Finite Group Databasebeta

← #34079881

Subgroups — #34079881

Order 19328.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C22⋊Q8×D151C212yesmaximal
2#23752549C212yesmaximal, complemented
3#23752546C212yesmaximal, complemented
4#23752453C211yesmaximal, characteristic, complemented
5#23752451C212yesmaximal, complemented
6#23752369C212yesmaximal, complemented
7#23752366C212yesmaximal, complemented
8C2×(C2×D151)⋊C8C211yesmaximal, characteristic
9#467×C151C211yesmaximal, characteristic, complemented
10C2×Q8×D151C2212yes—
11C22×C4×D151C2211yescharacteristic
12C2×Dic604C2211yescharacteristic, complemented
13C2×#14558994C2212yescomplemented
14C22×C151⋊C8C2211yescharacteristic
15#18012719C2212yes—
16#18012718C2212yes—
17#18012717—22no—
18#18012716—22no—
19#18012715C2212yes—
20C4⋊C4×D151—22no—
21C4⋊C4×D151C2212yes—
22C22⋊C4×D151—22no—
23#18012673C2211yescharacteristic, complemented
24#18012672C2212yescomplemented
25#18012664C2212yescomplemented
26#18012663C2212yescomplemented
27#18012662C2212yescomplemented
28(C2×D151)⋊C8C2212yes—
29(C2×D151)⋊C8C2212yes—
30C2×Q16×C151C2211yescharacteristic, complemented
31C22×C8×C151C2211yescharacteristic
32C22⋊Q8×C151C2212yes—
33#107×C151C2211yescharacteristic, complemented
34#103×C151C2212yescomplemented
35C23×D151D411yescharacteristic
36C2×Dic302—22no—
37C2×Dic302C2312yes—
38Q8×D151—42no—
39Q8×D151—42no—
40C22×Dic151D411yescharacteristic
41C2×C4×D151—22no—
42C2×C4×D151—22no—
43C2×C4×D151—41no—
44C2×C4×D151—41no—
45C2×C4×D151D412yes—
46C2×C4×D151C2312yes—
47Dic604—41no—
48#14558994—42no—
49C2×C151⋊C8—41no—
50C2×C151⋊C8C2312yes—
51C4⋊Dic151—22no—
52C4⋊Dic151C2312yes—
53Dic151⋊C4—22no—
54Dic151⋊C4—22no—
55Dic151⋊C4—22no—
56C22⋊Dic151—22no—
57(C2×D151)⋊C4—22no—
58(C2×D151)⋊C4—22no—
59C2×Q8×C151C2312yes—
60C22×C4×C151C2311yescharacteristic
61Q16×C151—41no—
62C2×C8×C151—41no—
63C2×C8×C151C2311yescharacteristic
64C2×C8×C151C2311yescharacteristic
65C4⋊C4×C151—22no—
66C4⋊C4×C151C2312yes—
67C22⋊C4×C151—22no—
68C22×D151—41no—
69C22×D151—41no—
70C22×D151Q1614yescomplemented
71C22×D151C2×D412yes—
72Dic302—22no—
73Dic302—22no—
74Dic302—44no—
75C2×Dic151—22no—
76C2×Dic151—22no—
77C2×Dic151—41no—
78C2×Dic151C2×D412yes—
79C4×D151—22no—
80C4×D151—22no—
81C4×D151—42no—
82C4×D151—44no—
83C4×D151—44no—
84C151⋊C8—22no—
85C23×C151C2×D411yescharacteristic
86Q8×C151—22no—
87Q8×C151—22no—
88C2×C4×C151—21no—
89C2×C4×C151—21no—
90C2×C4×C151—22no—
91C2×C4×C151—22no—
92C2×C4×C151C2×D411yescharacteristic
93C2×C4×C151C2411yescharacteristic
94C8×C151—21no—
95C8×C151—21no—
96C22×C151—21no—
97C22×C151—21no—
98C22×C151C2×Q1612yes—
99C22×C151C22×D411yescharacteristic
100C2×D151—22no—
101C2×D151—22no—
102C2×D151—44no—
103C2×D151C2×Q1614yes—
104C4×C151—21no—
105C4×C151—42no—
106C4×C151—42no—
107C4×C151H(5,𝔽2)11yescharacteristic
108C4×C151H(5,𝔽2)11yescharacteristic
109Dic151—22no—
110Dic151—42no—
111Dic151—42no—
112C2×C151—22no—
113C2×C151#53411yescharacteristic
114C2×C151C22×Q1611yescharacteristic
115C2×C151#57511yescharacteristic
116D151—24no—
117C151#318911yescharacteristic, complemented, Sylow
118#3189—1511nomaximal, Sylow
119C2×C22⋊Q8—1512no—
120#484—1512no—
121#484—1512no—
122#467—1511no—
123#467—1512no—
124#467D15111yescharacteristic, complemented
125#451—1512no—
126#451—1512no—
127C2×C22⋊C8—1511no—
128C22×Q8—1512no—
129C23×C4—1511no—
130C2×Q16—1512no—
131C2×Q16—1511no—
132C2×Q16C2×D15111yescharacteristic, complemented
133C22×C8—1511no—
134C22×C8C2×D15111yescharacteristic
135C22⋊Q8—3022no—
136C22⋊Q8—3022no—
137C22⋊Q8—1512no—
138C22⋊Q8—1512no—
139C22⋊Q8—1512no—
140C22⋊Q8C2×D15112yes—
141C2×C4⋊C4—3022no—
142C2×C4⋊C4—1512no—
143C2×C22⋊C4—3022no—
144#107—1511no—
145#107—1512no—
146#107C2×D15111yescharacteristic, complemented
147#103—1512no—
148#103—1512no—
149#103—1512no—
150#103C2×D15112yescomplemented
151C22⋊C8—1512no—
152C22⋊C8—1512no—
153C24—1511no—
154C2×Q8—3022no—
155C2×Q8—6042no—
156C2×Q8—6042no—
157C2×Q8—1512no—
158C2×Q8C22×D15112yes—
159C22×C4—3022no—
160C22×C4—3022no—
161C22×C4—6041no—
162C22×C4—6041no—
163C22×C4—1512no—
164C22×C4—1511no—
165C22×C4—1512no—
166C22×C4C22×D15111yescharacteristic
167Q16—41no—
168Q16—6041no—
169Q16—6042no—
170C2×C8—41no—
171C2×C8—6041no—
172C2×C8—1512no—
173C2×C8C22×D15111yescharacteristic
174C2×C8C22×D15111yescharacteristic
175C4⋊C4—22no—
176C4⋊C4—3022no—
177C4⋊C4—3022no—
178C4⋊C4—3022no—
179C4⋊C4—3022no—
180C4⋊C4—1512no—
181C4⋊C4C22×D15112yes—
182C22⋊C4—22no—
183C22⋊C4—3022no—
184C22⋊C4—3022no—
185C22⋊C4—3022no—
186C23—6041no—
187C23—6041no—
188C23—1512no—
189C23—1514no—
190C23D4×D15111yescharacteristic
191Q8—22no—
192Q8—22no—
193Q8—3022no—
194Q8—3022no—
195Q8—6044no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—3022no—
201C2×C4—3022no—
202C2×C4—3022no—
203C2×C4—3022no—
204C2×C4—6042no—
205C2×C4—6044no—
206C2×C4—6044no—
207C2×C4—6041no—
208C2×C4—1512no—
209C2×C4D4×D15111yescharacteristic
210C2×C4C23×D15111yescharacteristic
211C8—21no—
212C8—21no—
213C8—3022no—
214C22—21no—
215C22—21no—
216C22—3022no—
217C22—3022no—
218C22—6044no—
219C22—1514no—
220C22Q16×D15112yes—
221C22C2×D4×D15111yescharacteristic
222C4—21no—
223C4—42no—
224C4—42no—
225C4—3022no—
226C4—6042no—
227C4—6042no—
228C4#1801278411yescharacteristic
229C4#1801278511yescharacteristic
230C2—22no—
231C2—3024no—
232C2#2375277011yescharacteristic
233C2C2×Q16×D15111yescharacteristic
234C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#467×C151C2
socleC22×C151C22×D4
prime radicalC23×D151D4
hypercenter#467D151
hypocenterC151#3189
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #23752549C2semidirect
3. #23752546C2semidirect
4. #23752453C2semidirect
5. #23752451C2semidirect
6. #23752369C2semidirect
7. #23752366C2semidirect
9. #467×C151C2semidirect
12. C2×Dic604C22semidirect
13. C2×#14558994C22semidirect
23. #18012673C22semidirect
24. #18012672C22semidirect
25. #18012664C22semidirect
26. #18012663C22semidirect
27. #18012662C22semidirect
30. C2×Q16×C151C22semidirect
33. #107×C151C22semidirect
34. #103×C151C22semidirect
70. C22×D151Q16semidirect
117. C151#3189semidirect
124. #467D151semidirect
132. C2×Q16C2×D151semidirect
146. #107C2×D151semidirect
150. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1512
#237525492
#237525462
#237524532
#237524512
#237523692
#237523662
C2×(C2×D151)⋊C82
#467×C1512
#3189151