Finite Group Databasebeta

← #22625310

Subgroups — #22625310

Order 9344.

284 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 68 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#17989605C211yesmaximal, characteristic, complemented
2C4×C4⋊#64408C211yesmaximal, characteristic, complemented
3#17989439C212yesmaximal, complemented
4#17989438C212yesmaximal, complemented
5#17989134C211yesmaximal, characteristic
6C2×C4⋊#64408—21no—
7C2×C4×#64408—21no—
8#14556658—21no—
9#14556648C2212yes—
10C4×#10596833—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—24no—
26C4×#64408—42no—
27#11924028—42no—
28#11924028—42no—
29C2×Dic146—21no—
30C2×D292—21no—
31C2×D292C2×C411yescharacteristic
32C2×C22⋊D73—21no—
33C2×C22⋊D73—21no—
34C2×C22⋊D73—21no—
35C2×C4×D73—21no—
36C2×C4×D73D411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73C2311yescharacteristic
39C4⋊Dic73C2×C411yescharacteristic
40#11924007—21no—
41C22⋊Dic73—21no—
42#11924005—21no—
43#11924005—21no—
44C4×Dic73C2×C411yescharacteristic
45C4×Dic73D411yescharacteristic
46C4×Dic73D411yescharacteristic
47C2×D4×C73C2×C411yescharacteristic
48C22×C4×C73—21no—
49C4⋊C4×C73C2×C411yescharacteristic
50C22⋊C4×C73—21no—
51C42×C73C2×C411yescharacteristic
52C23×C73—21no—
53C22×D73—21no—
54C22×D73C2×D411yescharacteristic
55C2×#64408—24no—
56C2×#64408—42no—
57C2×#64408—42no—
58D4×C73—41no—
59C2×C4×C73—21no—
60C2×C4×C73—42no—
61C2×C4×C73C22⋊C411yescharacteristic
62C2×C4×C73C22⋊C411yescharacteristic
63C2×C4×C73C22×C411yescharacteristic
64C22⋊D73—41no—
65C22⋊D73—41no—
66C22⋊D73—42no—
67C22⋊D73—42no—
68C2×Dic73—21no—
69C2×Dic73C22⋊C411yescharacteristic
70C2×Dic73C22⋊C411yescharacteristic
71C2×Dic73C2×D411yescharacteristic
72D292—41no—
73D292—41no—
74D292—41no—
75C4×D73—22no—
76C4×D73—41no—
77C4×D73—42no—
78C4×D73D812yes—
79C4×D73SD1612yes—
80Dic146—42no—
81#10596833—42no—
82C22×C73—41no—
83C22×C73—41no—
84C22×C73—41no—
85C22×C73C2×C22⋊C411yescharacteristic
86C2×D73—21no—
87C2×D73—21no—
88C2×D73—41no—
89C2×D73—41no—
90C2×D73—41no—
91C2×D73C2×D811yescharacteristic
92C2×D73C2×SD1611yescharacteristic
93#64408—44no—
94C4×C73—21no—
95C4×C73—21no—
96C4×C73—41no—
97C4×C73#10212yes—
98Dic73—21no—
99Dic73—41no—
100Dic73#10212yes—
101Dic73#10412yes—
102C2×C73—81no—
103C2×C73#41011yescharacteristic
104C2×C73C2×#10211yescharacteristic
105C2×C73C2×#10411yescharacteristic
106D73—21no—
107D73—21no—
108D73—81no—
109#1502—731nomaximal, Sylow
110C73#150211yescharacteristic, complemented, Sylow
111#532—731no—
112#431—731no—
113C4×C4⋊C4—731no—
114#327—732no—
115#327—732no—
116C2×#41—1461no—
117C4⋊Q8—731no—
118#127—731no—
119#124—1461no—
120#121—731no—
121#121—731no—
122#121—1461no—
123C4×D4—731no—
124C4×D4—1461no—
125C4×D4#6440811yescharacteristic, complemented
126C2×C4⋊C4—1461no—
127C2×C42—731no—
128C2×C42—1461no—
129C4⋊C8—1461no—
130C22⋊C8—732no—
131C4×C8—1461no—
132#95—732no—
133#41—2922no—
134#41—2922no—
135C2×Q8—1461no—
136C2×D4—731no—
137C2×D4—1461no—
138C2×D4—1461no—
139C2×D4—1461no—
140C2×D4—1461no—
141C2×D4C2×#6440811yescharacteristic
142C22×C4—21no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—731no—
146C22×C4—1462no—
147C22×C4—1461no—
148C2×C8—1462no—
149C4⋊C4—731no—
150C4⋊C4—1461no—
151C4⋊C4—1464no—
152C4⋊C4C2×#6440811yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—1461no—
155C22⋊C4—1461no—
156C22⋊C4—1461no—
157C42—2922no—
158C42—731no—
159C42—731no—
160C42—731no—
161C42C2×#6440811yescharacteristic
162C23—21no—
163C23—731no—
164C23—1461no—
165Q8—2922no—
166D4—41no—
167D4—2921no—
168D4—2921no—
169D4—2921no—
170D4—2921no—
171D4—2921no—
172D4—2922no—
173D4—2922no—
174C2×C4—21no—
175C2×C4—42no—
176C2×C4—2921no—
177C2×C4—2922no—
178C2×C4—2922no—
179C2×C4—2922no—
180C2×C4—731no—
181C2×C4—731no—
182C2×C4—732no—
183C2×C4—732no—
184C2×C4—731no—
185C2×C4—1462no—
186C2×C4—1464no—
187C2×C4—1461no—
188C2×C4C22⋊#6440811yescharacteristic
189C2×C4C22⋊#6440811yescharacteristic
190C2×C4C22×#6440811yescharacteristic
191C8—2922no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—2921no—
196C22—2921no—
197C22—2921no—
198C22—731no—
199C22—731no—
200C22—1461no—
201C22—1461no—
202C22C2×C22⋊#6440811yescharacteristic
203C4—21no—
204C4—21no—
205C4—41no—
206C4—2924no—
207C4—2921no—
208C4—732no—
209C4—732no—
210C4—1461no—
211C4#1455665312yes—
212C2—81no—
213C2—5841no—
214C2—1461no—
215C2—1461no—
216C2#1798956611yescharacteristic
217C2C2×#1455665311yescharacteristic
218C2D73⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×D4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×D4#64408
hypocenterC73#1502
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #17989605C2semidirect
2. C4×C4⋊#64408C2semidirect
3. #17989439C2semidirect
4. #17989438C2semidirect
13. #14556590C4semidirect
14. #14556587C4semidirect
19. C4×D292C4semidirect
22. C4×D4×C73C4semidirect
110. C73#1502semidirect
125. C4×D4#64408semidirect