Finite Group Databasebeta

← #22590023

Subgroups — #22590023

Order 9088.

250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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#17986545C211yesmaximal, characteristic
2#17985983C211yesmaximal, characteristic, complemented
3#17985797C212yesmaximal, complemented
4#17985795C212yesmaximal, complemented
5#413×C71C211yesmaximal, characteristic, complemented
6C2×#11765865C411yescharacteristic
7C2×#11765849—21no—
8#14556126C2211yescharacteristic
9#14556124C411yescharacteristic
10#14556117C2211yescharacteristic
11#14556115C411yescharacteristic
12#14556100—21no—
13#14556100—21no—
14C4×C22⋊D71—21no—
15C4×C22⋊D71—21no—
16C2×C4×Dic71C411yescharacteristic
17#14556047C2212yes—
18#14556045—21no—
19C2×#41×C71C2211yescharacteristic
20C2×M16×C71—21no—
21#101×C71C2212yes—
22#100×C71—21no—
23#11765865—41no—
24#11765865—41no—
25C2×Dic142C2×C411yescharacteristic
26C2×D284C2×C411yescharacteristic
27C2×C22⋊D71—21no—
28C2×C22⋊D71—21no—
29C2×C22⋊D71—21no—
30C22×Dic71—21no—
31C2×C4×D71—21no—
32#11765849—22no—
33#11765849—41no—
34C2×C71⋊C8—41no—
35Dic71⋊C4—21no—
36Dic71⋊C4—21no—
37C22⋊Dic71—21no—
38C22⋊Dic71—21no—
39(C2×D71)⋊C4—21no—
40(C2×D71)⋊C4—21no—
41C4×Dic71—21no—
42C4×Dic71C2×C411yescharacteristic
43C4×Dic71C2×C411yescharacteristic
44#41×C71—41no—
45#41×C71—41no—
46C2×Q8×C71C2311yescharacteristic
47C2×D4×C71C2×C411yescharacteristic
48C2×D4×C71D411yescharacteristic
49C2×D4×C71D411yescharacteristic
50C22×C4×C71C2×C411yescharacteristic
51C22×C4×C71D411yescharacteristic
52C22×C4×C71D411yescharacteristic
53M16×C71—22no—
54M16×C71—41no—
55C2×C8×C71—41no—
56C23×C71C22⋊C411yescharacteristic
57C23×C71C22⋊C411yescharacteristic
58C23×C71C22⋊C411yescharacteristic
59C22×D71—21no—
60Q8×C71—41no—
61D4×C71—41no—
62D4×C71—41no—
63D4×C71—41no—
64C2×C4×C71—21no—
65C2×C4×C71—21no—
66C2×C4×C71—21no—
67C2×C4×C71—21no—
68C2×C4×C71—21no—
69C2×C4×C71—21no—
70C2×C4×C71C22⋊C411yescharacteristic
71C2×C4×C71C22×C411yescharacteristic
72C2×C4×C71C2×D411yescharacteristic
73C2×C4×C71C2×D411yescharacteristic
74C22⋊D71—42no—
75C22⋊D71—42no—
76C22⋊D71—42no—
77C2×Dic71—21no—
78C2×Dic71—21no—
79C2×Dic71—21no—
80C2×Dic71—42no—
81D284—41no—
82C4×D71—41no—
83C4×D71—41no—
84Dic142—41no—
85C8×C71—42no—
86C71⋊C8—42no—
87C22×C71—21no—
88C22×C71—21no—
89C22×C71—21no—
90C22×C71—41no—
91C22×C71—41no—
92C22×C71—41no—
93C22×C71C2×C22⋊C411yescharacteristic
94C2×D71—41no—
95C2×D71—41no—
96C2×D71—41no—
97C4×C71—21no—
98C4×C71—21no—
99C4×C71—21no—
100C4×C71#9911yescharacteristic
101C4×C71#9911yescharacteristic
102Dic71—22no—
103Dic71—41no—
104Dic71—41no—
105C2×C71—21no—
106C2×C71—41no—
107C2×C71—41no—
108C2×C71—41no—
109C2×C71C2×#9911yescharacteristic
110D71—81no—
111#2132—711nomaximal, Sylow
112C71#213211yescharacteristic, complemented, Sylow
113#532—711no—
114#413—711no—
115#413D7111yescharacteristic, complemented
116#356—712no—
117#355—712no—
118C2×#41—711no—
119C2×#41C2×D7111yescharacteristic
120C2×M16—21no—
121C2×M16—1421no—
122C4⋊Q8—711no—
123#127—711no—
124#124—711no—
125#124—711no—
126#121—1421no—
127#121—1421no—
128C4×D4—1421no—
129C4×D4—1421no—
130C2×C42—711no—
131#101—712no—
132#101C2×D7112yes—
133#100—21no—
134#100—1421no—
135#41—41no—
136#41—41no—
137#41—2841no—
138#41—2841no—
139C2×Q8—711no—
140C2×Q8C22×D7111yescharacteristic
141C2×D4—711no—
142C2×D4—1421no—
143C2×D4—1421no—
144C2×D4—1421no—
145C2×D4C4×D7111yescharacteristic
146C2×D4D28411yescharacteristic
147C2×D4C22⋊D7111yescharacteristic
148C22×C4—1421no—
149C22×C4—1421no—
150C22×C4C4×D7111yescharacteristic
151C22×C4D28411yescharacteristic
152C22×C4C22⋊D7111yescharacteristic
153M16—22no—
154M16—41no—
155M16—2841no—
156M16—1422no—
157C2×C8—41no—
158C2×C8—2841no—
159C4⋊C4—1421no—
160C4⋊C4—1421no—
161C22⋊C4—1421no—
162C22⋊C4—1421no—
163C22⋊C4—1421no—
164C22⋊C4—1421no—
165C42—711no—
166C42—711no—
167C42—1421no—
168C23—1421no—
169C23(C2×D71)⋊C411yescharacteristic
170C23(C2×D71)⋊C411yescharacteristic
171C23(C2×D71)⋊C411yescharacteristic
172Q8—41no—
173Q8—2841no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—2841no—
178D4—2842no—
179D4—2842no—
180D4—2842no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—2842no—
188C2×C4—2841no—
189C2×C4—2841no—
190C2×C4—1421no—
191C2×C4—1421no—
192C2×C4—1421no—
193C2×C4(C2×D71)⋊C411yescharacteristic
194C2×C4C2×C4×D7111yescharacteristic
195C2×C4C2×C22⋊D7111yescharacteristic
196C2×C4C2×D28411yescharacteristic
197C8—42no—
198C8—2842no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—2841no—
206C22—2841no—
207C22—2841no—
208C22C2×(C2×D71)⋊C411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—2841no—
213C4—2841no—
214C4—1422no—
215C4#1455604211yescharacteristic
216C4#1455604211yescharacteristic
217C2—21no—
218C2—41no—
219C2—41no—
220C2—41no—
221C2—5681no—
222C2C2×#1455604211yescharacteristic
subgroupG/H
centerC4#14556042
commutatorC2×C4×C71C22×C4
FrattiniC2×Q8C22×D71
Fitting#413×C71C2
socleC2×C71C2×#99
hypercenter#413D71
hypocenterC71#2132
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #17985983C2semidirect
3. #17985797C2semidirect
4. #17985795C2semidirect
5. #413×C71C2semidirect
112. C71#2132semidirect
115. #413D71semidirect