Finite Group Databasebeta

← #15837825

Subgroups — #15837825

Order 3328.

870 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 207 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#13125984C212yesmaximal
2#13120048C211yesmaximal, characteristic
3#13113878C218yesmaximal
4#13113335C212yesmaximal
5#13113160C211yesmaximal, characteristic
6C13×#3502C211yesmaximal, characteristic
7Q82×C13—22no—
8C13×#557—22no—
9C13×#557—24no—
10C13×#544—21no—
11C13×#544C2214yes—
12C13×#533—22no—
13C13×#533C2212yes—
14C13×#519—21no—
15C2×C4×Q8×C13C2211yescharacteristic
16C2×#88123C2211yescharacteristic
17#11718891—21no—
18#11718742—22no—
19#11718739—22no—
20#11718705C2218yes—
21#11718682—24no—
22#11718647C2214yes—
23#11718638—21no—
24C4×C4⋊Dic13C2211yescharacteristic
25#11718590—22no—
26#11718586C2212yes—
27#11718130C2218yes—
28#11718120C2214yes—
29C22×Q8×C13D411yescharacteristic
30C22×Dic26—21no—
31C13×C4⋊Q8—22no—
32C13×C4⋊Q8—22no—
33C13×C4⋊Q8—24no—
34C13×C4⋊Q8—28no—
35C13×C4⋊Q8D412yes—
36C13×C4⋊Q8D412yes—
37C13×#125—24no—
38C13×#125—24no—
39C13×#125—28no—
40C13×#125—22no—
41C13×C22⋊Q8—22no—
42C13×C22⋊Q8—24no—
43C13×C22⋊Q8C2314yes—
44C4×Q8×C13—24no—
45C4×Q8×C13—24no—
46C4×Q8×C13—24no—
47C4×Q8×C13—24no—
48C4×Q8×C13—22no—
49C4×Q8×C13—22no—
50C4×Q8×C13—22no—
51C4×Q8×C13D414yes—
52C13×#117—24no—
53C13×#117—22no—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C13×C4⋊C4C2312yes—
56C2×C42×C13D412yes—
57C2×C42×C13C2311yescharacteristic
58C2×C4⋊Dic13—21no—
59C2×C4⋊Dic13—21no—
60C2×C4⋊Dic13C2312yes—
61C2×C4×Dic13—21no—
62#88123—22no—
63#88123—22no—
64#88075—28no—
65#88071—24no—
66#88071—24no—
67#88071C2312yes—
68C22⋊#1055C2314yes—
69#88047—28no—
70C4⋊#1055—22no—
71C4×#1055—22no—
72#18411—131nomaximal, Sylow
73C2×Q8×C13—24no—
74C2×Q8×C13—22no—
75C2×Q8×C13—22no—
76C2×Q8×C13—22no—
77C2×Q8×C13Q1614yes—
78C2×Q8×C13C2×D414yes—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D412yes—
81C22×C4×C13C2×D412yes—
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2411yescharacteristic
84C22×Dic13—22no—
85C22×Dic13—22no—
86C2×Dic26—44no—
87C2×Dic26—41no—
88C2×Dic26—41no—
89C13×C4⋊C4—24no—
90C13×C4⋊C4—24no—
91C13×C4⋊C4—24no—
92C13×C4⋊C4—28no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4—24no—
99C13×C4⋊C4—24no—
100C13×C4⋊C4C2×D414yes—
101C13×C22⋊C4—24no—
102C42×C13—28no—
103C42×C13—22no—
104C42×C13—22no—
105C42×C13—24no—
106C42×C13C2×D412yes—
107C42×C13C2×D412yes—
108C4⋊Dic13—24no—
109C4⋊Dic13—42no—
110C4⋊Dic13—42no—
111C4×Dic13—42no—
112C2×#1055—24no—
113#3502D1311yescharacteristic
114#3230—132no—
115#2568—131no—
116#1617—138no—
117#1503—132no—
118#1461—131no—
119C23×C13C22×D411yescharacteristic
120Q8×C13—28no—
121Q8×C13—44no—
122Q8×C13—44no—
123Q8×C13—84no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—22no—
127C2×C4×C13—24no—
128C2×C4×C13—24no—
129C2×C4×C13—22no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12012yes—
134C2×C4×C13#12011yescharacteristic
135C2×C4×C13C2×Q1614yes—
136C2×C4×C13C2×Q1612yes—
137C2×C4×C13#13712yes—
138C2×C4×C13C22×D412yes—
139C2×Dic13—42no—
140C2×Dic13—44no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144Dic26—82no—
145Dic26—82no—
146#1055—44no—
147Q82—22no—
148#557—22no—
149#557—24no—
150#544—21no—
151#544C2×D1314yes—
152#533—22no—
153#533C2×D1312yes—
154C2×C4⋊Q8—131no—
155#519—21no—
156C2×C4×Q8C2×D1311yescharacteristic
157#500—262no—
158#487—262no—
159#484—138no—
160#477—264no—
161#431—132no—
162#400—134no—
163#391—261no—
164#391—262no—
165#382—261no—
166C4×C4⋊C4—131no—
167#328—138no—
168#324—134no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13C2×#12011yescharacteristic
172C22×C13C22×Q1611yescharacteristic
173C22×C13C2×#13711yescharacteristic
174C4×C13—24no—
175C4×C13—21no—
176C4×C13—22no—
177C4×C13—44no—
178C4×C13—42no—
179C4×C13—44no—
180C4×C13#45114yes—
181C4×C13#45412yes—
182Dic13—82no—
183Dic13—82no—
184C22×Q8—261no—
185C22×Q8C22⋊D1311yescharacteristic
186C4⋊Q8—22no—
187C4⋊Q8—22no—
188C4⋊Q8—24no—
189C4⋊Q8—28no—
190C4⋊Q8—262no—
191C4⋊Q8—262no—
192C4⋊Q8C22⋊D1312yes—
193C4⋊Q8C22⋊D1312yes—
194#125—24no—
195#125—24no—
196#125—28no—
197#125—22no—
198C22⋊Q8—22no—
199C22⋊Q8—24no—
200C22⋊Q8C22×D1314yes—
201C4×Q8—24no—
202C4×Q8—24no—
203C4×Q8—24no—
204C4×Q8—24no—
205C4×Q8—22no—
206C4×Q8—22no—
207C4×Q8—22no—
208C4×Q8C22⋊D1314yes—
209#117—24no—
210#117—22no—
211C2×C4⋊C4—132no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4C22⋊D1311yescharacteristic
215C2×C4⋊C4C22×D1312yes—
216C2×C42—261no—
217C2×C42C22⋊D1312yes—
218C2×C42C22×D1311yescharacteristic
219#107—268no—
220C4⋊C8—262no—
221#103—268no—
222C22⋊C8—134no—
223C4×C8—262no—
224#95—132no—
225#95—264no—
226#95—264no—
227C2×C13—21no—
228C2×C13—21no—
229C2×C13C2×#45111yescharacteristic
230C2×C13C2×#45411yescharacteristic
231C2×C13#302811yescharacteristic
232C2×Q8—24no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—524no—
237C2×Q8—521no—
238C2×Q8—521no—
239C2×Q8#610714yes—
240C2×Q8C2×C22⋊D1314yes—
241C22×C4—262no—
242C22×C4—262no—
243C22×C4C2×C22⋊D1312yes—
244C22×C4C2×C22⋊D1311yescharacteristic
245C22×C4C2×C22⋊D1312yes—
246C22×C4C2×C22⋊D1311yescharacteristic
247C22×C4C23×D1311yescharacteristic
248C2×C8—264no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—28no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—24no—
258C4⋊C4—24no—
259C4⋊C4—24no—
260C4⋊C4—264no—
261C4⋊C4—522no—
262C4⋊C4—522no—
263C4⋊C4C2×C22⋊D1314yes—
264C22⋊C4—24no—
265C42—28no—
266C42—22no—
267C42—22no—
268C42—24no—
269C42—522no—
270C42C2×C22⋊D1312yes—
271C42C2×C22⋊D1312yes—
272C13#1841111yescharacteristic, complemented, Sylow
273C23C22×C22⋊D1311yescharacteristic
274Q8—28no—
275Q8—44no—
276Q8—44no—
277Q8—84no—
278Q8—1042no—
279Q8—1042no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—522no—
289C2×C4—522no—
290C2×C4—524no—
291C2×C4—522no—
292C2×C4—522no—
293C2×C4#8819612yes—
294C2×C4C2×#610714yes—
295C2×C4C2×#610712yes—
296C2×C4#8820711yescharacteristic
297C2×C4#8820712yes—
298C2×C4#8820711yescharacteristic
299C2×C4C22×C22⋊D1312yes—
300C8—524no—
301C22—21no—
302C22—21no—
303C22C2×#8819611yescharacteristic
304C22C22×#610711yescharacteristic
305C22C2×#8820711yescharacteristic
306C4—21no—
307C4—22no—
308C4—24no—
309C4—44no—
310C4—42no—
311C4—44no—
312C4—1042no—
313C4—1042no—
314C4#1171888914yes—
315C4#1171890612yes—
316C2—21no—
317C2—21no—
318C2C2×#1171888911yescharacteristic
319C2C2×#1171890611yescharacteristic
320C2#1312424211yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#3502C2
socleC22×C13C2×#120
prime radicalC23×C13C22×D4
hypercenter#3502D13
hypocenterC13#18411
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
272. C13#18411semidirect

Maximal subgroups

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

subgroupindex
#131259842
#131200482
#131138782
#131133352
#131131602
C13×#35022
#1841113