Finite Group Databasebeta

← #22608420

Subgroups — #22608420

Order 9344.

304 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 77 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#17989098C211yesmaximal, characteristic
2C2×C22⋊#10596831C211yesmaximal, characteristic, complemented
3#17988323C212yesmaximal, complemented
4#17988320C212yesmaximal, complemented
5C4×C22⋊C4×C73C211yesmaximal, characteristic, complemented
6C2×#11924028C411yescharacteristic, complemented
7C22×#10596831—21no—
8#14556574—21no—
9#14556570C411yescharacteristic, complemented
10#14556570C2211yescharacteristic
11#14556565C411yescharacteristic, complemented
12#14556565C2211yescharacteristic
13#14556560—21no—
14C4×C22⋊D73—21no—
15C4×C22⋊D73—21no—
16#14556550C411yescharacteristic, complemented
17C22⋊#10596831—21no—
18C22⋊#10596831C2212yes—
19C23×C4×C73C2211yescharacteristic
20C2×C22⋊C4×C73—21no—
21C2×C42×C73—21no—
22#95×C73C2212yes—
23#11924028—42no—
24C2×Dic146C2×C411yescharacteristic
25C2×D292C2×C411yescharacteristic
26C2×C22⋊D73—21no—
27C2×C22⋊D73—21no—
28C2×C22⋊D73—21no—
29C2×C4×D73—21no—
30C2×#10596831—22no—
31C2×#10596831—42no—
32C4⋊Dic73C2×C411yescharacteristic
33C4⋊Dic73C2×C411yescharacteristic
34#11924007—21no—
35#11924007—21no—
36C22⋊Dic73—21no—
37C22⋊Dic73—21no—
38C22⋊Dic73—21no—
39#11924005—21no—
40#11924005—21no—
41C4×Dic73—21no—
42C24×C73D411yescharacteristic
43C22×C4×C73—22no—
44C22×C4×C73—42no—
45C22×C4×C73C2×C411yescharacteristic
46C22×C4×C73C2×C411yescharacteristic
47C22×C4×C73D411yescharacteristic
48C22×C4×C73D411yescharacteristic
49C22×C4×C73D411yescharacteristic
50C22×C4×C73C2311yescharacteristic
51C22⋊C4×C73—24no—
52C42×C73—42no—
53C23×C73—22no—
54C23×C73—22no—
55C23×C73—41no—
56C23×C73C22⋊C411yescharacteristic
57C23×C73C22⋊C411yescharacteristic
58C23×C73C2×D411yescharacteristic
59C22×D73—21no—
60C2×C4×C73—22no—
61C2×C4×C73—22no—
62C2×C4×C73—22no—
63C2×C4×C73—24no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73—42no—
68C2×C4×C73—42no—
69C2×C4×C73C22⋊C411yescharacteristic
70C2×C4×C73C22⋊C411yescharacteristic
71C2×C4×C73C22×C411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C22⋊D73—42no—
74C22⋊D73—42no—
75C22⋊D73—42no—
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—21no—
79D292—41no—
80C4×D73—42no—
81Dic146—41no—
82#10596831—42no—
83C22×C73—21no—
84C22×C73—21no—
85C22×C73—21no—
86C22×C73—21no—
87C22×C73—21no—
88C22×C73—21no—
89C22×C73—21no—
90C22×C73—44no—
91C22×C73#10412yes—
92C22×C73C2×C22⋊C411yescharacteristic
93C22×C73#13512yes—
94C2×D73—41no—
95C2×D73—41no—
96C2×D73—41no—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73—21no—
100C4×C73—44no—
101C4×C73#9912yes—
102Dic73—41no—
103Dic73—41no—
104Dic73—41no—
105C2×C73—22no—
106C2×C73—22no—
107C2×C73—41no—
108C2×C73C2×#9911yescharacteristic
109C2×C73#41611yescharacteristic
110C2×C73C2×#10411yescharacteristic
111D73—81no—
112#1501—731nomaximal, Sylow
113C73#150111yescharacteristic, complemented, Sylow
114#525—731no—
115C2×C22⋊C8—731no—
116C4×C22⋊C4D7311yescharacteristic, complemented
117#328—732no—
118#327—732no—
119C2×#41—731no—
120C23×C4C2×D7311yescharacteristic
121C22×C8—1461no—
122#123—1461no—
123C22⋊Q8—731no—
124C22⋊Q8—731no—
125#121—731no—
126#121—731no—
127#120—1461no—
128C4×D4—1461no—
129C4×D4—1461no—
130#117—731no—
131C2×C22⋊C4—21no—
132C2×C42—21no—
133C22⋊C8—732no—
134C22⋊C8—1461no—
135#95C2×D7312yes—
136C24C22⋊D7311yescharacteristic
137#41—2922no—
138C2×Q8—731no—
139C2×D4—731no—
140C2×D4—1461no—
141C2×D4—1461no—
142C2×D4—1461no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—1461no—
146C22×C4C4×D7311yescharacteristic
147C22×C4C4×D7311yescharacteristic
148C22×C4D29211yescharacteristic
149C22×C4D29211yescharacteristic
150C22×C4C22⋊D7311yescharacteristic
151C22×C4C22×D7311yescharacteristic
152C2×C8—2922no—
153C2×C8—1462no—
154C4⋊C4—731no—
155C4⋊C4—731no—
156C4⋊C4—1461no—
157C4⋊C4—1461no—
158C22⋊C4—24no—
159C22⋊C4—1461no—
160C22⋊C4—1461no—
161C22⋊C4—1461no—
162C22⋊C4—1461no—
163C22⋊C4—1461no—
164C42—42no—
165C42—1461no—
166C23—22no—
167C23—22no—
168C23—41no—
169C23—1461no—
170C23#1192400511yescharacteristic
171C23#1192400511yescharacteristic
172C23C2×C22⋊D7311yescharacteristic
173Q8—2921no—
174D4—2921no—
175D4—2922no—
176D4—2922no—
177D4—2922no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—2922no—
188C2×C4—1461no—
189C2×C4—1461no—
190C2×C4—1461no—
191C2×C4#1192400511yescharacteristic
192C2×C4#1192400511yescharacteristic
193C2×C4C2×C4×D7311yescharacteristic
194C2×C4C2×D29211yescharacteristic
195C8—2922no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—44no—
204C22—2921no—
205C22—2921no—
206C22—2921no—
207C22#1455651912yes—
208C22C2×#1192400511yescharacteristic
209C22#1455661112yes—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—44no—
214C4—2921no—
215C4—2921no—
216C4—2921no—
217C4#1455650512yes—
218C2—22no—
219C2—22no—
220C2—41no—
221C2—5841no—
222C2C2×#1455650511yescharacteristic
223C2#1798858111yescharacteristic
224C2C2×#1455651911yescharacteristic
subgroupG/H
centerC2×C4#11924005
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC4×C22⋊C4×C73C2
socleC22×C73C2×C22⋊C4
hypercenterC4×C22⋊C4D73
hypocenterC73#1501
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#10596831C2semidirect
3. #17988323C2semidirect
4. #17988320C2semidirect
5. C4×C22⋊C4×C73C2semidirect
6. C2×#11924028C4semidirect
9. #14556570C4semidirect
11. #14556565C4semidirect
16. #14556550C4semidirect
113. C73#1501semidirect
116. C4×C22⋊C4D73semidirect