Finite Group Databasebeta

← #34059994

Subgroups — #34059994

Order 19072.

248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 78 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#23750644C211yesmaximal, characteristic
2#23750643C211yesmaximal, characteristic
3#23750475C212yesmaximal, complemented
4Q8⋊#11924753C212yesmaximal, complemented
5C4×Q8×D149C211yesmaximal, characteristic
6#18011978—21no—
7C4⋊#11924753C2212yes—
8#18011968—21no—
9#18011968—21no—
10C4×#11924753—21no—
11C4×#11924753C2212yes—
12C2×Q8×D149C411yescharacteristic
13Q8×Dic149C2211yescharacteristic
14C4×Dic298—21no—
15C4×Dic298C411yescharacteristic
16#18011876—21no—
17#18011876C2211yescharacteristic
18C4⋊C4×D149—21no—
19C4⋊C4×D149C411yescharacteristic
20C42×D149—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic
23C2×#11924753—22no—
24C2×#11924753—22no—
25C2×Dic298—21no—
26C2×Dic298C2×C411yescharacteristic
27Q8×D149—22no—
28Q8×D149C814yescomplemented
29C2×C4×D149—21no—
30C2×C4×D149—21no—
31C2×C4×D149C2×C411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C2×C4×D149D411yescharacteristic
34C4⋊Dic149—21no—
35C4⋊Dic149C2×C411yescharacteristic
36#14558715—21no—
37#14558715—21no—
38#14558715—21no—
39C4×Dic149—21no—
40C4×Dic149—21no—
41C4×Dic149—21no—
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149C2311yescharacteristic
45C2×Q8×C149C2×C411yescharacteristic
46C4⋊C4×C149—21no—
47C4⋊C4×C149C2×C411yescharacteristic
48C42×C149—21no—
49C42×C149C2×C411yescharacteristic
50#11924753—42no—
51#11924753—42no—
52C22×D149C22⋊C411yescharacteristic
53Dic298—21no—
54Dic298—24no—
55Dic298C2×C812yes—
56C2×Dic149—21no—
57C2×Dic149—21no—
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C4×D149—24no—
62C4×D149—22no—
63C4×D149—41no—
64C4×D149—42no—
65C4×D149C2×C812yes—
66C4×D149M1612yes—
67Q8×C149—21no—
68Q8×C149C2×C812yes—
69C2×C4×C149—21no—
70C2×C4×C149—21no—
71C2×C4×C149C22⋊C411yescharacteristic
72C2×C4×C149C22⋊C411yescharacteristic
73C2×C4×C149C22×C411yescharacteristic
74C22×C149C2×C22⋊C411yescharacteristic
75C2×D149—21no—
76C2×D149—21no—
77C2×D149C22⋊C812yes—
78C4×C149—22no—
79C4×C149—21no—
80C4×C149—21no—
81C4×C149—41no—
82C4×C149C22×C811yescharacteristic
83C4×C149C2×M1611yescharacteristic
84Dic149—22no—
85Dic149—21no—
86Dic149—41no—
87Dic149C22⋊C812yes—
88Dic149#13712yes—
89C2×C149C2×C22⋊C811yescharacteristic
90C2×C149#41911yescharacteristic
91C2×C149#42111yescharacteristic
92D149—22no—
93C149#147911yescharacteristic, complemented, Sylow
94#1479—1491nomaximal, Sylow
95C2×C4×Q8—1491no—
96#431—1491no—
97#431—1491no—
98Q8⋊C8—1492no—
99Q8⋊C8—1492no—
100C22×Q8—1491no—
101C4×Q8—2981no—
102C4×Q8—2981no—
103C4×Q8—1491no—
104C4×Q8—1491no—
105C4×Q8—1491no—
106C4×Q8#1059701011yescharacteristic
107C2×C4⋊C4—2981no—
108C2×C4⋊C4—1491no—
109C2×C42—2981no—
110C2×C42—1491no—
111C4⋊C8—2981no—
112C4⋊C8—1492no—
113C22⋊C8—2981no—
114C22⋊C8—2981no—
115C4×C8—2981no—
116C4×C8—1492no—
117C2×Q8—2981no—
118C2×Q8—2982no—
119C2×Q8—1494no—
120C2×Q8—1491no—
121C2×Q8C2×#1059701011yescharacteristic
122C22×C4—2981no—
123C22×C4—2981no—
124C22×C4—1491no—
125C22×C4—1491no—
126C22×C4—1491no—
127C2×C8—2982no—
128C2×C8—2982no—
129C4⋊C4—21no—
130C4⋊C4—2981no—
131C4⋊C4—2981no—
132C4⋊C4—2981no—
133C4⋊C4—2981no—
134C4⋊C4—1491no—
135C4⋊C4C2×#1059701011yescharacteristic
136C42—21no—
137C42—2981no—
138C42—2981no—
139C42—2981no—
140C42—1491no—
141C42—1491no—
142C42—1491no—
143C42C2×#1059701011yescharacteristic
144C23—1491no—
145Q8—21no—
146Q8—2984no—
147Q8—2981no—
148Q8—1492no—
149Q8D149⋊C812yes—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—2984no—
153C2×C4—2982no—
154C2×C4—2981no—
155C2×C4—2981no—
156C2×C4—5961no—
157C2×C4—5962no—
158C2×C4—1491no—
159C2×C4—1491no—
160C2×C4—1491no—
161C2×C4—1492no—
162C2×C4—1492no—
163C2×C4C22⋊#1059701011yescharacteristic
164C2×C4C22⋊#1059701011yescharacteristic
165C2×C4C22×#1059701011yescharacteristic
166C8—5962no—
167C8—5962no—
168C22—2981no—
169C22—2981no—
170C22—1492no—
171C22C2×C22⋊#1059701011yescharacteristic
172C4—22no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—2982no—
177C4—2981no—
178C4—5961no—
179C4—1492no—
180C4—1492no—
181C4C2×D149⋊C811yescharacteristic
182C4D149⋊M1611yescharacteristic
183C2—2982no—
184C2D149⋊(C22⋊C8)11yescharacteristic
185C2#2375061811yescharacteristic
186C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC4×C149C22×C8
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC4×Dic149C23
hypercenterC4×Q8#10597010
hypocenterC149#1479
LCSG ▷ C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #23750475C2semidirect
4. Q8⋊#11924753C2semidirect
28. Q8×D149C8semidirect
93. C149#1479semidirect

Maximal subgroups

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

subgroupindex
#237506442
#237506432
#237504752
Q8⋊#119247532
C4×Q8×D1492
#1479149