Finite Group Databasebeta

← #15766113

Subgroups — #15766113

Order 3328.

352 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 77 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#13115779C211yesmaximal, characteristic
2#13113386C211yesmaximal, characteristic
3#13113347C211yesmaximal, characteristic
4#13112729C211yesmaximal, characteristic
5#13112700C211yesmaximal, characteristic
6#13112692C211yesmaximal, characteristic
7C13×#2606C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C13×#398—21no—
10C13×#398—21no—
11C13×#389—21no—
12C13×#389—21no—
13C13×#387—21no—
14C13×#387—21no—
15C13×#383C2211yescharacteristic
16C4×C13×C4⋊C4C2211yescharacteristic
17C13×#376C2211yescharacteristic
18#11718587C2211yescharacteristic
19#11718587C2211yescharacteristic
20C4×#6099C2211yescharacteristic
21#11718115—21no—
22#11718115—21no—
23#11718044—21no—
24#11718044—21no—
25#11718044—21no—
26#11718044—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C42×C13—21no—
35C2×C42×C13D411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C42×C13C2311yescharacteristic
38#88180—21no—
39#88178—21no—
40#88178—21no—
41C2×#6099—21no—
42#88124—21no—
43#88123Q811yescharacteristic
44#88123Q811yescharacteristic
45C4×Dic26—21no—
46C4×Dic26—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95D411yescharacteristic
54C13×#95D411yescharacteristic
55C13×#95D411yescharacteristic
56C13×#95D411yescharacteristic
57C22⋊#1055—21no—
58C22⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61#88043—21no—
62#88043—21no—
63#88043—21no—
64C4×#1055—21no—
65#10381—131nomaximal, Sylow
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C2×Dic26—21no—
76C2×Dic26—21no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—81no—
83C13×C4⋊C4—81no—
84C42×C13—41no—
85C42×C13—41no—
86C42×C13—42no—
87C42×C13C2×Q811yescharacteristic
88C42×C13#4111yescharacteristic
89C42×C13#4111yescharacteristic
90C42×C13#4111yescharacteristic
91C22⋊Dic13—41no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96#6101—41no—
97#6101—41no—
98C4×Dic13—41no—
99#6099—22no—
100#6099—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104#2606D1311yescharacteristic
105#1986—131no—
106#1515—131no—
107#1506—131no—
108#1300—131no—
109#1288—131no—
110#1285—131no—
111C23×C13#12011yescharacteristic
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13C22⋊Q811yescharacteristic
135C2×C4×C13C22⋊Q811yescharacteristic
136C2×C4×C13C22⋊Q811yescharacteristic
137C2×C4×C13#12411yescharacteristic
138C2×C4×C13#12411yescharacteristic
139C2×C4×C13#12411yescharacteristic
140C2×Dic13—41no—
141C2×Dic13—41no—
142Dic26—81no—
143Dic26—81no—
144#1055—42no—
145#1055—81no—
146#1055—81no—
147#533—131no—
148#432—131no—
149#432—131no—
150C4×M16—131no—
151#398—21no—
152#398—21no—
153#389—21no—
154#389—21no—
155#387—21no—
156#387—21no—
157#383C2×D1311yescharacteristic
158C4×C4⋊C4C2×D1311yescharacteristic
159#376C2×D1311yescharacteristic
160#339—261no—
161#339—261no—
162#328—261no—
163#328—261no—
164#328—261no—
165#328—261no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13#39311yescharacteristic
169C22×C13#45511yescharacteristic
170C22×C13#45611yescharacteristic
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—42no—
178C4×C13—42no—
179C4×C13—81no—
180C4×C13—81no—
181C4×C13—81no—
182C4×C13—81no—
183Dic13—81no—
184Dic13—81no—
185C2×M16—261no—
186C4⋊Q8—131no—
187C4⋊Q8—131no—
188#125—261no—
189C22⋊Q8—261no—
190C22⋊Q8—261no—
191C4×Q8—261no—
192C4×Q8—261no—
193#117—261no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C42—21no—
202C2×C42C22⋊D1311yescharacteristic
203C2×C42C22⋊D1311yescharacteristic
204C2×C42C22×D1311yescharacteristic
205C4⋊C8—261no—
206C4⋊C8—261no—
207C22⋊C8—261no—
208C22⋊C8—261no—
209#97—261no—
210#97—261no—
211#97—261no—
212C4×C8—261no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95C22⋊D1311yescharacteristic
220#95C22⋊D1311yescharacteristic
221#95C22⋊D1311yescharacteristic
222#95C22⋊D1311yescharacteristic
223C2×C13—21no—
224C2×C13—21no—
225C2×C13#202811yescharacteristic
226C2×C13#203111yescharacteristic
227C2×C13#203111yescharacteristic
228C2×Q8—261no—
229C2×Q8—261no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4C2×C22⋊D1311yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238C22×C4C2×C22⋊D1311yescharacteristic
239M16—262no—
240M16—521no—
241C2×C8—521no—
242C2×C8—521no—
243C2×C8—521no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—81no—
250C4⋊C4—81no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C22⋊C4—521no—
258C42—41no—
259C42—41no—
260C42—42no—
261C42—521no—
262C42Q8×D1311yescharacteristic
263C42#613111yescharacteristic
264C42#613111yescharacteristic
265C42#613111yescharacteristic
266C13#1038111yescharacteristic, complemented, Sylow
267C23#8820711yescharacteristic
268Q8—1041no—
269Q8—1041no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4#8820011yescharacteristic
295C2×C4#8820011yescharacteristic
296C2×C4#8820011yescharacteristic
297C2×C4#8820111yescharacteristic
298C2×C4#8820111yescharacteristic
299C2×C4#8820111yescharacteristic
300C8—522no—
301C8—1041no—
302C8—1041no—
303C22—21no—
304C22—21no—
305C22#1171889211yescharacteristic
306C22#1171890311yescharacteristic
307C22#1171890711yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—42no—
315C4—42no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—1041no—
321C4—1041no—
322C2—21no—
323C2—21no—
324C2#1311599411yescharacteristic
325C2#1311600511yescharacteristic
326C2#1311600511yescharacteristic
subgroupG/H
centerC22#11718892
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2606C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#2606D13
hypocenterC13#10381
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2606

Complements

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

NH ≅ G/Ntype
266. C13#10381semidirect

Maximal subgroups

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

subgroupindex
#131157792
#131133862
#131133472
#131127292
#131127002
#131126922
C13×#26062
#1038113