Finite Group Databasebeta

← #22625954

Subgroups — #22625954

Order 9344.

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

normal subgroups only

This group has 378 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×#14556649C212yesmaximal
3#17989530C211yesmaximal, characteristic, complemented
4#17989465C212yesmaximal, complemented
5C2×#14556573C211yesmaximal, characteristic
6#14556670—24no—
7C2×C4⋊#64408—21no—
8C2×C22⋊#64408C2212yes—
9C2×C22⋊#64408C2212yes—
10C2×C4×#64408—21no—
11#14556649—24no—
12(C2×#64408)⋊C4—21no—
13(C2×#64408)⋊C4—21no—
14C22×C22⋊D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556573—21no—
17#14556573—21no—
18#14556573—21no—
19#14556573—21no—
20C2×C4⋊Dic73C411yescharacteristic, complemented
21C2×#11924007C411yescharacteristic, complemented
22C2×C22⋊Dic73C411yescharacteristic, complemented
23C2×#11924005C2211yescharacteristic
24C2×C22⋊C4×C73C411yescharacteristic, complemented
25C22×#64408—22no—
26C22×#64408—22no—
27C4⋊#64408—24no—
28C22⋊#64408—22no—
29C22⋊#64408—22no—
30C22⋊#64408—22no—
31C22⋊#64408D414yes—
32C4×#64408—24no—
33C23×D73C2311yescharacteristic
34C2×C22⋊D73—21no—
35C2×C22⋊D73—21no—
36C2×C22⋊D73—22no—
37C2×C22⋊D73—22no—
38C22×Dic73C2×C411yescharacteristic
39C22×Dic73C2×C411yescharacteristic
40C22×Dic73C2×C411yescharacteristic
41C2×C4×D73—22no—
42C2×C4×D73—22no—
43C2×C4×D73D411yescharacteristic
44C2×C4×D73D411yescharacteristic
45C2×C4×D73D411yescharacteristic
46C2×C4×D73D411yescharacteristic
47C4⋊Dic73—21no—
48C4⋊Dic73—21no—
49#11924007—21no—
50#11924007—21no—
51C22⋊Dic73—21no—
52C22⋊Dic73—21no—
53#11924005—21no—
54#11924005—21no—
55C24×C73C2×C411yescharacteristic
56C22×C4×C73C2×C411yescharacteristic
57C22×C4×C73C2×C411yescharacteristic
58C22⋊C4×C73—21no—
59C22⋊C4×C73—21no—
60C23×C73—21no—
61C23×C73—22no—
62C23×C73—41no—
63C23×C73—41no—
64C23×C73C22×C411yescharacteristic
65C22×D73—41no—
66C22×D73—41no—
67C22×D73C2×D411yescharacteristic
68C22×D73C2×D411yescharacteristic
69C22×D73C2×D412yes—
70C22×D73#4112yes—
71C2×#64408—24no—
72C2×#64408—42no—
73C2×#64408—42no—
74C2×#64408—42no—
75C2×#64408—42no—
76C2×#64408—42no—
77C2×C4×C73—22no—
78C2×C4×C73—21no—
79C2×C4×C73—41no—
80C2×C4×C73C22⋊C411yescharacteristic
81C2×C4×C73C22⋊C411yescharacteristic
82C22⋊D73—41no—
83C22⋊D73—42no—
84C22⋊D73—41no—
85C2×Dic73—22no—
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—41no—
90C2×Dic73C22⋊C411yescharacteristic
91C2×Dic73C22⋊C411yescharacteristic
92C4×D73—21no—
93C4×D73—21no—
94C4×D73—22no—
95C4×D73—22no—
96C4×D73—21no—
97C4×D73—21no—
98C22×C73—21no—
99C22×C73—21no—
100C22×C73—41no—
101C22×C73—41no—
102C22×C73—41no—
103C22×C73—82no—
104C22×C73C2×C22⋊C411yescharacteristic
105C22×C73C4×D412yes—
106C2×D73—21no—
107C2×D73—21no—
108C2×D73—21no—
109C2×D73—21no—
110C2×D73—42no—
111C2×D73—42no—
112C2×D73#12011yescharacteristic
113C2×D73#12112yes—
114C2×D73#12311yescharacteristic
115#64408—44no—
116#64408—82no—
117C4×C73—21no—
118C4×C73—21no—
119C4×C73—41no—
120Dic73—21no—
121Dic73—21no—
122Dic73—41no—
123Dic73—41no—
124C2×C73—22no—
125C2×C73—81no—
126C2×C73#38611yescharacteristic
127C2×C73#41011yescharacteristic
128C2×C73#41011yescharacteristic
129D73—21no—
130D73—22no—
131D73—21no—
132#1899—731nomaximal, Sylow
133C73#189911yescharacteristic, complemented, Sylow
134C2×#123—731no—
135C2×#117—731no—
136C2×#99—732no—
137#381—731no—
138#342—732no—
139C22×D4—731no—
140C23×C4—731no—
141#123—1461no—
142#123—1461no—
143#123—1461no—
144#123—1461no—
145#117—1464no—
146C2×C4⋊C4—731no—
147C2×C4⋊C4—731no—
148C2×C4⋊C4—1461no—
149C2×C22⋊C4—732no—
150C2×C22⋊C4—731no—
151C2×C22⋊C4—731no—
152C2×C22⋊C4—732no—
153C2×C22⋊C4#6440811yescharacteristic, complemented
154C2×C42—1461no—
155#99—1464no—
156#95—1461no—
157#95—1461no—
158C24—731no—
159C24C2×#6440811yescharacteristic
160C2×D4—1462no—
161C2×D4—1461no—
162C2×D4—1461no—
163C2×D4—1462no—
164C22×C4—731no—
165C22×C4—731no—
166C22×C4—731no—
167C22×C4—731no—
168C22×C4—731no—
169C22×C4—731no—
170C22×C4—731no—
171C22×C4—1462no—
172C22×C4—1462no—
173C22×C4—1462no—
174C22×C4—1462no—
175C22×C4C2×#6440811yescharacteristic
176C22×C4C2×#6440811yescharacteristic
177C4⋊C4—1461no—
178C4⋊C4—1461no—
179C4⋊C4—1464no—
180C4⋊C4—1461no—
181C4⋊C4—1461no—
182C22⋊C4—21no—
183C22⋊C4—21no—
184C22⋊C4—734no—
185C22⋊C4—1461no—
186C22⋊C4—1461no—
187C22⋊C4—1462no—
188C22⋊C4—1462no—
189C22⋊C4—1461no—
190C22⋊C4—1461no—
191C22⋊C4—1462no—
192C42—1464no—
193C23—21no—
194C23—22no—
195C23—41no—
196C23—41no—
197C23—2921no—
198C23—2921no—
199C23—732no—
200C23—732no—
201C23—731no—
202C23—731no—
203C23C22×#6440811yescharacteristic
204D4—2922no—
205D4—2921no—
206D4—2921no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—2922no—
211C2×C4—2922no—
212C2×C4—2921no—
213C2×C4—2922no—
214C2×C4—2922no—
215C2×C4—2922no—
216C2×C4—731no—
217C2×C4—731no—
218C2×C4—1461no—
219C2×C4—1461no—
220C2×C4—1462no—
221C2×C4—1462no—
222C2×C4—1461no—
223C2×C4—1461no—
224C2×C4—1464no—
225C2×C4—1461no—
226C2×C4—1461no—
227C2×C4—1462no—
228C2×C4—1462no—
229C2×C4C22⋊#6440811yescharacteristic
230C2×C4C22⋊#6440811yescharacteristic
231C22—21no—
232C22—21no—
233C22—41no—
234C22—41no—
235C22—41no—
236C22—82no—
237C22—2922no—
238C22—2922no—
239C22—732no—
240C22—731no—
241C22—731no—
242C22—1461no—
243C22—1461no—
244C22—1461no—
245C22—1461no—
246C22C2×C22⋊#6440811yescharacteristic
247C22D4×#6440812yes—
248C4—21no—
249C4—21no—
250C4—41no—
251C4—2924no—
252C4—2921no—
253C4—2921no—
254C4—5842no—
255C4—1461no—
256C4—1461no—
257C2—22no—
258C2—81no—
259C2—1461no—
260C2—1462no—
261C2—1461no—
262C2#1798953511yescharacteristic
263C2#1798956611yescharacteristic
264C2#1798956711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C22⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C22⋊C4#64408
hypocenterC73#1899
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14556670C2semidirect
3. #17989530C2semidirect
4. #17989465C2semidirect
20. C2×C4⋊Dic73C4semidirect
21. C2×#11924007C4semidirect
22. C2×C22⋊Dic73C4semidirect
24. C2×C22⋊C4×C73C4semidirect
133. C73#1899semidirect
153. C2×C22⋊C4#64408semidirect