Finite Group Databasebeta

← #13148996

Subgroups — #13148996

Order 1728.

792 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721750C211yesmaximal, characteristic, complemented
2C3×#63455C211yesmaximal, characteristic, complemented
3C9×#889C211yesmaximal, characteristic, complemented
4#11721005C211yesmaximal, characteristic, complemented
5#11721004C211yesmaximal, characteristic, complemented
6C4×#6192C211yesmaximal, characteristic, complemented
7#11720983C211yesmaximal, characteristic, complemented
8#11720983C211yesmaximal, characteristic, complemented
9#11720978C211yesmaximal, characteristic, complemented
10#11720977C211yesmaximal, characteristic, complemented
11D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#11720946C211yesmaximal, characteristic, complemented
13#11720938C211yesmaximal, characteristic, complemented
14#11720934C211yesmaximal, characteristic, complemented
15#11720899C211yesmaximal, characteristic, complemented
16#10594415—31nomaximal
17#10589797—31nomaximal
18C2×C4⋊(C3⋊D9)C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C3×D36C2211yescharacteristic
21C2×C3×C4×D9C2211yescharacteristic
22C2×C3×C4×D9C2211yescharacteristic
23C2×#6192C2211yescharacteristic
24C2×#6192C2211yescharacteristic
25C2×#6192C2211yescharacteristic
26C2×#6192C2211yescharacteristic
27C2×(C3⋊D9)⋊C4C2211yescharacteristic
28C2×Dic3×D9C2211yescharacteristic
29C2×Dic3×D9C2211yescharacteristic
30C3×C9×C4⋊C4C2211yescharacteristic
31#88536C2211yescharacteristic
32#88536C2211yescharacteristic
33#88536C2211yescharacteristic
34#88534C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C9×C4⋊Dic3C2211yescharacteristic
38C9×Dic3⋊C4C2211yescharacteristic
39C9×Dic3⋊C4C2211yescharacteristic
40C9×Dic3⋊C4C2211yescharacteristic
41C9×Dic3⋊C4C2211yescharacteristic
42C4×C9×Dic3C2211yescharacteristic
43C3×C4×Dic9C2211yescharacteristic
44#88445C2211yescharacteristic
45#88445C2211yescharacteristic
46#88445C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49Dic3⋊Dic9C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64103—31no—
54C3×#893—31no—
55C3×#889D311yescharacteristic
56#63910—31no—
57#63909—31no—
58C4×#626—31no—
59#63886—31no—
60#63886—31no—
61#63881—31no—
62#63880—31no—
63D3×Dic3⋊C4—31no—
64#63868—31no—
65#63858—31no—
66#63850—31no—
67#63836—31no—
68C9×#125—31no—
69#63460—31no—
70#63460—31no—
71#63457—31no—
72#63457—31no—
73#63457—31no—
74#63457—31no—
75#63456—31no—
76#63456—31no—
77#63456—61no—
78#63455—31no—
79#63455D311yescharacteristic, complemented
80#63454—31no—
81C4⋊C4×D9—31no—
82C4×D36—31no—
83C4×D36—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3⋊Dic9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C4⋊(C3⋊D9)—41no—
94C4×C3⋊D9—41no—
95C2×C9×Dic3C2311yescharacteristic
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C3×D36—22no—
102C3×C4×D9—41no—
103C3×C4×D9—41no—
104#6192—22no—
105#6192—22no—
106#6192—22no—
107#6192—41no—
108(C3⋊D9)⋊C4—22no—
109Dic3×D9—22no—
110Dic3×D9—41no—
111#5695—91no—
112#5540—91no—
113C2×C4⋊(C3⋊D3)—31no—
114C2×C4×C3⋊D3—31no—
115C2×C3×D12—31no—
116C2×C3×C4×D3—31no—
117C2×C3×C4×D3—31no—
118C2×#626—31no—
119C2×#626—31no—
120C2×#626—31no—
121C2×#626—31no—
122C2×#624—31no—
123C2×D3×Dic3—31no—
124C2×D3×Dic3—31no—
125C32×C4⋊C4C2×D311yescharacteristic
126#3752—31no—
127#3752—31no—
128#3752—31no—
129#3750—31no—
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×C4⋊Dic3C2×D311yescharacteristic
133C3×Dic3⋊C4C2×D311yescharacteristic
134C3×Dic3⋊C4C2×D311yescharacteristic
135C3×Dic3⋊C4C2×D311yescharacteristic
136C3×Dic3⋊C4C2×D311yescharacteristic
137C3×C4×Dic3—31no—
138C3×C4×Dic3C2×D311yescharacteristic
139#3724—31no—
140Dic3⋊Dic3—31no—
141Dic3⋊Dic3—31no—
142#3722—31no—
143#3722—31no—
144#3722—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147Dic32—31no—
148C2×D36—31no—
149C2×D36—31no—
150C2×D36—31no—
151C2×D36—31no—
152C2×D36—31no—
153C2×D36—61no—
154C2×D36C2×D311yescharacteristic
155C2×C4×D9—31no—
156C2×C4×D9—31no—
157C2×C4×D9—31no—
158C2×C4×D9—31no—
159C2×C4×D9—61no—
160C2×C4×D9C2×D311yescharacteristic
161C2×C4×D9C2×D311yescharacteristic
162C9×C4⋊C4—21no—
163C9×C4⋊C4—31no—
164C9×C4⋊C4—31no—
165C9×C4⋊C4—31no—
166C9×C4⋊C4—31no—
167C9×C4⋊C4—31no—
168C9×C4⋊C4C2×D311yescharacteristic
169C42×C9—31no—
170(C2×D9)⋊C4—31no—
171(C2×D9)⋊C4—31no—
172(C2×D9)⋊C4—31no—
173(C2×D9)⋊C4—31no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—61no—
179(C2×D9)⋊C4—61no—
180(C2×D9)⋊C4—61no—
181(C2×D9)⋊C4C2×D311yescharacteristic
182(C2×D9)⋊C4C2×D311yescharacteristic
183C4⋊Dic9—31no—
184C4⋊Dic9—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—61no—
188C4×Dic9—31no—
189C4×Dic9C2×D311yescharacteristic
190C22×C3×C9C2411yescharacteristic
191C2×C3⋊D9—21no—
192C2×C3⋊D9—21no—
193C2×C3⋊D9—21no—
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#4112yes—
203C3×C4×C9—21no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C9×Dic3—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C9×Dic3#4112yes—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×#125—31no—
215C3×C4×D4—91no—
216#939—91no—
217#939—91no—
218#930—91no—
219#929—91no—
220C4×#67—91no—
221C2×Dic3⋊C4—91no—
222#898—91no—
223#898—91no—
224#895—91no—
225#895—91no—
226#895—91no—
227#895—91no—
228#894—91no—
229#894—91no—
230#894—91no—
231#894—181no—
232#893—31no—
233#893—91no—
234#892—91no—
235D3×C4⋊C4—91no—
236#889D911yescharacteristic, complemented
237#884—91no—
238#67⋊C4—91no—
239#67⋊C4—91no—
240#879—91no—
241#876—91no—
242C4×D12—91no—
243C4×D12—91no—
244#872—91no—
245C22×C3⋊D3—31no—
246C22×C3⋊D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C3⋊Dic3—31no—
253C2×C3⋊Dic3—31no—
254C4⋊(C3⋊D3)—121no—
255C4×C3⋊D3—121no—
256C2×C3×Dic3—31no—
257C2×C3×Dic3—31no—
258C2×C3×Dic3C22×D311yescharacteristic
259C2×C3×Dic3C22×D311yescharacteristic
260C2×C3×Dic3C22×D311yescharacteristic
261C2×C3×Dic3C22×D311yescharacteristic
262C3×D12—62no—
263C3×C4×D3—121no—
264C3×C4×D3—121no—
265#626—62no—
266#626—62no—
267#626—62no—
268#626—121no—
269#624—62no—
270D3×Dic3—62no—
271D3×Dic3—121no—
272C22×D9—31no—
273C22×D9—31no—
274C22×D9—61no—
275C22×D9—61no—
276C22×D9C22×D311yescharacteristic
277C22×D9C22×D311yescharacteristic
278C2×C4×C9—21no—
279C2×C4×C9—21no—
280C2×C4×C9—21no—
281C2×C4×C9—31no—
282C2×C4×C9—31no—
283C2×C4×C9—31no—
284C2×C4×C9—31no—
285C2×C4×C9C22×D311yescharacteristic
286C2×C4×C9C22×D311yescharacteristic
287C2×C4×C9C22×D311yescharacteristic
288C2×Dic9—31no—
289C2×Dic9—31no—
290C2×Dic9—61no—
291C2×Dic9—61no—
292C2×Dic9C22×D311yescharacteristic
293C2×Dic9C22×D311yescharacteristic
294D36—22no—
295D36—62no—
296D36—62no—
297D36—62no—
298D36—121no—
299D36—122no—
300D36—121no—
301C4×D9—41no—
302C4×D9—41no—
303C4×D9—62no—
304C4×D9—62no—
305C4×D9—121no—
306C4×D9—121no—
307C4×D9—122no—
308#553—271noSylow
309C2×C3×C9C2×#4111yescharacteristic
310C2×C3×C9C2×#4111yescharacteristic
311C2×C3×C9H(5,𝔽2)11yescharacteristic
312C3⋊D9—41no—
313C3⋊D9—41no—
314C3×D9—22no—
315C3×D9—41no—
316C2×C3×D4—91no—
317C22×C3×C4—91no—
318C22×C3×C4—91no—
319C2×#67—91no—
320C2×#67—91no—
321C2×#67—91no—
322C2×#67—91no—
323C22×Dic3—91no—
324C22×Dic3—91no—
325C2×D12—31no—
326C2×D12—91no—
327C2×D12—91no—
328C2×D12—91no—
329C2×D12—91no—
330C2×D12—91no—
331C2×D12—91no—
332C2×D12—181no—
333C2×C4×D3—31no—
334C2×C4×D3—31no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3—91no—
340C2×C4×D3—91no—
341C2×C4×D3—181no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4C2×D911yescharacteristic
349C3×C4⋊C4D3211yescharacteristic
350C3×C22⋊C4—91no—
351C3×C22⋊C4—91no—
352C3×C42—31no—
353C3×C42—91no—
354#217—91no—
355#217—91no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—91no—
359(C2×D3)⋊C4—91no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4—91no—
367(C2×D3)⋊C4—91no—
368(C2×D3)⋊C4—91no—
369(C2×D3)⋊C4—91no—
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—181no—
373(C2×D3)⋊C4—181no—
374(C2×D3)⋊C4—181no—
375C4⋊Dic3—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3C2×D911yescharacteristic
378Dic3⋊C4—91no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—181no—
385Dic3⋊C4C2×D911yescharacteristic
386Dic3⋊C4C2×D911yescharacteristic
387Dic3⋊C4C2×D911yescharacteristic
388Dic3⋊C4C2×D911yescharacteristic
389C4×Dic3—31no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3C2×D911yescharacteristic
393C22×C32C23×D311yescharacteristic
394C2×C3⋊D3—61no—
395C2×C3⋊D3—61no—
396C2×C3⋊D3—61no—
397C2×C3⋊D3—61no—
398C2×C3⋊D3—61no—
399C2×C3⋊D3—61no—
400C2×C3×D3—32no—
401C2×C3×D3—61no—
402C2×C3×D3—61no—
403C2×C3×D3—61no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—21no—
409C3⋊Dic3—61no—
410C3⋊Dic3—61no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—61no—
415C3×Dic3—61no—
416C3×Dic3#23912yes—
417C22×C9—21no—
418C22×C9C23×D311yescharacteristic
419C2×D9—21no—
420C2×D9—21no—
421C2×D9—21no—
422C2×D9—21no—
423C2×D9—21no—
424C2×D9—62no—
425C2×D9—61no—
426C2×D9—61no—
427C2×D9—61no—
428C2×D9—61no—
429C2×D9—61no—
430C2×D9—61no—
431C2×D9—121no—
432C2×D9—121no—
433C2×D9—121no—
434C2×D9—121no—
435C2×D9—121no—
436C2×D9#23512yes—
437C4×C9—21no—
438C4×C9—21no—
439C4×C9—21no—
440C4×C9—32no—
441C4×C9—41no—
442C4×C9—41no—
443C4×C9—41no—
444C4×C9—61no—
445C4×C9—61no—
446C4×C9—61no—
447Dic9—21no—
448Dic9—21no—
449Dic9—61no—
450Dic9—61no—
451Dic9—121no—
452Dic9—121no—
453#126—271no—
454#126—271no—
455#125—31no—
456#123—271no—
457#123—271no—
458#121—271no—
459#121—271no—
460#121—271no—
461#121—271no—
462C4×D4—91no—
463C4×D4—271no—
464C4×D4—271no—
465C4×D4—271no—
466#117—271no—
467C2×C4⋊C4—271no—
468C3×C9#55311yescharacteristic, complemented, Sylow
469C23×C3—91no—
470C23×C3—91no—
471C22×D3—31no—
472C22×D3—31no—
473C22×D3—91no—
474C22×D3—91no—
475C22×D3—91no—
476C22×D3—91no—
477C22×D3—181no—
478C22×D3—181no—
479C3×D4—182no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—361no—
490C2×C3×C4—361no—
491C2×C3×C4C22×D911yescharacteristic
492C2×C3×C4C22×D911yescharacteristic
493C2×C3×C4C22×D911yescharacteristic
494C2×C3×C4C2×D3211yescharacteristic
495C2×C3×C4C2×D3211yescharacteristic
496C2×C3×C4C2×D3211yescharacteristic
497#67—182no—
498#67—182no—
499#67—182no—
500#67—361no—
501C2×Dic3—31no—
502C2×Dic3—31no—
503C2×Dic3—91no—
504C2×Dic3—91no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—181no—
508C2×Dic3—181no—
509C2×Dic3—182no—
510C2×Dic3—361no—
511C2×Dic3C22×D911yescharacteristic
512C2×Dic3C22×D911yescharacteristic
513C2×Dic3C22×D911yescharacteristic
514C2×Dic3C22×D911yescharacteristic
515D12—62no—
516D12—182no—
517D12—182no—
518D12—182no—
519D12—361no—
520D12—361no—
521D12—362no—
522D12—361no—
523C4×D3—121no—
524C4×D3—121no—
525C4×D3—182no—
526C4×D3—182no—
527C4×D3—182no—
528C4×D3—361no—
529C4×D3—361no—
530C4×D3—361no—
531C4×D3—362no—
532C2×C32C2×#23911yescharacteristic
533C2×C32D3×#4111yescharacteristic
534C2×C32#100911yescharacteristic
535C3⋊D3—121no—
536C3⋊D3—121no—
537C3×D3—62no—
538C3×D3—121no—
539C2×C9—21no—
540C2×C9—21no—
541C2×C9—21no—
542C2×C9C2×#23511yescharacteristic
543C2×C9#100411yescharacteristic
544C2×C9D3×#4111yescharacteristic
545D9—22no—
546D9—41no—
547D9—122no—
548D9—121no—
549D9—121no—
550D9—241no—
551C2×D4—91no—
552C2×D4—271no—
553C2×D4—271no—
554C2×D4—271no—
555C2×D4—271no—
556C2×D4—271no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—271no—
560C22×C4—271no—
561C22×C4—271no—
562C22×C4—271no—
563C4⋊C4—31no—
564C4⋊C4—31no—
565C4⋊C4—31no—
566C4⋊C4—31no—
567C4⋊C4—31no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4D3×D911yescharacteristic
573C22⋊C4—91no—
574C22⋊C4—91no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C42—31no—
584C42—91no—
585C42—271no—
586C22×C3—21no—
587C22×C3—92no—
588C22×C3—181no—
589C22×C3—181no—
590C22×C3—181no—
591C22×C3—181no—
592C22×C3—181no—
593C22×C3C23×D911yescharacteristic
594C22×C3C22×D3211yescharacteristic
595C2×D3—32no—
596C2×D3—61no—
597C2×D3—61no—
598C2×D3—61no—
599C2×D3—61no—
600C2×D3—61no—
601C2×D3—182no—
602C2×D3—181no—
603C2×D3—181no—
604C2×D3—181no—
605C2×D3—181no—
606C2×D3—181no—
607C2×D3—181no—
608C2×D3—181no—
609C2×D3—181no—
610C2×D3—181no—
611C2×D3—181no—
612C2×D3—181no—
613C2×D3—181no—
614C2×D3—361no—
615C2×D3—361no—
616C2×D3—361no—
617C2×D3—361no—
618C2×D3—361no—
619C3×C4—21no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—32no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—61no—
630C3×C4—61no—
631C3×C4—61no—
632C3×C4—181no—
633C3×C4—181no—
634Dic3—21no—
635Dic3—21no—
636Dic3—21no—
637Dic3—61no—
638Dic3—61no—
639Dic3—181no—
640Dic3—181no—
641Dic3—181no—
642Dic3—181no—
643Dic3—361no—
644Dic3—361no—
645Dic3#370112yes—
646C32#569511yescharacteristic
647C9—21no—
648C9#554011yescharacteristic, complemented
649C23—91no—
650C23—91no—
651C23—271no—
652C23—271no—
653D4—182no—
654D4—542no—
655D4—542no—
656D4—542no—
657D4—1081no—
658D4—1081no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—91no—
664C2×C4—91no—
665C2×C4—271no—
666C2×C4—271no—
667C2×C4—361no—
668C2×C4—361no—
669C2×C4—542no—
670C2×C4—542no—
671C2×C4—1081no—
672C2×C4—1081no—
673C2×C4C2×D3×D911yescharacteristic
674C2×C4C2×D3×D911yescharacteristic
675C2×C4C2×D3×D911yescharacteristic
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—182no—
680C2×C3—361no—
681C2×C3C2×#370111yescharacteristic
682C2×C3#41×D911yescharacteristic
683C2×C3#6371511yescharacteristic
684C2×C3D3×#23511yescharacteristic
685C2×C3#6431411yescharacteristic
686C2×C3D3×#23911yescharacteristic
687D3—62no—
688D3—121no—
689D3—362no—
690D3—361no—
691D3—361no—
692D3—361no—
693D3—361no—
694D3—721no—
695C22—92no—
696C22—181no—
697C22—181no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—541no—
702C22—541no—
703C22—541no—
704C22—541no—
705C22—541no—
706C22—541no—
707C22C22×D3×D911yescharacteristic
708C4—21no—
709C4—21no—
710C4—21no—
711C4—32no—
712C4—61no—
713C4—61no—
714C4—61no—
715C4—181no—
716C4—181no—
717C4—541no—
718C4—541no—
719C3—21no—
720C3#1058979711yescharacteristic, complemented
721C3#1059441511yescharacteristic
722C2—182no—
723C2—361no—
724C2—1081no—
725C2—1081no—
726C2D9×#23511yescharacteristic
727C2#1172250111yescharacteristic
728C2D3×#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#553
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. #11721750C2semidirect
2. C3×#63455C2semidirect
3. C9×#889C2semidirect
4. #11721005C2semidirect
5. #11721004C2semidirect
6. C4×#6192C2semidirect
7. #11720983C2semidirect
8. #11720983C2semidirect
9. #11720978C2semidirect
10. #11720977C2semidirect
11. D9×Dic3⋊C4C2semidirect
12. #11720946C2semidirect
13. #11720938C2semidirect
14. #11720934C2semidirect
15. #11720899C2semidirect
79. #63455D3semidirect
236. #889D9semidirect
468. C3×C9#553semidirect
648. C9#5540semidirect
720. C3#10589797semidirect

Maximal subgroups

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

subgroupindex
#117217502
C3×#634552
C9×#8892
#117210052
#117210042
C4×#61922
#117209832
#117209782
#117209772
D9×Dic3⋊C42
#117209462
#117209382
#117209342
#117208992
#105944153
#105897973