Finite Group Databasebeta

← #34033676

Subgroups — #34033676

Order 18688.

356 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 77 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#22627135C212yesmaximal, complemented
2#22626955C214yesmaximal, complemented
3#22626656C211yesmaximal, characteristic
4#17989690—22no—
5#17989684C2214yes—
6#17989681—22no—
7C2×#14556679C412yes—
8#17989621—22no—
9#17989615—22no—
10#17989591C411yescharacteristic
11#17989562C2212yes—
12C4×#11924036C2211yescharacteristic
13#17989138C411yescharacteristic
14C2×#11924040—24no—
15#14556679—44no—
16C2×#11924038—22no—
17C2×#11924038C2×C412yes—
18C2×#11924036—22no—
19C2×#11924036C2×C411yescharacteristic
20C2×#11924036C2311yescharacteristic
21C4⋊#10596833—22no—
22#14556648—24no—
23C4×#10596833D412yes—
24C4×#10596833D412yes—
25C2×#11924029C2×C412yes—
26#14556588C811yescharacteristic
27#14556580C812yes—
28#14556566—22no—
29#14556553—22no—
30C42×D73C2×C411yescharacteristic
31C4⋊Q8×C73C811yescharacteristic
32#11924040—44no—
33#11924038—44no—
34#11924038—42no—
35#11924036—22no—
36#11924036—41no—
37#11924036—44no—
38C2×#10596833—22no—
39C2×#10596833C22⋊C411yescharacteristic
40C2×#10596833C22⋊C411yescharacteristic
41C2×#10596833C2×D412yes—
42#11924029—42no—
43#11924029—42no—
44C2×D292—22no—
45C2×D292—22no—
46C2×D292C2×C812yes—
47C2×C4×D73—22no—
48C2×C4×D73M1612yes—
49C2×C4×D73C22×C411yescharacteristic
50#11924005—24no—
51C4×Dic73C22⋊C412yes—
52C4×Dic73C2×C811yescharacteristic
53C2×Q8×C73C2×C812yes—
54C4⋊C4×C73—22no—
55C42×C73C2×C811yescharacteristic
56C22×D73—22no—
57C22×D73C2×M1611yescharacteristic
58Q8×C73—42no—
59C2×C4×C73—22no—
60C2×C4×C73C22⋊C812yes—
61C2×C4×C73C22×C811yescharacteristic
62C2×Dic73C22⋊C812yes—
63C2×Dic73C2×C22⋊C411yescharacteristic
64D292—42no—
65D292—44no—
66D292—44no—
67C4×D73—21no—
68C4×D73—21no—
69C4×D73—42no—
70C4×D73—42no—
71C4×D73—42no—
72#10596833—22no—
73#10596833—21no—
74#10596833—42no—
75#10596833#10012yes—
76C22×C73C2×C22⋊C811yescharacteristic
77C2×D73—22no—
78C2×D73—21no—
79C2×D73—44no—
80C2×D73—42no—
81C4×C73—22no—
82C4×C73—21no—
83C4×C73—42no—
84Dic73—22no—
85Dic73#41011yescharacteristic
86Dic73C2×#10011yescharacteristic
87#11491—731nomaximal, Sylow
88C2×C73#146011yescharacteristic
89C2×C73#211712yes—
90D73—41no—
91D73—82no—
92#2931—731no—
93#2163—732no—
94#1315—734no—
95C73#1149111yescharacteristic, complemented, Sylow
96C2×#131—732no—
97#532—731no—
98#436—1462no—
99C8×D4—1462no—
100#423—731no—
101#408—732no—
102C2×C4×C8—731no—
103C4⋊C16—1462no—
104C22⋊C16—734no—
105#346—1462no—
106C2×#41—732no—
107#131—2924no—
108C2×M16—732no—
109C2×M16—1462no—
110C22×C8—731no—
111C22×C8—731no—
112C22×C8—1462no—
113C4⋊Q8#1059684211yescharacteristic
114#127—731no—
115#124—732no—
116#121—1462no—
117C4×D4—1462no—
118C2×C42—731no—
119C2×C16—1464no—
120C4⋊C8—1462no—
121C22⋊C8—1464no—
122C4×C8—732no—
123C4×C8—732no—
124#41—2922no—
125#41—2922no—
126C2×Q8C2×#1059684212yes—
127C2×D4—732no—
128C2×D4—1462no—
129C2×D4—1462no—
130C22×C4—732no—
131C22×C4—731no—
132C22×C4—1462no—
133M16—2924no—
134M16—2922no—
135C2×C8—2924no—
136C2×C8—2921no—
137C2×C8—731no—
138C2×C8—731no—
139C2×C8—732no—
140C2×C8—1462no—
141C2×C8—1462no—
142C4⋊C4—22no—
143C22⋊C4—1464no—
144C42—732no—
145C42—731no—
146C42C2×#1059684211yescharacteristic
147C16—2924no—
148C23—731no—
149C23—1462no—
150Q8—42no—
151D4—2922no—
152D4—2924no—
153D4—2924no—
154C2×C4—22no—
155C2×C4—2922no—
156C2×C4—2922no—
157C2×C4—2922no—
158C2×C4—731no—
159C2×C4—732no—
160C2×C4—1461no—
161C2×C4—1461no—
162C2×C4C22⋊#1059684212yes—
163C2×C4C22×#1059684211yescharacteristic
164C8—2922no—
165C8—732no—
166C8—1462no—
167C8—1461no—
168C22—2924no—
169C22—2922no—
170C22—1462no—
171C22—1461no—
172C22C2×C22⋊#1059684211yescharacteristic
173C4—22no—
174C4—21no—
175C4—42no—
176C4—731no—
177C4—731no—
178C4—1462no—
179C2—2921no—
180C2—5842no—
181C2#2262704511yescharacteristic
182C2#2262711512yes—
subgroupG/H
centerC22C2×C22⋊#10596842
commutatorC2×C4×C73C22×C8
FrattiniC2×C4C22×#10596842
FittingC4⋊Q8×C73C8
socleC22×C73C2×C22⋊C8
prime radical#17989138C4
cosocleC2×#11924036C23
hypercenterC4⋊Q8#10596842
hypocenterC73#11491
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #22627135C2semidirect
2. #22626955C2semidirect
95. C73#11491semidirect

Maximal subgroups

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

subgroupindex
#226271352
#226269552
#226266562
#1149173