Finite Group Databasebeta

← #49120287

Subgroups — #49120287

Order 36224.

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

normal subgroups only

This group has 236 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#31827090C211yesmaximal, characteristic
2#31826801C211yesmaximal, characteristic, complemented
3#31826798C211yesmaximal, characteristic, complemented
4#31826402C211yesmaximal, characteristic
5#31826201C211yesmaximal, characteristic, complemented
6#31826188C211yesmaximal, characteristic
7#328×C283C211yesmaximal, characteristic, complemented
8#22583590—21no—
9#22583589C2211yescharacteristic
10#22583588—21no—
11#22583588—21no—
12#22583587—21no—
13#22583586—21no—
14C2×C4⋊Dic283—21no—
15C2×C4⋊Dic283C2211yescharacteristic
16C2×(C2×D283)⋊C4—21no—
17C2×(C2×D283)⋊C4C2211yescharacteristic
18C22⋊C4×D283—21no—
19#22583544—21no—
20#22583543—21no—
21#22583535—21no—
22#22583534—21no—
23C22⋊(C283⋊C8)C2211yescharacteristic
24C22⋊Q8×C283C2211yescharacteristic
25C22⋊C8×C283C2211yescharacteristic
26#95×C283C2211yescharacteristic
27C23×D283D411yescharacteristic
28C2×Dic566—21no—
29C2×Dic566D411yescharacteristic
30C22×Dic283—21no—
31C22×Dic283D411yescharacteristic
32C2×C4×D283—21no—
33C2×C4×D283—21no—
34C2×C283⋊C8—21no—
35C4⋊Dic283—21no—
36C4⋊Dic283—21no—
37C4⋊Dic283—21no—
38C4⋊Dic283—42no—
39C4⋊Dic283D411yescharacteristic
40Dic283⋊C4—21no—
41Dic283⋊C4—21no—
42Dic283⋊C4—21no—
43C22⋊Dic283—21no—
44(C2×D283)⋊C4—21no—
45(C2×D283)⋊C4—21no—
46(C2×D283)⋊C4—21no—
47(C2×D283)⋊C4—21no—
48(C2×D283)⋊C4—42no—
49C2×Q8×C283D411yescharacteristic
50C22×C4×C283—21no—
51C22×C4×C283C2311yescharacteristic
52C2×C8×C283—21no—
53C4⋊C4×C283—21no—
54C4⋊C4×C283D411yescharacteristic
55C22⋊C4×C283—21no—
56C22×D283—21no—
57C22×D283—21no—
58C22×D283—41no—
59C22×D283—41no—
60C22×D283Q1612yes—
61Dic566—41no—
62Dic566—81no—
63C2×Dic283—21no—
64C2×Dic283—21no—
65C2×Dic283—21no—
66C2×Dic283—41no—
67C2×Dic283—41no—
68C2×Dic283—41no—
69C2×Dic283—41no—
70C4×D283—81no—
71C4×D283—81no—
72C283⋊C8—41no—
73C23×C283C2×D411yescharacteristic
74Q8×C283—41no—
75C2×C4×C283—22no—
76C2×C4×C283—21no—
77C2×C4×C283—21no—
78C2×C4×C283—41no—
79C2×C4×C283—41no—
80C2×C4×C283—41no—
81C2×C4×C283C2×D411yescharacteristic
82C2×C4×C283C2×D411yescharacteristic
83C8×C283—41no—
84C22×C283—21no—
85C22×C283—21no—
86C22×C283#12011yescharacteristic
87C22×C283C2×Q1611yescharacteristic
88C22×C283#13711yescharacteristic
89C2×D283—22no—
90C2×D283—41no—
91C2×D283—41no—
92C2×D283—42no—
93C2×D283—81no—
94C4×C283—21no—
95C4×C283—21no—
96C4×C283—42no—
97C4×C283—41no—
98C4×C283—41no—
99Dic283—41no—
100Dic283—41no—
101Dic283—41no—
102Dic283—81no—
103C2×C283—21no—
104C2×C283—21no—
105C2×C283#45111yescharacteristic
106C2×C283#45311yescharacteristic
107C2×C283#45811yescharacteristic
108D283—42no—
109C283#161411yescharacteristic, complemented, Sylow
110#1614—2831nomaximal, Sylow
111#543—2831no—
112#484—2831no—
113#484—2831no—
114#399—2831no—
115#328—2831no—
116#328D28311yescharacteristic, complemented
117#323—2831no—
118C22⋊Q8—2831no—
119C22⋊Q8—5661no—
120C22⋊Q8—5661no—
121C22⋊Q8—5661no—
122C22⋊Q8—5661no—
123C22⋊Q8—5661no—
124C22⋊Q8C2×D28311yescharacteristic
125C2×C4⋊C4—2831no—
126C2×C4⋊C4—5661no—
127C2×C22⋊C4—2831no—
128C2×C22⋊C4—5661no—
129C2×C22⋊C4—5661no—
130#107—5661no—
131#107—5661no—
132#103—5661no—
133#103—5661no—
134C22⋊C8—2831no—
135C22⋊C8C2×D28311yescharacteristic
136#95C2×D28311yescharacteristic
137C24—2831no—
138C2×Q8—2831no—
139C2×Q8—5661no—
140C2×Q8D113211yescharacteristic
141C22×C4—21no—
142C22×C4—2831no—
143C22×C4—5661no—
144C22×C4—5661no—
145C22×C4—5661no—
146C22×C4C22×D28311yescharacteristic
147C2×C8—21no—
148C2×C8—5661no—
149C4⋊C4—21no—
150C4⋊C4—2831no—
151C4⋊C4—5661no—
152C4⋊C4—5661no—
153C4⋊C4—5661no—
154C4⋊C4—5661no—
155C4⋊C4—5661no—
156C4⋊C4—5661no—
157C4⋊C4—11322no—
158C4⋊C4D113211yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—5661no—
161C22⋊C4—5661no—
162C22⋊C4—5661no—
163C22⋊C4—5661no—
164C22⋊C4—5661no—
165C22⋊C4—11322no—
166C23—2832no—
167C23—5661no—
168C23—5661no—
169C23—11321no—
170C23—11321no—
171C23D4×D28311yescharacteristic
172Q8—41no—
173Q8—11321no—
174Q8—22641no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—5661no—
182C2×C4—5661no—
183C2×C4—5661no—
184C2×C4—11321no—
185C2×C4—11321no—
186C2×C4—11321no—
187C2×C4—11321no—
188C2×C4—22641no—
189C2×C4—22641no—
190C2×C4D4×D28311yescharacteristic
191C2×C4C2×D113211yescharacteristic
192C8—41no—
193C8—11321no—
194C22—21no—
195C22—21no—
196C22—5662no—
197C22—11322no—
198C22—11321no—
199C22—11321no—
200C22—22641no—
201C22#2258358011yescharacteristic
202C22Q16×D28311yescharacteristic
203C22#2258363911yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—11321no—
210C4—11321no—
211C4—11321no—
212C4—22641no—
213C2—21no—
214C2—21no—
215C2—11322no—
216C2#3182662211yescharacteristic
217C2#3182663411yescharacteristic
218C2#3182665611yescharacteristic
subgroupG/H
centerC22#22583580
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#328×C283C2
socleC22×C283#120
prime radicalC23×D283D4
hypercenter#328D283
hypocenterC283#1614
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #31826801C2semidirect
3. #31826798C2semidirect
5. #31826201C2semidirect
7. #328×C283C2semidirect
109. C283#1614semidirect
116. #328D283semidirect

Maximal subgroups

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

subgroupindex
#318270902
#318268012
#318267982
#318264022
#318262012
#318261882
#328×C2832
#1614283