Finite Group Databasebeta

← #22625951

Subgroups — #22625951

Order 9344.

358 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 70 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×#14556670C211yesmaximal, characteristic, complemented
2C2×#14556655C212yesmaximal, complemented
3#17989558C211yesmaximal, characteristic, complemented
4#17989457C212yesmaximal, complemented
5#17989097C211yesmaximal, characteristic
6C2×#11924038C2212yes—
7#14556670—24no—
8C2×C4⋊#64408—21no—
9C2×C22⋊#64408—21no—
10C2×C4×#64408C2212yes—
11#14556655—24no—
12#14556648—21no—
13C22⋊#10596833—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—22no—
27#11924038—22no—
28C2×#10596833—22no—
29C4⋊#64408—24no—
30C22⋊#64408—24no—
31C4×#64408—22no—
32C4×#64408D414yescomplemented
33C23×D73D411yescharacteristic
34#11924027—22no—
35#11924027—22no—
36C2×Dic146C2×C411yescharacteristic
37C2×C22⋊D73—21no—
38C2×C22⋊D73—21no—
39C22×Dic73—21no—
40C22×Dic73D411yescharacteristic
41C2×C4×D73—22no—
42C2×C4×D73—22no—
43C2×C4×D73C2×C411yescharacteristic
44C2×C4×D73D411yescharacteristic
45C2×C4×D73D411yescharacteristic
46C2×C4×D73C2311yescharacteristic
47C4⋊Dic73—21no—
48C4⋊Dic73C2×C411yescharacteristic
49#11924007—21no—
50C22⋊Dic73—21no—
51C22⋊Dic73—21no—
52#11924005—21no—
53#11924005—21no—
54C4×Dic73—21no—
55C2×D4×C73—21no—
56C2×D4×C73C2×C411yescharacteristic
57C22×C4×C73C2×C411yescharacteristic
58C4⋊C4×C73C2×C411yescharacteristic
59C22⋊C4×C73—21no—
60C23×C73—21no—
61C23×C73C22⋊C411yescharacteristic
62C22×D73—21no—
63C22×D73—21no—
64C22×D73—41no—
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—41no—
79C22⋊D73—41no—
80C2×Dic73—22no—
81C2×Dic73—21no—
82C2×Dic73—21no—
83C2×Dic73—42no—
84C2×Dic73C22⋊C411yescharacteristic
85C2×Dic73C2×D411yescharacteristic
86C4×D73—21no—
87C4×D73—21no—
88C4×D73—22no—
89C4×D73—22no—
90C4×D73C2×D412yes—
91C4×D73#4112yes—
92Dic146—22no—
93#10596833—42no—
94C22×C73—21no—
95C22×C73—21no—
96C22×C73—21no—
97C22×C73—41no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73C2×C22⋊C411yescharacteristic
101C2×D73—21no—
102C2×D73—21no—
103C2×D73—21no—
104C2×D73—21no—
105C2×D73—21no—
106C2×D73—42no—
107C2×D73—42no—
108C2×D73#12011yescharacteristic
109C2×D73#12311yescharacteristic
110#64408—44no—
111C4×C73—21no—
112C4×C73—41no—
113C4×C73C4×D412yes—
114Dic73—21no—
115Dic73—41no—
116Dic73—41no—
117Dic73#12112yes—
118C2×C73—41no—
119C2×C73—81no—
120C2×C73#38611yescharacteristic
121C2×C73#42111yescharacteristic
122C2×C73#42111yescharacteristic
123D73—21no—
124D73—21no—
125D73—41no—
126#1897—731nomaximal, Sylow
127C73#189711yescharacteristic, complemented, Sylow
128#525—731no—
129C2×#117—731no—
130C2×#104—732no—
131#407—731no—
132#339—732no—
133C2×#41—731no—
134C23×C4—731no—
135C2×M16—732no—
136#123—1461no—
137C22⋊Q8—731no—
138C22⋊Q8—731no—
139#121—731no—
140#121#6440811yescharacteristic, complemented
141#120—1461no—
142C4×D4—1461no—
143C4×D4—1461no—
144#117—731no—
145#117—1464no—
146C2×C4⋊C4—1461no—
147C2×C22⋊C4—1461no—
148C2×C42—732no—
149#104—1464no—
150C22⋊C8—1461no—
151C22⋊C8—1461no—
152C24—731no—
153#41—1462no—
154#41—1462no—
155C2×Q8—731no—
156C2×D4—21no—
157C2×D4—1461no—
158C2×D4—1461no—
159C2×D4C2×#6440811yescharacteristic
160C22×C4—731no—
161C22×C4—731no—
162C22×C4—731no—
163C22×C4—731no—
164C22×C4—731no—
165C22×C4—1462no—
166C22×C4—1462no—
167C22×C4—1461no—
168C22×C4—1462no—
169C22×C4C2×#6440811yescharacteristic
170M16—1462no—
171M16—1462no—
172C2×C8—1462no—
173C4⋊C4—731no—
174C4⋊C4—1461no—
175C4⋊C4—1464no—
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—734no—
185C42—1461no—
186C42—1462no—
187C23—21no—
188C23—2921no—
189C23—2921no—
190C23—731no—
191C23—731no—
192C23—1461no—
193C23—1461no—
194C23C22⋊#6440811yescharacteristic
195Q8—1462no—
196D4—22no—
197D4—42no—
198D4—2921no—
199D4—2921no—
200D4—2922no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—2922no—
204C2×C4—2922no—
205C2×C4—2922no—
206C2×C4—731no—
207C2×C4—732no—
208C2×C4—732no—
209C2×C4—731no—
210C2×C4—1462no—
211C2×C4—1461no—
212C2×C4—1461no—
213C2×C4—1464no—
214C2×C4—1461no—
215C2×C4—1461no—
216C2×C4—1462no—
217C2×C4—1462no—
218C2×C4C22⋊#6440811yescharacteristic
219C2×C4C22×#6440811yescharacteristic
220C8—2922no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—2922no—
228C22—2922no—
229C22—731no—
230C22—731no—
231C22—1461no—
232C22—1461no—
233C22—1461no—
234C22—1461no—
235C22—1461no—
236C22C2×C22⋊#6440811yescharacteristic
237C4—21no—
238C4—41no—
239C4—2924no—
240C4—2921no—
241C4—2921no—
242C4—732no—
243C4—1461no—
244C4D4×#6440812yes—
245C2—41no—
246C2—81no—
247C2—2921no—
248C2—1461no—
249C2—1461no—
250C2#1798953511yescharacteristic
251C2#1798958411yescharacteristic
252C2#1798958511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#121×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#121#64408
hypocenterC73#1897
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. C2×#14556670C2semidirect
2. C2×#14556655C2semidirect
3. #17989558C2semidirect
4. #17989457C2semidirect
17. #14556571C4semidirect
18. #14556570C4semidirect
19. #14556562C4semidirect
24. #121×C73C4semidirect
32. C4×#64408D4semidirect
127. C73#1897semidirect
140. #121#64408semidirect