Finite Group Databasebeta

← #34067663

Subgroups — #34067663

Order 19328.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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#23752722C211yesmaximal, characteristic
2C22⋊C8×D151C211yesmaximal, characteristic, complemented
3#23752074C211yesmaximal, characteristic, complemented
4#23751950C211yesmaximal, characteristic, complemented
5#23751948C211yesmaximal, characteristic, complemented
6#23751946C211yesmaximal, characteristic, complemented
7#327×C151C211yesmaximal, characteristic, complemented
8C2×#14559003C411yescharacteristic, complemented
9C22×C4×D151C2211yescharacteristic
10C2×C8×D151—21no—
11#18012721—21no—
12#18012719C411yescharacteristic, complemented
13#18012718C2211yescharacteristic
14#18012710C411yescharacteristic, complemented
15#18012707—21no—
16D4×Dic151—21no—
17(C22⋊D151)⋊C4—21no—
18#18012697C411yescharacteristic, complemented
19C2×(C2×D151)⋊C4—21no—
20C22⋊(C151⋊C8)C2211yescharacteristic
21(C2×D151)⋊C8—21no—
22C151⋊#95—21no—
23C151⋊#95C2211yescharacteristic
24#121×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C23×D151D411yescharacteristic
28#14559003—42no—
29C2×Dic302C2×C411yescharacteristic
30C2×C22⋊D151—21no—
31C2×C22⋊D151—21no—
32C22×Dic151—21no—
33C22×Dic151—21no—
34C22×Dic151D411yescharacteristic
35C2×C4×D151—42no—
36C2×C4×D151C2×C411yescharacteristic
37C2×C4×D151C2×C411yescharacteristic
38C2×C4×D151D411yescharacteristic
39C2×C4×D151D411yescharacteristic
40C2×C151⋊C8—21no—
41C8×D151—42no—
42C4⋊Dic151—21no—
43C4⋊Dic151C2×C411yescharacteristic
44Dic151⋊C4—21no—
45C22⋊Dic151—21no—
46C22⋊Dic151—21no—
47(C2×D151)⋊C4—21no—
48(C2×D151)⋊C4—21no—
49(C2×D151)⋊C4—42no—
50C4×Dic151—21no—
51C2×D4×C151—21no—
52C2×D4×C151C2×C411yescharacteristic
53C22×C4×C151—21no—
54C22×C4×C151C2311yescharacteristic
55C2×C8×C151—21no—
56C4⋊C4×C151C2×C411yescharacteristic
57C22⋊C4×C151—21no—
58C22×D151—21no—
59C22×D151—21no—
60C22×D151—22no—
61C22×D151—41no—
62C22×D151C22⋊C411yescharacteristic
63C22×D151C22⋊C411yescharacteristic
64Dic302—41no—
65C22⋊D151—42no—
66C22⋊D151—42no—
67C2×Dic151—21no—
68C2×Dic151—21no—
69C2×Dic151—41no—
70C2×Dic151—42no—
71C2×Dic151—41no—
72C2×Dic151—41no—
73C2×Dic151—41no—
74C2×Dic151C22⋊C411yescharacteristic
75C2×Dic151C22⋊C411yescharacteristic
76C4×D151—22no—
77C4×D151—22no—
78C4×D151—41no—
79C4×D151—41no—
80C151⋊C8—41no—
81C23×C151—21no—
82C23×C151C2×D411yescharacteristic
83D4×C151—41no—
84D4×C151—41no—
85D4×C151—41no—
86C2×C4×C151—21no—
87C2×C4×C151—41no—
88C2×C4×C151—41no—
89C2×C4×C151—41no—
90C2×C4×C151—41no—
91C2×C4×C151C22×C411yescharacteristic
92C2×C4×C151C2×D411yescharacteristic
93C8×C151—41no—
94C22×C151—21no—
95C22×C151—21no—
96C22×C151—41no—
97C22×C151—41no—
98C22×C151—41no—
99C22×C151C2×C22⋊C411yescharacteristic
100C22×C151#13511yescharacteristic
101C22×C151#13511yescharacteristic
102C2×D151—21no—
103C2×D151—21no—
104C2×D151—21no—
105C2×D151—21no—
106C2×D151—21no—
107C2×D151—42no—
108C2×D151—42no—
109C2×D151#9912yes—
110C4×C151—21no—
111C4×C151—21no—
112C4×C151—41no—
113C4×C151—81no—
114Dic151—21no—
115Dic151—21no—
116Dic151—41no—
117Dic151—41no—
118Dic151—81no—
119C2×C151—21no—
120C2×C151—21no—
121C2×C151—81no—
122C2×C151C2×#9911yescharacteristic
123C2×C151#41611yescharacteristic
124C2×C151#42111yescharacteristic
125D151—22no—
126D151—41no—
127C151#151611yescharacteristic, complemented, Sylow
128#1516—1511nomaximal, Sylow
129#525—1511no—
130C2×C22⋊C8—1511no—
131#381—1511no—
132#328—1511no—
133#328—1511no—
134#327—1511no—
135#327D15111yescharacteristic, complemented
136C2×#41—1511no—
137C23×C4—1511no—
138C22×C8—3021no—
139#123—3021no—
140C22⋊Q8—1511no—
141C22⋊Q8—1511no—
142#121—1511no—
143#121C2×D15111yescharacteristic
144#120—3021no—
145C4×D4—3021no—
146C4×D4—3021no—
147#117—1511no—
148C2×C22⋊C4—3021no—
149C22⋊C8—3021no—
150C22⋊C8—1511no—
151C22⋊C8C2×D15111yescharacteristic
152#95—3021no—
153#95—1511no—
154#95C2×D15111yescharacteristic
155C24—1511no—
156#41—6042no—
157C2×Q8—1511no—
158C2×D4—21no—
159C2×D4—3021no—
160C2×D4—3021no—
161C2×D4C4×D15111yescharacteristic
162C22×C4—21no—
163C22×C4—3021no—
164C22×C4—3021no—
165C22×C4—6042no—
166C22×C4—1511no—
167C22×C4—1511no—
168C22×C4—1511no—
169C22×C4—1511no—
170C22×C4—1511no—
171C22×C4C22×D15111yescharacteristic
172C2×C8—21no—
173C2×C8—3021no—
174C2×C8—6042no—
175C4⋊C4—3021no—
176C4⋊C4—3021no—
177C4⋊C4—1511no—
178C4⋊C4C4×D15111yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—3021no—
181C22⋊C4—3021no—
182C22⋊C4—3021no—
183C22⋊C4—3021no—
184C22⋊C4—6042no—
185C42—3021no—
186C23—21no—
187C23—3022no—
188C23—3021no—
189C23—3021no—
190C23—6041no—
191C23—1511no—
192C23—1511no—
193C23D4×D15111yescharacteristic
194Q8—6041no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—6042no—
199D4—6042no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—3022no—
206C2×C4—3022no—
207C2×C4—3021no—
208C2×C4—3021no—
209C2×C4—6041no—
210C2×C4—6041no—
211C2×C4—6041no—
212C2×C4—6042no—
213C2×C4—6041no—
214C2×C4—6041no—
215C2×C4—6041no—
216C2×C4—1511no—
217C2×C4—1511no—
218C2×C4C2×C4×D15111yescharacteristic
219C2×C4D4×D15111yescharacteristic
220C8—41no—
221C8—6041no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—3021no—
228C22—3021no—
229C22—3021no—
230C22—3021no—
231C22—3021no—
232C22—6042no—
233C22—6042no—
234C22—1512no—
235C22C22⋊C4×D15111yescharacteristic
236C22#1801275811yescharacteristic
237C22#1801276011yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—3021no—
243C4—3021no—
244C4—6041no—
245C4—6041no—
246C4—12081no—
247C2—21no—
248C2—21no—
249C2—81no—
250C2—3022no—
251C2—6041no—
252C2#99×D15111yescharacteristic
253C2#2375220511yescharacteristic
254C2#2375222711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D151
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#327×C151C2
socleC22×C151C2×C22⋊C4
prime radical#23752722C2
cosocleC22×C4×C151C23
hypercenter#327D151
hypocenterC151#1516
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D151C2semidirect
3. #23752074C2semidirect
4. #23751950C2semidirect
5. #23751948C2semidirect
6. #23751946C2semidirect
7. #327×C151C2semidirect
8. C2×#14559003C4semidirect
12. #18012719C4semidirect
14. #18012710C4semidirect
18. #18012697C4semidirect
127. C151#1516semidirect
135. #327D151semidirect

Maximal subgroups

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

subgroupindex
#237527222
C22⋊C8×D1512
#237520742
#237519502
#237519482
#237519462
#327×C1512
#1516151