Finite Group Databasebeta

← #34070762

Subgroups — #34070762

Order 19328.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#23752784C211yesmaximal, characteristic
2#23752193C211yesmaximal, characteristic
3#23752184C211yesmaximal, characteristic
4#23752003C211yesmaximal, characteristic, complemented
5#23752002C211yesmaximal, characteristic, complemented
6#23752001C211yesmaximal, characteristic, complemented
7#352×C151C211yesmaximal, characteristic, complemented
8C2×#14559003C2211yescharacteristic
9C22×Dic302C411yescharacteristic, complemented
10M16×D151—21no—
11#18012738—21no—
12#18012725—21no—
13#18012723C411yescharacteristic, complemented
14#18012722C411yescharacteristic, complemented
15#18012720C2211yescharacteristic
16#18012717—21no—
17#18012716—21no—
18#18012695—21no—
19#18012695C411yescharacteristic, complemented
20#18012657—21no—
21#18012656C2211yescharacteristic
22#18012654C2211yescharacteristic
23#18012653—21no—
24#123×C151C2211yescharacteristic
25#100×C151C2211yescharacteristic
26#99×C151C2211yescharacteristic
27#14559003—41no—
28#14559003—41no—
29C2×Dic302—21no—
30C2×Dic302—21no—
31C2×Dic302—41no—
32C2×Dic302—41no—
33C2×Dic302D411yescharacteristic
34C2×C22⋊D151C2×C411yescharacteristic
35C2×C22⋊D151D411yescharacteristic
36C22×Dic151C2×C411yescharacteristic
37C22×Dic151C2×C411yescharacteristic
38C22×Dic151D411yescharacteristic
39C2×C4×D151D411yescharacteristic
40#14558988—21no—
41#14558987—41no—
42C8×D151—41no—
43C4⋊Dic151—21no—
44Dic151⋊C4—21no—
45Dic151⋊C4—21no—
46Dic151⋊C4—21no—
47Dic151⋊C4—41no—
48C22⋊Dic151—21no—
49C22⋊Dic151—21no—
50C22⋊Dic151C2×C411yescharacteristic
51(C2×D151)⋊C4—21no—
52(C2×D151)⋊C4—21no—
53C4×Dic151—21no—
54C4×Dic151—41no—
55C2×D4×C151C2311yescharacteristic
56C22×C4×C151C2×C411yescharacteristic
57M16×C151—21no—
58C4⋊C4×C151—21no—
59C22⋊C4×C151—21no—
60C22⋊C4×C151—21no—
61C22⋊C4×C151C2×C411yescharacteristic
62C22×D151C22⋊C411yescharacteristic
63Dic302—41no—
64Dic302—42no—
65Dic302—41no—
66Dic302—41no—
67C22⋊D151—41no—
68C22⋊D151—41no—
69C2×Dic151—21no—
70C2×Dic151—21no—
71C2×Dic151—21no—
72C2×Dic151—21no—
73C2×Dic151—21no—
74C2×Dic151—21no—
75C2×Dic151—41no—
76C2×Dic151—41no—
77C2×Dic151C22⋊C411yescharacteristic
78C2×Dic151C22⋊C411yescharacteristic
79C2×Dic151C22⋊C411yescharacteristic
80C4×D151—21no—
81C4×D151—21no—
82C151⋊C8—41no—
83C23×C151C22×C411yescharacteristic
84C23×C151C2×D411yescharacteristic
85D4×C151—41no—
86C2×C4×C151—21no—
87C2×C4×C151—21no—
88C2×C4×C151—41no—
89C2×C4×C151—41no—
90C2×C4×C151C2×D411yescharacteristic
91C8×C151—41no—
92C22×C151—21no—
93C22×C151—21no—
94C22×C151—41no—
95C22×C151—41no—
96C22×C151C2×C22⋊C411yescharacteristic
97C2×D151—21no—
98C2×D151—41no—
99C4×C151—21no—
100C4×C151—41no—
101C4×C151—41no—
102C4×C151—81no—
103Dic151—21no—
104Dic151—21no—
105Dic151—41no—
106Dic151—41no—
107Dic151—81no—
108Dic151#9911yescharacteristic
109Dic151#9911yescharacteristic
110C2×C151—21no—
111C2×C151—41no—
112C2×C151—41no—
113C2×C151C2×#9911yescharacteristic
114D151—41no—
115C151#212311yescharacteristic, complemented, Sylow
116#2123—1511nomaximal, Sylow
117#536—1511no—
118#413—1511no—
119#410—1511no—
120#352—1511no—
121#352—1511no—
122#352—1511no—
123#352D15111yescharacteristic, complemented
124C2×#41—1511no—
125C22×Q8—1511no—
126C2×M16—3021no—
127C4⋊Q8—3021no—
128#124—3021no—
129#123—1511no—
130#123—1511no—
131#123—1511no—
132#123C2×D15111yescharacteristic
133C22⋊Q8—3021no—
134C22⋊Q8—3021no—
135#117—3021no—
136#117—1511no—
137#101—3021no—
138#100—1511no—
139#100C2×D15111yescharacteristic
140#99—3021no—
141#99—1511no—
142#99C2×D15111yescharacteristic
143#41—6041no—
144#41—6041no—
145C2×Q8—3021no—
146C2×Q8—3021no—
147C2×Q8—6041no—
148C2×Q8—6041no—
149C2×Q8—1511no—
150C2×D4—1511no—
151C2×D4—1511no—
152C2×D4C22×D15111yescharacteristic
153C22×C4—1511no—
154C22×C4—1511no—
155C22×C4—1511no—
156C22×C4—1511no—
157C22×C4C4×D15111yescharacteristic
158M16—21no—
159M16—3021no—
160M16—6041no—
161C2×C8—6041no—
162C4⋊C4—21no—
163C4⋊C4—3021no—
164C4⋊C4—3021no—
165C4⋊C4—3021no—
166C4⋊C4—3021no—
167C4⋊C4—6041no—
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—3021no—
171C22⋊C4—3021no—
172C22⋊C4—3021no—
173C22⋊C4—3021no—
174C22⋊C4—1511no—
175C22⋊C4C4×D15111yescharacteristic
176C42—3021no—
177C42—6041no—
178C23—1511no—
179C23C2×C4×D15111yescharacteristic
180C23D4×D15111yescharacteristic
181Q8—6041no—
182Q8—6042no—
183Q8—6041no—
184Q8—6041no—
185D4—41no—
186D4—6041no—
187D4—6041no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—3021no—
193C2×C4—3021no—
194C2×C4—3021no—
195C2×C4—3021no—
196C2×C4—3021no—
197C2×C4—3021no—
198C2×C4—3021no—
199C2×C4—3021no—
200C2×C4—6041no—
201C2×C4—6041no—
202C2×C4—1511no—
203C2×C4—1511no—
204C2×C4—1511no—
205C2×C4D4×D15111yescharacteristic
206C8—41no—
207C8—6041no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—3021no—
213C22—6041no—
214C22C22⋊C4×D15111yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—3021no—
220C4—3021no—
221C4—6041no—
222C4—6041no—
223C4—1511no—
224C4—1511no—
225C4—12081no—
226C2—21no—
227C2—41no—
228C2—41no—
229C2—6041no—
230C2#99×D15111yescharacteristic
subgroupG/H
centerC2#99×D151
commutatorC23×C151C22×C4
FrattiniC2×D4C22×D151
Fitting#352×C151C2
socleC2×C151C2×#99
prime radicalC2×#14559003C22
cosocleC2×D4×C151C23
hypercenter#352D151
hypocenterC151#2123
LCSG ▷ C23×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #23752003C2semidirect
5. #23752002C2semidirect
6. #23752001C2semidirect
7. #352×C151C2semidirect
9. C22×Dic302C4semidirect
13. #18012723C4semidirect
14. #18012722C4semidirect
19. #18012695C4semidirect
115. C151#2123semidirect
123. #352D151semidirect

Maximal subgroups

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

subgroupindex
#237527842
#237521932
#237521842
#237520032
#237520022
#237520012
#352×C1512
#2123151