Finite Group Databasebeta

← #22609165

Subgroups — #22609165

Order 9344.

240 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 55 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#17989242C211yesmaximal, characteristic
2#17988990C211yesmaximal, characteristic, complemented
3#17988789C211yesmaximal, characteristic, complemented
4#17988332C211yesmaximal, characteristic, complemented
5D4⋊#10596831C211yesmaximal, characteristic, complemented
6#17988314C211yesmaximal, characteristic, complemented
7#474×C73C211yesmaximal, characteristic, complemented
8C2×#11924028—21no—
9C2×#11924015—21no—
10#14556591C2211yescharacteristic
11#14556573—22no—
12#14556570—21no—
13#14556562—21no—
14C4×D292C2211yescharacteristic
15C4⋊C4×D73—21no—
16#14556524—22no—
17C4⋊#10596831C2211yescharacteristic
18#14556515—21no—
19C4×#10596831C2211yescharacteristic
20C4⋊Q8×C73C2211yescharacteristic
21C4×D4×C73C2211yescharacteristic
22#107×C73—21no—
23C4⋊C8×C73C2211yescharacteristic
24#102×C73—21no—
25#11924028—42no—
26#11924028—42no—
27C2×Dic146—21no—
28C2×D292D411yescharacteristic
29C2×C22⋊D73—22no—
30C2×C4×D73—22no—
31C2×C4×D73—21no—
32#11924015—42no—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73D411yescharacteristic
37C4⋊Dic73D412yes—
38#11924007—22no—
39C22⋊Dic73—22no—
40#11924005—21no—
41C2×Q8×C73—21no—
42C2×D4×C73D411yescharacteristic
43C22×C4×C73—21no—
44C2×C8×C73—21no—
45C4⋊C4×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73D411yescharacteristic
48C22⋊C4×C73—21no—
49C42×C73C2311yescharacteristic
50C23×C73—21no—
51C22×D73—21no—
52Q8×C73—41no—
53Q8×C73—41no—
54D4×C73—21no—
55D4×C73—21no—
56C2×C4×C73—21no—
57C2×C4×C73—41no—
58C2×C4×C73—41no—
59C2×C4×C73—41no—
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C22⋊D73—44no—
64C2×Dic73—21no—
65C2×Dic73—22no—
66D292—21no—
67D292D812yes—
68C4×D73—44no—
69C4×D73—41no—
70C4×D73—41no—
71Dic146—41no—
72Dic146—41no—
73C8×C73—41no—
74#10596831—22no—
75#10596831—41no—
76C22×C73—41no—
77C22×C73—41no—
78C22×C73—41no—
79C22×C73#12011yescharacteristic
80C2×D73—22no—
81C2×D73—41no—
82C2×D73—41no—
83C4×C73—21no—
84C4×C73—41no—
85C4×C73—81no—
86C4×C73C2×D811yescharacteristic
87C4×C73#13511yescharacteristic
88C4×C73AGL(1,ℤ/8)11yescharacteristic
89C4×C73#13711yescharacteristic
90Dic73—42no—
91Dic73—41no—
92C2×C73—81no—
93C2×C73#44711yescharacteristic
94C2×C73#45211yescharacteristic
95C2×C73#45611yescharacteristic
96D73—42no—
97#1647—731nomaximal, Sylow
98C73#164711yescharacteristic, complemented, Sylow
99#547—731no—
100#500—731no—
101#474D7311yescharacteristic, complemented
102#461—731no—
103#332—731no—
104D4⋊C8—731no—
105D4⋊C8—731no—
106C2×#41—1461no—
107C2×SD16—1461no—
108C4⋊Q8—731no—
109C4⋊Q8C2×D7311yescharacteristic
110#123—1462no—
111C22⋊Q8—1461no—
112#121—1461no—
113C4×D4—731no—
114C4×D4C2×D7311yescharacteristic
115C2×C4⋊C4—1461no—
116#107—21no—
117#107—1462no—
118C4⋊C8—731no—
119C4⋊C8C2×D7311yescharacteristic
120#103—1461no—
121#102—21no—
122C4×C8—731no—
123#41—2922no—
124#41—2922no—
125C2×Q8—21no—
126C2×Q8—1461no—
127C2×D4—731no—
128C2×D4—1462no—
129C2×D4C22⋊D7311yescharacteristic
130C22×C4—21no—
131C22×C4—1462no—
132C22×C4—1461no—
133SD16—2922no—
134C2×C8—21no—
135C2×C8—1461no—
136C2×C8—1461no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—731no—
140C4⋊C4—732no—
141C4⋊C4—1462no—
142C4⋊C4—1461no—
143C4⋊C4C22⋊D7311yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—1462no—
146C22⋊C4—1461no—
147C42C22×D7311yescharacteristic
148C23—21no—
149C23—1461no—
150Q8—41no—
151Q8—41no—
152Q8—2921no—
153Q8—2921no—
154D4—21no—
155D4—21no—
156D4—2924no—
157D4—732no—
158D4—1461no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—2924no—
164C2×C4—2921no—
165C2×C4—2921no—
166C2×C4—1461no—
167C2×C4—1462no—
168C2×C4D4×D7311yescharacteristic
169C2×C4D4×D7311yescharacteristic
170C2×C4C2×C22⋊D7311yescharacteristic
171C8—41no—
172C8—2921no—
173C8—1462no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—2921no—
178C22—2921no—
179C22—1462no—
180C22#1455655911yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—2922no—
185C4—2921no—
186C4D8×D7311yescharacteristic
187C4#1455661111yescharacteristic
188C4#1455661511yescharacteristic
189C4#1455662211yescharacteristic
190C2—81no—
191C2—2922no—
192C2#1798871911yescharacteristic
193C2#1798874711yescharacteristic
194C2#1798876811yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#474×C73C2
socleC22×C73#120
hypercenter#474D73
hypocenterC73#1647
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #17988990C2semidirect
3. #17988789C2semidirect
4. #17988332C2semidirect
5. D4⋊#10596831C2semidirect
6. #17988314C2semidirect
7. #474×C73C2semidirect
98. C73#1647semidirect
101. #474D73semidirect