Finite Group Databasebeta

← #34054939

Subgroups — #34054939

Order 19072.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750235C211yesmaximal, characteristic, complemented
2#23750099C211yesmaximal, characteristic
3#23749966C211yesmaximal, characteristic, complemented
4#23749928C211yesmaximal, characteristic, complemented
5#23749924C211yesmaximal, characteristic, complemented
6#23749829C211yesmaximal, characteristic, complemented
7#23749829C211yesmaximal, characteristic, complemented
8#23749778C211yesmaximal, characteristic
9#23749775C211yesmaximal, characteristic
10#23749728C211yesmaximal, characteristic, complemented
11#23749724C211yesmaximal, characteristic, complemented
12#23749712C211yesmaximal, characteristic, complemented
13#23749710C211yesmaximal, characteristic, complemented
14#23749683C211yesmaximal, characteristic, complemented
15#485×C149C211yesmaximal, characteristic, complemented
16C22×D596C2211yescharacteristic
17C2×#14558725C2211yescharacteristic
18C2×#14558725C2211yescharacteristic
19C2×#14558723C2211yescharacteristic
20C2×#14558723C2211yescharacteristic
21#18011909C2211yescharacteristic, complemented
22#18011904—21no—
23#18011904—21no—
24#18011902—21no—
25#18011902C2211yescharacteristic, complemented
26#18011901—21no—
27#18011890C2211yescharacteristic
28Q8×Dic149C2211yescharacteristic, complemented
29#18011876C2211yescharacteristic, complemented
30C4×D596—21no—
31C4×D596—21no—
32#18011873C2211yescharacteristic
33#18011873C2211yescharacteristic
34#18011873C2211yescharacteristic
35#18011873C2211yescharacteristic
36#18011870C2211yescharacteristic
37C22⋊C4×D149—21no—
38C22⋊C4×D149—21no—
39#18011844C2211yescharacteristic, complemented
40#18011842C2211yescharacteristic, complemented
41#18011840C2211yescharacteristic, complemented
42#18011840C2211yescharacteristic, complemented
43#18011834C2211yescharacteristic, complemented
44#18011834C2211yescharacteristic, complemented
45#18011833C2211yescharacteristic
46#18011833C2211yescharacteristic
47#18011831C2211yescharacteristic
48#18011831C2211yescharacteristic
49C22⋊#11924746C2211yescharacteristic
50#18011821C2211yescharacteristic, complemented
51C8×Dic149C2211yescharacteristic, complemented
52C22⋊Q8×C149C2211yescharacteristic
53#117×C149C2211yescharacteristic
54#107×C149C2211yescharacteristic, complemented
55#106×C149C2211yescharacteristic, complemented
56#103×C149C2211yescharacteristic, complemented
57#103×C149C2211yescharacteristic, complemented
58C22⋊C8×C149C2211yescharacteristic
59C23×D149—21no—
60C2×Dic298C2311yescharacteristic
61C2×D596—22no—
62C2×D596—22no—
63C2×D596—21no—
64C2×D596C2311yescharacteristic
65C2×D596C2311yescharacteristic
66C2×C4×D149—21no—
67C2×C4×D149—21no—
68C2×C4×D149—21no—
69C2×C4×D149—21no—
70#14558725—22no—
71#14558725—22no—
72#14558723—22no—
73#14558723—22no—
74C2×#11924746C2311yescharacteristic
75C2×#11924746C2311yescharacteristic
76C4⋊Dic149—21no—
77C4⋊Dic149—21no—
78C4⋊Dic149D411yescharacteristic
79C4⋊Dic149D411yescharacteristic
80C4⋊Dic149C2311yescharacteristic
81#14558715—21no—
82#14558715—21no—
83#14558715—21no—
84#14558715—21no—
85#14558715—21no—
86C22⋊Dic149—21no—
87C22⋊Dic149D411yescharacteristic
88C22⋊Dic149D411yescharacteristic
89#14558713—21no—
90#14558713—21no—
91#14558713—21no—
92#14558713—21no—
93C4×Dic149—21no—
94C4×Dic149—21no—
95C4×Dic149C2311yescharacteristic
96C4×Dic149C2311yescharacteristic
97C2×Q8×C149C2311yescharacteristic
98C22×C4×C149C2311yescharacteristic
99C2×C8×C149C2311yescharacteristic
100C2×C8×C149C2311yescharacteristic
101C4⋊C4×C149—21no—
102C4⋊C4×C149C2311yescharacteristic
103C4⋊C4×C149C2311yescharacteristic
104C4⋊C4×C149C2311yescharacteristic
105C22⋊C4×C149—21no—
106C22⋊C4×C149—21no—
107C42×C149—21no—
108C22×D149—21no—
109C22×D149—21no—
110C22×D149—24no—
111C22×D149—81no—
112C22×D149—81no—
113Dic298—21no—
114Dic298—21no—
115D596—24no—
116D596—21no—
117D596—21no—
118D596#4112yes—
119D596#4112yes—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149C2×D411yescharacteristic
123C2×Dic149C2×D411yescharacteristic
124C2×Dic149C2×D411yescharacteristic
125C2×Dic149C2×D411yescharacteristic
126C4×D149—81no—
127C4×D149—81no—
128C4×D149—81no—
129C4×D149—81no—
130#11924746—21no—
131#11924746—21no—
132C23×C149C2×D411yescharacteristic
133Q8×C149—21no—
134Q8×C149—21no—
135C2×C4×C149—21no—
136C2×C4×C149—21no—
137C2×C4×C149—21no—
138C2×C4×C149—21no—
139C2×C4×C149—21no—
140C2×C4×C149—21no—
141C2×C4×C149C2×D411yescharacteristic
142C2×C4×C149C2411yescharacteristic
143C8×C149—21no—
144C8×C149—21no—
145C22×C149—21no—
146C22×C149—21no—
147C22×C149—21no—
148C22×C149C22×D411yescharacteristic
149C2×D149—22no—
150C2×D149—22no—
151C2×D149—41no—
152C2×D149—41no—
153C2×D149—41no—
154C2×D149—41no—
155C2×D149—84no—
156C4×C149—21no—
157C4×C149—41no—
158C4×C149—41no—
159C4×C149—41no—
160C4×C149—41no—
161C4×C149C2×#4111yescharacteristic
162C4×C149C2×#4111yescharacteristic
163Dic149—21no—
164Dic149—21no—
165Dic149—21no—
166Dic149—21no—
167Dic149—41no—
168Dic149—41no—
169C2×C149—41no—
170C2×C149#52511yescharacteristic
171C2×C149#57711yescharacteristic
172C2×C149#57711yescharacteristic
173D149—42no—
174D149—42no—
175C149#312311yescharacteristic, complemented, Sylow
176#3123—1491nomaximal, Sylow
177#541—1491no—
178#518—1491no—
179#485—1491no—
180#485D14911yescharacteristic, complemented
181#478—1491no—
182#478—1491no—
183#461—1491no—
184#461—1491no—
185#450—1491no—
186#450—1491no—
187#440—1491no—
188#440—1491no—
189C4×SD16—1491no—
190C4×SD16—1491no—
191#433—1491no—
192C22×D4—1491no—
193C2×SD16—1491no—
194C2×SD16—1491no—
195C2×SD16—1491no—
196C2×SD16—1491no—
197C4⋊Q8—1491no—
198#126—2981no—
199#126—2981no—
200#125—2981no—
201#125—2981no—
202#125—1491no—
203C22⋊Q8—1491no—
204C22⋊Q8C2×D14911yescharacteristic
205C4×Q8—1491no—
206C4×Q8—1491no—
207C4×D4—2981no—
208C4×D4—2981no—
209C4×D4—1491no—
210C4×D4—1491no—
211C4×D4—1491no—
212C4×D4—1491no—
213#117—1491no—
214#117C2×D14911yescharacteristic
215C2×C22⋊C4—2981no—
216C2×C22⋊C4—2981no—
217#107—1491no—
218#107C2×D14911yescharacteristic, complemented
219#106—1491no—
220#106C2×D14911yescharacteristic, complemented
221C4⋊C8—1491no—
222C4⋊C8—1491no—
223#103—1491no—
224#103—1491no—
225#103C2×D14911yescharacteristic, complemented
226#103C2×D14911yescharacteristic, complemented
227#102—1491no—
228#102—1491no—
229#102—1491no—
230#102—1491no—
231C22⋊C8—1491no—
232C22⋊C8C2×D14911yescharacteristic
233#97—1491no—
234C4×C8—1491no—
235C24—2981no—
236C2×Q8—1491no—
237C2×Q8C22×D14911yescharacteristic
238C2×D4—2982no—
239C2×D4—2982no—
240C2×D4—2981no—
241C2×D4—1491no—
242C2×D4—1491no—
243C22×C4—2981no—
244C22×C4—2981no—
245C22×C4—2981no—
246C22×C4—2981no—
247C22×C4C22×D14911yescharacteristic
248SD16—2982no—
249SD16—2982no—
250SD16—2982no—
251SD16—2982no—
252C2×C8—1491no—
253C2×C8—1491no—
254C2×C8C22×D14911yescharacteristic
255C2×C8C22×D14911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—2981no—
258C4⋊C4—2981no—
259C4⋊C4—2981no—
260C4⋊C4—2981no—
261C4⋊C4—2981no—
262C4⋊C4—2981no—
263C4⋊C4—2981no—
264C4⋊C4—1491no—
265C4⋊C4—1491no—
266C4⋊C4—1491no—
267C4⋊C4C22×D14911yescharacteristic
268C4⋊C4C22×D14911yescharacteristic
269C4⋊C4C22×D14911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—2981no—
273C22⋊C4—2981no—
274C22⋊C4—2981no—
275C22⋊C4—2981no—
276C22⋊C4—2981no—
277C22⋊C4—1491no—
278C22⋊C4—1491no—
279C42—21no—
280C42—2981no—
281C42—2981no—
282C42—1491no—
283C42—1491no—
284C23—2984no—
285C23—2981no—
286C23—2981no—
287C23—11921no—
288C23—11921no—
289C23D4×D14911yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—2981no—
293Q8—2981no—
294D4—2984no—
295D4—2981no—
296D4—2981no—
297D4—1492no—
298D4—1492no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—2981no—
306C2×C4—2981no—
307C2×C4—1491no—
308C2×C4—1491no—
309C2×C4—1491no—
310C2×C4—1491no—
311C2×C4—11921no—
312C2×C4—11921no—
313C2×C4—11921no—
314C2×C4—11921no—
315C2×C4D4×D14911yescharacteristic
316C2×C4C23×D14911yescharacteristic
317C8—21no—
318C8—21no—
319C8—2981no—
320C8—2981no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—2982no—
325C22—2982no—
326C22—5961no—
327C22—5961no—
328C22—5961no—
329C22—5961no—
330C22—11924no—
331C22C2×D4×D14911yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—2981no—
338C4—2981no—
339C4—2981no—
340C4—2981no—
341C4—5961no—
342C4—5961no—
343C4#41×D14911yescharacteristic
344C4#41×D14911yescharacteristic
345C2—41no—
346C2—5962no—
347C2—5962no—
348C2#2375013311yescharacteristic
349C2#2375043211yescharacteristic
350C2#2375043411yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#485×C149C2
socleC22×C149C22×D4
prime radicalC22×D596C22
hypercenter#485D149
hypocenterC149#3123
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #23750235C2semidirect
3. #23749966C2semidirect
4. #23749928C2semidirect
5. #23749924C2semidirect
6. #23749829C2semidirect
7. #23749829C2semidirect
10. #23749728C2semidirect
11. #23749724C2semidirect
12. #23749712C2semidirect
13. #23749710C2semidirect
14. #23749683C2semidirect
15. #485×C149C2semidirect
21. #18011909C22semidirect
25. #18011902C22semidirect
28. Q8×Dic149C22semidirect
29. #18011876C22semidirect
39. #18011844C22semidirect
40. #18011842C22semidirect
41. #18011840C22semidirect
42. #18011840C22semidirect
43. #18011834C22semidirect
44. #18011834C22semidirect
50. #18011821C22semidirect
51. C8×Dic149C22semidirect
54. #107×C149C22semidirect
55. #106×C149C22semidirect
56. #103×C149C22semidirect
57. #103×C149C22semidirect
175. C149#3123semidirect
180. #485D149semidirect
218. #107C2×D149semidirect
220. #106C2×D149semidirect
225. #103C2×D149semidirect
226. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502352
#237500992
#237499662
#237499282
#237499242
#237498292
#237497782
#237497752
#237497282
#237497242
#237497122
#237497102
#237496832
#485×C1492
#3123149