Finite Group Databasebeta

← #34059999

Subgroups — #34059999

Order 19072.

216 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 70 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#23750642C211yesmaximal, characteristic
2C2×C4⋊#11924753C211yesmaximal, characteristic
3#23750475C212yesmaximal, complemented
4Q8⋊#11924753C212yesmaximal, complemented
5#23750177C211yesmaximal, characteristic
6C22×#11924753—21no—
7#18011978—21no—
8C4⋊#11924753—21no—
9C4⋊#11924753C2212yes—
10C22⋊#11924753—21no—
11C4×#11924753C2212yes—
12#18011910C411yescharacteristic
13#18011909C411yescharacteristic
14#18011901—21no—
15#18011890C411yescharacteristic
16#18011888—21no—
17Q8×Dic149C2211yescharacteristic
18#18011876—21no—
19#18011876C2211yescharacteristic
20#18011867—21no—
21C2×C4×Dic149C2211yescharacteristic
22C22⋊Q8×C149C411yescharacteristic
23C2×#11924753—22no—
24C2×#11924753—22no—
25C2×#11924753—42no—
26C2×Dic298—21no—
27C2×Dic298C2×C411yescharacteristic
28C22×Dic149D411yescharacteristic
29C22×Dic149D411yescharacteristic
30C4⋊Dic149—21no—
31C4⋊Dic149C2×C411yescharacteristic
32#14558715—21no—
33#14558715—21no—
34#14558715—21no—
35#14558715—21no—
36#14558715—21no—
37C22⋊Dic149—21no—
38C4×Dic149—21no—
39C4×Dic149—21no—
40C4×Dic149C2×C411yescharacteristic
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149C2311yescharacteristic
44C2×Q8×C149C2×C411yescharacteristic
45C22×C4×C149C2×C411yescharacteristic
46C4⋊C4×C149—21no—
47C4⋊C4×C149C2×C411yescharacteristic
48C22⋊C4×C149—21no—
49#11924753—42no—
50#11924753—42no—
51Dic298—22no—
52Dic298—42no—
53C2×Dic149—21no—
54C2×Dic149—21no—
55C2×Dic149—41no—
56C2×Dic149C22⋊C411yescharacteristic
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149SD1612yes—
59C2×Dic149Q1612yes—
60C2×Dic149C2×D411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C23×C149C22⋊C411yescharacteristic
63Q8×C149—22no—
64C2×C4×C149—22no—
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149C22⋊C411yescharacteristic
68C2×C4×C149C22×C411yescharacteristic
69C22×C149—21no—
70C22×C149—21no—
71C22×C149#10312yes—
72C22×C149C2×C22⋊C411yescharacteristic
73C4×C149—21no—
74C4×C149—41no—
75C4×C149—41no—
76C4×C149#13112yes—
77Dic149—21no—
78Dic149—21no—
79Dic149—41no—
80Dic149—41no—
81Dic149#10312yes—
82Dic149C2×SD1611yescharacteristic
83Dic149C2×Q1611yescharacteristic
84C2×C149—22no—
85C2×C149#40811yescharacteristic
86C2×C149C2×#10311yescharacteristic
87C2×C149#42111yescharacteristic
88C149#148111yescharacteristic, complemented, Sylow
89#1481—1491nomaximal, Sylow
90#533—1491no—
91#431—1491no—
92C2×C4⋊C8—1491no—
93Q8⋊C8—1492no—
94Q8⋊C8—1492no—
95C22×C8—2981no—
96C4⋊Q8—1491no—
97C4⋊Q8—1491no—
98#125—2981no—
99C22⋊Q8—2981no—
100C22⋊Q8—1491no—
101C22⋊Q8#1059701011yescharacteristic
102C4×Q8—2981no—
103C4×Q8—1491no—
104C4×Q8—1491no—
105#117—2981no—
106C2×C42—1491no—
107C4⋊C8—2981no—
108C4⋊C8—2981no—
109C4⋊C8—1492no—
110C22⋊C8—2981no—
111C4×C8—1492no—
112C2×Q8—2981no—
113C2×Q8—1491no—
114C2×Q8C2×#1059701011yescharacteristic
115C22×C4—1491no—
116C22×C4—1491no—
117C22×C4C2×#1059701011yescharacteristic
118C2×C8—2982no—
119C2×C8—2982no—
120C2×C8—5962no—
121C4⋊C4—21no—
122C4⋊C4—2981no—
123C4⋊C4—2981no—
124C4⋊C4—2981no—
125C4⋊C4—2981no—
126C4⋊C4—2981no—
127C4⋊C4—2981no—
128C4⋊C4—1491no—
129C4⋊C4C2×#1059701011yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—2981no—
132C42—2981no—
133C42—2981no—
134C42—1491no—
135C42—1491no—
136C42—1491no—
137C42—1491no—
138C23C22⋊#1059701011yescharacteristic
139Q8—22no—
140Q8—2982no—
141Q8—5962no—
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—2981no—
146C2×C4—2981no—
147C2×C4—5961no—
148C2×C4—1491no—
149C2×C4—1491no—
150C2×C4—1492no—
151C2×C4—1492no—
152C2×C4—1491no—
153C2×C4—1491no—
154C2×C4C22⋊#1059701011yescharacteristic
155C2×C4C22×#1059701011yescharacteristic
156C8—5962no—
157C8—5962no—
158C22—21no—
159C22—21no—
160C22#1801197412yes—
161C22C2×C22⋊#1059701011yescharacteristic
162C4—21no—
163C4—41no—
164C4—41no—
165C4—2981no—
166C4—2981no—
167C4—5961no—
168C4—5961no—
169C4—1491no—
170C4—1492no—
171C4—1491no—
172C4#1801199812yes—
173C2—22no—
174C2#2375059811yescharacteristic
175C2C2×#1801197411yescharacteristic
176C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×C149C22⋊C4
cosocleC4×Dic149C23
hypercenterC22⋊Q8#10597010
hypocenterC149#1481
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #23750475C2semidirect
4. Q8⋊#11924753C2semidirect
88. C149#1481semidirect

Maximal subgroups

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

subgroupindex
#237506422
C2×C4⋊#119247532
#237504752
Q8⋊#119247532
#237501772
#1481149