Finite Group Databasebeta

← #11918332

Subgroups — #11918332

Order 1152.

1437 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#563C211yesmaximal, characteristic, complemented
2#10589835C212yesmaximal, complemented
3#10589834C212yesmaximal, complemented
4#10589812C212yesmaximal, complemented
5#10589807C212yesmaximal, complemented
6#10589806C212yesmaximal, complemented
7#10589804C212yesmaximal, complemented
8#10589801C211yesmaximal, characteristic, complemented
9#10589801C211yesmaximal, characteristic, complemented
10#10589793C211yesmaximal, characteristic, complemented
11#10589793C211yesmaximal, characteristic, complemented
12#10589785C211yesmaximal, characteristic, complemented
13#10589782C211yesmaximal, characteristic, complemented
14#10589760C212yesmaximal, complemented
15#10589759C212yesmaximal, complemented
16#10589746C212yesmaximal, complemented
17#10589745C212yesmaximal, complemented
18#10589743C212yesmaximal, complemented
19#10589739C212yesmaximal, complemented
20#87126—31nomaximal
21C9×C4⋊Q8C2212yescomplemented
22C9×#126C2212yescomplemented
23C9×#126C2212yescomplemented
24C9×#125C2211yescharacteristic, complemented
25C9×#125C2211yescharacteristic, complemented
26C9×#124C2211yescharacteristic
27C9×#123C2212yes—
28C9×C22⋊Q8C2212yescomplemented
29C9×C22⋊Q8C2212yescomplemented
30#63509C2212yes—
31#63509C2212yes—
32#63509C2212yescomplemented
33#63508C2212yescomplemented
34#63508C2211yescharacteristic, complemented
35Q8×Dic9C2212yescomplemented
36Q8×Dic9C2211yescharacteristic, complemented
37#63500C2211yescharacteristic
38#63499C2212yes—
39D4×Dic9C2211yescharacteristic
40#63492C2212yes—
41C4×#611C2212yes—
42C2×(C2×D9)⋊C4C2212yescomplemented
43#63488C2212yescomplemented
44#63460C2212yescomplemented
45#63460C2212yescomplemented
46#63460C2212yescomplemented
47#63460C2212yescomplemented
48#63460C2212yescomplemented
49#63460C2212yescomplemented
50#63460C2212yescomplemented
51#63460C2212yescomplemented
52#63460C2212yescomplemented
53#63459C2211yescharacteristic, complemented
54#63459C2212yescomplemented
55#63459C2212yescomplemented
56#63459C2212yescomplemented
57#63459C2211yescharacteristic, complemented
58#63458C2212yescomplemented
59#63458C2212yescomplemented
60#63457C2211yescharacteristic
61#63457C2212yes—
62#63457C2211yescharacteristic
63#63456C2212yes—
64#63456C2212yes—
65#63456C2212yes—
66#63456C2212yescomplemented
67#63456C2212yescomplemented
68#63455C2211yescharacteristic
69#63455C2211yescharacteristic
70#63455C2212yescomplemented
71#63455C2212yescomplemented
72#63454C2212yescomplemented
73#63454C2212yescomplemented
74#63454C2212yescomplemented
75#63450C2212yescomplemented
76#63450C2212yescomplemented
77#63449C2211yescharacteristic, complemented
78#63449C2212yescomplemented
79#63449C2211yescharacteristic, complemented
80#63448C2212yes—
81#63447C2212yes—
82#63447C2212yes—
83#63447C2212yes—
84#63447C2212yes—
85#63447C2212yescomplemented
86#63446C2212yes—
87#63445C2212yes—
88#63445C2212yescomplemented
89#63444C2212yes—
90#63444C2212yes—
91#63444C2212yescomplemented
92#611⋊C4C2212yes—
93#611⋊C4C2212yescomplemented
94C22⋊C4×D9C2212yescomplemented
95C22⋊C4×D9C2212yescomplemented
96#63441C2212yescomplemented
97#63441C2212yescomplemented
98#63440C2212yescomplemented
99#63439C2212yescomplemented
100#63437C2211yescharacteristic
101#63437C2211yescharacteristic
102#63437C2212yescomplemented
103C4×D36C2212yes—
104#63434C2212yescomplemented
105C42×D9C2211yescharacteristic, complemented
106#63432C2211yescharacteristic, complemented
107C4×Dic18C2212yescomplemented
108C3×#563D311yescharacteristic
109#5733—32no—
110#5732—32no—
111#5710—32no—
112#5705—32no—
113#5704—32no—
114#5702—32no—
115#5699—31no—
116#5699—31no—
117#5691—31no—
118#5691—31no—
119#5683—31no—
120#5680—31no—
121#5658—32no—
122#5657—32no—
123#5644—32no—
124#5643—32no—
125#5641—32no—
126#5637—32no—
127C23×D9C2312yes—
128C2×Q8×C9C2311yescharacteristic
129C2×Q8×C9C2312yes—
130C2×D4×C9C2311yescharacteristic
131C22×C4×C9C2312yes—
132C2×#611C2312yes—
133C2×#611C2312yes—
134C2×#611C2312yes—
135C22×Dic9C2312yes—
136C2×D36C2312yes—
137C2×D36C2312yes—
138C2×D36C2311yescharacteristic
139C2×D36C2311yescharacteristic
140C2×D36C2312yes—
141C2×C4×D9C2312yes—
142C2×C4×D9C2311yescharacteristic
143C2×C4×D9C2311yescharacteristic
144C2×C4×D9C2311yescharacteristic
145C2×C4×D9C2312yes—
146C2×C4×D9C2312yes—
147C2×C4×D9C2312yes—
148C2×Dic18C2312yes—
149C2×Dic18C2311yescharacteristic
150C2×Dic18C2311yescharacteristic
151C2×Dic18C2312yes—
152C9×C4⋊C4C2311yescharacteristic
153C9×C4⋊C4C2311yescharacteristic
154C9×C4⋊C4C2312yes—
155C9×C4⋊C4C2312yes—
156C9×C4⋊C4C2312yes—
157C9×C4⋊C4C2312yes—
158C9×C4⋊C4C2312yes—
159C9×C4⋊C4C2312yes—
160C9×C4⋊C4C2311yescharacteristic
161C9×C4⋊C4C2311yescharacteristic
162C9×C22⋊C4C2312yes—
163C9×C22⋊C4C2312yes—
164C9×C22⋊C4C2312yes—
165C9×C22⋊C4C2312yes—
166C9×C22⋊C4C2312yes—
167C42×C9C2311yescharacteristic
168C42×C9C2312yes—
169#3676C2312yes—
170#3676C2312yes—
171#3676C2312yes—
172(C2×D9)⋊C4C2312yes—
173(C2×D9)⋊C4C2312yes—
174(C2×D9)⋊C4C2312yes—
175(C2×D9)⋊C4C2312yes—
176(C2×D9)⋊C4C2312yes—
177(C2×D9)⋊C4C2312yes—
178(C2×D9)⋊C4C2312yes—
179(C2×D9)⋊C4C2312yes—
180(C2×D9)⋊C4C2312yes—
181(C2×D9)⋊C4C2312yes—
182(C2×D9)⋊C4C2312yes—
183(C2×D9)⋊C4C2312yes—
184(C2×D9)⋊C4C2312yes—
185(C2×D9)⋊C4C2312yes—
186(C2×D9)⋊C4C2312yes—
187(C2×D9)⋊C4C2312yes—
188(C2×D9)⋊C4C2312yes—
189(C2×D9)⋊C4C2312yes—
190(C2×D9)⋊C4C2312yes—
191C4⋊Dic9C2312yes—
192C4⋊Dic9C2312yes—
193C4⋊Dic9C2312yes—
194C4⋊Dic9C2311yescharacteristic
195C4⋊Dic9C2311yescharacteristic
196C4⋊Dic9C2312yes—
197C4⋊Dic9C2312yes—
198Dic9⋊C4C2312yes—
199Dic9⋊C4C2312yes—
200Dic9⋊C4C2312yes—
201Dic9⋊C4C2312yes—
202Dic9⋊C4C2312yes—
203Dic9⋊C4C2312yes—
204Dic9⋊C4C2312yes—
205C4×Dic9C2312yes—
206C4×Dic9C2312yes—
207C4×Dic9C2312yes—
208C4×Dic9C2311yescharacteristic
209C4×Dic9C2312yes—
210C4×Dic9C2312yes—
211C4×Dic9C2311yescharacteristic
212C4×Dic9C2311yescharacteristic
213C4×Dic9C2312yes—
214#3568—91noSylow
215C3×C4⋊Q8C2×D312yes—
216C3×#126C2×D312yes—
217C3×#126C2×D312yes—
218C3×#125C2×D311yescharacteristic
219C3×#125C2×D311yescharacteristic
220C3×#124C2×D311yescharacteristic
221C3×#123C2×D312yes—
222C3×C22⋊Q8C2×D312yes—
223C3×C22⋊Q8C2×D312yes—
224#947—32no—
225#947—32no—
226#947—32no—
227#946—32no—
228#946—31no—
229Q8×Dic3—32no—
230Q8×Dic3—31no—
231#938—31no—
232#937—32no—
233D4×Dic3—31no—
234#930—32no—
235C4×#67—32no—
236C2×(C2×D3)⋊C4—32no—
237#926—32no—
238#898—32no—
239#898—32no—
240#898—32no—
241#898—32no—
242#898—32no—
243#898—32no—
244#898—32no—
245#898—32no—
246#898—32no—
247#897—31no—
248#897—32no—
249#897—32no—
250#897—32no—
251#897—31no—
252#896—32no—
253#896—32no—
254#895—31no—
255#895—32no—
256#895—31no—
257#894—32no—
258#894—32no—
259#894—32no—
260#894—32no—
261#894—32no—
262#893—31no—
263#893—32no—
264#893—32no—
265#893—31no—
266#892—32no—
267#892—32no—
268#892—32no—
269#888—32no—
270#888—32no—
271#887—31no—
272#887—32no—
273#887—31no—
274#886—32no—
275#885—32no—
276#885—32no—
277#885—32no—
278#885—32no—
279#885—32no—
280#884—32no—
281#883—32no—
282#883—32no—
283#882—32no—
284#882—32no—
285#882—32no—
286#67⋊C4—32no—
287#67⋊C4—32no—
288D3×C22⋊C4—32no—
289D3×C22⋊C4—32no—
290#879—32no—
291#879—32no—
292#878—32no—
293#877—32no—
294#875—31no—
295#875—31no—
296#875—32no—
297C4×D12—32no—
298#872—32no—
299C42×D3—31no—
300#870—31no—
301C4×Dic6—32no—
302C23×C9C2412yes—
303C22×D9—42no—
304C22×D9—42no—
305C22×D9—42no—
306C22×D9C2412yes—
307C22×D9C2412yes—
308C22×D9C2411yescharacteristic
309Q8×C9—42no—
310Q8×C9—41no—
311D4×C9—41no—
312C2×C4×C9—42no—
313C2×C4×C9C2412yes—
314C2×C4×C9C2412yes—
315C2×C4×C9C2411yescharacteristic
316C2×C4×C9C2411yescharacteristic
317C2×C4×C9C2412yes—
318C2×C4×C9C2411yescharacteristic
319C2×C4×C9C2412yes—
320C2×C4×C9C2412yes—
321#611—42no—
322#611—42no—
323#611—42no—
324C2×Dic9—42no—
325C2×Dic9C2411yescharacteristic
326C2×Dic9C2411yescharacteristic
327C2×Dic9C2411yescharacteristic
328C2×Dic9C2412yes—
329C2×Dic9C2412yes—
330C2×Dic9C2412yes—
331C2×Dic9C2412yes—
332D36—42no—
333D36—41no—
334D36—41no—
335D36—42no—
336D36—42no—
337C4×D9—42no—
338C4×D9—42no—
339C4×D9—42no—
340C4×D9—41no—
341C4×D9—42no—
342C4×D9—41no—
343C4×D9—41no—
344Dic18—41no—
345Dic18—41no—
346Dic18—42no—
347Dic18—42no—
348#563—91no—
349#563—91no—
350#563D911yescharacteristic, complemented
351H(3,𝔽4)—91no—
352#556—92no—
353#556—92no—
354#556—92no—
355#551—92no—
356#551—92no—
357#551—92no—
358#542—92no—
359#542—92no—
360#542—92no—
361#538—92no—
362#538—92no—
363#538—92no—
364#529—91no—
365#529—91no—
366#529—91no—
367C23×D3—32no—
368C2×C3×Q8C22×D312yes—
369C2×C3×Q8C22×D311yescharacteristic
370C2×C3×D4C22×D311yescharacteristic
371C22×C3×C4C22×D312yes—
372C2×#67—32no—
373C2×#67—32no—
374C2×#67—32no—
375C22×Dic3—32no—
376C2×D12—32no—
377C2×D12—31no—
378C2×D12—31no—
379C2×D12—32no—
380C2×D12—32no—
381C2×C4×D3—31no—
382C2×C4×D3—31no—
383C2×C4×D3—31no—
384C2×C4×D3—32no—
385C2×C4×D3—32no—
386C2×C4×D3—32no—
387C2×C4×D3—32no—
388C2×Dic6—32no—
389C2×Dic6—32no—
390C2×Dic6—31no—
391C2×Dic6—31no—
392C3×C4⋊C4C22×D311yescharacteristic
393C3×C4⋊C4C22×D311yescharacteristic
394C3×C4⋊C4C22×D312yes—
395C3×C4⋊C4C22×D312yes—
396C3×C4⋊C4C22×D312yes—
397C3×C4⋊C4C22×D312yes—
398C3×C4⋊C4C22×D312yes—
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C4⋊C4C22×D311yescharacteristic
401C3×C4⋊C4C22×D312yes—
402C3×C22⋊C4C22×D312yes—
403C3×C22⋊C4C22×D312yes—
404C3×C22⋊C4C22×D312yes—
405C3×C22⋊C4C22×D312yes—
406C3×C22⋊C4C22×D312yes—
407C3×C42C22×D312yes—
408C3×C42C22×D311yescharacteristic
409#217—32no—
410#217—32no—
411#217—32no—
412(C2×D3)⋊C4—32no—
413(C2×D3)⋊C4—32no—
414(C2×D3)⋊C4—32no—
415(C2×D3)⋊C4—32no—
416(C2×D3)⋊C4—32no—
417(C2×D3)⋊C4—32no—
418(C2×D3)⋊C4—32no—
419(C2×D3)⋊C4—32no—
420(C2×D3)⋊C4—32no—
421(C2×D3)⋊C4—32no—
422(C2×D3)⋊C4—32no—
423(C2×D3)⋊C4—32no—
424(C2×D3)⋊C4—32no—
425(C2×D3)⋊C4—32no—
426(C2×D3)⋊C4—32no—
427(C2×D3)⋊C4—32no—
428(C2×D3)⋊C4—32no—
429(C2×D3)⋊C4—32no—
430(C2×D3)⋊C4—32no—
431C4⋊Dic3—32no—
432C4⋊Dic3—31no—
433C4⋊Dic3—31no—
434C4⋊Dic3—32no—
435C4⋊Dic3—32no—
436C4⋊Dic3—32no—
437C4⋊Dic3—32no—
438Dic3⋊C4—32no—
439Dic3⋊C4—32no—
440Dic3⋊C4—32no—
441Dic3⋊C4—32no—
442Dic3⋊C4—32no—
443Dic3⋊C4—32no—
444Dic3⋊C4—32no—
445C4×Dic3—32no—
446C4×Dic3—32no—
447C4×Dic3—31no—
448C4×Dic3—31no—
449C4×Dic3—31no—
450C4×Dic3—32no—
451C4×Dic3—32no—
452C4×Dic3—32no—
453C4×Dic3—32no—
454C22×C9—22no—
455C22×C9—22no—
456C22×C9—22no—
457C22×C9C2511yescharacteristic
458C2×D9—21no—
459C2×D9—21no—
460C2×D9—22no—
461C2×D9—22no—
462C2×D9—22no—
463C2×D9—21no—
464C2×D9—22no—
465C2×D9—22no—
466C2×D9—22no—
467C2×D9—84no—
468C4×C9—22no—
469C4×C9—21no—
470C4×C9—22no—
471C4×C9—21no—
472C4×C9—22no—
473C4×C9—21no—
474C4×C9—22no—
475C4×C9—22no—
476Dic9—22no—
477Dic9—22no—
478Dic9—22no—
479Dic9—22no—
480Dic9—21no—
481Dic9—21no—
482Dic9—21no—
483C4⋊Q8—92no—
484C4⋊Q8—92no—
485C4⋊Q8C2×D912yescomplemented
486#126—92no—
487#126—92no—
488#126—92no—
489#126—92no—
490#126—92no—
491#126—92no—
492#126—92no—
493#126—92no—
494#126—92no—
495#126—92no—
496#126—92no—
497#126C2×D912yescomplemented
498#126C2×D912yescomplemented
499#125—91no—
500#125C2×D911yescharacteristic, complemented
501#125C2×D911yescharacteristic, complemented
502#124—92no—
503#124—92no—
504#124—92no—
505#124—92no—
506#124—92no—
507#124—92no—
508#124—92no—
509#124—92no—
510#124—91no—
511#124—91no—
512#124—92no—
513#124C2×D911yescharacteristic
514#123—92no—
515#123—92no—
516#123—92no—
517#123—92no—
518#123—92no—
519#123—92no—
520#123—92no—
521#123—92no—
522#123C2×D912yes—
523C22⋊Q8—91no—
524C22⋊Q8—92no—
525C22⋊Q8—91no—
526C22⋊Q8—91no—
527C22⋊Q8—92no—
528C22⋊Q8—92no—
529C22⋊Q8—92no—
530C22⋊Q8—92no—
531C22⋊Q8—92no—
532C22⋊Q8—92no—
533C22⋊Q8C2×D912yescomplemented
534C22⋊Q8C2×D912yescomplemented
535#121—91no—
536#121—92no—
537#121—91no—
538#121—91no—
539#121—92no—
540#121—92no—
541#120—92no—
542#120—92no—
543#120—92no—
544#120—92no—
545C4×Q8—91no—
546C4×Q8—92no—
547C4×Q8—91no—
548C4×Q8—91no—
549C4×Q8—92no—
550C4×Q8—92no—
551C4×D4—91no—
552C4×D4—92no—
553C4×D4—92no—
554C4×D4—92no—
555C4×D4—91no—
556C4×D4—91no—
557C4×D4—92no—
558C4×D4—92no—
559C4×D4—92no—
560#117—92no—
561#117—92no—
562#117—92no—
563#117—92no—
564#117—92no—
565#117—92no—
566C2×C22⋊C4—92no—
567C2×C22⋊C4—92no—
568C2×C22⋊C4—92no—
569C2×C42—91no—
570C23×C3C23×D312yes—
571C22×D3—32no—
572C22×D3—32no—
573C22×D3—31no—
574C22×D3—122no—
575C22×D3—122no—
576C22×D3—122no—
577C3×Q8—42no—
578C3×Q8—41no—
579C3×D4—41no—
580C2×C3×C4—42no—
581C2×C3×C4C23×D312yes—
582C2×C3×C4C23×D312yes—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C23×D312yes—
586C2×C3×C4C23×D311yescharacteristic
587C2×C3×C4C23×D312yes—
588C2×C3×C4C23×D312yes—
589#67—122no—
590#67—122no—
591#67—122no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—122no—
600D12—122no—
601D12—122no—
602D12—122no—
603D12—121no—
604D12—121no—
605C4×D3—122no—
606C4×D3—121no—
607C4×D3—122no—
608C4×D3—122no—
609C4×D3—122no—
610C4×D3—121no—
611C4×D3—121no—
612Dic6—121no—
613Dic6—121no—
614Dic6—122no—
615Dic6—122no—
616C2×C9—42no—
617C2×C9#58511yescharacteristic
618C2×C9#58511yescharacteristic
619C2×C9#58511yescharacteristic
620D9—41no—
621D9—42no—
622D9—42no—
623C24—92no—
624C2×Q8—92no—
625C2×Q8—92no—
626C2×Q8—91no—
627C2×Q8—91no—
628C2×Q8C22×D912yes—
629C2×Q8C22×D911yescharacteristic
630C2×D4—92no—
631C2×D4—92no—
632C2×D4—92no—
633C2×D4—91no—
634C2×D4—91no—
635C2×D4—92no—
636C2×D4—92no—
637C2×D4—92no—
638C2×D4C22×D911yescharacteristic
639C22×C4—92no—
640C22×C4—91no—
641C22×C4—91no—
642C22×C4—91no—
643C22×C4—92no—
644C22×C4—92no—
645C22×C4—92no—
646C22×C4—92no—
647C22×C4C22×D912yes—
648C4⋊C4—92no—
649C4⋊C4—92no—
650C4⋊C4—92no—
651C4⋊C4—92no—
652C4⋊C4—92no—
653C4⋊C4—92no—
654C4⋊C4—92no—
655C4⋊C4—92no—
656C4⋊C4—92no—
657C4⋊C4—91no—
658C4⋊C4—92no—
659C4⋊C4—91no—
660C4⋊C4—92no—
661C4⋊C4—92no—
662C4⋊C4C22×D912yes—
663C4⋊C4C22×D912yes—
664C4⋊C4C22×D912yes—
665C4⋊C4C22×D911yescharacteristic
666C4⋊C4C22×D911yescharacteristic
667C4⋊C4C22×D912yes—
668C4⋊C4C22×D912yes—
669C4⋊C4C22×D911yescharacteristic
670C4⋊C4C22×D911yescharacteristic
671C4⋊C4C22×D912yes—
672C22⋊C4—92no—
673C22⋊C4—92no—
674C22⋊C4—92no—
675C22⋊C4—92no—
676C22⋊C4—92no—
677C22⋊C4—92no—
678C22⋊C4—92no—
679C22⋊C4—92no—
680C22⋊C4—92no—
681C22⋊C4—92no—
682C22⋊C4—92no—
683C22⋊C4—92no—
684C22⋊C4—92no—
685C22⋊C4—92no—
686C22⋊C4—92no—
687C22⋊C4—92no—
688C22⋊C4—92no—
689C22⋊C4—92no—
690C22⋊C4—92no—
691C22⋊C4—92no—
692C22⋊C4—92no—
693C22⋊C4—92no—
694C22⋊C4C22×D912yes—
695C22⋊C4C22×D912yes—
696C22⋊C4C22×D912yes—
697C22⋊C4C22×D912yes—
698C22⋊C4C22×D912yes—
699C42—91no—
700C42—91no—
701C42—91no—
702C42—92no—
703C42—92no—
704C42—92no—
705C42—92no—
706C42—92no—
707C42—92no—
708C42C22×D911yescharacteristic
709C42C22×D912yes—
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—22no—
713C22×C3C24×D311yescharacteristic
714C2×D3—61no—
715C2×D3—62no—
716C2×D3—62no—
717C2×D3—61no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—61no—
721C2×D3—62no—
722C2×D3—62no—
723C2×D3—244no—
724C3×C4—22no—
725C3×C4—21no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—21no—
730C3×C4—22no—
731C3×C4—21no—
732Dic3—61no—
733Dic3—62no—
734Dic3—62no—
735Dic3—62no—
736Dic3—62no—
737Dic3—61no—
738Dic3—61no—
739C9#356811yescharacteristic, complemented, Sylow
740C23—92no—
741C23—92no—
742C23—91no—
743C23—362no—
744C23—362no—
745C23—362no—
746C23C23×D912yes—
747Q8—42no—
748Q8—41no—
749Q8—362no—
750Q8—362no—
751Q8—361no—
752Q8—361no—
753D4—41no—
754D4—362no—
755D4—362no—
756D4—362no—
757D4—361no—
758D4—361no—
759D4—362no—
760D4—362no—
761D4—362no—
762C2×C4—42no—
763C2×C4—91no—
764C2×C4—91no—
765C2×C4—91no—
766C2×C4—92no—
767C2×C4—92no—
768C2×C4—92no—
769C2×C4—92no—
770C2×C4—362no—
771C2×C4—361no—
772C2×C4—362no—
773C2×C4—362no—
774C2×C4—361no—
775C2×C4—361no—
776C2×C4—362no—
777C2×C4—362no—
778C2×C4C23×D912yes—
779C2×C4C23×D912yes—
780C2×C4C23×D911yescharacteristic
781C2×C4C23×D911yescharacteristic
782C2×C4C23×D911yescharacteristic
783C2×C4C23×D912yes—
784C2×C4C23×D912yes—
785C2×C4C23×D912yes—
786C2×C3—42no—
787C2×C3#596611yescharacteristic
788C2×C3#596811yescharacteristic
789C2×C3#596811yescharacteristic
790D3—122no—
791D3—122no—
792D3—121no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—181no—
797C22—182no—
798C22—182no—
799C22—181no—
800C22—181no—
801C22—182no—
802C22—182no—
803C22—182no—
804C22—182no—
805C22—724no—
806C22C24×D911yescharacteristic
807C4—22no—
808C4—22no—
809C4—21no—
810C4—22no—
811C4—22no—
812C4—21no—
813C4—21no—
814C4—22no—
815C4—181no—
816C4—181no—
817C4—181no—
818C4—182no—
819C4—182no—
820C4—182no—
821C4—182no—
822C3#8712611yescharacteristic
823C2—42no—
824C2—362no—
825C2—362no—
826C2—361no—
827C2#1059314111yescharacteristic
828C2#1059314311yescharacteristic
829C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#563C2
hypercenter#563D9
hypocenterC9#3568
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #563

Complements

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

NH ≅ G/Ntype
1. C9×#563C2semidirect
2. #10589835C2semidirect
3. #10589834C2semidirect
4. #10589812C2semidirect
5. #10589807C2semidirect
6. #10589806C2semidirect
7. #10589804C2semidirect
8. #10589801C2semidirect
9. #10589801C2semidirect
10. #10589793C2semidirect
11. #10589793C2semidirect
12. #10589785C2semidirect
13. #10589782C2semidirect
14. #10589760C2semidirect
15. #10589759C2semidirect
16. #10589746C2semidirect
17. #10589745C2semidirect
18. #10589743C2semidirect
19. #10589739C2semidirect
21. C9×C4⋊Q8C22semidirect
22. C9×#126C22semidirect
23. C9×#126C22semidirect
24. C9×#125C22semidirect
25. C9×#125C22semidirect
28. C9×C22⋊Q8C22semidirect
29. C9×C22⋊Q8C22semidirect
32. #63509C22semidirect
33. #63508C22semidirect
34. #63508C22semidirect
35. Q8×Dic9C22semidirect
36. Q8×Dic9C22semidirect
42. C2×(C2×D9)⋊C4C22semidirect
43. #63488C22semidirect
44. #63460C22semidirect
45. #63460C22semidirect
46. #63460C22semidirect
47. #63460C22semidirect
48. #63460C22semidirect
49. #63460C22semidirect
50. #63460C22semidirect
51. #63460C22semidirect
52. #63460C22semidirect
53. #63459C22semidirect
54. #63459C22semidirect
55. #63459C22semidirect
56. #63459C22semidirect
57. #63459C22semidirect
58. #63458C22semidirect
59. #63458C22semidirect
66. #63456C22semidirect
67. #63456C22semidirect
70. #63455C22semidirect
71. #63455C22semidirect
72. #63454C22semidirect
73. #63454C22semidirect
74. #63454C22semidirect
75. #63450C22semidirect
76. #63450C22semidirect
77. #63449C22semidirect
78. #63449C22semidirect
79. #63449C22semidirect
85. #63447C22semidirect
88. #63445C22semidirect
91. #63444C22semidirect
93. #611⋊C4C22semidirect
94. C22⋊C4×D9C22semidirect
95. C22⋊C4×D9C22semidirect
96. #63441C22semidirect
97. #63441C22semidirect
98. #63440C22semidirect
99. #63439C22semidirect
102. #63437C22semidirect
104. #63434C22semidirect
105. C42×D9C22semidirect
106. #63432C22semidirect
107. C4×Dic18C22semidirect
350. #563D9semidirect
485. C4⋊Q8C2×D9semidirect
497. #126C2×D9semidirect
498. #126C2×D9semidirect
500. #125C2×D9semidirect
501. #125C2×D9semidirect
533. C22⋊Q8C2×D9semidirect
534. C22⋊Q8C2×D9semidirect
739. C9#3568semidirect

Maximal subgroups

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

subgroupindex
C9×#5632
#105898352
#105898342
#105898122
#105898072
#105898062
#105898042
#105898012
#105897932
#105897852
#105897822
#105897602
#105897592
#105897462
#105897452
#105897432
#105897392
#871263