Finite Group Databasebeta

← #22625199

Subgroups — #22625199

Order 9344.

280 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 60 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#17989558C211yesmaximal, characteristic, complemented
2#17989555C211yesmaximal, characteristic, complemented
3#17989433C212yesmaximal, complemented
4#17989431C212yesmaximal, complemented
5C2×#14556576C211yesmaximal, characteristic
6C2×#11924038—21no—
7C2×#11924036—21no—
8#14556648—21no—
9#14556648—21no—
10C22⋊#10596833C2212yes—
11C22⋊#10596833C2212yes—
12C22×D292C411yescharacteristic
13C22×C4×D73C2211yescharacteristic
14#14556576—21no—
15#14556576—21no—
16#14556576—21no—
17#14556576—21no—
18C2×#11924007C2211yescharacteristic
19C2×#11924005C411yescharacteristic
20C2×#11924005C411yescharacteristic
21C2×#11924005C2211yescharacteristic
22C2×C4⋊C4×C73C411yescharacteristic
23#11924038—42no—
24#11924036—42no—
25C2×#10596833—22no—
26C2×#10596833—22no—
27C23×D73C2×C411yescharacteristic
28C23×D73C2×C411yescharacteristic
29C2×D292—21no—
30C2×D292—21no—
31C2×D292—42no—
32C22×Dic73C2×C411yescharacteristic
33C22×Dic73C2311yescharacteristic
34C2×C4×D73—42no—
35C2×C4×D73D411yescharacteristic
36C2×C4×D73D411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73D411yescharacteristic
39#11924007—21no—
40#11924007—21no—
41#11924005—21no—
42#11924005—21no—
43#11924005—21no—
44#11924005—21no—
45#11924005—21no—
46#11924005—21no—
47C22×C4×C73C2×C411yescharacteristic
48C22×C4×C73C2×C411yescharacteristic
49C22×C4×C73C2×C411yescharacteristic
50C4⋊C4×C73—21no—
51C4⋊C4×C73—21no—
52C23×C73C22×C411yescharacteristic
53C22×D73—22no—
54C22×D73—22no—
55C22×D73—21no—
56C22×D73—22no—
57C22×D73—41no—
58C22×D73—41no—
59C22×D73—41no—
60C22×D73C22⋊C411yescharacteristic
61C22×D73C22⋊C411yescharacteristic
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73C22⋊C411yescharacteristic
68C2×C4×C73C22⋊C411yescharacteristic
69C2×Dic73—21no—
70C2×Dic73—22no—
71C2×Dic73—41no—
72C2×Dic73C2×D411yescharacteristic
73C2×Dic73C2×D411yescharacteristic
74D292—42no—
75D292—42no—
76C4×D73—22no—
77C4×D73—22no—
78C4×D73—41no—
79C4×D73—41no—
80#10596833—42no—
81#10596833—42no—
82C22×C73—21no—
83C22×C73—21no—
84C22×C73C2×C22⋊C411yescharacteristic
85C22×C73#13112yes—
86C2×D73—21no—
87C2×D73—21no—
88C2×D73—21no—
89C2×D73—21no—
90C2×D73—21no—
91C2×D73—44no—
92C2×D73—41no—
93C2×D73—41no—
94C2×D73—41no—
95C2×D73—82no—
96C2×D73#9912yes—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73—41no—
100C4×C73—41no—
101Dic73—21no—
102Dic73—21no—
103Dic73—41no—
104C2×C73—22no—
105C2×C73#40811yescharacteristic
106C2×C73C2×#9911yescharacteristic
107C2×C73#41311yescharacteristic
108D73—22no—
109D73—41no—
110D73—81no—
111#1468—731nomaximal, Sylow
112C73#146811yescharacteristic, complemented, Sylow
113C2×#123—731no—
114#407—731no—
115C2×C22⋊C8—731no—
116#324—732no—
117#323—732no—
118C22×D4—731no—
119C23×C4—731no—
120C2×M16—1461no—
121C22×C8—1461no—
122#123—1461no—
123#123—1461no—
124#123—1461no—
125#123—1461no—
126C2×C4⋊C4—731no—
127C2×C4⋊C4#6440811yescharacteristic
128C2×C22⋊C4—731no—
129C2×C22⋊C4—731no—
130C2×C22⋊C4—731no—
131C22⋊C8—732no—
132C22⋊C8—732no—
133C22⋊C8—1461no—
134C22⋊C8—1461no—
135C24—731no—
136C24—731no—
137C2×D4—2922no—
138C2×D4—1461no—
139C2×D4—1461no—
140C22×C4—2922no—
141C22×C4—731no—
142C22×C4—731no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—731no—
146C22×C4—731no—
147C22×C4C2×#6440811yescharacteristic
148C22×C4C2×#6440811yescharacteristic
149C22×C4C2×#6440811yescharacteristic
150M16—2922no—
151C2×C8—2922no—
152C2×C8—1462no—
153C2×C8—1462no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—1461no—
157C4⋊C4—1461no—
158C22⋊C4—1461no—
159C22⋊C4—1461no—
160C22⋊C4—1461no—
161C22⋊C4—1461no—
162C22⋊C4—1461no—
163C22⋊C4—1461no—
164C23—2921no—
165C23—2921no—
166C23—2921no—
167C23—731no—
168C23—731no—
169C23—1462no—
170C23—1461no—
171C23—1462no—
172C23—1462no—
173C23C22×#6440811yescharacteristic
174D4—2922no—
175D4—2922no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—2921no—
182C2×C4—2921no—
183C2×C4—2921no—
184C2×C4—731no—
185C2×C4—731no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4—1462no—
189C2×C4—1461no—
190C2×C4C22⋊#6440811yescharacteristic
191C2×C4C22⋊#6440811yescharacteristic
192C8—2922no—
193C8—2922no—
194C22—21no—
195C22—21no—
196C22—2924no—
197C22—2921no—
198C22—2921no—
199C22—2921no—
200C22—5842no—
201C22—732no—
202C22—1461no—
203C22—1461no—
204C22—1461no—
205C22—1461no—
206C22—1461no—
207C22C2×C22⋊#6440811yescharacteristic
208C22#1455667912yes—
209C4—21no—
210C4—21no—
211C4—41no—
212C4—41no—
213C4—2921no—
214C4—1461no—
215C4—1461no—
216C2—22no—
217C2—2921no—
218C2—5841no—
219C2—1462no—
220C2#1798956211yescharacteristic
221C2D73⋊#9911yescharacteristic
222C2#1798957311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C4⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C4⋊C4#64408
hypocenterC73#1468
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #17989558C2semidirect
2. #17989555C2semidirect
3. #17989433C2semidirect
4. #17989431C2semidirect
112. C73#1468semidirect