Finite Group Databasebeta

← #34077459

Subgroups — #34077459

Order 19328.

644 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 189 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
1C2×#18012737C211yesmaximal, characteristic, complemented
2C2×#18012719C211yesmaximal, characteristic
3C2×#18012715C211yesmaximal, characteristic
4C2×C42×D151C211yesmaximal, characteristic
5#23752118C211yesmaximal, characteristic, complemented
6#23752109C214yesmaximal, complemented
7#23752081C211yesmaximal, characteristic, complemented
8#23752071C214yesmaximal
9#391×C151C211yesmaximal, characteristic, complemented
10C22×Dic302C2211yescharacteristic
11C22×C4×D151C2211yescharacteristic
12C22×C4×D151C2212yes—
13#18012737—24no—
14#18012719—24no—
15#18012715—24no—
16C2×C4⋊Dic151C2211yescharacteristic
17C2×C4⋊Dic151C2212yes—
18C2×Dic151⋊C4C2212yes—
19C2×Dic151⋊C4C2214yes—
20C2×Dic151⋊C4C2214yes—
21C2×(C2×D151)⋊C4C2212yes—
22C2×(C2×D151)⋊C4C2212yes—
23C2×C4×Dic151C2212yes—
24C2×C4×Dic151C2211yescharacteristic
25C42×D151—24no—
26C151⋊#95C2214yes—
27C22×Q8×C151C2211yescharacteristic
28C2×C4⋊C4×C151C2211yescharacteristic
29C2×C42×C151C2211yescharacteristic
30#95×C151C2214yes—
31C23×D151C2311yescharacteristic
32C2×Dic302—22no—
33C2×Dic302—22no—
34C2×Dic302—22no—
35C22×Dic151C2312yes—
36C22×Dic151C2312yes—
37C22×Dic151C2311yescharacteristic
38C22×Dic151C2312yes—
39C2×C4×D151—24no—
40C2×C4×D151—24no—
41C2×C4×D151—22no—
42C2×C4×D151—22no—
43C2×C4×D151D414yes—
44C2×C4×D151Q818yescomplemented
45C4⋊Dic151—24no—
46C4⋊Dic151—22no—
47Dic151⋊C4—24no—
48Dic151⋊C4—28no—
49Dic151⋊C4—28no—
50(C2×D151)⋊C4—24no—
51(C2×D151)⋊C4—24no—
52C4×Dic151—24no—
53C4×Dic151D414yes—
54C2×Q8×C151—22no—
55C2×Q8×C151—22no—
56C2×Q8×C151—22no—
57C22×C4×C151C2312yes—
58C22×C4×C151C2312yes—
59C22×C4×C151C2312yes—
60C22×C4×C151C2311yescharacteristic
61C4⋊C4×C151—22no—
62C42×C151—22no—
63C22×D151—21no—
64C22×D151—22no—
65C22×D151—21no—
66C22×D151C2×D412yes—
67C22×D151C2×Q814yes—
68Dic302—44no—
69C2×Dic151—21no—
70C2×Dic151—21no—
71C2×Dic151—22no—
72C2×Dic151—22no—
73C2×Dic151—22no—
74C2×Dic151—24no—
75C2×Dic151—22no—
76C2×Dic151C2×D412yes—
77C2×Dic151C2×D414yes—
78C2×Dic151C2×Q814yes—
79C2×Dic151#4114yes—
80C4×D151—28no—
81C4×D151—216no—
82C23×C151C2411yescharacteristic
83Q8×C151—44no—
84C2×C4×C151—22no—
85C2×C4×C151—22no—
86C2×C4×C151—22no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151—24no—
91C2×C4×C151C2×D412yes—
92C2×C4×C151C2×D412yes—
93C2×C4×C151C2×Q814yes—
94C2×C4×C151#4112yes—
95C22×C151C22×D411yescharacteristic
96C22×C151C22×D411yescharacteristic
97C22×C151C22×Q812yes—
98C22×C151C2×#4112yes—
99C22×C151C2×#4111yescharacteristic
100C2×D151—22no—
101C2×D151—24no—
102C2×D151—22no—
103C2×D151—24no—
104C2×D151C4⋊Q814yescomplemented
105C4×C151—24no—
106C4×C151—42no—
107C4×C151—42no—
108C4×C151#12114yes—
109Dic151—22no—
110Dic151—42no—
111Dic151—42no—
112Dic151C22⋊Q818yescomplemented
113C2×C151C2×#12111yescharacteristic
114C2×C151C2×C22⋊Q812yes—
115C2×C151C2×C4⋊Q811yescharacteristic
116C2×C151#53211yescharacteristic
117C2×C151#53312yes—
118D151—24no—
119C151#285711yescharacteristic, complemented, Sylow
120#2857—1511nomaximal, Sylow
121C2×C4⋊Q8—1511no—
122C2×C22⋊Q8—1511no—
123C2×C22⋊Q8—1511no—
124C22×C42—1511no—
125#391—1511no—
126#391D15111yescharacteristic, complemented
127#389—1514no—
128#384—1511no—
129#380—1514no—
130C22×Q8—1511no—
131C22×Q8C2×D15111yescharacteristic
132C23×C4—1511no—
133C23×C4—1512no—
134C4⋊Q8—3024no—
135C22⋊Q8—3024no—
136C22⋊Q8—3024no—
137C2×C4⋊C4—1512no—
138C2×C4⋊C4—1511no—
139C2×C4⋊C4—1512no—
140C2×C4⋊C4—1514no—
141C2×C4⋊C4—1514no—
142C2×C4⋊C4C2×D15111yescharacteristic
143C2×C22⋊C4—1512no—
144C2×C22⋊C4—1512no—
145C2×C42—3024no—
146C2×C42—1512no—
147C2×C42—1511no—
148C2×C42C2×D15111yescharacteristic
149#95—1514no—
150#95C2×D15114yes—
151C24—1511no—
152C2×Q8—22no—
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—3022no—
156C2×Q8—3022no—
157C2×Q8—3022no—
158C22×C4—3024no—
159C22×C4—3024no—
160C22×C4—3022no—
161C22×C4—3022no—
162C22×C4—1512no—
163C22×C4—1512no—
164C22×C4—1511no—
165C22×C4—1514no—
166C22×C4—1518no—
167C22×C4—1512no—
168C22×C4C22×D15112yes—
169C22×C4C22×D15112yes—
170C22×C4C22×D15112yes—
171C22×C4C22×D15111yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—3028no—
174C4⋊C4—3024no—
175C4⋊C4—3028no—
176C4⋊C4—3024no—
177C4⋊C4—3022no—
178C22⋊C4—3024no—
179C22⋊C4—3024no—
180C42—22no—
181C42—3024no—
182C42—1514no—
183C23—3021no—
184C23—3022no—
185C23—3021no—
186C23—1512no—
187C23—1514no—
188C23C23×D15111yescharacteristic
189Q8—44no—
190Q8—6044no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—22no—
198C2×C4—30216no—
199C2×C4—3021no—
200C2×C4—3021no—
201C2×C4—3028no—
202C2×C4—3022no—
203C2×C4—3022no—
204C2×C4—3022no—
205C2×C4—3024no—
206C2×C4—3022no—
207C2×C4—1512no—
208C2×C4—1514no—
209C2×C4—1514no—
210C2×C4—1514no—
211C2×C4D4×D15112yes—
212C2×C4D4×D15112yes—
213C2×C4Q8×D15114yes—
214C2×C4#1455900412yes—
215C22—3024no—
216C22—3022no—
217C22—3024no—
218C22—3022no—
219C22—1514no—
220C22C2×D4×D15111yescharacteristic
221C22C2×D4×D15111yescharacteristic
222C22C2×Q8×D15112yes—
223C22#41×D15112yes—
224C22C2×#1455900411yescharacteristic
225C4—24no—
226C4—42no—
227C4—42no—
228C4—3022no—
229C4—6042no—
230C4—6042no—
231C4—1518no—
232C4#1801271214yes—
233C2—3024no—
234C2C2×#1801271211yescharacteristic
235C2C22⋊Q8×D15112yes—
236C2C4⋊Q8×D15111yescharacteristic
237C2#2375276111yescharacteristic
238C2#2375276612yes—
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#391×C151C2
prime radicalC23×D151C23
hypercenter#391D151
hypocenterC151#2857
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#18012737C2semidirect
5. #23752118C2semidirect
6. #23752109C2semidirect
7. #23752081C2semidirect
9. #391×C151C2semidirect
44. C2×C4×D151Q8semidirect
104. C2×D151C4⋊Q8semidirect
112. Dic151C22⋊Q8semidirect
119. C151#2857semidirect
126. #391D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127372
C2×#180127192
C2×#180127152
C2×C42×D1512
#237521182
#237521092
#237520812
#237520712
#391×C1512
#2857151