #63862C22semidirect
94. #63861C22semidirect
95. #63861C22semidirect
96. #63861C22semidirect
97. #63859C22semidirect
98. #63856C22semidirect
99. #63855C22semidirect
104. Dic3×Dic6C22semidirect
105. #63839C22semidirect
106. #63838C22semidirect
107. #63836C22semidirect
127. #5640D3semidirect
239. C3×C22⋊Q8C2×D3semidirect
257. #944C2×D3semidirect
273. #929C2×D3semidirect
277. C4×#67C2×D3semidirect
296. #898C2×D3semidirect
303. #896C2×D3semidirect
304. #896C2×D3semidirect
319. #892C2×D3semidirect
327. #887C2×D3semidirect
342. #885C2×D3semidirect
343. #885C2×D3semidirect
370. #879C2×D3semidirect
717. C22⋊Q8D32semidirect
1005. C32#3568semidirect
1097. C3#86548semidirect

Maximal subgroups

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

subgroupindex
#105960952
C3×#56402
#105954392
#105953842
#105953522
#105950852
#105950332
#105949632
#105946552
#105946532
#105946402
#105945892
#105945652
#105945072
#105943322
#105943062
#105943012
#105941522
#105941382
#865483