Finite Group Databasebeta

← #34080186

Subgroups — #34080186

Order 19328.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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#23752823C211yesmaximal, characteristic, complemented
2#23752787C211yesmaximal, characteristic
3#23752604C211yesmaximal, characteristic, complemented
4#23752580C211yesmaximal, characteristic, complemented
5#23752567C211yesmaximal, characteristic, complemented
6#23752436C212yesmaximal, complemented
7#23752420C212yesmaximal, complemented
8#23752373C212yesmaximal
9#23752366C212yesmaximal, complemented
10#23752271C211yesmaximal, characteristic, complemented
11#494×C151C211yesmaximal, characteristic, complemented
12C2×#14559005C2211yescharacteristic
13C2×Q8×D151C2211yescharacteristic
14C2×#14558994C2212yes—
15C2×#14558991C2212yes—
16#18012737C2211yescharacteristic
17#18012734—22no—
18#18012731C2211yescharacteristic
19#18012729—22no—
20#18012728C2211yescharacteristic
21#18012727C2211yescharacteristic
22#18012724—22no—
23#18012717—22no—
24#18012715C2212yes—
25Q8×Dic151C2212yes—
26#18012696C2211yescharacteristic
27Dic151⋊C8C2212yes—
28#18012664C2212yes—
29#18012663C2212yes—
30#18012663C2212yes—
31#18012661C2212yes—
32(C2×D151)⋊C8C2212yes—
33#18012650C2211yescharacteristic
34C2×Q16×C151C2212yes—
35C2×Q16×C151C2212yes—
36C4⋊Q8×C151C2211yescharacteristic
37C4⋊Q8×C151C2211yescharacteristic
38C4×C8×C151C2211yescharacteristic
39#14559005—42no—
40C2×Dic302—21no—
41C2×Dic302C2311yescharacteristic
42Q8×D151—42no—
43C2×D604—21no—
44C2×D604C2311yescharacteristic
45C2×C4×D151—21no—
46C2×C4×D151—21no—
47C2×C4×D151C2311yescharacteristic
48#14558994—42no—
49#14558991—42no—
50C2×C151⋊C8C2312yes—
51C4⋊Dic151—22no—
52C4⋊Dic151C2312yes—
53Dic151⋊C4—22no—
54Dic151⋊C4—22no—
55Dic151⋊C4—22no—
56Dic151⋊C4D412yes—
57(C2×D151)⋊C4—22no—
58(C2×D151)⋊C4—22no—
59(C2×D151)⋊C4—22no—
60(C2×D151)⋊C4D412yes—
61C4×Dic151—22no—
62C4×Dic151C2311yescharacteristic
63C2×Q8×C151C2312yes—
64C2×Q8×C151C2311yescharacteristic
65C2×Q8×C151C2311yescharacteristic
66Q16×C151—42no—
67Q16×C151—42no—
68C2×C8×C151C2312yes—
69C4⋊C4×C151—22no—
70C4⋊C4×C151—22no—
71C42×C151C2311yescharacteristic
72C22×D151—21no—
73C22×D151C2×D411yescharacteristic
74Dic302—22no—
75Dic302—42no—
76D604—22no—
77D604—42no—
78C2×Dic151—22no—
79C2×Dic151—21no—
80C2×Dic151C2×D412yes—
81C2×Dic151C2×D411yescharacteristic
82C4×D151—22no—
83C4×D151—42no—
84C4×D151—42no—
85C151⋊C8—22no—
86Q8×C151—22no—
87Q8×C151—22no—
88Q8×C151—22no—
89Q8×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—21no—
92C2×C4×C151—21no—
93C2×C4×C151C2×D412yes—
94C2×C4×C151C2411yescharacteristic
95C8×C151—22no—
96C22×C151C22×D411yescharacteristic
97C2×D151—21no—
98C2×D151—22no—
99C2×D151—41no—
100C2×D151—42no—
101C4×C151—22no—
102C4×C151—42no—
103C4×C151—41no—
104C4×C151—41no—
105C4×C151H(5,𝔽2)12yes—
106Dic151—21no—
107Dic151—22no—
108Dic151—41no—
109Dic151—42no—
110C2×C151#53511yescharacteristic
111C2×C151#57812yes—
112D151—41no—
113D151—81no—
114C151#322311yescharacteristic, complemented, Sylow
115#3223—1511nomaximal, Sylow
116#541—1511no—
117#536—1511no—
118#497—1511no—
119#494D15111yescharacteristic, complemented
120#491—1511no—
121#488—1511no—
122#464—1512no—
123#462—1512no—
124#452—1512no—
125#451—1512no—
126#433—1511no—
127C2×#41—1511no—
128C22×Q8—1511no—
129C2×Q16—1512no—
130C2×Q16C2×D15112yes—
131C2×Q16C2×D15112yes—
132C2×SD16—1512no—
133C4⋊Q8—1511no—
134C4⋊Q8C2×D15111yescharacteristic
135C4⋊Q8C2×D15111yescharacteristic
136#126—3022no—
137#125—3022no—
138#125—1511no—
139#124—1511no—
140#124—1511no—
141#123—3022no—
142C22⋊Q8—3022no—
143C22⋊Q8—1512no—
144C4×Q8—1512no—
145#117—1511no—
146C4⋊C8—1512no—
147#103—1512no—
148#103—1512no—
149#103—1512no—
150#102—1512no—
151C22⋊C8—1512no—
152#97—1511no—
153C4×C8C2×D15111yescharacteristic
154#41—6042no—
155C2×Q8—3021no—
156C2×Q8—6042no—
157C2×Q8—1511no—
158C2×Q8C22×D15111yescharacteristic
159C2×Q8C22×D15111yescharacteristic
160C2×Q8C22×D15112yes—
161C2×D4—3021no—
162C2×D4—1511no—
163C22×C4—3021no—
164C22×C4—3021no—
165C22×C4—1511no—
166Q16—42no—
167Q16—42no—
168Q16—6042no—
169SD16—6042no—
170C2×C8—1512no—
171C2×C8C22×D15112yes—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—3022no—
175C4⋊C4—3022no—
176C4⋊C4—3022no—
177C4⋊C4—3022no—
178C4⋊C4—1512no—
179C4⋊C4—1512no—
180C22⋊C4—3022no—
181C22⋊C4—3022no—
182C22⋊C4—3022no—
183C22⋊C4—1512no—
184C42—3022no—
185C42—1511no—
186C42C22×D15111yescharacteristic
187C23—3021no—
188C23—1511no—
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—22no—
193Q8—3022no—
194Q8—6042no—
195D4—3022no—
196D4—6042no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—3022no—
201C2×C4—3022no—
202C2×C4—3021no—
203C2×C4—6042no—
204C2×C4—6042no—
205C2×C4—1512no—
206C2×C4—1511no—
207C2×C4D4×D15112yes—
208C2×C4C23×D15111yescharacteristic
209C8—22no—
210C8—3022no—
211C22—3022no—
212C22—3021no—
213C22—6042no—
214C22—6041no—
215C22C2×D4×D15111yescharacteristic
216C4—22no—
217C4—41no—
218C4—41no—
219C4—42no—
220C4—3022no—
221C4—3021no—
222C4—6042no—
223C4—6041no—
224C4#1801278412yes—
225C2—6041no—
226C2—12081no—
227C2#2375277511yescharacteristic
228C2#2375302512yes—
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#494×C151C2
socleC22×C151C22×D4
prime radicalC2×#14559005C22
hypercenter#494D151
hypocenterC151#3223
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #23752823C2semidirect
3. #23752604C2semidirect
4. #23752580C2semidirect
5. #23752567C2semidirect
6. #23752436C2semidirect
7. #23752420C2semidirect
9. #23752366C2semidirect
10. #23752271C2semidirect
11. #494×C151C2semidirect
114. C151#3223semidirect
119. #494D151semidirect

Maximal subgroups

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

subgroupindex
#237528232
#237527872
#237526042
#237525802
#237525672
#237524362
#237524202
#237523732
#237523662
#237522712
#494×C1512
#3223151