Finite Group Databasebeta

← #36463642

Subgroups — #36463642

Order 22784.

306 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 85 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#26028895C211yesmaximal, characteristic
2#26022052C212yesmaximal, complemented
3#26018194C211yesmaximal, characteristic, complemented
4#26018177C212yesmaximal
5C89×#1323C211yesmaximal, characteristic, complemented
6#19152066C411yescharacteristic
7#19151658—22no—
8#19151650—22no—
9#19151625C411yescharacteristic
10#19151566C411yescharacteristic
11#19151564C2211yescharacteristic
12M16×Dic89C411yescharacteristic
13C2×C8×Dic89C2211yescharacteristic
14#19151416—22no—
15C22⋊#13083549C2212yes—
16#19151373—22no—
17#424×C89C2211yescharacteristic
18C22⋊C16×C89C2212yes—
19C2×#13083574C2×C411yescharacteristic
20C2×#13083558C2×C411yescharacteristic
21C22×#10623494C2×C411yescharacteristic
22#15667977C812yes—
23#15667974C812yes—
24#15667972—22no—
25#15667969—21no—
26C2×C4×Dic89C2×C411yescharacteristic
27C42×D89—21no—
28C2×#13083549—22no—
29C4⋊#10623494—22no—
30#15667924—22no—
31#15667924—22no—
32#15667922—21no—
33C8×Dic89—21no—
34C8×Dic89D412yes—
35C8×Dic89D412yes—
36C2×M16×C89C2×C411yescharacteristic
37C22×C8×C89C2311yescharacteristic
38#117×C89C2×C411yescharacteristic
39C2×C16×C89—22no—
40C4⋊C8×C89—22no—
41#13083574—41no—
42#13083574—41no—
43C2×Dic178C2×C811yescharacteristic
44C2×D356C2×C811yescharacteristic
45C2×C22⋊D89—21no—
46C22×Dic89M1612yes—
47C2×C4×D89—21no—
48C2×C4×D89—22no—
49#13083558—41no—
50C2×#10623494—21no—
51C2×#10623494—41no—
52C2×#10623494C22⋊C412yes—
53#13083553—22no—
54#13083551—22no—
55C4×Dic89—22no—
56C4×Dic89C22⋊C411yescharacteristic
57C4×Dic89C22⋊C411yescharacteristic
58C4×Dic89C2×C812yes—
59#13083549—42no—
60C22×C4×C89C22×C411yescharacteristic
61M16×C89—41no—
62C2×C8×C89—21no—
63C2×C8×C89—41no—
64C2×C8×C89C2×D412yes—
65C4⋊C4×C89C2×C812yes—
66C22⋊C4×C89—21no—
67C42×C89—21no—
68C16×C89—42no—
69C23×C89C2×M1611yescharacteristic
70C22×D89—21no—
71C2×C4×C89—21no—
72C2×C4×C89—21no—
73C2×C4×C89—22no—
74C2×C4×C89C2×C22⋊C411yescharacteristic
75C2×C4×C89C22×C811yescharacteristic
76C22⋊D89—42no—
77C2×Dic89—21no—
78C2×Dic89—42no—
79C2×Dic89C22⋊C812yes—
80C2×Dic89C22⋊C812yes—
81D356—41no—
82C4×D89—44no—
83C4×D89—41no—
84C4×D89—41no—
85Dic178—41no—
86C8×C89—22no—
87C8×C89—41no—
88#10623494—22no—
89#10623494—41no—
90C22×C89—22no—
91C22×C89—21no—
92C22×C89C2×C22⋊C811yescharacteristic
93C2×D89—42no—
94C2×D89—41no—
95C4×C89—21no—
96C4×C89—42no—
97C4×C89#41011yescharacteristic
98C4×C89#41311yescharacteristic
99Dic89—22no—
100Dic89—22no—
101Dic89—41no—
102#11463—891nomaximal, Sylow
103C2×C89—41no—
104C2×C89#145811yescharacteristic
105C2×C89#211712yes—
106D89—81no—
107#2922—891no—
108#2163—892no—
109#1323—891no—
110#1323D8911yescharacteristic, complemented
111#1315—892no—
112C89#1146311yescharacteristic, complemented, Sylow
113C4×#41—891no—
114#433—1782no—
115#431—1782no—
116#424—891no—
117#424C2×D8911yescharacteristic
118#408—891no—
119#408—891no—
120C4×M16—891no—
121C2×C4×C8—891no—
122C4⋊C16—1782no—
123C22⋊C16—892no—
124C22⋊C16C2×D8912yes—
125#346—1782no—
126C2×#41—891no—
127C2×M16—891no—
128C2×M16C4×D8911yescharacteristic
129C22×C8—891no—
130C22×C8C22×D8911yescharacteristic
131C4×Q8—892no—
132C4×D4—892no—
133C4×D4—1782no—
134#117—1781no—
135#117C4×D8911yescharacteristic
136C2×C42—891no—
137C2×C42—1781no—
138C2×C16—22no—
139C2×C16—1782no—
140C4⋊C8—22no—
141C4⋊C8—1782no—
142C22⋊C8—1782no—
143C22⋊C8—1782no—
144#97—1781no—
145C4×C8—892no—
146C4×C8—892no—
147C4×C8—1781no—
148#41—3561no—
149#41—3561no—
150C2×Q8—891no—
151C2×D4—891no—
152C2×D4—1781no—
153C22×C4—892no—
154C22×C4—1782no—
155C22×C4—1781no—
156C22×C4C2×C4×D8911yescharacteristic
157M16—41no—
158M16—3561no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—892no—
162C2×C8—3561no—
163C2×C8—1781no—
164C2×C8D4×D8912yes—
165C4⋊C4—1782no—
166C4⋊C4C8×D8912yes—
167C22⋊C4—21no—
168C22⋊C4—1782no—
169C42—21no—
170C42—892no—
171C42—891no—
172C42—891no—
173C42—1782no—
174C16—42no—
175C16—3562no—
176C23—1781no—
177C23M16×D8911yescharacteristic
178Q8—3561no—
179D4—3561no—
180D4—3562no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—892no—
185C2×C4—892no—
186C2×C4—3564no—
187C2×C4—3561no—
188C2×C4—3561no—
189C2×C4—3562no—
190C2×C4—1781no—
191C2×C4C22⋊C4×D8911yescharacteristic
192C2×C4C2×C8×D8911yescharacteristic
193C8—22no—
194C8—41no—
195C8—3561no—
196C8—1782no—
197C22—21no—
198C22—22no—
199C22—3561no—
200C22—3562no—
201C22C22⋊C8×D8911yescharacteristic
202C4—21no—
203C4—42no—
204C4—3561no—
205C4—1782no—
206C4—1782no—
207C4#1915157011yescharacteristic
208C4#1915158111yescharacteristic
209C2—41no—
210C2—7121no—
211C2#2601856511yescharacteristic
212C2#2602187812yes—
subgroupG/H
centerC2×C4C22⋊C4×D89
commutatorC2×C4×C89C22×C8
FrattiniC22×C8C22×D89
FittingC89×#1323C2
socleC22×C89C2×C22⋊C8
prime radicalC2×#13083574C2×C4
cosocleC22×C8×C89C23
hypercenter#1323D89
hypocenterC89#11463
LCSG ▷ C2×C4×C89 ▷ C22×C89 ▷ C89
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #26022052C2semidirect
3. #26018194C2semidirect
5. C89×#1323C2semidirect
110. #1323D89semidirect
112. C89#11463semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260288952
#260220522
#260181942
#260181772
C89×#13232
#1146389