Finite Group Databasebeta

← #15752122

Subgroups — #15752122

Order 3328.

350 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 87 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#13116394C211yesmaximal, characteristic
2#13116312C211yesmaximal, characteristic
3#13116244C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic
5#13112659C211yesmaximal, characteristic
6#13112659C211yesmaximal, characteristic
7C13×#2809C211yesmaximal, characteristic
8C13×#400—21no—
9C13×#398—21no—
10C13×#398—21no—
11C13×#391—21no—
12C13×#391C2211yescharacteristic
13C13×#389C2211yescharacteristic
14C13×#389C2211yescharacteristic
15C13×#387—21no—
16C13×#387—21no—
17C2×#88075—21no—
18C2×#88048—21no—
19#11718596C2211yescharacteristic
20#11718121—21no—
21#11718121—21no—
22#11718121—21no—
23#11718121—21no—
24#11718116C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C22×#1055—21no—
43C22×#1055—21no—
44C22×#1055—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54#88075—42no—
55#88048—42no—
56#7813—131nomaximal, Sylow
57C2×Q8×C13—21no—
58C2×Q8×C13—41no—
59C2×Q8×C13—41no—
60C2×Q8×C13SD1612yes—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—41no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—81no—
83C13×C4⋊C4—81no—
84C42×C13—41no—
85C42×C13—81no—
86C4⋊Dic13—42no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C2×#1055—22no—
92C2×#1055—41no—
93C2×#1055—41no—
94C2×#1055—41no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100#2809D1311yescharacteristic
101#2099—131no—
102#2084—131no—
103#2072—131no—
104#1272—131no—
105#1271—131no—
106#1271—131no—
107C23×C13#12011yescharacteristic
108Q8×C13—42no—
109Q8×C13—81no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
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×C13C2×SD1611yescharacteristic
135C2×C4×C13#13511yescharacteristic
136C2×C4×C13#13511yescharacteristic
137C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C2×C4×C13#13711yescharacteristic
140C2×Dic13—81no—
141C2×Dic13—81no—
142C2×Dic13—81no—
143#1055—42no—
144#1055—81no—
145#1055—81no—
146C2×#106—261no—
147C2×#103—261no—
148#400—21no—
149#398—21no—
150#398—21no—
151#391—21no—
152#391C2×D1311yescharacteristic
153#389C2×D1311yescharacteristic
154#389C2×D1311yescharacteristic
155#387—21no—
156#387—21no—
157#384—131no—
158#340—261no—
159#340—261no—
160#340—261no—
161#340—261no—
162#336—131no—
163#336—131no—
164#336—131no—
165C22×C13#44811yescharacteristic
166C22×C13#44911yescharacteristic
167C22×C13#45211yescharacteristic
168C22×C13#45411yescharacteristic
169C22×C13#45511yescharacteristic
170C22×C13#45611yescharacteristic
171C22×C13#45811yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—42no—
179C4×C13—81no—
180C4×C13—81no—
181C4×C13—81no—
182C4×C13—81no—
183C4×C13—81no—
184Dic13—161no—
185C22×Q8C22⋊D1311yescharacteristic
186C22×C8—261no—
187C22×C8—261no—
188C22×C8—261no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4—261no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4C22⋊D1311yescharacteristic
197C2×C4⋊C4C22⋊D1311yescharacteristic
198C2×C4⋊C4C22⋊D1311yescharacteristic
199C2×C4⋊C4C22⋊D1311yescharacteristic
200C2×C4⋊C4C22⋊D1311yescharacteristic
201C2×C42—21no—
202C2×C42C22×D1311yescharacteristic
203#106—522no—
204#103—522no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214C2×C13#160811yescharacteristic
215C2×C13#160911yescharacteristic
216C2×C13#161511yescharacteristic
217C2×C13#162611yescharacteristic
218C2×C13#164611yescharacteristic
219C2×C13#165311yescharacteristic
220C2×C13#166411yescharacteristic
221C2×Q8—21no—
222C2×Q8—41no—
223C2×Q8—41no—
224C2×Q8#610612yes—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—521no—
232C22×C4C2×C22⋊D1311yescharacteristic
233C22×C4C2×C22⋊D1311yescharacteristic
234C22×C4C2×C22⋊D1311yescharacteristic
235C2×C8—262no—
236C2×C8—521no—
237C2×C8—521no—
238C2×C8—521no—
239C2×C8—521no—
240C2×C8—521no—
241C2×C8—521no—
242C2×C8—521no—
243C2×C8—521no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—522no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C42—41no—
263C42—81no—
264C13#781311yescharacteristic, complemented, Sylow
265C23#8820711yescharacteristic
266Q8—42no—
267Q8—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
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—1041no—
293C2×C4—1041no—
294C2×C4—1041no—
295C2×C4C2×#610611yescharacteristic
296C2×C4#8819611yescharacteristic
297C2×C4#8820311yescharacteristic
298C2×C4#8820411yescharacteristic
299C2×C4#8820411yescharacteristic
300C2×C4#8820511yescharacteristic
301C8—522no—
302C8—1041no—
303C8—1041no—
304C22#1171888811yescharacteristic
305C22#1171889911yescharacteristic
306C22#1171890011yescharacteristic
307C22#1171890311yescharacteristic
308C22#1171890411yescharacteristic
309C22#1171890611yescharacteristic
310C22#1171890711yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—2081no—
324C2#1311382711yescharacteristic
325C2#1311383311yescharacteristic
326C2#1311386711yescharacteristic
327C2#1311393211yescharacteristic
328C2#1311406411yescharacteristic
329C2#1311411311yescharacteristic
330C2#1311417011yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2809C2
socle, prime radicalC23×C13#120
hypercenter#2809D13
hypocenterC13#7813
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2809

Complements

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

NH ≅ G/Ntype
264. C13#7813semidirect

Maximal subgroups

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

subgroupindex
#131163942
#131163122
#131162442
#131126622
#131126592
C13×#28092
#781313