Finite Group Databasebeta

← #15756962

Subgroups — #15756962

Order 3328.

348 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 95 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#13123920C211yesmaximal, characteristic
2#13115776C211yesmaximal, characteristic
3#13113622C211yesmaximal, characteristic
4#13113621C211yesmaximal, characteristic
5#13113159C211yesmaximal, characteristic
6#13112735C211yesmaximal, characteristic
7C13×#1302C211yesmaximal, characteristic
8C2×C4×Dic26C2211yescharacteristic
9C13×#432C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C2×C13×#97C2211yescharacteristic
12#11718587C2211yescharacteristic
13#11718586C2211yescharacteristic
14C2×C4⋊#1055C2211yescharacteristic
15#11718489—21no—
16#11718489—21no—
17#11718380—21no—
18#11718379—21no—
19#11718362—21no—
20#11718362—21no—
21#11718142—21no—
22#11718142—21no—
23#11718072—21no—
24#11718071—21no—
25#11718061C412yes—
26#11718061C412yes—
27#11718050—21no—
28#11718049—21no—
29C22×Dic26Q811yescharacteristic
30C22×C8×C13—21no—
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13Q811yescharacteristic
33C2×#6101C2×C411yescharacteristic
34C2×#6101C2×C411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C22×#1055—21no—
38C4×Dic26—21no—
39C4×Dic26—21no—
40C4×Dic26—21no—
41C4×Dic26—21no—
42C13×C4⋊C8—21no—
43C13×C4⋊C8D411yescharacteristic
44C13×C4⋊C8D411yescharacteristic
45C13×C22⋊C8—21no—
46C13×C22⋊C8C2×C412yes—
47C13×#97—21no—
48C13×#97—21no—
49C13×#97—21no—
50C4×C8×C13—21no—
51C22⋊#1055—21no—
52C22⋊#1055C2×C412yes—
53#88055—21no—
54#88055—21no—
55#88054—21no—
56#88054—21no—
57#88054—21no—
58#88054—21no—
59C8×Dic13—21no—
60C8×Dic13—21no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055D411yescharacteristic
65C4⋊#1055D411yescharacteristic
66#88043—21no—
67C4×#1055—21no—
68#8865—131nomaximal, Sylow
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×Q811yescharacteristic
72C22×Dic13C4⋊C411yescharacteristic
73C22×Dic13C4⋊C411yescharacteristic
74C22×Dic13C4⋊C411yescharacteristic
75C22×Dic13C4⋊C411yescharacteristic
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×Dic26—22no—
79C2×Dic26—41no—
80C2×C8×C13—22no—
81C2×C8×C13—22no—
82C2×C8×C13—21no—
83C2×C8×C13—21no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C42×C13C2×D411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C42×C13#4111yescharacteristic
89C42×C13#4111yescharacteristic
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C2×#1055—22no—
101C2×#1055—21no—
102C2×#1055—21no—
103C2×#1055—42no—
104C2×#1055—41no—
105#2983—131no—
106#1985—131no—
107#1573—131no—
108#1573—131no—
109#1461—131no—
110#1302—131no—
111#1302D1311yescharacteristic
112C23×C13C2×C4⋊C411yescharacteristic
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—41no—
118C2×C4×C13C4×D411yescharacteristic
119C2×C4×C13C4×D411yescharacteristic
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13C22⋊Q811yescharacteristic
122C2×C4×C13C22⋊Q811yescharacteristic
123C2×C4×C13#12311yescharacteristic
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13#10812yes—
134Dic26—42no—
135Dic26—42no—
136C8×C13—42no—
137C8×C13—42no—
138C8×C13—41no—
139C8×C13—41no—
140#1055—42no—
141#1055—41no—
142#1055—41no—
143#1055—81no—
144C2×C4×Q8—131no—
145#446—261no—
146#446—261no—
147#446—261no—
148#446—261no—
149#432—131no—
150#432—261no—
151#432C2×D1311yescharacteristic
152#431—131no—
153#431—261no—
154#431C2×D1311yescharacteristic
155C2×C4⋊C8—131no—
156C2×#97C2×D1311yescharacteristic
157#336—261no—
158#336—261no—
159#335—261no—
160#335—261no—
161#334—261no—
162#334—261no—
163#324—132no—
164#324—132no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13#38511yescharacteristic
168C22×C13C2×#10811yescharacteristic
169C22×C13#43011yescharacteristic
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13#45411yescharacteristic
176C4×C13#45611yescharacteristic
177Dic13—22no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181C22×Q8—131no—
182C22×C8—21no—
183C22×C8—261no—
184C4×Q8—261no—
185C4×Q8—261no—
186C4×Q8—261no—
187C4×Q8—261no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—131no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42C22×D1311yescharacteristic
194C4⋊C8—21no—
195C4⋊C8—131no—
196C4⋊C8—131no—
197C4⋊C8—261no—
198C4⋊C8—261no—
199C4⋊C8—261no—
200C4⋊C8—261no—
201C4⋊C8—261no—
202C4⋊C8—261no—
203C4⋊C8—261no—
204C4⋊C8D5211yescharacteristic
205C4⋊C8D5211yescharacteristic
206C22⋊C8—21no—
207C22⋊C8—132no—
208C22⋊C8—261no—
209C22⋊C8C4×D1312yes—
210#97—21no—
211#97—21no—
212#97—21no—
213#97—261no—
214#97—261no—
215#97—261no—
216C4×C8—21no—
217C4×C8—261no—
218C4×C8—261no—
219C4×C8—261no—
220C2×C13—21no—
221C2×C13—21no—
222C2×C13#185511yescharacteristic
223C2×C13#185711yescharacteristic
224C2×C13#186811yescharacteristic
225C2×Q8—262no—
226C2×Q8—261no—
227C2×Q8—261no—
228C2×Q8—521no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4C2×C4×D1311yescharacteristic
234C22×C4D4×D1311yescharacteristic
235C22×C4Q8×D1311yescharacteristic
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—262no—
243C2×C8—261no—
244C2×C8—261no—
245C2×C8—522no—
246C2×C8—521no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C42—261no—
254C42—261no—
255C42—261no—
256C42—261no—
257C42C2×D5211yescharacteristic
258C42#612711yescharacteristic
259C42D4×D1311yescharacteristic
260C42#612911yescharacteristic
261C13#886511yescharacteristic, complemented, Sylow
262C23C4⋊C4×D1311yescharacteristic
263Q8—522no—
264Q8—522no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—132no—
271C2×C4—261no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4C4×D5211yescharacteristic
281C2×C4#8813511yescharacteristic
282C2×C4#8813611yescharacteristic
283C2×C4#8813711yescharacteristic
284C2×C4#8815011yescharacteristic
285C2×C4#8815111yescharacteristic
286C8—42no—
287C8—42no—
288C8—41no—
289C8—41no—
290C8—522no—
291C8—521no—
292C8—521no—
293C8—1041no—
294C22—21no—
295C22—21no—
296C22#1171832911yescharacteristic
297C22D13×#10811yescharacteristic
298C22#1171855411yescharacteristic
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—262no—
305C4—521no—
306C4—521no—
307C4—521no—
308C4#1171848711yescharacteristic
309C4#1171848811yescharacteristic
310C2—21no—
311C2—21no—
312C2#1311504211yescharacteristic
313C2#1311505211yescharacteristic
314C2#1311512311yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1302C2
socleC22×C13#385
prime radicalC23×C13C2×C4⋊C4
cosocleC2×C42×C13C23
hypercenter#1302D13
hypocenterC13#8865
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1302

Complements

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

NH ≅ G/Ntype
261. C13#8865semidirect

Maximal subgroups

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

subgroupindex
#131239202
#131157762
#131136222
#131136212
#131131592
#131127352
C13×#13022
#886513