Finite Group Databasebeta

← #15773676

Subgroups — #15773676

Order 3328.

368 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 79 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#13120657C211yesmaximal, characteristic
2#13114919C211yesmaximal, characteristic
3#13112867C214yesmaximal, complemented
4C13×#1464C211yesmaximal, characteristic
5C2×C13×#117C2211yescharacteristic
6C2×#88123C411yescharacteristic
7C13×#432—21no—
8#11718873—21no—
9#11718868—21no—
10#11718647—21no—
11#11718640C2212yes—
12#11718610—21no—
13#11718608C412yes—
14#11718597C411yescharacteristic
15#11718589—21no—
16C13×#324C2212yes—
17C13×#323—21no—
18#11718122—21no—
19#11718122C2212yes—
20C23×C4×C13D411yescharacteristic
21C22×Dic26C2×C412yes—
22C13×#117—41no—
23C13×#117—41no—
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C13×C4⋊C4C2311yescharacteristic
26C2×C13×C22⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4D411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C22⋊Dic13—22no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×#6101—22no—
35C2×#6099—22no—
36#88123—41no—
37#88123—41no—
38C13×C4⋊C8—41no—
39C13×C22⋊C8—22no—
40C13×#97—41no—
41#88071—22no—
42#88071—21no—
43#88071—22no—
44#88071C2×C412yes—
45C22⋊#1055—41no—
46C22⋊#1055—41no—
47#11819—131nomaximal, Sylow
48C24×C13C22⋊C411yescharacteristic
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—41no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22×C411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×Dic13—22no—
60C22×Dic13—22no—
61C2×Dic26—42no—
62C2×Dic26—82no—
63C2×C8×C13—42no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—41no—
66C13×C22⋊C4—41no—
67C13×C22⋊C4—41no—
68C42×C13—21no—
69C42×C13—21no—
70C42×C13—21no—
71C42×C13—21no—
72C22⋊Dic13—82no—
73C4⋊Dic13—42no—
74C4⋊Dic13—42no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77#6101—82no—
78#6099—42no—
79#6099—42no—
80C2×#1055—42no—
81#2628—131no—
82#1822—131no—
83#1464D1311yescharacteristic
84#1354—134no—
85C23×C13—21no—
86C23×C13—21no—
87C23×C13—21no—
88C23×C13—41no—
89C23×C13—41no—
90C23×C13C2×C22⋊C411yescharacteristic
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13#9911yescharacteristic
106C2×C4×C13#9911yescharacteristic
107C2×C4×C13#13712yes—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—42no—
114Dic26—84no—
115C8×C13—82no—
116#1055—82no—
117C2×C4⋊Q8—131no—
118C2×#117C2×D1311yescharacteristic
119#432—21no—
120#407—261no—
121#400—261no—
122#399—261no—
123#395—132no—
124#393—132no—
125#389—261no—
126#382—131no—
127#380—261no—
128#343—132no—
129#343—261no—
130#324C2×D1312yes—
131#323—21no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—42no—
135C22×C13—41no—
136C22×C13—41no—
137C22×C13—41no—
138C22×C13—81no—
139C22×C13C2×#9911yescharacteristic
140C22×C13#41911yescharacteristic
141C22×C13#42111yescharacteristic
142C4×C13—22no—
143C4×C13—21no—
144C4×C13—21no—
145C4×C13—41no—
146C4×C13—41no—
147C4×C13—41no—
148C4×C13—41no—
149Dic13—82no—
150Dic13—82no—
151C22×Q8—132no—
152C23×C4D5211yescharacteristic
153C2×M16—262no—
154C4⋊Q8—521no—
155C4⋊Q8—521no—
156#117—41no—
157#117—41no—
158C2×C4⋊C4—261no—
159C2×C4⋊C4—261no—
160C2×C4⋊C4—261no—
161C2×C4⋊C4—262no—
162C2×C4⋊C4D5211yescharacteristic
163C2×C4⋊C4C22×D1311yescharacteristic
164C2×C22⋊C4—262no—
165C2×C22⋊C4C4×D1311yescharacteristic
166C2×C22⋊C4C22⋊D1311yescharacteristic
167C2×C42C4×D1311yescharacteristic
168C2×C42C22⋊D1311yescharacteristic
169C4⋊C8—41no—
170C22⋊C8—22no—
171C22⋊C8—521no—
172C22⋊C8—521no—
173#97—41no—
174#95—132no—
175#95—261no—
176#95—262no—
177#95—262no—
178C2×C13—21no—
179C2×C13—21no—
180C2×C13—81no—
181C2×C13#151111yescharacteristic
182C2×C13#212211yescharacteristic
183C2×C13#213511yescharacteristic
184C24#610311yescharacteristic
185C2×Q8—522no—
186C2×Q8—1042no—
187C22×C4—22no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—41no—
191C22×C4—262no—
192C22×C4—262no—
193C22×C4#610311yescharacteristic
194C22×C4#610311yescharacteristic
195C22×C4#610311yescharacteristic
196C22×C4C2×C4×D1311yescharacteristic
197C22×C4C2×D5211yescharacteristic
198C22×C4C2×C22⋊D1311yescharacteristic
199M16—522no—
200M16—522no—
201C2×C8—42no—
202C2×C8—522no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—522no—
206C4⋊C4—522no—
207C4⋊C4—521no—
208C4⋊C4—521no—
209C4⋊C4—1042no—
210C22⋊C4—41no—
211C22⋊C4—41no—
212C22⋊C4—1042no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C13#1181911yescharacteristic, complemented, Sylow
218C23—21no—
219C23—21no—
220C23—21no—
221C23—41no—
222C23—41no—
223C23C2×#610311yescharacteristic
224Q8—1044no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—522no—
240C2×C4—522no—
241C2×C4—522no—
242C2×C4—522no—
243C2×C4—522no—
244C2×C4—522no—
245C2×C4#8804611yescharacteristic
246C2×C4#8804611yescharacteristic
247C2×C4#8816312yes—
248C8—82no—
249C8—1042no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22C2×#8804611yescharacteristic
258C22#1171878111yescharacteristic
259C22#1171880011yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—41no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—1042no—
268C4—1042no—
269C2—21no—
270C2—21no—
271C2—81no—
272C2#1311337011yescharacteristic
273C2#1311648511yescharacteristic
274C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1464C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1464D13
hypocenterC13#11819
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #13112867C2semidirect
217. C13#11819semidirect

Maximal subgroups

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

subgroupindex
#131206572
#131149192
#131128672
C13×#14642
#1181913