Finite Group Databasebeta

← #34055534

Subgroups — #34055534

Order 19072.

418 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750138C212yesmaximal, complemented
2#23749964C212yesmaximal, complemented
3#23749951C212yesmaximal, complemented
4#23749878C211yesmaximal, characteristic, complemented
5#23749873C212yesmaximal, complemented
6#23749786C212yesmaximal, complemented
7#23749773C212yesmaximal, complemented
8#23749588C211yesmaximal, characteristic, complemented
9#470×C149C211yesmaximal, characteristic, complemented
10C2×#14558737C2212yes—
11C22×C4×D149C2211yescharacteristic
12C2×#14558723C2212yescomplemented
13C2×D1192C2211yescharacteristic, complemented
14C2×#14558720C2211yescharacteristic
15#18011896—22no—
16#18011887C2212yes—
17#18011886C2212yes—
18#18011885C2212yes—
19#18011881—22no—
20#18011873—22no—
21#18011871—22no—
22#18011869C2212yes—
23#18011844C2212yescomplemented
24#18011843C2211yescharacteristic, complemented
25#18011835C2212yescomplemented
26#18011833C2212yescomplemented
27#18011831C2212yescomplemented
28#18011823C2212yes—
29#18011823C2212yes—
30C2×Q16×C149C2211yescharacteristic, complemented
31C2×M16×C149C2211yescharacteristic
32C22⋊Q8×C149C2212yes—
33#106×C149C2211yescharacteristic, complemented
34#103×C149C2212yescomplemented
35C23×D149D411yescharacteristic
36#14558737—42no—
37#14558737—42no—
38C2×D596—22no—
39C2×D596—22no—
40C2×D596C2312yes—
41C2×C22⋊D149—22no—
42C22×Dic149D411yescharacteristic
43C2×C4×D149—22no—
44C2×C4×D149—41no—
45C2×C4×D149—41no—
46C2×C4×D149D412yes—
47C2×C4×D149C2312yes—
48#14558723—42no—
49D1192—41no—
50#14558720—41no—
51C2×#11924746C2312yes—
52C4⋊Dic149C2312yes—
53#14558715—22no—
54#14558713—22no—
55#14558713—22no—
56#14558713—22no—
57#14558713—22no—
58C4×Dic149—22no—
59C2×Q8×C149C2312yes—
60C22×C4×C149C2311yescharacteristic
61Q16×C149—41no—
62M16×C149—41no—
63C2×C8×C149C2311yescharacteristic
64C2×C8×C149C2311yescharacteristic
65C4⋊C4×C149—22no—
66C4⋊C4×C149C2312yes—
67C22⋊C4×C149—22no—
68C22×D149—22no—
69C22×D149—41no—
70C22×D149—42no—
71C22×D149C2×D412yes—
72D596—22no—
73D596—22no—
74D596—44no—
75D596—44no—
76C22⋊D149—44no—
77C2×Dic149—22no—
78C2×Dic149—41no—
79C2×Dic149C2×D412yes—
80C4×D149—22no—
81C4×D149—22no—
82C4×D149—42no—
83C4×D149—44no—
84#11924746—22no—
85C23×C149C2×D411yescharacteristic
86Q8×C149—22no—
87Q8×C149—22no—
88C2×C4×C149—21no—
89C2×C4×C149—21no—
90C2×C4×C149—22no—
91C2×C4×C149—22no—
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2411yescharacteristic
94C8×C149—21no—
95C8×C149—21no—
96C22×C149—21no—
97C22×C149—22no—
98C22×C149C22×D411yescharacteristic
99C2×D149—22no—
100C2×D149—22no—
101C2×D149—22no—
102C2×D149—44no—
103C2×D149—42no—
104C2×D149—42no—
105C2×D149—42no—
106C4×C149—21no—
107C4×C149—42no—
108C4×C149—42no—
109C4×C149H(5,𝔽2)11yescharacteristic
110C4×C149H(5,𝔽2)11yescharacteristic
111Dic149—22no—
112Dic149—42no—
113C2×C149—41no—
114C2×C149#53411yescharacteristic
115C2×C149#57512yes—
116D149—42no—
117D149—82no—
118C149#319711yescharacteristic, complemented, Sylow
119#3197—1491nomaximal, Sylow
120#525—1492no—
121#485—1492no—
122#482—1492no—
123#470D14911yescharacteristic, complemented
124#469—1491no—
125#468—1492no—
126#452—1492no—
127#449—1492no—
128#407—1491no—
129C2×#41—1492no—
130C23×C4—1491no—
131C2×Q16C2×D14911yescharacteristic, complemented
132C2×SD16—1492no—
133C2×D8—1491no—
134C2×M16—1491no—
135C2×M16C2×D14911yescharacteristic
136#123—2982no—
137C22⋊Q8—1492no—
138C22⋊Q8C2×D14912yes—
139#121—1492no—
140#121—1492no—
141#120—2982no—
142C4×D4—2982no—
143C4×D4—2982no—
144#117—1492no—
145#107—1492no—
146#106—1491no—
147#106C2×D14911yescharacteristic, complemented
148#103—1492no—
149#103C2×D14912yescomplemented
150#102—1492no—
151#102—1492no—
152C22⋊C8—1492no—
153C22⋊C8—1492no—
154C24—1491no—
155#41—5962no—
156#41—5962no—
157C2×Q8C22×D14912yes—
158C2×D4—2982no—
159C2×D4—2982no—
160C2×D4—2982no—
161C2×D4—1492no—
162C22×C4—2982no—
163C22×C4—5961no—
164C22×C4—5961no—
165C22×C4—1492no—
166C22×C4—1491no—
167C22×C4—1492no—
168C22×C4C22×D14911yescharacteristic
169Q16—41no—
170SD16—5962no—
171D8—5961no—
172M16—41no—
173M16—5961no—
174C2×C8—1492no—
175C2×C8C22×D14911yescharacteristic
176C2×C8C22×D14911yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—2982no—
179C4⋊C4—1492no—
180C4⋊C4C22×D14912yes—
181C22⋊C4—22no—
182C22⋊C4—2982no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C22⋊C4—2982no—
186C42—2982no—
187C23—2982no—
188C23—5961no—
189C23—5962no—
190C23—1492no—
191C23D4×D14911yescharacteristic
192Q8—22no—
193Q8—22no—
194D4—2982no—
195D4—2982no—
196D4—5964no—
197D4—5964no—
198D4—5964no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—2982no—
204C2×C4—2982no—
205C2×C4—2982no—
206C2×C4—5962no—
207C2×C4—5964no—
208C2×C4—5961no—
209C2×C4—1492no—
210C2×C4D4×D14911yescharacteristic
211C2×C4C23×D14911yescharacteristic
212C8—21no—
213C8—21no—
214C8—2982no—
215C22—22no—
216C22—21no—
217C22—2982no—
218C22—2982no—
219C22—2982no—
220C22—5964no—
221C22—5962no—
222C22—5962no—
223C22—5962no—
224C22C2×D4×D14911yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—2982no—
229C4—5962no—
230C4#1801195611yescharacteristic
231C4#1801195711yescharacteristic
232C2—41no—
233C2—5962no—
234C2—11922no—
235C2#2375018311yescharacteristic
236C2#2375042412yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#470×C149C2
socleC22×C149C22×D4
hypercenter#470D149
hypocenterC149#3197
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #23750138C2semidirect
2. #23749964C2semidirect
3. #23749951C2semidirect
4. #23749878C2semidirect
5. #23749873C2semidirect
6. #23749786C2semidirect
7. #23749773C2semidirect
8. #23749588C2semidirect
9. #470×C149C2semidirect
12. C2×#14558723C22semidirect
13. C2×D1192C22semidirect
23. #18011844C22semidirect
24. #18011843C22semidirect
25. #18011835C22semidirect
26. #18011833C22semidirect
27. #18011831C22semidirect
30. C2×Q16×C149C22semidirect
33. #106×C149C22semidirect
34. #103×C149C22semidirect
118. C149#3197semidirect
123. #470D149semidirect
131. C2×Q16C2×D149semidirect
147. #106C2×D149semidirect
149. #103C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237501382
#237499642
#237499512
#237498782
#237498732
#237497862
#237497732
#237495882
#470×C1492
#3197149