Finite Group Databasebeta

← #36443738

Subgroups — #36443738

Order 22784.

350 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 87 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#26021815C212yesmaximal
2#26021790C211yesmaximal, characteristic
3#26018078C211yesmaximal, characteristic
4#26018075C212yesmaximal
5C89×#2809C211yesmaximal, characteristic
6C2×#15667945—21no—
7C2×#15667936—21no—
8#19151468C2211yescharacteristic
9#19151360—22no—
10#19151360—22no—
11#19151353C2211yescharacteristic
12#19151353C2212yes—
13#400×C89—21no—
14#398×C89—22no—
15#391×C89—21no—
16#391×C89C2211yescharacteristic
17#389×C89C2212yes—
18#387×C89—22no—
19C22×#10623494—21no—
20C22×#10623494—22no—
21C2×C4⋊Dic89—22no—
22C2×C4⋊Dic89—21no—
23#15667945—42no—
24#15667936—42no—
25C22×Q8×C89D411yescharacteristic
26C2×C4⋊C4×C89—22no—
27C2×C4⋊C4×C89—21no—
28C2×C4⋊C4×C89—21no—
29C2×C4⋊C4×C89D412yes—
30C2×C4⋊C4×C89D412yes—
31C2×C4⋊C4×C89D411yescharacteristic
32C2×C42×C89—21no—
33C2×C42×C89C2311yescharacteristic
34#95×C89—21no—
35#95×C89—22no—
36#95×C89—22no—
37#95×C89—22no—
38#95×C89—22no—
39C22×Dic89—41no—
40C2×#10623494—22no—
41C2×#10623494—41no—
42C2×#10623494—41no—
43C2×#10623494—42no—
44C2×#10623494—42no—
45C2×#10623494—42no—
46C4⋊Dic89—41no—
47C4⋊Dic89—41no—
48C4⋊Dic89—44no—
49C2×Q8×C89—21no—
50C2×Q8×C89—41no—
51C2×Q8×C89—41no—
52C2×Q8×C89Q1612yes—
53C22×C4×C89—21no—
54C22×C4×C89—21no—
55C22×C4×C89—22no—
56C22×C4×C89—22no—
57C22×C4×C89C2×D411yescharacteristic
58C22×C4×C89C2×D412yes—
59C4⋊C4×C89—22no—
60C4⋊C4×C89—22no—
61C4⋊C4×C89—42no—
62C4⋊C4×C89—41no—
63C4⋊C4×C89—42no—
64C4⋊C4×C89—42no—
65C4⋊C4×C89—81no—
66C4⋊C4×C89—81no—
67C42×C89—41no—
68C42×C89—81no—
69C23×C89#12011yescharacteristic
70Q8×C89—42no—
71Q8×C89—81no—
72C2×C4×C89—21no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89—21no—
76C2×C4×C89—22no—
77C2×C4×C89—41no—
78C2×C4×C89—41no—
79C2×C4×C89—42no—
80C2×C4×C89—42no—
81C2×C4×C89—42no—
82C2×C4×C89—41no—
83C2×C4×C89—42no—
84C2×C4×C89—42no—
85C2×C4×C89—42no—
86C2×C4×C89—42no—
87C2×C4×C89C2×Q1611yescharacteristic
88C2×C4×C89#13512yes—
89C2×C4×C89#13712yes—
90C2×C4×C89#13711yescharacteristic
91C2×Dic89—81no—
92C2×Dic89—82no—
93#10623494—42no—
94#10623494—82no—
95C22×C89#45111yescharacteristic
96C22×C89#45212yes—
97C22×C89#45311yescharacteristic
98C22×C89#45412yes—
99C22×C89#45811yescharacteristic
100C4×C89—21no—
101C4×C89—21no—
102C4×C89—22no—
103C4×C89—22no—
104C4×C89—42no—
105C4×C89—82no—
106C4×C89—82no—
107C4×C89—81no—
108Dic89—161no—
109#7831—891nomaximal, Sylow
110C2×C89#161411yescharacteristic
111C2×C89#161512yes—
112C2×C89#163411yescharacteristic
113C2×C89#163612yes—
114C2×C89#165711yescharacteristic
115#2809D8911yescharacteristic
116#2100—892no—
117#2095—891no—
118#1272—891no—
119#1271—892no—
120C89#783111yescharacteristic, complemented, Sylow
121C2×#107—1781no—
122C2×#103—1781no—
123#400—21no—
124#398—22no—
125#391—21no—
126#391C2×D8911yescharacteristic
127#389C2×D8912yes—
128#387—22no—
129#384—891no—
130#340—1782no—
131#340—1782no—
132#336—891no—
133#336—892no—
134C22×Q8C22⋊D8911yescharacteristic
135C22×C8—1782no—
136C22×C8—1781no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—1782no—
141C2×C4⋊C4—1781no—
142C2×C4⋊C4C22⋊D8912yes—
143C2×C4⋊C4C22⋊D8912yes—
144C2×C4⋊C4C22⋊D8911yescharacteristic
145C2×C42—21no—
146C2×C42C22×D8911yescharacteristic
147#107—3562no—
148#103—3562no—
149#95—21no—
150#95—22no—
151#95—22no—
152#95—22no—
153#95—22no—
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8#1308356412yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—3561no—
163C22×C4C2×C22⋊D8911yescharacteristic
164C22×C4C2×C22⋊D8912yes—
165C2×C8—3561no—
166C2×C8—3561no—
167C2×C8—3562no—
168C2×C8—3562no—
169C2×C8—3562no—
170C2×C8—1782no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—81no—
178C4⋊C4—81no—
179C4⋊C4—3561no—
180C4⋊C4—3561no—
181C4⋊C4—3564no—
182C42—41no—
183C42—81no—
184C23#1566798111yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—7121no—
203C2×C4—7122no—
204C2×C4C2×#1308356411yescharacteristic
205C2×C4#1566803212yes—
206C2×C4#1566804212yes—
207C2×C4#1566804311yescharacteristic
208C8—3562no—
209C8—7122no—
210C22#1915175411yescharacteristic
211C22#1915176012yes—
212C22#1915176611yescharacteristic
213C22#1915177112yes—
214C22#1915178811yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—82no—
221C4—82no—
222C4—81no—
223C4—14241no—
224C2#2601927711yescharacteristic
225C2#2601928312yes—
226C2#2601939711yescharacteristic
227C2#2601941012yes—
228C2#2601955011yescharacteristic
subgroupG/H
centerC23#15667981
commutator, cosocleC2×C42×C89C23
FrattiniC2×C42C22×D89
FittingC89×#2809C2
socle, prime radicalC23×C89#120
hypercenter#2809D89
hypocenterC89#7831
LCSG ▷ C2×C42×C89 ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2809

Complements

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

NH ≅ G/Ntype
120. C89#7831semidirect

Maximal subgroups

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

subgroupindex
#260218152
#260217902
#260180782
#260180752
C89×#28092
#783189