Finite Group Databasebeta

← #34060169

Subgroups — #34060169

Order 19072.

218 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 58 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#23750646C211yesmaximal, characteristic, complemented
2C2×#18011966C211yesmaximal, characteristic, complemented
3#23750482C212yesmaximal, complemented
4#23750481C212yesmaximal, complemented
5#23750161C211yesmaximal, characteristic
6C22×#11924753—21no—
7C4⋊#11924753—21no—
8C22⋊#11924753—21no—
9#18011966—21no—
10#18011966C2212yes—
11#18011966C2212yes—
12#18011906—21no—
13#18011902C2211yescharacteristic
14#18011900C2211yescharacteristic
15#18011895—21no—
16#18011885C411yescharacteristic
17Q8×Dic149C411yescharacteristic
18#18011873C411yescharacteristic
19#18011871—21no—
20#18011869—21no—
21C2×C4×Dic149C2211yescharacteristic
22C22⋊Q8×C149C411yescharacteristic
23C2×#11924753—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×D596C2×C411yescharacteristic
27C2×C22⋊D149—21no—
28C22×Dic149D411yescharacteristic
29C22×Dic149D411yescharacteristic
30C2×C4×D149—21no—
31C4⋊Dic149—21no—
32C4⋊Dic149—21no—
33C4⋊Dic149C2×C411yescharacteristic
34#14558715—21no—
35#14558713—21no—
36#14558713—21no—
37#14558713—21no—
38#14558713—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—24no—
50#11924753—42no—
51C22×D149—21no—
52D596—41no—
53C22⋊D149—42no—
54C2×Dic149—22no—
55C2×Dic149—21no—
56C2×Dic149—41no—
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C4×D149—42no—
62C23×C149C22⋊C411yescharacteristic
63Q8×C149—41no—
64C2×C4×C149—21no—
65C2×C4×C149—21no—
66C2×C4×C149—41no—
67C2×C4×C149C22⋊C411yescharacteristic
68C2×C4×C149C22×C411yescharacteristic
69C22×C149—21no—
70C22×C149—21no—
71C22×C149#10412yes—
72C22×C149C2×C22⋊C411yescharacteristic
73C2×D149—41no—
74C2×D149—41no—
75C2×D149—41no—
76C4×C149—21no—
77C4×C149—21no—
78C4×C149—41no—
79C4×C149—41no—
80Dic149—21no—
81Dic149—21no—
82Dic149—21no—
83Dic149—21no—
84Dic149—41no—
85C2×C149—22no—
86C2×C149#41311yescharacteristic
87C2×C149C2×#10411yescharacteristic
88C2×C149#42111yescharacteristic
89D149—81no—
90C149#153211yescharacteristic, complemented, Sylow
91#1532—1491nomaximal, Sylow
92#529—1491no—
93#432—1491no—
94C2×#97—1491no—
95#330—1492no—
96#329—1492no—
97C22×C8—2981no—
98#126—2981no—
99#125—1491no—
100#124—1491no—
101#123—2981no—
102C22⋊Q8#1059701011yescharacteristic
103#121—1491no—
104C4×Q8—1491no—
105C4×D4—2981no—
106C4×D4—1491no—
107#117—2981no—
108C2×C42—1491no—
109C4⋊C8—2981no—
110C22⋊C8—2981no—
111#97—2981no—
112#97—1492no—
113#97—1492no—
114C2×Q8C2×#1059701011yescharacteristic
115C2×D4—2981no—
116C2×D4—1491no—
117C22×C4—2981no—
118C22×C4—1491no—
119C22×C4—1491no—
120C22×C4C2×#1059701011yescharacteristic
121C2×C8—2984no—
122C2×C8—2982no—
123C2×C8—2982no—
124C4⋊C4—21no—
125C4⋊C4—2981no—
126C4⋊C4—2981no—
127C4⋊C4—2981no—
128C4⋊C4—1491no—
129C4⋊C4C2×#1059701011yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—2981no—
132C22⋊C4—2981no—
133C22⋊C4—2981no—
134C22⋊C4—2981no—
135C42—2981no—
136C42—1491no—
137C42—1491no—
138C42—1491no—
139C42—1491no—
140C23—2981no—
141C23C22⋊#1059701011yescharacteristic
142Q8—41no—
143D4—5961no—
144D4—5962no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—2982no—
149C2×C4—2981no—
150C2×C4—5962no—
151C2×C4—5961no—
152C2×C4—1491no—
153C2×C4—1491no—
154C2×C4—1491no—
155C2×C4—1491no—
156C2×C4C22⋊#1059701011yescharacteristic
157C2×C4C22×#1059701011yescharacteristic
158C8—2984no—
159C8—5962no—
160C22—21no—
161C22—21no—
162C22—5961no—
163C22—5961no—
164C22—5961no—
165C22#1801197612yes—
166C22C2×C22⋊#1059701011yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—2981no—
172C4—2981no—
173C4—2981no—
174C4—2981no—
175C4—5961no—
176C2—22no—
177C2—11921no—
178C2#2375061211yescharacteristic
179C2C2×#1801197611yescharacteristic
180C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radical#18011885C4
cosocleC4×Dic149C23
hypercenterC22⋊Q8#10597010
hypocenterC149#1532
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #23750646C2semidirect
2. C2×#18011966C2semidirect
3. #23750482C2semidirect
4. #23750481C2semidirect
90. C149#1532semidirect

Maximal subgroups

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

subgroupindex
#237506462
C2×#180119662
#237504822
#237504812
#237501612
#1532149