Finite Group Databasebeta

← #49134263

Subgroups — #49134263

Order 36224.

348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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#31827193C211yesmaximal, characteristic
2#31827190C211yesmaximal, characteristic
3#31826844C211yesmaximal, characteristic
4#31826843C212yesmaximal
5#31826676C211yesmaximal, characteristic
6#31826674C212yesmaximal
7#31826673C212yesmaximal
8#31826589C211yesmaximal, characteristic
9C4×#17985382C211yesmaximal, characteristic
10#31826557C212yesmaximal
11#462×C283C211yesmaximal, characteristic
12C2×Dic1132C2212yes—
13C2×#17985382C2212yes—
14C2×#17985382C2211yescharacteristic
15C2×#17985382C2212yes—
16#22583610C2211yescharacteristic
17#22583608C2212yes—
18#22583608C2212yes—
19#22583602—21no—
20#22583601—21no—
21#22583600—22no—
22#22583600—22no—
23Q8×Dic283C2212yes—
24C4×Dic566—21no—
25C4×Dic566C2211yescharacteristic
26C4×Dic566C2211yescharacteristic
27#22583575—21no—
28#22583575C2212yes—
29#22583543C2211yescharacteristic
30Dic283⋊C8C2212yes—
31#22583535C2212yes—
32#22583534C2211yescharacteristic
33#22583533C2211yescharacteristic
34C4×C283⋊C8C2211yescharacteristic
35C8×Dic283C2212yes—
36C2×Q16×C283C2212yes—
37C4⋊Q8×C283C2211yescharacteristic
38C4×Q8×C283C2211yescharacteristic
39C4⋊C8×C283C2211yescharacteristic
40#103×C283C2212yes—
41C2×Dic566D411yescharacteristic
42C2×Dic566C2312yes—
43C2×Dic566C2311yescharacteristic
44Dic1132—42no—
45#17985382—24no—
46#17985382—22no—
47#17985382—42no—
48C2×C283⋊C8C2311yescharacteristic
49C2×C283⋊C8C2311yescharacteristic
50C4⋊Dic283—22no—
51C4⋊Dic283—21no—
52C4⋊Dic283—21no—
53C4⋊Dic283D411yescharacteristic
54C4⋊Dic283C2311yescharacteristic
55Dic283⋊C4—22no—
56Dic283⋊C4—22no—
57Dic283⋊C4—22no—
58Dic283⋊C4—22no—
59Dic283⋊C4—22no—
60Dic283⋊C4—21no—
61Dic283⋊C4D412yes—
62C4×Dic283—22no—
63C4×Dic283—22no—
64C4×Dic283—21no—
65C4×Dic283C2312yes—
66C2×Q8×C283C2312yes—
67C2×Q8×C283C2311yescharacteristic
68Q16×C283—42no—
69C2×C8×C283C2312yes—
70C4⋊C4×C283—21no—
71C4⋊C4×C283—21no—
72C4⋊C4×C283—21no—
73C4⋊C4×C283C2311yescharacteristic
74C42×C283—21no—
75C42×C283C2311yescharacteristic
76Dic566—22no—
77Dic566—21no—
78Dic566—22no—
79Dic566—21no—
80Dic566Q1614yescomplemented
81C2×Dic283—21no—
82C2×Dic283—21no—
83C2×Dic283—22no—
84C2×Dic283C2×D412yes—
85C2×Dic283C2×D412yes—
86C283⋊C8—21no—
87C283⋊C8#4112yes—
88Q8×C283—22no—
89Q8×C283—21no—
90Q8×C283—21no—
91Q8×C283—22no—
92C2×C4×C283—21no—
93C2×C4×C283—21no—
94C2×C4×C283—22no—
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283C2×D411yescharacteristic
97C2×C4×C283C2411yescharacteristic
98C8×C283—22no—
99C22×C283C22×D411yescharacteristic
100C4×C283—21no—
101C4×C283—41no—
102C4×C283—42no—
103C4×C283—41no—
104C4×C283C2×Q1612yes—
105C4×C283C2×#4111yescharacteristic
106C4×C283H(5,𝔽2)11yescharacteristic
107Dic283—22no—
108Dic283—41no—
109Dic283—42no—
110Dic283—41no—
111Dic283C2×Q1614yes—
112C2×C283#55011yescharacteristic
113C2×C283C22×Q1611yescharacteristic
114C2×C283#57811yescharacteristic
115C283#339511yescharacteristic, complemented, Sylow
116#3395—2831nomaximal, Sylow
117#557—2831no—
118#557—2831no—
119#494—2832no—
120#494—2831no—
121#462—2832no—
122#462—2831no—
123#462—2832no—
124#462D28311yescharacteristic
125C8×Q8—2831no—
126C4×Q16—2831no—
127C4×Q16—2832no—
128C2×Q16—2831no—
129C2×Q16—2832no—
130C2×Q16—2832no—
131C2×Q16—2832no—
132C2×Q16C2×D28312yes—
133C4⋊Q8—2832no—
134C4⋊Q8—2832no—
135C4⋊Q8—2831no—
136C4⋊Q8C2×D28311yescharacteristic
137#125—5661no—
138#125—5662no—
139#125—5662no—
140#125—5661no—
141C4×Q8—2831no—
142C4×Q8—2832no—
143C4×Q8—2832no—
144C4×Q8—2831no—
145C4×Q8—5661no—
146C4×Q8—5661no—
147C4×Q8C2×D28311yescharacteristic
148#107—2831no—
149C4⋊C8—2832no—
150C4⋊C8C2×D28311yescharacteristic
151#103—2831no—
152#103—2832no—
153#103—2831no—
154#103C2×D28312yes—
155C4×C8—2832no—
156C4×C8—2831no—
157C2×Q8—2831no—
158C2×Q8—2832no—
159C2×Q8—2831no—
160C2×Q8C22×D28311yescharacteristic
161C2×Q8C22×D28312yes—
162Q16—42no—
163Q16—5662no—
164Q16—5664no—
165Q16—11322no—
166Q16—11322no—
167C2×C8—2831no—
168C2×C8—2831no—
169C2×C8C22×D28312yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—2832no—
174C4⋊C4—2831no—
175C4⋊C4—2831no—
176C4⋊C4—5662no—
177C4⋊C4—5662no—
178C4⋊C4—5662no—
179C4⋊C4—5662no—
180C4⋊C4—5662no—
181C4⋊C4—5662no—
182C4⋊C4—5661no—
183C4⋊C4—5661no—
184C4⋊C4—5661no—
185C4⋊C4C22×D28311yescharacteristic
186C42—21no—
187C42—2832no—
188C42—5662no—
189C42—5662no—
190C42—5661no—
191C42C22×D28311yescharacteristic
192Q8—21no—
193Q8—22no—
194Q8—21no—
195Q8—22no—
196Q8—2834no—
197Q8—5662no—
198Q8—5661no—
199Q8—5661no—
200Q8—5662no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—2832no—
205C2×C4—2832no—
206C2×C4—5661no—
207C2×C4—5662no—
208C2×C4—5661no—
209C2×C4D4×D28311yescharacteristic
210C2×C4D4×D28311yescharacteristic
211C2×C4C23×D28311yescharacteristic
212C8—22no—
213C8—2832no—
214C8—5661no—
215C22C2×D4×D28311yescharacteristic
216C4—21no—
217C4—41no—
218C4—41no—
219C4—42no—
220C4—2834no—
221C4—5662no—
222C4—11321no—
223C4—11322no—
224C4—11321no—
225C4Q16×D28312yes—
226C4#41×D28311yescharacteristic
227C4#2258365511yescharacteristic
228C2#3182713311yescharacteristic
229C2C2×Q16×D28311yescharacteristic
230C2#3182728111yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#462×C283C2
socle, prime radicalC22×C283C22×D4
hypercenter#462D283
hypocenterC283#3395
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
80. Dic566Q16semidirect
115. C283#3395semidirect

Maximal subgroups

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

subgroupindex
#318271932
#318271902
#318268442
#318268432
#318266762
#318266742
#318266732
#318265892
C4×#179853822
#318265572
#462×C2832
#3395283