Finite Group Databasebeta

← #11918404

Subgroups — #11918404

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#10596051C211yesmaximal, characteristic, complemented
2C3×#5568C212yesmaximal, complemented
3#10595439C211yesmaximal, characteristic, complemented
4#10595383C212yesmaximal, complemented
5#10595352C211yesmaximal, characteristic, complemented
6#10594652C212yesmaximal, complemented
7#10594642C212yesmaximal, complemented
8#10594638C212yesmaximal, complemented
9#10594589C211yesmaximal, characteristic, complemented
10#10594507C211yesmaximal, characteristic, complemented
11#10594421C212yesmaximal, complemented
12#10594330C212yesmaximal, complemented
13#10594019C212yesmaximal, complemented
14#10594017C212yesmaximal, complemented
15#10594016C212yesmaximal, complemented
16#10593980C211yesmaximal, characteristic, complemented
17#10593979C211yesmaximal, characteristic, complemented
18#10593940C212yesmaximal, complemented
19#10593878C212yesmaximal, complemented
20#87002—32nomaximal
21C32×C4×Q8C2211yescharacteristic, complemented
22#64156C2211yescharacteristic
23#64155C2211yescharacteristic, complemented
24#64107C2212yescomplemented
25#64104C2211yescharacteristic
26#64103C2212yescomplemented
27#64099C2211yescharacteristic, complemented
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2212yescomplemented
30#64081C2212yescomplemented
31C42×C3⋊D3C2211yescharacteristic, complemented
32C3×#947C2212yes—
33C3×#944C2212yescomplemented
34C3×#898C2212yescomplemented
35C3×#898C2212yescomplemented
36C3×#896C2212yescomplemented
37C3×#896C2212yescomplemented
38C3×#893C2212yes—
39C3×#887C2212yescomplemented
40C3×#876C2212yescomplemented
41C3×#876C2212yescomplemented
42C3×#875C2212yes—
43C3×#872C2212yescomplemented
44C3×#872C2212yescomplemented
45C3×C4×Dic6C2212yescomplemented
46#63923C2212yes—
47#63923C2212yescomplemented
48#63922C2212yes—
49#63922C2212yes—
50#63921C2212yescomplemented
51D3×(C2×D3)⋊C4C2212yescomplemented
52D3×(C2×D3)⋊C4C2212yescomplemented
53#63918C2212yescomplemented
54C4×#627C2211yescharacteristic, complemented
55#63915C2211yescharacteristic
56#63915C2211yescharacteristic
57#63912C2211yescharacteristic
58#63912C2211yescharacteristic
59#63910C2212yes—
60#63909C2212yes—
61#63907C2212yes—
62#63907C2212yescomplemented
63#63905C2212yes—
64C4×#626C2212yescomplemented
65#63902C2211yescharacteristic
66C4×#625C2211yescharacteristic
67#63899C2212yescomplemented
68#63897C2212yes—
69#63893C2212yescomplemented
70#63891C2212yes—
71#63888C2212yescomplemented
72#63888C2212yescomplemented
73#63887C2212yescomplemented
74#63886C2212yes—
75#63884C2212yes—
76#63881C2212yes—
77#63881C2212yescomplemented
78#63880C2212yes—
79#63878C2212yescomplemented
80#63877C2212yescomplemented
81#63870C2211yescharacteristic, complemented
82#63870C2211yescharacteristic, complemented
83#63868C2212yescomplemented
84#63868C2212yescomplemented
85#63868C2212yescomplemented
86#63865C2211yescharacteristic, complemented
87#63865C2211yescharacteristic, complemented
88#63865C2212yescomplemented
89#63864C2212yescomplemented
90#63862C2212yescomplemented
91#63861C2212yescomplemented
92#63861C2212yescomplemented
93#63859C2212yescomplemented
94#63856C2212yescomplemented
95#63853C2212yes—
96#63853C2212yescomplemented
97#63853C2212yescomplemented
98#63852C2212yes—
99#63852C2212yes—
100#63852C2212yes—
101#63852C2212yescomplemented
102#63850C2212yes—
103#63848C2212yescomplemented
104#63839C2212yescomplemented
105#63838C2211yescharacteristic, complemented
106#63837C2212yescomplemented
107#63836C2212yescomplemented
108C3×#556—32no—
109#5735—32no—
110#5733—32no—
111#5712—32no—
112#5706—32no—
113#5705—32no—
114#5704—32no—
115#5704—32no—
116#5704—32no—
117#5702—32no—
118#5702—32no—
119#5683—32no—
120#5679—32no—
121#5678—32no—
122#5669—32no—
123#5646—32no—
124#5644—32no—
125#5640—32no—
126#5637—32no—
127#5584—32no—
128#5582—32no—
129#5582—32no—
130#5580—32no—
131#5580—61no—
132#5568—32no—
133#5568D312yescomplemented
134#5560—32no—
135#5556—32no—
136#5534—32no—
137#5528—32no—
138#5527—32no—
139#5527—32no—
140C22×D32C2312yes—
141C2×C32×Q8C2311yescharacteristic
142C2×C4⋊(C3⋊D3)C2311yescharacteristic
143C2×C4⋊(C3⋊D3)C2312yes—
144C2×C4×C3⋊D3C2311yescharacteristic
145C2×C4×C3⋊D3C2311yescharacteristic
146C2×C4×C3⋊D3C2311yescharacteristic
147C2×C4×C3⋊D3C2312yes—
148C2×C3×D12C2312yes—
149C2×C3×C4×D3C2312yes—
150C2×C3×C4×D3C2312yes—
151C2×C3×Dic6C2312yes—
152C2×C3×Dic6C2312yes—
153C2×#627C2312yes—
154C2×#627C2311yescharacteristic
155C2×#627C2311yescharacteristic
156C2×#626C2312yes—
157C2×#626C2312yes—
158C2×#626C2312yes—
159C2×#626C2312yes—
160C2×#625C2311yescharacteristic
161C2×#625C2311yescharacteristic
162C2×#624C2312yes—
163C2×D3×Dic3C2312yes—
164C2×D3×Dic3C2312yes—
165C32×C4⋊C4C2312yes—
166C32×C4⋊C4C2311yescharacteristic
167C32×C42C2311yescharacteristic
168C32×C42C2312yes—
169#3752C2312yes—
170#3752C2312yes—
171#3752C2312yes—
172#3752C2312yes—
173#3752C2312yes—
174C4⋊(C3⋊Dic3)C2311yescharacteristic
175C4⋊(C3⋊Dic3)C2312yes—
176#3750C2312yes—
177#3750C2312yes—
178C4×C3⋊Dic3C2311yescharacteristic
179C4×C3⋊Dic3C2311yescharacteristic
180C4×C3⋊Dic3C2311yescharacteristic
181C3×(C2×D3)⋊C4C2312yes—
182C3×(C2×D3)⋊C4C2312yes—
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×Dic3⋊C4C2312yes—
199C3×Dic3⋊C4C2312yes—
200C3×C4×Dic3C2312yes—
201C3×C4×Dic3C2312yes—
202C3×C4×Dic3C2312yes—
203C3×C4×Dic3C2312yes—
204#3724C2311yescharacteristic
205#3724C2312yes—
206#3724C2311yescharacteristic
207#3724C2311yescharacteristic
208#3724C2311yescharacteristic
209Dic3⋊Dic3C2312yes—
210Dic3⋊Dic3C2312yes—
211Dic3⋊Dic3C2312yes—
212Dic3⋊Dic3C2312yes—
213#3722C2312yes—
214#3722C2312yes—
215#3722C2312yes—
216#3722C2312yes—
217#3722C2312yes—
218#3722C2312yes—
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×#126—32no—
232C3×#126—32no—
233C3×#124—32no—
234C3×#124—32no—
235C3×C22⋊Q8—32no—
236C3×C22⋊Q8—32no—
237C3×C4×Q8—21no—
238C3×C4×Q8—32no—
239C3×C4×Q8—32no—
240C3×C4×Q8C2×D312yescomplemented
241C3×C4×D4—32no—
242C3×#117—32no—
243C3×#117—32no—
244#947—32no—
245#947—32no—
246#947—32no—
247#947—32no—
248#947—61no—
249#947C2×D312yes—
250#946—32no—
251#946—32no—
252#946—32no—
253#946—32no—
254#946—32no—
255#946—61no—
256#944—32no—
257#944C2×D312yescomplemented
258#939—32no—
259#937—32no—
260#937—32no—
261#935—32no—
262#930—32no—
263#929—32no—
264#929—32no—
265C4×#67—32no—
266C4×#67—32no—
267C2×(C2×D3)⋊C4—32no—
268C2×(C2×D3)⋊C4—32no—
269#924—32no—
270#898—32no—
271#898—32no—
272#898—32no—
273#898—32no—
274#898—32no—
275#898—32no—
276#898—32no—
277#898—32no—
278#898—32no—
279#898—32no—
280#898—62no—
281#898C2×D312yescomplemented
282#898C2×D312yescomplemented
283#897—32no—
284#896—32no—
285#896—32no—
286#896—32no—
287#896—32no—
288#896—32no—
289#896—32no—
290#896—32no—
291#896C2×D312yescomplemented
292#896C2×D312yescomplemented
293#895—32no—
294#895—32no—
295#895—32no—
296#895—32no—
297#895—61no—
298#894—32no—
299#894—32no—
300#894—32no—
301#894—32no—
302#894—32no—
303#894—32no—
304#894—32no—
305#894—32no—
306#894—32no—
307#894—62no—
308#893—32no—
309#893—32no—
310#893C2×D312yes—
311#892—32no—
312#892—32no—
313#890—32no—
314#890—61no—
315#889—32no—
316#889—32no—
317#888—32no—
318#888—32no—
319#887—32no—
320#887—32no—
321#887C2×D312yescomplemented
322#886—32no—
323#885—32no—
324#885—32no—
325#885—32no—
326#885—32no—
327#885—32no—
328#885—32no—
329#885—32no—
330#885—32no—
331#884—32no—
332#884—32no—
333#884—32no—
334#883—32no—
335#883—32no—
336#883—32no—
337#883—32no—
338#883—32no—
339#882—32no—
340#882—32no—
341#882—32no—
342#882—32no—
343#882—32no—
344#882—32no—
345#67⋊C4—32no—
346#67⋊C4—32no—
347#67⋊C4—32no—
348#67⋊C4—32no—
349D3×C22⋊C4—32no—
350D3×C22⋊C4—32no—
351D3×C22⋊C4—32no—
352D3×C22⋊C4—32no—
353#879—32no—
354#879—32no—
355#879—32no—
356#879—32no—
357#878—32no—
358#878—32no—
359#878—32no—
360#877—32no—
361#877—32no—
362#876—32no—
363#876—32no—
364#876—32no—
365#876—32no—
366#876C2×D312yescomplemented
367#876C2×D312yescomplemented
368#875—32no—
369#875—32no—
370#875—32no—
371#875—32no—
372#875—32no—
373#875C2×D312yes—
374C4×D12—32no—
375C4×D12—32no—
376C4×D12—32no—
377C4×D12—32no—
378C4×D12—32no—
379C4×D12—61no—
380C4×D12—62no—
381#872—32no—
382#872—32no—
383#872—32no—
384#872—32no—
385#872—62no—
386#872C2×D312yescomplemented
387#872C2×D312yescomplemented
388C42×D3—32no—
389C42×D3—61no—
390#869—32no—
391C4×Dic6—32no—
392C4×Dic6—32no—
393C4×Dic6C2×D312yescomplemented
394C22×C3⋊D3C2412yes—
395C22×C3⋊D3C2411yescharacteristic
396C22×C3×D3C2412yes—
397C22×C3×D3C2412yes—
398C2×D32—42no—
399C2×D32—42no—
400C2×D32—42no—
401C32×Q8—41no—
402C2×C32×C4C2411yescharacteristic
403C2×C32×C4C2412yes—
404C2×C32×C4C2412yes—
405C2×C32×C4C2411yescharacteristic
406C2×C32×C4C2411yescharacteristic
407C2×C3⋊Dic3C2411yescharacteristic
408C2×C3⋊Dic3C2412yes—
409C2×C3⋊Dic3C2411yescharacteristic
410C2×C3⋊Dic3C2411yescharacteristic
411C4⋊(C3⋊D3)—41no—
412C4⋊(C3⋊D3)—42no—
413C4×C3⋊D3—41no—
414C4×C3⋊D3—42no—
415C4×C3⋊D3—41no—
416C4×C3⋊D3—41no—
417C2×C3×Dic3C2412yes—
418C2×C3×Dic3C2412yes—
419C2×C3×Dic3C2412yes—
420C2×C3×Dic3C2412yes—
421C2×C3×Dic3C2412yes—
422C2×C3×Dic3C2412yes—
423C3×D12—42no—
424C3×C4×D3—42no—
425C3×C4×D3—42no—
426C3×Dic6—42no—
427C3×Dic6—42no—
428#627—42no—
429#627—41no—
430#627—41no—
431#626—42no—
432#626—42no—
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—32no—
445#556—92no—
446#556—92no—
447#551—92no—
448#551—92no—
449#551—92no—
450#542—92no—
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—
466C22×C3×C4—32no—
467C22×C3×C4—32no—
468C2×#67—32no—
469C2×#67—32no—
470C2×#67—32no—
471C2×#67—32no—
472C2×#67—32no—
473C2×#67—32no—
474C22×Dic3—32no—
475C22×Dic3—32no—
476C2×D12—32no—
477C2×D12—32no—
478C2×D12—32no—
479C2×D12—32no—
480C2×D12—32no—
481C2×D12—32no—
482C2×D12—32no—
483C2×D12—62no—
484C2×D12—61no—
485C2×D12C22×D312yes—
486C2×C4×D3—32no—
487C2×C4×D3—32no—
488C2×C4×D3—32no—
489C2×C4×D3—32no—
490C2×C4×D3—32no—
491C2×C4×D3—32no—
492C2×C4×D3—32no—
493C2×C4×D3—32no—
494C2×C4×D3—32no—
495C2×C4×D3—61no—
496C2×C4×D3—61no—
497C2×C4×D3—61no—
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⋊C4—32no—
517C3×C4⋊C4—32no—
518C3×C4⋊C4C22×D312yes—
519C3×C4⋊C4C22×D312yes—
520C3×C4⋊C4C22×D312yes—
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⋊C4—32no—
531C3×C42—21no—
532C3×C42—22no—
533C3×C42—32no—
534C3×C42—32no—
535C3×C42—32no—
536C3×C42—32no—
537C3×C42C22×D312yes—
538C3×C42C22×D312yes—
539C3×C42C22×D312yes—
540#217—32no—
541#217—32no—
542#217—32no—
543#217—32no—
544#217—32no—
545#217—32no—
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—32no—
571(C2×D3)⋊C4—32no—
572(C2×D3)⋊C4—32no—
573(C2×D3)⋊C4—32no—
574(C2×D3)⋊C4—62no—
575(C2×D3)⋊C4—62no—
576(C2×D3)⋊C4—62no—
577(C2×D3)⋊C4—62no—
578(C2×D3)⋊C4—62no—
579(C2×D3)⋊C4C22×D312yes—
580(C2×D3)⋊C4C22×D312yes—
581(C2×D3)⋊C4C22×D312yes—
582(C2×D3)⋊C4C22×D312yes—
583(C2×D3)⋊C4C22×D312yes—
584(C2×D3)⋊C4C22×D312yes—
585(C2×D3)⋊C4C22×D312yes—
586(C2×D3)⋊C4C22×D312yes—
587(C2×D3)⋊C4C22×D312yes—
588(C2×D3)⋊C4C22×D312yes—
589C4⋊Dic3—32no—
590C4⋊Dic3—32no—
591C4⋊Dic3—32no—
592C4⋊Dic3—32no—
593C4⋊Dic3—32no—
594C4⋊Dic3—32no—
595C4⋊Dic3—32no—
596C4⋊Dic3—62no—
597C4⋊Dic3—61no—
598C4⋊Dic3C22×D312yes—
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—32no—
612Dic3⋊C4—32no—
613Dic3⋊C4—62no—
614Dic3⋊C4—62no—
615Dic3⋊C4C22×D312yes—
616Dic3⋊C4C22×D312yes—
617Dic3⋊C4C22×D312yes—
618Dic3⋊C4C22×D312yes—
619Dic3⋊C4C22×D312yes—
620Dic3⋊C4C22×D312yes—
621Dic3⋊C4C22×D312yes—
622Dic3⋊C4C22×D312yes—
623C4×Dic3—32no—
624C4×Dic3—32no—
625C4×Dic3—32no—
626C4×Dic3—32no—
627C4×Dic3—32no—
628C4×Dic3—32no—
629C4×Dic3—32no—
630C4×Dic3—61no—
631C4×Dic3—61no—
632C4×Dic3—61no—
633C4×Dic3C22×D312yes—
634C4×Dic3C22×D312yes—
635C4×Dic3C22×D312yes—
636C4×Dic3C22×D312yes—
637C22×C32C2511yescharacteristic
638C2×C3⋊D3—21no—
639C2×C3⋊D3—22no—
640C2×C3⋊D3—21no—
641C2×C3⋊D3—21no—
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—21no—
653C32×C4—22no—
654C32×C4—22no—
655C32×C4—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—32no—
672#126—32no—
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—92no—
688#124—92no—
689#124—92no—
690#124—92no—
691#124—92no—
692#124—91no—
693#124—91no—
694#124—92no—
695#124—92no—
696#124—91no—
697#123—92no—
698#123—92no—
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—92no—
709C22⋊Q8—92no—
710C22⋊Q8—92no—
711C22⋊Q8—91no—
712C22⋊Q8—91no—
713C22⋊Q8—92no—
714C22⋊Q8—92no—
715C22⋊Q8—92no—
716C22⋊Q8—92no—
717C22⋊Q8—91no—
718#121—91no—
719#121—91no—
720#121—92no—
721#121—92no—
722#121—92no—
723#121—91no—
724#120—92no—
725#120—92no—
726#120—92no—
727#120—92no—
728C4×Q8—32no—
729C4×Q8—32no—
730C4×Q8—91no—
731C4×Q8—92no—
732C4×Q8—91no—
733C4×Q8D3211yescharacteristic, complemented
734C4×D4—32no—
735C4×D4—92no—
736C4×D4—92no—
737C4×D4—91no—
738C4×D4—92no—
739C4×D4—92no—
740C4×D4—91no—
741C4×D4—92no—
742C4×D4—91no—
743#117—32no—
744#117—32no—
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—32no—
754C23×C3—32no—
755C22×D3—32no—
756C22×D3—32no—
757C22×D3—32no—
758C22×D3—61no—
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—
773C2×C3×C4—21no—
774C2×C3×C4—21no—
775C2×C3×C4—21no—
776C2×C3×C4—22no—
777C2×C3×C4—22no—
778C2×C3×C4—32no—
779C2×C3×C4—32no—
780C2×C3×C4—32no—
781C2×C3×C4—32no—
782C2×C3×C4—32no—
783C2×C3×C4—32no—
784C2×C3×C4—122no—
785C2×C3×C4—122no—
786C2×C3×C4C23×D312yes—
787C2×C3×C4C23×D312yes—
788C2×C3×C4C23×D312yes—
789C2×C3×C4C23×D312yes—
790C2×C3×C4C23×D312yes—
791C2×C3×C4C23×D312yes—
792C2×C3×C4C23×D312yes—
793#67—122no—
794#67—122no—
795#67—122no—
796#67—122no—
797#67—122no—
798#67—122no—
799C2×Dic3—32no—
800C2×Dic3—32no—
801C2×Dic3—32no—
802C2×Dic3—32no—
803C2×Dic3—32no—
804C2×Dic3—61no—
805C2×Dic3—61no—
806C2×Dic3—61no—
807C2×Dic3—62no—
808C2×Dic3—122no—
809C2×Dic3—122no—
810C2×Dic3C23×D312yes—
811C2×Dic3C23×D312yes—
812C2×Dic3C23×D312yes—
813C2×Dic3C23×D312yes—
814C2×Dic3C23×D312yes—
815C2×Dic3C23×D312yes—
816D12—42no—
817D12—122no—
818D12—122no—
819D12—122no—
820D12—122no—
821D12—124no—
822D12—122no—
823D12—122no—
824D12—122no—
825D12—122no—
826C4×D3—42no—
827C4×D3—42no—
828C4×D3—122no—
829C4×D3—122no—
830C4×D3—122no—
831C4×D3—122no—
832C4×D3—122no—
833C4×D3—122no—
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#58511yescharacteristic
848C2×C32#58511yescharacteristic
849C2×C32#58511yescharacteristic
850C3⋊D3—41no—
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—92no—
863C2×D4—92no—
864C2×D4—92no—
865C2×D4—92no—
866C2×D4—91no—
867C2×D4—91no—
868C2×D4—91no—
869C2×D4—92no—
870C22×C4—32no—
871C22×C4—32no—
872C22×C4—92no—
873C22×C4—92no—
874C22×C4—92no—
875C22×C4—91no—
876C22×C4—91no—
877C22×C4—91no—
878C22×C4—92no—
879C4⋊C4—32no—
880C4⋊C4—32no—
881C4⋊C4—32no—
882C4⋊C4—32no—
883C4⋊C4—32no—
884C4⋊C4—32no—
885C4⋊C4—32no—
886C4⋊C4—32no—
887C4⋊C4—32no—
888C4⋊C4—92no—
889C4⋊C4—92no—
890C4⋊C4—92no—
891C4⋊C4—92no—
892C4⋊C4—91no—
893C4⋊C4—91no—
894C4⋊C4—92no—
895C4⋊C4—91no—
896C4⋊C4—91no—
897C4⋊C4—92no—
898C4⋊C4—92no—
899C4⋊C4—91no—
900C4⋊C4—92no—
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⋊C4—92no—
930C42—32no—
931C42—32no—
932C42—32no—
933C42—32no—
934C42—92no—
935C42—92no—
936C42—91no—
937C42—91no—
938C42—91no—
939C42C2×D3211yescharacteristic
940C42C2×D3212yes—
941C22×C3—21no—
942C22×C3—62no—
943C22×C3—62no—
944C22×C3—62no—
945C22×C3—62no—
946C22×C3—62no—
947C22×C3—62no—
948C22×C3C24×D312yes—
949C2×D3—22no—
950C2×D3—22no—
951C2×D3—22no—
952C2×D3—22no—
953C2×D3—22no—
954C2×D3—22no—
955C2×D3—62no—
956C2×D3—62no—
957C2×D3—62no—
958C2×D3—62no—
959C2×D3—62no—
960C2×D3—62no—
961C2×D3—62no—
962C2×D3—62no—
963C2×D3—62no—
964C2×D3—62no—
965C2×D3—121no—
966C2×D3—121no—
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—22no—
980C3×C4—22no—
981C3×C4—41no—
982C3×C4—42no—
983C3×C4—42no—
984C3×C4—62no—
985C3×C4—62no—
986C3×C4—62no—
987C3×C4—62no—
988C3×C4—62no—
989C3×C4—62no—
990Dic3—22no—
991Dic3—22no—
992Dic3—22no—
993Dic3—22no—
994Dic3—22no—
995Dic3—22no—
996Dic3—62no—
997Dic3—62no—
998Dic3—62no—
999Dic3—62no—
1000Dic3—62no—
1001Dic3—121no—
1002Dic3—122no—
1003Dic3—121no—
1004Dic3—121no—
1005C32#356811yescharacteristic, complemented, Sylow
1006C23—32no—
1007C23—32no—
1008C23—92no—
1009C23—91no—
1010C23—362no—
1011C23—362no—
1012C23—362no—
1013Q8—41no—
1014Q8—122no—
1015Q8—122no—
1016Q8—362no—
1017Q8—361no—
1018Q8—361no—
1019D4—122no—
1020D4—361no—
1021D4—362no—
1022D4—362no—
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—91no—
1035C2×C4—91no—
1036C2×C4—91no—
1037C2×C4—92no—
1038C2×C4—122no—
1039C2×C4—122no—
1040C2×C4—361no—
1041C2×C4—362no—
1042C2×C4—361no—
1043C2×C4—361no—
1044C2×C4—362no—
1045C2×C4—362no—
1046C2×C4—362no—
1047C2×C4C22×D3211yescharacteristic
1048C2×C4C22×D3212yes—
1049C2×C4C22×D3212yes—
1050C2×C4C22×D3211yescharacteristic
1051C2×C4C22×D3211yescharacteristic
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—122no—
1056C2×C3—122no—
1057C2×C3#596412yes—
1058C2×C3#596412yes—
1059C2×C3#596812yes—
1060D3—42no—
1061D3—42no—
1062D3—122no—
1063D3—122no—
1064D3—122no—
1065D3—122no—
1066D3—242no—
1067C22—62no—
1068C22—62no—
1069C22—62no—
1070C22—62no—
1071C22—62no—
1072C22—62no—
1073C22—181no—
1074C22—182no—
1075C22—181no—
1076C22—182no—
1077C22—181no—
1078C22—182no—
1079C22—724no—
1080C22C23×D3211yescharacteristic
1081C4—21no—
1082C4—22no—
1083C4—21no—
1084C4—21no—
1085C4—22no—
1086C4—62no—
1087C4—62no—
1088C4—62no—
1089C4—62no—
1090C4—62no—
1091C4—62no—
1092C4—181no—
1093C4—182no—
1094C4—181no—
1095C4—181no—
1096C3—21no—
1097C3#8700212yescomplemented
1098C2—122no—
1099C2—122no—
1100C2—362no—
1101C2—361no—
1102C2#1059666911yescharacteristic
1103C2#1059668911yescharacteristic
1104C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3568
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596051C2semidirect
2. C3×#5568C2semidirect
3. #10595439C2semidirect
4. #10595383C2semidirect
5. #10595352C2semidirect
6. #10594652C2semidirect
7. #10594642C2semidirect
8. #10594638C2semidirect
9. #10594589C2semidirect
10. #10594507C2semidirect
11. #10594421C2semidirect
12. #10594330C2semidirect
13. #10594019C2semidirect
14. #10594017C2semidirect
15. #10594016C2semidirect
16. #10593980C2semidirect
17. #10593979C2semidirect
18. #10593940C2semidirect
19. #10593878C2semidirect
21. C32×C4×Q8C22semidirect
23. #64155C22semidirect
24. #64107C22semidirect
26. #64103C22semidirect
27. #64099C22semidirect
29. C4×C4⋊(C3⋊D3)C22semidirect
30. #64081C22semidirect
31. C42×C3⋊D3C22semidirect
33. C3×#944C22semidirect
34. C3×#898C22semidirect
35. C3×#898C22semidirect
36. C3×#896C22semidirect
37. C3×#896C22semidirect
39. C3×#887C22semidirect
40. C3×#876C22semidirect
41. C3×#876C22semidirect
43. C3×#872C22semidirect
44. C3×#872C22semidirect
45. C3×C4×Dic6C22semidirect
47. #63923C22semidirect
50. #63921C22semidirect
51. D3×(C2×D3)⋊C4C22semidirect
52. D3×(C2×D3)⋊C4C22semidirect
53. #63918C22semidirect
54. C4×#627C22semidirect
62. #63907C22semidirect
64. C4×#626C22semidirect
67. #63899C22semidirect
69. #63893C22semidirect
71. #63888C22semidirect
72. #63888C22semidirect
73. #63887C22semidirect
77. #63881C22semidirect
79. #63878C22semidirect
80. #63877C22semidirect
81. #63870C22semidirect
82. #63870C22semidirect
83. #63868C22semidirect
84. #63868C22semidirect
85. #63868C22semidirect
86. #63865C22semidirect
87. #63865C22semidirect
88. #63865C22semidirect
89. #63864C22semidirect
90. #63862C22semidirect
91. #63861C22semidirect
92. #63861C22semidirect
93. #63859C22semidirect
94. #63856C22semidirect
96. #63853C22semidirect
97. #63853C22semidirect
101. #63852C22semidirect
103. #63848C22semidirect
104. #63839C22semidirect
105. #63838C22semidirect
106. #63837C22semidirect
107. #63836C22semidirect
133. #5568D3semidirect
240. C3×C4×Q8C2×D3semidirect
257. #944C2×D3semidirect
281. #898C2×D3semidirect
282. #898C2×D3semidirect
291. #896C2×D3semidirect
292. #896C2×D3semidirect
321. #887C2×D3semidirect
366. #876C2×D3semidirect
367. #876C2×D3semidirect
386. #872C2×D3semidirect
387. #872C2×D3semidirect
393. C4×Dic6C2×D3semidirect
733. C4×Q8D32semidirect
1005. C32#3568semidirect
1097. C3#87002semidirect

Maximal subgroups

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

subgroupindex
#105960512
C3×#55682
#105954392
#105953832
#105953522
#105946522
#105946422
#105946382
#105945892
#105945072
#105944212
#105943302
#105940192
#105940172
#105940162
#105939802
#105939792
#105939402
#105938782
#870023