Finite Group Databasebeta

← #13148358

Subgroups — #13148358

Order 1728.

808 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721727C211yesmaximal, characteristic, complemented
2C9×#67⋊C4C211yesmaximal, characteristic, complemented
3C3×#611⋊C4C211yesmaximal, characteristic, complemented
4#11721290C211yesmaximal, characteristic, complemented
5#11721288C211yesmaximal, characteristic, complemented
6#11721277C211yesmaximal, characteristic, complemented
7C2×#88442C211yesmaximal, characteristic, complemented
8#11721041C211yesmaximal, characteristic, complemented
9C4×#6194C211yesmaximal, characteristic, complemented
10#11720963C211yesmaximal, characteristic, complemented
11#11720954C211yesmaximal, characteristic, complemented
12#11720947C211yesmaximal, characteristic, complemented
13#11720938C211yesmaximal, characteristic, complemented
14#11720931C211yesmaximal, characteristic, complemented
15#11720928C211yesmaximal, characteristic, complemented
16#10594231—31nomaximal
17#10589642—31nomaximal
18C2×#6233C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic
25C2×C4×D3×C9C2211yescharacteristic
26C2×C3×C4×D9C2211yescharacteristic
27C2×#6195C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C3×C9×C22⋊C4C2211yescharacteristic
31#88536C2211yescharacteristic
32#88534C2211yescharacteristic
33C4×C3⋊Dic9C2211yescharacteristic
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C3×(C2×D9)⋊C4C2211yescharacteristic
36C9×Dic3⋊C4C2211yescharacteristic
37C4×C9×Dic3C2211yescharacteristic
38C3×Dic9⋊C4C2211yescharacteristic
39C3×C4×Dic9C2211yescharacteristic
40(C2×D3)⋊Dic9C2211yescharacteristic
41(C2×D3)⋊Dic9C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46Dic3⋊Dic9C2211yescharacteristic
47#88442C2211yescharacteristic
48#88442C2211yescharacteristic
49#88442C2211yescharacteristic
50#88442C2211yescharacteristic
51#88442C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53#64090—31no—
54C3×#67⋊C4—31no—
55C3×#67⋊C4D311yescharacteristic
56#63980—31no—
57#63978—31no—
58#63978—31no—
59C2×#3724—31no—
60#63912—31no—
61C4×#625—31no—
62#63874—31no—
63#63870—31no—
64#63859—31no—
65#63859—31no—
66#63850—31no—
67#63850—31no—
68C4×D4×C9—31no—
69#63501—31no—
70#63501—31no—
71#63492—31no—
72#63491—31no—
73C4×#611—31no—
74C2×Dic9⋊C4—31no—
75#63456—31no—
76#63451—31no—
77#63446—31no—
78#611⋊C4—31no—
79#611⋊C4—61no—
80#611⋊C4D311yescharacteristic, complemented
81#63441—31no—
82#63438—31no—
83#63434—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90#6233—22no—
91C2×C3⋊Dic9—22no—
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C4×C3⋊D9—22no—
96C9×#67—22no—
97C3×#611—22no—
98C2×C9×Dic3—41no—
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C3×Dic9—41no—
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C4×D3×C9—41no—
107C3×C4×D9—41no—
108#6195—41no—
109#6194—22no—
110#6192—41no—
111#5540—91no—
112#5540—91no—
113C2×#638—31no—
114C22×C3⋊Dic3—31no—
115C2×C4×C3⋊D3—31no—
116C2×C3×#67—31no—
117C2×C3×#67C2×D311yescharacteristic
118C22×C3×Dic3—31no—
119C22×C3×Dic3C2×D311yescharacteristic
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3C2×D311yescharacteristic
122C2×#626—31no—
123C2×#626—31no—
124C2×#625—31no—
125C32×C22⋊C4C2×D311yescharacteristic
126#3752—31no—
127#3750—31no—
128C4×C3⋊Dic3—31no—
129C3×(C2×D3)⋊C4—31no—
130C3×(C2×D3)⋊C4C2×D311yescharacteristic
131C3×Dic3⋊C4—31no—
132C3×Dic3⋊C4C2×D311yescharacteristic
133C3×C4×Dic3—31no—
134C3×C4×Dic3C2×D311yescharacteristic
135#3724—31no—
136#3724—31no—
137#3724—31no—
138#3724—31no—
139#3724—31no—
140Dic3⋊Dic3—31no—
141Dic3⋊Dic3—31no—
142#3722—31no—
143#3722—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148C2×D4×C9—31no—
149C22×C4×C9—31no—
150C22×C4×C9—31no—
151C2×#611—31no—
152C2×#611—31no—
153C2×#611—31no—
154C2×#611—61no—
155C2×#611C2×D311yescharacteristic
156C22×Dic9—31no—
157C22×Dic9—61no—
158C22×Dic9C2×D311yescharacteristic
159C2×D36—31no—
160C2×C4×D9—31no—
161C2×C4×D9—61no—
162C2×C4×D9C2×D311yescharacteristic
163C9×C4⋊C4—31no—
164C9×C22⋊C4—21no—
165C9×C22⋊C4—31no—
166C9×C22⋊C4C2×D311yescharacteristic
167C42×C9—31no—
168#3676—31no—
169#3676—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—61no—
176(C2×D9)⋊C4C2×D311yescharacteristic
177C4⋊Dic9—31no—
178Dic9⋊C4—31no—
179Dic9⋊C4—31no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—61no—
186Dic9⋊C4C2×D311yescharacteristic
187C4×Dic9—31no—
188C4×Dic9—61no—
189C4×Dic9C2×D311yescharacteristic
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9#4112yes—
193C22×C3×C9C2411yescharacteristic
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
197C2×D3×C9—21no—
198C2×D3×C9—21no—
199C2×D3×C9—21no—
200C2×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9—21no—
203C3×C4×C9—21no—
204C3×C4×C9—21no—
205C3⋊Dic9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9#4112yes—
208C9×Dic3—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C3×Dic9—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×C4×D4—31no—
215C3×C4×D4—91no—
216#939—91no—
217#939—91no—
218#939—91no—
219#939—91no—
220#930—91no—
221#930—91no—
222#929—91no—
223#929—91no—
224C4×#67—91no—
225C4×#67—91no—
226C2×Dic3⋊C4—91no—
227C2×Dic3⋊C4—91no—
228#894—91no—
229#894—91no—
230#889—91no—
231#889—91no—
232#884—91no—
233#884—91no—
234#67⋊C4—31no—
235#67⋊C4—91no—
236#67⋊C4—91no—
237#67⋊C4—181no—
238#67⋊C4D911yescharacteristic, complemented
239#879—91no—
240#879—91no—
241#876—91no—
242#876—91no—
243#872—91no—
244#872—91no—
245C23×C32C22×D311yescharacteristic
246C22×C3⋊D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251#638—62no—
252C2×C3⋊Dic3—31no—
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—62no—
256C4×C3⋊D3—62no—
257C3×#67—22no—
258C3×#67—62no—
259C2×C3×Dic3—31no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—41no—
263C2×C3×Dic3—121no—
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C2×C3×Dic3C22×D311yescharacteristic
267C3×C4×D3—41no—
268C3×C4×D3—121no—
269#626—121no—
270#626—121no—
271#625—62no—
272C23×C9—21no—
273C23×C9—31no—
274C23×C9C22×D311yescharacteristic
275C22×D9—31no—
276C22×D9—61no—
277C22×D9C22×D311yescharacteristic
278D4×C9—62no—
279C2×C4×C9—21no—
280C2×C4×C9—21no—
281C2×C4×C9—31no—
282C2×C4×C9—31no—
283C2×C4×C9—31no—
284C2×C4×C9—121no—
285C2×C4×C9—121no—
286C2×C4×C9C22×D311yescharacteristic
287C2×C4×C9C22×D311yescharacteristic
288#611—22no—
289#611—62no—
290#611—64no—
291#611—62no—
292#611—121no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—31no—
296C2×Dic9—41no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—62no—
301C2×Dic9—122no—
302C2×Dic9C22×D311yescharacteristic
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305D36—121no—
306C4×D9—41no—
307C4×D9—62no—
308C4×D9—122no—
309#553—271noSylow
310C2×C3×C9—22no—
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9H(5,𝔽2)11yescharacteristic
314C3⋊D9—41no—
315D3×C9—41no—
316C3×D9—41no—
317C2×C3×D4—31no—
318C2×C3×D4—91no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—91no—
322C22×C3×C4—91no—
323C2×#67—31no—
324C2×#67—91no—
325C2×#67—91no—
326C2×#67—91no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—91no—
330C2×#67—181no—
331C2×#67C2×D911yescharacteristic
332C22×Dic3—31no—
333C22×Dic3—91no—
334C22×Dic3—91no—
335C22×Dic3—181no—
336C22×Dic3C2×D911yescharacteristic
337C2×D12—91no—
338C2×D12—91no—
339C2×C4×D3—31no—
340C2×C4×D3—91no—
341C2×C4×D3—91no—
342C2×C4×D3—181no—
343C2×C4×D3C2×D911yescharacteristic
344C3×C4⋊C4—31no—
345C3×C4⋊C4—91no—
346C3×C22⋊C4—21no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—91no—
349C3×C22⋊C4C2×D911yescharacteristic
350C3×C22⋊C4D3211yescharacteristic
351C3×C42—31no—
352C3×C42—91no—
353#217—91no—
354#217—91no—
355#217—91no—
356#217—91no—
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—181no—
369(C2×D3)⋊C4C2×D911yescharacteristic
370C4⋊Dic3—91no—
371C4⋊Dic3—91no—
372Dic3⋊C4—31no—
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—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—181no—
388Dic3⋊C4C2×D911yescharacteristic
389C4×Dic3—31no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—181no—
393C4×Dic3C2×D911yescharacteristic
394C22×C32—21no—
395C22×C32—21no—
396C22×C32#23512yes—
397C22×C32C23×D311yescharacteristic
398C2×C3⋊D3—61no—
399C2×C3⋊D3—61no—
400C2×C3⋊D3—61no—
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C2×C3×D3—61no—
407C32×C4—21no—
408C32×C4—21no—
409C3⋊Dic3—32no—
410C3⋊Dic3—61no—
411C3⋊Dic3—61no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—61no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C22×C9—21no—
419C22×C9—21no—
420C22×C9—21no—
421C22×C9—22no—
422C22×C9—41no—
423C22×C9—41no—
424C22×C9—61no—
425C22×C9—61no—
426C22×C9—61no—
427C22×C9#23512yes—
428C22×C9C23×D311yescharacteristic
429C2×D9—21no—
430C2×D9—21no—
431C2×D9—21no—
432C2×D9—62no—
433C2×D9—61no—
434C2×D9—61no—
435C2×D9—61no—
436C2×D9—121no—
437C2×D9—121no—
438C4×C9—21no—
439C4×C9—21no—
440C4×C9—41no—
441C4×C9—41no—
442C4×C9—61no—
443C4×C9—61no—
444C4×C9—61no—
445Dic9—21no—
446Dic9—21no—
447Dic9—21no—
448Dic9—32no—
449Dic9—62no—
450Dic9—62no—
451Dic9—61no—
452Dic9—61no—
453Dic9—121no—
454#126—271no—
455#126—271no—
456#125—271no—
457#123—271no—
458#123—271no—
459#121—271no—
460#121—271no—
461#121—271no—
462#121—271no—
463C4×D4—31no—
464C4×D4—91no—
465C4×D4—271no—
466C4×D4—271no—
467#117—271no—
468C2×C4⋊C4—271no—
469C3×C9#55311yescharacteristic, complemented, Sylow
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—91no—
473C23×C3C22×D911yescharacteristic
474C23×C3C2×D3211yescharacteristic
475C22×D3—31no—
476C22×D3—91no—
477C22×D3—91no—
478C22×D3—181no—
479C22×D3C22×D911yescharacteristic
480C3×D4—62no—
481C3×D4—182no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—31no—
487C2×C3×C4—91no—
488C2×C3×C4—91no—
489C2×C3×C4—91no—
490C2×C3×C4—121no—
491C2×C3×C4—121no—
492C2×C3×C4—361no—
493C2×C3×C4—361no—
494C2×C3×C4C22×D911yescharacteristic
495C2×C3×C4C22×D911yescharacteristic
496C2×C3×C4C2×D3211yescharacteristic
497C2×C3×C4C2×D3211yescharacteristic
498#67—22no—
499#67—62no—
500#67—182no—
501#67—182no—
502#67—184no—
503#67—182no—
504#67—182no—
505#67—361no—
506#67—361no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—41no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—121no—
518C2×Dic3—181no—
519C2×Dic3—181no—
520C2×Dic3—181no—
521C2×Dic3—182no—
522C2×Dic3—182no—
523C2×Dic3—362no—
524C2×Dic3C22×D911yescharacteristic
525C2×Dic3C22×D911yescharacteristic
526C2×Dic3C22×D911yescharacteristic
527D12—361no—
528D12—361no—
529C4×D3—41no—
530C4×D3—121no—
531C4×D3—182no—
532C4×D3—182no—
533C4×D3—362no—
534C2×C32—22no—
535C2×C32C2×#23511yescharacteristic
536C2×C32#100411yescharacteristic
537C2×C32D3×#4111yescharacteristic
538C3⋊D3—121no—
539C3×D3—41no—
540C3×D3—121no—
541C2×C9—22no—
542C2×C9—21no—
543C2×C9—21no—
544C2×C9—21no—
545C2×C9—42no—
546C2×C9—121no—
547C2×C9C2×#23511yescharacteristic
548C2×C9#100411yescharacteristic
549C2×C9D3×#4111yescharacteristic
550D9—41no—
551D9—122no—
552D9—121no—
553C2×D4—31no—
554C2×D4—91no—
555C2×D4—271no—
556C2×D4—271no—
557C2×D4—271no—
558C2×D4—271no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—91no—
562C22×C4—91no—
563C22×C4—271no—
564C22×C4—271no—
565C4⋊C4—31no—
566C4⋊C4—91no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C4⋊C4—271no—
575C22⋊C4—31no—
576C22⋊C4—91no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4D3×D911yescharacteristic
585C42—31no—
586C42—91no—
587C42—271no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—22no—
593C22×C3—21no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—61no—
597C22×C3—61no—
598C22×C3—61no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3—181no—
602C22×C3#369712yes—
603C22×C3C23×D911yescharacteristic
604C22×C3#379812yes—
605C22×C3C22×D3211yescharacteristic
606C2×D3—21no—
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—61no—
610C2×D3—61no—
611C2×D3—61no—
612C2×D3—182no—
613C2×D3—181no—
614C2×D3—181no—
615C2×D3—181no—
616C2×D3—181no—
617C2×D3—181no—
618C2×D3—181no—
619C2×D3—361no—
620C2×D3—361no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—61no—
630C3×C4—181no—
631C3×C4—181no—
632C3×C4—181no—
633Dic3—21no—
634Dic3—21no—
635Dic3—21no—
636Dic3—61no—
637Dic3—61no—
638Dic3—61no—
639Dic3—92no—
640Dic3—92no—
641Dic3—182no—
642Dic3—182no—
643Dic3—181no—
644Dic3—181no—
645Dic3—181no—
646Dic3—181no—
647Dic3—361no—
648C32#554011yescharacteristic
649C9—21no—
650C9#554011yescharacteristic, complemented
651C23—31no—
652C23—91no—
653C23—271no—
654C23C2×D3×D911yescharacteristic
655D4—62no—
656D4—182no—
657D4—542no—
658D4—542no—
659D4—1081no—
660D4—1081no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—31no—
664C2×C4—91no—
665C2×C4—91no—
666C2×C4—91no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—271no—
670C2×C4—271no—
671C2×C4—271no—
672C2×C4—361no—
673C2×C4—361no—
674C2×C4—542no—
675C2×C4—542no—
676C2×C4C2×D3×D911yescharacteristic
677C2×C4C2×D3×D911yescharacteristic
678C2×C3—22no—
679C2×C3—22no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—42no—
684C2×C3—121no—
685C2×C3—361no—
686C2×C3C2×#369711yescharacteristic
687C2×C3#6371011yescharacteristic
688C2×C3#41×D911yescharacteristic
689C2×C3C2×#379811yescharacteristic
690C2×C3#6431211yescharacteristic
691C2×C3#6431311yescharacteristic
692D3—41no—
693D3—121no—
694D3—362no—
695D3—361no—
696D3—361no—
697C22—21no—
698C22—21no—
699C22—61no—
700C22—61no—
701C22—61no—
702C22—181no—
703C22—181no—
704C22—181no—
705C22—541no—
706C22—541no—
707C22—541no—
708C22#8864012yes—
709C22C22×D3×D911yescharacteristic
710C4—21no—
711C4—21no—
712C4—61no—
713C4—61no—
714C4—61no—
715C4—181no—
716C4—181no—
717C4—181no—
718C4—272no—
719C4—541no—
720C4—541no—
721C3—21no—
722C3#1058964211yescharacteristic, complemented
723C3#1059423111yescharacteristic
724C2—22no—
725C2—121no—
726C2—361no—
727C2—1081no—
728C2C2×#8864011yescharacteristic
729C2#1172249811yescharacteristic
730C2#1172249911yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#553
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. #11721727C2semidirect
2. C9×#67⋊C4C2semidirect
3. C3×#611⋊C4C2semidirect
4. #11721290C2semidirect
5. #11721288C2semidirect
6. #11721277C2semidirect
7. C2×#88442C2semidirect
8. #11721041C2semidirect
9. C4×#6194C2semidirect
10. #11720963C2semidirect
11. #11720954C2semidirect
12. #11720947C2semidirect
13. #11720938C2semidirect
14. #11720931C2semidirect
15. #11720928C2semidirect
80. #611⋊C4D3semidirect
238. #67⋊C4D9semidirect
469. C3×C9#553semidirect
650. C9#5540semidirect
722. C3#10589642semidirect

Maximal subgroups

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

subgroupindex
#117217272
C9×#67⋊C42
C3×#611⋊C42
#117212902
#117212882
#117212772
C2×#884422
#117210412
C4×#61942
#117209632
#117209542
#117209472
#117209382
#117209312
#117209282
#105942313
#105896423