Finite Group Databasebeta

← #13148031

Subgroups — #13148031

Order 1728.

804 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721725C211yesmaximal, characteristic, complemented
2C9×#885C211yesmaximal, characteristic, complemented
3C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
4#11721285C211yesmaximal, characteristic
5#11721280C211yesmaximal, characteristic, complemented
6D9×#217C211yesmaximal, characteristic, complemented
7#11721246C211yesmaximal, characteristic, complemented
8#11721031C211yesmaximal, characteristic, complemented
9#11721028C211yesmaximal, characteristic, complemented
10#11721012C211yesmaximal, characteristic, complemented
11#11720989C211yesmaximal, characteristic, complemented
12#11720984C211yesmaximal, characteristic, complemented
13#11720974C211yesmaximal, characteristic, complemented
14#11720944C211yesmaximal, characteristic, complemented
15#11720943C211yesmaximal, characteristic, complemented
16#10594092—31nomaximal
17#10589781—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C2×C9×#67C2211yescharacteristic
20C2×C3×C4×D9C2211yescharacteristic
21C2×C3×C4×D9C2211yescharacteristic
22C2×C9×Dic6C2211yescharacteristic, complemented
23C2×#6194C2211yescharacteristic
24C2×#6194C2211yescharacteristic
25C2×D3×Dic9C2211yescharacteristic, complemented
26C2×Dic3×D9C2211yescharacteristic
27C2×Dic3×D9C2211yescharacteristic
28C3×C9×C22⋊C4C2211yescharacteristic
29#88551C2211yescharacteristic
30#88551C2211yescharacteristic
31C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
32#88534C2211yescharacteristic, complemented
33#88534C2211yescharacteristic, complemented
34C4×C3⋊Dic9C2211yescharacteristic, complemented
35C9×#217C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C4×C9×Dic3C2211yescharacteristic, complemented
42(C2×D3)⋊Dic9C2211yescharacteristic, complemented
43(C2×D9)⋊Dic3C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic, complemented
48#88442C2211yescharacteristic, complemented
49#88442C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64088—31no—
54C3×#885D311yescharacteristic
55C3×D3×C22⋊C4—31no—
56#63976—31no—
57#63969—31no—
58D3×#217—31no—
59#63956—31no—
60#63905—31no—
61#63902—31no—
62#63891—31no—
63#63887—31no—
64#63879—31no—
65#63877—31no—
66#63856—31no—
67#63855—31no—
68C9×#124—31no—
69#63508—31no—
70#63508—31no—
71#63499—31no—
72#63497—31no—
73#63445—31no—
74#63445—31no—
75#611⋊C4—31no—
76#611⋊C4—31no—
77C22⋊C4×D9—31no—
78C22⋊C4×D9D311yescharacteristic, complemented
79#63441—31no—
80#63441—31no—
81#63441—61no—
82#63434—31no—
83#63434—31no—
84C23×C3×C9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9—22no—
87C22×C3×D9—22no—
88C22×C3×D9—41no—
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C9×#67—41no—
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C3×C4×D9—22no—
104C3×C4×D9—41no—
105C9×Dic6—41no—
106#6194—22no—
107#6194—22no—
108D3×Dic9—41no—
109Dic3×D9—22no—
110Dic3×D9—41no—
111#5679—91no—
112#5495—91no—
113C23×C3×D3—31no—
114C2×C3×#67C2×D311yescharacteristic
115C2×C3×C4×D3—31no—
116C2×C3×C4×D3—31no—
117C2×C3×Dic6C2×D311yescharacteristic
118C2×#625—31no—
119C2×#625—31no—
120C2×D3×Dic3—31no—
121C2×D3×Dic3—31no—
122C2×D3×Dic3—31no—
123C23×D9C2×D311yescharacteristic
124C32×C22⋊C4C2×D311yescharacteristic
125#3757—31no—
126#3757—31no—
127C4⋊(C3⋊Dic3)—31no—
128#3750—31no—
129#3750—31no—
130C4×C3⋊Dic3—31no—
131C3×#217—31no—
132C3×#217C2×D311yescharacteristic
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×(C2×D3)⋊C4C2×D311yescharacteristic
136C3×(C2×D3)⋊C4C2×D311yescharacteristic
137C3×C4×Dic3C2×D311yescharacteristic
138#3724—31no—
139#3724—31no—
140Dic3⋊Dic3—31no—
141Dic3⋊Dic3—31no—
142Dic3⋊Dic3—31no—
143(C2×D3)⋊Dic3—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148Dic32—31no—
149C2×Q8×C9—31no—
150C2×D4×C9—31no—
151C2×#611—31no—
152C2×#611—31no—
153C22×Dic9—31no—
154C2×C4×D9—31no—
155C2×C4×D9—31no—
156C2×C4×D9C2×D311yescharacteristic
157C2×C4×D9C2×D311yescharacteristic
158C9×C22⋊C4—21no—
159C9×C22⋊C4—31no—
160C9×C22⋊C4—31no—
161C9×C22⋊C4—31no—
162C9×C22⋊C4C2×D311yescharacteristic
163C42×C9—31no—
164#3676—31no—
165#3676—31no—
166#3676—31no—
167#3676—61no—
168#3676—61no—
169#3676C2×D311yescharacteristic
170(C2×D9)⋊C4—31no—
171(C2×D9)⋊C4—31no—
172(C2×D9)⋊C4—31no—
173(C2×D9)⋊C4—31no—
174(C2×D9)⋊C4C2×D311yescharacteristic
175(C2×D9)⋊C4C2×D311yescharacteristic
176C4⋊Dic9—31no—
177C4⋊Dic9—31no—
178C4⋊Dic9—61no—
179Dic9⋊C4—31no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—61no—
186Dic9⋊C4—61no—
187C4×Dic9—31no—
188C4×Dic9—31no—
189C4×Dic9—61no—
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9—21no—
193C22×C3×C9C2411yescharacteristic
194C2×D3×C9—21no—
195C2×D3×C9—21no—
196C2×D3×C9—21no—
197C2×C3×D9—21no—
198C2×C3×D9—21no—
199C2×C3×D9—21no—
200C2×C3×D9—21no—
201C2×C3×D9—44no—
202C2×C3×D9#4112yes—
203C2×C3×D9#4112yes—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9—21no—
209C3⋊Dic9—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C9×Dic3—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#124—31no—
216C2×C3×C22⋊C4—91no—
217#953—91no—
218C2×#217—91no—
219#946—91no—
220#946—91no—
221#937—91no—
222#935—91no—
223#929—91no—
224C4×#67—91no—
225#926—91no—
226#924—91no—
227#886—91no—
228#885D911yescharacteristic, complemented
229#883—91no—
230#883—91no—
231#883—91no—
232#67⋊C4—91no—
233#67⋊C4—91no—
234#67⋊C4—91no—
235D3×C22⋊C4—31no—
236D3×C22⋊C4—91no—
237#879—91no—
238#879—91no—
239#879—91no—
240#879—91no—
241#879—181no—
242#878—91no—
243#877—91no—
244#872—91no—
245#872—91no—
246C23×C32C22×D311yescharacteristic
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3—62no—
250C22×C3×D3—62no—
251C22×C3×D3—121no—
252C22×C3×D3C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C3×#67—41no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3C22×D311yescharacteristic
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C3×C4×D3—62no—
266C3×C4×D3—121no—
267C3×Dic6—41no—
268#625—62no—
269#625—62no—
270D3×Dic3—62no—
271D3×Dic3—121no—
272D3×Dic3—121no—
273C23×C9—21no—
274C23×C9—31no—
275C23×C9C22×D311yescharacteristic
276C22×D9—22no—
277C22×D9—22no—
278C22×D9—41no—
279C22×D9C22×D311yescharacteristic
280C22×D9C22×D311yescharacteristic
281Q8×C9—121no—
282D4×C9—121no—
283C2×C4×C9—21no—
284C2×C4×C9—21no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9—31no—
288C2×C4×C9C22×D311yescharacteristic
289C2×C4×C9C22×D311yescharacteristic
290#611—62no—
291#611—62no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—31no—
296C2×Dic9—61no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—121no—
301C2×Dic9C22×D311yescharacteristic
302C2×Dic9C22×D311yescharacteristic
303C4×D9—22no—
304C4×D9—41no—
305C4×D9—62no—
306C4×D9—121no—
307#551—271noSylow
308C2×C3×C9—41no—
309C2×C3×C9C2×#4111yescharacteristic
310C2×C3×C9C2×#4111yescharacteristic
311C2×C3×C9H(5,𝔽2)11yescharacteristic
312D3×C9—41no—
313C3×D9—22no—
314C3×D9—22no—
315C24×C3—91no—
316C23×D3—31no—
317C2×C3×Q8—31no—
318C2×C3×D4—31no—
319C22×C3×C4—91no—
320C22×C3×C4—91no—
321C2×#67—91no—
322C2×#67—91no—
323C2×#67—91no—
324C2×#67—91no—
325C2×#67C2×D911yescharacteristic
326C22×Dic3—91no—
327C22×Dic3—91no—
328C22×Dic3—91no—
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—91no—
332C2×C4×D3—91no—
333C2×C4×D3—91no—
334C2×Dic6C2×D911yescharacteristic, complemented
335C3×C22⋊C4—21no—
336C3×C22⋊C4—31no—
337C3×C22⋊C4—31no—
338C3×C22⋊C4—31no—
339C3×C22⋊C4—91no—
340C3×C22⋊C4—91no—
341C3×C22⋊C4—91no—
342C3×C22⋊C4C2×D911yescharacteristic
343C3×C22⋊C4D3211yescharacteristic
344C3×C42—31no—
345#217—31no—
346#217—91no—
347#217—91no—
348#217—91no—
349#217—91no—
350#217—91no—
351#217—91no—
352#217—91no—
353#217—91no—
354#217—91no—
355#217—181no—
356#217—181no—
357#217C2×D911yescharacteristic
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
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)⋊C4C2×D911yescharacteristic, complemented
366(C2×D3)⋊C4C2×D911yescharacteristic, complemented
367C4⋊Dic3—91no—
368C4⋊Dic3—91no—
369C4⋊Dic3—91no—
370C4⋊Dic3—91no—
371C4⋊Dic3—91no—
372C4⋊Dic3—181no—
373Dic3⋊C4—91no—
374Dic3⋊C4—91no—
375Dic3⋊C4—91no—
376Dic3⋊C4—91no—
377Dic3⋊C4—91no—
378Dic3⋊C4—91no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—181no—
385Dic3⋊C4—181no—
386C4×Dic3—91no—
387C4×Dic3—91no—
388C4×Dic3—91no—
389C4×Dic3—91no—
390C4×Dic3—181no—
391C4×Dic3C2×D911yescharacteristic, complemented
392C22×C32—21no—
393C22×C32—21no—
394C22×C32—21no—
395C22×C32C23×D311yescharacteristic
396C2×C3×D3—21no—
397C2×C3×D3—21no—
398C2×C3×D3—21no—
399C2×C3×D3—32no—
400C2×C3×D3—32no—
401C2×C3×D3—61no—
402C2×C3×D3—61no—
403C2×C3×D3—61no—
404C2×C3×D3—61no—
405C2×C3×D3—124no—
406C32×C4—21no—
407C32×C4—21no—
408C3⋊Dic3—61no—
409C3⋊Dic3—61no—
410C3⋊Dic3—61no—
411C3⋊Dic3—61no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—61no—
416C3×Dic3—61no—
417C22×C9—21no—
418C22×C9—21no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—41no—
422C22×C9—41no—
423C22×C9—41no—
424C22×C9—61no—
425C22×C9—61no—
426C22×C9—61no—
427C22×C9C23×D311yescharacteristic
428C2×D9—21no—
429C2×D9—21no—
430C2×D9—21no—
431C2×D9—21no—
432C2×D9—44no—
433C2×D9#23512yes—
434C2×D9#23712yes—
435C4×C9—21no—
436C4×C9—21no—
437C4×C9—41no—
438C4×C9—41no—
439C4×C9—61no—
440C4×C9—61no—
441C4×C9—61no—
442Dic9—21no—
443Dic9—21no—
444Dic9—61no—
445Dic9—61no—
446Dic9—61no—
447Dic9—61no—
448Dic9—121no—
449Dic9—121no—
450Dic9—121no—
451Dic9—121no—
452#126—271no—
453#126—271no—
454#124—31no—
455#123—271no—
456#123—271no—
457#123—271no—
458C22⋊Q8—271no—
459C22⋊Q8—271no—
460#120—271no—
461C4×D4—271no—
462C4×D4—271no—
463#117—271no—
464#117—271no—
465C2×C22⋊C4—91no—
466C2×C22⋊C4—271no—
467C3×C9#55111yescharacteristic, complemented, Sylow
468C23×C3—21no—
469C23×C3—31no—
470C23×C3—91no—
471C23×C3—91no—
472C23×C3—182no—
473C23×C3—182no—
474C23×C3—361no—
475C23×C3C22×D911yescharacteristic
476C23×C3C2×D3211yescharacteristic
477C22×D3—31no—
478C22×D3—31no—
479C22×D3—62no—
480C22×D3—62no—
481C22×D3—121no—
482C22×D3C22×D911yescharacteristic
483C3×Q8—121no—
484C3×D4—121no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—91no—
491C2×C3×C4—91no—
492C2×C3×C4—182no—
493C2×C3×C4—361no—
494C2×C3×C4C22×D911yescharacteristic
495C2×C3×C4C22×D911yescharacteristic
496C2×C3×C4C2×D3211yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498#67—41no—
499#67—182no—
500#67—182no—
501#67—182no—
502#67—182no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—91no—
510C2×Dic3—91no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—181no—
514C2×Dic3—181no—
515C2×Dic3—181no—
516C2×Dic3—181no—
517C2×Dic3—182no—
518C2×Dic3—361no—
519C2×Dic3—361no—
520C2×Dic3C22×D911yescharacteristic
521C2×Dic3C22×D911yescharacteristic
522C2×Dic3C22×D911yescharacteristic
523C4×D3—62no—
524C4×D3—121no—
525C4×D3—182no—
526C4×D3—361no—
527C4×D3—361no—
528Dic6—41no—
529C2×C32—41no—
530C2×C32#100411yescharacteristic
531C2×C32D3×#4111yescharacteristic
532C2×C32D3×#4111yescharacteristic
533C3×D3—41no—
534C3×D3—62no—
535C3×D3—62no—
536C2×C9—21no—
537C2×C9—21no—
538C2×C9—21no—
539C2×C9—41no—
540C2×C9—81no—
541C2×C9—121no—
542C2×C9C2×#23511yescharacteristic
543C2×C9C2×#23711yescharacteristic
544C2×C9#100411yescharacteristic
545D9—22no—
546D9—22no—
547C24—91no—
548C2×Q8—31no—
549C2×D4—31no—
550C2×D4—271no—
551C2×D4—271no—
552C22×C4—91no—
553C22×C4—91no—
554C22×C4—271no—
555C22×C4—271no—
556C22×C4—271no—
557C4⋊C4—271no—
558C4⋊C4—271no—
559C4⋊C4—271no—
560C4⋊C4—271no—
561C4⋊C4—271no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C22⋊C4—31no—
566C22⋊C4—31no—
567C22⋊C4—31no—
568C22⋊C4—91no—
569C22⋊C4—91no—
570C22⋊C4—91no—
571C22⋊C4—271no—
572C22⋊C4—271no—
573C22⋊C4—271no—
574C22⋊C4—271no—
575C22⋊C4—271no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4D3×D911yescharacteristic
579C42—31no—
580C42—271no—
581C42—271no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—21no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—61no—
593C22×C3—61no—
594C22×C3—61no—
595C22×C3—92no—
596C22×C3—92no—
597C22×C3—181no—
598C22×C3—181no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3—364no—
602C22×C3C23×D911yescharacteristic
603C22×C3C22×D3211yescharacteristic
604C2×D3—21no—
605C2×D3—21no—
606C2×D3—21no—
607C2×D3—32no—
608C2×D3—32no—
609C2×D3—61no—
610C2×D3—61no—
611C2×D3—61no—
612C2×D3—61no—
613C2×D3—124no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—61no—
621C3×C4—61no—
622C3×C4—61no—
623C3×C4—181no—
624C3×C4—181no—
625Dic3—21no—
626Dic3—21no—
627Dic3—21no—
628Dic3—61no—
629Dic3—61no—
630Dic3—181no—
631Dic3—181no—
632Dic3—181no—
633Dic3—181no—
634Dic3—181no—
635Dic3—181no—
636Dic3—181no—
637Dic3—181no—
638Dic3—361no—
639Dic3—361no—
640Dic3—361no—
641Dic3—361no—
642C32#567911yescharacteristic
643C9—21no—
644C9#549511yescharacteristic, complemented
645C23—31no—
646C23—91no—
647C23—91no—
648C23—182no—
649C23—182no—
650C23—361no—
651C23C2×D3×D911yescharacteristic
652Q8—121no—
653D4—121no—
654D4—542no—
655D4—542no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—91no—
660C2×C4—91no—
661C2×C4—182no—
662C2×C4—271no—
663C2×C4—271no—
664C2×C4—271no—
665C2×C4—271no—
666C2×C4—361no—
667C2×C4—542no—
668C2×C4—1081no—
669C2×C4—1081no—
670C2×C4C2×D3×D911yescharacteristic
671C2×C4C2×D3×D911yescharacteristic
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—41no—
676C2×C3—41no—
677C2×C3—81no—
678C2×C3—121no—
679C2×C3—182no—
680C2×C3—182no—
681C2×C3#6371011yescharacteristic
682C2×C3#41×D911yescharacteristic
683C2×C3#41×D911yescharacteristic
684C2×C3D3×#23511yescharacteristic
685C2×C3D3×#23711yescharacteristic
686C2×C3#6431311yescharacteristic
687D3—41no—
688D3—62no—
689D3—62no—
690C22—21no—
691C22—21no—
692C22—21no—
693C22—61no—
694C22—61no—
695C22—61no—
696C22—92no—
697C22—92no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—181no—
702C22—364no—
703C22C22×D3×D911yescharacteristic
704C4—21no—
705C4—21no—
706C4—61no—
707C4—61no—
708C4—61no—
709C4—181no—
710C4—181no—
711C4—541no—
712C4—541no—
713C4—541no—
714C4—541no—
715C3—21no—
716C3#1058978111yescharacteristic, complemented
717C3#1059409211yescharacteristic
718C2—41no—
719C2—121no—
720C2—182no—
721C2—182no—
722C2D9×#23511yescharacteristic
723C2D9×#23711yescharacteristic
724C2#1172249911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radical#11721285C2
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#551
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721725C2semidirect
2. C9×#885C2semidirect
3. C3×C22⋊C4×D9C2semidirect
5. #11721280C2semidirect
6. D9×#217C2semidirect
7. #11721246C2semidirect
8. #11721031C2semidirect
9. #11721028C2semidirect
10. #11721012C2semidirect
11. #11720989C2semidirect
12. #11720984C2semidirect
13. #11720974C2semidirect
14. #11720944C2semidirect
15. #11720943C2semidirect
22. C2×C9×Dic6C22semidirect
25. C2×D3×Dic9C22semidirect
31. C4⋊(C3⋊Dic9)C22semidirect
32. #88534C22semidirect
33. #88534C22semidirect
34. C4×C3⋊Dic9C22semidirect
37. C9×(C2×D3)⋊C4C22semidirect
38. C9×(C2×D3)⋊C4C22semidirect
41. C4×C9×Dic3C22semidirect
42. (C2×D3)⋊Dic9C22semidirect
47. Dic3⋊Dic9C22semidirect
48. #88442C22semidirect
49. #88442C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
78. C22⋊C4×D9D3semidirect
228. #885D9semidirect
334. C2×Dic6C2×D9semidirect
365. (C2×D3)⋊C4C2×D9semidirect
366. (C2×D3)⋊C4C2×D9semidirect
391. C4×Dic3C2×D9semidirect
467. C3×C9#551semidirect
644. C9#5495semidirect
716. C3#10589781semidirect

Maximal subgroups

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

subgroupindex
#117217252
C9×#8852
C3×C22⋊C4×D92
#117212852
#117212802
D9×#2172
#117212462
#117210312
#117210282
#117210122
#117209892
#117209842
#117209742
#117209442
#117209432
#105940923
#105897813