Finite Group Databasebeta

← #20256322

Subgroups — #20256322

Order 6016.

326 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 133 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×Dic94C211yesmaximal, characteristic
2#15689851C211yesmaximal, characteristic
3#15689532C212yesmaximal
4#15689521C211yesmaximal, characteristic
5#15689431C212yesmaximal
6#15689419C211yesmaximal, characteristic
7#15689409C211yesmaximal, characteristic
8#15689409C212yesmaximal
9#15689231C212yesmaximal
10C4×Dic188C211yesmaximal, characteristic
11C47×#446C211yesmaximal, characteristic
12C2×Dic188C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094024C2212yes—
16#13094023—21no—
17#13094023—22no—
18#13094022—21no—
19#13094016C2212yes—
20#13094014—22no—
21Q8×Dic47—21no—
22C4×Dic94C2211yescharacteristic
23C4×Dic94C2211yescharacteristic
24C4×Dic94C2212yes—
25C4×Dic94C2212yes—
26#13093989—21no—
27#13093958C2211yescharacteristic
28#13093958C2212yes—
29#13093956C2212yes—
30#13093956C2212yes—
31#13093956C2212yes—
32#13093949C2211yescharacteristic
33#13093949C2211yescharacteristic
34#13093949C2212yes—
35#13093949C2212yes—
36C4×Q8×C47C2211yescharacteristic
37C4⋊C8×C47C2211yescharacteristic
38C4⋊C8×C47C2212yes—
39#97×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47D411yescharacteristic
42C2×Dic94—21no—
43C2×Dic94—22no—
44C2×Dic94—21no—
45C2×Dic94C2311yescharacteristic
46C2×Dic94C2311yescharacteristic
47C2×C8×C47C2311yescharacteristic
48C2×C8×C47C2312yes—
49C2×C8×C47C2311yescharacteristic
50C4⋊C4×C47D411yescharacteristic
51C4⋊C4×C47D412yes—
52C42×C47C2312yes—
53C42×C47C2311yescharacteristic
54C4⋊Dic47—22no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47C2312yes—
58C4⋊Dic47C2311yescharacteristic
59C4⋊Dic47C2312yes—
60C4⋊Dic47C2311yescharacteristic
61Dic47⋊C4—22no—
62Dic47⋊C4—21no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4—21no—
66Dic47⋊C4—22no—
67C4×Dic47—22no—
68C4×Dic47—21no—
69C4×Dic47—22no—
70C4×Dic47—21no—
71Dic188Q814yescomplemented
72Q8×C47—22no—
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2411yescharacteristic
78C2×Dic47—21no—
79C2×Dic47—21no—
80C2×Dic47—21no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—21no—
84Dic94—21no—
85Dic94—21no—
86Dic94—42no—
87Dic94—82no—
88Dic94—81no—
89Dic94C2×Q812yes—
90Dic94C2×Q812yes—
91C8×C47—21no—
92C8×C47—22no—
93C8×C47C2×Q812yes—
94C22×C47C22×D411yescharacteristic
95C4×C47—22no—
96C4×C47—22no—
97C4×C47—21no—
98C4×C47#13712yes—
99C4×C47C22×Q811yescharacteristic
100C4×C472−1+411yescharacteristic
101Dic47—22no—
102Dic47—22no—
103Dic47—42no—
104Dic47—41no—
105Dic47—42no—
106Dic47—41no—
107#3387—471nomaximal, Sylow
108C2×C47D4×Q811yescharacteristic
109C2×C47C2×#13711yescharacteristic
110C2×C47#57711yescharacteristic
111Q82—471no—
112#557—471no—
113#501—472no—
114#498—471no—
115#479—472no—
116#477—471no—
117#475—472no—
118#475—471no—
119#446D4711yescharacteristic
120#441—472no—
121C4×Q16—471no—
122C47#338711yescharacteristic, complemented, Sylow
123C2×Q16—471no—
124C4⋊Q8—471no—
125C4⋊Q8—472no—
126C4⋊Q8—471no—
127C4⋊Q8—941no—
128C4⋊Q8—941no—
129C4⋊Q8—942no—
130#125—472no—
131#125—942no—
132C4×Q8—471no—
133C4×Q8—472no—
134C4×Q8—471no—
135C4×Q8—472no—
136C4×Q8—941no—
137C4×Q8—941no—
138C4×Q8C2×D4711yescharacteristic
139#107—471no—
140#107—472no—
141#106—472no—
142#106—472no—
143#106—472no—
144C4⋊C8C2×D4711yescharacteristic
145C4⋊C8C2×D4712yes—
146#103—471no—
147#103—471no—
148#103—472no—
149#103—472no—
150#97C2×D4712yes—
151C4×C8C2×D4711yescharacteristic
152C2×Q8—471no—
153C2×Q8—471no—
154C2×Q8—942no—
155C2×Q8—941no—
156C2×Q8—941no—
157C2×Q8D18811yescharacteristic
158Q16—474no—
159C2×C8C22×D4711yescharacteristic
160C2×C8C22×D4712yes—
161C2×C8C22×D4711yescharacteristic
162C4⋊C4—472no—
163C4⋊C4—471no—
164C4⋊C4—472no—
165C4⋊C4—471no—
166C4⋊C4—941no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4—941no—
170C4⋊C4—942no—
171C4⋊C4—942no—
172C4⋊C4—942no—
173C4⋊C4—941no—
174C4⋊C4—941no—
175C4⋊C4D18811yescharacteristic
176C4⋊C4D18812yes—
177C42—942no—
178C42—941no—
179C42—942no—
180C42—941no—
181C42C22×D4711yescharacteristic
182C42C22×D4712yes—
183Q8—22no—
184Q8—472no—
185Q8—472no—
186Q8—941no—
187Q8—941no—
188Q8—3762no—
189Q8—3761no—
190Q8—1882no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—941no—
194C2×C4—942no—
195C2×C4—942no—
196C2×C4—941no—
197C2×C4C2×D18812yes—
198C2×C4C2×D18812yes—
199C2×C4C2×D18811yescharacteristic
200C2×C4C2×D18811yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—21no—
203C8—22no—
204C8Q8×D4712yes—
205C22C22×D18811yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—942no—
210C4—942no—
211C4—1882no—
212C4—1882no—
213C4—1881no—
214C4—1881no—
215C4#1309405712yes—
216C4C2×Q8×D4711yescharacteristic
217C4#1309407111yescharacteristic
218C2Q8×D18811yescharacteristic
219C2C2×#1309405711yescharacteristic
220C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#446C2
socleC22×C47C22×D4
hypercenter#446D47
hypocenterC47#3387
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
71. Dic188Q8semidirect
122. C47#3387semidirect