Finite Group Databasebeta

← #15752129

Subgroups — #15752129

Order 3328.

378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 91 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#13116379C211yesmaximal, characteristic
2#13116312C211yesmaximal, characteristic
3#13116244C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic
5#13112662C211yesmaximal, characteristic
6#13112659C211yesmaximal, characteristic
7C13×#2806C211yesmaximal, characteristic
8C13×#398—21no—
9C13×#398—21no—
10C13×#395—21no—
11C13×#391—21no—
12C13×#391C2211yescharacteristic
13C13×#391C2211yescharacteristic
14C13×#389—21no—
15C13×#389C2211yescharacteristic
16C13×#387—21no—
17C2×#88075—21no—
18C2×#88075—21no—
19C2×#88048—21no—
20C2×#88048—21no—
21#11718596C2211yescharacteristic
22#11718121—21no—
23#11718121—21no—
24#11718116C2211yescharacteristic
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13D411yescharacteristic
28C22×Q8×C13D411yescharacteristic
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×C13×C4⋊C4D411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C42×C13—21no—
39C2×C42×C13C2311yescharacteristic
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C22×#1055—21no—
44C22×#1055—21no—
45C22×#1055—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#88075—42no—
56#88048—42no—
57#88048—42no—
58#7814—131nomaximal, Sylow
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13—21no—
62C2×Q8×C13—41no—
63C2×Q8×C13—41no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C2×Q8×C13SD1612yes—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—41no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—81no—
84C13×C4⋊C4—81no—
85C13×C4⋊C4—81no—
86C13×C4⋊C4—81no—
87C13×C4⋊C4SD1612yes—
88C42×C13—41no—
89C42×C13—81no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C2×#1055—22no—
97C2×#1055—22no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105#2806D1311yescharacteristic
106#2096—131no—
107#2084—131no—
108#2072—131no—
109#1272—131no—
110#1272—131no—
111#1271—131no—
112C23×C13#12011yescharacteristic
113Q8×C13—42no—
114Q8×C13—42no—
115Q8×C13—81no—
116Q8×C13—81no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
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×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13C2×SD1611yescharacteristic
142C2×C4×C13C2×SD1611yescharacteristic
143C2×C4×C13#13511yescharacteristic
144C2×C4×C13#13711yescharacteristic
145C2×C4×C13#13711yescharacteristic
146C2×C4×C13#13711yescharacteristic
147C2×Dic13—81no—
148C2×Dic13—81no—
149C2×Dic13—81no—
150#1055—42no—
151#1055—42no—
152#1055—81no—
153C2×#106—261no—
154C2×#106—261no—
155C2×#103—261no—
156C2×#103—261no—
157#398—21no—
158#398—21no—
159#395—21no—
160#391—21no—
161#391C2×D1311yescharacteristic
162#391C2×D1311yescharacteristic
163#389—21no—
164#389C2×D1311yescharacteristic
165#387—21no—
166#384—131no—
167#340—261no—
168#340—261no—
169#336—131no—
170#336—131no—
171#336—131no—
172C22×C13#44811yescharacteristic
173C22×C13#44811yescharacteristic
174C22×C13#45211yescharacteristic
175C22×C13#45311yescharacteristic
176C22×C13#45511yescharacteristic
177C22×C13#45611yescharacteristic
178C22×C13#45811yescharacteristic
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—42no—
186C4×C13—42no—
187C4×C13—81no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13—81no—
191Dic13—161no—
192C22×Q8C22⋊D1311yescharacteristic
193C22×Q8C22⋊D1311yescharacteristic
194C22×C8—261no—
195C22×C8—261no—
196C22×C8—261no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4C22⋊D1311yescharacteristic
206C2×C4⋊C4C22⋊D1311yescharacteristic
207C2×C4⋊C4C22⋊D1311yescharacteristic
208C2×C4⋊C4C22⋊D1311yescharacteristic
209C2×C42—21no—
210C2×C42C22×D1311yescharacteristic
211#106—522no—
212#106—522no—
213#103—522no—
214#103—522no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223C2×C13#160811yescharacteristic
224C2×C13#161111yescharacteristic
225C2×C13#161811yescharacteristic
226C2×C13#162311yescharacteristic
227C2×C13#164311yescharacteristic
228C2×C13#165311yescharacteristic
229C2×C13#166111yescharacteristic
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8#610612yes—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—521no—
245C22×C4C2×C22⋊D1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247C22×C4C2×C22⋊D1311yescharacteristic
248C2×C8—262no—
249C2×C8—262no—
250C2×C8—521no—
251C2×C8—521no—
252C2×C8—521no—
253C2×C8—521no—
254C2×C8—521no—
255C2×C8—521no—
256C2×C8—521no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—521no—
268C4⋊C4—521no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C4⋊C4#610612yes—
274C42—41no—
275C42—81no—
276C13#781411yescharacteristic, complemented, Sylow
277C23#8820711yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—1041no—
307C2×C4—1041no—
308C2×C4—1041no—
309C2×C4C2×#610611yescharacteristic
310C2×C4C2×#610611yescharacteristic
311C2×C4#8819611yescharacteristic
312C2×C4#8819611yescharacteristic
313C2×C4#8820411yescharacteristic
314C2×C4#8820511yescharacteristic
315C8—522no—
316C8—522no—
317C8—1041no—
318C22#1171888811yescharacteristic
319C22#1171888811yescharacteristic
320C22#1171890011yescharacteristic
321C22#1171890211yescharacteristic
322C22#1171890311yescharacteristic
323C22#1171890411yescharacteristic
324C22#1171890711yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—42no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—2081no—
338C2#1311382711yescharacteristic
339C2#1311384411yescharacteristic
340C2#1311388411yescharacteristic
341C2#1311391411yescharacteristic
342C2#1311404311yescharacteristic
343C2#1311411311yescharacteristic
344C2#1311415311yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2806C2
socle, prime radicalC23×C13#120
hypercenter#2806D13
hypocenterC13#7814
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2806

Complements

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

NH ≅ G/Ntype
276. C13#7814semidirect

Maximal subgroups

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

subgroupindex
#131163792
#131163122
#131162442
#131126622
#131126592
C13×#28062
#781413