Finite Group Databasebeta

← #22608564

Subgroups — #22608564

Order 9344.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#17989136C211yesmaximal, characteristic
2#17988642C212yesmaximal, complemented
3#17988327C211yesmaximal, characteristic, complemented
4#17988326C212yesmaximal, complemented
5#329×C73C211yesmaximal, characteristic, complemented
6C2×#11924029C411yescharacteristic
7C2×#11924027C411yescharacteristic
8#14556589C411yescharacteristic
9#14556587C411yescharacteristic
10#14556579C2211yescharacteristic
11#14556564—22no—
12#14556551—22no—
13C42×D73C2211yescharacteristic
14#14556520—22no—
15#14556503—22no—
16#14556502C2212yes—
17#124×C73C2211yescharacteristic
18#97×C73C2212yes—
19#11924029—42no—
20#11924027—42no—
21C2×Dic146C2×C411yescharacteristic
22C2×D292—21no—
23C2×D292C2×C411yescharacteristic
24C2×C22⋊D73—21no—
25C2×C22⋊D73—22no—
26C22×Dic73—21no—
27C2×C4×D73—21no—
28C2×C4×D73C2×C411yescharacteristic
29C2×C4×D73D412yes—
30C2×#10596831—22no—
31#11924007—22no—
32#11924005—22no—
33C4×Dic73C2×C411yescharacteristic
34C4×Dic73D412yes—
35C2×Q8×C73C2×C411yescharacteristic
36C2×D4×C73C2×C411yescharacteristic
37C2×C8×C73—22no—
38C22⋊C4×C73—22no—
39C42×C73C2311yescharacteristic
40C23×C73—21no—
41C22×D73—21no—
42C22×D73C22⋊C411yescharacteristic
43Q8×C73—41no—
44D4×C73—41no—
45C2×C4×C73—21no—
46C2×C4×C73C22×C411yescharacteristic
47C2×C4×C73C2×D412yes—
48C22⋊D73—44no—
49C22⋊D73—42no—
50C2×Dic73—21no—
51C2×Dic73—42no—
52C2×Dic73C22⋊C412yes—
53C2×Dic73C22⋊C411yescharacteristic
54D292—41no—
55D292—42no—
56C4×D73—22no—
57C4×D73—42no—
58C4×D73—42no—
59Dic146—41no—
60C8×C73—42no—
61#10596831—42no—
62C22×C73—41no—
63C22×C73—42no—
64C22×C73C2×C22⋊C411yescharacteristic
65C2×D73—21no—
66C2×D73—22no—
67C2×D73—41no—
68C2×D73—42no—
69C4×C73—21no—
70C4×C73—22no—
71C4×C73—41no—
72Dic73—22no—
73Dic73—41no—
74Dic73#10012yes—
75C2×C73—81no—
76C2×C73C2×#10011yescharacteristic
77C2×C73#42112yes—
78D73—41no—
79D73—81no—
80#1536—731nomaximal, Sylow
81C73#153611yescharacteristic, complemented, Sylow
82#532—731no—
83#432—732no—
84#329—731no—
85#329—732no—
86#329D7311yescharacteristic, complemented
87C2×#41—731no—
88C2×#41—731no—
89C4⋊Q8—731no—
90#127—731no—
91#124—731no—
92#124C2×D7311yescharacteristic
93#121—1462no—
94C4×D4—1462no—
95C2×C42—731no—
96C4⋊C8—1462no—
97C22⋊C8—1462no—
98#97—732no—
99#97C2×D7312yes—
100#41—2922no—
101#41—2922no—
102C2×Q8—731no—
103C2×Q8C4×D7311yescharacteristic
104C2×D4—731no—
105C2×D4—1461no—
106C2×D4—1462no—
107C2×D4—1461no—
108C2×D4C4×D7311yescharacteristic
109C22×C4—732no—
110C22×C4—731no—
111C22×C4—1461no—
112C22×C4—1461no—
113C2×C8—22no—
114C2×C8—1462no—
115C4⋊C4—1462no—
116C22⋊C4—22no—
117C22⋊C4—1462no—
118C42—731no—
119C42—732no—
120C42C22×D7311yescharacteristic
121C23—21no—
122C23—731no—
123C23—1461no—
124Q8—41no—
125Q8—2921no—
126D4—41no—
127D4—2921no—
128D4—2922no—
129D4—2922no—
130D4—2924no—
131C2×C4—21no—
132C2×C4—2922no—
133C2×C4—2922no—
134C2×C4—2922no—
135C2×C4—731no—
136C2×C4—732no—
137C2×C4—1462no—
138C2×C4—1461no—
139C2×C4C2×C4×D7311yescharacteristic
140C2×C4D4×D7312yes—
141C8—42no—
142C8—2922no—
143C22—41no—
144C22—42no—
145C22—2921no—
146C22—2922no—
147C22—1461no—
148C22—1462no—
149C22C22⋊C4×D7311yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—2921no—
154C4—732no—
155C4—1462no—
156C2—81no—
157C2—2921no—
158C2—5841no—
159C2#100×D7311yescharacteristic
160C2#1798860212yes—
subgroupG/H
centerC22C22⋊C4×D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#329×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#329D73
hypocenterC73#1536
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #17988642C2semidirect
3. #17988327C2semidirect
4. #17988326C2semidirect
5. #329×C73C2semidirect
81. C73#1536semidirect
86. #329D73semidirect