Finite Group Databasebeta

← #22611249

Subgroups — #22611249

Order 9344.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11924017C211yesmaximal, characteristic
2C2×#14556516C211yesmaximal, characteristic, complemented
3C2×#14556513C211yesmaximal, characteristic
4#17988493C211yesmaximal, characteristic, complemented
5#17988489C211yesmaximal, characteristic
6#17988350C211yesmaximal, characteristic, complemented
7C2×C4⋊C8×C73C211yesmaximal, characteristic, complemented
8C22×Dic146C2211yescharacteristic
9C22×D292C2211yescharacteristic
10C2×#11924017—22no—
11C2×#11924017—22no—
12C2×#11924017—22no—
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924005—21no—
16C2×#11924005—21no—
17#14556516—22no—
18#14556513—22no—
19#14556498—21no—
20#14556498—21no—
21C22×C8×C73C2211yescharacteristic
22C22×C8×C73C2211yescharacteristic
23C2×C42×C73C2211yescharacteristic
24C4⋊C8×C73—22no—
25C23×D73—21no—
26C2×Dic146—21no—
27C2×Dic146—21no—
28C2×Dic146—21no—
29C2×Dic146—21no—
30C2×Dic146—21no—
31C2×Dic146D412yes—
32C2×D292—21no—
33C2×D292—21no—
34C2×D292—21no—
35C2×D292—21no—
36C2×D292—21no—
37C2×D292D412yes—
38C22×Dic73—21no—
39C22×Dic73—21no—
40C22×Dic73—21no—
41#11924017—28no—
42C4⋊Dic73—21no—
43C4⋊Dic73—21no—
44C4⋊Dic73—21no—
45C4⋊Dic73—21no—
46#11924005—42no—
47#11924005—42no—
48C22×C4×C73D411yescharacteristic
49C22×C4×C73D411yescharacteristic
50C22×C4×C73C2311yescharacteristic
51C2×C8×C73—21no—
52C2×C8×C73—21no—
53C2×C8×C73—21no—
54C2×C8×C73—21no—
55C2×C8×C73—21no—
56C2×C8×C73D412yes—
57C42×C73—21no—
58C42×C73—21no—
59C23×C73C2×D411yescharacteristic
60C22×D73—22no—
61C22×D73—41no—
62C22×D73—41no—
63C22×D73—41no—
64C22×D73—41no—
65C22×D73—41no—
66C22×D73—41no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73SD1612yescomplemented
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73#4111yescharacteristic
77C2×C4×C73#4111yescharacteristic
78C2×C4×C73#4111yescharacteristic
79C2×Dic73—22no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84C2×Dic73—41no—
85C2×Dic73—41no—
86C2×Dic73—41no—
87C2×Dic73—41no—
88D292—22no—
89D292—22no—
90D292—41no—
91D292—41no—
92Dic146—22no—
93Dic146—22no—
94Dic146—41no—
95Dic146—41no—
96C8×C73—22no—
97C8×C73—41no—
98C22×C73#12111yescharacteristic
99C22×C73#12111yescharacteristic
100C22×C73#12111yescharacteristic
101C22×C73C2×SD1611yescharacteristic
102C22×C73#13511yescharacteristic
103C22×C73AGL(1,ℤ/8)11yescharacteristic
104C22×C73#13711yescharacteristic
105C2×D73—42no—
106C2×D73—42no—
107C2×D73—42no—
108C2×D73—81no—
109C2×D73—81no—
110C2×D73—81no—
111C2×D73—81no—
112C4×C73—22no—
113C4×C73—41no—
114C4×C73#12011yescharacteristic
115C4×C73#12311yescharacteristic
116C4×C73#12311yescharacteristic
117C4×C73#12411yescharacteristic
118Dic73—42no—
119Dic73—81no—
120Dic73—81no—
121C2×C73#39411yescharacteristic
122C2×C73#46011yescharacteristic
123C2×C73#46111yescharacteristic
124C2×C73#46311yescharacteristic
125C2×C73#46411yescharacteristic
126C2×C73#46511yescharacteristic
127C2×C73#46811yescharacteristic
128D73—82no—
129#2055—731nomaximal, Sylow
130C73#205511yescharacteristic, complemented, Sylow
131C22×SD16—731no—
132C2×C4⋊C8D7311yescharacteristic, complemented
133C2×#103—731no—
134C2×#102—731no—
135#391—731no—
136#390—731no—
137#340—731no—
138C22×Q8—731no—
139C22×D4—731no—
140C2×SD16—1462no—
141C2×SD16—1462no—
142C2×SD16—1462no—
143C22×C8C2×D7311yescharacteristic
144C22×C8C2×D7311yescharacteristic
145C2×C4⋊C4—731no—
146C2×C4⋊C4—731no—
147C2×C22⋊C4—1461no—
148C2×C22⋊C4—1461no—
149C2×C42C2×D7311yescharacteristic
150C4⋊C8—22no—
151#103—1462no—
152#102—1462no—
153#95—1461no—
154#95—1461no—
155C24—1461no—
156C2×Q8—732no—
157C2×Q8—1461no—
158C2×Q8—1461no—
159C2×Q8—1461no—
160C2×Q8—1461no—
161C2×Q8—1461no—
162C2×D4—732no—
163C2×D4—1461no—
164C2×D4—1461no—
165C2×D4—1461no—
166C2×D4—1461no—
167C2×D4—1461no—
168C22×C4—1461no—
169C22×C4—1461no—
170C22×C4—1461no—
171C22×C4D29211yescharacteristic
172C22×C4D29211yescharacteristic
173C22×C4C22×D7311yescharacteristic
174SD16—1468no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8C22⋊D7312yes—
181C4⋊C4—1461no—
182C4⋊C4—1461no—
183C4⋊C4—1461no—
184C4⋊C4—1461no—
185C22⋊C4—2922no—
186C22⋊C4—2922no—
187C42—21no—
188C42—21no—
189C23—2921no—
190C23—2921no—
191C23—2921no—
192C23—2921no—
193C23—2921no—
194C23—2921no—
195C23—1462no—
196C23C2×D29211yescharacteristic
197Q8—2921no—
198Q8—2921no—
199Q8—1462no—
200Q8—1462no—
201D4—2921no—
202D4—2921no—
203D4—1462no—
204D4—1462no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—2921no—
211C2×C4—2921no—
212C2×C4—2921no—
213C2×C4—2921no—
214C2×C4—2921no—
215C2×C4—2921no—
216C2×C4—2921no—
217C2×C4—2921no—
218C2×C4—1462no—
219C2×C4#1192401712yescomplemented
220C2×C4D4×D7311yescharacteristic
221C2×C4D4×D7311yescharacteristic
222C2×C4C2×C22⋊D7311yescharacteristic
223C2×C4#1192402811yescharacteristic
224C2×C4#1192402911yescharacteristic
225C2×C4#1192402911yescharacteristic
226C8—22no—
227C8—41no—
228C22—2922no—
229C22—2922no—
230C22—2922no—
231C22—5841no—
232C22—5841no—
233C22—5841no—
234C22—5841no—
235C22#1455656511yescharacteristic
236C22#1455656611yescharacteristic
237C22#1455656611yescharacteristic
238C22C2×#1192401711yescharacteristic
239C22#1455661311yescharacteristic
240C22#1455661911yescharacteristic
241C22#1455662411yescharacteristic
242C4—22no—
243C4—41no—
244C4—2922no—
245C4—5841no—
246C4—5841no—
247C4#1455655911yescharacteristic
248C4#1455657611yescharacteristic
249C4#1455657611yescharacteristic
250C4#1455658011yescharacteristic
251C2—5842no—
252C2#1798850411yescharacteristic
253C2#1798878811yescharacteristic
254C2#1798879311yescharacteristic
255C2#1798880311yescharacteristic
256C2#1798881011yescharacteristic
257C2#1798881611yescharacteristic
258C2#1798883311yescharacteristic
subgroupG/H
centerC23C2×D292
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×C4⋊C8×C73C2
socleC23×C73C2×D4
hypercenterC2×C4⋊C8D73
hypocenterC73#2055
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14556516C2semidirect
4. #17988493C2semidirect
6. #17988350C2semidirect
7. C2×C4⋊C8×C73C2semidirect
72. C2×C4×C73SD16semidirect
130. C73#2055semidirect
132. C2×C4⋊C8D73semidirect
219. C2×C4#11924017semidirect