Finite Group Databasebeta

← #13148924

Subgroups — #13148924

Order 1728.

814 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721751C211yesmaximal, characteristic, complemented
2C3×#63456C211yesmaximal, characteristic, complemented
3C9×#889C211yesmaximal, characteristic, complemented
4#11721006C211yesmaximal, characteristic, complemented
5#11721005C211yesmaximal, characteristic, complemented
6#11721005C211yesmaximal, characteristic, complemented
7#11721005C211yesmaximal, characteristic, complemented
8#11721004C211yesmaximal, characteristic, complemented
9#11721002C211yesmaximal, characteristic, complemented
10#11720997C211yesmaximal, characteristic, complemented
11#11720988C211yesmaximal, characteristic, complemented
12#11720983C211yesmaximal, characteristic, complemented
13#11720978C211yesmaximal, characteristic, complemented
14#11720941C211yesmaximal, characteristic, complemented
15#11720898C211yesmaximal, characteristic, complemented
16#10594467—31nomaximal
17#10589799—31nomaximal
18C2×C4⋊(C3⋊D9)C2211yescharacteristic
19C2×C4⋊(C3⋊D9)C2211yescharacteristic
20C2×C4⋊(C3⋊D9)C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×#6192C2211yescharacteristic
25C2×#6192C2211yescharacteristic
26C2×#6192C2211yescharacteristic
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×(C3⋊D9)⋊C4C2211yescharacteristic
31C2×(C3⋊D9)⋊C4C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C3×C9×C4⋊C4C2211yescharacteristic
34#88536C2211yescharacteristic
35#88536C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C9×C4⋊Dic3C2211yescharacteristic
40C9×Dic3⋊C4C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic
42C9×Dic3⋊C4C2211yescharacteristic
43C9×Dic3⋊C4C2211yescharacteristic
44C4×C9×Dic3C2211yescharacteristic
45C3×Dic9⋊C4C2211yescharacteristic
46#88445C2211yescharacteristic
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49#88445C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64104—31no—
54C3×#894—31no—
55C3×#889D311yescharacteristic
56#63911—31no—
57#63910—31no—
58#63910—31no—
59#63910—31no—
60#63909—31no—
61#63904—31no—
62#63897—31no—
63#63890—31no—
64#63886—31no—
65#63881—31no—
66#63853—31no—
67#63836—31no—
68C9×#125—31no—
69#63457—31no—
70#63457—31no—
71#63457—31no—
72#63457—31no—
73#63457—31no—
74#63457—31no—
75#63457—61no—
76#63456—31no—
77#63456—31no—
78#63456—31no—
79#63456D311yescharacteristic, complemented
80#63455—31no—
81#63455—31no—
82#63436—31no—
83#63434—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×C3⋊D9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C4⋊(C3⋊D9)—41no—
94C4⋊(C3⋊D9)—41no—
95C4⋊(C3⋊D9)—41no—
96C4×C3⋊D9—41no—
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C3×D36—41no—
104C3×C4×D9—41no—
105#6192—22no—
106#6192—22no—
107#6192—41no—
108#6192—41no—
109#6192—41no—
110#6192—41no—
111(C3⋊D9)⋊C4—22no—
112(C3⋊D9)⋊C4—41no—
113Dic3×D9—41no—
114#5697—91no—
115#5663—91no—
116C2×C4⋊(C3⋊D3)—31no—
117C2×C4⋊(C3⋊D3)—31no—
118C2×C4⋊(C3⋊D3)—31no—
119C2×C4×C3⋊D3—31no—
120C2×C3×D12—31no—
121C2×C3×C4×D3—31no—
122C2×#626—31no—
123C2×#626—31no—
124C2×#626—31no—
125C2×#626—31no—
126C2×#626—31no—
127C2×#626—31no—
128C2×#624—31no—
129C2×#624—31no—
130C2×D3×Dic3—31no—
131C32×C4⋊C4C2×D311yescharacteristic
132#3752—31no—
133#3752—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4—31no—
137C3×C4⋊Dic3C2×D311yescharacteristic
138C3×Dic3⋊C4—31no—
139C3×Dic3⋊C4C2×D311yescharacteristic
140C3×Dic3⋊C4C2×D311yescharacteristic
141C3×Dic3⋊C4C2×D311yescharacteristic
142C3×Dic3⋊C4C2×D311yescharacteristic
143C3×C4×Dic3C2×D311yescharacteristic
144Dic3⋊Dic3—31no—
145#3722—31no—
146#3722—31no—
147#3722—31no—
148#3722—31no—
149(C2×D3)⋊Dic3—31no—
150Dic32—31no—
151C2×D36—31no—
152C2×D36—31no—
153C2×D36—31no—
154C2×D36—31no—
155C2×D36—31no—
156C2×D36—31no—
157C2×D36—31no—
158C2×D36—31no—
159C2×D36—31no—
160C2×D36—61no—
161C2×D36—61no—
162C2×D36—61no—
163C2×D36C2×D311yescharacteristic
164C2×C4×D9—31no—
165C2×C4×D9—31no—
166C2×C4×D9—31no—
167C2×C4×D9—31no—
168C2×C4×D9—61no—
169C2×C4×D9C2×D311yescharacteristic
170C9×C4⋊C4—21no—
171C9×C4⋊C4—31no—
172C9×C4⋊C4—31no—
173C9×C4⋊C4—31no—
174C9×C4⋊C4—31no—
175C9×C4⋊C4—31no—
176C9×C4⋊C4C2×D311yescharacteristic
177C42×C9—31no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—31no—
184(C2×D9)⋊C4—31no—
185(C2×D9)⋊C4—61no—
186(C2×D9)⋊C4—61no—
187(C2×D9)⋊C4C2×D311yescharacteristic
188(C2×D9)⋊C4C2×D311yescharacteristic
189(C2×D9)⋊C4C2×D311yescharacteristic
190Dic9⋊C4—31no—
191Dic9⋊C4C2×D311yescharacteristic
192C4×Dic9—31no—
193C22×C3×C9C2411yescharacteristic
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—21no—
200C2×C3⋊D9—21no—
201C2×C3⋊D9—21no—
202C2×C3⋊D9—21no—
203C2×C3×D9—21no—
204C2×C3×D9—21no—
205C2×C3×D9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C3×C4×C9—21no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3⋊Dic9—21no—
213C9×Dic3—21no—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3#4112yes—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×#125—31no—
220C3×#123—91no—
221#940—91no—
222#939—91no—
223#930—91no—
224C4×#67—91no—
225#895—91no—
226#895—91no—
227#895—91no—
228#895—91no—
229#895—91no—
230#895—91no—
231#895—91no—
232#895—181no—
233#894—31no—
234#894—91no—
235#894—91no—
236#894—91no—
237#894—91no—
238#893—91no—
239#893—91no—
240#892—91no—
241#889D911yescharacteristic, complemented
242#886—91no—
243#884—91no—
244#884—91no—
245#884—91no—
246#883—91no—
247#67⋊C4—91no—
248#874—91no—
249#872—91no—
250C22×C3⋊D3—31no—
251C22×C3⋊D3—31no—
252C22×C3⋊D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C3⋊Dic3—31no—
259C4⋊(C3⋊D3)—121no—
260C4⋊(C3⋊D3)—121no—
261C4⋊(C3⋊D3)—121no—
262C4×C3⋊D3—121no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C2×C3×Dic3C22×D311yescharacteristic
269C3×D12—121no—
270C3×C4×D3—121no—
271#626—62no—
272#626—62no—
273#626—121no—
274#626—121no—
275#626—121no—
276#626—121no—
277#624—62no—
278#624—121no—
279D3×Dic3—121no—
280C22×D9—31no—
281C22×D9—31no—
282C22×D9—31no—
283C22×D9—61no—
284C22×D9—61no—
285C22×D9—61no—
286C22×D9C22×D311yescharacteristic
287C22×D9C22×D311yescharacteristic
288C2×C4×C9—21no—
289C2×C4×C9—21no—
290C2×C4×C9—21no—
291C2×C4×C9—31no—
292C2×C4×C9—31no—
293C2×C4×C9—31no—
294C2×C4×C9—31no—
295C2×C4×C9C22×D311yescharacteristic
296C2×C4×C9C22×D311yescharacteristic
297C2×C4×C9C22×D311yescharacteristic
298C2×Dic9—31no—
299C2×Dic9—61no—
300C2×Dic9C22×D311yescharacteristic
301C2×Dic9C22×D311yescharacteristic
302D36—41no—
303D36—62no—
304D36—62no—
305D36—121no—
306D36—121no—
307D36—121no—
308D36—122no—
309D36—122no—
310D36—122no—
311D36—121no—
312D36—121no—
313D36—121no—
314D36—121no—
315C4×D9—41no—
316C4×D9—62no—
317C4×D9—121no—
318C4×D9—121no—
319C4×D9—121no—
320C4×D9—122no—
321#540—271noSylow
322C2×C3×C9C2×#4111yescharacteristic
323C2×C3×C9H(5,𝔽2)11yescharacteristic
324C2×C3×C9H(5,𝔽2)11yescharacteristic
325C3⋊D9—41no—
326C3⋊D9—41no—
327C3⋊D9—41no—
328C3×D9—41no—
329C3×D9—41no—
330C2×C3×D4—91no—
331C22×C3×C4—91no—
332C2×#67—91no—
333C2×#67—91no—
334C2×#67—91no—
335C2×#67—91no—
336C2×#67—91no—
337C2×#67—91no—
338C22×Dic3—91no—
339C2×D12—31no—
340C2×D12—91no—
341C2×D12—91no—
342C2×D12—91no—
343C2×D12—91no—
344C2×D12—91no—
345C2×D12—91no—
346C2×D12—91no—
347C2×D12—91no—
348C2×D12—91no—
349C2×D12—91no—
350C2×D12—91no—
351C2×D12—91no—
352C2×D12—181no—
353C2×D12—181no—
354C2×D12—181no—
355C2×C4×D3—31no—
356C2×C4×D3—91no—
357C2×C4×D3—91no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×C4×D3—91no—
362C2×C4×D3—91no—
363C2×C4×D3—181no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—31no—
370C3×C4⋊C4—91no—
371C3×C4⋊C4C2×D911yescharacteristic
372C3×C4⋊C4D3211yescharacteristic
373C3×C22⋊C4—91no—
374C3×C22⋊C4—91no—
375C3×C22⋊C4—91no—
376C3×C42—31no—
377#217—91no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—181no—
395(C2×D3)⋊C4—181no—
396C4⋊Dic3—91no—
397C4⋊Dic3C2×D911yescharacteristic
398Dic3⋊C4—31no—
399Dic3⋊C4—91no—
400Dic3⋊C4C2×D911yescharacteristic
401Dic3⋊C4C2×D911yescharacteristic
402Dic3⋊C4C2×D911yescharacteristic
403Dic3⋊C4C2×D911yescharacteristic
404C4×Dic3—91no—
405C4×Dic3—91no—
406C4×Dic3C2×D911yescharacteristic
407C22×C32C23×D311yescharacteristic
408C2×C3⋊D3—61no—
409C2×C3⋊D3—61no—
410C2×C3⋊D3—61no—
411C2×C3⋊D3—61no—
412C2×C3⋊D3—61no—
413C2×C3⋊D3—61no—
414C2×C3⋊D3—61no—
415C2×C3⋊D3—61no—
416C2×C3⋊D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422C2×C3×D3—61no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C3⋊Dic3—61no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—61no—
431C3×Dic3—61no—
432C3×Dic3#23912yes—
433C22×C9—21no—
434C22×C9C23×D311yescharacteristic
435C2×D9—21no—
436C2×D9—21no—
437C2×D9—21no—
438C2×D9—21no—
439C2×D9—21no—
440C2×D9—21no—
441C2×D9—62no—
442C2×D9—61no—
443C2×D9—61no—
444C2×D9—61no—
445C2×D9—61no—
446C2×D9—61no—
447C2×D9—61no—
448C2×D9—61no—
449C2×D9—61no—
450C2×D9—61no—
451C2×D9—121no—
452C2×D9—121no—
453C2×D9—121no—
454C2×D9—121no—
455C2×D9—121no—
456C2×D9—121no—
457C2×D9—121no—
458C2×D9—121no—
459C4×C9—22no—
460C4×C9—21no—
461C4×C9—21no—
462C4×C9—21no—
463C4×C9—32no—
464C4×C9—41no—
465C4×C9—41no—
466C4×C9—61no—
467C4×C9—61no—
468C4×C9—61no—
469Dic9—21no—
470Dic9—21no—
471Dic9—61no—
472Dic9—121no—
473#127—271no—
474#125—31no—
475#123—91no—
476#123—271no—
477#123—271no—
478#123—271no—
479#121—271no—
480#121—271no—
481#121—271no—
482#121—271no—
483#121—271no—
484#121—271no—
485C4×D4—271no—
486C4×D4—271no—
487#117—271no—
488C3×C9#54011yescharacteristic, complemented, Sylow
489C23×C3—91no—
490C23×C3—91no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—91no—
494C22×D3—91no—
495C22×D3—91no—
496C22×D3—91no—
497C22×D3—91no—
498C22×D3—91no—
499C22×D3—181no—
500C22×D3—181no—
501C22×D3—181no—
502C3×D4—361no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—91no—
511C2×C3×C4—91no—
512C2×C3×C4—361no—
513C2×C3×C4C22×D911yescharacteristic
514C2×C3×C4C22×D911yescharacteristic
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C2×D3211yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519#67—182no—
520#67—182no—
521#67—361no—
522#67—361no—
523#67—361no—
524#67—361no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—181no—
530C2×Dic3—361no—
531C2×Dic3C22×D911yescharacteristic
532C2×Dic3C22×D911yescharacteristic
533C2×Dic3C22×D911yescharacteristic
534C2×Dic3C22×D911yescharacteristic
535D12—121no—
536D12—182no—
537D12—182no—
538D12—361no—
539D12—361no—
540D12—361no—
541D12—361no—
542D12—361no—
543D12—361no—
544D12—362no—
545D12—362no—
546D12—362no—
547D12—361no—
548D12—361no—
549D12—361no—
550D12—361no—
551C4×D3—121no—
552C4×D3—182no—
553C4×D3—182no—
554C4×D3—361no—
555C4×D3—361no—
556C4×D3—361no—
557C4×D3—361no—
558C4×D3—361no—
559C4×D3—362no—
560C2×C32C2×#23911yescharacteristic
561C2×C32#100911yescharacteristic
562C2×C32#100911yescharacteristic
563C3⋊D3—121no—
564C3⋊D3—121no—
565C3⋊D3—121no—
566C3×D3—121no—
567C3×D3—121no—
568C2×C9—21no—
569C2×C9—21no—
570C2×C9—21no—
571C2×C9#100411yescharacteristic
572C2×C9D3×#4111yescharacteristic
573C2×C9#100911yescharacteristic
574D9—41no—
575D9—41no—
576D9—122no—
577D9—121no—
578D9—121no—
579D9—121no—
580D9—241no—
581D9—241no—
582C2×D4—91no—
583C2×D4—271no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C2×D4—271no—
588C2×D4—271no—
589C2×D4—271no—
590C2×D4—271no—
591C2×D4—271no—
592C22×C4—91no—
593C22×C4—271no—
594C22×C4—271no—
595C22×C4—271no—
596C22×C4—271no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—91no—
603C4⋊C4—271no—
604C4⋊C4D3×D911yescharacteristic
605C22⋊C4—91no—
606C22⋊C4—91no—
607C22⋊C4—91no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C22⋊C4—271no—
612C22⋊C4—271no—
613C22⋊C4—271no—
614C22⋊C4—271no—
615C42—31no—
616C42—271no—
617C22×C3—21no—
618C22×C3—181no—
619C22×C3—181no—
620C22×C3—181no—
621C22×C3—181no—
622C22×C3—181no—
623C22×C3—181no—
624C22×C3C23×D911yescharacteristic
625C22×C3C22×D3211yescharacteristic
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—182no—
633C2×D3—181no—
634C2×D3—181no—
635C2×D3—181no—
636C2×D3—181no—
637C2×D3—181no—
638C2×D3—181no—
639C2×D3—181no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—181no—
650C2×D3—181no—
651C2×D3—361no—
652C2×D3—361no—
653C2×D3—361no—
654C2×D3—361no—
655C2×D3—361no—
656C2×D3—361no—
657C2×D3—361no—
658C2×D3—361no—
659C3×C4—22no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—32no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—181no—
673C3×C4—181no—
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—61no—
678Dic3—61no—
679Dic3—181no—
680Dic3—181no—
681Dic3—361no—
682Dic3#370112yes—
683C32#569711yescharacteristic
684C9—21no—
685C9#566311yescharacteristic, complemented
686C23—91no—
687C23—91no—
688C23—271no—
689C23—271no—
690C23—271no—
691D4—361no—
692D4—542no—
693D4—542no—
694D4—1081no—
695D4—1081no—
696D4—1081no—
697D4—1081no—
698D4—1081no—
699D4—1081no—
700D4—1081no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—271no—
708C2×C4—361no—
709C2×C4—542no—
710C2×C4—1081no—
711C2×C4—1081no—
712C2×C4—1081no—
713C2×C4C2×D3×D911yescharacteristic
714C2×C4C2×D3×D911yescharacteristic
715C2×C4C2×D3×D911yescharacteristic
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—361no—
720C2×C3—361no—
721C2×C3C2×#370111yescharacteristic
722C2×C3#6371511yescharacteristic
723C2×C3#6371511yescharacteristic
724C2×C3#6430811yescharacteristic
725C2×C3#6431411yescharacteristic
726C2×C3D3×#23911yescharacteristic
727D3—121no—
728D3—121no—
729D3—362no—
730D3—361no—
731D3—361no—
732D3—361no—
733D3—361no—
734D3—361no—
735D3—361no—
736D3—721no—
737D3—721no—
738C22—181no—
739C22—181no—
740C22—181no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22—541no—
745C22—541no—
746C22—541no—
747C22—541no—
748C22—541no—
749C22—541no—
750C22—541no—
751C22—541no—
752C22—541no—
753C22C22×D3×D911yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—32no—
758C4—61no—
759C4—61no—
760C4—61no—
761C4—181no—
762C4—181no—
763C4—541no—
764C3—21no—
765C3#1058979911yescharacteristic, complemented
766C3#1059446711yescharacteristic
767C2—361no—
768C2—361no—
769C2—1081no—
770C2—1081no—
771C2—1081no—
772C2#1172247811yescharacteristic
773C2#1172250111yescharacteristic
774C2D3×#370111yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#540
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721751C2semidirect
2. C3×#63456C2semidirect
3. C9×#889C2semidirect
4. #11721006C2semidirect
5. #11721005C2semidirect
6. #11721005C2semidirect
7. #11721005C2semidirect
8. #11721004C2semidirect
9. #11721002C2semidirect
10. #11720997C2semidirect
11. #11720988C2semidirect
12. #11720983C2semidirect
13. #11720978C2semidirect
14. #11720941C2semidirect
15. #11720898C2semidirect
79. #63456D3semidirect
241. #889D9semidirect
488. C3×C9#540semidirect
685. C9#5663semidirect
765. C3#10589799semidirect

Maximal subgroups

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

subgroupindex
#117217512
C3×#634562
C9×#8892
#117210062
#117210052
#117210042
#117210022
#117209972
#117209882
#117209832
#117209782
#117209412
#117208982
#105944673
#105897993