Finite Group Databasebeta

← #13148064

Subgroups — #13148064

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
2C3×#63444C211yesmaximal, characteristic
3C9×#879C211yesmaximal, characteristic, complemented
4#11721269C211yesmaximal, characteristic, complemented
5D9×#217C211yesmaximal, characteristic, complemented
6D9×#217C211yesmaximal, characteristic, complemented
7#11721257C211yesmaximal, characteristic, complemented
8#11720999C211yesmaximal, characteristic, complemented
9#11720998C211yesmaximal, characteristic, complemented
10#11720991C211yesmaximal, characteristic, complemented
11Dic3×D36C211yesmaximal, characteristic, complemented
12#11720981C211yesmaximal, characteristic, complemented
13#11720981C211yesmaximal, characteristic, complemented
14#11720975C211yesmaximal, characteristic, complemented
15#11720974C211yesmaximal, characteristic, complemented
16#10594115—31nomaximal
17#10589807—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C2×C3×#611C2211yescharacteristic
20C2×C3×D36C2211yescharacteristic
21C2×C3×D36C2211yescharacteristic
22C2×Dic3×D9C2211yescharacteristic
23C2×Dic3×D9C2211yescharacteristic
24C2×Dic3×D9C2211yescharacteristic
25C2×Dic3×D9C2211yescharacteristic
26C2×Dic3×D9C2211yescharacteristic, complemented
27C2×#6189C2211yescharacteristic, complemented
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
36C9×#217C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C3×(C2×D9)⋊C4C2211yescharacteristic
39C9×C4⋊Dic3C2211yescharacteristic, complemented
40C9×Dic3⋊C4C2211yescharacteristic, complemented
41C9×Dic3⋊C4C2211yescharacteristic, complemented
42C4×C9×Dic3C2211yescharacteristic, complemented
43(C2×D9)⋊Dic3C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64088—31no—
54C3×#882—31no—
55C3×#879D311yescharacteristic
56#63969—31no—
57D3×#217—31no—
58D3×#217—31no—
59#63959—31no—
60#63899—31no—
61#63898—31no—
62#63893—31no—
63Dic3×D12—31no—
64#63884—31no—
65#63884—31no—
66#63878—31no—
67#63877—31no—
68C9×#126—31no—
69#63459—31no—
70#63458—31no—
71#63456—31no—
72#63456—31no—
73#63455—31no—
74#63454—31no—
75#63447—31no—
76#63445—31no—
77#63444D311yescharacteristic
78C22⋊C4×D9—31no—
79C22⋊C4×D9—31no—
80#63441—31no—
81#63441—61no—
82C4×D36—31no—
83#63434—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3×D9—22no—
86C22×C3×D9—22no—
87C22×C3×D9—41no—
88C22×C3×D9C2311yescharacteristic
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
97C3×#611—41no—
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C3×D36—22no—
104C3×D36—22no—
105Dic3×D9—22no—
106Dic3×D9—22no—
107Dic3×D9—41no—
108Dic3×D9—41no—
109Dic3×D9—41no—
110#6189—41no—
111#5705—91no—
112#5587—91no—
113C23×C3×D3—31no—
114C2×C3×#67—31no—
115C2×C3×D12—31no—
116C2×C3×D12—31no—
117C2×#627—31no—
118C2×D3×Dic3—31no—
119C2×D3×Dic3—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×#217C2×D311yescharacteristic
132C3×#217C2×D311yescharacteristic
133C3×(C2×D3)⋊C4—31no—
134C3×(C2×D3)⋊C4—31no—
135C3×C4⋊Dic3C2×D311yescharacteristic
136C3×Dic3⋊C4C2×D311yescharacteristic
137C3×Dic3⋊C4C2×D311yescharacteristic
138C3×C4×Dic3C2×D311yescharacteristic
139#3724—31no—
140Dic3⋊Dic3—31no—
141(C2×D3)⋊Dic3—31no—
142(C2×D3)⋊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×#611C2×D311yescharacteristic
150C2×D36C2×D311yescharacteristic
151C2×D36C2×D311yescharacteristic
152C2×C4×D9—31no—
153C2×C4×D9—31no—
154C2×C4×D9—31no—
155C2×C4×D9—31no—
156C2×C4×D9—31no—
157C2×Dic18—31no—
158C9×C4⋊C4—31no—
159C9×C4⋊C4—31no—
160C9×C4⋊C4—31no—
161C9×C22⋊C4—21no—
162C9×C22⋊C4—31no—
163C9×C22⋊C4—31no—
164C9×C22⋊C4C2×D311yescharacteristic
165C42×C9—31no—
166#3676—31no—
167#3676—31no—
168#3676—61no—
169#3676—61no—
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)⋊C4C2×D311yescharacteristic
178(C2×D9)⋊C4C2×D311yescharacteristic
179C4⋊Dic9—31no—
180C4⋊Dic9—31no—
181C4⋊Dic9—61no—
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×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—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—
213C9×Dic3—21no—
214C3×Dic9—21no—
215C3×#126—31no—
216C3×#120—91no—
217C2×#217—91no—
218C2×#217—91no—
219#936—91no—
220#935—91no—
221#935—91no—
222#935—91no—
223D4×Dic3—91no—
224D4×Dic3—91no—
225#897—91no—
226#896—91no—
227#894—91no—
228#894—91no—
229#893—91no—
230#892—91no—
231#885—91no—
232#883—91no—
233#882—31no—
234D3×C22⋊C4—91no—
235D3×C22⋊C4—91no—
236#879—91no—
237#879—91no—
238#879—181no—
239#879D911yescharacteristic, complemented
240#878—91no—
241#878—91no—
242#877—91no—
243#877—91no—
244C4×D12—91no—
245#872—91no—
246C23×C32C22×D311yescharacteristic
247C22×C3×D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3—31no—
250C22×C3×D3—62no—
251C22×C3×D3—62no—
252C22×C3×D3—121no—
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—121no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3C22×D311yescharacteristic
262C2×C3×Dic3C22×D311yescharacteristic
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C3×D12—62no—
266C3×D12—62no—
267#627—121no—
268D3×Dic3—62no—
269D3×Dic3—62no—
270D3×Dic3—121no—
271D3×Dic3—121no—
272D3×Dic3—121no—
273C23×C9—21no—
274C23×C9C22×D311yescharacteristic
275C22×D9—22no—
276C22×D9—22no—
277C22×D9—41no—
278C22×D9C22×D311yescharacteristic
279C22×D9C22×D311yescharacteristic
280C22×D9C22×D311yescharacteristic
281C2×C4×C9—21no—
282C2×C4×C9—21no—
283C2×C4×C9—31no—
284C2×C4×C9—31no—
285C2×C4×C9—31no—
286C2×C4×C9—31no—
287C2×C4×C9C22×D311yescharacteristic
288C2×C4×C9C22×D311yescharacteristic
289#611—41no—
290C2×Dic9—31no—
291C2×Dic9—31no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—61no—
295C2×Dic9—61no—
296C2×Dic9—61no—
297C2×Dic9—61no—
298C2×Dic9C22×D311yescharacteristic
299D36—22no—
300D36—22no—
301C4×D9—62no—
302C4×D9—62no—
303C4×D9—121no—
304C4×D9—121no—
305C4×D9—121no—
306Dic18—121no—
307#551—271noSylow
308C2×C3×C9—41no—
309C2×C3×C9C2×#4111yescharacteristic
310C2×C3×C9C2×#4111yescharacteristic
311C2×C3×C9H(5,𝔽2)11yescharacteristic
312C3×D9—22no—
313C3×D9—22no—
314C3×D9—41no—
315C24×C3—91no—
316C23×D3—31no—
317C2×C3×D4—91no—
318C2×C3×D4—91no—
319C2×C3×D4—91no—
320C2×#67—31no—
321C22×Dic3—91no—
322C22×Dic3—91no—
323C22×Dic3—91no—
324C22×Dic3—91no—
325C22×Dic3—91no—
326C2×D12—31no—
327C2×D12—31no—
328C2×C4×D3—91no—
329C2×C4×D3—91no—
330C2×C4×D3—91no—
331C2×C4×D3—91no—
332C2×C4×D3—91no—
333C2×Dic6—91no—
334C2×Dic6—91no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—31no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—91no—
342C3×C22⋊C4—91no—
343C3×C22⋊C4C2×D911yescharacteristic
344C3×C22⋊C4D3211yescharacteristic
345C3×C42—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—91no—
356#217—91no—
357#217—181no—
358#217—181no—
359#217C2×D911yescharacteristic
360#217C2×D911yescharacteristic
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
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—
370C4⋊Dic3—91no—
371C4⋊Dic3—91no—
372C4⋊Dic3—91no—
373C4⋊Dic3—181no—
374C4⋊Dic3C2×D911yescharacteristic, complemented
375Dic3⋊C4—91no—
376Dic3⋊C4—91no—
377Dic3⋊C4—91no—
378Dic3⋊C4—91no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—181no—
383Dic3⋊C4—181no—
384Dic3⋊C4C2×D911yescharacteristic, complemented
385Dic3⋊C4C2×D911yescharacteristic, complemented
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—32no—
397C2×C3×D3—32no—
398C2×C3×D3—61no—
399C2×C3×D3—61no—
400C2×C3×D3—61no—
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—21no—
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×C9C23×D311yescharacteristic
425C2×D9—21no—
426C2×D9—21no—
427C2×D9—21no—
428C2×D9—21no—
429C2×D9—21no—
430C2×D9—21no—
431C2×D9—21no—
432C2×D9—44no—
433C2×D9#23712yes—
434C2×D9#23712yes—
435C4×C9—21no—
436C4×C9—21no—
437C4×C9—41no—
438C4×C9—41no—
439C4×C9—61no—
440C4×C9—61no—
441C4×C9—61no—
442C4×C9—61no—
443Dic9—21no—
444Dic9—61no—
445Dic9—61no—
446Dic9—61no—
447Dic9—61no—
448Dic9—121no—
449Dic9—121no—
450Dic9—121no—
451Dic9—121no—
452#126—31no—
453#126—271no—
454#124—271no—
455#123—271no—
456#123—271no—
457#123—271no—
458C22⋊Q8—271no—
459C22⋊Q8—271no—
460#120—91no—
461C4×D4—271no—
462C4×D4—271no—
463#117—271no—
464#117—271no—
465C2×C22⋊C4—271no—
466C2×C22⋊C4—271no—
467C3×C9#55111yescharacteristic, complemented, Sylow
468C23×C3—21no—
469C23×C3—91no—
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—31no—
480C22×D3—62no—
481C22×D3—62no—
482C22×D3—121no—
483C3×D4—182no—
484C3×D4—182no—
485C3×D4—361no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—91no—
493C2×C3×C4C22×D911yescharacteristic
494C2×C3×C4C22×D911yescharacteristic
495C2×C3×C4C2×D3211yescharacteristic
496C2×C3×C4C2×D3211yescharacteristic
497#67—121no—
498C2×Dic3—31no—
499C2×Dic3—91no—
500C2×Dic3—91no—
501C2×Dic3—91no—
502C2×Dic3—91no—
503C2×Dic3—91no—
504C2×Dic3—91no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—181no—
508C2×Dic3—181no—
509C2×Dic3—181no—
510C2×Dic3—181no—
511C2×Dic3—182no—
512C2×Dic3—182no—
513C2×Dic3—361no—
514C2×Dic3—361no—
515C2×Dic3—361no—
516C2×Dic3C22×D911yescharacteristic
517C2×Dic3C22×D911yescharacteristic
518C2×Dic3C22×D911yescharacteristic
519C2×Dic3C22×D911yescharacteristic
520D12—62no—
521D12—62no—
522C4×D3—182no—
523C4×D3—182no—
524C4×D3—361no—
525C4×D3—361no—
526C4×D3—361no—
527Dic6—361no—
528Dic6—361no—
529C2×C32—41no—
530C2×C32D3×#4111yescharacteristic
531C2×C32D3×#4111yescharacteristic
532C2×C32#100911yescharacteristic
533C3×D3—62no—
534C3×D3—62no—
535C3×D3—121no—
536C2×C9—21no—
537C2×C9—21no—
538C2×C9—21no—
539C2×C9—41no—
540C2×C9—81no—
541C2×C9C2×#23711yescharacteristic
542C2×C9C2×#23711yescharacteristic
543C2×C9#100411yescharacteristic
544D9—22no—
545D9—22no—
546D9—41no—
547C24—91no—
548C2×Q8—271no—
549C2×D4—91no—
550C2×D4—91no—
551C2×D4—91no—
552C22×C4—271no—
553C22×C4—271no—
554C22×C4—271no—
555C22×C4—271no—
556C22×C4—271no—
557C4⋊C4—31no—
558C4⋊C4—31no—
559C4⋊C4—31no—
560C4⋊C4—271no—
561C4⋊C4—271no—
562C4⋊C4—271no—
563C4⋊C4—271no—
564C4⋊C4—271no—
565C22⋊C4—31no—
566C22⋊C4—31no—
567C22⋊C4—91no—
568C22⋊C4—91no—
569C22⋊C4—271no—
570C22⋊C4—271no—
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—92no—
593C22×C3—92no—
594C22×C3—181no—
595C22×C3—181no—
596C22×C3—181no—
597C22×C3—181no—
598C22×C3—181no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3—364no—
602C22×C3C23×D911yescharacteristic
603C22×C3C22×D3211yescharacteristic
604C2×D3—32no—
605C2×D3—32no—
606C2×D3—61no—
607C2×D3—61no—
608C2×D3—61no—
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—61no—
624C3×C4—181no—
625Dic3—21no—
626Dic3—21no—
627Dic3—21no—
628Dic3—21no—
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#570511yescharacteristic
643C9—21no—
644C9#558711yescharacteristic, complemented
645C23—91no—
646C23—91no—
647C23—91no—
648C23—182no—
649C23—182no—
650C23—361no—
651C23C2×D3×D911yescharacteristic
652Q8—1081no—
653D4—182no—
654D4—182no—
655D4—361no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—31no—
660C2×C4—91no—
661C2×C4—271no—
662C2×C4—271no—
663C2×C4—271no—
664C2×C4—271no—
665C2×C4—542no—
666C2×C4—542no—
667C2×C4—1081no—
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—182no—
679C2×C3—182no—
680C2×C3—361no—
681C2×C3#41×D911yescharacteristic
682C2×C3#41×D911yescharacteristic
683C2×C3#6371511yescharacteristic
684C2×C3#6430711yescharacteristic
685C2×C3D3×#23711yescharacteristic
686C2×C3D3×#23711yescharacteristic
687D3—62no—
688D3—62no—
689D3—121no—
690C22—21no—
691C22—21no—
692C22—21no—
693C22—92no—
694C22—92no—
695C22—181no—
696C22—181no—
697C22—181no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—181no—
702C22—364no—
703C22C22×D3×D911yescharacteristic
704C4—21no—
705C4—21no—
706C4—61no—
707C4—61no—
708C4—61no—
709C4—61no—
710C4—181no—
711C4—541no—
712C4—541no—
713C4—541no—
714C4—541no—
715C3—21no—
716C3#1058980711yescharacteristic, complemented
717C3#1059411511yescharacteristic
718C2—41no—
719C2—182no—
720C2—182no—
721C2—361no—
722C2#1172247711yescharacteristic
723C2D9×#23711yescharacteristic
724C2D9×#23711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC3×#63444C2
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
3. C9×#879C2semidirect
4. #11721269C2semidirect
5. D9×#217C2semidirect
6. D9×#217C2semidirect
7. #11721257C2semidirect
8. #11720999C2semidirect
9. #11720998C2semidirect
10. #11720991C2semidirect
11. Dic3×D36C2semidirect
12. #11720981C2semidirect
13. #11720981C2semidirect
14. #11720975C2semidirect
15. #11720974C2semidirect
26. C2×Dic3×D9C22semidirect
27. C2×#6189C22semidirect
31. C4⋊(C3⋊Dic9)C22semidirect
32. #88534C22semidirect
33. #88534C22semidirect
34. C4×C3⋊Dic9C22semidirect
39. C9×C4⋊Dic3C22semidirect
40. C9×Dic3⋊C4C22semidirect
41. C9×Dic3⋊C4C22semidirect
42. C4×C9×Dic3C22semidirect
47. (C2×D9)⋊Dic3C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic3×Dic9C22semidirect
239. #879D9semidirect
374. C4⋊Dic3C2×D9semidirect
384. Dic3⋊C4C2×D9semidirect
385. Dic3⋊C4C2×D9semidirect
391. C4×Dic3C2×D9semidirect
467. C3×C9#551semidirect
644. C9#5587semidirect
716. C3#10589807semidirect

Maximal subgroups

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

subgroupindex
#117217252
C3×#634442
C9×#8792
#117212692
D9×#2172
#117212572
#117209992
#117209982
#117209912
Dic3×D362
#117209812
#117209752
#117209742
#105941153
#105898073