Finite Group Databasebeta

← #15761411

Subgroups — #15761411

Order 3328.

282 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 89 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#13113627C211yesmaximal, characteristic
2#13113501C211yesmaximal, characteristic
3#13113257C211yesmaximal, characteristic
4#13113128C211yesmaximal, characteristic
5#13112725C211yesmaximal, characteristic
6#13112673C211yesmaximal, characteristic
7C13×#1493C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#423C2211yescharacteristic
10C2×C4×C8×C13C2211yescharacteristic
11#11718586C2211yescharacteristic
12#11718586C2211yescharacteristic
13#11718586C2211yescharacteristic
14C4×#6099C2211yescharacteristic
15C13×Q8⋊C8—22no—
16#11718139C411yescharacteristic
17#11718139C411yescharacteristic
18#11718139C411yescharacteristic
19#11718139C411yescharacteristic
20Q8⋊#1055—21no—
21Q8⋊#1055—21no—
22#11718072—21no—
23#11718071—21no—
24#11718046—22no—
25C2×C13×M16—21no—
26C22×C8×C13—21no—
27C13×C4⋊Q8C2×C411yescharacteristic
28C13×C4⋊Q8C2×C411yescharacteristic
29C13×#125—21no—
30C13×C22⋊Q8—21no—
31C13×C22⋊Q8—21no—
32C4×Q8×C13—21no—
33C4×Q8×C13—21no—
34C13×#117—21no—
35C2×C42×C13C2311yescharacteristic
36C2×#6099—21no—
37C13×C4⋊C8—21no—
38C13×C4⋊C8—21no—
39C4×C8×C13—21no—
40C4×C8×C13D412yes—
41C22⋊#1055—21no—
42C22⋊#1055—21no—
43C22⋊#1055—21no—
44C4⋊#1055C2×C411yescharacteristic
45C4⋊#1055C2×C411yescharacteristic
46C4⋊#1055C2×C411yescharacteristic
47C4⋊#1055C2×C411yescharacteristic
48C4⋊#1055D411yescharacteristic
49C4⋊#1055D411yescharacteristic
50#88043—21no—
51C4×#1055—21no—
52C4×#1055—21no—
53C4×#1055—21no—
54C4×#1055—21no—
55#9587—131nomaximal, Sylow
56C2×Q8×C13—21no—
57C2×Q8×C13—21no—
58C22×C4×C13#4111yescharacteristic
59C22×C4×C13#4111yescharacteristic
60C22×C4×C13#4111yescharacteristic
61C13×M16—81no—
62C2×C8×C13—22no—
63C2×C8×C13—41no—
64C2×C8×C13—41no—
65C2×C8×C13—41no—
66C13×C4⋊C4—21no—
67C13×C4⋊C4—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—41no—
71C13×C4⋊C4—41no—
72C13×C22⋊C4—41no—
73C42×C13—41no—
74C42×C13C22×C411yescharacteristic
75C42×C13C2×D411yescharacteristic
76C42×C13C2×D411yescharacteristic
77C42×C13#4111yescharacteristic
78#6099—22no—
79#6099—41no—
80C2×#1055—21no—
81C2×#1055—21no—
82C2×#1055—21no—
83C2×#1055—21no—
84C2×#1055—21no—
85C2×#1055—21no—
86C2×#1055—41no—
87#1574—131no—
88#1544—131no—
89#1493D1311yescharacteristic
90#1485—131no—
91#1452—131no—
92#1299—131no—
93#1278—131no—
94C23×C13#12611yescharacteristic
95Q8×C13—41no—
96Q8×C13—41no—
97Q8×C13—41no—
98Q8×C13—41no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13#11711yescharacteristic
108C2×C4×C13C4×D411yescharacteristic
109C2×C4×C13C4×D411yescharacteristic
110C2×C4×C13#12111yescharacteristic
111C2×C4×C13#12311yescharacteristic
112C2×C4×C13#12411yescharacteristic
113C8×C13—42no—
114C8×C13—81no—
115#1055—42no—
116#1055—41no—
117#1055—41no—
118#1055—41no—
119#1055—41no—
120#1055—41no—
121#1055—41no—
122#533C2×D1311yescharacteristic
123#431—131no—
124#431—131no—
125#431—131no—
126#423C2×D1311yescharacteristic
127C4×M16—131no—
128C2×C4×C8C2×D1311yescharacteristic
129#335—261no—
130#334—261no—
131#332—131no—
132#332—131no—
133#332—131no—
134#332—131no—
135Q8⋊C8—22no—
136Q8⋊C8—261no—
137Q8⋊C8—261no—
138#322—262no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13#38811yescharacteristic
143C4×C13—21no—
144C4×C13—21no—
145C4×C13—21no—
146C4×C13—81no—
147C4×C13—81no—
148C4×C13#44311yescharacteristic
149C4×C13#44411yescharacteristic
150C4×C13#44411yescharacteristic
151C4×C13#44411yescharacteristic
152C4×C13#47111yescharacteristic
153C4×C13#47311yescharacteristic
154C2×M16—21no—
155C2×M16—261no—
156C22×C8—21no—
157C4⋊Q8C4×D1311yescharacteristic
158C4⋊Q8C4×D1311yescharacteristic
159#125—21no—
160C22⋊Q8—21no—
161C22⋊Q8—21no—
162C4×Q8—21no—
163C4×Q8—21no—
164#117—21no—
165C2×C42C22×D1311yescharacteristic
166C4⋊C8—21no—
167C4⋊C8—21no—
168C4⋊C8—131no—
169C4⋊C8—131no—
170C4⋊C8—131no—
171C4⋊C8—131no—
172C4⋊C8—131no—
173C4⋊C8—131no—
174C22⋊C8—261no—
175C22⋊C8—261no—
176C22⋊C8—261no—
177#97—261no—
178C4×C8—21no—
179C4×C8—261no—
180C4×C8—261no—
181C4×C8—261no—
182C4×C8—261no—
183C4×C8C22⋊D1312yes—
184C2×C13—41no—
185C2×C13#192911yescharacteristic
186C2×C13#193011yescharacteristic
187C2×C13#193811yescharacteristic
188C2×Q8—21no—
189C2×Q8—21no—
190C22×C4#612711yescharacteristic
191C22×C4#612911yescharacteristic
192C22×C4#612911yescharacteristic
193M16—81no—
194M16—262no—
195M16—521no—
196C2×C8—22no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—261no—
201C2×C8—261no—
202C2×C8—261no—
203C2×C8—261no—
204C2×C8—261no—
205C2×C8—261no—
206C2×C8—521no—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—21no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C22⋊C4—41no—
214C42—41no—
215C42C2×C4×D1311yescharacteristic
216C42D4×D1311yescharacteristic
217C42#612911yescharacteristic
218C42C2×C22⋊D1311yescharacteristic
219C13#958711yescharacteristic, complemented, Sylow
220C23#8813311yescharacteristic
221Q8—41no—
222Q8—41no—
223Q8—41no—
224Q8—41no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4#8813111yescharacteristic
234C2×C4#8813511yescharacteristic
235C2×C4#8813911yescharacteristic
236C2×C4C4×C22⋊D1311yescharacteristic
237C2×C4#8818911yescharacteristic
238C2×C4#8819211yescharacteristic
239C8—42no—
240C8—81no—
241C8—522no—
242C8—521no—
243C8—521no—
244C8—521no—
245C8—521no—
246C8—521no—
247C8—521no—
248C22—21no—
249C22—21no—
250C22—21no—
251C22#1171860511yescharacteristic
252C4—21no—
253C4—21no—
254C4—21no—
255C4—81no—
256C4—81no—
257C4#1171848411yescharacteristic
258C4#1171848411yescharacteristic
259C4#1171880511yescharacteristic
260C4#1171880611yescharacteristic
261C4#1171883811yescharacteristic
262C4#1171885311yescharacteristic
263C2—41no—
264C2#1311548111yescharacteristic
265C2#1311548811yescharacteristic
266C2#1311554411yescharacteristic
subgroupG/H
centerC2×C4#88192
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1493C2
socleC22×C13#388
prime radicalC23×C13#126
cosocleC2×C42×C13C23
hypercenter#1493D13
hypocenterC13#9587
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
219. C13#9587semidirect

Maximal subgroups

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

subgroupindex
#131136272
#131135012
#131132572
#131131282
#131127252
#131126732
C13×#14932
#958713