Finite Group Databasebeta

← #22625361

Subgroups — #22625361

Order 9344.

264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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#17989606C211yesmaximal, characteristic, complemented
2#17989531C211yesmaximal, characteristic, complemented
3#17989439C212yesmaximal, complemented
4#17989438C212yesmaximal, complemented
5#17989134C211yesmaximal, characteristic
6C2×C4⋊#64408—21no—
7C4⋊#10596833—21no—
8#14556648C2212yes—
9C4×#10596833—21no—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4C2212yes—
12C2×#11924028—21no—
13#14556590C411yescharacteristic, complemented
14#14556587C411yescharacteristic, complemented
15#14556577—21no—
16#14556566C2211yescharacteristic
17#14556564—21no—
18#14556562C2211yescharacteristic
19C4×D292C411yescharacteristic, complemented
20C4×C22⋊D73—21no—
21C42×D73C2211yescharacteristic
22C4×D4×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24C2×#10596833—22no—
25C4⋊#64408—42no—
26#11924028—42no—
27#11924028—42no—
28C2×Dic146—21no—
29C2×D292—21no—
30C2×D292C2×C411yescharacteristic
31C2×C22⋊D73—21no—
32C2×C22⋊D73—21no—
33C2×C22⋊D73—21no—
34C2×C4×D73—21no—
35C2×C4×D73D411yescharacteristic
36C2×C4×D73D411yescharacteristic
37C2×C4×D73C2311yescharacteristic
38C4⋊Dic73C2×C411yescharacteristic
39#11924007—21no—
40C22⋊Dic73—21no—
41#11924005—21no—
42#11924005—21no—
43C4×Dic73C2×C411yescharacteristic
44C4×Dic73D411yescharacteristic
45C4×Dic73D411yescharacteristic
46C2×D4×C73C2×C411yescharacteristic
47C22×C4×C73—21no—
48C4⋊C4×C73C2×C411yescharacteristic
49C22⋊C4×C73—21no—
50C42×C73C2×C411yescharacteristic
51C23×C73—21no—
52C22×D73—21no—
53C22×D73C2×D411yescharacteristic
54C2×#64408—42no—
55C2×#64408—42no—
56C2×#64408—42no—
57D4×C73—41no—
58C2×C4×C73—21no—
59C2×C4×C73—42no—
60C2×C4×C73C22⋊C411yescharacteristic
61C2×C4×C73C22⋊C411yescharacteristic
62C2×C4×C73C22×C411yescharacteristic
63C22⋊D73—42no—
64C22⋊D73—41no—
65C22⋊D73—41no—
66C22⋊D73—42no—
67C2×Dic73—21no—
68C2×Dic73C22⋊C411yescharacteristic
69C2×Dic73C22⋊C411yescharacteristic
70C2×Dic73C2×D411yescharacteristic
71D292—41no—
72D292—41no—
73D292—41no—
74C4×D73—41no—
75C4×D73—41no—
76C4×D73—42no—
77C4×D73D812yes—
78C4×D73SD1612yes—
79Dic146—42no—
80#10596833—42no—
81C22×C73—41no—
82C22×C73—41no—
83C22×C73—41no—
84C22×C73C2×C22⋊C411yescharacteristic
85C2×D73—21no—
86C2×D73—21no—
87C2×D73—41no—
88C2×D73—41no—
89C2×D73—41no—
90C2×D73C2×D811yescharacteristic
91C2×D73C2×SD1611yescharacteristic
92#64408—82no—
93C4×C73—21no—
94C4×C73—21no—
95C4×C73—41no—
96C4×C73#10212yes—
97Dic73—21no—
98Dic73—21no—
99Dic73—41no—
100Dic73#10212yes—
101C2×C73—81no—
102C2×C73#41011yescharacteristic
103C2×C73C2×#10211yescharacteristic
104C2×C73#42111yescharacteristic
105D73—21no—
106D73—21no—
107D73—81no—
108#1517—731nomaximal, Sylow
109C73#151711yescharacteristic, complemented, Sylow
110#532—731no—
111#431—731no—
112#382—731no—
113#327—732no—
114#327—732no—
115C2×#41—1461no—
116C4⋊Q8—731no—
117#127—731no—
118#124—1461no—
119#121—731no—
120#121—731no—
121#121—1461no—
122C4×D4—731no—
123C4×D4—1461no—
124C4×D4#6440811yescharacteristic, complemented
125C2×C4⋊C4—1461no—
126C2×C42—731no—
127C4⋊C8—1461no—
128C22⋊C8—732no—
129C4×C8—1461no—
130#95—732no—
131#95—1461no—
132#41—2922no—
133#41—2922no—
134C2×Q8—1461no—
135C2×D4—731no—
136C2×D4—1461no—
137C2×D4—1461no—
138C2×D4—1461no—
139C2×D4—1461no—
140C2×D4C2×#6440811yescharacteristic
141C22×C4—21no—
142C22×C4—731no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—1462no—
146C22×C4—1461no—
147C2×C8—1462no—
148C4⋊C4—2922no—
149C4⋊C4—731no—
150C4⋊C4—1461no—
151C4⋊C4C2×#6440811yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—1461no—
154C22⋊C4—1461no—
155C22⋊C4—1461no—
156C42—731no—
157C42—731no—
158C42—731no—
159C42C2×#6440811yescharacteristic
160C23—21no—
161C23—731no—
162C23—1461no—
163Q8—2922no—
164D4—41no—
165D4—2921no—
166D4—2921no—
167D4—2921no—
168D4—2921no—
169D4—2921no—
170D4—2922no—
171D4—2922no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—2921no—
175C2×C4—2921no—
176C2×C4—2922no—
177C2×C4—2922no—
178C2×C4—2922no—
179C2×C4—2922no—
180C2×C4—731no—
181C2×C4—732no—
182C2×C4—732no—
183C2×C4—731no—
184C2×C4—731no—
185C2×C4—1461no—
186C2×C4C22⋊#6440811yescharacteristic
187C2×C4C22⋊#6440811yescharacteristic
188C2×C4C22×#6440811yescharacteristic
189C8—2922no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—2921no—
194C22—2921no—
195C22—2921no—
196C22—731no—
197C22—731no—
198C22—1461no—
199C22—1461no—
200C22C2×C22⋊#6440811yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—2921no—
205C4—5842no—
206C4—732no—
207C4—1461no—
208C4—1461no—
209C4#1455665312yes—
210C2—81no—
211C2—5841no—
212C2—1461no—
213C2—1461no—
214C2#1798956611yescharacteristic
215C2C2×#1455665311yescharacteristic
216C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×D4#64408
hypocenterC73#1517
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #17989606C2semidirect
2. #17989531C2semidirect
3. #17989439C2semidirect
4. #17989438C2semidirect
13. #14556590C4semidirect
14. #14556587C4semidirect
19. C4×D292C4semidirect
22. C4×D4×C73C4semidirect
109. C73#1517semidirect
124. C4×D4#64408semidirect