Finite Group Databasebeta

← #34070142

Subgroups — #34070142

Order 19328.

394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#18012772C211yesmaximal, characteristic, complemented
2#23752781C211yesmaximal, characteristic
3C2×#18012727C211yesmaximal, characteristic, complemented
4C2×#18012667C211yesmaximal, characteristic, complemented
5#23752220C211yesmaximal, characteristic, complemented
6C2×#18012655C211yesmaximal, characteristic, complemented
7#339×C151C211yesmaximal, characteristic, complemented
8C2×#14559004C2211yescharacteristic
9C22×Dic302C2211yescharacteristic
10C22×D604C2211yescharacteristic
11#18012772—22no—
12#18012772—22no—
13C2×Dic604—21no—
14C2×#14558993—21no—
15C2×#14558988C2211yescharacteristic
16#18012736—21no—
17#18012727—22no—
18#18012727—21no—
19#18012727—22no—
20#18012714—22no—
21#18012709—22no—
22C2×(C2×D151)⋊C4—22no—
23#18012667—22no—
24#18012662—22no—
25#18012655—22no—
26C2×M16×C151C2211yescharacteristic
27#117×C151C2211yescharacteristic
28C2×C42×C151C2211yescharacteristic
29C23×D151D412yes—
30#14559004—21no—
31#14559004—21no—
32#14559004—21no—
33#14559004—21no—
34C2×Dic302—21no—
35C2×Dic302—21no—
36C2×Dic302—21no—
37C2×Dic302—21no—
38C2×Dic302—21no—
39C2×Dic302D411yescharacteristic
40C2×Dic302D412yescomplemented
41C2×D604—24no—
42C2×D604—21no—
43C2×D604—21no—
44C2×D604—21no—
45C2×D604—21no—
46C2×D604—21no—
47C2×D604—21no—
48C2×D604D411yescharacteristic
49C2×C22⋊D151—21no—
50C22×Dic151—21no—
51C2×C4×D151—21no—
52Dic604—24no—
53#14558993—24no—
54#14558988—21no—
55#14558988—21no—
56C2×C151⋊C8—21no—
57(C2×D151)⋊C4—28no—
58(C2×D151)⋊C4—24no—
59C22×C4×C151—21no—
60C22×C4×C151C2311yescharacteristic
61M16×C151—21no—
62M16×C151D412yescomplemented
63C2×C8×C151—21no—
64C4⋊C4×C151D412yes—
65C22⋊C4×C151—21no—
66C42×C151—21no—
67C42×C151—21no—
68C42×C151D412yescomplemented
69C22×D151—22no—
70C22×D151—22no—
71C22×D151—21no—
72C22×D151—22no—
73C22×D151—44no—
74Dic302—22no—
75Dic302—21no—
76Dic302—22no—
77Dic302—21no—
78Dic302—41no—
79Dic302—41no—
80D604—21no—
81D604—21no—
82D604—41no—
83D604—41no—
84D604—41no—
85D604—41no—
86D604—84no—
87C22⋊D151—41no—
88C22⋊D151—41no—
89C2×Dic151—21no—
90C2×Dic151—22no—
91C2×Dic151—41no—
92C2×Dic151—41no—
93C4×D151—41no—
94C4×D151—41no—
95C151⋊C8—41no—
96C23×C151C2×D411yescharacteristic
97C2×C4×C151—22no—
98C2×C4×C151—22no—
99C2×C4×C151—42no—
100C2×C4×C151C2×D411yescharacteristic
101C2×C4×C151C2×D411yescharacteristic
102C2×C4×C151C2×D411yescharacteristic
103C2×C4×C151C2×D411yescharacteristic
104C2×C4×C151C2×D411yescharacteristic
105C2×C4×C151#4111yescharacteristic
106C8×C151—22no—
107C22×C151—22no—
108C22×C151#12011yescharacteristic
109C22×C151#12011yescharacteristic
110C22×C151#12111yescharacteristic
111C2×D151—44no—
112C2×D151—41no—
113C2×D151—42no—
114C2×D151—42no—
115C2×D151—44no—
116C2×D151—82no—
117C4×C151—42no—
118C4×C151—42no—
119C4×C151#12011yescharacteristic
120C4×C151#12111yescharacteristic
121C4×C151#12111yescharacteristic
122C4×C151#12711yescharacteristic
123Dic151—41no—
124Dic151—42no—
125C2×C151—21no—
126C2×C151—21no—
127C2×C151#39211yescharacteristic
128C2×C151#45512yes—
129D151—81no—
130D151—82no—
131C151#200411yescharacteristic, complemented, Sylow
132#2004—1511nomaximal, Sylow
133C2×#137—1511no—
134#535—1511no—
135C2×#124—1511no—
136C2×#104—1511no—
137#419—1511no—
138C2×#100—1511no—
139#339D15111yescharacteristic, complemented
140C2×#41—1511no—
141C22×Q8—1511no—
142C22×D4—1511no—
143#137—3022no—
144#137—3022no—
145C2×Q16—3021no—
146C2×SD16—3021no—
147C2×M16—1511no—
148C2×M16C2×D15111yescharacteristic
149#127—3021no—
150#124—3022no—
151#124—3021no—
152#124—3022no—
153#121—3022no—
154#120—3022no—
155#117C2×D15111yescharacteristic
156C2×C22⋊C4—3022no—
157C2×C42C2×D15111yescharacteristic
158#104—3022no—
159#103—3022no—
160#100—3022no—
161C24—1512no—
162#41—3021no—
163#41—3021no—
164#41—3021no—
165#41—3021no—
166C2×Q8—3021no—
167C2×Q8—3021no—
168C2×Q8—3021no—
169C2×Q8—3021no—
170C2×Q8—3021no—
171C2×Q8—1511no—
172C2×Q8—1512no—
173C2×D4—3024no—
174C2×D4—3021no—
175C2×D4—3021no—
176C2×D4—3021no—
177C2×D4—3021no—
178C2×D4—3021no—
179C2×D4—3021no—
180C2×D4—3021no—
181C2×D4—1511no—
182C22×C4—21no—
183C22×C4—3021no—
184C22×C4—3021no—
185C22×C4C22×D15111yescharacteristic
186Q16—3024no—
187SD16—3024no—
188M16—21no—
189M16—3021no—
190M16—3021no—
191M16D60412yescomplemented
192C2×C8—21no—
193C2×C8—3021no—
194C4⋊C4D60412yes—
195C22⋊C4—21no—
196C22⋊C4—3028no—
197C22⋊C4—3024no—
198C42—21no—
199C42—21no—
200C42D60412yescomplemented
201C23—3022no—
202C23—3022no—
203C23—3021no—
204C23—3022no—
205C23—6044no—
206C23D4×D15111yescharacteristic
207Q8—3022no—
208Q8—3021no—
209Q8—3022no—
210Q8—3021no—
211Q8—6041no—
212Q8—6041no—
213D4—3021no—
214D4—3021no—
215D4—6041no—
216D4—6041no—
217D4—6041no—
218D4—6041no—
219D4—6041no—
220D4—6041no—
221D4—12084no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—3022no—
226C2×C4—3021no—
227C2×C4—6041no—
228C2×C4—6041no—
229C2×C4—6041no—
230C2×C4—6041no—
231C2×C4D4×D15111yescharacteristic
232C2×C4D4×D15111yescharacteristic
233C2×C4C2×D60411yescharacteristic
234C2×C4C2×D60411yescharacteristic
235C2×C4C2×D60411yescharacteristic
236C2×C4#1455900511yescharacteristic
237C8—22no—
238C8—6041no—
239C22—22no—
240C22—6044no—
241C22—6041no—
242C22—6042no—
243C22—6042no—
244C22—6044no—
245C22—12082no—
246C22#1801270911yescharacteristic
247C22#1801270911yescharacteristic
248C22#1801271411yescharacteristic
249C4—42no—
250C4—42no—
251C4—6041no—
252C4—6042no—
253C4#1801270911yescharacteristic
254C4#1801271411yescharacteristic
255C4#1801271411yescharacteristic
256C4#1801273611yescharacteristic
257C2—21no—
258C2—21no—
259C2—12082no—
260C2—12081no—
261C2#2375212211yescharacteristic
262C2#2375239112yes—
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#339×C151C2
socleC22×C151#120
prime radical#23752781C2
hypercenter#339D151
hypocenterC151#2004
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#18012772C2semidirect
3. C2×#18012727C2semidirect
4. C2×#18012667C2semidirect
5. #23752220C2semidirect
6. C2×#18012655C2semidirect
7. #339×C151C2semidirect
40. C2×Dic302D4semidirect
62. M16×C151D4semidirect
68. C42×C151D4semidirect
131. C151#2004semidirect
139. #339D151semidirect
191. M16D604semidirect
200. C42D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127722
#237527812
C2×#180127272
C2×#180126672
#237522202
C2×#180126552
#339×C1512
#2004151