Finite Group Databasebeta

← #22625914

Subgroups — #22625914

Order 9344.

376 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C22×#11924038C211yesmaximal, characteristic, complemented
2C2×#14556655C212yesmaximal, complemented
3C4×C22⋊#64408C211yesmaximal, characteristic, complemented
4#17989457C212yesmaximal, complemented
5#17989097C211yesmaximal, characteristic
6C2×#11924038—24no—
7C2×#11924038—21no—
8C2×#11924038C2212yes—
9C22×#10596833—21no—
10C2×C22⋊#64408—21no—
11C2×C4×#64408C2212yes—
12#14556655—24no—
13(C2×#64408)⋊C4—21no—
14C2×#11924027C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556573—21no—
17#14556571C411yescharacteristic, complemented
18#14556570C411yescharacteristic, complemented
19#14556562C411yescharacteristic, complemented
20#14556559—21no—
21D4×Dic73—21no—
22#14556551—21no—
23#14556549C2211yescharacteristic
24#121×C73C411yescharacteristic, complemented
25C22×#64408—22no—
26#11924038—24no—
27#11924038—22no—
28#11924038D414yescomplemented
29C2×#10596833—24no—
30C2×#10596833—22no—
31C22⋊#64408—24no—
32C4×#64408—22no—
33C4×#64408—22no—
34C23×D73D411yescharacteristic
35#11924027—22no—
36#11924027—22no—
37C2×Dic146C2×C411yescharacteristic
38C2×C22⋊D73—21no—
39C2×C22⋊D73—21no—
40C22×Dic73—21no—
41C22×Dic73D411yescharacteristic
42C2×C4×D73—22no—
43C2×C4×D73—22no—
44C2×C4×D73C2×C411yescharacteristic
45C2×C4×D73D411yescharacteristic
46C2×C4×D73D411yescharacteristic
47C2×C4×D73C2311yescharacteristic
48C4⋊Dic73—21no—
49C4⋊Dic73C2×C411yescharacteristic
50#11924007—21no—
51C22⋊Dic73—21no—
52C22⋊Dic73—21no—
53#11924005—21no—
54#11924005—21no—
55C4×Dic73—21no—
56C2×D4×C73—21no—
57C2×D4×C73C2×C411yescharacteristic
58C22×C4×C73C2×C411yescharacteristic
59C4⋊C4×C73C2×C411yescharacteristic
60C22⋊C4×C73—21no—
61C23×C73—21no—
62C23×C73C22⋊C411yescharacteristic
63C22×D73—22no—
64C22×D73—22no—
65C22×D73—41no—
66C22×D73C22⋊C411yescharacteristic
67C22×D73C2×D411yescharacteristic
68C2×#64408—24no—
69C2×#64408—42no—
70C2×#64408—42no—
71D4×C73—22no—
72D4×C73—42no—
73C2×C4×C73—22no—
74C2×C4×C73—21no—
75C2×C4×C73C22⋊C411yescharacteristic
76C2×C4×C73C22×C411yescharacteristic
77C22⋊D73—42no—
78C22⋊D73—42no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—21no—
82C2×Dic73—21no—
83C2×Dic73—41no—
84C2×Dic73—41no—
85C2×Dic73C22⋊C411yescharacteristic
86C2×Dic73C2×D411yescharacteristic
87C4×D73—22no—
88C4×D73—22no—
89C4×D73—21no—
90C4×D73—21no—
91C4×D73C2×D412yes—
92C4×D73#4112yes—
93Dic146—22no—
94#10596833—24no—
95C22×C73—21no—
96C22×C73—21no—
97C22×C73—41no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73#10412yescomplemented
101C22×C73C2×C22⋊C411yescharacteristic
102C2×D73—21no—
103C2×D73—21no—
104C2×D73—21no—
105C2×D73—21no—
106C2×D73—21no—
107C2×D73—44no—
108C2×D73#12112yes—
109#64408—44no—
110C4×C73—21no—
111C4×C73—41no—
112C4×C73C4×D412yes—
113Dic73—21no—
114Dic73—41no—
115Dic73—41no—
116Dic73#12011yescharacteristic
117Dic73#12311yescharacteristic
118C2×C73—22no—
119C2×C73—81no—
120C2×C73#38611yescharacteristic
121C2×C73C2×#10411yescharacteristic
122C2×C73#42111yescharacteristic
123D73—22no—
124D73—41no—
125#1871—731nomaximal, Sylow
126C73#187111yescharacteristic, complemented, Sylow
127C22×M16—731no—
128#525—731no—
129C2×#104—732no—
130C4×C22⋊C4—731no—
131#339—732no—
132C2×#41—731no—
133C23×C4—731no—
134C2×M16—732no—
135C2×M16—1464no—
136C2×M16—1461no—
137C22×C8—1461no—
138#123—1461no—
139C22⋊Q8—731no—
140C22⋊Q8—731no—
141#121—731no—
142#121#6440811yescharacteristic, complemented
143#120—1461no—
144C4×D4—1461no—
145C4×D4—1461no—
146#117—731no—
147C2×C22⋊C4—1461no—
148C2×C42—732no—
149#104—1464no—
150#95—1461no—
151C24—731no—
152#41—1462no—
153#41—1462no—
154C2×Q8—731no—
155C2×D4—21no—
156C2×D4—1461no—
157C2×D4—1461no—
158C2×D4C2×#6440811yescharacteristic
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—731no—
163C22×C4—731no—
164C22×C4—1462no—
165C22×C4—1462no—
166C22×C4—1461no—
167C22×C4—1462no—
168C22×C4C2×#6440811yescharacteristic
169M16—734no—
170M16—1462no—
171M16—1464no—
172C2×C8—1462no—
173C2×C8—1464no—
174C4⋊C4—731no—
175C4⋊C4—1461no—
176C4⋊C4—1461no—
177C4⋊C4C2×#6440811yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—1461no—
180C22⋊C4—1461no—
181C22⋊C4—1461no—
182C22⋊C4—1464no—
183C22⋊C4—1461no—
184C42—1461no—
185C42—1462no—
186C42—1462no—
187C23—21no—
188C23—2921no—
189C23—731no—
190C23—731no—
191C23—1462no—
192C23—1462no—
193C23C22⋊#6440811yescharacteristic
194Q8—1462no—
195D4—22no—
196D4—42no—
197D4—2922no—
198D4—2922no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—2922no—
202C2×C4—2922no—
203C2×C4—2921no—
204C2×C4—2921no—
205C2×C4—731no—
206C2×C4—732no—
207C2×C4—732no—
208C2×C4—731no—
209C2×C4—1461no—
210C2×C4—1461no—
211C2×C4—1462no—
212C2×C4—1464no—
213C2×C4—1461no—
214C2×C4—1461no—
215C2×C4—1461no—
216C2×C4—1461no—
217C2×C4—1462no—
218C2×C4C22⋊#6440811yescharacteristic
219C2×C4C22×#6440811yescharacteristic
220C8—1464no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—2924no—
227C22—732no—
228C22—1461no—
229C22—1461no—
230C22—1461no—
231C22—1461no—
232C22—1461no—
233C22#1455665512yescomplemented
234C22C2×C22⋊#6440811yescharacteristic
235C4—21no—
236C4—41no—
237C4—2924no—
238C4—2921no—
239C4—2921no—
240C4—731no—
241C4—731no—
242C4—1461no—
243C4D4×#6440812yes—
244C2—22no—
245C2—81no—
246C2—2921no—
247C2—1462no—
248C2#1798953511yescharacteristic
249C2C2×#1455665511yescharacteristic
250C2#1798958411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#121×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#121#64408
hypocenterC73#1871
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C22×#11924038C2semidirect
2. C2×#14556655C2semidirect
3. C4×C22⋊#64408C2semidirect
4. #17989457C2semidirect
17. #14556571C4semidirect
18. #14556570C4semidirect
19. #14556562C4semidirect
24. #121×C73C4semidirect
28. #11924038D4semidirect
100. C22×C73#104semidirect
126. C73#1871semidirect
142. #121#64408semidirect
233. C22#14556655semidirect