Finite Group Databasebeta

← #15773239

Subgroups — #15773239

Order 3328.

432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114575C211yesmaximal, characteristic
3#13112867C214yesmaximal, complemented
4C13×#1458C211yesmaximal, characteristic
5C2×C13×#117C2211yescharacteristic
6C22×#6099—21no—
7C2×#88123C411yescharacteristic
8C13×#431—21no—
9#11718873—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—24no—
36C2×#6099—22no—
37C2×#6099—41no—
38C2×#6099—42no—
39C22×#1055—41no—
40#88123—41no—
41#88123—41no—
42C13×C4⋊C8—41no—
43C13×C22⋊C8—22no—
44C4×C8×C13—41no—
45#88071—22no—
46#88071—21no—
47#88071—22no—
48#88071C2×C412yes—
49#11724—131nomaximal, Sylow
50C24×C13C22⋊C411yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13SD1612yes—
58C22×C4×C13Q1612yes—
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×Dic13—22no—
63C22×Dic13—22no—
64C2×Dic26—42no—
65C2×Dic26—82no—
66C2×C8×C13—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C22⋊C4—41no—
70C13×C22⋊C4—41no—
71C42×C13—21no—
72C42×C13—21no—
73C42×C13—21no—
74C42×C13—21no—
75C22⋊Dic13—82no—
76C4⋊Dic13—42no—
77C4⋊Dic13—41no—
78C4⋊Dic13—41no—
79C4⋊Dic13—42no—
80#6101—82no—
81#6099—24no—
82#6099—44no—
83#6099—42no—
84C2×#1055—42no—
85C2×#1055—44no—
86#2628—131no—
87#1742—131no—
88#1458D1311yescharacteristic
89#1354—134no—
90C23×C13—21no—
91C23×C13—21no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13#10312yes—
95C23×C13C2×C22⋊C411yescharacteristic
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13#9911yescharacteristic
111C2×C4×C13#9911yescharacteristic
112C2×C4×C13#10312yes—
113C2×C4×C13#10412yes—
114C2×C4×C13C2×SD1611yescharacteristic
115C2×C4×C13C2×Q1611yescharacteristic
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122Dic26—84no—
123C8×C13—82no—
124#1055—44no—
125C22×M16—261no—
126C2×C4⋊Q8—131no—
127C2×#117C2×D1311yescharacteristic
128#431—21no—
129#400—261no—
130#399—261no—
131#395—132no—
132#393—132no—
133#389—261no—
134#382—131no—
135#380—261no—
136#343—132no—
137#343—261no—
138#324C2×D1312yes—
139#323—21no—
140C22×C13—21no—
141C22×C13—21no—
142C22×C13—22no—
143C22×C13—42no—
144C22×C13—41no—
145C22×C13—41no—
146C22×C13—81no—
147C22×C13C2×#9911yescharacteristic
148C22×C13C2×#10311yescharacteristic
149C22×C13C2×#10411yescharacteristic
150C4×C13—21no—
151C4×C13—21no—
152C4×C13—41no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13#32812yes—
157C4×C13#32812yes—
158Dic13—82no—
159Dic13—82no—
160C22×Q8—132no—
161C23×C4D5211yescharacteristic
162C2×M16—264no—
163C2×M16—262no—
164C2×M16—521no—
165C2×M16—522no—
166C22×C8—521no—
167C4⋊Q8—521no—
168C4⋊Q8—521no—
169#117—41no—
170#117—41no—
171C2×C4⋊C4—261no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—262no—
175C2×C4⋊C4D5211yescharacteristic
176C2×C4⋊C4C22×D1311yescharacteristic
177C2×C22⋊C4—262no—
178C2×C22⋊C4C4×D1311yescharacteristic
179C2×C22⋊C4C22⋊D1311yescharacteristic
180C2×C42C4×D1311yescharacteristic
181C2×C42C22⋊D1311yescharacteristic
182C4⋊C8—41no—
183C22⋊C8—22no—
184C4×C8—41no—
185#95—132no—
186#95—261no—
187#95—262no—
188#95—262no—
189C2×C13—21no—
190C2×C13—21no—
191C2×C13—42no—
192C2×C13C2×#32811yescharacteristic
193C2×C13#212211yescharacteristic
194C2×C13#213511yescharacteristic
195C24#610311yescharacteristic
196C2×Q8—522no—
197C2×Q8—1042no—
198C22×C4—22no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—262no—
202C22×C4—262no—
203C22×C4#609512yes—
204C22×C4Dic5212yes—
205C22×C4#610311yescharacteristic
206C22×C4#610311yescharacteristic
207C22×C4#610311yescharacteristic
208C22×C4C2×C4×D1311yescharacteristic
209C22×C4C2×D5211yescharacteristic
210C22×C4C2×C22⋊D1311yescharacteristic
211M16—264no—
212M16—524no—
213M16—522no—
214C2×C8—42no—
215C2×C8—522no—
216C2×C8—524no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—522no—
220C4⋊C4—522no—
221C4⋊C4—521no—
222C4⋊C4—521no—
223C4⋊C4—1042no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—1042no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—21no—
231C13#1172411yescharacteristic, complemented, Sylow
232C23—21no—
233C23—21no—
234C23—41no—
235C23—41no—
236C23#8805612yes—
237C23C2×#610311yescharacteristic
238Q8—1044no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—522no—
254C2×C4—522no—
255C2×C4—522no—
256C2×C4—522no—
257C2×C4—522no—
258C2×C4—522no—
259C2×C4#8804611yescharacteristic
260C2×C4#8804611yescharacteristic
261C2×C4#8805612yes—
262C2×C4#8806512yes—
263C2×C4C2×#609511yescharacteristic
264C2×C4C2×Dic5211yescharacteristic
265C8—82no—
266C8—524no—
267C22—21no—
268C22—21no—
269C22—22no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—81no—
274C22C2×#8804611yescharacteristic
275C22C2×#8805611yescharacteristic
276C22C2×#8806511yescharacteristic
277C4—21no—
278C4—21no—
279C4—41no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—1042no—
284C4—1042no—
285C4#1171805912yes—
286C4#1171805912yes—
287C2—21no—
288C2—21no—
289C2—42no—
290C2C2×#1171805911yescharacteristic
291C2#1311648511yescharacteristic
292C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1458C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1458D13
hypocenterC13#11724
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
3. #13112867C2semidirect
231. C13#11724semidirect

Maximal subgroups

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

subgroupindex
#131206572
#131145752
#131128672
C13×#14582
#1172413