Finite Group Databasebeta

← #22610644

Subgroups — #22610644

Order 9344.

222 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 81 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#17988614C211yesmaximal, characteristic, complemented
2C2×#14556518C211yesmaximal, characteristic
3#17988554C211yesmaximal, characteristic
4C2×#14556501C211yesmaximal, characteristic, complemented
5#17988352C211yesmaximal, characteristic, complemented
6#17988346C211yesmaximal, characteristic, complemented
7#416×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10C22×#10596831C2211yescharacteristic
11C2×C4×Dic73C2211yescharacteristic
12C4⋊#10596831—22no—
13#14556518—22no—
14C22⋊#10596831—22no—
15#14556501—22no—
16C2×#41×C73C2211yescharacteristic
17C22×C8×C73C2211yescharacteristic
18#117×C73C2211yescharacteristic
19#103×C73C412yescomplemented
20#102×C73C412yescomplemented
21C22×Dic73—21no—
22#11924012—21no—
23#11924012—21no—
24#11924012—21no—
25#11924012—21no—
26C2×#10596831—21no—
27C2×#10596831—21no—
28C2×#10596831—21no—
29C2×#10596831—21no—
30C2×#10596831D412yes—
31C4×Dic73—21no—
32C4×Dic73D412yes—
33#41×C73—21no—
34#41×C73—21no—
35#41×C73—21no—
36#41×C73—21no—
37C2×Q8×C73C2×C411yescharacteristic
38C2×D4×C73—21no—
39C2×D4×C73C2×C411yescharacteristic
40C22×C4×C73—21no—
41C22×C4×C73C2311yescharacteristic
42C2×C8×C73—21no—
43C2×C8×C73—21no—
44C2×C8×C73C2×C412yes—
45C4⋊C4×C73C2×C412yes—
46C22⋊C4×C73—21no—
47C42×C73—21no—
48C23×C73—21no—
49C23×C73#4111yescharacteristic
50Q8×C73—21no—
51Q8×C73—21no—
52D4×C73—21no—
53D4×C73—21no—
54D4×C73—41no—
55D4×C73—41no—
56C2×C4×C73—22no—
57C2×C4×C73—21no—
58C2×C4×C73—41no—
59C2×C4×C73—41no—
60C2×C4×C73C22×C411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C2×C4×C73#4111yescharacteristic
64C2×C4×C73#4111yescharacteristic
65C2×C4×C73#4111yescharacteristic
66C2×Dic73—22no—
67C2×Dic73—42no—
68C8×C73—22no—
69#10596831—22no—
70#10596831—41no—
71#10596831—41no—
72C22×C73—22no—
73C22×C73—41no—
74C22×C73—42no—
75C22×C73C4×D411yescharacteristic
76C22×C73#12311yescharacteristic
77C22×C73#12611yescharacteristic
78C4×C73—41no—
79C4×C73—42no—
80C4×C73#11711yescharacteristic
81C4×C73C4×D411yescharacteristic
82C4×C73#12111yescharacteristic
83C4×C73#12411yescharacteristic
84Dic73—42no—
85C2×C73—21no—
86C2×C73—21no—
87C2×C73—81no—
88C2×C73#38811yescharacteristic
89C2×C73#44412yes—
90#1938—731nomaximal, Sylow
91C73#193811yescharacteristic, complemented, Sylow
92#424—731no—
93C2×#104—731no—
94#416D7311yescharacteristic
95#408—731no—
96C2×#97—731no—
97#341—731no—
98#339—731no—
99C2×#41C2×D7311yescharacteristic
100C2×M16—731no—
101C2×M16—731no—
102C22×C8—731no—
103C22×C8C2×D7311yescharacteristic
104#117C2×D7311yescharacteristic
105C2×C42—731no—
106C4⋊C8—1462no—
107#104—1462no—
108#103Dic7312yescomplemented
109#102Dic7312yescomplemented
110C22⋊C8—1462no—
111#97—1462no—
112#41—21no—
113#41—21no—
114#41—21no—
115#41—21no—
116C2×Q8C2×Dic7311yescharacteristic
117C2×D4—21no—
118C2×D4C2×Dic7311yescharacteristic
119C22×C4—21no—
120C22×C4—1461no—
121C22×C4C22×D7311yescharacteristic
122M16—1461no—
123M16—1461no—
124M16—1461no—
125M16—1461no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—732no—
129C2×C8—1461no—
130C2×C8—1461no—
131C2×C8—1461no—
132C2×C8—1461no—
133C2×C8C2×Dic7312yes—
134C4⋊C4C2×Dic7312yes—
135C22⋊C4—21no—
136C42—21no—
137C42—732no—
138C42—1461no—
139C23—21no—
140C23#1192402711yescharacteristic
141Q8—21no—
142Q8—21no—
143D4—21no—
144D4—21no—
145D4—41no—
146D4—41no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—2922no—
152C2×C4—1462no—
153C2×C4C22×Dic7311yescharacteristic
154C2×C4D4×D7311yescharacteristic
155C2×C4D4×D7311yescharacteristic
156C2×C4#1192402711yescharacteristic
157C2×C4#1192402811yescharacteristic
158C2×C4#1192402811yescharacteristic
159C8—22no—
160C8—2921no—
161C8—2921no—
162C8—1462no—
163C22—22no—
164C22—42no—
165C22—41no—
166C22D4×Dic7311yescharacteristic
167C22#1455657311yescharacteristic
168C22#1455658411yescharacteristic
169C4—42no—
170C4—41no—
171C4—2922no—
172C4#1455655011yescharacteristic
173C4D4×Dic7311yescharacteristic
174C4#1455656411yescharacteristic
175C4#1455657711yescharacteristic
176C2—21no—
177C2—21no—
178C2—81no—
179C2#1798848011yescharacteristic
180C2#1798870912yes—
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#416×C73C2
socleC22×C73C4×D4
hypercenter#416D73
hypocenterC73#1938
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #17988614C2semidirect
4. C2×#14556501C2semidirect
5. #17988352C2semidirect
6. #17988346C2semidirect
19. #103×C73C4semidirect
20. #102×C73C4semidirect
91. C73#1938semidirect
108. #103Dic73semidirect
109. #102Dic73semidirect