Finite Group Databasebeta

← #22625369

Subgroups — #22625369

Order 9344.

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

normal subgroups only

This group has 288 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
1C2×#14556648C211yesmaximal, characteristic
2#17989529C211yesmaximal, characteristic
3#17989441C212yesmaximal, complemented
4#17989440C212yesmaximal, complemented
5C22⋊Q8×D73C211yesmaximal, characteristic
6C22×#10596833—21no—
7C2×C4⋊#64408—21no—
8C2×C22⋊#64408—21no—
9#14556648—21no—
10#14556648C2212yes—
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—
24C2×#10596833—22no—
25C2×#10596833—42no—
26C4⋊#64408—42no—
27C22⋊#64408—42no—
28C23×D73D411yescharacteristic
29C2×Dic146—21no—
30C2×Dic146C2×C411yescharacteristic
31Q8×D73—42no—
32C22×Dic73D411yescharacteristic
33C2×C4×D73—21no—
34C2×C4×D73—21no—
35C2×C4×D73—42no—
36C2×C4×D73C2×C411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73D411yescharacteristic
39C2×C4×D73C2311yescharacteristic
40C4⋊Dic73—21no—
41C4⋊Dic73C2×C411yescharacteristic
42#11924007—21no—
43#11924007—21no—
44#11924007—21no—
45C22⋊Dic73—21no—
46#11924005—21no—
47#11924005—21no—
48C2×Q8×C73C2×C411yescharacteristic
49C22×C4×C73C2×C411yescharacteristic
50C4⋊C4×C73—21no—
51C4⋊C4×C73C2×C411yescharacteristic
52C22⋊C4×C73—21no—
53C23×C73C22⋊C411yescharacteristic
54C22×D73—41no—
55C22×D73—41no—
56C22×D73C22⋊C411yescharacteristic
57C22×D73SD1612yes—
58C22×D73Q1612yes—
59C22×D73C2×D411yescharacteristic
60C2×#64408—42no—
61C2×#64408—42no—
62C2×#64408—42no—
63Q8×C73—41no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—41no—
67C2×C4×C73C22⋊C411yescharacteristic
68C2×C4×C73C22×C411yescharacteristic
69C2×Dic73—22no—
70C2×Dic73—21no—
71C2×Dic73—21no—
72C2×Dic73C22⋊C411yescharacteristic
73C2×Dic73C2×D411yescharacteristic
74C4×D73—22no—
75C4×D73—22no—
76C4×D73—41no—
77C4×D73—41no—
78C4×D73—42no—
79C4×D73—42no—
80Dic146—42no—
81Dic146—41no—
82#10596833—42no—
83C22×C73—21no—
84C22×C73—21no—
85C22×C73#10312yes—
86C22×C73C2×C22⋊C411yescharacteristic
87C2×D73—21no—
88C2×D73—21no—
89C2×D73—21no—
90C2×D73—21no—
91C2×D73—42no—
92C2×D73—42no—
93C2×D73#10312yes—
94C2×D73C2×SD1611yescharacteristic
95C2×D73C2×Q1611yescharacteristic
96#64408—82no—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73—41no—
100C4×C73—41no—
101Dic73—21no—
102Dic73—41no—
103Dic73—41no—
104Dic73#9912yes—
105C2×C73—22no—
106C2×C73C2×#9911yescharacteristic
107C2×C73C2×#10311yescharacteristic
108C2×C73#42111yescharacteristic
109D73—21no—
110D73—22no—
111D73—21no—
112#1520—731nomaximal, Sylow
113C73#152011yescharacteristic, complemented, Sylow
114C2×C22⋊Q8—731no—
115C2×C22⋊C8—731no—
116#380—731no—
117#328—732no—
118#328—732no—
119C22×Q8—731no—
120C23×C4—731no—
121C22×C8—1461no—
122C22⋊Q8—731no—
123C22⋊Q8—731no—
124C22⋊Q8—731no—
125C22⋊Q8—1461no—
126C22⋊Q8—1461no—
127C22⋊Q8#6440811yescharacteristic, complemented
128C2×C4⋊C4—731no—
129C2×C4⋊C4—1461no—
130C2×C4⋊C4—1461no—
131C2×C22⋊C4—1461no—
132C2×C22⋊C4—1461no—
133C22⋊C8—732no—
134C22⋊C8—1461no—
135#95—732no—
136C24—731no—
137C2×Q8—2922no—
138C2×Q8—731no—
139C2×Q8—1461no—
140C2×Q8C2×#6440811yescharacteristic
141C22×C4—2922no—
142C22×C4—731no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—731no—
146C22×C4—731no—
147C22×C4—1461no—
148C22×C4—1461no—
149C22×C4—1462no—
150C22×C4C2×#6440811yescharacteristic
151C2×C8—2922no—
152C2×C8—1462no—
153C4⋊C4—21no—
154C4⋊C4—2922no—
155C4⋊C4—731no—
156C4⋊C4—1461no—
157C4⋊C4—1461no—
158C4⋊C4—1461no—
159C4⋊C4—1461no—
160C4⋊C4C2×#6440811yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—2922no—
163C22⋊C4—1461no—
164C22⋊C4—1461no—
165C22⋊C4—1461no—
166C23—2921no—
167C23—2921no—
168C23—732no—
169C23—732no—
170C23—731no—
171C23—731no—
172C23C22⋊#6440811yescharacteristic
173Q8—41no—
174Q8—2921no—
175Q8—2922no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—2921no—
180C2×C4—2921no—
181C2×C4—2922no—
182C2×C4—2922no—
183C2×C4—2922no—
184C2×C4—2922no—
185C2×C4—2922no—
186C2×C4—731no—
187C2×C4—731no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4—1461no—
191C2×C4—1461no—
192C2×C4—1462no—
193C2×C4C22⋊#6440811yescharacteristic
194C2×C4C22×#6440811yescharacteristic
195C8—2922no—
196C22—21no—
197C22—21no—
198C22—2922no—
199C22—2922no—
200C22—731no—
201C22—732no—
202C22—731no—
203C22—1461no—
204C22—1461no—
205C22—1461no—
206C22—1461no—
207C22#1455665412yes—
208C22C2×C22⋊#6440811yescharacteristic
209C4—21no—
210C4—21no—
211C4—41no—
212C4—41no—
213C4—2921no—
214C4—2921no—
215C4—5842no—
216C4—732no—
217C4—1461no—
218C2—22no—
219C2—1461no—
220C2—1462no—
221C2—1461no—
222C2D73⋊#9911yescharacteristic
223C2C2×#1455665411yescharacteristic
224C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22⋊Q8#64408
hypocenterC73#1520
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
113. C73#1520semidirect
127. C22⋊Q8#64408semidirect