Finite Group Databasebeta

← #44400835

Subgroups — #44400835

Order 29056.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C22×Dic908C211yesmaximal, characteristic
2C22×#16813874C211yesmaximal, characteristic
3C2×#20300286C211yesmaximal, characteristic
4C2×#20300211C211yesmaximal, characteristic
5#28408937C211yesmaximal, characteristic
6#28408786C211yesmaximal, characteristic
7C2×#103×C227C211yesmaximal, characteristic
8C22×Dic454C2211yescharacteristic
9C22×Dic454C2211yescharacteristic
10C2×Dic908—22no—
11C2×Dic908—22no—
12C2×Dic908—22no—
13C2×#16813874—22no—
14C2×#16813874—22no—
15C2×#16813874—22no—
16C22×C227⋊C8C2211yescharacteristic
17#20300286—22no—
18#20300286—22no—
19C2×Dic227⋊C4—22no—
20C2×C4×Dic227C2211yescharacteristic
21#20300211—22no—
22C227⋊#95—22no—
23C22×Q8×C227C2211yescharacteristic
24C22×C8×C227C2211yescharacteristic
25C2×C4⋊C4×C227C2211yescharacteristic
26#103×C227—22no—
27C2×Dic454—21no—
28C2×Dic454—21no—
29C2×Dic454—21no—
30C2×Dic454—21no—
31C2×Dic454—21no—
32C2×Dic454—21no—
33C2×Dic454—21no—
34C2×Dic454—21no—
35C2×Dic454—21no—
36C2×Dic454—21no—
37C2×Dic454D412yes—
38C2×Dic454D412yes—
39C22×Dic227—21no—
40C22×Dic227—21no—
41C22×Dic227D412yes—
42Dic908—28no—
43#16813874—28no—
44C2×C227⋊C8—21no—
45C2×C227⋊C8—21no—
46C2×C227⋊C8D412yes—
47Dic227⋊C4—28no—
48C4×Dic227—21no—
49C4×Dic227—21no—
50C2×Q8×C227—21no—
51C2×Q8×C227—21no—
52C2×Q8×C227—21no—
53C2×Q8×C227—21no—
54C2×Q8×C227—21no—
55C2×Q8×C227D412yes—
56C22×C4×C227—21no—
57C22×C4×C227—21no—
58C22×C4×C227C2311yescharacteristic
59C2×C8×C227—21no—
60C2×C8×C227—21no—
61C2×C8×C227D412yes—
62C4⋊C4×C227—21no—
63C4⋊C4×C227—21no—
64Dic454—22no—
65Dic454—22no—
66Dic454—22no—
67Dic454—22no—
68Dic454—41no—
69Dic454—41no—
70Dic454—41no—
71Dic454—41no—
72C2×Dic227—22no—
73C2×Dic227—22no—
74C2×Dic227—22no—
75C2×Dic227—22no—
76C2×Dic227—41no—
77C2×Dic227—41no—
78C2×Dic227—41no—
79C2×Dic227—41no—
80C2×Dic227Q1614yescomplemented
81C227⋊C8—22no—
82C23×C227C2×D411yescharacteristic
83Q8×C227—22no—
84Q8×C227—22no—
85Q8×C227—41no—
86Q8×C227—41no—
87C2×C4×C227—22no—
88C2×C4×C227—41no—
89C2×C4×C227—41no—
90C2×C4×C227—41no—
91C2×C4×C227—42no—
92C2×C4×C227C2×D411yescharacteristic
93C2×C4×C227C2×D411yescharacteristic
94C2×C4×C227C2×D411yescharacteristic
95C2×C4×C227C2×D411yescharacteristic
96C2×C4×C227C2×D411yescharacteristic
97C2×C4×C227#4111yescharacteristic
98C8×C227—22no—
99C22×C227#12011yescharacteristic
100C22×C227#12111yescharacteristic
101C22×C227#12711yescharacteristic
102C22×C227C2×Q1612yes—
103C22×C227#13712yes—
104C4×C227—42no—
105C4×C227—81no—
106C4×C227#12011yescharacteristic
107C4×C227#12011yescharacteristic
108C4×C227#12111yescharacteristic
109C4×C227#12111yescharacteristic
110Dic227—24no—
111Dic227—42no—
112Dic227—42no—
113C2×C227#39211yescharacteristic
114C2×C227#45112yes—
115C2×C227#46212yes—
116C2×C227#49411yescharacteristic
117C2×C227#49711yescharacteristic
118C227#201611yescharacteristic, complemented, Sylow
119#2016—2271nomaximal, Sylow
120C22×Q16—2271no—
121C22×Q16—2271no—
122C2×C4⋊Q8—2271no—
123C2×#103—2271no—
124C2×#103D22711yescharacteristic
125#391—2271no—
126#336—2271no—
127C22×Q8—2271no—
128C22×Q8—2271no—
129C22×Q8C2×D22711yescharacteristic
130C2×Q16—4542no—
131C2×Q16—4542no—
132C2×Q16—4542no—
133C2×Q16—4542no—
134C2×Q16—4542no—
135C2×Q16—4542no—
136C22×C8—2271no—
137C22×C8C2×D22711yescharacteristic
138C4⋊Q8—4542no—
139C4⋊Q8—4542no—
140C2×C4⋊C4—4542no—
141C2×C4⋊C4C2×D22711yescharacteristic
142C2×C42—2271no—
143#103—22no—
144#103—4542no—
145#95—4542no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—4541no—
152C2×Q8—4541no—
153C2×Q8—4541no—
154C2×Q8—4541no—
155C2×Q8—4541no—
156C2×Q8—4541no—
157C2×Q8—4541no—
158C2×Q8—4541no—
159C2×Q8—4541no—
160C2×Q8—4541no—
161C2×Q8—2272no—
162C2×Q8—2272no—
163C2×Q8D90812yes—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—4541no—
167C22×C4—4541no—
168C22×C4—2272no—
169C22×C4C22×D22711yescharacteristic
170Q16—4548no—
171Q16—4548no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—4541no—
175C2×C8—4541no—
176C2×C8—2272no—
177C2×C8C22⋊D22712yes—
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—4548no—
181C42—4541no—
182C42—4541no—
183C23D4×D22711yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—41no—
187Q8—41no—
188Q8—9081no—
189Q8—9081no—
190Q8—9081no—
191Q8—9081no—
192Q8—4542no—
193Q8—4542no—
194Q8—4542no—
195Q8—4542no—
196C2×C4—22no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—9081no—
202C2×C4—9081no—
203C2×C4—9081no—
204C2×C4—9081no—
205C2×C4—4542no—
206C2×C4—4542no—
207C2×C4—4542no—
208C2×C4—4542no—
209C2×C4—2274no—
210C2×C4D4×D22711yescharacteristic
211C2×C4D4×D22711yescharacteristic
212C2×C4D4×D22711yescharacteristic
213C2×C4C2×C22⋊D22711yescharacteristic
214C2×C4C2×D90811yescharacteristic
215C2×C4#1681388411yescharacteristic
216C8—22no—
217C8—4542no—
218C22#2030025811yescharacteristic
219C22#2030026111yescharacteristic
220C22#2030028411yescharacteristic
221C22Q16×D22712yes—
222C22#2030031712yes—
223C4—42no—
224C4—81no—
225C4—9082no—
226C4—9082no—
227C4—4544no—
228C4#2030025611yescharacteristic
229C4#2030025811yescharacteristic
230C4#2030026111yescharacteristic
231C4#2030026211yescharacteristic
232C2#2840894111yescharacteristic
233C2#2840918912yes—
234C2#2840924112yes—
235C2#2840941011yescharacteristic
236C2#2840942311yescharacteristic
subgroupG/H
centerC23D4×D227
commutator, cosocleC22×C4×C227C23
FrattiniC22×C4C22×D227
FittingC2×#103×C227C2
socle, prime radicalC23×C227C2×D4
hypercenterC2×#103D227
hypocenterC227#2016
LCSG ▷ C22×C4×C227 ▷ C2×C227 ▷ C227
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
80. C2×Dic227Q16semidirect
118. C227#2016semidirect

Maximal subgroups

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

subgroupindex
C22×Dic9082
C22×#168138742
C2×#203002862
C2×#203002112
#284089372
#284087862
C2×#103×C2272
#2016227