Finite Group Databasebeta

← #34010190

Subgroups — #34010190

Order 18688.

270 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 66 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#22626304C212yesmaximal
2#22624880C212yesmaximal
3#22624878C212yesmaximal
4#22618864C211yesmaximal, characteristic
5#17989510—22no—
6#17989483C2214yes—
7#17989479—22no—
8#17989140C411yescharacteristic
9#17988716—22no—
10#17988711—22no—
11#17988613C2211yescharacteristic
12#17988610C2211yescharacteristic
13#17988545C411yescharacteristic
14#17988543C2211yescharacteristic
15C2×C8×Dic73C411yescharacteristic
16#424×C73C411yescharacteristic
17#14556665—24no—
18C2×#11924012C2311yescharacteristic
19C22×#10596831C2×C411yescharacteristic
20#14556590—21no—
21#14556582—21no—
22#14556568—22no—
23C4×Dic146—22no—
24#14556550C2×C411yescharacteristic
25C2×C4×Dic73C2×C411yescharacteristic
26#14556520—22no—
27#14556520—22no—
28#14556502D412yes—
29#14556501—21no—
30C4×#10596831D412yes—
31C8×Dic73—21no—
32C8×Dic73—21no—
33C8×Dic73—21no—
34C2×M16×C73C2×C411yescharacteristic
35C22×C8×C73C2×C411yescharacteristic
36#117×C73C2×C411yescharacteristic
37C4⋊C8×C73—22no—
38#11924031—44no—
39C2×Dic146—22no—
40C22×Dic73—21no—
41#11924012—41no—
42C2×#10596831—22no—
43C2×#10596831C22⋊C411yescharacteristic
44C2×#10596831C22⋊C411yescharacteristic
45C2×#10596831C2×D412yes—
46C4⋊Dic73—22no—
47C4⋊Dic73—21no—
48#11924007—22no—
49#11924007—22no—
50C22⋊Dic73M1612yes—
51C4×Dic73—21no—
52C4×Dic73—21no—
53C4×Dic73M1611yescharacteristic
54C4×Dic73M1611yescharacteristic
55C22×C4×C73C22×C411yescharacteristic
56M16×C73—41no—
57C2×C8×C73—21no—
58C2×C8×C73—21no—
59C2×C8×C73—41no—
60C4⋊C4×C73—21no—
61C22⋊C4×C73—21no—
62C42×C73C22⋊C412yes—
63C23×C73C2×M1611yescharacteristic
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—22no—
67C2×C4×C73C2×C22⋊C411yescharacteristic
68C2×C4×C73C2×M1611yescharacteristic
69C2×Dic73—21no—
70C2×Dic73—21no—
71C2×Dic73—22no—
72C2×Dic73—42no—
73Dic146—44no—
74C8×C73—41no—
75C8×C73—41no—
76#10596831—22no—
77#10596831—21no—
78#10596831#10112yes—
79C22×C73—21no—
80C22×C73—41no—
81C22×C73#40711yescharacteristic
82C4×C73—21no—
83C4×C73—42no—
84C4×C73#41011yescharacteristic
85C4×C73C2×#10111yescharacteristic
86Dic73—22no—
87Dic73—42no—
88Dic73—41no—
89#11539—731nomaximal, Sylow
90C2×C73—21no—
91C2×C73—41no—
92C2×C73#146711yescharacteristic
93#2960—731no—
94#2166—732no—
95#1328—732no—
96#1327—732no—
97C73#1153911yescharacteristic, complemented, Sylow
98#533—731no—
99#446—1462no—
100C8×Q8—1462no—
101#424—731no—
102#424#6440811yescharacteristic
103#423—731no—
104#405—731no—
105#405—731no—
106C2×C4×C8—731no—
107#364—1462no—
108#349—734no—
109#347—1462no—
110C2×M16—731no—
111C2×M16C2×#6440811yescharacteristic
112C22×C8—731no—
113C22×C8C2×#6440811yescharacteristic
114C4⋊Q8—1461no—
115#125—1461no—
116C22⋊Q8—1462no—
117C4×Q8—1462no—
118#117—731no—
119#117C2×#6440811yescharacteristic
120C2×C42—731no—
121M32—1464no—
122C4⋊C8—22no—
123C4⋊C8—1462no—
124C4⋊C8—1462no—
125#97—732no—
126#97—1461no—
127C4×C8—732no—
128C4×C8—1461no—
129C4×C8—1461no—
130C4×C8—1461no—
131C2×Q8—1462no—
132C22×C4—1461no—
133C22×C4C22×#6440811yescharacteristic
134M16—41no—
135M16—2921no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—41no—
139C2×C8—731no—
140C2×C8—731no—
141C2×C8—732no—
142C2×C8—1462no—
143C4⋊C4—21no—
144C4⋊C4—1462no—
145C4⋊C4—1462no—
146C4⋊C4—1462no—
147C4⋊C4—1461no—
148C22⋊C4—21no—
149C22⋊C4—732no—
150C42—731no—
151C42—731no—
152C42—1461no—
153C42—1461no—
154C42C22⋊#6440812yes—
155C16—2924no—
156C23D73⋊M1611yescharacteristic
157Q8—2924no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—2922no—
162C2×C4—1461no—
163C2×C4—1462no—
164C2×C4—1461no—
165C2×C4C2×C22⋊#6440811yescharacteristic
166C2×C4D73⋊M1611yescharacteristic
167C8—41no—
168C8—41no—
169C8—732no—
170C8—1462no—
171C8—1461no—
172C22—21no—
173C22—41no—
174C22#1798955911yescharacteristic
175C4—21no—
176C4—42no—
177C4—2921no—
178C4—2922no—
179C4—1462no—
180C4#1798956711yescharacteristic
181C4D73⋊#10111yescharacteristic
182C2—21no—
183C2—41no—
184C2#2262519511yescharacteristic
subgroupG/H
centerC4#17989567
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#424×C73C4
socleC2×C73#1467
prime radicalC23×C73C2×M16
cosocleC2×#11924012C23
hypercenter#424#64408
hypocenterC73#11539
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
97. C73#11539semidirect

Maximal subgroups

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

subgroupindex
#226263042
#226248802
#226248782
#226188642
#1153973