Finite Group Databasebeta

← #22586914

Subgroups — #22586914

Order 9088.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#17986530C211yesmaximal, characteristic
2#17986049C211yesmaximal, characteristic, complemented
3#17985866C211yesmaximal, characteristic, complemented
4#17985737C211yesmaximal, characteristic, complemented
5#17985735C211yesmaximal, characteristic, complemented
6#17985733C211yesmaximal, characteristic
7#327×C71C211yesmaximal, characteristic
8#14556121—21no—
9#14556119C411yescharacteristic, complemented
10#14556115C411yescharacteristic, complemented
11#14556109—21no—
12#14556107C2211yescharacteristic
13#14556093C411yescharacteristic, complemented
14D4×Dic71—21no—
15D4×Dic71C411yescharacteristic, complemented
16#14556084—21no—
17C2×C4×Dic71C2211yescharacteristic
18Dic71⋊C8—21no—
19C22⋊(C71⋊C8)C2211yescharacteristic
20C8×Dic71—21no—
21C71⋊#95—21no—
22C71⋊#95—21no—
23C71⋊#95C2211yescharacteristic
24#121×C71C2211yescharacteristic
25C22⋊C8×C71C2211yescharacteristic
26#95×C71C2211yescharacteristic
27C2×Dic142C2×C411yescharacteristic
28C22×Dic71—21no—
29C22×Dic71—21no—
30C22×Dic71D411yescharacteristic
31C22×Dic71D411yescharacteristic
32C2×C71⋊C8—21no—
33C4⋊Dic71—21no—
34C4⋊Dic71C2×C411yescharacteristic
35Dic71⋊C4—21no—
36Dic71⋊C4—21no—
37Dic71⋊C4—21no—
38C22⋊Dic71—21no—
39C22⋊Dic71—21no—
40C22⋊Dic71—21no—
41C22⋊Dic71—21no—
42C4×Dic71—21no—
43C4×Dic71C2×C411yescharacteristic
44C4×Dic71C2×C411yescharacteristic
45C4×Dic71D411yescharacteristic
46C4×Dic71D411yescharacteristic
47C2×D4×C71—21no—
48C2×D4×C71C2×C411yescharacteristic
49C22×C4×C71—21no—
50C22×C4×C71C2311yescharacteristic
51C2×C8×C71—21no—
52C4⋊C4×C71C2×C411yescharacteristic
53C22⋊C4×C71—21no—
54C23×C71—21no—
55C23×C71C2×D411yescharacteristic
56D4×C71—41no—
57D4×C71—41no—
58D4×C71—41no—
59C2×C4×C71—21no—
60C2×C4×C71—41no—
61C2×C4×C71—41no—
62C2×C4×C71—41no—
63C2×C4×C71—41no—
64C2×C4×C71C22×C411yescharacteristic
65C2×C4×C71C2×D411yescharacteristic
66C2×Dic71—21no—
67C2×Dic71—21no—
68C2×Dic71—21no—
69C2×Dic71—21no—
70C2×Dic71—41no—
71C2×Dic71—42no—
72C2×Dic71—41no—
73C2×Dic71—41no—
74C2×Dic71—41no—
75C2×Dic71C22⋊C411yescharacteristic
76C2×Dic71C22⋊C411yescharacteristic
77C2×Dic71C22⋊C411yescharacteristic
78C2×Dic71C22⋊C411yescharacteristic
79Dic142—41no—
80C8×C71—41no—
81C71⋊C8—41no—
82C22×C71—21no—
83C22×C71—21no—
84C22×C71—41no—
85C22×C71—41no—
86C22×C71—41no—
87C22×C71C2×C22⋊C411yescharacteristic
88C22×C71#13511yescharacteristic
89C22×C71#13511yescharacteristic
90C4×C71—21no—
91C4×C71—21no—
92C4×C71—41no—
93C4×C71—81no—
94Dic71—21no—
95Dic71—21no—
96Dic71—21no—
97Dic71—21no—
98Dic71—41no—
99Dic71—41no—
100Dic71—81no—
101C2×C71—21no—
102C2×C71—21no—
103C2×C71—81no—
104C2×C71#41011yescharacteristic
105C2×C71#41611yescharacteristic
106C2×C71#42111yescharacteristic
107#1521—711nomaximal, Sylow
108C71#152111yescharacteristic, complemented, Sylow
109#529—711no—
110#431—711no—
111#383—711no—
112#328—711no—
113#328—711no—
114#327—711no—
115#327D7111yescharacteristic
116#126—1421no—
117#125—711no—
118#124—711no—
119#123—1421no—
120C22⋊Q8—711no—
121#121C2×D7111yescharacteristic
122C4×Q8—711no—
123C4×D4—711no—
124C4×D4—1421no—
125#117—1421no—
126C2×C42—711no—
127C4⋊C8—1421no—
128C22⋊C8—711no—
129C22⋊C8C2×D7111yescharacteristic
130C4×C8—1421no—
131#95—711no—
132#95—1421no—
133#95—1421no—
134#95C2×D7111yescharacteristic
135C2×Q8—711no—
136C2×D4—21no—
137C2×D4C4×D7111yescharacteristic
138C22×C4—21no—
139C22×C4—711no—
140C22×C4—711no—
141C22×C4—1421no—
142C22×C4—1421no—
143C22×C4C22×D7111yescharacteristic
144C2×C8—21no—
145C2×C8—1421no—
146C4⋊C4—711no—
147C4⋊C4—1421no—
148C4⋊C4—1421no—
149C4⋊C4—1421no—
150C4⋊C4—1421no—
151C4⋊C4C4×D7111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—1421no—
154C22⋊C4—1421no—
155C22⋊C4—1421no—
156C22⋊C4—1421no—
157C42—711no—
158C42—711no—
159C42—711no—
160C42—711no—
161C42—1421no—
162C23—21no—
163C23D4×D7111yescharacteristic
164Q8—2841no—
165D4—41no—
166D4—41no—
167D4—41no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—2842no—
174C2×C4—2841no—
175C2×C4—2841no—
176C2×C4—2841no—
177C2×C4—2841no—
178C2×C4—711no—
179C2×C4—711no—
180C2×C4—711no—
181C2×C4—711no—
182C2×C4—1421no—
183C2×C4—1421no—
184C2×C4—1421no—
185C2×C4—1421no—
186C2×C4C2×C4×D7111yescharacteristic
187C2×C4D4×D7111yescharacteristic
188C8—41no—
189C8—2841no—
190C22—21no—
191C22—21no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22C22⋊C4×D7111yescharacteristic
196C22#1455614711yescharacteristic
197C22#1455614911yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—81no—
202C4—2841no—
203C4—2841no—
204C4—5681no—
205C4—1421no—
206C4—1421no—
207C4—1421no—
208C4—1421no—
209C2—21no—
210C2—21no—
211C2—81no—
212C2#1798597111yescharacteristic
213C2#1798599211yescharacteristic
214C2#1798601411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D71
commutatorC2×C4×C71C22×C4
FrattiniC22×C4C22×D71
Fitting#327×C71C2
socleC22×C71C2×C22⋊C4
hypercenter#327D71
hypocenterC71#1521
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. #17986049C2semidirect
3. #17985866C2semidirect
4. #17985737C2semidirect
5. #17985735C2semidirect
9. #14556119C4semidirect
10. #14556115C4semidirect
13. #14556093C4semidirect
15. D4×Dic71C4semidirect
108. C71#1521semidirect