Finite Group Databasebeta

← #22610231

Subgroups — #22610231

Order 9344.

376 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 93 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×#11924012C211yesmaximal, characteristic, complemented
2#17989098C211yesmaximal, characteristic
3C2×#14556519C212yesmaximal, complemented
4#17988347C212yesmaximal, complemented
5C4×C22⋊C4×C73C211yesmaximal, characteristic, complemented
6C2×#11924028C2211yescharacteristic
7C2×#11924012—24no—
8C2×#11924012—21no—
9C2×#11924012C2212yes—
10C22×#10596831—21no—
11#14556574—21no—
12#14556570C411yescharacteristic, complemented
13#14556570C411yescharacteristic, complemented
14#14556565C411yescharacteristic, complemented
15#14556565C411yescharacteristic, complemented
16#14556560—21no—
17C4×C22⋊D73—21no—
18C4×C22⋊D73—21no—
19#14556550C2211yescharacteristic
20#14556519—24no—
21C23×C4×C73C2211yescharacteristic
22C2×C22⋊C4×C73—21no—
23C2×C42×C73C2212yes—
24#95×C73—21no—
25#11924028—22no—
26#11924028—22no—
27C2×Dic146C2×C411yescharacteristic
28C2×D292C2×C411yescharacteristic
29C2×C22⋊D73—21no—
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C2×C4×D73—21no—
33#11924012—24no—
34#11924012—22no—
35#11924012D414yescomplemented
36C2×#10596831—24no—
37C2×#10596831—22no—
38C4⋊Dic73C2×C411yescharacteristic
39C4⋊Dic73C2×C411yescharacteristic
40#11924007—21no—
41#11924007—21no—
42C22⋊Dic73—21no—
43C22⋊Dic73—21no—
44C22⋊Dic73—21no—
45#11924005—21no—
46#11924005—21no—
47C4×Dic73—21no—
48C24×C73D411yescharacteristic
49C22×C4×C73—22no—
50C22×C4×C73—22no—
51C22×C4×C73—22no—
52C22×C4×C73C2×C411yescharacteristic
53C22×C4×C73C2×C411yescharacteristic
54C22×C4×C73D411yescharacteristic
55C22×C4×C73D411yescharacteristic
56C22×C4×C73D411yescharacteristic
57C22×C4×C73C2311yescharacteristic
58C22⋊C4×C73—24no—
59C42×C73—22no—
60C42×C73—22no—
61C23×C73—22no—
62C23×C73—22no—
63C23×C73—41no—
64C23×C73C22⋊C411yescharacteristic
65C23×C73C22⋊C411yescharacteristic
66C23×C73C2×D411yescharacteristic
67C22×D73—21no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—21no—
75C2×C4×C73—24no—
76C2×C4×C73—42no—
77C2×C4×C73—42no—
78C2×C4×C73C22⋊C411yescharacteristic
79C2×C4×C73C22⋊C411yescharacteristic
80C2×C4×C73C22×C411yescharacteristic
81C2×C4×C73C2×D412yes—
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73#4112yes—
84C22⋊D73—42no—
85C22⋊D73—42no—
86C22⋊D73—42no—
87C2×Dic73—21no—
88C2×Dic73—21no—
89C2×Dic73—21no—
90D292—22no—
91C4×D73—41no—
92C4×D73—41no—
93Dic146—22no—
94#10596831—24no—
95C22×C73—21no—
96C22×C73—21no—
97C22×C73—21no—
98C22×C73—21no—
99C22×C73—21no—
100C22×C73—21no—
101C22×C73—21no—
102C22×C73—44no—
103C22×C73#10412yescomplemented
104C22×C73C2×C22⋊C411yescharacteristic
105C22×C73#12112yes—
106C2×D73—41no—
107C2×D73—41no—
108C2×D73—41no—
109C4×C73—21no—
110C4×C73—21no—
111C4×C73—44no—
112C4×C73C4×D412yes—
113C4×C73#12011yescharacteristic
114C4×C73#12311yescharacteristic
115Dic73—41no—
116Dic73—41no—
117Dic73—41no—
118C2×C73—22no—
119C2×C73—22no—
120C2×C73—41no—
121C2×C73#38611yescharacteristic
122C2×C73C2×#10411yescharacteristic
123C2×C73#42111yescharacteristic
124D73—81no—
125#1871—731nomaximal, Sylow
126C73#187111yescharacteristic, complemented, Sylow
127C22×M16—731no—
128#525—731no—
129C2×#104—732no—
130C4×C22⋊C4D7311yescharacteristic, complemented
131#339—732no—
132C2×#41—731no—
133C23×C4C2×D7311yescharacteristic
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—731no—
143#120—1461no—
144C4×D4—1461no—
145C4×D4—1461no—
146#117—731no—
147C2×C22⋊C4—21no—
148C2×C42C2×D7312yes—
149#104—1464no—
150#95—21no—
151C24C22⋊D7311yescharacteristic
152#41—1462no—
153#41—1462no—
154C2×Q8—731no—
155C2×D4—731no—
156C2×D4—1461no—
157C2×D4—1461no—
158C2×D4—1461no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—1461no—
163C22×C4C4×D7311yescharacteristic
164C22×C4C4×D7311yescharacteristic
165C22×C4D29211yescharacteristic
166C22×C4D29211yescharacteristic
167C22×C4C22⋊D7311yescharacteristic
168C22×C4C22×D7311yescharacteristic
169M16—734no—
170M16—1464no—
171M16—1462no—
172C2×C8—1464no—
173C2×C8—1462no—
174C4⋊C4—731no—
175C4⋊C4—731no—
176C4⋊C4—1461no—
177C4⋊C4—1461no—
178C22⋊C4—24no—
179C22⋊C4—1461no—
180C22⋊C4—1461no—
181C22⋊C4—1461no—
182C22⋊C4—1461no—
183C22⋊C4—1461no—
184C42—22no—
185C42—22no—
186C42—1461no—
187C23—22no—
188C23—22no—
189C23—41no—
190C23—1461no—
191C23#1192400511yescharacteristic
192C23#1192400511yescharacteristic
193C23C2×C22⋊D7311yescharacteristic
194Q8—1462no—
195D4—2922no—
196D4—2922no—
197D4—2922no—
198D4—1462no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—24no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—2921no—
210C2×C4—2921no—
211C2×C4—1461no—
212C2×C4—1461no—
213C2×C4—1461no—
214C2×C4#1192400511yescharacteristic
215C2×C4#1192400511yescharacteristic
216C2×C4C2×C4×D7311yescharacteristic
217C2×C4D4×D7312yes—
218C2×C4C2×D29211yescharacteristic
219C2×C4#1192402712yes—
220C8—1464no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—44no—
229C22—2921no—
230C22—2921no—
231C22—2921no—
232C22#1455651912yescomplemented
233C22C2×#1192400511yescharacteristic
234C22#1455656312yes—
235C4—21no—
236C4—21no—
237C4—44no—
238C4—2921no—
239C4—2921no—
240C4—2921no—
241C4#1455655112yes—
242C4#1455656111yescharacteristic
243C4#1455657511yescharacteristic
244C2—22no—
245C2—22no—
246C2—41no—
247C2—5841no—
248C2#1798846411yescharacteristic
249C2C2×#1455651911yescharacteristic
250C2#1798860511yescharacteristic
subgroupG/H
centerC2×C4C2×D292
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC4×C22⋊C4×C73C2
socleC22×C73C2×C22⋊C4
hypercenterC4×C22⋊C4D73
hypocenterC73#1871
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#11924012C2semidirect
3. C2×#14556519C2semidirect
4. #17988347C2semidirect
5. C4×C22⋊C4×C73C2semidirect
12. #14556570C4semidirect
13. #14556570C4semidirect
14. #14556565C4semidirect
15. #14556565C4semidirect
35. #11924012D4semidirect
103. C22×C73#104semidirect
126. C73#1871semidirect
130. C4×C22⋊C4D73semidirect
232. C22#14556519semidirect