Finite Group Databasebeta

← #22586893

Subgroups — #22586893

Order 9088.

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#17986509C211yesmaximal, characteristic
2C22⋊C8×D71C211yesmaximal, characteristic, complemented
3#17985861C211yesmaximal, characteristic, complemented
4#17985737C211yesmaximal, characteristic, complemented
5#17985735C211yesmaximal, characteristic, complemented
6#17985733C211yesmaximal, characteristic, complemented
7#327×C71C211yesmaximal, characteristic, complemented
8C2×#11765864C411yescharacteristic, complemented
9C22×C4×D71C2211yescharacteristic
10C2×C8×D71—21no—
11#14556110—21no—
12#14556108C411yescharacteristic, complemented
13#14556107C2211yescharacteristic
14#14556099C411yescharacteristic, complemented
15#14556096—21no—
16D4×Dic71—21no—
17(C22⋊D71)⋊C4—21no—
18#14556086C411yescharacteristic, complemented
19C2×(C2×D71)⋊C4—21no—
20C22⋊(C71⋊C8)C2211yescharacteristic
21(C2×D71)⋊C8—21no—
22C71⋊#95—21no—
23C71⋊#95C2211yescharacteristic
24#121×C71C2211yescharacteristic
25C22⋊C8×C71C2211yescharacteristic
26#95×C71C2211yescharacteristic
27C23×D71D411yescharacteristic
28#11765864—42no—
29C2×Dic142C2×C411yescharacteristic
30C2×C22⋊D71—21no—
31C2×C22⋊D71—21no—
32C22×Dic71—21no—
33C22×Dic71—21no—
34C22×Dic71D411yescharacteristic
35C2×C4×D71—42no—
36C2×C4×D71C2×C411yescharacteristic
37C2×C4×D71C2×C411yescharacteristic
38C2×C4×D71D411yescharacteristic
39C2×C4×D71D411yescharacteristic
40C2×C71⋊C8—21no—
41C8×D71—42no—
42C4⋊Dic71—21no—
43C4⋊Dic71C2×C411yescharacteristic
44Dic71⋊C4—21no—
45C22⋊Dic71—21no—
46C22⋊Dic71—21no—
47(C2×D71)⋊C4—21no—
48(C2×D71)⋊C4—21no—
49(C2×D71)⋊C4—42no—
50C4×Dic71—21no—
51C2×D4×C71—21no—
52C2×D4×C71C2×C411yescharacteristic
53C22×C4×C71—21no—
54C22×C4×C71C2311yescharacteristic
55C2×C8×C71—21no—
56C4⋊C4×C71C2×C411yescharacteristic
57C22⋊C4×C71—21no—
58C23×C71—21no—
59C23×C71C2×D411yescharacteristic
60C22×D71—21no—
61C22×D71—21no—
62C22×D71—22no—
63C22×D71—41no—
64C22×D71C22⋊C411yescharacteristic
65C22×D71C22⋊C411yescharacteristic
66D4×C71—41no—
67D4×C71—41no—
68D4×C71—41no—
69C2×C4×C71—21no—
70C2×C4×C71—41no—
71C2×C4×C71—41no—
72C2×C4×C71—41no—
73C2×C4×C71—41no—
74C2×C4×C71C22×C411yescharacteristic
75C2×C4×C71C2×D411yescharacteristic
76C22⋊D71—42no—
77C22⋊D71—42no—
78C2×Dic71—21no—
79C2×Dic71—21no—
80C2×Dic71—41no—
81C2×Dic71—42no—
82C2×Dic71—41no—
83C2×Dic71—41no—
84C2×Dic71—41no—
85C2×Dic71C22⋊C411yescharacteristic
86C2×Dic71C22⋊C411yescharacteristic
87C4×D71—22no—
88C4×D71—22no—
89C4×D71—41no—
90C4×D71—41no—
91Dic142—41no—
92C8×C71—41no—
93C71⋊C8—41no—
94C22×C71—21no—
95C22×C71—21no—
96C22×C71—41no—
97C22×C71—41no—
98C22×C71—41no—
99C22×C71C2×C22⋊C411yescharacteristic
100C22×C71#13511yescharacteristic
101C22×C71#13511yescharacteristic
102C2×D71—21no—
103C2×D71—21no—
104C2×D71—21no—
105C2×D71—21no—
106C2×D71—21no—
107C2×D71—42no—
108C2×D71—42no—
109C2×D71#9912yes—
110C4×C71—21no—
111C4×C71—21no—
112C4×C71—41no—
113C4×C71—81no—
114Dic71—21no—
115Dic71—21no—
116Dic71—41no—
117Dic71—41no—
118Dic71—81no—
119C2×C71—21no—
120C2×C71—21no—
121C2×C71—81no—
122C2×C71C2×#9911yescharacteristic
123C2×C71#41611yescharacteristic
124C2×C71#42111yescharacteristic
125D71—22no—
126D71—41no—
127#1516—711nomaximal, Sylow
128C71#151611yescharacteristic, complemented, Sylow
129#525—711no—
130C2×C22⋊C8—711no—
131#381—711no—
132#328—711no—
133#328—711no—
134#327—711no—
135#327D7111yescharacteristic, complemented
136C2×#41—711no—
137C23×C4—711no—
138C22×C8—1421no—
139#123—1421no—
140C22⋊Q8—711no—
141C22⋊Q8—711no—
142#121—711no—
143#121C2×D7111yescharacteristic
144#120—1421no—
145C4×D4—1421no—
146C4×D4—1421no—
147#117—711no—
148C2×C22⋊C4—1421no—
149C22⋊C8—711no—
150C22⋊C8—1421no—
151C22⋊C8C2×D7111yescharacteristic
152#95—711no—
153#95—1421no—
154#95C2×D7111yescharacteristic
155C24—711no—
156#41—2842no—
157C2×Q8—711no—
158C2×D4—21no—
159C2×D4—1421no—
160C2×D4—1421no—
161C2×D4C4×D7111yescharacteristic
162C22×C4—21no—
163C22×C4—2842no—
164C22×C4—711no—
165C22×C4—711no—
166C22×C4—711no—
167C22×C4—711no—
168C22×C4—711no—
169C22×C4—1421no—
170C22×C4—1421no—
171C22×C4C22×D7111yescharacteristic
172C2×C8—21no—
173C2×C8—2842no—
174C2×C8—1421no—
175C4⋊C4—711no—
176C4⋊C4—1421no—
177C4⋊C4—1421no—
178C4⋊C4C4×D7111yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—2842no—
181C22⋊C4—1421no—
182C22⋊C4—1421no—
183C22⋊C4—1421no—
184C22⋊C4—1421no—
185C42—1421no—
186C23—21no—
187C23—2841no—
188C23—711no—
189C23—711no—
190C23—1422no—
191C23—1421no—
192C23—1421no—
193C23D4×D7111yescharacteristic
194Q8—2841no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—2842no—
199D4—2842no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—2841no—
206C2×C4—2841no—
207C2×C4—2842no—
208C2×C4—2841no—
209C2×C4—2841no—
210C2×C4—2841no—
211C2×C4—2841no—
212C2×C4—711no—
213C2×C4—711no—
214C2×C4—1422no—
215C2×C4—1422no—
216C2×C4—1421no—
217C2×C4—1421no—
218C2×C4C2×C4×D7111yescharacteristic
219C2×C4D4×D7111yescharacteristic
220C8—41no—
221C8—2841no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—2842no—
228C22—2842no—
229C22—712no—
230C22—1421no—
231C22—1421no—
232C22—1421no—
233C22—1421no—
234C22—1421no—
235C22C22⋊C4×D7111yescharacteristic
236C22#1455614711yescharacteristic
237C22#1455614911yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—2841no—
243C4—2841no—
244C4—5681no—
245C4—1421no—
246C4—1421no—
247C2—21no—
248C2—21no—
249C2—81no—
250C2—2841no—
251C2—1422no—
252C2#99×D7111yescharacteristic
253C2#1798599211yescharacteristic
254C2#1798601411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#327×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#327D71
hypocenterC71#1516
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D71C2semidirect
3. #17985861C2semidirect
4. #17985737C2semidirect
5. #17985735C2semidirect
6. #17985733C2semidirect
7. #327×C71C2semidirect
8. C2×#11765864C4semidirect
12. #14556108C4semidirect
14. #14556099C4semidirect
18. #14556086C4semidirect
128. C71#1516semidirect
135. #327D71semidirect