Finite Group Databasebeta

← #22608539

Subgroups — #22608539

Order 9344.

216 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 69 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#17989121C211yesmaximal, characteristic
2C4×#11924012C211yesmaximal, characteristic, complemented
3#17988328C212yesmaximal, complemented
4#17988326C212yesmaximal, complemented
5#432×C73C211yesmaximal, characteristic, complemented
6C2×#11924012—21no—
7#14556585—21no—
8#14556583C2211yescharacteristic
9#14556579C2211yescharacteristic
10#14556574—21no—
11#14556570C411yescharacteristic
12#14556565C411yescharacteristic
13C4×Dic146C411yescharacteristic
14C4×D292C411yescharacteristic
15C4×C22⋊D73—21no—
16#14556548—21no—
17#14556502C2212yes—
18C4×#10596831—21no—
19C2×C42×C73C2211yescharacteristic
20C4⋊C8×C73—21no—
21C22⋊C8×C73—21no—
22#97×C73C2212yes—
23C2×Dic146C2×C411yescharacteristic
24C2×D292C2×C411yescharacteristic
25C2×C22⋊D73—21no—
26C2×C4×D73—21no—
27#11924012—24no—
28C2×#10596831—22no—
29C4⋊Dic73C2×C411yescharacteristic
30C4⋊Dic73C2×C411yescharacteristic
31#11924007—21no—
32#11924007—21no—
33#11924007—21no—
34#11924007—21no—
35C22⋊Dic73—21no—
36#11924005—21no—
37#11924005—21no—
38#11924005—21no—
39#11924005—21no—
40C4×Dic73—21no—
41C22×C4×C73C2×C411yescharacteristic
42C22×C4×C73D411yescharacteristic
43C22×C4×C73D411yescharacteristic
44C2×C8×C73—22no—
45C42×C73C2×C411yescharacteristic
46C42×C73D411yescharacteristic
47C42×C73D411yescharacteristic
48C42×C73C2311yescharacteristic
49C23×C73C22⋊C411yescharacteristic
50C22×D73—21no—
51C2×C4×C73—22no—
52C2×C4×C73—41no—
53C2×C4×C73—41no—
54C2×C4×C73C22⋊C411yescharacteristic
55C2×C4×C73C22⋊C411yescharacteristic
56C2×C4×C73C22⋊C411yescharacteristic
57C2×C4×C73C22×C411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C22⋊D73—42no—
61C2×Dic73—21no—
62C2×Dic73—21no—
63C2×Dic73—21no—
64D292—41no—
65C4×D73—42no—
66Dic146—41no—
67C8×C73—42no—
68#10596831—24no—
69C22×C73—21no—
70C22×C73—21no—
71C22×C73—21no—
72C22×C73C2×C22⋊C411yescharacteristic
73C2×D73—41no—
74C2×D73—41no—
75C2×D73—41no—
76C4×C73—21no—
77C4×C73—21no—
78C4×C73—21no—
79C4×C73—21no—
80C4×C73—21no—
81C4×C73#10412yes—
82Dic73—41no—
83Dic73—41no—
84Dic73—41no—
85C2×C73—41no—
86C2×C73#41311yescharacteristic
87C2×C73C2×#10411yescharacteristic
88C2×C73#42111yescharacteristic
89D73—81no—
90#1529—731nomaximal, Sylow
91C73#152911yescharacteristic, complemented, Sylow
92#529—731no—
93#432D7311yescharacteristic, complemented
94C4×M16—731no—
95#330—732no—
96#329—732no—
97C2×M16—1461no—
98#126—1461no—
99#125—731no—
100#124—731no—
101#123—1461no—
102C22⋊Q8—731no—
103#121—731no—
104C4×Q8—731no—
105C4×D4—731no—
106C4×D4—1461no—
107#117—1461no—
108C2×C42C2×D7311yescharacteristic
109C4⋊C8—21no—
110C22⋊C8—21no—
111#97—732no—
112#97C2×D7312yes—
113C4×C8—1461no—
114C2×Q8—731no—
115C2×D4—731no—
116C2×D4—1461no—
117C22×C4—1461no—
118C22×C4C4×D7311yescharacteristic
119C22×C4D29211yescharacteristic
120C22×C4C22⋊D7311yescharacteristic
121M16—1464no—
122C2×C8—22no—
123C2×C8—1462no—
124C4⋊C4—731no—
125C4⋊C4—731no—
126C4⋊C4—1461no—
127C4⋊C4—1461no—
128C4⋊C4—1461no—
129C4⋊C4—1461no—
130C22⋊C4—1461no—
131C22⋊C4—1461no—
132C22⋊C4—1461no—
133C22⋊C4—1461no—
134C22⋊C4—1461no—
135C42—1461no—
136C42C4×D7311yescharacteristic
137C42D29211yescharacteristic
138C42C22⋊D7311yescharacteristic
139C42C22×D7311yescharacteristic
140C23—1461no—
141C23#1192400511yescharacteristic
142Q8—2921no—
143D4—2921no—
144D4—2922no—
145C2×C4—22no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—2922no—
149C2×C4—1461no—
150C2×C4—1461no—
151C2×C4—1461no—
152C2×C4#1192400511yescharacteristic
153C2×C4#1192400511yescharacteristic
154C2×C4#1192400511yescharacteristic
155C2×C4C2×C4×D7311yescharacteristic
156C2×C4C2×C22⋊D7311yescharacteristic
157C2×C4C2×D29211yescharacteristic
158C8—42no—
159C8—1464no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—2921no—
164C22—2921no—
165C22—2921no—
166C22C2×#1192400511yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—2921no—
173C4—2921no—
174C4—2921no—
175C4#1455651712yes—
176C2—41no—
177C2—5841no—
178C2#1798856911yescharacteristic
179C2C2×#1455651711yescharacteristic
180C2#1798860511yescharacteristic
subgroupG/H
centerC22C2×#11924005
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#432×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#432D73
hypocenterC73#1529
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C4×#11924012C2semidirect
3. #17988328C2semidirect
4. #17988326C2semidirect
5. #432×C73C2semidirect
91. C73#1529semidirect
93. #432D73semidirect