Finite Group Databasebeta

← #22625357

Subgroups — #22625357

Order 9344.

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

normal subgroups only

This group has 284 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
1C2×#14556648C211yesmaximal, characteristic, complemented
2#17989530C211yesmaximal, characteristic, complemented
3#17989441C212yesmaximal, complemented
4#17989438C212yesmaximal, complemented
5#17989094C211yesmaximal, characteristic
6C22×#10596833—21no—
7C2×C22⋊#64408—21no—
8#14556648—21no—
9#14556648C2212yes—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4C2212yes—
12C22×C4×D73C2211yescharacteristic
13#14556572—21no—
14#14556567C411yescharacteristic, complemented
15#14556567C2211yescharacteristic
16#14556562C411yescharacteristic, complemented
17#14556562C2211yescharacteristic
18#14556559—21no—
19C4×C22⋊D73—21no—
20C4×C22⋊D73—21no—
21#14556550C411yescharacteristic, complemented
22C2×#41×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24C2×#10596833—22no—
25C2×#10596833—42no—
26C22⋊#64408—42no—
27C23×D73D411yescharacteristic
28C2×C22⋊D73—21no—
29C2×C22⋊D73—21no—
30C22×Dic73D411yescharacteristic
31C2×C4×D73—42no—
32C2×C4×D73C2×C411yescharacteristic
33C2×C4×D73D411yescharacteristic
34C2×C4×D73D411yescharacteristic
35C2×C4×D73C2311yescharacteristic
36C4⋊Dic73C2×C411yescharacteristic
37C4⋊Dic73C2×C411yescharacteristic
38#11924007—21no—
39#11924007—21no—
40C22⋊Dic73—21no—
41C22⋊Dic73—21no—
42C22⋊Dic73—21no—
43#11924005—21no—
44#11924005—21no—
45C4×Dic73—21no—
46#41×C73—42no—
47C2×Q8×C73C2×C411yescharacteristic
48C2×D4×C73—21no—
49C2×D4×C73C2×C411yescharacteristic
50C22×C4×C73—21no—
51C22×C4×C73C2×C411yescharacteristic
52C23×C73—21no—
53C23×C73C22⋊C411yescharacteristic
54C22×D73—22no—
55C22×D73—22no—
56C22×D73—41no—
57C22×D73C22⋊C411yescharacteristic
58C22×D73C2×D411yescharacteristic
59C2×#64408—42no—
60C2×#64408—42no—
61C2×#64408—42no—
62Q8×C73—41no—
63D4×C73—41no—
64D4×C73—42no—
65C2×C4×C73—22no—
66C2×C4×C73—21no—
67C2×C4×C73—42no—
68C2×C4×C73C22⋊C411yescharacteristic
69C2×C4×C73C22×C411yescharacteristic
70C22⋊D73—42no—
71C22⋊D73—42no—
72C2×Dic73—22no—
73C2×Dic73—21no—
74C2×Dic73—21no—
75C2×Dic73C22⋊C411yescharacteristic
76C2×Dic73C2×D411yescharacteristic
77C4×D73—41no—
78C4×D73—41no—
79C4×D73—41no—
80C4×D73—41no—
81#10596833—42no—
82C22×C73—21no—
83C22×C73—21no—
84C22×C73—41no—
85C22×C73—41no—
86C22×C73—41no—
87C22×C73#9912yes—
88C22×C73C2×C22⋊C411yescharacteristic
89C2×D73—21no—
90C2×D73—21no—
91C2×D73—21no—
92C2×D73—21no—
93C2×D73—21no—
94C2×D73—44no—
95C2×D73#13512yes—
96#64408—82no—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73—41no—
100Dic73—21no—
101Dic73—21no—
102Dic73—41no—
103Dic73—41no—
104C2×C73—22no—
105C2×C73—81no—
106C2×C73C2×#9911yescharacteristic
107C2×C73#41611yescharacteristic
108C2×C73#42111yescharacteristic
109D73—22no—
110D73—41no—
111#1516—731nomaximal, Sylow
112C73#151611yescharacteristic, complemented, Sylow
113#525—731no—
114C2×C22⋊C8—731no—
115#381—731no—
116#328—732no—
117#327—732no—
118C2×#41#6440811yescharacteristic, complemented
119C23×C4—731no—
120C22×C8—1461no—
121#123—1461no—
122C22⋊Q8—731no—
123C22⋊Q8—731no—
124#121—731no—
125#121—731no—
126#120—1461no—
127C4×D4—1461no—
128C4×D4—1461no—
129#117—731no—
130C2×C22⋊C4—1461no—
131C22⋊C8—732no—
132C22⋊C8—1461no—
133#95—732no—
134#95—1461no—
135C24—731no—
136#41—42no—
137C2×Q8C2×#6440811yescharacteristic
138C2×D4—21no—
139C2×D4—1461no—
140C2×D4—1461no—
141C2×D4C2×#6440811yescharacteristic
142C22×C4—21no—
143C22×C4—2922no—
144C22×C4—731no—
145C22×C4—731no—
146C22×C4—731no—
147C22×C4—731no—
148C22×C4—731no—
149C22×C4—1462no—
150C22×C4C2×#6440811yescharacteristic
151C2×C8—2922no—
152C2×C8—1462no—
153C4⋊C4—731no—
154C4⋊C4—731no—
155C4⋊C4—1461no—
156C4⋊C4—1461no—
157C22⋊C4—2922no—
158C22⋊C4—1461no—
159C22⋊C4—1461no—
160C22⋊C4—1461no—
161C22⋊C4—1461no—
162C22⋊C4—1461no—
163C42—1461no—
164C23—21no—
165C23—2921no—
166C23—731no—
167C23—731no—
168C23—1462no—
169C23—1462no—
170C23C22⋊#6440811yescharacteristic
171Q8—41no—
172D4—41no—
173D4—42no—
174D4—2922no—
175D4—2922no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—2921no—
180C2×C4—2921no—
181C2×C4—2921no—
182C2×C4—2921no—
183C2×C4—2922no—
184C2×C4—2922no—
185C2×C4—2922no—
186C2×C4—731no—
187C2×C4—731no—
188C2×C4—1461no—
189C2×C4—1461no—
190C2×C4—1462no—
191C2×C4C22⋊#6440811yescharacteristic
192C2×C4C22×#6440811yescharacteristic
193C8—2922no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—2924no—
200C22—732no—
201C22—1461no—
202C22—1461no—
203C22—1461no—
204C22—1461no—
205C22—1461no—
206C22#1455664912yes—
207C22C2×C22⋊#6440811yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—2921no—
212C4—2921no—
213C4—5842no—
214C4—1461no—
215C4—1461no—
216C2—22no—
217C2—81no—
218C2—2921no—
219C2—1462no—
220C2C2×#1455664911yescharacteristic
221C2#1798957711yescharacteristic
222C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC2×#41×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×#41#64408
hypocenterC73#1516
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14556648C2semidirect
2. #17989530C2semidirect
3. #17989441C2semidirect
4. #17989438C2semidirect
14. #14556567C4semidirect
16. #14556562C4semidirect
21. #14556550C4semidirect
22. C2×#41×C73C4semidirect
112. C73#1516semidirect
118. C2×#41#64408semidirect