Finite Group Databasebeta

← #22609064

Subgroups — #22609064

Order 9344.

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

normal subgroups only

This group has 214 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#17989297C211yesmaximal, characteristic
2#17988966C211yesmaximal, characteristic, complemented
3#17988874C211yesmaximal, characteristic
4#17988335C211yesmaximal, characteristic, complemented
5Q8⋊#10596831C211yesmaximal, characteristic, complemented
6#17988314C211yesmaximal, characteristic
7#477×C73C211yesmaximal, characteristic, complemented
8C2×#11924018—22no—
9#14556591C2211yescharacteristic
10#14556583—21no—
11#14556569—22no—
12#14556567—21no—
13C4×D292—21no—
14C4×D292C2211yescharacteristic
15C4⋊C4×D73—21no—
16#14556522—21no—
17C4⋊#10596831C2211yescharacteristic
18#14556511—21no—
19C4×#10596831C2211yescharacteristic
20C4⋊Q8×C73C2211yescharacteristic
21C4×Q8×C73C2211yescharacteristic
22#107×C73—21no—
23C4⋊C8×C73C2211yescharacteristic
24#103×C73—21no—
25C2×Dic146D412yes—
26C2×D292D411yescharacteristic
27C2×C4×D73—21no—
28C2×C4×D73—22no—
29#11924018—44no—
30C2×#10596831—21no—
31C2×#10596831—21no—
32C4⋊Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73D411yescharacteristic
35#11924007—22no—
36#11924007—22no—
37#11924005—22no—
38#11924005—21no—
39C2×Q8×C73—21no—
40C2×Q8×C73D411yescharacteristic
41C2×C8×C73—21no—
42C4⋊C4×C73—21no—
43C4⋊C4×C73—21no—
44C4⋊C4×C73—21no—
45C4⋊C4×C73D411yescharacteristic
46C42×C73—21no—
47C42×C73C2311yescharacteristic
48C22×D73—21no—
49Q8×C73—21no—
50Q8×C73—21no—
51Q8×C73—42no—
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73—41no—
55C2×C4×C73C2×D411yescharacteristic
56C2×C4×C73C2×D411yescharacteristic
57C2×C4×C73C2×D411yescharacteristic
58C2×Dic73—21no—
59C2×Dic73—22no—
60D292—21no—
61D292Q1612yescomplemented
62C4×D73—41no—
63C4×D73—41no—
64C4×D73—82no—
65Dic146—42no—
66C8×C73—41no—
67#10596831—22no—
68#10596831—41no—
69C22×C73#12011yescharacteristic
70C2×D73—22no—
71C2×D73—41no—
72C2×D73—41no—
73C4×C73—21no—
74C4×C73—41no—
75C4×C73—41no—
76C4×C73—81no—
77C4×C73C2×Q1611yescharacteristic
78C4×C73#13511yescharacteristic
79C4×C73#13711yescharacteristic
80C4×C73#13711yescharacteristic
81Dic73—41no—
82Dic73—42no—
83C2×C73#45111yescharacteristic
84C2×C73#45211yescharacteristic
85C2×C73#45311yescharacteristic
86D73—42no—
87#1632—731nomaximal, Sylow
88C73#163211yescharacteristic, complemented, Sylow
89#554—731no—
90#494—731no—
91#477D7311yescharacteristic, complemented
92#476—731no—
93#333—731no—
94Q8⋊C8—731no—
95D4⋊C8—731no—
96C2×Q16—1462no—
97C4⋊Q8—731no—
98C4⋊Q8C2×D7311yescharacteristic
99#125—1461no—
100C22⋊Q8—1462no—
101C22⋊Q8—1461no—
102C4×Q8C2×D7311yescharacteristic
103C4×D4—731no—
104C4×D4—1461no—
105C2×C4⋊C4—1461no—
106#107—21no—
107#106—1461no—
108C4⋊C8—731no—
109C4⋊C8C2×D7311yescharacteristic
110#103—21no—
111#102—1461no—
112C4×C8—731no—
113C2×Q8—21no—
114C2×Q8—732no—
115C2×Q8C22⋊D7311yescharacteristic
116C2×D4—731no—
117C22×C4—1462no—
118C22×C4—1461no—
119Q16—2924no—
120C2×C8—21no—
121C2×C8—1461no—
122C2×C8—1461no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—731no—
127C4⋊C4—1462no—
128C4⋊C4—1462no—
129C4⋊C4—1461no—
130C4⋊C4—1461no—
131C4⋊C4C22⋊D7311yescharacteristic
132C22⋊C4—1462no—
133C22⋊C4—1461no—
134C42—21no—
135C42C22×D7311yescharacteristic
136C23—1461no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—2922no—
141D4—732no—
142D4—1461no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—2921no—
147C2×C4—2921no—
148C2×C4—5842no—
149C2×C4—1461no—
150C2×C4—1462no—
151C2×C4D4×D7311yescharacteristic
152C2×C4D4×D7311yescharacteristic
153C2×C4C2×C22⋊D7311yescharacteristic
154C8—41no—
155C8—2921no—
156C8—1462no—
157C22—2921no—
158C22—2921no—
159C22—1462no—
160C22#1455655911yescharacteristic
161C4—21no—
162C4—41no—
163C4—41no—
164C4—81no—
165C4—2921no—
166C4—2922no—
167C4Q16×D7311yescharacteristic
168C4#1455661111yescharacteristic
169C4#1455662211yescharacteristic
170C4#1455662311yescharacteristic
171C2—2922no—
172C2#1798874111yescharacteristic
173C2#1798874711yescharacteristic
174C2#1798875311yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#477×C73C2
socleC22×C73#120
hypercenter#477D73
hypocenterC73#1632
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #17988966C2semidirect
4. #17988335C2semidirect
5. Q8⋊#10596831C2semidirect
7. #477×C73C2semidirect
61. D292Q16semidirect
88. C73#1632semidirect
91. #477D73semidirect