Finite Group Databasebeta

← #34079354

Subgroups — #34079354

Order 19328.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#23752817C211yesmaximal, characteristic, complemented
2#23752686C211yesmaximal, characteristic, complemented
3#23752537C212yesmaximal, complemented
4#23752513C212yesmaximal, complemented
5#23752408C212yesmaximal, complemented
6#23752348C212yesmaximal, complemented
7#23752325C212yesmaximal, complemented
8C4×D1208C212yesmaximal, complemented
9#433×C151C211yesmaximal, characteristic, complemented
10C22×D604C2211yescharacteristic
11C2×D1208C2212yes—
12C2×D1208C2212yes—
13#18012736C2211yescharacteristic, complemented
14#18012731C2211yescharacteristic, complemented
15#18012724—22no—
16#18012713C2212yes—
17#18012712—22no—
18C4×D604C2212yes—
19C4×D604C2212yes—
20C4×D604C2212yescomplemented
21#18012701—22no—
22#18012698C2211yescharacteristic
23C22⋊C4×D151—22no—
24#18012673C2212yescomplemented
25#18012671C2212yescomplemented
26#18012661C2212yes—
27#18012661C2212yes—
28#18012661C2212yescomplemented
29#18012661C2212yescomplemented
30#117×C151C2211yescharacteristic
31C4⋊C8×C151C2212yescomplemented
32C22⋊C8×C151C2212yes—
33#97×C151C2211yescharacteristic, complemented
34C4×C8×C151C2211yescharacteristic, complemented
35C23×D151—21no—
36C2×D604—24no—
37C2×D604—21no—
38C2×D604—22no—
39C2×D604C2312yes—
40C2×D604C2312yes—
41C2×C22⋊D151—22no—
42C2×C4×D151—22no—
43C2×C4×D151—22no—
44C2×C4×D151—22no—
45D1208—24no—
46D1208—24no—
47C4⋊Dic151C2312yes—
48C4⋊Dic151C2312yes—
49Dic151⋊C4—22no—
50C22⋊Dic151—21no—
51(C2×D151)⋊C4—22no—
52(C2×D151)⋊C4—22no—
53(C2×D151)⋊C4—22no—
54(C2×D151)⋊C4—22no—
55C4×Dic151—21no—
56C22×C4×C151C2311yescharacteristic
57C2×C8×C151C2312yes—
58C2×C8×C151C2312yes—
59C4⋊C4×C151D412yes—
60C22⋊C4×C151D412yes—
61C42×C151C2311yescharacteristic
62C42×C151C2311yescharacteristic
63C22×D151—22no—
64C22×D151—24no—
65C22×D151—22no—
66C22×D151—82no—
67D604—24no—
68D604—22no—
69D604—22no—
70D604—22no—
71D604—82no—
72D604#4114yes—
73C22⋊D151—82no—
74C2×Dic151—22no—
75C2×Dic151—22no—
76C4×D151—82no—
77C4×D151—82no—
78C4×D151—82no—
79C23×C151C2×D411yescharacteristic
80C2×C4×C151—22no—
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2×D412yes—
83C2×C4×C151C2×D412yes—
84C2×C4×C151C2411yescharacteristic
85C8×C151—22no—
86C8×C151—22no—
87C22×C151—21no—
88C22×C151—22no—
89C22×C151C22×D411yescharacteristic
90C2×D151—24no—
91C2×D151—42no—
92C2×D151—42no—
93C2×D151—42no—
94C2×D151—42no—
95C2×D151—42no—
96C2×D151—84no—
97C4×C151—21no—
98C4×C151—22no—
99C4×C151—22no—
100C4×C151C2×#4112yes—
101Dic151—42no—
102Dic151—42no—
103C2×C151—41no—
104C2×C151#52511yescharacteristic
105C2×C151#57612yes—
106D151—44no—
107D151—82no—
108C151#312211yescharacteristic, complemented, Sylow
109#3122—1511nomaximal, Sylow
110#540—1511no—
111#518—1511no—
112#482—1512no—
113#478—1512no—
114#459—1512no—
115#447—1512no—
116#442—1512no—
117C4×D8—1512no—
118#433D15111yescharacteristic, complemented
119C22×D4—1511no—
120C2×D8—1512no—
121C2×D8—1512no—
122#127—1511no—
123#125—1511no—
124#123—3022no—
125#121—3022no—
126#121—1512no—
127C4×D4—3022no—
128C4×D4—1512no—
129C4×D4—1512no—
130C4×D4—1512no—
131#117—1511no—
132#117C2×D15111yescharacteristic
133C2×C22⋊C4—3022no—
134#107—1512no—
135#106—1512no—
136C4⋊C8C2×D15112yescomplemented
137#102—1512no—
138#102—1512no—
139#102—1512no—
140#102—1512no—
141C22⋊C8C2×D15112yes—
142#97C2×D15111yescharacteristic, complemented
143C4×C8C2×D15111yescharacteristic, complemented
144C24—3021no—
145C2×D4—3024no—
146C2×D4—3022no—
147C2×D4—3021no—
148C2×D4—3022no—
149C2×D4—1512no—
150C2×D4—1512no—
151C22×C4—3022no—
152C22×C4—3022no—
153C22×C4—3022no—
154C22×C4C22×D15111yescharacteristic
155D8—3024no—
156D8—3024no—
157C2×C8C22×D15112yes—
158C2×C8C22×D15112yes—
159C4⋊C4—3022no—
160C4⋊C4—1512no—
161C4⋊C4—1512no—
162C4⋊C4D60412yes—
163C22⋊C4—3021no—
164C22⋊C4—3022no—
165C22⋊C4—3022no—
166C22⋊C4—3022no—
167C22⋊C4—3022no—
168C22⋊C4D60412yes—
169C42—3021no—
170C42C22×D15111yescharacteristic
171C42C22×D15111yescharacteristic
172C23—3024no—
173C23—3022no—
174C23—3022no—
175C23—12082no—
176C23C2×D60411yescharacteristic
177D4—3024no—
178D4—3022no—
179D4—3022no—
180D4—3022no—
181D4—1514no—
182D4—12082no—
183D4—12082no—
184C2×C4—22no—
185C2×C4—3022no—
186C2×C4—3022no—
187C2×C4—12082no—
188C2×C4—12082no—
189C2×C4—12082no—
190C2×C4C2×D60411yescharacteristic
191C2×C4C2×D60412yes—
192C2×C4C2×D60412yes—
193C2×C4C23×D15111yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—3024no—
199C22—6042no—
200C22—6042no—
201C22—6042no—
202C22—6042no—
203C22—6042no—
204C22—12084no—
205C22C22×D60411yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—6042no—
210C4—6042no—
211C4#41×D15112yes—
212C2—41no—
213C2—6044no—
214C2—12082no—
215C2#2375272411yescharacteristic
216C2#2375301712yes—
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#433×C151C2
socleC22×C151C22×D4
hypercenter#433D151
hypocenterC151#3122
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23752817C2semidirect
2. #23752686C2semidirect
3. #23752537C2semidirect
4. #23752513C2semidirect
5. #23752408C2semidirect
6. #23752348C2semidirect
7. #23752325C2semidirect
8. C4×D1208C2semidirect
9. #433×C151C2semidirect
13. #18012736C22semidirect
14. #18012731C22semidirect
20. C4×D604C22semidirect
24. #18012673C22semidirect
25. #18012671C22semidirect
28. #18012661C22semidirect
29. #18012661C22semidirect
31. C4⋊C8×C151C22semidirect
33. #97×C151C22semidirect
34. C4×C8×C151C22semidirect
108. C151#3122semidirect
118. #433D151semidirect
136. C4⋊C8C2×D151semidirect
142. #97C2×D151semidirect
143. C4×C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237528172
#237526862
#237525372
#237525132
#237524082
#237523482
#237523252
C4×D12082
#433×C1512
#3122151