Finite Group Databasebeta

← #44450802

Subgroups — #44450802

Order 29824.

228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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#28417060C211yesmaximal, characteristic
2#28416766C211yesmaximal, characteristic, complemented
3#28416763C211yesmaximal, characteristic, complemented
4#28416362C211yesmaximal, characteristic
5#28416171C211yesmaximal, characteristic, complemented
6#28416158C211yesmaximal, characteristic
7#328×C233C211yesmaximal, characteristic, complemented
8#21418515—21no—
9#21418514C2211yescharacteristic
10#21418513—21no—
11#21418513—21no—
12#21418512—21no—
13#21418511—21no—
14C2×C4⋊Dic233C2211yescharacteristic
15C2×#16836571—21no—
16C2×#16836571C2211yescharacteristic
17C22⋊C4×D233—21no—
18#21418467—21no—
19#21418466—21no—
20#21418460—21no—
21#21418459—21no—
22C22⋊#14272338C2211yescharacteristic
23#21418442—21no—
24C22⋊Q8×C233C2211yescharacteristic
25C22⋊C8×C233C2211yescharacteristic
26#95×C233C2211yescharacteristic
27C23×D233D411yescharacteristic
28C2×Dic466—21no—
29C2×Dic466D411yescharacteristic
30C22×Dic233—21no—
31C22×Dic233D411yescharacteristic
32C2×C4×D233—21no—
33C2×C4×D233—21no—
34C2×#14272338—21no—
35C4⋊Dic233—21no—
36C4⋊Dic233—21no—
37C4⋊Dic233—21no—
38C4⋊Dic233D411yescharacteristic
39#16836573—21no—
40#16836573—21no—
41#16836573—21no—
42C22⋊Dic233—21no—
43#16836571—21no—
44#16836571—21no—
45#16836571—21no—
46#16836571—21no—
47#16836571—42no—
48C2×Q8×C233D411yescharacteristic
49C22×C4×C233—21no—
50C22×C4×C233C2311yescharacteristic
51C2×C8×C233—21no—
52C4⋊C4×C233—21no—
53C4⋊C4×C233D411yescharacteristic
54C22⋊C4×C233—21no—
55C22×D233—21no—
56C22×D233—21no—
57C22×D233—41no—
58C22×D233—41no—
59C22×D233SD1612yes—
60Dic466—41no—
61Dic466—81no—
62C2×Dic233—21no—
63C2×Dic233—21no—
64C2×Dic233—21no—
65C2×Dic233—41no—
66C2×Dic233—41no—
67C2×Dic233—41no—
68C2×Dic233—41no—
69C4×D233—81no—
70C4×D233—81no—
71#14272338—41no—
72C23×C233C2×D411yescharacteristic
73Q8×C233—41no—
74C2×C4×C233—21no—
75C2×C4×C233—21no—
76C2×C4×C233—41no—
77C2×C4×C233—41no—
78C2×C4×C233—41no—
79C2×C4×C233—41no—
80C2×C4×C233C2×D411yescharacteristic
81C2×C4×C233C2×D411yescharacteristic
82C8×C233—41no—
83C22×C233—21no—
84C22×C233—21no—
85C22×C233#12011yescharacteristic
86C22×C233C2×SD1611yescharacteristic
87C22×C233#13711yescharacteristic
88C2×D233—22no—
89C2×D233—41no—
90C2×D233—41no—
91C2×D233—42no—
92C2×D233—81no—
93C4×C233—21no—
94C4×C233—21no—
95C4×C233—41no—
96C4×C233—41no—
97C4×C233—81no—
98Dic233—41no—
99Dic233—41no—
100Dic233—41no—
101Dic233—81no—
102C2×C233—21no—
103C2×C233—21no—
104C2×C233#44811yescharacteristic
105C2×C233#45511yescharacteristic
106C2×C233#45811yescharacteristic
107D233—42no—
108C233#160811yescharacteristic, complemented, Sylow
109#1608—2331nomaximal, Sylow
110#543—2331no—
111#483—2331no—
112#483—2331no—
113#397—2331no—
114#328—2331no—
115#328D23311yescharacteristic, complemented
116#323—2331no—
117C22⋊Q8—4661no—
118C22⋊Q8—4661no—
119C22⋊Q8—4661no—
120C22⋊Q8—4661no—
121C22⋊Q8—4661no—
122C22⋊Q8—2331no—
123C22⋊Q8C2×D23311yescharacteristic
124C2×C4⋊C4—2331no—
125C2×C22⋊C4—4661no—
126C2×C22⋊C4—4661no—
127C2×C22⋊C4—2331no—
128#106—4661no—
129#106—4661no—
130#103—4661no—
131#103—4661no—
132C22⋊C8—2331no—
133C22⋊C8C2×D23311yescharacteristic
134#95—4661no—
135#95C2×D23311yescharacteristic
136C24—2331no—
137C2×Q8—4661no—
138C2×Q8—2331no—
139C2×Q8D93211yescharacteristic
140C22×C4—21no—
141C22×C4—4661no—
142C22×C4—4661no—
143C22×C4—4661no—
144C22×C4—2331no—
145C22×C4C22×D23311yescharacteristic
146C2×C8—21no—
147C2×C8—4661no—
148C4⋊C4—21no—
149C4⋊C4—4661no—
150C4⋊C4—4661no—
151C4⋊C4—4661no—
152C4⋊C4—4661no—
153C4⋊C4—4661no—
154C4⋊C4—4661no—
155C4⋊C4—2331no—
156C4⋊C4D93211yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—9322no—
159C22⋊C4—4661no—
160C22⋊C4—4661no—
161C22⋊C4—4661no—
162C22⋊C4—4661no—
163C22⋊C4—4661no—
164C23—9321no—
165C23—9321no—
166C23—4661no—
167C23—4661no—
168C23—2332no—
169C23D4×D23311yescharacteristic
170Q8—41no—
171Q8—18641no—
172Q8—9321no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—18641no—
180C2×C4—18641no—
181C2×C4—9321no—
182C2×C4—9321no—
183C2×C4—9321no—
184C2×C4—9321no—
185C2×C4—4661no—
186C2×C4—4661no—
187C2×C4—4661no—
188C2×C4D4×D23311yescharacteristic
189C2×C4C2×D93211yescharacteristic
190C8—41no—
191C8—9321no—
192C22—21no—
193C22—21no—
194C22—18641no—
195C22—9322no—
196C22—9321no—
197C22—9321no—
198C22—4662no—
199C22#2141850511yescharacteristic
200C22SD16×D23311yescharacteristic
201C22#2141856711yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—18641no—
208C4—9321no—
209C4—9321no—
210C4—9321no—
211C2—21no—
212C2—21no—
213C2—9322no—
214C2#2841657511yescharacteristic
215C2#2841661411yescharacteristic
216C2#2841662611yescharacteristic
subgroupG/H
centerC22#21418505
commutator, cosocleC22×C4×C233C23
FrattiniC22×C4C22×D233
Fitting#328×C233C2
socleC22×C233#120
prime radicalC23×D233D4
hypercenter#328D233
hypocenterC233#1608
LCSG ▷ C22×C4×C233 ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #28416766C2semidirect
3. #28416763C2semidirect
5. #28416171C2semidirect
7. #328×C233C2semidirect
108. C233#1608semidirect
115. #328D233semidirect

Maximal subgroups

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

subgroupindex
#284170602
#284167662
#284167632
#284163622
#284161712
#284161582
#328×C2332
#1608233