Finite Group Databasebeta

← #22608971

Subgroups — #22608971

Order 9344.

202 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 51 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#17989216C211yesmaximal, characteristic
2#17988922C211yesmaximal, characteristic
3#17988525C211yesmaximal, characteristic
4#17988325C211yesmaximal, characteristic
5#17988324C211yesmaximal, characteristic
6#17988312C211yesmaximal, characteristic
7#484×C73C211yesmaximal, characteristic
8#14556590—21no—
9#14556589—21no—
10#14556581—21no—
11#14556581—21no—
12#14556570C2211yescharacteristic
13#14556568—21no—
14#14556547—21no—
15C2×#11924007C2211yescharacteristic
16#14556524—21no—
17#14556514—21no—
18C22⋊#10596831C2211yescharacteristic
19#14556498—21no—
20#14556498—21no—
21#14556498C2211yescharacteristic
22C22⋊Q8×C73C2211yescharacteristic
23C2×C4⋊C4×C73C2211yescharacteristic
24#107×C73—21no—
25#103×C73—21no—
26C22⋊C8×C73C2211yescharacteristic
27C2×Dic146—21no—
28C2×Dic146D411yescharacteristic
29C22×Dic73—21no—
30C22×Dic73D411yescharacteristic
31C22×Dic73D411yescharacteristic
32C2×#10596831—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73D411yescharacteristic
35#11924007—21no—
36#11924007—21no—
37#11924007—21no—
38#11924007—21no—
39#11924007—21no—
40#11924007—21no—
41#11924007—21no—
42C22⋊Dic73—21no—
43C4×Dic73—21no—
44C4×Dic73—21no—
45C2×Q8×C73D411yescharacteristic
46C22×C4×C73—21no—
47C22×C4×C73C2311yescharacteristic
48C2×C8×C73—21no—
49C4⋊C4×C73—21no—
50C4⋊C4×C73—21no—
51C4⋊C4×C73—21no—
52C4⋊C4×C73D411yescharacteristic
53C22⋊C4×C73—21no—
54C23×C73C2×D411yescharacteristic
55Q8×C73—41no—
56C2×C4×C73—21no—
57C2×C4×C73—21no—
58C2×C4×C73—41no—
59C2×C4×C73—42no—
60C2×C4×C73—41no—
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C2×Dic73—21no—
64C2×Dic73—21no—
65C2×Dic73—21no—
66C2×Dic73—21no—
67C2×Dic73—21no—
68C2×Dic73—41no—
69C2×Dic73—41no—
70C2×Dic73—41no—
71C2×Dic73—41no—
72C2×Dic73Q1612yes—
73Dic146—41no—
74Dic146—81no—
75C8×C73—41no—
76#10596831—41no—
77C22×C73—21no—
78C22×C73—21no—
79C22×C73#12011yescharacteristic
80C22×C73C2×Q1611yescharacteristic
81C22×C73#13711yescharacteristic
82C4×C73—21no—
83C4×C73—21no—
84C4×C73—41no—
85C4×C73—41no—
86C4×C73—81no—
87Dic73—22no—
88Dic73—41no—
89Dic73—41no—
90Dic73—41no—
91Dic73—81no—
92C2×C73—21no—
93C2×C73—21no—
94C2×C73#45111yescharacteristic
95C2×C73#45411yescharacteristic
96C2×C73#45811yescharacteristic
97#1617—731nomaximal, Sylow
98C73#161711yescharacteristic, complemented, Sylow
99#544—731no—
100#484—731no—
101#484D7311yescharacteristic
102#400—731no—
103#328—731no—
104#328—731no—
105#324—731no—
106C4⋊Q8—1461no—
107C4⋊Q8—1461no—
108#125—1461no—
109#125—1461no—
110C22⋊Q8—731no—
111C22⋊Q8—1461no—
112C22⋊Q8C2×D7311yescharacteristic
113#117—1461no—
114C2×C4⋊C4—731no—
115C2×C4⋊C4C2×D7311yescharacteristic
116#107—21no—
117#107—1461no—
118#103—21no—
119#103—1461no—
120C22⋊C8—731no—
121C22⋊C8C2×D7311yescharacteristic
122#95—731no—
123#95—1461no—
124#95—1461no—
125C2×Q8—731no—
126C2×Q8—1461no—
127C2×Q8C22⋊D7311yescharacteristic
128C22×C4—21no—
129C22×C4—731no—
130C22×C4—731no—
131C22×C4—1461no—
132C22×C4C22×D7311yescharacteristic
133C2×C8—21no—
134C2×C8—1461no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—731no—
139C4⋊C4—1461no—
140C4⋊C4—1461no—
141C4⋊C4—1461no—
142C4⋊C4—1461no—
143C4⋊C4—1461no—
144C4⋊C4—1461no—
145C4⋊C4—1461no—
146C4⋊C4—1461no—
147C4⋊C4C22⋊D7311yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—1461no—
150C42—1461no—
151C42—1461no—
152C23D4×D7311yescharacteristic
153Q8—41no—
154Q8—2921no—
155Q8—5841no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4—2921no—
162C2×C4—2921no—
163C2×C4—2921no—
164C2×C4—2921no—
165C2×C4—732no—
166C2×C4—1461no—
167C2×C4—1461no—
168C2×C4—1461no—
169C2×C4—1461no—
170C2×C4—1461no—
171C2×C4D4×D7311yescharacteristic
172C2×C4C2×C22⋊D7311yescharacteristic
173C8—41no—
174C8—2921no—
175C22—21no—
176C22—21no—
177C22#1455655911yescharacteristic
178C22Q16×D7311yescharacteristic
179C22#1455662311yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—2921no—
186C4—2921no—
187C4—2921no—
188C4—5841no—
189C4—1462no—
190C2—21no—
191C2—21no—
192C2#1798874111yescharacteristic
193C2#1798875811yescharacteristic
194C2#1798877611yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#484×C73C2
socleC22×C73#120
hypercenter#484D73
hypocenterC73#1617
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
98. C73#1617semidirect