Finite Group Databasebeta

← #22625371

Subgroups — #22625371

Order 9344.

288 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 70 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#17989555C211yesmaximal, characteristic
2#17989529C211yesmaximal, characteristic
3#17989441C214yesmaximal, complemented
4C2×#14556567C211yesmaximal, characteristic
5C2×#11924036—21no—
6C2×C4⋊#64408—21no—
7C2×C22⋊#64408—21no—
8#14556648C2212yes—
9C22⋊#10596833—21no—
10(C2×#64408)⋊C4C2212yes—
11C22×C4×D73C2211yescharacteristic
12#14556567—21no—
13#14556567—21no—
14#14556567C412yescomplemented
15#14556567C2212yes—
16C2×C4⋊Dic73C411yescharacteristic, complemented
17C2×#11924007—21no—
18C2×#11924005—21no—
19C22×Q8×C73C411yescharacteristic, complemented
20C22×#64408—22no—
21#11924036—42no—
22C2×#10596833—22no—
23C4⋊#64408—42no—
24C22⋊#64408—42no—
25C23×D73D411yescharacteristic
26C22×Dic73—21no—
27C22×Dic73D411yescharacteristic
28C2×C4×D73—42no—
29C2×C4×D73C2×C411yescharacteristic
30C2×C4×D73D411yescharacteristic
31C2×C4×D73D411yescharacteristic
32C2×C4×D73C2311yescharacteristic
33C4⋊Dic73—21no—
34C4⋊Dic73C2×C412yes—
35#11924007—22no—
36#11924007—22no—
37#11924005—22no—
38#11924005—22no—
39C2×Q8×C73—21no—
40C2×Q8×C73—42no—
41C2×Q8×C73C2×C412yes—
42C22×C4×C73—21no—
43C22×C4×C73C2×C411yescharacteristic
44C23×C73C22⋊C411yescharacteristic
45C22×D73—41no—
46C22×D73—41no—
47C22×D73C22⋊C411yescharacteristic
48C22×D73SD1612yes—
49C22×D73Q1612yes—
50C22×D73C2×D411yescharacteristic
51C2×#64408—42no—
52C2×#64408—42no—
53C2×#64408—42no—
54Q8×C73—42no—
55Q8×C73—42no—
56C2×C4×C73—22no—
57C2×C4×C73—22no—
58C2×C4×C73—42no—
59C2×C4×C73C22⋊C411yescharacteristic
60C2×C4×C73C22×C411yescharacteristic
61C2×Dic73—22no—
62C2×Dic73—41no—
63C2×Dic73—42no—
64C2×Dic73C22⋊C411yescharacteristic
65C2×Dic73C2×D411yescharacteristic
66C4×D73—22no—
67C4×D73—22no—
68C4×D73—41no—
69C4×D73—41no—
70#10596833—42no—
71C22×C73—21no—
72C22×C73—21no—
73C22×C73#10312yes—
74C22×C73C2×C22⋊C411yescharacteristic
75C2×D73—21no—
76C2×D73—21no—
77C2×D73—21no—
78C2×D73—21no—
79C2×D73—42no—
80C2×D73—42no—
81C2×D73#10312yes—
82C2×D73C2×SD1611yescharacteristic
83C2×D73C2×Q1611yescharacteristic
84#64408—82no—
85C4×C73—21no—
86C4×C73—42no—
87C4×C73#9912yes—
88Dic73—21no—
89Dic73—21no—
90Dic73—42no—
91C2×C73—22no—
92C2×C73C2×#9911yescharacteristic
93C2×C73C2×#10311yescharacteristic
94C2×C73#42111yescharacteristic
95D73—21no—
96D73—22no—
97D73—21no—
98#1520—731nomaximal, Sylow
99C73#152011yescharacteristic, complemented, Sylow
100C2×C22⋊Q8—731no—
101C2×C22⋊C8—731no—
102#380—731no—
103#328—734no—
104C22×Q8#6440811yescharacteristic, complemented
105C23×C4—731no—
106C22×C8—1461no—
107C22⋊Q8—732no—
108C22⋊Q8—732no—
109C22⋊Q8—1461no—
110C22⋊Q8—1461no—
111C2×C4⋊C4—731no—
112C2×C4⋊C4—1461no—
113C2×C4⋊C4—1461no—
114C2×C22⋊C4—1461no—
115C2×C22⋊C4—1461no—
116C22⋊C8—732no—
117C22⋊C8—1461no—
118#95—732no—
119C24—731no—
120C2×Q8—21no—
121C2×Q8—42no—
122C2×Q8C2×#6440812yes—
123C22×C4—21no—
124C22×C4—2922no—
125C22×C4—731no—
126C22×C4—731no—
127C22×C4—731no—
128C22×C4—731no—
129C22×C4—731no—
130C22×C4—1462no—
131C22×C4—1461no—
132C22×C4C2×#6440811yescharacteristic
133C2×C8—2922no—
134C2×C8—1462no—
135C4⋊C4—2922no—
136C4⋊C4—732no—
137C4⋊C4—1462no—
138C4⋊C4—1462no—
139C4⋊C4—1461no—
140C22⋊C4—2922no—
141C22⋊C4—1462no—
142C22⋊C4—1462no—
143C23—2921no—
144C23—2921no—
145C23—732no—
146C23—732no—
147C23—731no—
148C23—731no—
149C23C22⋊#6440811yescharacteristic
150Q8—42no—
151Q8—42no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—42no—
155C2×C4—2921no—
156C2×C4—2921no—
157C2×C4—2922no—
158C2×C4—2922no—
159C2×C4—2922no—
160C2×C4—2922no—
161C2×C4—2921no—
162C2×C4—731no—
163C2×C4—731no—
164C2×C4—1462no—
165C2×C4—1462no—
166C2×C4—1462no—
167C2×C4C22⋊#6440811yescharacteristic
168C2×C4C22×#6440811yescharacteristic
169C8—2922no—
170C22—21no—
171C22—21no—
172C22—2922no—
173C22—2922no—
174C22—731no—
175C22—732no—
176C22—731no—
177C22—1461no—
178C22—1461no—
179C22—1461no—
180C22—1461no—
181C22#1455665412yes—
182C22C2×C22⋊#6440811yescharacteristic
183C4—21no—
184C4—42no—
185C4—2922no—
186C4—5842no—
187C4—1461no—
188C4—1461no—
189C4#1455664912yes—
190C2—22no—
191C2—1461no—
192C2—1462no—
193C2—1461no—
194C2C2×#1455664911yescharacteristic
195C2C2×#1455665411yescharacteristic
196C2#1798958611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×Q8#64408
hypocenterC73#1520
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #17989441C2semidirect
14. #14556567C4semidirect
16. C2×C4⋊Dic73C4semidirect
19. C22×Q8×C73C4semidirect
99. C73#1520semidirect
104. C22×Q8#64408semidirect