Finite Group Databasebeta

← #22625340

Subgroups — #22625340

Order 9344.

274 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 58 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
2#17989530C211yesmaximal, characteristic
3#17989441C212yesmaximal, complemented
4#17989440C212yesmaximal, complemented
5C22⋊Q8×D73C211yesmaximal, characteristic
6C2×#11924038—21no—
7C2×C22⋊#64408—21no—
8#14556648C2212yes—
9C22⋊#10596833—21no—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4C2212yes—
12C2×Q8×D73C411yescharacteristic, complemented
13C22×C4×D73C2211yescharacteristic
14#14556571C2211yescharacteristic
15#14556570C411yescharacteristic, complemented
16#14556569—21no—
17#14556568—21no—
18#14556567C2211yescharacteristic
19C4⋊C4×D73—21no—
20C4⋊C4×D73C411yescharacteristic, complemented
21C22⋊C4×D73—21no—
22C22⋊Q8×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24#11924038—42no—
25C2×#10596833—22no—
26C22⋊#64408—42no—
27C23×D73D411yescharacteristic
28C2×Dic146—21no—
29C2×Dic146C2×C411yescharacteristic
30Q8×D73—42no—
31C22×Dic73D411yescharacteristic
32C2×C4×D73—21no—
33C2×C4×D73—21no—
34C2×C4×D73—42no—
35C2×C4×D73C2×C411yescharacteristic
36C2×C4×D73D411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73C2311yescharacteristic
39C4⋊Dic73—21no—
40C4⋊Dic73C2×C411yescharacteristic
41#11924007—21no—
42#11924007—21no—
43#11924007—21no—
44C22⋊Dic73—21no—
45#11924005—21no—
46#11924005—21no—
47C2×Q8×C73C2×C411yescharacteristic
48C22×C4×C73C2×C411yescharacteristic
49C4⋊C4×C73—21no—
50C4⋊C4×C73C2×C411yescharacteristic
51C22⋊C4×C73—21no—
52C23×C73C22⋊C411yescharacteristic
53C22×D73—22no—
54C22×D73—22no—
55C22×D73—41no—
56C22×D73C22⋊C411yescharacteristic
57C22×D73C2×D411yescharacteristic
58C2×#64408—42no—
59C2×#64408—42no—
60C2×#64408—42no—
61Q8×C73—41no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—41no—
65C2×C4×C73C22⋊C411yescharacteristic
66C2×C4×C73C22×C411yescharacteristic
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73—41no—
70C2×Dic73C22⋊C411yescharacteristic
71C2×Dic73C2×D411yescharacteristic
72C4×D73—22no—
73C4×D73—22no—
74C4×D73—41no—
75C4×D73—41no—
76C4×D73—42no—
77C4×D73—42no—
78Dic146—42no—
79Dic146—41no—
80#10596833—42no—
81C22×C73—21no—
82C22×C73—21no—
83C22×C73—21no—
84C22×C73C2×C22⋊C411yescharacteristic
85C2×D73—21no—
86C2×D73—21no—
87C2×D73—21no—
88C2×D73—21no—
89C2×D73—44no—
90C2×D73#9912yes—
91C2×D73#13712yes—
92#64408—82no—
93C4×C73—21no—
94C4×C73—21no—
95C4×C73—41no—
96C4×C73—41no—
97Dic73—21no—
98Dic73—21no—
99Dic73—41no—
100Dic73—41no—
101C2×C73—41no—
102C2×C73C2×#9911yescharacteristic
103C2×C73#41911yescharacteristic
104C2×C73#42111yescharacteristic
105D73—22no—
106D73—22no—
107#1511—731nomaximal, Sylow
108C73#151111yescharacteristic, complemented, Sylow
109C2×C22⋊Q8—731no—
110#407—731no—
111#381—731no—
112#328—732no—
113#328—732no—
114C22×Q8—731no—
115C23×C4—731no—
116C2×M16—1461no—
117C22⋊Q8—731no—
118C22⋊Q8—731no—
119C22⋊Q8—731no—
120C22⋊Q8—1461no—
121C22⋊Q8—1461no—
122C22⋊Q8#6440811yescharacteristic, complemented
123C2×C4⋊C4—731no—
124C2×C4⋊C4—1461no—
125C2×C22⋊C4—1461no—
126C2×C22⋊C4—1461no—
127C22⋊C8—732no—
128C22⋊C8—1461no—
129#95—732no—
130#95—1461no—
131C24—731no—
132C2×Q8—2922no—
133C2×Q8—731no—
134C2×Q8—1461no—
135C2×Q8C2×#6440811yescharacteristic
136C22×C4—2922no—
137C22×C4—731no—
138C22×C4—731no—
139C22×C4—731no—
140C22×C4—731no—
141C22×C4—731no—
142C22×C4—1461no—
143C22×C4—1461no—
144C22×C4—1462no—
145C22×C4C2×#6440811yescharacteristic
146M16—2922no—
147C2×C8—1462no—
148C4⋊C4—21no—
149C4⋊C4—731no—
150C4⋊C4—1461no—
151C4⋊C4—1461no—
152C4⋊C4—1461no—
153C4⋊C4—1461no—
154C4⋊C4C2×#6440811yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—2922no—
157C22⋊C4—1461no—
158C22⋊C4—1461no—
159C22⋊C4—1461no—
160C23—2921no—
161C23—731no—
162C23—731no—
163C23—1462no—
164C23—1462no—
165C23C22⋊#6440811yescharacteristic
166Q8—41no—
167Q8—2921no—
168Q8—2922no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—2921no—
173C2×C4—2921no—
174C2×C4—2922no—
175C2×C4—2922no—
176C2×C4—2922no—
177C2×C4—2922no—
178C2×C4—2922no—
179C2×C4—2921no—
180C2×C4—731no—
181C2×C4—731no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4—1461no—
185C2×C4—1461no—
186C2×C4C22⋊#6440811yescharacteristic
187C2×C4C22×#6440811yescharacteristic
188C8—2922no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—2924no—
193C22—732no—
194C22—732no—
195C22—1461no—
196C22—1461no—
197C22—1461no—
198C22—1461no—
199C22C2×C22⋊#6440811yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4—2921no—
205C4—2921no—
206C4—5842no—
207C4—1461no—
208C4—1461no—
209C2—41no—
210C2—1462no—
211C2—1462no—
212C2D73⋊#9911yescharacteristic
213C2#1798958011yescharacteristic
214C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22⋊Q8#64408
hypocenterC73#1511
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #17989441C2semidirect
4. #17989440C2semidirect
12. C2×Q8×D73C4semidirect
15. #14556570C4semidirect
20. C4⋊C4×D73C4semidirect
22. C22⋊Q8×C73C4semidirect
108. C73#1511semidirect
122. C22⋊Q8#64408semidirect