Finite Group Databasebeta

← #34080335

Subgroups — #34080335

Order 19328.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C4⋊Q8×D151C211yesmaximal, characteristic, complemented
2#23752749C211yesmaximal, characteristic
3#23752620C212yesmaximal, complemented
4#23752573C212yesmaximal, complemented
5#23752541C212yesmaximal, complemented
6#23752527C212yesmaximal
7#23752507C211yesmaximal, characteristic, complemented
8#23752503C211yesmaximal, characteristic, complemented
9#23752499C211yesmaximal, characteristic, complemented
10#23752268C211yesmaximal, characteristic, complemented
11#477×C151C211yesmaximal, characteristic, complemented
12C2×Q8×D151—21no—
13#18012739C2211yescharacteristic
14#18012738—21no—
15#18012738C2212yes—
16#18012737—21no—
17#18012734—21no—
18#18012730C2211yescharacteristic
19#18012728C2211yescharacteristic
20#18012724—21no—
21#18012715C2211yescharacteristic
22#18012714C2211yescharacteristic
23C4×D604—21no—
24C4×D604C2211yescharacteristic
25#18012696—21no—
26C4⋊C4×D151—21no—
27C4⋊C4×D151C2212yes—
28C42×D151C2211yescharacteristic
29#18012672C2212yes—
30#18012671C2212yes—
31#18012670C2212yes—
32C4⋊(C151⋊C8)C2211yescharacteristic
33#18012663C2212yes—
34#18012661C2212yes—
35#18012659C2212yes—
36(C2×D151)⋊C8C2212yes—
37#18012649C2212yes—
38C4⋊Q8×C151C2211yescharacteristic
39C4×Q8×C151C2211yescharacteristic
40#107×C151C2212yes—
41C4⋊C8×C151C2211yescharacteristic
42#103×C151C2212yes—
43C2×Dic302—22no—
44C2×Dic302—21no—
45Q8×D151—44no—
46C2×D604—21no—
47C2×D604C2311yescharacteristic
48C2×C4×D151—22no—
49C2×C4×D151—21no—
50C2×C4×D151D411yescharacteristic
51C2×C4×D151D411yescharacteristic
52C2×C4×D151C2311yescharacteristic
53C2×C151⋊C8C2312yes—
54C4⋊Dic151—21no—
55C4⋊Dic151—21no—
56C4⋊Dic151C2312yes—
57C4⋊Dic151C2311yescharacteristic
58Dic151⋊C4—22no—
59Dic151⋊C4—22no—
60Dic151⋊C4—21no—
61Dic151⋊C4—21no—
62(C2×D151)⋊C4—21no—
63(C2×D151)⋊C4—21no—
64(C2×D151)⋊C4—21no—
65(C2×D151)⋊C4—21no—
66(C2×D151)⋊C4—21no—
67C4×Dic151D411yescharacteristic
68C4×Dic151D411yescharacteristic
69C4×Dic151C2311yescharacteristic
70C2×Q8×C151—21no—
71C2×Q8×C151C2311yescharacteristic
72C2×C8×C151C2312yes—
73C4⋊C4×C151—21no—
74C4⋊C4×C151—21no—
75C4⋊C4×C151C2311yescharacteristic
76C4⋊C4×C151C2312yes—
77C42×C151—21no—
78C42×C151C2311yescharacteristic
79C22×D151—21no—
80C22×D151C2×D411yescharacteristic
81Dic302—44no—
82Dic302—42no—
83D604—21no—
84D604—21no—
85D604—42no—
86C2×Dic151—21no—
87C2×Dic151—22no—
88C2×Dic151C2×D411yescharacteristic
89C2×Dic151C2×D411yescharacteristic
90C2×Dic151C2×D411yescharacteristic
91C4×D151—22no—
92C4×D151—22no—
93C4×D151—21no—
94C4×D151—21no—
95C4×D151—44no—
96C4×D151—42no—
97C151⋊C8—22no—
98Q8×C151—21no—
99Q8×C151—21no—
100Q8×C151—42no—
101C2×C4×C151—22no—
102C2×C4×C151—21no—
103C2×C4×C151—21no—
104C2×C4×C151C2×D411yescharacteristic
105C2×C4×C151C2×D411yescharacteristic
106C2×C4×C151C2411yescharacteristic
107C8×C151—22no—
108C22×C151C22×D411yescharacteristic
109C2×D151—21no—
110C2×D151—21no—
111C2×D151—41no—
112C2×D151—41no—
113C2×D151—41no—
114C2×D151AGL(1,ℤ/8)12yes—
115C4×C151—21no—
116C4×C151—41no—
117C4×C151—42no—
118C4×C151—41no—
119C4×C151#13712yes—
120C4×C1512−1+411yescharacteristic
121C4×C1512−1+411yescharacteristic
122Dic151—21no—
123Dic151—21no—
124Dic151—21no—
125Dic151—42no—
126Dic151—41no—
127C2×C151#53611yescharacteristic
128C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C151C2×#13711yescharacteristic
130D151—22no—
131D151—81no—
132C151#323811yescharacteristic, complemented, Sylow
133#3238—1511nomaximal, Sylow
134C2×C4⋊Q8—1511no—
135#529—1511no—
136#501—1512no—
137#489—1512no—
138#483—1512no—
139#480—1512no—
140#477—1511no—
141#477D15111yescharacteristic, complemented
142#476—1511no—
143#476—1511no—
144#432—1511no—
145C22×Q8—3021no—
146C4⋊Q8—3021no—
147C4⋊Q8—3021no—
148C4⋊Q8—1512no—
149C4⋊Q8—1511no—
150C4⋊Q8C2×D15111yescharacteristic
151#126—3021no—
152#125—1511no—
153#124—1511no—
154#123—3021no—
155C22⋊Q8—1511no—
156#121—1511no—
157C4×Q8C2×D15111yescharacteristic
158C4×D4—3021no—
159C4×D4—1511no—
160#117—3021no—
161C2×C4⋊C4—3021no—
162C2×C4⋊C4—1512no—
163C2×C42—1511no—
164#107—1512no—
165#107C2×D15112yes—
166#106—1512no—
167#106—1512no—
168C4⋊C8—1511no—
169C4⋊C8C2×D15111yescharacteristic
170#103—1512no—
171#103C2×D15112yes—
172#102—1512no—
173#102—1512no—
174C22⋊C8—1512no—
175#97—1512no—
176C2×Q8—21no—
177C2×Q8—3022no—
178C2×Q8—3021no—
179C2×Q8—6044no—
180C2×Q8C22×D15111yescharacteristic
181C2×D4—3021no—
182C2×D4—1511no—
183C22×C4—3022no—
184C22×C4—3021no—
185C22×C4—1511no—
186C22×C4—1511no—
187C22×C4—1511no—
188C2×C8—1512no—
189C2×C8C22×D15112yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—3022no—
193C4⋊C4—3022no—
194C4⋊C4—3021no—
195C4⋊C4—3021no—
196C4⋊C4—3021no—
197C4⋊C4—3021no—
198C4⋊C4—1512no—
199C4⋊C4—1511no—
200C4⋊C4C22×D15112yes—
201C4⋊C4C22×D15111yescharacteristic
202C22⋊C4—3021no—
203C22⋊C4—3021no—
204C22⋊C4—3021no—
205C22⋊C4—3021no—
206C22⋊C4—3021no—
207C42—21no—
208C42—1511no—
209C42—1511no—
210C42—1511no—
211C42C22×D15111yescharacteristic
212C23—3021no—
213C23—1511no—
214Q8—21no—
215Q8—21no—
216Q8—42no—
217Q8—6042no—
218Q8—6044no—
219D4—3021no—
220D4—3021no—
221D4—6042no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—3022no—
226C2×C4—3022no—
227C2×C4—3021no—
228C2×C4—3021no—
229C2×C4—3021no—
230C2×C4—3022no—
231C2×C4—6044no—
232C2×C4—6042no—
233C2×C4—1511no—
234C2×C4—1511no—
235C2×C4—1511no—
236C2×C4D4×D15111yescharacteristic
237C2×C4D4×D15111yescharacteristic
238C2×C4C23×D15111yescharacteristic
239C8—22no—
240C8—3022no—
241C22—3021no—
242C22—3021no—
243C22—6041no—
244C22—6041no—
245C22—6041no—
246C22—1512no—
247C22C2×D4×D15111yescharacteristic
248C4—21no—
249C4—42no—
250C4—41no—
251C4—41no—
252C4—3021no—
253C4—3021no—
254C4—3021no—
255C4—6042no—
256C4—6041no—
257C4#1801277112yes—
258C4#1801278611yescharacteristic
259C4#1801278711yescharacteristic
260C2—3022no—
261C2—12081no—
262C2#2375278511yescharacteristic
263C2AGL(1,ℤ/8)×D15111yescharacteristic
264C2C2×#1801277111yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#477×C151C2
socleC22×C151C22×D4
prime radical#18012714C22
hypercenter#477D151
hypocenterC151#3238
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D151C2semidirect
3. #23752620C2semidirect
4. #23752573C2semidirect
5. #23752541C2semidirect
7. #23752507C2semidirect
8. #23752503C2semidirect
9. #23752499C2semidirect
10. #23752268C2semidirect
11. #477×C151C2semidirect
132. C151#3238semidirect
141. #477D151semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1512
#237527492
#237526202
#237525732
#237525412
#237525272
#237525072
#237525032
#237524992
#237522682
#477×C1512
#3238151