Finite Group Databasebeta

← #22626120

Subgroups — #22626120

Order 9344.

324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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#17989529C211yesmaximal, characteristic
2C4×C22⋊#64408C211yesmaximal, characteristic
3#17989465C214yesmaximal
4C2×#14556567C211yesmaximal, characteristic
5C2×C4⋊#64408—21no—
6C2×C22⋊#64408C2212yes—
7C2×C22⋊#64408C2212yes—
8C2×C4×#64408—21no—
9(C2×#64408)⋊C4—21no—
10(C2×#64408)⋊C4—21no—
11C22×C4×D73C2211yescharacteristic
12#14556567—21no—
13#14556567—21no—
14#14556567—21no—
15#14556567—21no—
16C2×C4⋊Dic73C411yescharacteristic, complemented
17C2×#11924007C412yescomplemented
18C2×#11924005C2212yes—
19C22×Q8×C73C411yescharacteristic, complemented
20C22×#64408—22no—
21C22×#64408—22no—
22C4⋊#64408—42no—
23C22⋊#64408—22no—
24C22⋊#64408—24no—
25C22⋊#64408Q814yescomplemented
26C4×#64408—42no—
27C23×D73C2311yescharacteristic
28C22×Dic73C2×C412yes—
29C22×Dic73C2×C411yescharacteristic
30C2×C4×D73—42no—
31C2×C4×D73D411yescharacteristic
32C2×C4×D73D411yescharacteristic
33C2×C4×D73D411yescharacteristic
34C2×C4×D73D411yescharacteristic
35C4⋊Dic73—21no—
36C4⋊Dic73—21no—
37#11924007—22no—
38#11924007—22no—
39#11924005—22no—
40#11924005—22no—
41C2×Q8×C73—21no—
42C2×Q8×C73—21no—
43C2×Q8×C73—42no—
44C22×C4×C73C2×C412yes—
45C22×C4×C73C2×C411yescharacteristic
46C23×C73C22×C411yescharacteristic
47C22×D73—41no—
48C22×D73—41no—
49C22×D73C2×D411yescharacteristic
50C22×D73C2×D411yescharacteristic
51C22×D73C2×Q812yes—
52C22×D73#4112yes—
53C2×#64408—24no—
54C2×#64408—42no—
55C2×#64408—42no—
56C2×#64408—42no—
57C2×#64408—42no—
58C2×#64408—42no—
59Q8×C73—42no—
60Q8×C73—42no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—42no—
64C2×C4×C73C22⋊C411yescharacteristic
65C2×C4×C73C22⋊C411yescharacteristic
66C2×Dic73—22no—
67C2×Dic73—41no—
68C2×Dic73—42no—
69C2×Dic73C22⋊C411yescharacteristic
70C2×Dic73C22⋊C411yescharacteristic
71C4×D73—22no—
72C4×D73—22no—
73C4×D73—41no—
74C4×D73—41no—
75C22×C73—21no—
76C22×C73—21no—
77C22×C73C2×C22⋊C411yescharacteristic
78C22×C73C4×Q812yes—
79C2×D73—21no—
80C2×D73—21no—
81C2×D73—21no—
82C2×D73—21no—
83C2×D73—42no—
84C2×D73—42no—
85C2×D73C22⋊Q812yes—
86C2×D73#12411yescharacteristic
87C2×D73C4⋊Q811yescharacteristic
88#64408—44no—
89#64408—82no—
90C4×C73—21no—
91C4×C73—42no—
92C4×C73#9912yes—
93Dic73—21no—
94Dic73—21no—
95Dic73—42no—
96C2×C73—22no—
97C2×C73#39111yescharacteristic
98C2×C73C2×#9911yescharacteristic
99C2×C73#41011yescharacteristic
100D73—22no—
101D73—21no—
102D73—21no—
103#1996—731nomaximal, Sylow
104C73#199611yescharacteristic, complemented, Sylow
105C2×C22⋊Q8—731no—
106#380—731no—
107C4×C22⋊C4—731no—
108#342—734no—
109C22×Q8#6440811yescharacteristic, complemented
110C23×C4—731no—
111C22⋊Q8—1461no—
112C22⋊Q8—1461no—
113C22⋊Q8—1461no—
114C22⋊Q8—1461no—
115C2×C4⋊C4—732no—
116C2×C4⋊C4—731no—
117C2×C4⋊C4—1461no—
118C2×C22⋊C4—732no—
119C2×C22⋊C4—732no—
120C2×C22⋊C4—732no—
121C2×C42—1461no—
122#95—1461no—
123#95—1461no—
124C24—731no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—42no—
128C22×C4—2922no—
129C22×C4—731no—
130C22×C4—731no—
131C22×C4—731no—
132C22×C4—732no—
133C22×C4—731no—
134C22×C4—731no—
135C22×C4—1462no—
136C22×C4—1462no—
137C22×C4C2×#6440812yes—
138C22×C4C2×#6440811yescharacteristic
139C4⋊C4—2922no—
140C4⋊C4—1462no—
141C4⋊C4—1462no—
142C4⋊C4—1461no—
143C4⋊C4—1461no—
144C22⋊C4—734no—
145C22⋊C4—1462no—
146C22⋊C4—1462no—
147C22⋊C4—1464no—
148C22⋊C4—1462no—
149C42—2922no—
150C23—2921no—
151C23—2921no—
152C23—732no—
153C23—732no—
154C23—731no—
155C23—731no—
156C23C22×#6440811yescharacteristic
157Q8—42no—
158Q8—42no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—2921no—
163C2×C4—2921no—
164C2×C4—2922no—
165C2×C4—2922no—
166C2×C4—2922no—
167C2×C4—2922no—
168C2×C4—2922no—
169C2×C4—2922no—
170C2×C4—2921no—
171C2×C4—731no—
172C2×C4—731no—
173C2×C4—1464no—
174C2×C4—1462no—
175C2×C4—1462no—
176C2×C4—1462no—
177C2×C4C22⋊#6440811yescharacteristic
178C2×C4C22⋊#6440811yescharacteristic
179C22—21no—
180C22—21no—
181C22—2922no—
182C22—2922no—
183C22—731no—
184C22—732no—
185C22—731no—
186C22—1461no—
187C22—1461no—
188C22—1461no—
189C22—1461no—
190C22C2×C22⋊#6440811yescharacteristic
191C22Q8×#6440812yes—
192C4—21no—
193C4—42no—
194C4—2924no—
195C4—2922no—
196C4—5842no—
197C4—1461no—
198C4—1461no—
199C4#1455664912yes—
200C2—22no—
201C2—1462no—
202C2—1461no—
203C2—1461no—
204C2(C2×#64408)⋊Q811yescharacteristic
205C2C2×#1455664911yescharacteristic
206C2#1798956811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC22×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22×Q8#64408
hypocenterC73#1996
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
16. C2×C4⋊Dic73C4semidirect
17. C2×#11924007C4semidirect
19. C22×Q8×C73C4semidirect
25. C22⋊#64408Q8semidirect
104. C73#1996semidirect
109. C22×Q8#64408semidirect