Finite Group Databasebeta

← C89×#7395 #36385243

Subgroups — C89×#7395 #36385243

Order 22784.

284 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C89×#2022C211yesmaximal, characteristic
2C89×#1317C211yesmaximal, characteristic, complemented
3C89×#1306C211yesmaximal, characteristic, complemented
4#534×C89C411yescharacteristic
5C2×#123×C89—21no—
6C2×#99×C89—21no—
7#407×C89—21no—
8#381×C89C2211yescharacteristic
9#342×C89C411yescharacteristic
10#323×C89—21no—
11C22×D4×C89—21no—
12C23×C4×C89D411yescharacteristic
13C2×M16×C89—41no—
14#123×C89—42no—
15#123×C89—41no—
16#123×C89—41no—
17#123×C89—41no—
18#121×C89—41no—
19#120×C89—41no—
20C2×C4⋊C4×C89—41no—
21C2×C22⋊C4×C89—21no—
22C2×C22⋊C4×C89—41no—
23C2×C22⋊C4×C89C2×C411yescharacteristic
24C2×C22⋊C4×C89D411yescharacteristic
25#99×C89—42no—
26C22⋊C8×C89—22no—
27C22⋊C8×C89—41no—
28C22⋊C8×C89—41no—
29#95×C89—41no—
30C24×C89—21no—
31C24×C89C22⋊C411yescharacteristic
32C2×D4×C89—41no—
33C2×D4×C89—41no—
34C2×D4×C89—41no—
35C2×D4×C89—41no—
36C2×D4×C89—41no—
37C2×D4×C89—41no—
38C2×D4×C89—41no—
39C22×C4×C89—21no—
40C22×C4×C89—21no—
41C22×C4×C89—21no—
42C22×C4×C89—21no—
43C22×C4×C89—21no—
44C22×C4×C89—41no—
45C22×C4×C89—41no—
46C22×C4×C89—41no—
47C22×C4×C89D811yescharacteristic
48C22×C4×C89SD1611yescharacteristic
49M16×C89—81no—
50M16×C89—81no—
51C2×C8×C89—42no—
52C2×C8×C89—81no—
53C4⋊C4×C89—42no—
54C4⋊C4×C89—42no—
55C4⋊C4×C89—41no—
56C22⋊C4×C89—22no—
57C22⋊C4×C89—42no—
58C22⋊C4×C89—42no—
59C22⋊C4×C89—42no—
60C22⋊C4×C89—41no—
61C22⋊C4×C89—41no—
62C22⋊C4×C89—41no—
63C23×C89—21no—
64C23×C89—21no—
65C23×C89—41no—
66C23×C89—41no—
67C23×C89—41no—
68C23×C89—81no—
69C23×C89—82no—
70C23×C89#9911yescharacteristic
71C23×C89#10211yescharacteristic
72C23×C89#10411yescharacteristic
73D4×C89—81no—
74D4×C89—81no—
75D4×C89—81no—
76D4×C89—81no—
77D4×C89—161no—
78C2×C4×C89—21no—
79C2×C4×C89—21no—
80C2×C4×C89—41no—
81C2×C4×C89—41no—
82C2×C4×C89—41no—
83C2×C4×C89—41no—
84C2×C4×C89—42no—
85C2×C4×C89—41no—
86C2×C4×C89—41no—
87C2×C4×C89—41no—
88C2×C4×C89—41no—
89C2×C4×C89—41no—
90C2×C4×C89—81no—
91C2×C4×C89—82no—
92C2×C4×C89—81no—
93C2×C4×C89—81no—
94C8×C89—82no—
95C8×C89—161no—
96C22×C89—21no—
97C22×C89—21no—
98C22×C89—41no—
99C22×C89—42no—
100C22×C89—41no—
101C22×C89—41no—
102C22×C89—81no—
103C22×C89—82no—
104C22×C89—82no—
105C22×C89—81no—
106C22×C89—161no—
107C22×C89#32711yescharacteristic
108C22×C89AΣL(1,𝔽16)11yescharacteristic
109C22×C89#35311yescharacteristic
110C4×C89—41no—
111C4×C89—41no—
112C4×C89—81no—
113C4×C89—81no—
114C4×C89—82no—
115C4×C89—81no—
116#7395C8911yesmaximal, characteristic, direct product factor, Sylow
117C2×C89—21no—
118C2×C89—21no—
119C2×C89—21no—
120C2×C89—41no—
121C2×C89—41no—
122C2×C89—161no—
123C2×C89#134311yescharacteristic
124#2022C2×C8911yescharacteristic
125#1317C2×C8911yescharacteristic, complemented
126#1306C2×C8911yescharacteristic, complemented
127C89#739511yescharacteristic, direct product factor, Sylow
128#534C4×C8911yescharacteristic
129C2×#123—21no—
130C2×#99—21no—
131#407—21no—
132#381C22×C8911yescharacteristic
133#342C4×C8911yescharacteristic
134#323—21no—
135C22×D4—21no—
136C23×C4D4×C8911yescharacteristic
137C2×M16—41no—
138#123—42no—
139#123—41no—
140#123—41no—
141#123—41no—
142#121—41no—
143#120—41no—
144C2×C4⋊C4—41no—
145C2×C22⋊C4—21no—
146C2×C22⋊C4—41no—
147C2×C22⋊C4C2×C4×C8911yescharacteristic
148C2×C22⋊C4D4×C8911yescharacteristic
149#99—42no—
150C22⋊C8—22no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153#95—41no—
154C24—21no—
155C24C22⋊C4×C8911yescharacteristic
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—41no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4D8×C8911yescharacteristic
172C22×C4SD16×C8911yescharacteristic
173M16—81no—
174M16—81no—
175C2×C8—42no—
176C2×C8—81no—
177C4⋊C4—41no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C22⋊C4—22no—
181C22⋊C4—42no—
182C22⋊C4—42no—
183C22⋊C4—42no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C23—21no—
188C23—21no—
189C23—41no—
190C23—41no—
191C23—41no—
192C23—81no—
193C23—82no—
194C23#99×C8911yescharacteristic
195C23#102×C8911yescharacteristic
196C23#104×C8911yescharacteristic
197D4—81no—
198D4—81no—
199D4—81no—
200D4—81no—
201D4—161no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4—82no—
216C2×C4—81no—
217C2×C4—81no—
218C8—82no—
219C8—161no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—81no—
227C22—82no—
228C22—82no—
229C22—81no—
230C22—161no—
231C22#327×C8911yescharacteristic
232C22AΣL(1,𝔽16)×C8911yescharacteristic
233C22#353×C8911yescharacteristic
234C4—41no—
235C4—41no—
236C4—81no—
237C4—81no—
238C4—82no—
239C4—81no—
240C2—21no—
241C2—21no—
242C2—21no—
243C2—41no—
244C2—41no—
245C2—161no—
246C2C89×#134311yescharacteristic
subgroupG/H
center, socleC2×C89#1343
commutatorC2×C22⋊C4C2×C4×C89
Frattini, cosocle#381C22×C89
prime radical#534×C89C4
LCSG ▷ C2×C22⋊C4 ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C89 ◁ C23×C89 ◁ C24×C89 ◁ #381×C89 ◁ G

Complements

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

NH ≅ G/Ntype
2. C89×#1317C2semidirect
3. C89×#1306C2semidirect
116. #7395C89direct (N × H)
125. #1317C2×C89semidirect
126. #1306C2×C89semidirect
127. C89#7395direct (N × H)

Maximal subgroups

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

subgroupindex
C89×#20222
C89×#13172
C89×#13062
#739589