Finite Group Databasebeta

← #46823558

Subgroups — #46823558

Order 34432.

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×Dic538C211yesmaximal, characteristic
2#31771330C211yesmaximal, characteristic
3#31770955C211yesmaximal, characteristic
4#31770954C212yesmaximal
5#31770901C211yesmaximal, characteristic
6#31770898C212yesmaximal
7#31770813C212yesmaximal
8#31770729C211yesmaximal, characteristic
9Q16×Dic269C212yesmaximal
10C4×#16864392C211yesmaximal, characteristic
11#462×C269C211yesmaximal, characteristic
12C2×#16864392C2211yescharacteristic
13#22575453—21no—
14#22575453C2211yescharacteristic
15#22575452—22no—
16#22575452C2212yes—
17#22575451C2212yes—
18#22575444—21no—
19#22575443—22no—
20Q8×Dic269C2212yes—
21Q8×Dic269C2212yes—
22C4×Dic538—21no—
23C4×Dic538C2211yescharacteristic
24C4×Dic538C2211yescharacteristic
25#22575418—21no—
26#22575387C2212yes—
27#22575386C2211yescharacteristic
28#22575382C2212yes—
29#22575378C2212yes—
30#22575377C2212yes—
31#22575377C2211yescharacteristic
32#22575377C2212yes—
33#22575376C2211yescharacteristic
34C4×#14524130C2211yescharacteristic
35C8×Dic269C2212yes—
36C2×Q16×C269C2212yes—
37C4⋊Q8×C269C2211yescharacteristic
38C4×Q8×C269C2211yescharacteristic
39C4⋊C8×C269C2211yescharacteristic
40#103×C269C2212yes—
41C2×Dic538—22no—
42C2×Dic538—21no—
43C2×Dic538D411yescharacteristic
44C2×Dic538C2311yescharacteristic
45#16864392—22no—
46C2×#14524130C2311yescharacteristic
47C2×#14524130C2311yescharacteristic
48C4⋊Dic269—22no—
49C4⋊Dic269—22no—
50C4⋊Dic269—21no—
51C4⋊Dic269D411yescharacteristic
52C4⋊Dic269C2312yes—
53C4⋊Dic269C2311yescharacteristic
54#16864381—22no—
55#16864381—22no—
56#16864381—22no—
57#16864381—21no—
58#16864381D412yes—
59C4×Dic269—22no—
60C4×Dic269—22no—
61C4×Dic269—21no—
62C4×Dic269C2312yes—
63C2×Q8×C269C2312yes—
64C2×Q8×C269C2311yescharacteristic
65Q16×C269—24no—
66C2×C8×C269C2312yes—
67C4⋊C4×C269—21no—
68C4⋊C4×C269—21no—
69C4⋊C4×C269—21no—
70C4⋊C4×C269C2311yescharacteristic
71C42×C269—21no—
72C42×C269C2311yescharacteristic
73Dic538—21no—
74Dic538—21no—
75Dic538—82no—
76Dic538—81no—
77Dic538Q1614yescomplemented
78C2×Dic269—21no—
79C2×Dic269—21no—
80C2×Dic269—22no—
81C2×Dic269C2×D412yes—
82C2×Dic269C2×D412yes—
83#14524130—21no—
84#14524130—21no—
85Q8×C269—21no—
86Q8×C269—22no—
87Q8×C269—22no—
88Q8×C269#4112yes—
89C2×C4×C269—21no—
90C2×C4×C269—21no—
91C2×C4×C269—22no—
92C2×C4×C269C2×D411yescharacteristic
93C2×C4×C269C2×D411yescharacteristic
94C2×C4×C269C2411yescharacteristic
95C8×C269—22no—
96C22×C269C22×D411yescharacteristic
97C4×C269—22no—
98C4×C269—21no—
99C4×C269—42no—
100C4×C269—41no—
101C4×C269C2×Q1612yes—
102C4×C269C2×#4111yescharacteristic
103C4×C2692−1+411yescharacteristic
104Dic269—22no—
105Dic269—41no—
106Dic269—41no—
107Dic269—42no—
108Dic269C2×Q1614yes—
109C2×C269#54811yescharacteristic
110C2×C269C22×Q1611yescharacteristic
111C2×C269#57711yescharacteristic
112C269#336311yescharacteristic, complemented, Sylow
113#3363—2691nomaximal, Sylow
114Q82—2691no—
115#557—2691no—
116#487—2691no—
117#487—2692no—
118#477—2691no—
119#477—2692no—
120#462—2692no—
121#462D26911yescharacteristic
122C8×Q8—2691no—
123C4×Q16—2692no—
124C4×Q16—2691no—
125C2×Q16—2691no—
126C2×Q16C2×D26912yes—
127C4⋊Q8—2692no—
128C4⋊Q8—2692no—
129C4⋊Q8—2691no—
130C4⋊Q8—5381no—
131C4⋊Q8—5382no—
132C4⋊Q8C2×D26911yescharacteristic
133#125—5382no—
134#125—5381no—
135C4×Q8—2691no—
136C4×Q8—2692no—
137C4×Q8—2692no—
138C4×Q8—2691no—
139C4×Q8—5381no—
140C4×Q8—5381no—
141C4×Q8C2×D26911yescharacteristic
142#107—2692no—
143#107—2691no—
144C4⋊C8—2692no—
145C4⋊C8C2×D26911yescharacteristic
146#103—2691no—
147#103—2692no—
148#103—2692no—
149#103—2692no—
150#103—2691no—
151#103C2×D26912yes—
152C4×C8—2692no—
153C4×C8—2691no—
154C2×Q8—2691no—
155C2×Q8—2691no—
156C2×Q8—5382no—
157C2×Q8—5381no—
158C2×Q8C22×D26912yes—
159C2×Q8C22×D26911yescharacteristic
160Q16—24no—
161Q16—5382no—
162C2×C8—2691no—
163C2×C8—2691no—
164C2×C8C22×D26912yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—2692no—
169C4⋊C4—2691no—
170C4⋊C4—2692no—
171C4⋊C4—2691no—
172C4⋊C4—5382no—
173C4⋊C4—5382no—
174C4⋊C4—5382no—
175C4⋊C4—5382no—
176C4⋊C4—5382no—
177C4⋊C4—5381no—
178C4⋊C4—5381no—
179C4⋊C4C22×D26911yescharacteristic
180C42—21no—
181C42—2692no—
182C42—5382no—
183C42—5382no—
184C42—5381no—
185C42C22×D26911yescharacteristic
186Q8—21no—
187Q8—22no—
188Q8—22no—
189Q8—2694no—
190Q8—5381no—
191Q8—5381no—
192Q8—21521no—
193Q8—21522no—
194Q8#1686440112yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—2692no—
199C2×C4—2692no—
200C2×C4—5381no—
201C2×C4—5382no—
202C2×C4—5381no—
203C2×C4D4×D26911yescharacteristic
204C2×C4D4×D26911yescharacteristic
205C2×C4C23×D26911yescharacteristic
206C8—22no—
207C8—5381no—
208C8—5381no—
209C22C2×D4×D26911yescharacteristic
210C4—21no—
211C4—22no—
212C4—41no—
213C4—42no—
214C4—2694no—
215C4—5382no—
216C4—10762no—
217C4—10761no—
218C4—10761no—
219C4Q16×D26912yes—
220C4C2×#1686440111yescharacteristic
221C4#2257550011yescharacteristic
222C2#3177126111yescharacteristic
223C2C2×Q16×D26911yescharacteristic
224C2#3177141411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#462×C269C2
socle, prime radicalC22×C269C22×D4
hypercenter#462D269
hypocenterC269#3363
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
77. Dic538Q16semidirect
112. C269#3363semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic5382
#317713302
#317709552
#317709542
#317709012
#317708982
#317708132
#317707292
Q16×Dic2692
C4×#168643922
#462×C2692
#3363269