Finite Group Databasebeta

← #13148440

Subgroups — #13148440

Order 1728.

838 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721727C211yesmaximal, characteristic, complemented
2C9×#885C211yesmaximal, characteristic, complemented
3C3×#63445C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic
5#11721275C211yesmaximal, characteristic, complemented
6#611⋊Dic3C211yesmaximal, characteristic, complemented
7#11721266C211yesmaximal, characteristic, complemented
8#11721048C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11720984C211yesmaximal, characteristic, complemented
11#11720966C211yesmaximal, characteristic, complemented
12#11720962C211yesmaximal, characteristic, complemented
13#11720943C211yesmaximal, characteristic, complemented
14#11720929C211yesmaximal, characteristic, complemented
15#11720898C211yesmaximal, characteristic, complemented
16#10594305—31nomaximal
17#10589781—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic, complemented
21C2×C4×C3⋊D9C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C3×C4×D9C2211yescharacteristic
25C2×C9×Dic6C2211yescharacteristic, complemented
26C2×(C3⋊D9)⋊C4C2211yescharacteristic
27C2×Dic3×D9C2211yescharacteristic
28C3×C9×C22⋊C4C2211yescharacteristic, complemented
29#88536C2211yescharacteristic
30#88534C2211yescharacteristic, complemented
31C4×C3⋊Dic9C2211yescharacteristic, complemented
32C9×#217C2211yescharacteristic, complemented
33C3×#3676C2211yescharacteristic, complemented
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C4×C9×Dic3C2211yescharacteristic, complemented
38C3×C4⋊Dic9C2211yescharacteristic, complemented
39C3×Dic9⋊C4C2211yescharacteristic, complemented
40(C2×D3)⋊Dic9C2211yescharacteristic
41(C2×D3)⋊Dic9C2211yescharacteristic
42(C2×D3)⋊Dic9C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47Dic3⋊Dic9C2211yescharacteristic, complemented
48Dic9⋊Dic3C2211yescharacteristic, complemented
49Dic9⋊Dic3C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64090—31no—
54C3×#885D311yescharacteristic
55C3×#883—31no—
56#63983—31no—
57#63975—31no—
58#67⋊Dic3—31no—
59#63962—31no—
60#63921—31no—
61D3×(C2×D3)⋊C4—31no—
62#63887—31no—
63#63871—31no—
64#63862—31no—
65#63858—31no—
66#63855—31no—
67#63836—31no—
68C9×#124—31no—
69#63508—31no—
70#63508—31no—
71#63499—31no—
72#63497—31no—
73#63445—31no—
74#63445D311yescharacteristic, complemented
75#611⋊C4—31no—
76#611⋊C4—31no—
77#611⋊C4—61no—
78C22⋊C4×D9—31no—
79C22⋊C4×D9—31no—
80#63441—31no—
81#63441—31no—
82#63434—31no—
83#63434—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×D3×D9—22no—
89C2×D3×D9—22no—
90C2×D3×D9—41no—
91C2×C3×C4×C9C2311yescharacteristic
92C2×C3×C4×C9C2311yescharacteristic
93#6233—22no—
94C2×C3⋊Dic9—41no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C4×C3⋊D9—41no—
99C9×#67—41no—
100C3×#611—22no—
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C3×C4×D9—22no—
108C9×Dic6—41no—
109(C3⋊D9)⋊C4—22no—
110Dic3×D9—41no—
111#5679—91no—
112#5658—91no—
113C22×D32—31no—
114C2×#638—31no—
115C22×C3⋊Dic3—31no—
116C2×C4×C3⋊D3—31no—
117C2×C3×#67—31no—
118C2×C3×#67C2×D311yescharacteristic
119C2×C3×C4×D3—31no—
120C2×C3×Dic6C2×D311yescharacteristic
121C2×#624—31no—
122C2×D3×Dic3—31no—
123C23×D9—31no—
124C32×C22⋊C4C2×D311yescharacteristic
125#3752—31no—
126#3750—31no—
127C4×C3⋊Dic3—31no—
128C3×#217—31no—
129C3×#217C2×D311yescharacteristic
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4C2×D311yescharacteristic
132C3×(C2×D3)⋊C4C2×D311yescharacteristic
133C3×C4⋊Dic3—31no—
134C3×Dic3⋊C4—31no—
135C3×C4×Dic3C2×D311yescharacteristic
136Dic3⋊Dic3—31no—
137Dic3⋊Dic3—31no—
138Dic3⋊Dic3—31no—
139Dic3⋊Dic3—31no—
140Dic3⋊Dic3—31no—
141#3722—31no—
142#3722—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—61no—
153C2×#611C2×D311yescharacteristic
154C22×Dic9—31no—
155C22×Dic9—61no—
156C2×C4×D9—31no—
157C2×C4×D9—31no—
158C2×C4×D9—31no—
159C2×C4×D9—61no—
160C2×C4×D9C2×D311yescharacteristic
161C9×C22⋊C4—21no—
162C9×C22⋊C4—31no—
163C9×C22⋊C4—31no—
164C9×C22⋊C4—31no—
165C9×C22⋊C4C2×D311yescharacteristic, complemented
166C42×C9—31no—
167#3676—31no—
168#3676—31no—
169#3676—31no—
170#3676C2×D311yescharacteristic, complemented
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—61no—
177(C2×D9)⋊C4C2×D311yescharacteristic
178C4⋊Dic9—31no—
179C4⋊Dic9C2×D311yescharacteristic, complemented
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—61no—
186Dic9⋊C4C2×D311yescharacteristic, complemented
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#4112yes—
197C2×D3×C9—21no—
198C2×D3×C9—21no—
199C2×D3×C9—21no—
200C2×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9#4112yes—
203D3×D9—44no—
204C3×C4×C9—21no—
205C3×C4×C9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#124—31no—
216C3×#123—91no—
217#946—91no—
218#946—91no—
219#937—91no—
220#937—91no—
221#935—91no—
222D4×Dic3—91no—
223C2×(C2×D3)⋊C4—91no—
224#926—91no—
225#898—91no—
226#898—91no—
227#897—91no—
228#892—91no—
229#886—91no—
230#885D911yescharacteristic, complemented
231#883—31no—
232#883—91no—
233#883—91no—
234#67⋊C4—91no—
235#67⋊C4—91no—
236#67⋊C4—91no—
237#67⋊C4—181no—
238D3×C22⋊C4—91no—
239D3×C22⋊C4—91no—
240D3×C22⋊C4—91no—
241#879—91no—
242#879—91no—
243#878—91no—
244#872—91no—
245#872—91no—
246C23×C32C22×D311yescharacteristic
247C22×C3⋊D3—31no—
248C22×C3×D3—31no—
249C22×C3×D3C22×D311yescharacteristic
250C2×D32—62no—
251C2×D32—62no—
252C2×D32—121no—
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255#638—62no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3⋊Dic3—121no—
260C4×C3⋊D3—121no—
261C3×#67—41no—
262C3×#67—62no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3C22×D311yescharacteristic
267C2×C3×Dic3C22×D311yescharacteristic
268C2×C3×Dic3C22×D311yescharacteristic
269C3×C4×D3—62no—
270C3×Dic6—41no—
271#624—62no—
272D3×Dic3—121no—
273C23×C9—21no—
274C23×C9—31no—
275C23×C9C22×D311yescharacteristic
276C22×D9—31no—
277C22×D9—61no—
278C22×D9—62no—
279C22×D9—62no—
280C22×D9—121no—
281C22×D9C22×D311yescharacteristic
282Q8×C9—121no—
283D4×C9—121no—
284C2×C4×C9—21no—
285C2×C4×C9—21no—
286C2×C4×C9—31no—
287C2×C4×C9—31no—
288C2×C4×C9—31no—
289C2×C4×C9C22×D311yescharacteristic
290C2×C4×C9C22×D311yescharacteristic
291#611—22no—
292#611—62no—
293#611—64no—
294C2×Dic9—31no—
295C2×Dic9—31no—
296C2×Dic9—31no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—121no—
301C2×Dic9—122no—
302C2×Dic9C22×D311yescharacteristic
303C2×Dic9C22×D311yescharacteristic
304C2×Dic9C22×D311yescharacteristic
305C4×D9—22no—
306C4×D9—62no—
307C4×D9—121no—
308C4×D9—122no—
309C4×D9—121no—
310#551—271noSylow
311C2×C3×C9—41no—
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9C2×#4111yescharacteristic
314C2×C3×C9H(5,𝔽2)11yescharacteristic
315C3⋊D9—22no—
316D3×C9—41no—
317C3×D9—22no—
318C23×D3—91no—
319C23×D3—91no—
320C2×C3×Q8—31no—
321C2×C3×D4—31no—
322C2×C3×D4—91no—
323C22×C3×C4—91no—
324C2×#67—31no—
325C2×#67—91no—
326C2×#67—91no—
327C2×#67—181no—
328C2×#67C2×D911yescharacteristic
329C22×Dic3—91no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332C22×Dic3—181no—
333C2×C4×D3—31no—
334C2×C4×D3—91no—
335C2×C4×D3—91no—
336C2×C4×D3—91no—
337C2×C4×D3—91no—
338C2×C4×D3—91no—
339C2×C4×D3—181no—
340C2×Dic6C2×D911yescharacteristic, complemented
341C3×C4⋊C4—91no—
342C3×C4⋊C4—91no—
343C3×C22⋊C4—21no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349C3×C22⋊C4C2×D911yescharacteristic, complemented
350C3×C22⋊C4D3211yescharacteristic
351C3×C42—31no—
352#217—31no—
353#217—91no—
354#217—91no—
355#217—91no—
356#217—91no—
357#217—91no—
358#217C2×D911yescharacteristic, complemented
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)⋊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—181no—
372(C2×D3)⋊C4C2×D911yescharacteristic
373(C2×D3)⋊C4C2×D911yescharacteristic
374C4⋊Dic3—31no—
375C4⋊Dic3—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—91no—
380Dic3⋊C4—31no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—181no—
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—181no—
394C4×Dic3C2×D911yescharacteristic, complemented
395C22×C32—21no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32C23×D311yescharacteristic
399C2×C3⋊D3—32no—
400C2×C3⋊D3—61no—
401C2×C3⋊D3—61no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—32no—
406C2×C3×D3—61no—
407C2×C3×D3—61no—
408D32—124no—
409C32×C4—21no—
410C32×C4—21no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3⋊Dic3—61no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—61no—
418C3×Dic3—61no—
419C3×Dic3—61no—
420C22×C9—22no—
421C22×C9—21no—
422C22×C9—21no—
423C22×C9—21no—
424C22×C9—21no—
425C22×C9—41no—
426C22×C9—41no—
427C22×C9—61no—
428C22×C9—61no—
429C22×C9—61no—
430C22×C9C23×D311yescharacteristic
431C2×D9—21no—
432C2×D9—21no—
433C2×D9—32no—
434C2×D9—62no—
435C2×D9—61no—
436C2×D9—61no—
437C2×D9—121no—
438C2×D9—121no—
439C2×D9—124no—
440C2×D9#23712yes—
441C4×C9—21no—
442C4×C9—21no—
443C4×C9—41no—
444C4×C9—41no—
445C4×C9—61no—
446C4×C9—61no—
447C4×C9—61no—
448Dic9—21no—
449Dic9—21no—
450Dic9—21no—
451Dic9—62no—
452Dic9—62no—
453Dic9—61no—
454Dic9—61no—
455Dic9—61no—
456Dic9—121no—
457#126—271no—
458#126—271no—
459#124—31no—
460#123—91no—
461#123—271no—
462#123—271no—
463C22⋊Q8—271no—
464C22⋊Q8—271no—
465#120—271no—
466C4×D4—271no—
467C4×D4—271no—
468#117—271no—
469#117—271no—
470C2×C22⋊C4—271no—
471C2×C22⋊C4—271no—
472C3×C9#55111yescharacteristic, complemented, Sylow
473C23×C3—21no—
474C23×C3—31no—
475C23×C3—91no—
476C23×C3C22×D911yescharacteristic
477C23×C3C2×D3211yescharacteristic
478C22×D3—31no—
479C22×D3—91no—
480C22×D3—91no—
481C22×D3—181no—
482C22×D3—182no—
483C22×D3—182no—
484C22×D3—182no—
485C22×D3—182no—
486C22×D3—361no—
487C22×D3—361no—
488C22×D3C22×D911yescharacteristic
489C3×Q8—121no—
490C3×D4—121no—
491C3×D4—182no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—91no—
498C2×C3×C4—91no—
499C2×C3×C4—91no—
500C2×C3×C4—182no—
501C2×C3×C4C22×D911yescharacteristic
502C2×C3×C4C22×D911yescharacteristic
503C2×C3×C4C2×D3211yescharacteristic
504C2×C3×C4C2×D3211yescharacteristic
505#67—41no—
506#67—62no—
507#67—182no—
508#67—182no—
509#67—184no—
510C2×Dic3—31no—
511C2×Dic3—31no—
512C2×Dic3—31no—
513C2×Dic3—91no—
514C2×Dic3—91no—
515C2×Dic3—91no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—91no—
519C2×Dic3—181no—
520C2×Dic3—181no—
521C2×Dic3—181no—
522C2×Dic3—361no—
523C2×Dic3—361no—
524C2×Dic3—361no—
525C2×Dic3—362no—
526C2×Dic3C22×D911yescharacteristic
527C2×Dic3C22×D911yescharacteristic
528C2×Dic3C22×D911yescharacteristic
529C4×D3—62no—
530C4×D3—182no—
531C4×D3—182no—
532C4×D3—361no—
533C4×D3—361no—
534C4×D3—362no—
535C4×D3—361no—
536Dic6—41no—
537C2×C32—41no—
538C2×C32#100411yescharacteristic
539C2×C32D3×#4111yescharacteristic
540C2×C32D3×#4111yescharacteristic
541C3⋊D3—62no—
542C3×D3—41no—
543C3×D3—62no—
544C2×C9—21no—
545C2×C9—21no—
546C2×C9—21no—
547C2×C9—42no—
548C2×C9—41no—
549C2×C9—121no—
550C2×C9C2×#23711yescharacteristic
551C2×C9D3×#4111yescharacteristic
552C2×C9#100911yescharacteristic
553D9—22no—
554D9—62no—
555D9—122no—
556C24—271no—
557C2×Q8—31no—
558C2×D4—31no—
559C2×D4—91no—
560C2×D4—271no—
561C22×C4—91no—
562C22×C4—271no—
563C22×C4—271no—
564C22×C4—271no—
565C22×C4—271no—
566C4⋊C4—91no—
567C4⋊C4—91no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C4⋊C4—271no—
573C4⋊C4—271no—
574C22⋊C4—31no—
575C22⋊C4—31no—
576C22⋊C4—31no—
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C22⋊C4—271no—
583C22⋊C4—271no—
584C22⋊C4—271no—
585C22⋊C4—271no—
586C22⋊C4—271no—
587C22⋊C4D3×D911yescharacteristic, complemented
588C42—31no—
589C42—271no—
590C42—271no—
591C22×C3—22no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—61no—
602C22×C3—61no—
603C22×C3—61no—
604C22×C3—92no—
605C22×C3—181no—
606C22×C3—181no—
607C22×C3C23×D911yescharacteristic
608C22×C3C22×D3211yescharacteristic
609C2×D3—21no—
610C2×D3—21no—
611C2×D3—21no—
612C2×D3—32no—
613C2×D3—61no—
614C2×D3—61no—
615C2×D3—92no—
616C2×D3—92no—
617C2×D3—182no—
618C2×D3—181no—
619C2×D3—181no—
620C2×D3—181no—
621C2×D3—181no—
622C2×D3—361no—
623C2×D3—361no—
624C2×D3—364no—
625C2×D3—364no—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—61no—
633C3×C4—61no—
634C3×C4—61no—
635C3×C4—181no—
636C3×C4—181no—
637C3×C4—181no—
638Dic3—21no—
639Dic3—21no—
640Dic3—21no—
641Dic3—61no—
642Dic3—61no—
643Dic3—61no—
644Dic3—182no—
645Dic3—182no—
646Dic3—181no—
647Dic3—181no—
648Dic3—181no—
649Dic3—181no—
650Dic3—181no—
651Dic3—181no—
652Dic3—361no—
653C32#567911yescharacteristic
654C9—21no—
655C9#565811yescharacteristic, complemented
656C23—31no—
657C23—91no—
658C23—271no—
659C23—542no—
660C23—542no—
661C23—1081no—
662C23C2×D3×D911yescharacteristic
663Q8—121no—
664D4—121no—
665D4—182no—
666D4—542no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—91no—
671C2×C4—91no—
672C2×C4—91no—
673C2×C4—182no—
674C2×C4—271no—
675C2×C4—271no—
676C2×C4—271no—
677C2×C4—542no—
678C2×C4—1081no—
679C2×C4—1081no—
680C2×C4—1081no—
681C2×C4C2×D3×D911yescharacteristic
682C2×C4C2×D3×D911yescharacteristic
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—42no—
687C2×C3—41no—
688C2×C3—41no—
689C2×C3—121no—
690C2×C3—182no—
691C2×C3#6371011yescharacteristic
692C2×C3#41×D911yescharacteristic
693C2×C3#41×D911yescharacteristic
694C2×C3#6430611yescharacteristic
695C2×C3D3×#23711yescharacteristic
696C2×C3#6431411yescharacteristic
697D3—41no—
698D3—62no—
699D3—182no—
700D3—182no—
701D3—362no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—61no—
706C22—61no—
707C22—61no—
708C22—92no—
709C22—181no—
710C22—181no—
711C22—272no—
712C22—541no—
713C22—541no—
714C22—1084no—
715C22C22×D3×D911yescharacteristic
716C4—21no—
717C4—21no—
718C4—61no—
719C4—61no—
720C4—61no—
721C4—181no—
722C4—181no—
723C4—181no—
724C4—541no—
725C4—541no—
726C4—541no—
727C3—21no—
728C3#1058978111yescharacteristic, complemented
729C3#1059430511yescharacteristic
730C2—41no—
731C2—121no—
732C2—182no—
733C2—542no—
734C2#1172247511yescharacteristic
735C2D9×#23711yescharacteristic
736C2#1172250011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radical#11721292C2
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. #11721727C2semidirect
2. C9×#885C2semidirect
3. C3×#63445C2semidirect
5. #11721275C2semidirect
6. #611⋊Dic3C2semidirect
7. #11721266C2semidirect
8. #11721048C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11720984C2semidirect
11. #11720966C2semidirect
12. #11720962C2semidirect
13. #11720943C2semidirect
14. #11720929C2semidirect
15. #11720898C2semidirect
20. C22×C3⋊Dic9C22semidirect
25. C2×C9×Dic6C22semidirect
28. C3×C9×C22⋊C4C22semidirect
30. #88534C22semidirect
31. C4×C3⋊Dic9C22semidirect
32. C9×#217C22semidirect
33. C3×#3676C22semidirect
37. C4×C9×Dic3C22semidirect
38. C3×C4⋊Dic9C22semidirect
39. C3×Dic9⋊C4C22semidirect
47. Dic3⋊Dic9C22semidirect
48. Dic9⋊Dic3C22semidirect
49. Dic9⋊Dic3C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
74. #63445D3semidirect
165. C9×C22⋊C4C2×D3semidirect
170. #3676C2×D3semidirect
179. C4⋊Dic9C2×D3semidirect
186. Dic9⋊C4C2×D3semidirect
230. #885D9semidirect
340. C2×Dic6C2×D9semidirect
349. C3×C22⋊C4C2×D9semidirect
358. #217C2×D9semidirect
394. C4×Dic3C2×D9semidirect
472. C3×C9#551semidirect
587. C22⋊C4D3×D9semidirect
655. C9#5658semidirect
728. C3#10589781semidirect

Maximal subgroups

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

subgroupindex
#117217272
C9×#8852
C3×#634452
#117212922
#117212752
#611⋊Dic32
#117212662
#117210482
D9×(C2×D3)⋊C42
#117209842
#117209662
#117209622
#117209432
#117209292
#117208982
#105943053
#105897813