Finite Group Databasebeta

← #355×D73 #22611607

Subgroups — #355×D73 #22611607

Order 9344.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D73C211yesmaximal, characteristic
2#101×D73C212yesmaximal, complemented
3#17988384C211yesmaximal, characteristic, complemented
4#17988383C212yesmaximal, complemented
5#355×C73C211yesmaximal, characteristic, complemented
6C2×Q8×D73C2211yescharacteristic
7C2×D4×D73C411yescharacteristic
8M16×D73—22no—
9#14556580C2211yescharacteristic
10#14556579C411yescharacteristic
11#14556578C411yescharacteristic
12#14556577—22no—
13C22⋊C4×D73—22no—
14C42×D73C411yescharacteristic
15#14556510C2212yescomplemented
16#14556509—22no—
17#124×C73C2211yescharacteristic
18#101×C73C2212yescomplemented
19C23×D73—21no—
20C2×Dic146C2×C411yescharacteristic
21C2×Dic146D412yes—
22Q8×D73—41no—
23Q8×D73—41no—
24C2×D292C2×C411yescharacteristic
25C2×C22⋊D73—21no—
26D4×D73—41no—
27D4×D73—41no—
28C2×C4×D73—21no—
29C2×C4×D73C2×C411yescharacteristic
30C2×C4×D73D412yes—
31#11924012—22no—
32#11924011—42no—
33C8×D73—42no—
34C22⋊Dic73—22no—
35#11924005—22no—
36#11924005—22no—
37C4×Dic73—21no—
38C4×Dic73C2×C411yescharacteristic
39C2×Q8×C73C2311yescharacteristic
40C2×D4×C73C2×C411yescharacteristic
41M16×C73—22no—
42C22⋊C4×C73—22no—
43C42×C73C2×C411yescharacteristic
44C23×C73—21no—
45C22×D73—21no—
46C22×D73—44no—
47C22×D73—41no—
48C22×D73—41no—
49C22×D73C22⋊C411yescharacteristic
50Q8×C73—41no—
51D4×C73—41no—
52C2×C4×C73—21no—
53C2×C4×C73C22×C411yescharacteristic
54C2×C4×C73C2×D412yes—
55C22⋊D73—42no—
56C2×Dic73—21no—
57C2×Dic73C22⋊C411yescharacteristic
58C2×Dic73C22⋊C412yes—
59D292—41no—
60C4×D73—22no—
61C4×D73—22no—
62C4×D73—21no—
63C4×D73—21no—
64C4×D73—42no—
65Dic146—41no—
66Dic146—42no—
67C8×C73—42no—
68#10596831—42no—
69C22×C73—42no—
70C22×C73—41no—
71C22×C73C2×C22⋊C411yescharacteristic
72C2×D73—22no—
73C2×D73—42no—
74C2×D73—41no—
75C2×D73—82no—
76C2×D73—82no—
77C2×D73#9911yescharacteristic
78C2×D73#9911yescharacteristic
79C4×C73—22no—
80C4×C73—21no—
81C4×C73—41no—
82Dic73—22no—
83Dic73—21no—
84Dic73—41no—
85C2×C73—21no—
86C2×C73—81no—
87C2×C73C2×#9911yescharacteristic
88D73—21no—
89D73—81no—
90D73#35512yesdirect product factor
91C2×#355—731nomaximal, Sylow
92C73C2×#35511yescharacteristic, complemented, Sylow
93C2×#124—731no—
94C2×#101—732no—
95#355—731no—
96#355—732no—
97#355D7311yescharacteristic, direct product factor
98C22×Q8—731no—
99C22×D4—731no—
100C2×M16—1462no—
101#124—731no—
102#124—731no—
103#124—731no—
104#124—1462no—
105#124C2×D7311yescharacteristic
106C2×C22⋊C4—1462no—
107C2×C42—731no—
108#101—732no—
109#101—1462no—
110#101C2×D7312yescomplemented
111C24—1461no—
112C2×Q8—2921no—
113C2×Q8—2921no—
114C2×Q8—731no—
115C2×Q8—732no—
116C2×Q8C22×D7311yescharacteristic
117C2×D4—2921no—
118C2×D4—2921no—
119C2×D4—731no—
120C2×D4—1461no—
121C2×D4C4×D7311yescharacteristic
122C22×C4—731no—
123C22×C4—732no—
124C22×C4—1461no—
125M16—22no—
126M16—2922no—
127M16—1462no—
128C2×C8—2922no—
129C22⋊C4—22no—
130C22⋊C4—1462no—
131C22⋊C4—1462no—
132C22⋊C4—1462no—
133C42—731no—
134C42—1461no—
135C42C4×D7311yescharacteristic
136C23—21no—
137C23—2921no—
138C23—2921no—
139C23—2924no—
140C23—731no—
141C23—1461no—
142Q8—41no—
143Q8—2922no—
144Q8—2921no—
145D4—41no—
146D4—2921no—
147D4—2922no—
148C2×C4—21no—
149C2×C4—2922no—
150C2×C4—731no—
151C2×C4—732no—
152C2×C4—1462no—
153C2×C4—1462no—
154C2×C4—1461no—
155C2×C4—1461no—
156C2×C4—1461no—
157C2×C4C2×C4×D7311yescharacteristic
158C2×C4D4×D7312yes—
159C8—42no—
160C8—2922no—
161C22—42no—
162C22—41no—
163C22—2922no—
164C22—2921no—
165C22—5842no—
166C22—5842no—
167C22—731no—
168C22—731no—
169C22—1462no—
170C22C22⋊C4×D7311yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—2921no—
175C4—1461no—
176C4—1462no—
177C2—21no—
178C2—81no—
179C2—5841no—
180C2—732no—
181C2—1461no—
182C2#99×D7311yescharacteristic
subgroupG/H
centerC2#99×D73
commutatorC2×C4×C73C22×C4
FrattiniC2×Q8C22×D73
Fitting#355×C73C2
socleC2×C73C2×#99
hypercenter#355D73
hypocenterC73C2×#355
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D73C2semidirect
3. #17988384C2semidirect
4. #17988383C2semidirect
5. #355×C73C2semidirect
15. #14556510C22semidirect
18. #101×C73C22semidirect
90. D73#355direct (N × H)
92. C73C2×#355semidirect
97. #355D73direct (N × H)
110. #101C2×D73semidirect