Finite Group Databasebeta

← #34070128

Subgroups — #34070128

Order 19328.

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

normal subgroups only

This group has 478 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×#18012767C211yesmaximal, characteristic, complemented
2#23752781C211yesmaximal, characteristic, complemented
3C2×#18012736C211yesmaximal, characteristic, complemented
4C2×#18012667C211yesmaximal, characteristic, complemented
5#23752216C211yesmaximal, characteristic, complemented
6C2×#18012655C211yesmaximal, characteristic, complemented
7#339×C151C211yesmaximal, characteristic, complemented
8C2×#14559004C2211yescharacteristic
9C22×D604—22no—
10C22×D604C2211yescharacteristic
11C22×D604C2211yescharacteristic
12#18012767—22no—
13#18012767—22no—
14C2×#14558993—21no—
15C2×D1208—21no—
16C2×#14558988C2211yescharacteristic
17#18012736—22no—
18#18012736—22no—
19#18012736—21no—
20#18012727—21no—
21#18012714—22no—
22#18012709—22no—
23#18012667—22no—
24#18012659—22no—
25#18012655—22no—
26C2×M16×C151C2211yescharacteristic
27#117×C151C2211yescharacteristic
28C2×C42×C151C2211yescharacteristic
29C23×D151—21no—
30C23×D151D412yes—
31#14559004—21no—
32#14559004—21no—
33#14559004—21no—
34#14559004—21no—
35C2×Dic302D411yescharacteristic, complemented
36C2×D604—28no—
37C2×D604—24no—
38C2×D604—21no—
39C2×D604—21no—
40C2×D604—21no—
41C2×D604—21no—
42C2×D604—21no—
43C2×D604—21no—
44C2×D604—21no—
45C2×D604—21no—
46C2×D604—21no—
47C2×D604—21no—
48C2×D604—21no—
49C2×D604—48no—
50C2×D604D411yescharacteristic, complemented
51C2×D604D412yescomplemented
52C2×C22⋊D151—21no—
53C2×C4×D151—21no—
54#14558993—24no—
55D1208—24no—
56#14558988—21no—
57#14558988—21no—
58C2×C151⋊C8—21no—
59(C2×D151)⋊C4—24no—
60C22×C4×C151—21no—
61C22×C4×C151C2311yescharacteristic
62M16×C151—21no—
63M16×C151D412yescomplemented
64C2×C8×C151—21no—
65C4⋊C4×C151D412yescomplemented
66C22⋊C4×C151—21no—
67C42×C151—21no—
68C42×C151—21no—
69C42×C151D412yescomplemented
70C22×D151—22no—
71C22×D151—21no—
72C22×D151—22no—
73C22×D151—22no—
74C22×D151—22no—
75C22×D151—44no—
76C22×D151—44no—
77C22×D151—41no—
78C22×D151—41no—
79Dic302—21no—
80Dic302—21no—
81D604—21no—
82D604—22no—
83D604—22no—
84D604—21no—
85D604—416no—
86D604—41no—
87D604—41no—
88D604—41no—
89D604—41no—
90D604—41no—
91D604—41no—
92D604—84no—
93C22⋊D151—41no—
94C22⋊D151—41no—
95C2×Dic151—21no—
96C4×D151—41no—
97C4×D151—41no—
98C151⋊C8—41no—
99C23×C151C2×D411yescharacteristic
100C2×C4×C151—24no—
101C2×C4×C151—22no—
102C2×C4×C151—22no—
103C2×C4×C151C2×D411yescharacteristic
104C2×C4×C151C2×D411yescharacteristic
105C2×C4×C151C2×D411yescharacteristic
106C2×C4×C151C2×D411yescharacteristic
107C2×C4×C151C2×D411yescharacteristic
108C2×C4×C151#4111yescharacteristic
109C8×C151—22no—
110C22×C151—22no—
111C22×C151#12011yescharacteristic
112C22×C151#12011yescharacteristic
113C22×C151#12111yescharacteristic
114C2×D151—44no—
115C2×D151—44no—
116C2×D151—41no—
117C2×D151—42no—
118C2×D151—42no—
119C2×D151—42no—
120C2×D151—44no—
121C2×D151—82no—
122C2×D151—82no—
123C2×D151—82no—
124C4×C151—24no—
125C4×C151—42no—
126C4×C151#12011yescharacteristic
127C4×C151#12111yescharacteristic
128C4×C151#12111yescharacteristic
129C4×C151#12711yescharacteristic
130Dic151—41no—
131C2×C151—21no—
132C2×C151—21no—
133C2×C151#39211yescharacteristic
134C2×C151#45312yes—
135D151—81no—
136D151—82no—
137D151—82no—
138C151#200211yescharacteristic, complemented, Sylow
139#2002—1511nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1511no—
141#535—1511no—
142C2×#127—1511no—
143C2×#104—1511no—
144#418—1511no—
145C2×#100—1511no—
146#339D15111yescharacteristic, complemented
147C2×#41—1511no—
148C22×D4—3022no—
149C22×D4—1511no—
150C22×D4—1511no—
151AGL(1,ℤ/8)—3022no—
152AGL(1,ℤ/8)—3022no—
153C2×SD16—3021no—
154C2×D8—3021no—
155C2×M16—1511no—
156C2×M16C2×D15111yescharacteristic
157#127—3022no—
158#127—3021no—
159#127—3022no—
160#124—3021no—
161#121—3022no—
162#120—3022no—
163#117C2×D15111yescharacteristic
164C2×C42C2×D15111yescharacteristic
165#104—3022no—
166#102—3022no—
167#100—3022no—
168C24—3021no—
169C24—1512no—
170#41—3021no—
171#41—3021no—
172#41—3021no—
173#41—3021no—
174C2×Q8—1511no—
175C2×D4—3028no—
176C2×D4—3024no—
177C2×D4—3021no—
178C2×D4—3021no—
179C2×D4—3021no—
180C2×D4—3021no—
181C2×D4—3021no—
182C2×D4—3021no—
183C2×D4—3021no—
184C2×D4—3021no—
185C2×D4—3021no—
186C2×D4—3021no—
187C2×D4—3021no—
188C2×D4—3021no—
189C2×D4—6048no—
190C2×D4—1511no—
191C2×D4—1512no—
192C22×C4—21no—
193C22×C4—3021no—
194C22×C4C22×D15111yescharacteristic
195SD16—3024no—
196D8—3024no—
197M16—21no—
198M16—3021no—
199M16—3021no—
200M16D60412yescomplemented
201C2×C8—21no—
202C2×C8—3021no—
203C4⋊C4D60412yescomplemented
204C22⋊C4—21no—
205C22⋊C4—3024no—
206C42—21no—
207C42—21no—
208C42D60412yescomplemented
209C23—3022no—
210C23—3022no—
211C23—3022no—
212C23—3021no—
213C23—3022no—
214C23—6044no—
215C23—6044no—
216C23—6041no—
217C23—6041no—
218C23D4×D15111yescharacteristic
219Q8—3021no—
220Q8—3021no—
221D4—3021no—
222D4—3022no—
223D4—3022no—
224D4—3021no—
225D4—60416no—
226D4—6041no—
227D4—6041no—
228D4—6041no—
229D4—6041no—
230D4—6041no—
231D4—6041no—
232D4—6041no—
233D4—6041no—
234D4—12084no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—3021no—
239C2×C4—6041no—
240C2×C4—6041no—
241C2×C4D4×D15111yescharacteristic
242C2×C4D4×D15111yescharacteristic
243C2×C4C2×D60411yescharacteristic
244C2×C4C2×D60411yescharacteristic
245C2×C4C2×D60411yescharacteristic
246C2×C4#1455900511yescharacteristic
247C8—22no—
248C8—6041no—
249C22—22no—
250C22—6044no—
251C22—6044no—
252C22—6041no—
253C22—6042no—
254C22—6042no—
255C22—6042no—
256C22—6044no—
257C22—12082no—
258C22—12082no—
259C22—12082no—
260C22#1801270911yescharacteristic
261C22#1801270911yescharacteristic
262C22#1801271411yescharacteristic
263C4—24no—
264C4—42no—
265C4—6041no—
266C4#1801270911yescharacteristic
267C4#1801271411yescharacteristic
268C4#1801271411yescharacteristic
269C4#1801273611yescharacteristic
270C2—21no—
271C2—21no—
272C2—12082no—
273C2—12082no—
274C2—12081no—
275C2#2375212211yescharacteristic
276C2#2375238112yes—
subgroupG/H
centerC22#18012709
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#339×C151C2
socleC22×C151#120
hypercenter#339D151
hypocenterC151#2002
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×#18012767C2semidirect
2. #23752781C2semidirect
3. C2×#18012736C2semidirect
4. C2×#18012667C2semidirect
5. #23752216C2semidirect
6. C2×#18012655C2semidirect
7. #339×C151C2semidirect
35. C2×Dic302D4semidirect
50. C2×D604D4semidirect
51. C2×D604D4semidirect
63. M16×C151D4semidirect
65. C4⋊C4×C151D4semidirect
69. C42×C151D4semidirect
138. C151#2002semidirect
146. #339D151semidirect
200. M16D604semidirect
203. C4⋊C4D604semidirect
208. C42D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127672
#237527812
C2×#180127362
C2×#180126672
#237522162
C2×#180126552
#339×C1512
#2002151