Finite Group Databasebeta

← #22625249

Subgroups — #22625249

Order 9344.

234 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 62 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#17989588C211yesmaximal, characteristic, complemented
2C4×#11924038C211yesmaximal, characteristic, complemented
3#17989437C212yesmaximal, complemented
4#17989435C212yesmaximal, complemented
5#17989122C211yesmaximal, characteristic
6C2×#11924038—21no—
7C2×#11924036—21no—
8#14556658—21no—
9C4⋊#10596833C2212yes—
10#14556646—21no—
11C4×#10596833C2212yes—
12#14556586—21no—
13#14556579C411yescharacteristic
14#14556576—21no—
15#14556571C411yescharacteristic
16#14556566C411yescharacteristic
17#14556556C2211yescharacteristic
18#14556553—21no—
19#14556553C2211yescharacteristic
20#14556549—21no—
21C42×D73C2211yescharacteristic
22#125×C73C411yescharacteristic
23#11924038—24no—
24#11924036—42no—
25C2×#10596833—22no—
26C2×#10596833—22no—
27C2×Dic146C2×C411yescharacteristic
28C2×D292—21no—
29C2×D292C2×C411yescharacteristic
30C2×C4×D73—21no—
31C2×C4×D73C2×C411yescharacteristic
32C2×C4×D73D411yescharacteristic
33C2×C4×D73D411yescharacteristic
34C4⋊Dic73—21no—
35#11924007—21no—
36#11924005—21no—
37#11924005—21no—
38#11924005—21no—
39#11924005—21no—
40#11924005—21no—
41C4×Dic73—21no—
42C4×Dic73D411yescharacteristic
43C4×Dic73D411yescharacteristic
44C4×Dic73C2311yescharacteristic
45C4⋊C4×C73—21no—
46C4⋊C4×C73—21no—
47C4⋊C4×C73C2×C411yescharacteristic
48C4⋊C4×C73C2×C411yescharacteristic
49C42×C73C2×C411yescharacteristic
50C22×D73—21no—
51C22×D73C22⋊C411yescharacteristic
52C2×C4×C73—21no—
53C2×C4×C73—21no—
54C2×C4×C73C22⋊C411yescharacteristic
55C2×C4×C73C22⋊C411yescharacteristic
56C2×C4×C73C22×C411yescharacteristic
57C2×Dic73—21no—
58C2×Dic73C22⋊C411yescharacteristic
59C2×Dic73C2×D411yescharacteristic
60C2×Dic73C2×D411yescharacteristic
61D292—22no—
62D292—42no—
63C4×D73—22no—
64C4×D73—22no—
65C4×D73—21no—
66C4×D73—21no—
67C4×D73—41no—
68C4×D73—41no—
69Dic146—22no—
70#10596833—24no—
71#10596833—42no—
72C22×C73C2×C22⋊C411yescharacteristic
73C2×D73—21no—
74C2×D73—21no—
75C2×D73—41no—
76C2×D73—41no—
77C2×D73—41no—
78C2×D73#10412yes—
79C4×C73—21no—
80C4×C73—21no—
81C4×C73—41no—
82C4×C73—41no—
83C4×C73#13112yes—
84Dic73—21no—
85Dic73—21no—
86Dic73—41no—
87Dic73AGL(1,ℤ/8)11yescharacteristic
88Dic73#13711yescharacteristic
89C2×C73#40811yescharacteristic
90C2×C73#41711yescharacteristic
91C2×C73C2×#10411yescharacteristic
92D73—22no—
93D73—81no—
94#1483—731nomaximal, Sylow
95C73#148311yescharacteristic, complemented, Sylow
96#529—731no—
97C2×C4⋊C8—731no—
98C4×M16—731no—
99Q8⋊C8—732no—
100D4⋊C8—732no—
101C2×M16—1461no—
102C22×C8—1461no—
103#126—1461no—
104#125#6440811yescharacteristic
105#124—731no—
106#123—1461no—
107C22⋊Q8—731no—
108#121—731no—
109C4×Q8—731no—
110C4×D4—731no—
111C4×D4—1461no—
112#117—1461no—
113C2×C42—731no—
114C4⋊C8—732no—
115C4⋊C8—1461no—
116#97—1461no—
117C4×C8—732no—
118C2×Q8—731no—
119C2×D4—731no—
120C2×D4—1461no—
121C22×C4—731no—
122C22×C4—731no—
123C22×C4—731no—
124C22×C4—1461no—
125M16—1464no—
126C2×C8—2922no—
127C2×C8—1462no—
128C2×C8—1462no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—1461no—
132C4⋊C4—1461no—
133C4⋊C4C2×#6440811yescharacteristic
134C4⋊C4C2×#6440811yescharacteristic
135C22⋊C4—1461no—
136C22⋊C4—1461no—
137C22⋊C4—1461no—
138C22⋊C4—1461no—
139C22⋊C4—1461no—
140C42—731no—
141C42—731no—
142C42—731no—
143C42—1461no—
144C42C2×#6440811yescharacteristic
145C23—731no—
146C23—1461no—
147Q8—1462no—
148D4—2922no—
149D4—1462no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—2921no—
153C2×C4—2921no—
154C2×C4—731no—
155C2×C4—731no—
156C2×C4—731no—
157C2×C4—1461no—
158C2×C4—1461no—
159C2×C4—1462no—
160C2×C4—1461no—
161C2×C4—1462no—
162C2×C4C22⋊#6440811yescharacteristic
163C2×C4C22⋊#6440811yescharacteristic
164C2×C4C22×#6440811yescharacteristic
165C8—2922no—
166C8—1464no—
167C22—2921no—
168C22—2921no—
169C22—2921no—
170C22—732no—
171C22—1461no—
172C22—1461no—
173C22C2×C22⋊#6440811yescharacteristic
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—2921no—
179C4—731no—
180C4—731no—
181C4—1461no—
182C4—1461no—
183C4#1455667912yes—
184C2—5841no—
185C2—1462no—
186C2#1798956211yescharacteristic
187C2#1798957811yescharacteristic
188C2D73⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#125×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#125#64408
hypocenterC73#1483
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #17989588C2semidirect
2. C4×#11924038C2semidirect
3. #17989437C2semidirect
4. #17989435C2semidirect
95. C73#1483semidirect