Finite Group Databasebeta

← #22626193

Subgroups — #22626193

Order 9344.

234 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 54 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#17989573C211yesmaximal, characteristic
2#17989566C211yesmaximal, characteristic
3#17989489C214yesmaximal, complemented
4#17989161C211yesmaximal, characteristic
5D73⋊M16—21no—
6#14556670—21no—
7#14556652—21no—
8#14556651C2212yes—
9#14556650—21no—
10#14556649C2212yes—
11C2×#11924028C2211yescharacteristic
12#14556589—21no—
13#14556580—21no—
14#14556574C412yescomplemented
15#14556574C2212yes—
16#14556567—21no—
17#14556567—21no—
18#14556550C411yescharacteristic, complemented
19C22×Q8×C73C411yescharacteristic, complemented
20#11924038—41no—
21#11924037—22no—
22#11924036—41no—
23C4⋊#64408—41no—
24C22⋊#64408—22no—
25C4×#64408—41no—
26#11924028—41no—
27#11924028—41no—
28C2×Dic146D411yescharacteristic
29C2×D292D411yescharacteristic
30C2×C22⋊D73C2×C411yescharacteristic
31C2×C22⋊D73C2311yescharacteristic
32C2×C4×D73D411yescharacteristic
33C2×C4×D73D411yescharacteristic
34C4⋊Dic73—21no—
35#11924007—22no—
36#11924007—22no—
37C22⋊Dic73C2×C412yes—
38#11924005—22no—
39#11924005—22no—
40C4×Dic73—21no—
41C2×Q8×C73—21no—
42C2×Q8×C73—21no—
43C2×Q8×C73—41no—
44C2×Q8×C73—41no—
45C22×C4×C73C2×C412yes—
46C22×C4×C73C2×C411yescharacteristic
47C23×C73C22×C411yescharacteristic
48C22×D73C22⋊C411yescharacteristic
49C22×D73C2×D411yescharacteristic
50C2×#64408—42no—
51Q8×C73—42no—
52Q8×C73—41no—
53Q8×C73—41no—
54C2×C4×C73—21no—
55C2×C4×C73—21no—
56C2×C4×C73—22no—
57C2×C4×C73—42no—
58C2×C4×C73C22⋊C411yescharacteristic
59C2×C4×C73C22⋊C411yescharacteristic
60C22⋊D73—41no—
61C22⋊D73—41no—
62C2×Dic73—22no—
63C2×Dic73C22⋊C411yescharacteristic
64C2×Dic73C2×D411yescharacteristic
65D292—41no—
66C4×D73—21no—
67C4×D73—21no—
68C4×D73—21no—
69C4×D73—21no—
70Dic146—41no—
71#10596833—42no—
72C22×C73—21no—
73C22×C73—41no—
74C22×C73C2×C22⋊C411yescharacteristic
75C2×D73—21no—
76C2×D73—21no—
77C2×D73—41no—
78C2×D73—41no—
79#64408—82no—
80C4×C73—21no—
81C4×C73—42no—
82C4×C73#9911yescharacteristic
83C4×C73#9911yescharacteristic
84Dic73—21no—
85Dic73—21no—
86Dic73—42no—
87C2×C73—21no—
88C2×C73—41no—
89C2×C73C2×#9911yescharacteristic
90D73—41no—
91D73—41no—
92#2123—731nomaximal, Sylow
93C73#212311yescharacteristic, complemented, Sylow
94#536—731no—
95#413—731no—
96#410—731no—
97#352—734no—
98C2×#41—731no—
99C22×Q8#6440811yescharacteristic, complemented
100C2×M16—1461no—
101C4⋊Q8—1461no—
102#124—1461no—
103#123—732no—
104#123—732no—
105C22⋊Q8—1461no—
106C22⋊Q8—1461no—
107#117—731no—
108#117—1461no—
109#101—1461no—
110#100—732no—
111#99—732no—
112#99—1461no—
113#41—2921no—
114#41—2921no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—41no—
118C2×Q8—41no—
119C2×Q8—731no—
120C2×D4—731no—
121C2×D4—731no—
122C2×D4—731no—
123C22×C4—731no—
124C22×C4—731no—
125C22×C4C2×#6440812yes—
126C22×C4C2×#6440811yescharacteristic
127M16—2921no—
128M16—1462no—
129C2×C8—2921no—
130C4⋊C4—2921no—
131C4⋊C4—1462no—
132C4⋊C4—1462no—
133C4⋊C4—1461no—
134C22⋊C4—732no—
135C22⋊C4—1462no—
136C22⋊C4—1462no—
137C22⋊C4—1462no—
138C42—2921no—
139C42—1461no—
140C23—731no—
141C23—731no—
142C23C22×#6440811yescharacteristic
143Q8—42no—
144Q8—41no—
145Q8—41no—
146Q8—2921no—
147D4—2921no—
148D4—2921no—
149D4—2921no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—2922no—
155C2×C4—731no—
156C2×C4—731no—
157C2×C4—1462no—
158C2×C4—1461no—
159C2×C4—1461no—
160C2×C4—1461no—
161C2×C4—1461no—
162C2×C4C22⋊#6440811yescharacteristic
163C2×C4C22⋊#6440811yescharacteristic
164C8—2922no—
165C22—21no—
166C22—41no—
167C22—2921no—
168C22—2921no—
169C22—1461no—
170C22—1461no—
171C22C2×C22⋊#6440811yescharacteristic
172C4—21no—
173C4—42no—
174C4—2922no—
175C4—5842no—
176C4—1461no—
177C4—1461no—
178C4#1455664911yescharacteristic
179C4#1455664911yescharacteristic
180C2—21no—
181C2—41no—
182C2—2921no—
183C2—2921no—
184C2C2×#1455664911yescharacteristic
subgroupG/H
centerC2C2×#14556649
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC22×Q8×C73C4
socleC2×C73C2×#99
hypercenterC22×Q8#64408
hypocenterC73#2123
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #17989489C2semidirect
14. #14556574C4semidirect
18. #14556550C4semidirect
19. C22×Q8×C73C4semidirect
93. C73#2123semidirect
99. C22×Q8#64408semidirect