Finite Group Databasebeta

← #22625415

Subgroups — #22625415

Order 9344.

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

normal subgroups only

This group has 200 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#17989610C211yesmaximal, characteristic, complemented
2#17989609C211yesmaximal, characteristic, complemented
3#17989444C212yesmaximal, complemented
4#17989442C212yesmaximal, complemented
5#17989119C211yesmaximal, characteristic
6#14556658—21no—
7C4⋊#10596833—21no—
8#14556648—21no—
9#14556648—21no—
10#14556646C2212yes—
11#14556646C2212yes—
12#14556584—21no—
13#14556582C2211yescharacteristic
14#14556578C2211yescharacteristic
15#14556573—21no—
16#14556571C411yescharacteristic
17#14556562C411yescharacteristic
18C4×Dic146C411yescharacteristic
19C4×C22⋊D73—21no—
20#14556550—21no—
21C42×D73C2211yescharacteristic
22C4×D4×C73C411yescharacteristic
23C2×#10596833—22no—
24C2×#10596833—22no—
25C2×Dic146C2×C411yescharacteristic
26C2×C22⋊D73—21no—
27C2×C4×D73C2×C411yescharacteristic
28C2×C4×D73D411yescharacteristic
29C2×C4×D73D411yescharacteristic
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32C4⋊Dic73C2×C411yescharacteristic
33#11924007—21no—
34#11924007—21no—
35C22⋊Dic73—21no—
36C22⋊Dic73—21no—
37C22⋊Dic73—21no—
38#11924005—21no—
39C4×Dic73—21no—
40C4×Dic73D411yescharacteristic
41C4×Dic73D411yescharacteristic
42C4×Dic73C2311yescharacteristic
43C2×D4×C73C2×C411yescharacteristic
44C22×C4×C73—21no—
45C4⋊C4×C73C2×C411yescharacteristic
46C22⋊C4×C73—21no—
47C42×C73C2×C411yescharacteristic
48C23×C73—21no—
49C22×D73C22⋊C411yescharacteristic
50D4×C73—41no—
51C2×C4×C73—21no—
52C2×C4×C73—42no—
53C2×C4×C73C22⋊C411yescharacteristic
54C2×C4×C73C22⋊C411yescharacteristic
55C2×C4×C73C22×C411yescharacteristic
56C22⋊D73—42no—
57C2×Dic73—21no—
58C2×Dic73—21no—
59C2×Dic73C22⋊C411yescharacteristic
60C2×Dic73C2×D411yescharacteristic
61C2×Dic73C2×D411yescharacteristic
62C4×D73—41no—
63C4×D73—41no—
64C4×D73—41no—
65Dic146—41no—
66#10596833—42no—
67#10596833—42no—
68C22×C73—41no—
69C22×C73—41no—
70C22×C73—41no—
71C22×C73C2×C22⋊C411yescharacteristic
72C2×D73—21no—
73C2×D73—21no—
74C2×D73—21no—
75C4×C73—21no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—41no—
79Dic73—21no—
80Dic73—21no—
81Dic73—21no—
82Dic73—41no—
83Dic73—41no—
84C2×C73—81no—
85C2×C73#41311yescharacteristic
86C2×C73#42111yescharacteristic
87C2×C73#42111yescharacteristic
88D73—41no—
89#1535—731nomaximal, Sylow
90C73#153511yescharacteristic, complemented, Sylow
91#529—731no—
92#432—731no—
93#432—731no—
94#330—732no—
95#329—732no—
96#126—1461no—
97#125—731no—
98#124—731no—
99#123—1461no—
100C22⋊Q8—731no—
101#121—731no—
102C4×Q8—731no—
103C4×D4—1461no—
104C4×D4#6440811yescharacteristic
105#117—1461no—
106C2×C42—731no—
107C4⋊C8—1461no—
108C4⋊C8—1461no—
109C22⋊C8—1461no—
110C22⋊C8—1461no—
111#97—732no—
112#97—732no—
113C2×Q8—731no—
114C2×D4—1461no—
115C2×D4C2×#6440811yescharacteristic
116C22×C4—21no—
117C22×C4—731no—
118C22×C4—731no—
119C22×C4—731no—
120C2×C8—1462no—
121C2×C8—1462no—
122C4⋊C4—731no—
123C4⋊C4—1461no—
124C4⋊C4—1461no—
125C4⋊C4—1461no—
126C4⋊C4—1461no—
127C4⋊C4C2×#6440811yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—1461no—
130C22⋊C4—1461no—
131C22⋊C4—1461no—
132C22⋊C4—1461no—
133C42—731no—
134C42—731no—
135C42—731no—
136C42—1461no—
137C42C2×#6440811yescharacteristic
138C23—21no—
139C23—731no—
140Q8—2921no—
141D4—41no—
142D4—2922no—
143C2×C4—21no—
144C2×C4—42no—
145C2×C4—2921no—
146C2×C4—2921no—
147C2×C4—2921no—
148C2×C4—731no—
149C2×C4—731no—
150C2×C4—731no—
151C2×C4—1461no—
152C2×C4—1461no—
153C2×C4C22⋊#6440811yescharacteristic
154C2×C4C22⋊#6440811yescharacteristic
155C2×C4C22×#6440811yescharacteristic
156C8—2922no—
157C8—2922no—
158C22—41no—
159C22—41no—
160C22—41no—
161C22—1461no—
162C22—1461no—
163C22—1461no—
164C22C2×C22⋊#6440811yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—41no—
169C4—2921no—
170C4—2921no—
171C4—1461no—
172C4—1461no—
173C4—1461no—
174C2—81no—
175C2—2921no—
176C2#1798957311yescharacteristic
177C2#1798958411yescharacteristic
178C2#1798958511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×D4#64408
hypocenterC73#1535
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #17989610C2semidirect
2. #17989609C2semidirect
3. #17989444C2semidirect
4. #17989442C2semidirect
90. C73#1535semidirect