Finite Group Databasebeta

← #22610902

Subgroups — #22610902

Order 9344.

276 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#14556590C211yesmaximal, characteristic
2C2×#14556501C211yesmaximal, characteristic
3#17988452C211yesmaximal, characteristic
4#17988350C211yesmaximal, characteristic
5#17988349C211yesmaximal, characteristic
6#17988349C211yesmaximal, characteristic
7#340×C73C211yesmaximal, characteristic
8C22×Dic146—21no—
9C22×#10596831C2211yescharacteristic
10#14556590—22no—
11#14556590C414yescomplemented
12C2×C4⋊Dic73C2211yescharacteristic
13C2×C4⋊Dic73C2211yescharacteristic
14C2×#11924007—21no—
15C2×C4×Dic73C2211yescharacteristic
16#14556501—22no—
17#14556498—21no—
18#14556498—21no—
19C22×C8×C73C2211yescharacteristic
20C2×C4⋊C4×C73C2211yescharacteristic
21C2×C4⋊C4×C73C2211yescharacteristic
22C2×Dic146—24no—
23C2×Dic146—42no—
24C2×Dic146—42no—
25C22×Dic73—21no—
26C22×Dic73—21no—
27C22×Dic73D411yescharacteristic
28C22×Dic73D411yescharacteristic
29C2×#10596831—21no—
30C2×#10596831—21no—
31C2×#10596831Q812yescomplemented
32C4⋊Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73C2×C412yes—
36#11924007—24no—
37C4×Dic73C2×C412yes—
38C4×Dic73D412yes—
39C22×C4×C73—21no—
40C22×C4×C73—21no—
41C22×C4×C73C2311yescharacteristic
42C2×C8×C73—21no—
43C2×C8×C73—21no—
44C2×C8×C73Q812yescomplemented
45C4⋊C4×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73—21no—
48C4⋊C4×C73C2×C412yes—
49C23×C73C2×D411yescharacteristic
50C2×C4×C73—22no—
51C2×C4×C73—41no—
52C2×C4×C73—41no—
53C2×C4×C73—41no—
54C2×C4×C73—41no—
55C2×C4×C73—41no—
56C2×C4×C73C22×C411yescharacteristic
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×Q811yescharacteristic
59C2×C4×C73C2×Q811yescharacteristic
60C2×C4×C73#4111yescharacteristic
61C2×C4×C73#4111yescharacteristic
62C2×Dic73—21no—
63C2×Dic73—21no—
64C2×Dic73—21no—
65C2×Dic73—21no—
66C2×Dic73—22no—
67C2×Dic73—41no—
68C2×Dic73—41no—
69C2×Dic73—41no—
70C2×Dic73—41no—
71C2×Dic73—41no—
72C2×Dic73C22⋊C412yes—
73C2×Dic73C22⋊C412yes—
74Dic146—48no—
75C8×C73—22no—
76#10596831—22no—
77C22×C73C2×C22⋊C411yescharacteristic
78C22×C73#12411yescharacteristic
79C22×C73C4⋊Q811yescharacteristic
80C22×C73AGL(1,ℤ/8)11yescharacteristic
81C22×C73AGL(1,ℤ/8)11yescharacteristic
82C22×C73#13711yescharacteristic
83C22×C73#13711yescharacteristic
84C4×C73—42no—
85C4×C73—81no—
86C4×C73C4×Q811yescharacteristic
87C4×C73C4×Q811yescharacteristic
88C4×C73C22⋊Q811yescharacteristic
89C4×C73C22⋊Q811yescharacteristic
90Dic73—22no—
91Dic73—22no—
92Dic73—42no—
93Dic73—81no—
94C2×C73#39111yescharacteristic
95C2×C73#41811yescharacteristic
96C2×C73#41911yescharacteristic
97C2×C73#48911yescharacteristic
98C2×C73#48911yescharacteristic
99C2×C73#50111yescharacteristic
100C2×C73#50111yescharacteristic
101#1993—731nomaximal, Sylow
102C73#199311yescharacteristic, complemented, Sylow
103C2×C4⋊Q8—731no—
104C2×#97—731no—
105#382—731no—
106#340—731no—
107#340—731no—
108#340—731no—
109#340D7311yescharacteristic
110C22×Q8—1461no—
111C22×C8—731no—
112C22×C8C2×D7311yescharacteristic
113C4⋊Q8—734no—
114C4⋊Q8—1462no—
115C2×C4⋊C4—731no—
116C2×C4⋊C4—731no—
117C2×C4⋊C4—1461no—
118C2×C4⋊C4C2×D7311yescharacteristic
119C2×C4⋊C4C2×D7311yescharacteristic
120C2×C42—731no—
121#97—1462no—
122#95—1461no—
123#95—1461no—
124C2×Q8—2922no—
125C2×Q8—2922no—
126C2×Q8—1464no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4—731no—
130C22×C4—731no—
131C22×C4—1461no—
132C22×C4—1461no—
133C22×C4C22×D7311yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—732no—
137C2×C8—1461no—
138C2×C8—1461no—
139C2×C8Dic14612yescomplemented
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—732no—
144C4⋊C4—1464no—
145C4⋊C4—1461no—
146C4⋊C4—1461no—
147C4⋊C4—1461no—
148C4⋊C4C4×D7312yes—
149C42—732no—
150C42—732no—
151C23D4×D7311yescharacteristic
152Q8—2928no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—2921no—
160C2×C4—2921no—
161C2×C4—2921no—
162C2×C4—2921no—
163C2×C4—2921no—
164C2×C4—732no—
165C2×C4—732no—
166C2×C4—1462no—
167C2×C4—1461no—
168C2×C4—1461no—
169C2×C4—1461no—
170C2×C4—1461no—
171C2×C4C2×C4×D7311yescharacteristic
172C2×C4D4×D7311yescharacteristic
173C2×C4Q8×D7311yescharacteristic
174C2×C4C2×Dic14611yescharacteristic
175C2×C4#1192402711yescharacteristic
176C2×C4#1192402811yescharacteristic
177C8—22no—
178C8—1462no—
179C22C22⋊C4×D7311yescharacteristic
180C22#1455657711yescharacteristic
181C22#1455659011yescharacteristic
182C22#1455661511yescharacteristic
183C22#1455661811yescharacteristic
184C22#1455662011yescharacteristic
185C22#1455662311yescharacteristic
186C4—42no—
187C4—81no—
188C4—2922no—
189C4—5841no—
190C4—1462no—
191C4—1462no—
192C4#1455655611yescharacteristic
193C4C4×Dic14611yescharacteristic
194C4#1455656811yescharacteristic
195C4#1455656911yescharacteristic
196C2#1798849111yescharacteristic
197C2#1798859011yescharacteristic
198C2#1798859411yescharacteristic
199C2#1798894511yescharacteristic
200C2#1798894811yescharacteristic
201C2#1798899411yescharacteristic
202C2#1798899511yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#340×C73C2
socleC23×C73C2×D4
hypercenter#340D73
hypocenterC73#1993
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
11. #14556590C4semidirect
31. C2×#10596831Q8semidirect
44. C2×C8×C73Q8semidirect
102. C73#1993semidirect
139. C2×C8Dic146semidirect