Finite Group Databasebeta

← #13069708

Subgroups — #13069708

Order 1408.

390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C22×C11×SD16C211yesmaximal, characteristic
2C22×#4326C211yesmaximal, characteristic, complemented
3C2×#66989C211yesmaximal, characteristic
4#10622843C211yesmaximal, characteristic, complemented
5C2×#66896C211yesmaximal, characteristic
6C2×#66880C211yesmaximal, characteristic, complemented
7#10622188C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2211yescharacteristic
9C22×D4×C11C2211yescharacteristic
10C22×Dic22C2211yescharacteristic
11C2×C11×SD16—22no—
12C2×C11×SD16—22no—
13C2×C11×SD16—22no—
14C22×C8×C11C2211yescharacteristic
15C2×C22⋊Dic11—22no—
16C2×#4326—22no—
17C2×#4326—22no—
18C2×#4326—22no—
19#66989—22no—
20#66989—22no—
21C2×C4⋊Dic11C2211yescharacteristic
22C2×C4×Dic11C2211yescharacteristic
23C22×C11⋊C8C2211yescharacteristic
24#66896—22no—
25C11⋊#95—22no—
26#66880—22no—
27C24×C11—21no—
28C2×Q8×C11—21no—
29C2×Q8×C11—21no—
30C2×Q8×C11—21no—
31C2×Q8×C11—21no—
32C2×Q8×C11—21no—
33C2×Q8×C11D412yes—
34C2×D4×C11—21no—
35C2×D4×C11—21no—
36C2×D4×C11—21no—
37C2×D4×C11—21no—
38C2×D4×C11—21no—
39C2×D4×C11D412yes—
40C22×C4×C11—21no—
41C22×C4×C11C2311yescharacteristic
42C22×Dic11—21no—
43C22×Dic11—21no—
44C22×Dic11D412yes—
45C2×Dic22—21no—
46C2×Dic22—21no—
47C2×Dic22—21no—
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22D412yes—
51C11×SD16—28no—
52C2×C8×C11—21no—
53C2×C8×C11—21no—
54C2×C8×C11D412yes—
55C22⋊Dic11—28no—
56#4326—28no—
57C4⋊Dic11—21no—
58C4⋊Dic11—21no—
59C4×Dic11—21no—
60C4×Dic11—21no—
61C2×C11⋊C8—21no—
62C2×C11⋊C8—21no—
63C2×C11⋊C8D412yes—
64#2015—111nomaximal, Sylow
65C23×C11—22no—
66C23×C11—41no—
67C23×C11—41no—
68C23×C11—42no—
69C23×C11—42no—
70C23×C11C2×D411yescharacteristic
71Q8×C11—22no—
72Q8×C11—22no—
73Q8×C11—41no—
74Q8×C11—41no—
75D4×C11—22no—
76D4×C11—22no—
77D4×C11—41no—
78D4×C11—41no—
79C2×C4×C11—22no—
80C2×C4×C11—41no—
81C2×C4×C11—41no—
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2×D411yescharacteristic
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11#4111yescharacteristic
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—41no—
93C2×Dic11—41no—
94C2×Dic11—41no—
95C2×Dic11—42no—
96Dic22—22no—
97Dic22—22no—
98Dic22—41no—
99Dic22—41no—
100C8×C11—22no—
101C11⋊C8—22no—
102C22×Q16—111no—
103C22×SD16D1111yescharacteristic
104C2×#124—111no—
105C2×#103—111no—
106C2×#102—111no—
107#391—111no—
108#336—111no—
109C22×C11—42no—
110C22×C11—44no—
111C22×C11—82no—
112C22×C11—81no—
113C22×C11—81no—
114C22×C11#12011yescharacteristic
115C22×C11#12111yescharacteristic
116C22×C11#12711yescharacteristic
117C22×C11#13512yes—
118C22×C11#13712yes—
119C4×C11—42no—
120C4×C11#12011yescharacteristic
121C4×C11#12011yescharacteristic
122C4×C11#12111yescharacteristic
123C4×C11#12111yescharacteristic
124Dic11—42no—
125Dic11—42no—
126Dic11—81no—
127C22×Q8—111no—
128C22×Q8C2×D1111yescharacteristic
129C22×D4C2×D1111yescharacteristic
130C2×Q16—222no—
131C2×Q16—222no—
132C2×Q16—222no—
133C2×SD16—22no—
134C2×SD16—22no—
135C2×SD16—22no—
136C22×C8—111no—
137C22×C8C2×D1111yescharacteristic
138#124—222no—
139#124—222no—
140C2×C4⋊C4—111no—
141C2×C22⋊C4—222no—
142C2×C42—111no—
143#103—222no—
144#102—222no—
145#95—222no—
146C2×C11—82no—
147C2×C11#39211yescharacteristic
148C2×C11#45212yes—
149C2×C11#46412yes—
150C2×C11#49511yescharacteristic
151C2×C11#49711yescharacteristic
152C24—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—112no—
159C2×Q8—221no—
160C2×Q8—221no—
161C2×Q8—221no—
162C2×Q8—221no—
163C2×Q8—221no—
164C2×Q8C22⋊D1112yes—
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4C22⋊D1112yes—
171C22×C4—21no—
172C22×C4—112no—
173C22×C4—221no—
174C22×C4—221no—
175C22×C4C22×D1111yescharacteristic
176Q16—228no—
177SD16—28no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—112no—
181C2×C8—221no—
182C2×C8—221no—
183C2×C8C22⋊D1112yes—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C22⋊C4—228no—
187C42—221no—
188C42—221no—
189C11#201511yescharacteristic, complemented, Sylow
190C23—22no—
191C23—42no—
192C23—42no—
193C23—41no—
194C23—41no—
195C23D4×D1111yescharacteristic
196Q8—22no—
197Q8—22no—
198Q8—41no—
199Q8—41no—
200Q8—222no—
201Q8—222no—
202Q8—441no—
203Q8—441no—
204D4—22no—
205D4—22no—
206D4—41no—
207D4—41no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—441no—
216C2×C4—441no—
217C2×C4—442no—
218C2×C4—441no—
219C2×C4D4×D1111yescharacteristic
220C2×C4D4×D1111yescharacteristic
221C2×C4#434111yescharacteristic
222C2×C4C2×C22⋊D1111yescharacteristic
223C2×C4C2×C22⋊D1111yescharacteristic
224C2×C4C2×C22⋊D1111yescharacteristic
225C8—22no—
226C8—222no—
227C22—44no—
228C22—42no—
229C22—82no—
230C22—81no—
231C22—81no—
232C22#6696812yes—
233C22#6696912yes—
234C22#6699011yescharacteristic
235C22#6699211yescharacteristic
236C22#6699311yescharacteristic
237C4—42no—
238C4—442no—
239C4—442no—
240C4—881no—
241C4#6699011yescharacteristic
242C4#6699111yescharacteristic
243C4#6699211yescharacteristic
244C4#6700611yescharacteristic
245C2—82no—
246C2#1062277912yes—
247C2#1062278011yescharacteristic
248C2#1062278111yescharacteristic
249C2#1062278612yes—
250C2#1062283611yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC22×C11×SD16C2
socleC23×C11C2×D4
prime radicalC22×D4×C11C22
hypercenterC22×SD16D11
hypocenterC11#2015
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C22×#4326C2semidirect
4. #10622843C2semidirect
6. C2×#66880C2semidirect
7. #10622188C2semidirect
189. C11#2015semidirect

Maximal subgroups

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

subgroupindex
C22×C11×SD162
C22×#43262
C2×#669892
#106228432
C2×#668962
C2×#668802
#106221882
#201511