Finite Group Databasebeta

← #22610347

Subgroups — #22610347

Order 9344.

342 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 85 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#17989354C211yesmaximal, characteristic, complemented
2#17989094C211yesmaximal, characteristic
3#17988550C212yesmaximal, complemented
4#17988359C212yesmaximal, complemented
5#413×C73C211yesmaximal, characteristic, complemented
6C22×C4×D73C2211yescharacteristic
7#14556598—24no—
8C2×#11924012—22no—
9C2×#11924012C2212yes—
10#14556572C412yes—
11#14556567—21no—
12#14556562—21no—
13#14556559C412yes—
14C4×C22⋊D73—22no—
15#14556550C2211yescharacteristic
16#14556503—24no—
17C2×#41×C73C2211yescharacteristic
18C2×M16×C73C2212yes—
19#101×C73—21no—
20#100×C73—21no—
21C23×D73C2×C411yescharacteristic
22C2×C22⋊D73—22no—
23C22×Dic73C2×C411yescharacteristic
24C2×C4×D73—22no—
25C2×C4×D73—21no—
26C2×C4×D73—21no—
27C2×C4×D73—22no—
28#11924012—24no—
29#11924012—22no—
30#11924012—22no—
31C2×#10596831—24no—
32C2×#10596831D414yescomplemented
33C4⋊Dic73—21no—
34#11924007—22no—
35C22⋊Dic73—22no—
36C22⋊Dic73C2×C412yes—
37#11924005—22no—
38C4×Dic73—21no—
39#41×C73—22no—
40#41×C73—22no—
41C2×Q8×C73D411yescharacteristic
42C2×D4×C73C2×C412yes—
43C2×D4×C73D411yescharacteristic
44C22×C4×C73D412yes—
45C22×C4×C73C2311yescharacteristic
46M16×C73—22no—
47M16×C73—22no—
48C2×C8×C73—22no—
49C23×C73C22⋊C412yes—
50C23×C73C22×C411yescharacteristic
51C22×D73—21no—
52C22×D73—22no—
53C22×D73—42no—
54Q8×C73—22no—
55D4×C73—24no—
56D4×C73—22no—
57C2×C4×C73—22no—
58C2×C4×C73—22no—
59C2×C4×C73C22⋊C412yes—
60C2×C4×C73C2×D412yes—
61C2×C4×C73C2×D411yescharacteristic
62C2×C4×C73C2×D411yescharacteristic
63C2×C4×C73#4112yes—
64C22⋊D73—44no—
65C2×Dic73—22no—
66C2×Dic73—21no—
67C2×Dic73—22no—
68C4×D73—41no—
69C4×D73—42no—
70C4×D73—41no—
71C8×C73—42no—
72#10596831—24no—
73C22×C73—22no—
74C22×C73—41no—
75C22×C73—42no—
76C22×C73C2×C22⋊C411yescharacteristic
77C22×C73C4×D412yes—
78C2×D73—22no—
79C2×D73—24no—
80C2×D73—41no—
81C2×D73—42no—
82C2×D73—41no—
83C4×C73—22no—
84C4×C73#12011yescharacteristic
85C4×C73#12112yes—
86C4×C73#12311yescharacteristic
87Dic73—42no—
88Dic73—41no—
89C2×C73—21no—
90C2×C73—22no—
91C2×C73—42no—
92C2×C73#38611yescharacteristic
93D73—42no—
94#1891—731nomaximal, Sylow
95C73#189111yescharacteristic, complemented, Sylow
96#568—731no—
97#525—731no—
98#413D7311yescharacteristic, complemented
99#407—732no—
100#344—732no—
101C2×#41C2×D7311yescharacteristic
102C23×C4—731no—
103#131—1464no—
104C2×M16—732no—
105C2×M16—1462no—
106C2×M16C2×D7312yes—
107#123—732no—
108C22⋊Q8—1461no—
109#121—1461no—
110#120—732no—
111C4×D4—1462no—
112#117—731no—
113#101—21no—
114#100—21no—
115C22⋊C8—1464no—
116C24—731no—
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D7311yescharacteristic
120C2×D4—1462no—
121C2×D4C4×D7312yes—
122C2×D4C22⋊D7311yescharacteristic
123C22×C4—731no—
124C22×C4—1462no—
125C22×C4—1461no—
126C22×C4—1461no—
127C22×C4—1462no—
128C22×C4D29212yes—
129C22×C4C22×D7311yescharacteristic
130M16—22no—
131M16—22no—
132M16—1464no—
133M16—1462no—
134M16—1462no—
135C2×C8—22no—
136C2×C8—734no—
137C2×C8—1464no—
138C4⋊C4—1462no—
139C4⋊C4—1461no—
140C22⋊C4—732no—
141C22⋊C4—1462no—
142C22⋊C4—1462no—
143C42—1461no—
144C23—2922no—
145C23—1461no—
146C23—1462no—
147C23#1192400512yes—
148C23C2×C4×D7311yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—2924no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—2921no—
156C2×C4—2922no—
157C2×C4—2921no—
158C2×C4—1462no—
159C2×C4—1461no—
160C2×C4—1462no—
161C2×C4#1192400512yes—
162C2×C4D4×D7312yes—
163C2×C4C2×C22⋊D7311yescharacteristic
164C2×C4C2×D29211yescharacteristic
165C2×C4#1192402712yes—
166C8—42no—
167C8—1464no—
168C22—22no—
169C22—41no—
170C22—42no—
171C22—2921no—
172C22—2922no—
173C22—2921no—
174C22—1462no—
175C22—1464no—
176C22C2×#1192400511yescharacteristic
177C22#1455655112yes—
178C4—22no—
179C4—2922no—
180C4—2921no—
181C4#1455656111yescharacteristic
182C4#1455656312yes—
183C4#1455657511yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—2922no—
188C2#1798846411yescharacteristic
subgroupG/H
centerC4#14556561
commutatorC23×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#413×C73C2
socleC2×C73#386
hypercenter#413D73
hypocenterC73#1891
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #17989354C2semidirect
3. #17988550C2semidirect
4. #17988359C2semidirect
5. #413×C73C2semidirect
32. C2×#10596831D4semidirect
95. C73#1891semidirect
98. #413D73semidirect