Finite Group Databasebeta

← #22625795

Subgroups — #22625795

Order 9344.

336 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 80 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#17989590C212yesmaximal, complemented
2C2×#14556651C212yesmaximal
3#17989467C212yesmaximal, complemented
4C2×C4×C22⋊D73C211yesmaximal, characteristic
5C2×#11924037C2214yes—
6#14556658—22no—
7C4⋊#10596833—22no—
8#14556651—24no—
9C22×C22⋊D73C2211yescharacteristic
10C22×C4×D73C411yescharacteristic
11C4×C22⋊D73—22no—
12C4×C22⋊D73—22no—
13C2×#11924007C2211yescharacteristic
14C2×C22⋊Dic73C411yescharacteristic
15C2×#11924005C411yescharacteristic
16C2×C4×Dic73C2211yescharacteristic
17C23×C4×C73C411yescharacteristic
18#11924037—24no—
19#11924037—24no—
20C2×#10596833—24no—
21C23×D73C2×C411yescharacteristic
22C2×C22⋊D73—22no—
23C2×C22⋊D73—22no—
24C2×C22⋊D73D412yes—
25C2×C22⋊D73Q812yes—
26C22×Dic73C2×C411yescharacteristic
27C22×Dic73C2×C411yescharacteristic
28C22×Dic73C2311yescharacteristic
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31C2×C4×D73—42no—
32#11924007—22no—
33C22⋊Dic73—22no—
34#11924005—22no—
35C4×Dic73D412yes—
36C4×Dic73D412yes—
37C24×C73C2×C411yescharacteristic
38C22×C4×C73—21no—
39C22×C4×C73—21no—
40C22×C4×C73—42no—
41C22×C4×C73C2×C411yescharacteristic
42C22×C4×C73C2×C411yescharacteristic
43C23×C73—21no—
44C23×C73—21no—
45C23×C73—41no—
46C23×C73—41no—
47C23×C73C4⋊C412yes—
48C23×C73C22×C411yescharacteristic
49C22×D73—21no—
50C22×D73—21no—
51C22×D73—41no—
52C22×D73—41no—
53C22×D73C4⋊C412yes—
54C2×C4×C73—22no—
55C2×C4×C73—21no—
56C2×C4×C73—42no—
57C2×C4×C73—42no—
58C2×C4×C73—41no—
59C2×C4×C73C22⋊C411yescharacteristic
60C2×C4×C73C22⋊C411yescharacteristic
61C22⋊D73—24no—
62C22⋊D73—24no—
63C2×Dic73—21no—
64C2×Dic73—41no—
65C2×Dic73—41no—
66C2×Dic73C22⋊C412yes—
67C2×Dic73C2×D411yescharacteristic
68C2×Dic73C2×D412yes—
69C2×Dic73C2×Q811yescharacteristic
70C2×Dic73#4112yes—
71C4×D73—42no—
72C4×D73—42no—
73#10596833—44no—
74C22×C73—21no—
75C22×C73—21no—
76C22×C73—22no—
77C22×C73—42no—
78C22×C73—42no—
79C22×C73—41no—
80C22×C73—41no—
81C22×C73C2×C22⋊C411yescharacteristic
82C22×C73C2×C4⋊C411yescharacteristic
83C22×C73#11711yescharacteristic
84C2×D73—22no—
85C2×D73—42no—
86C2×D73—41no—
87C2×D73—41no—
88C2×D73—42no—
89C4×C73—21no—
90C4×C73—41no—
91C4×C73#10012yescomplemented
92Dic73—22no—
93Dic73—41no—
94Dic73#12112yes—
95Dic73C22⋊Q812yes—
96C2×C73—21no—
97C2×C73—21no—
98C2×C73—42no—
99C2×C73#38011yescharacteristic
100C2×C73C2×#10011yescharacteristic
101C2×C73#41311yescharacteristic
102D73—42no—
103#1800—731nomaximal, Sylow
104C73#180011yescharacteristic, complemented, Sylow
105C2×C4×D4—731no—
106#423—732no—
107C2×#100—732no—
108#343—732no—
109C22×D4—731no—
110C23×C4—731no—
111C23×C4#6440811yescharacteristic
112C2×M16—734no—
113C4×D4—1462no—
114C4×D4—1462no—
115C2×C4⋊C4—731no—
116C2×C22⋊C4—731no—
117C2×C22⋊C4—731no—
118C2×C42—731no—
119C4⋊C8—1462no—
120C4⋊C8—1462no—
121#100—1464no—
122C24—731no—
123C24C2×#6440811yescharacteristic
124C2×D4—732no—
125C2×D4—732no—
126C2×D4—1462no—
127C2×D4—1462no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—42no—
131C22×C4—2922no—
132C22×C4—731no—
133C22×C4—731no—
134C22×C4—731no—
135C22×C4—1461no—
136C22×C4—1461no—
137C22×C4C2×#6440811yescharacteristic
138C22×C4C2×#6440811yescharacteristic
139M16—1464no—
140M16—1464no—
141C2×C8—1464no—
142C4⋊C4—1462no—
143C22⋊C4—1462no—
144C22⋊C4—1462no—
145C42—732no—
146C42—732no—
147C23—21no—
148C23—21no—
149C23—41no—
150C23—41no—
151C23—2921no—
152C23—2921no—
153C23—732no—
154C23—1461no—
155C23—1461no—
156C23C4⋊#6440812yes—
157C23C22×#6440811yescharacteristic
158D4—1464no—
159D4—1464no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—41no—
165C2×C4—2922no—
166C2×C4—2922no—
167C2×C4—2921no—
168C2×C4—2921no—
169C2×C4—732no—
170C2×C4—731no—
171C2×C4—731no—
172C2×C4—732no—
173C2×C4—732no—
174C2×C4—1461no—
175C2×C4C22⋊#6440811yescharacteristic
176C2×C4C22⋊#6440811yescharacteristic
177C8—2924no—
178C22—21no—
179C22—21no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—41no—
185C22—2922no—
186C22—2922no—
187C22—2921no—
188C22—2921no—
189C22—1462no—
190C22C2×C22⋊#6440811yescharacteristic
191C22C2×C4⋊#6440811yescharacteristic
192C22#1455667011yescharacteristic
193C4—21no—
194C4—41no—
195C4—2921no—
196C4—732no—
197C4—732no—
198C4—1462no—
199C4#1455665112yescomplemented
200C2—21no—
201C2—21no—
202C2—42no—
203C2—2922no—
204C2#1798952911yescharacteristic
205C2C2×#1455665111yescharacteristic
206C2#1798957311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC23×C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC23×C4#64408
hypocenterC73#1800
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #17989590C2semidirect
3. #17989467C2semidirect
91. C4×C73#100semidirect
104. C73#1800semidirect
199. C4#14556651semidirect