Finite Group Databasebeta

← #22608484

Subgroups — #22608484

Order 9344.

284 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 63 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
1#17989097C211yesmaximal, characteristic
2C22⋊C8×D73C211yesmaximal, characteristic, complemented
3#17988449C211yesmaximal, characteristic, complemented
4#17988325C211yesmaximal, characteristic, complemented
5#17988323C211yesmaximal, characteristic, complemented
6#17988321C211yesmaximal, characteristic, complemented
7#327×C73C211yesmaximal, characteristic, complemented
8C2×#11924027C411yescharacteristic, complemented
9C22×C4×D73C2211yescharacteristic
10C2×C8×D73—21no—
11#14556573—21no—
12#14556571C411yescharacteristic, complemented
13#14556570C2211yescharacteristic
14#14556562C411yescharacteristic, complemented
15#14556559—21no—
16D4×Dic73—21no—
17#14556551—21no—
18#14556549C411yescharacteristic, complemented
19C2×#11924005—21no—
20C22⋊#10596831C2211yescharacteristic
21#14556503—21no—
22#14556498—21no—
23#14556498C2211yescharacteristic
24#121×C73C2211yescharacteristic
25C22⋊C8×C73C2211yescharacteristic
26#95×C73C2211yescharacteristic
27C23×D73D411yescharacteristic
28#11924027—42no—
29C2×Dic146C2×C411yescharacteristic
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C22×Dic73—21no—
33C22×Dic73—21no—
34C22×Dic73D411yescharacteristic
35C2×C4×D73—42no—
36C2×C4×D73C2×C411yescharacteristic
37C2×C4×D73C2×C411yescharacteristic
38C2×C4×D73D411yescharacteristic
39C2×C4×D73D411yescharacteristic
40C2×#10596831—21no—
41C8×D73—42no—
42C4⋊Dic73—21no—
43C4⋊Dic73C2×C411yescharacteristic
44#11924007—21no—
45C22⋊Dic73—21no—
46C22⋊Dic73—21no—
47#11924005—21no—
48#11924005—21no—
49#11924005—42no—
50C4×Dic73—21no—
51C2×D4×C73—21no—
52C2×D4×C73C2×C411yescharacteristic
53C22×C4×C73—21no—
54C22×C4×C73C2311yescharacteristic
55C2×C8×C73—21no—
56C4⋊C4×C73C2×C411yescharacteristic
57C22⋊C4×C73—21no—
58C23×C73—21no—
59C23×C73C2×D411yescharacteristic
60C22×D73—21no—
61C22×D73—21no—
62C22×D73—22no—
63C22×D73—41no—
64C22×D73C22⋊C411yescharacteristic
65C22×D73C22⋊C411yescharacteristic
66D4×C73—41no—
67D4×C73—41no—
68D4×C73—41no—
69C2×C4×C73—21no—
70C2×C4×C73—41no—
71C2×C4×C73—41no—
72C2×C4×C73—41no—
73C2×C4×C73—41no—
74C2×C4×C73C22×C411yescharacteristic
75C2×C4×C73C2×D411yescharacteristic
76C22⋊D73—42no—
77C22⋊D73—42no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—41no—
81C2×Dic73—42no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84C2×Dic73—41no—
85C2×Dic73C22⋊C411yescharacteristic
86C2×Dic73C22⋊C411yescharacteristic
87C4×D73—22no—
88C4×D73—22no—
89C4×D73—41no—
90C4×D73—41no—
91Dic146—41no—
92C8×C73—41no—
93#10596831—41no—
94C22×C73—21no—
95C22×C73—21no—
96C22×C73—41no—
97C22×C73—41no—
98C22×C73—41no—
99C22×C73C2×C22⋊C411yescharacteristic
100C22×C73#13511yescharacteristic
101C22×C73#13511yescharacteristic
102C2×D73—21no—
103C2×D73—21no—
104C2×D73—21no—
105C2×D73—21no—
106C2×D73—21no—
107C2×D73—42no—
108C2×D73—42no—
109C2×D73#9912yes—
110C4×C73—21no—
111C4×C73—21no—
112C4×C73—41no—
113C4×C73—81no—
114Dic73—21no—
115Dic73—21no—
116Dic73—41no—
117Dic73—41no—
118Dic73—81no—
119C2×C73—21no—
120C2×C73—21no—
121C2×C73—81no—
122C2×C73C2×#9911yescharacteristic
123C2×C73#41611yescharacteristic
124C2×C73#42111yescharacteristic
125D73—22no—
126D73—41no—
127#1516—731nomaximal, Sylow
128C73#151611yescharacteristic, complemented, Sylow
129#525—731no—
130C2×C22⋊C8—731no—
131#381—731no—
132#328—731no—
133#328—731no—
134#327—731no—
135#327D7311yescharacteristic, complemented
136C2×#41—731no—
137C23×C4—731no—
138C22×C8—1461no—
139#123—1461no—
140C22⋊Q8—731no—
141C22⋊Q8—731no—
142#121—731no—
143#121C2×D7311yescharacteristic
144#120—1461no—
145C4×D4—1461no—
146C4×D4—1461no—
147#117—731no—
148C2×C22⋊C4—1461no—
149C22⋊C8—731no—
150C22⋊C8—1461no—
151C22⋊C8C2×D7311yescharacteristic
152#95—731no—
153#95—1461no—
154#95C2×D7311yescharacteristic
155C24—731no—
156#41—2922no—
157C2×Q8—731no—
158C2×D4—21no—
159C2×D4—1461no—
160C2×D4—1461no—
161C2×D4C4×D7311yescharacteristic
162C22×C4—21no—
163C22×C4—2922no—
164C22×C4—731no—
165C22×C4—731no—
166C22×C4—731no—
167C22×C4—731no—
168C22×C4—731no—
169C22×C4—1461no—
170C22×C4—1461no—
171C22×C4C22×D7311yescharacteristic
172C2×C8—21no—
173C2×C8—2922no—
174C2×C8—1461no—
175C4⋊C4—731no—
176C4⋊C4—1461no—
177C4⋊C4—1461no—
178C4⋊C4C4×D7311yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—2922no—
181C22⋊C4—1461no—
182C22⋊C4—1461no—
183C22⋊C4—1461no—
184C22⋊C4—1461no—
185C42—1461no—
186C23—21no—
187C23—2921no—
188C23—731no—
189C23—731no—
190C23—1462no—
191C23—1461no—
192C23—1461no—
193C23D4×D7311yescharacteristic
194Q8—2921no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—2922no—
199D4—2922no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—2921no—
206C2×C4—2921no—
207C2×C4—2922no—
208C2×C4—2921no—
209C2×C4—2921no—
210C2×C4—2921no—
211C2×C4—2921no—
212C2×C4—731no—
213C2×C4—731no—
214C2×C4—1462no—
215C2×C4—1462no—
216C2×C4—1461no—
217C2×C4—1461no—
218C2×C4C2×C4×D7311yescharacteristic
219C2×C4D4×D7311yescharacteristic
220C8—41no—
221C8—2921no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—2922no—
228C22—2922no—
229C22—732no—
230C22—1461no—
231C22—1461no—
232C22—1461no—
233C22—1461no—
234C22—1461no—
235C22C22⋊C4×D7311yescharacteristic
236C22#1455661011yescharacteristic
237C22#1455661211yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—2921no—
243C4—2921no—
244C4—5841no—
245C4—1461no—
246C4—1461no—
247C2—21no—
248C2—21no—
249C2—81no—
250C2—2921no—
251C2—1462no—
252C2#99×D7311yescharacteristic
253C2#1798858011yescharacteristic
254C2#1798860211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#327×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#327D73
hypocenterC73#1516
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D73C2semidirect
3. #17988449C2semidirect
4. #17988325C2semidirect
5. #17988323C2semidirect
6. #17988321C2semidirect
7. #327×C73C2semidirect
8. C2×#11924027C4semidirect
12. #14556571C4semidirect
14. #14556562C4semidirect
18. #14556549C4semidirect
128. C73#1516semidirect
135. #327D73semidirect