Finite Group Databasebeta

← #15767682

Subgroups — #15767682

Order 3328.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115772C211yesmaximal, characteristic
2#13114964C211yesmaximal, characteristic
3#13114842C211yesmaximal, characteristic
4#13114842C211yesmaximal, characteristic
5#13112720C211yesmaximal, characteristic
6#13112720C211yesmaximal, characteristic
7C13×#1277C211yesmaximal, characteristic
8C2×C4×Dic26C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C2×#88056—21no—
13C2×#88056—21no—
14#11718596C2211yescharacteristic
15#11718596C2211yescharacteristic
16C2×C4⋊#1055C2211yescharacteristic
17#11718143—21no—
18#11718143—21no—
19#11718143—21no—
20#11718143—21no—
21#11718142—21no—
22#11718142—21no—
23C22×Dic26D411yescharacteristic
24C22×C8×C13—21no—
25C22×C8×C13—21no—
26C22×C8×C13D411yescharacteristic
27C22×C8×C13D411yescharacteristic
28C2×C42×C13C2311yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13D411yescharacteristic
36C2×#6101—21no—
37C2×C4×Dic13—21no—
38C22×#1055—21no—
39C4×Dic26—21no—
40C4×Dic26—21no—
41C4×Dic26—21no—
42C4×Dic26—21no—
43C13×C4⋊C8—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C4×C8×C13—21no—
48C4×C8×C13—21no—
49#88056—42no—
50#88056—42no—
51C4⋊#1055—21no—
52C4⋊#1055—21no—
53#10626—131nomaximal, Sylow
54C22×C4×C13C2×D411yescharacteristic
55C22×C4×C13C2×D411yescharacteristic
56C22×C4×C13#4111yescharacteristic
57C22×Dic13—21no—
58C22×Dic13—21no—
59C22×Dic13—41no—
60C22×Dic13—41no—
61C2×Dic26—21no—
62C2×Dic26—21no—
63C2×Dic26—21no—
64C2×Dic26—21no—
65C2×Dic26—21no—
66C2×Dic26SD1612yes—
67C2×C8×C13—21no—
68C2×C8×C13—21no—
69C2×C8×C13—21no—
70C2×C8×C13—21no—
71C2×C8×C13—21no—
72C2×C8×C13—21no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C42×C13#4111yescharacteristic
80C42×C13#4111yescharacteristic
81C42×C13#4111yescharacteristic
82C42×C13#4111yescharacteristic
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93C4⋊Dic13—81no—
94C4⋊Dic13—81no—
95#6101—41no—
96#6101—41no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102#1984—131no—
103#1834—131no—
104#1803—131no—
105#1803—131no—
106#1296—131no—
107#1296—131no—
108#1277D1311yescharacteristic
109C23×C13#12111yescharacteristic
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13#12311yescharacteristic
113C2×C4×C13#12311yescharacteristic
114C2×C4×C13#12311yescharacteristic
115C2×C4×C13#12411yescharacteristic
116C2×C4×C13#12611yescharacteristic
117C2×C4×C13#12611yescharacteristic
118C2×C4×C13C2×SD1611yescharacteristic
119C2×C4×C13#13511yescharacteristic
120C2×C4×C13#13511yescharacteristic
121C2×C4×C13#13511yescharacteristic
122C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C13#13711yescharacteristic
124C2×C4×C13#13711yescharacteristic
125C2×C4×C13#13711yescharacteristic
126C2×Dic13—22no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—81no—
133C2×Dic13—81no—
134C2×Dic13—81no—
135C2×Dic13—81no—
136C2×Dic13—81no—
137C2×Dic13—81no—
138Dic26—22no—
139Dic26—22no—
140Dic26—41no—
141Dic26—41no—
142C8×C13—41no—
143C8×C13—41no—
144C8×C13—81no—
145C8×C13—81no—
146#1055—81no—
147C2×C4×Q8—131no—
148C2×C4⋊C8—131no—
149C2×C4⋊C8C2×D1311yescharacteristic
150C2×C4⋊C8C2×D1311yescharacteristic
151C2×#103—261no—
152C2×#103—261no—
153C2×C4×C8C2×D1311yescharacteristic
154#384—131no—
155#384—131no—
156#340—261no—
157#340—261no—
158#340—261no—
159#340—261no—
160#336—261no—
161#336—261no—
162C22×C13#39711yescharacteristic
163C22×C13#46411yescharacteristic
164C22×C13#46411yescharacteristic
165C22×C13#46511yescharacteristic
166C22×C13#46811yescharacteristic
167C22×C13#47211yescharacteristic
168C22×C13#47311yescharacteristic
169C4×C13—21no—
170C4×C13—21no—
171C4×C13#48111yescharacteristic
172C4×C13#48211yescharacteristic
173C4×C13#48311yescharacteristic
174C4×C13#48511yescharacteristic
175C4×C13#48511yescharacteristic
176C4×C13#48511yescharacteristic
177C4×C13#48811yescharacteristic
178C4×C13#49111yescharacteristic
179Dic13—42no—
180Dic13—81no—
181Dic13—161no—
182Dic13—161no—
183C22×Q8—131no—
184C22×C8—21no—
185C22×C8—21no—
186C22×C8—261no—
187C22×C8D5211yescharacteristic
188C22×C8D5211yescharacteristic
189C4×Q8—261no—
190C4×Q8—261no—
191C4×Q8—261no—
192C4×Q8—261no—
193C2×C4⋊C4—131no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C42—261no—
202C2×C42C22×D1311yescharacteristic
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—261no—
208C4⋊C8—261no—
209#103—522no—
210#103—522no—
211C4×C8—21no—
212C4×C8—21no—
213C2×C13#167811yescharacteristic
214C2×C13#168011yescharacteristic
215C2×C13#169811yescharacteristic
216C2×C13#170011yescharacteristic
217C2×C13#207411yescharacteristic
218C2×C13#207711yescharacteristic
219C2×C13#207811yescharacteristic
220C2×Q8—132no—
221C2×Q8—261no—
222C2×Q8—261no—
223C2×Q8—261no—
224C2×Q8—261no—
225C2×Q8—261no—
226C22×C4—261no—
227C22×C4—261no—
228C22×C4—521no—
229C22×C4—521no—
230C22×C4C2×D5211yescharacteristic
231C22×C4D4×D1311yescharacteristic
232C22×C4#613111yescharacteristic
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—521no—
246C2×C8—521no—
247C2×C8—521no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—1041no—
261C4⋊C4—1041no—
262C42—521no—
263C42—521no—
264C42#612711yescharacteristic
265C42#612711yescharacteristic
266C42#612911yescharacteristic
267C42#612911yescharacteristic
268C13#1062611yescharacteristic, complemented, Sylow
269C23#8814911yescharacteristic
270Q8—262no—
271Q8—262no—
272Q8—521no—
273Q8—521no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—262no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—1041no—
283C2×C4—1041no—
284C2×C4—1041no—
285C2×C4—1041no—
286C2×C4—1041no—
287C2×C4—1041no—
288C2×C4#8812911yescharacteristic
289C2×C4#8813711yescharacteristic
290C2×C4#8813711yescharacteristic
291C2×C4#8814011yescharacteristic
292C2×C4#8815211yescharacteristic
293C2×C4#8815211yescharacteristic
294C2×C4#8815811yescharacteristic
295C2×C4#8815811yescharacteristic
296C2×C4#8816311yescharacteristic
297C2×C4#8816311yescharacteristic
298C2×C4#8816511yescharacteristic
299C2×C4SD16×D1311yescharacteristic
300C2×C4#8817011yescharacteristic
301C2×C4#8817211yescharacteristic
302C8—41no—
303C8—41no—
304C8—81no—
305C8—81no—
306C8—1041no—
307C22#1171833511yescharacteristic
308C22#1171850611yescharacteristic
309C22#1171850611yescharacteristic
310C22#1171852511yescharacteristic
311C22#1171854711yescharacteristic
312C22#1171855711yescharacteristic
313C22#1171855811yescharacteristic
314C4—21no—
315C4—21no—
316C4—522no—
317C4—1041no—
318C4—2081no—
319C4—2081no—
320C4#1171835811yescharacteristic
321C4#1171836411yescharacteristic
322C4#1171838411yescharacteristic
323C4#1171838411yescharacteristic
324C4#1171843811yescharacteristic
325C4#1171844011yescharacteristic
326C4#1171846611yescharacteristic
327C4#1171847611yescharacteristic
328C2#1311425311yescharacteristic
329C2#1311426711yescharacteristic
330C2#1311437711yescharacteristic
331C2#1311439111yescharacteristic
332C2#1311625611yescharacteristic
333C2#1311627111yescharacteristic
334C2#1311627811yescharacteristic
subgroupG/H
centerC23#88149
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1277C2
socle, prime radicalC23×C13#121
hypercenter#1277D13
hypocenterC13#10626
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
268. C13#10626semidirect

Maximal subgroups

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

subgroupindex
#131157722
#131149642
#131148422
#131127202
C13×#12772
#1062613