Finite Group Databasebeta

← #13148948

Subgroups — #13148948

Order 1728.

776 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721745C211yesmaximal, characteristic, complemented
2C9×#894C211yesmaximal, characteristic, complemented
3C3×#63457C211yesmaximal, characteristic, complemented
4#11721043C211yesmaximal, characteristic, complemented
5#11721037C211yesmaximal, characteristic, complemented
6#11721031C211yesmaximal, characteristic, complemented
7#11721021C211yesmaximal, characteristic, complemented
8#11721016C211yesmaximal, characteristic, complemented
9#11721012C211yesmaximal, characteristic, complemented
10#11720982C211yesmaximal, characteristic, complemented
11#11720982C211yesmaximal, characteristic, complemented
12#11720982C211yesmaximal, characteristic, complemented
13#11720981C211yesmaximal, characteristic, complemented
14#11720976C211yesmaximal, characteristic, complemented
15#11720975C211yesmaximal, characteristic, complemented
16#10594580—31nomaximal
17#10589765—31nomaximal
18C2×C9×D12C2211yescharacteristic
19C2×C4×D3×C9C2211yescharacteristic
20C2×C3×D36C2211yescharacteristic
21C2×C3×D36C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×C4×D9C2211yescharacteristic
24C2×#6194C2211yescharacteristic
25C2×#6194C2211yescharacteristic
26C2×#6194C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic
30C2×D3×Dic9C2211yescharacteristic
31C2×Dic3×D9C2211yescharacteristic
32C2×Dic3×D9C2211yescharacteristic
33C3×C9×C4⋊C4C2211yescharacteristic
34C4⋊(C3⋊Dic9)C2211yescharacteristic
35#88534C2211yescharacteristic
36#88534C2211yescharacteristic
37#88534C2211yescharacteristic
38#88534C2211yescharacteristic
39C4×C3⋊Dic9C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C9×(C2×D3)⋊C4C2211yescharacteristic
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C3×(C2×D9)⋊C4C2211yescharacteristic
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C9×Dic3⋊C4C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50(C2×D9)⋊Dic3C2211yescharacteristic
51Dic3⋊Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53#64098—31no—
54C3×#895—31no—
55C3×#894D311yescharacteristic
56#63914—31no—
57#63908—31no—
58#63905—31no—
59#63891—31no—
60#63885—31no—
61#63885—31no—
62#63885—31no—
63#63885—31no—
64#63884—31no—
65#63879—31no—
66#63879—31no—
67#63878—31no—
68C9×#123—31no—
69#63502—31no—
70#63501—31no—
71#63492—31no—
72C4×#611—31no—
73#63457D311yescharacteristic, complemented
74#63456—31no—
75#63454—31no—
76#63451—31no—
77#63451—61no—
78#63448—31no—
79#63446—31no—
80#63446—31no—
81#63446—31no—
82#63445—31no—
83#611⋊C4—31no—
84C22×D3×C9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C3×Dic9C2311yescharacteristic
99C9×D12—41no—
100C4×D3×C9—41no—
101C3×D36—41no—
102C3×D36—41no—
103C3×D36—41no—
104C3×C4×D9—41no—
105#6194—22no—
106#6194—22no—
107#6194—41no—
108#6194—41no—
109#6194—41no—
110#6194—41no—
111D3×Dic9—41no—
112Dic3×D9—22no—
113Dic3×D9—41no—
114#5663—91no—
115#5615—91no—
116C2×C3×D12—31no—
117C2×C3×D12—31no—
118C2×C3×D12—31no—
119C2×C3×D12C2×D311yescharacteristic
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3C2×D311yescharacteristic
122C2×#625—31no—
123C2×#625—31no—
124C2×#625—31no—
125C2×#625—31no—
126C2×#625—31no—
127C2×#625—31no—
128C2×D3×Dic3—31no—
129C2×D3×Dic3—31no—
130C2×D3×Dic3—31no—
131C32×C4⋊C4C2×D311yescharacteristic
132C4⋊(C3⋊Dic3)—31no—
133#3750—31no—
134#3750—31no—
135#3750—31no—
136#3750—31no—
137C4×C3⋊Dic3—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4C2×D311yescharacteristic
141C3×(C2×D3)⋊C4C2×D311yescharacteristic
142C3×(C2×D3)⋊C4C2×D311yescharacteristic
143C3×Dic3⋊C4C2×D311yescharacteristic
144Dic3⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150Dic32—31no—
151C2×D4×C9—31no—
152C22×C4×C9—31no—
153C2×#611—31no—
154C2×#611—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×#611—31no—
159C22×Dic9—31no—
160C2×D36C2×D311yescharacteristic
161C2×D36C2×D311yescharacteristic
162C2×D36C2×D311yescharacteristic
163C2×C4×D9—31no—
164C2×C4×D9—31no—
165C2×C4×D9C2×D311yescharacteristic
166C9×C4⋊C4—21no—
167C9×C4⋊C4—31no—
168C9×C4⋊C4C2×D311yescharacteristic
169C9×C22⋊C4—31no—
170C9×C22⋊C4—31no—
171C9×C22⋊C4—31no—
172#3676—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—31no—
186Dic9⋊C4—61no—
187Dic9⋊C4—61no—
188Dic9⋊C4—61no—
189Dic9⋊C4—61no—
190C4×Dic9—31no—
191C4×Dic9—31no—
192C4×Dic9—61no—
193C22×C3×C9C2411yescharacteristic
194C2×D3×C9—21no—
195C2×D3×C9—21no—
196C2×D3×C9—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—
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—
213C3⋊Dic9—21no—
214C3⋊Dic9—21no—
215C3⋊Dic9#4112yes—
216C9×Dic3—21no—
217C9×Dic3—21no—
218C3×Dic9—21no—
219C3×#123—31no—
220C3×#121—91no—
221#940—91no—
222#940—91no—
223#939—91no—
224#939—91no—
225#939—91no—
226#939—91no—
227#938—91no—
228#935—91no—
229#930—91no—
230#929—91no—
231C4×#67—91no—
232C4×#67—91no—
233#895—31no—
234#894—91no—
235#894D911yescharacteristic, complemented
236#892—91no—
237#889—91no—
238#889—91no—
239#889—181no—
240#886—91no—
241#884—91no—
242#884—91no—
243#884—91no—
244#884—91no—
245#883—91no—
246#883—91no—
247#67⋊C4—91no—
248#67⋊C4—91no—
249#877—91no—
250C22×C3×D3—31no—
251C22×C3×D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3C22×D311yescharacteristic
254C22×C3×D3C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C22×D311yescharacteristic
257C2×C32×C4C22×D311yescharacteristic
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—31no—
260C2×C3⋊Dic3—31no—
261C2×C3⋊Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C3×D12—41no—
266C3×D12—121no—
267C3×D12—121no—
268C3×D12—121no—
269C3×C4×D3—41no—
270C3×C4×D3—121no—
271#625—62no—
272#625—62no—
273#625—121no—
274#625—121no—
275#625—121no—
276#625—121no—
277D3×Dic3—62no—
278D3×Dic3—121no—
279D3×Dic3—121no—
280C23×C9—31no—
281C23×C9—31no—
282C22×D9C22×D311yescharacteristic
283C22×D9C22×D311yescharacteristic
284C22×D9C22×D311yescharacteristic
285D4×C9—121no—
286C2×C4×C9—21no—
287C2×C4×C9—21no—
288C2×C4×C9—21no—
289C2×C4×C9—31no—
290C2×C4×C9—31no—
291C2×C4×C9—121no—
292C2×C4×C9C22×D311yescharacteristic
293C2×C4×C9C22×D311yescharacteristic
294C2×C4×C9C22×D311yescharacteristic
295#611—62no—
296#611—62no—
297#611—121no—
298#611—121no—
299#611—121no—
300#611—121no—
301C2×Dic9—31no—
302C2×Dic9—31no—
303C2×Dic9—31no—
304C2×Dic9—31no—
305C2×Dic9—61no—
306C2×Dic9—61no—
307C2×Dic9—61no—
308C2×Dic9—61no—
309C2×Dic9—121no—
310C2×Dic9C22×D311yescharacteristic
311D36—41no—
312D36—41no—
313D36—41no—
314C4×D9—41no—
315C4×D9—62no—
316C4×D9—121no—
317#540—271noSylow
318C2×C3×C9C2×#4111yescharacteristic
319C2×C3×C9H(5,𝔽2)11yescharacteristic
320C2×C3×C9H(5,𝔽2)11yescharacteristic
321D3×C9—41no—
322D3×C9—41no—
323C3×D9—41no—
324C3×D9—41no—
325C3×D9—41no—
326C2×C3×D4—31no—
327C2×C3×D4—91no—
328C2×C3×D4—91no—
329C2×C3×D4—91no—
330C22×C3×C4—31no—
331C22×C3×C4—91no—
332C2×#67—91no—
333C2×#67—91no—
334C2×#67—91no—
335C2×#67—91no—
336C2×#67—91no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C22×Dic3—91no—
345C22×Dic3—91no—
346C22×Dic3—91no—
347C2×D12—31no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12C2×D911yescharacteristic
351C2×C4×D3—31no—
352C2×C4×D3—91no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×C4×D3C2×D911yescharacteristic
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4C2×D911yescharacteristic
359C3×C4⋊C4D3211yescharacteristic
360C3×C22⋊C4—31no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—91no—
364C3×C22⋊C4—91no—
365#217—91no—
366#217—91no—
367#217—91no—
368#217—91no—
369#217—91no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—91no—
377(C2×D3)⋊C4C2×D911yescharacteristic
378(C2×D3)⋊C4C2×D911yescharacteristic
379(C2×D3)⋊C4C2×D911yescharacteristic
380C4⋊Dic3—91no—
381C4⋊Dic3—91no—
382C4⋊Dic3—91no—
383C4⋊Dic3—181no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—181no—
394Dic3⋊C4—181no—
395Dic3⋊C4—181no—
396Dic3⋊C4—181no—
397Dic3⋊C4C2×D911yescharacteristic
398C4×Dic3—91no—
399C4×Dic3—91no—
400C4×Dic3—91no—
401C4×Dic3—91no—
402C4×Dic3—181no—
403C22×C32C23×D311yescharacteristic
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
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—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—21no—
422C3⋊Dic3—32no—
423C3⋊Dic3—61no—
424C3⋊Dic3—61no—
425C3⋊Dic3—61no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—61no—
429C22×C9—21no—
430C22×C9—61no—
431C22×C9—61no—
432C22×C9—61no—
433C22×C9—61no—
434C22×C9—61no—
435C22×C9—61no—
436C22×C9C23×D311yescharacteristic
437C2×D9—21no—
438C2×D9—21no—
439C2×D9—21no—
440C2×D9—21no—
441C2×D9—21no—
442C2×D9—21no—
443C2×D9—21no—
444C2×D9—21no—
445C2×D9—21no—
446C4×C9—21no—
447C4×C9—21no—
448C4×C9—21no—
449C4×C9—41no—
450C4×C9—41no—
451C4×C9—41no—
452C4×C9—61no—
453C4×C9—61no—
454Dic9—21no—
455Dic9—32no—
456Dic9—62no—
457Dic9—61no—
458Dic9—61no—
459Dic9—61no—
460Dic9—121no—
461Dic9—121no—
462Dic9—121no—
463#127—271no—
464#125—271no—
465#123—31no—
466#123—271no—
467#123—271no—
468#123—271no—
469#121—91no—
470#121—271no—
471#121—271no—
472#121—271no—
473#121—271no—
474#121—271no—
475C4×D4—271no—
476C4×D4—271no—
477#117—271no—
478C3×C9#54011yescharacteristic, complemented, Sylow
479C23×C3—31no—
480C23×C3—31no—
481C23×C3—91no—
482C23×C3—91no—
483C23×C3—91no—
484C22×D3—31no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3C22×D911yescharacteristic
488C22×D3C22×D911yescharacteristic
489C3×D4—121no—
490C3×D4—361no—
491C3×D4—361no—
492C3×D4—361no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—91no—
499C2×C3×C4—121no—
500C2×C3×C4—361no—
501C2×C3×C4C22×D911yescharacteristic
502C2×C3×C4C22×D911yescharacteristic
503C2×C3×C4C22×D911yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505C2×C3×C4C2×D3211yescharacteristic
506C2×C3×C4C2×D3211yescharacteristic
507#67—182no—
508#67—182no—
509#67—182no—
510#67—182no—
511#67—361no—
512#67—361no—
513#67—361no—
514#67—361no—
515#67—361no—
516#67—361no—
517#67—361no—
518#67—361no—
519C2×Dic3—31no—
520C2×Dic3—91no—
521C2×Dic3—91no—
522C2×Dic3—91no—
523C2×Dic3—91no—
524C2×Dic3—91no—
525C2×Dic3—91no—
526C2×Dic3—91no—
527C2×Dic3—91no—
528C2×Dic3—181no—
529C2×Dic3—181no—
530C2×Dic3—181no—
531C2×Dic3—181no—
532C2×Dic3—182no—
533C2×Dic3—361no—
534C2×Dic3—361no—
535C2×Dic3C22×D911yescharacteristic
536C2×Dic3C22×D911yescharacteristic
537D12—41no—
538D12—121no—
539D12—121no—
540D12—121no—
541C4×D3—41no—
542C4×D3—121no—
543C4×D3—182no—
544C4×D3—361no—
545C4×D3—361no—
546C2×C32#100411yescharacteristic
547C2×C32D3×#4111yescharacteristic
548C2×C32#100911yescharacteristic
549C3×D3—41no—
550C3×D3—41no—
551C3×D3—121no—
552C3×D3—121no—
553C3×D3—121no—
554C2×C9—21no—
555C2×C9—21no—
556C2×C9—21no—
557C2×C9—121no—
558C2×C9—121no—
559C2×C9#100411yescharacteristic
560C2×C9#100411yescharacteristic
561C2×C9D3×#4111yescharacteristic
562D9—41no—
563D9—41no—
564D9—41no—
565C2×D4—31no—
566C2×D4—91no—
567C2×D4—91no—
568C2×D4—91no—
569C2×D4—271no—
570C2×D4—271no—
571C2×D4—271no—
572C2×D4—271no—
573C2×D4—271no—
574C2×D4—271no—
575C22×C4—31no—
576C22×C4—91no—
577C22×C4—271no—
578C22×C4—271no—
579C22×C4—271no—
580C4⋊C4—31no—
581C4⋊C4—271no—
582C4⋊C4—271no—
583C4⋊C4—271no—
584C4⋊C4—271no—
585C4⋊C4—271no—
586C4⋊C4—271no—
587C4⋊C4D3×D911yescharacteristic
588C22⋊C4—31no—
589C22⋊C4—31no—
590C22⋊C4—31no—
591C22⋊C4—91no—
592C22⋊C4—91no—
593C22⋊C4—271no—
594C22⋊C4—271no—
595C22⋊C4—271no—
596C22⋊C4—271no—
597C22⋊C4—271no—
598C42—271no—
599C42—271no—
600C22×C3—21no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—61no—
604C22×C3—61no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3—181no—
608C22×C3—181no—
609C22×C3—181no—
610C22×C3—181no—
611C22×C3—181no—
612C22×C3—181no—
613C22×C3—181no—
614C22×C3—181no—
615C22×C3—181no—
616C22×C3C23×D911yescharacteristic
617C22×C3C22×D3211yescharacteristic
618C2×D3—21no—
619C2×D3—21no—
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—61no—
625C2×D3—61no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—181no—
645Dic3—21no—
646Dic3—21no—
647Dic3—61no—
648Dic3—92no—
649Dic3—92no—
650Dic3—182no—
651Dic3—181no—
652Dic3—181no—
653Dic3—181no—
654Dic3—181no—
655Dic3—181no—
656Dic3—181no—
657Dic3—361no—
658Dic3—361no—
659Dic3—361no—
660C32#566311yescharacteristic
661C9—21no—
662C9#561511yescharacteristic, complemented
663C23—31no—
664C23—31no—
665C23—91no—
666C23—91no—
667C23—91no—
668D4—121no—
669D4—361no—
670D4—361no—
671D4—361no—
672D4—542no—
673D4—542no—
674D4—1081no—
675D4—1081no—
676D4—1081no—
677D4—1081no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—91no—
681C2×C4—121no—
682C2×C4—271no—
683C2×C4—271no—
684C2×C4—271no—
685C2×C4—271no—
686C2×C4—361no—
687C2×C4—542no—
688C2×C4—1081no—
689C2×C4—1081no—
690C2×C4C2×D3×D911yescharacteristic
691C2×C4C2×D3×D911yescharacteristic
692C2×C4C2×D3×D911yescharacteristic
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—21no—
696C2×C3—121no—
697C2×C3—121no—
698C2×C3—361no—
699C2×C3—361no—
700C2×C3—361no—
701C2×C3#6371011yescharacteristic
702C2×C3#41×D911yescharacteristic
703C2×C3#6371511yescharacteristic
704C2×C3#6430711yescharacteristic
705C2×C3#6431311yescharacteristic
706C2×C3#6431911yescharacteristic
707D3—41no—
708D3—41no—
709D3—121no—
710D3—121no—
711D3—121no—
712C22—61no—
713C22—61no—
714C22—61no—
715C22—61no—
716C22—61no—
717C22—61no—
718C22—181no—
719C22—181no—
720C22—181no—
721C22—181no—
722C22—181no—
723C22—181no—
724C22—181no—
725C22—181no—
726C22—181no—
727C22C22×D3×D911yescharacteristic
728C4—21no—
729C4—21no—
730C4—21no—
731C4—61no—
732C4—61no—
733C4—181no—
734C4—272no—
735C4—541no—
736C4—541no—
737C4—541no—
738C3—21no—
739C3#1058976511yescharacteristic, complemented
740C3#1059458011yescharacteristic
741C2—121no—
742C2—121no—
743C2—361no—
744C2—361no—
745C2—361no—
746C2#1172247711yescharacteristic
747C2#1172249911yescharacteristic
748C2#1172251411yescharacteristic
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. #11721745C2semidirect
2. C9×#894C2semidirect
3. C3×#63457C2semidirect
4. #11721043C2semidirect
5. #11721037C2semidirect
6. #11721031C2semidirect
7. #11721021C2semidirect
8. #11721016C2semidirect
9. #11721012C2semidirect
10. #11720982C2semidirect
11. #11720982C2semidirect
12. #11720982C2semidirect
13. #11720981C2semidirect
14. #11720976C2semidirect
15. #11720975C2semidirect
73. #63457D3semidirect
235. #894D9semidirect
478. C3×C9#540semidirect
662. C9#5615semidirect
739. C3#10589765semidirect

Maximal subgroups

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

subgroupindex
#117217452
C9×#8942
C3×#634572
#117210432
#117210372
#117210312
#117210212
#117210162
#117210122
#117209822
#117209812
#117209762
#117209752
#105945803
#105897653