Finite Group Databasebeta

← #49133934

Subgroups — #49133934

Order 36224.

336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q8×Dic566C211yesmaximal, characteristic
2#31827190C211yesmaximal, characteristic
3#31826815C211yesmaximal, characteristic
4#31826814C212yesmaximal
5#31826761C211yesmaximal, characteristic
6#31826758C212yesmaximal
7#31826673C212yesmaximal
8#31826589C211yesmaximal, characteristic
9Q16×Dic283C212yesmaximal
10C4×#17985382C211yesmaximal, characteristic
11#462×C283C211yesmaximal, characteristic
12C2×#17985382C2211yescharacteristic
13#22583610—21no—
14#22583610C2211yescharacteristic
15#22583609—22no—
16#22583609C2212yes—
17#22583608C2212yes—
18#22583601—21no—
19#22583600—22no—
20Q8×Dic283C2212yes—
21Q8×Dic283C2212yes—
22C4×Dic566—21no—
23C4×Dic566C2211yescharacteristic
24C4×Dic566C2211yescharacteristic
25#22583575—21no—
26#22583544C2212yes—
27#22583543C2211yescharacteristic
28Dic283⋊C8C2212yes—
29#22583535C2212yes—
30#22583534C2212yes—
31#22583534C2211yescharacteristic
32#22583534C2212yes—
33#22583533C2211yescharacteristic
34C4×C283⋊C8C2211yescharacteristic
35C8×Dic283C2212yes—
36C2×Q16×C283C2212yes—
37C4⋊Q8×C283C2211yescharacteristic
38C4×Q8×C283C2211yescharacteristic
39C4⋊C8×C283C2211yescharacteristic
40#103×C283C2212yes—
41C2×Dic566—22no—
42C2×Dic566—21no—
43C2×Dic566D411yescharacteristic
44C2×Dic566C2311yescharacteristic
45#17985382—22no—
46C2×C283⋊C8C2311yescharacteristic
47C2×C283⋊C8C2311yescharacteristic
48C4⋊Dic283—22no—
49C4⋊Dic283—22no—
50C4⋊Dic283—21no—
51C4⋊Dic283D411yescharacteristic
52C4⋊Dic283C2311yescharacteristic
53C4⋊Dic283C2312yes—
54Dic283⋊C4—22no—
55Dic283⋊C4—22no—
56Dic283⋊C4—22no—
57Dic283⋊C4—21no—
58Dic283⋊C4D412yes—
59C4×Dic283—22no—
60C4×Dic283—22no—
61C4×Dic283—21no—
62C4×Dic283C2312yes—
63C2×Q8×C283C2312yes—
64C2×Q8×C283C2311yescharacteristic
65Q16×C283—24no—
66C2×C8×C283C2312yes—
67C4⋊C4×C283—21no—
68C4⋊C4×C283—21no—
69C4⋊C4×C283—21no—
70C4⋊C4×C283C2311yescharacteristic
71C42×C283—21no—
72C42×C283C2311yescharacteristic
73Dic566—21no—
74Dic566—21no—
75Dic566—82no—
76Dic566—81no—
77Dic566Q1614yescomplemented
78C2×Dic283—21no—
79C2×Dic283—21no—
80C2×Dic283—22no—
81C2×Dic283C2×D412yes—
82C2×Dic283C2×D412yes—
83C283⋊C8—21no—
84C283⋊C8—21no—
85Q8×C283—21no—
86Q8×C283—22no—
87Q8×C283—22no—
88Q8×C283#4112yes—
89C2×C4×C283—21no—
90C2×C4×C283—21no—
91C2×C4×C283—22no—
92C2×C4×C283C2×D411yescharacteristic
93C2×C4×C283C2×D411yescharacteristic
94C2×C4×C283C2411yescharacteristic
95C8×C283—22no—
96C22×C283C22×D411yescharacteristic
97C4×C283—22no—
98C4×C283—21no—
99C4×C283—42no—
100C4×C283—41no—
101C4×C283C2×Q1612yes—
102C4×C283C2×#4111yescharacteristic
103C4×C2832−1+411yescharacteristic
104Dic283—22no—
105Dic283—41no—
106Dic283—41no—
107Dic283—42no—
108Dic283C2×Q1614yes—
109C2×C283#54811yescharacteristic
110C2×C283C22×Q1611yescharacteristic
111C2×C283#57711yescharacteristic
112C283#336311yescharacteristic, complemented, Sylow
113#3363—2831nomaximal, Sylow
114Q82—2831no—
115#557—2831no—
116#487—2831no—
117#487—2832no—
118#477—2831no—
119#477—2832no—
120#462—2832no—
121#462D28311yescharacteristic
122C8×Q8—2831no—
123C4×Q16—2832no—
124C4×Q16—2831no—
125C2×Q16—2831no—
126C2×Q16C2×D28312yes—
127C4⋊Q8—2832no—
128C4⋊Q8—2832no—
129C4⋊Q8—2831no—
130C4⋊Q8—5661no—
131C4⋊Q8—5662no—
132C4⋊Q8C2×D28311yescharacteristic
133#125—5662no—
134#125—5661no—
135C4×Q8—2831no—
136C4×Q8—2832no—
137C4×Q8—2832no—
138C4×Q8—2831no—
139C4×Q8—5661no—
140C4×Q8—5661no—
141C4×Q8C2×D28311yescharacteristic
142#107—2832no—
143#107—2831no—
144C4⋊C8—2832no—
145C4⋊C8C2×D28311yescharacteristic
146#103—2831no—
147#103—2832no—
148#103—2832no—
149#103—2832no—
150#103—2831no—
151#103C2×D28312yes—
152C4×C8—2832no—
153C4×C8—2831no—
154C2×Q8—2831no—
155C2×Q8—2831no—
156C2×Q8—5662no—
157C2×Q8—5661no—
158C2×Q8C22×D28312yes—
159C2×Q8C22×D28311yescharacteristic
160Q16—24no—
161Q16—5662no—
162C2×C8—2831no—
163C2×C8—2831no—
164C2×C8C22×D28312yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—2832no—
169C4⋊C4—2831no—
170C4⋊C4—2832no—
171C4⋊C4—2831no—
172C4⋊C4—5662no—
173C4⋊C4—5662no—
174C4⋊C4—5662no—
175C4⋊C4—5662no—
176C4⋊C4—5662no—
177C4⋊C4—5661no—
178C4⋊C4—5661no—
179C4⋊C4C22×D28311yescharacteristic
180C42—21no—
181C42—2832no—
182C42—5662no—
183C42—5662no—
184C42—5661no—
185C42C22×D28311yescharacteristic
186Q8—21no—
187Q8—22no—
188Q8—22no—
189Q8—2834no—
190Q8—5661no—
191Q8—5661no—
192Q8—22641no—
193Q8—22642no—
194Q8#1798539112yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—2832no—
199C2×C4—2832no—
200C2×C4—5661no—
201C2×C4—5662no—
202C2×C4—5661no—
203C2×C4D4×D28311yescharacteristic
204C2×C4D4×D28311yescharacteristic
205C2×C4C23×D28311yescharacteristic
206C8—22no—
207C8—5661no—
208C8—5661no—
209C22C2×D4×D28311yescharacteristic
210C4—21no—
211C4—22no—
212C4—41no—
213C4—42no—
214C4—2834no—
215C4—5662no—
216C4—11322no—
217C4—11321no—
218C4—11321no—
219C4Q16×D28312yes—
220C4C2×#1798539111yescharacteristic
221C4#2258365711yescharacteristic
222C2#3182712111yescharacteristic
223C2C2×Q16×D28311yescharacteristic
224C2#3182727411yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#462×C283C2
socle, prime radicalC22×C283C22×D4
hypercenter#462D283
hypocenterC283#3363
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
77. Dic566Q16semidirect
112. C283#3363semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic5662
#318271902
#318268152
#318268142
#318267612
#318267582
#318266732
#318265892
Q16×Dic2832
C4×#179853822
#462×C2832
#3363283