Finite Group Databasebeta

← #22619399

Subgroups — #22619399

Order 9344.

484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14556621C212yesmaximal, complemented
2C2×C4×Dic146C211yesmaximal, characteristic, complemented
3#17988806C214yesmaximal, complemented
4#17988794C212yesmaximal, complemented
5#17988784C212yesmaximal, complemented
6#17988611C211yesmaximal, characteristic, complemented
7#17988588C212yesmaximal, complemented
8#532×C73C211yesmaximal, characteristic
9C22×Dic146C2211yescharacteristic
10#14556621—28no—
11C2×#11924018C2214yes—
12C2×#11924016C2214yes—
13C2×#11924012C2212yes—
14C4×Dic146—21no—
15C4×Dic146—21no—
16C4×Dic146C2212yes—
17C4×Dic146C2212yes—
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007—21no—
20C2×C4×Dic73—21no—
21C4⋊#10596831C2212yes—
22C4⋊#10596831C2212yes—
23#14556515C2214yes—
24#14556512C2214yes—
25C2×#41×C73C2212yes—
26C4⋊Q8×C73C2211yescharacteristic
27#127×C73C2211yescharacteristic
28#124×C73C2212yes—
29#121×C73—21no—
30#121×C73—21no—
31C4×D4×C73—21no—
32C4×D4×C73—21no—
33C2×C42×C73C2211yescharacteristic
34C2×Dic146—21no—
35C2×Dic146—22no—
36C2×Dic146D414yescomplemented
37C2×Dic146C2312yes—
38C22×Dic73—21no—
39C22×Dic73—21no—
40#11924018—28no—
41#11924016—28no—
42#11924012—24no—
43C2×#10596831C2314yes—
44C4⋊Dic73—21no—
45C4⋊Dic73C2312yes—
46#11924007—22no—
47#11924007—22no—
48C4×Dic73—22no—
49C4×Dic73—22no—
50#41×C73—24no—
51#41×C73—24no—
52C2×Q8×C73C2312yes—
53C2×D4×C73—22no—
54C2×D4×C73—21no—
55C2×D4×C73—21no—
56C2×D4×C73C2312yes—
57C22×C4×C73—22no—
58C22×C4×C73D411yescharacteristic
59C22×C4×C73D411yescharacteristic
60C22×C4×C73C2311yescharacteristic
61C4⋊C4×C73—21no—
62C4⋊C4×C73—21no—
63C22⋊C4×C73—22no—
64C22⋊C4×C73—22no—
65C42×C73D411yescharacteristic
66C42×C73D411yescharacteristic
67C42×C73C2311yescharacteristic
68C42×C73C2311yescharacteristic
69C23×C73—22no—
70C23×C73C2×D411yescharacteristic
71Q8×C73—22no—
72Q8×C73—22no—
73D4×C73—22no—
74D4×C73—22no—
75D4×C73—42no—
76D4×C73—44no—
77D4×C73—42no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—41no—
81C2×C4×C73—44no—
82C2×C4×C73C2×D412yes—
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73#4112yes—
89C2×C4×C73C2411yescharacteristic
90C2×Dic73—24no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—42no—
94Dic146—24no—
95Dic146—22no—
96Dic146C2×D414yes—
97#10596831—24no—
98C22×C73—21no—
99C22×C73—21no—
100C22×C73—42no—
101C22×C73—42no—
102C22×C73—42no—
103C22×C73#12112yes—
104C22×C73C22×D411yescharacteristic
105C4×C73—21no—
106C4×C73—21no—
107C4×C73—21no—
108C4×C73—42no—
109C4×C73#12112yes—
110C4×C73#13712yescomplemented
111C4×C73C22×D411yescharacteristic
112C4×C73C2×#4111yescharacteristic
113Dic73—24no—
114Dic73—42no—
115C2×C73—22no—
116C2×C73—82no—
117C2×C73C2×#12111yescharacteristic
118C2×C73C2×#13711yescharacteristic
119C2×C73#57511yescharacteristic
120#3037—731nomaximal, Sylow
121C73#303711yescharacteristic, complemented, Sylow
122C2×#137—732no—
123#532D7311yescharacteristic
124C2×C4×Q8—731no—
125#464—734no—
126#462—732no—
127#460—732no—
128#423—731no—
129#417—732no—
130C2×#41C2×D7312yes—
131C22×Q8—731no—
132#137—1468no—
133C2×Q16—734no—
134C2×SD16—734no—
135C2×M16—732no—
136C4⋊Q8C2×D7311yescharacteristic
137#127C2×D7311yescharacteristic
138#124C2×D7312yes—
139#121—21no—
140#121—21no—
141C4×Q8—732no—
142C4×Q8—732no—
143C4×Q8—1461no—
144C4×Q8—1461no—
145C4×D4—21no—
146C4×D4—21no—
147C2×C4⋊C4—731no—
148C2×C4⋊C4—1461no—
149C2×C42—1461no—
150C2×C42C2×D7311yescharacteristic
151C4⋊C8—732no—
152C4⋊C8—732no—
153#103—734no—
154#102—734no—
155#41—24no—
156#41—24no—
157C2×Q8—734no—
158C2×Q8—732no—
159C2×Q8—1461no—
160C2×Q8—1462no—
161C2×Q8C22×D7312yes—
162C2×D4—22no—
163C2×D4—21no—
164C2×D4—21no—
165C2×D4C22×D7312yes—
166C22×C4—22no—
167C22×C4—1461no—
168C22×C4—1461no—
169C22×C4C22⋊D7311yescharacteristic
170C22×C4C22⋊D7311yescharacteristic
171C22×C4C22×D7311yescharacteristic
172Q16—1468no—
173SD16—1468no—
174M16—1464no—
175C2×C8—734no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—732no—
179C4⋊C4—1462no—
180C4⋊C4—1462no—
181C4⋊C4—1461no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C42—1462no—
185C42—1462no—
186C42C22⋊D7311yescharacteristic
187C42C22⋊D7311yescharacteristic
188C42C22×D7311yescharacteristic
189C42C22×D7311yescharacteristic
190C23—22no—
191C23C2×C22⋊D7311yescharacteristic
192Q8—22no—
193Q8—22no—
194Q8—734no—
195Q8—1464no—
196Q8—1462no—
197D4—22no—
198D4—22no—
199D4—42no—
200D4—44no—
201D4—42no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—44no—
206C2×C4—2922no—
207C2×C4—1462no—
208C2×C4—1464no—
209C2×C4—1462no—
210C2×C4D4×D7312yes—
211C2×C4C2×C22⋊D7311yescharacteristic
212C2×C4C2×C22⋊D7311yescharacteristic
213C2×C4C2×C22⋊D7311yescharacteristic
214C2×C4C2×C22⋊D7311yescharacteristic
215C2×C4C2×C22⋊D7311yescharacteristic
216C2×C4#1192402712yes—
217C2×C4C23×D7311yescharacteristic
218C8—1464no—
219C22—21no—
220C22—21no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22#1455656212yes—
225C22C22×C22⋊D7311yescharacteristic
226C4—21no—
227C4—21no—
228C4—21no—
229C4—42no—
230C4—2922no—
231C4—1464no—
232C4#1455656212yes—
233C4#1455662112yescomplemented
234C4C2×D4×D7311yescharacteristic
235C4C2×#1192402711yescharacteristic
236C2—22no—
237C2—82no—
238C2C2×#1455656211yescharacteristic
239C2C2×#1455662111yescharacteristic
240C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#532×C73C2
socleC22×C73C22×D4
hypercenter#532D73
hypocenterC73#3037
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. C2×#14556621C2semidirect
2. C2×C4×Dic146C2semidirect
3. #17988806C2semidirect
4. #17988794C2semidirect
5. #17988784C2semidirect
6. #17988611C2semidirect
7. #17988588C2semidirect
36. C2×Dic146D4semidirect
110. C4×C73#137semidirect
121. C73#3037semidirect
233. C4#14556621semidirect