Finite Group Databasebeta

← #15766060

Subgroups — #15766060

Order 3328.

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

normal subgroups only

This group has 364 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#13118144C211yesmaximal, characteristic
2#13115818C211yesmaximal, characteristic
3#13113335C211yesmaximal, characteristic
4#13112739C211yesmaximal, characteristic
5#13112738C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic
7C13×#1503C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C4×C13×C4⋊C4C2211yescharacteristic
11#11718647—21no—
12#11718645—21no—
13C4×C4⋊Dic13—21no—
14C4×C4⋊Dic13C2211yescharacteristic
15#11718593C2211yescharacteristic
16C4×#6101—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19#11718322—21no—
20#11718321—21no—
21C13×#328—21no—
22C13×#328—21no—
23#11718130—21no—
24#11718130—21no—
25#11718124—21no—
26#11718124—21no—
27C13×C4⋊Q8Q811yescharacteristic
28C13×C4⋊Q8Q811yescharacteristic
29C13×#125—21no—
30C13×C22⋊Q8—21no—
31C13×C22⋊Q8—21no—
32C4×Q8×C13—21no—
33C4×Q8×C13—21no—
34C13×#117—21no—
35C2×C13×C4⋊C4—21no—
36C2×C42×C13—21no—
37C2×C42×C13C2311yescharacteristic
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×#6099—21no—
47C13×C4⋊C8—21no—
48C13×C22⋊C8—21no—
49C4×C8×C13—21no—
50C13×#95D411yescharacteristic
51C13×#95D411yescharacteristic
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071D411yescharacteristic
59#88071D411yescharacteristic
60C22⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4×#1055—21no—
65#10373—131nomaximal, Sylow
66C2×Q8×C13—21no—
67C2×Q8×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C2×C8×C13—41no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C22⋊C4—41no—
86C42×C13—41no—
87C42×C13—41no—
88C42×C13—41no—
89C42×C13C2×Q811yescharacteristic
90C42×C13#4111yescharacteristic
91C42×C13#4111yescharacteristic
92C42×C13#4111yescharacteristic
93C4⋊Dic13—42no—
94C4⋊Dic13—42no—
95C4⋊Dic13—42no—
96#6101—42no—
97#6101—42no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—41no—
103C4×Dic13—41no—
104#6099—41no—
105#6099—41no—
106C2×#1055—41no—
107C2×#1055—41no—
108#2402—131no—
109#1995—131no—
110#1503—131no—
111#1503D1311yescharacteristic
112#1303—131no—
113#1303—131no—
114#1274—131no—
115C23×C13#12011yescharacteristic
116Q8×C13—81no—
117Q8×C13—81no—
118C2×C4×C13—22no—
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×C13C22⋊Q811yescharacteristic
129C2×C4×C13C22⋊Q811yescharacteristic
130C2×C4×C13C22⋊Q811yescharacteristic
131C2×C4×C13#12411yescharacteristic
132C2×C4×C13#12411yescharacteristic
133C2×C4×C13#12411yescharacteristic
134C2×C4×C13#13511yescharacteristic
135C2×C4×C13#13511yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C2×C4×C13#13711yescharacteristic
138C2×Dic13—22no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C8×C13—81no—
151#1055—81no—
152#1055—81no—
153#533C2×D1311yescharacteristic
154#431—131no—
155#431C2×D1311yescharacteristic
156#423—131no—
157#400—261no—
158#400—261no—
159#398—261no—
160#398—261no—
161C4×C4⋊C4—131no—
162C4×C4⋊C4—261no—
163C4×C4⋊C4—261no—
164C4×C4⋊C4C2×D1311yescharacteristic
165#376—131no—
166#339—261no—
167#339—261no—
168#328—21no—
169#328—21no—
170#328—261no—
171#328—261no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13#39311yescharacteristic
175C22×C13#45211yescharacteristic
176C22×C13#45211yescharacteristic
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—42no—
182C4×C13—81no—
183C4×C13—81no—
184C4×C13—81no—
185C4×C13#47911yescharacteristic
186C4×C13#47911yescharacteristic
187C4×C13#48811yescharacteristic
188C4×C13#49111yescharacteristic
189Dic13—42no—
190Dic13—81no—
191Dic13—81no—
192Dic13—81no—
193C2×M16—261no—
194C4⋊Q8Dic2611yescharacteristic
195C4⋊Q8Dic2611yescharacteristic
196#125—21no—
197C22⋊Q8—21no—
198C22⋊Q8—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201#117—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C42—21no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42—261no—
212C2×C42C22×D1311yescharacteristic
213C4⋊C8—21no—
214C4⋊C8—261no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C22⋊C8—21no—
218C22⋊C8—261no—
219C4×C8—21no—
220C4×C8—261no—
221#95—131no—
222#95—131no—
223#95—261no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228#95—261no—
229#95C22⋊D1311yescharacteristic
230#95C22⋊D1311yescharacteristic
231C2×C13—21no—
232C2×C13—21no—
233C2×C13#202611yescharacteristic
234C2×C13#203111yescharacteristic
235C2×C13#203111yescharacteristic
236C2×Q8—21no—
237C2×Q8—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4D4×D1311yescharacteristic
245C22×C4D4×D1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247M16—521no—
248M16—521no—
249C2×C8—41no—
250C2×C8—521no—
251C2×C8—521no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—42no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—522no—
260C4⋊C4—522no—
261C4⋊C4—522no—
262C4⋊C4—522no—
263C4⋊C4—522no—
264C22⋊C4—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42—261no—
269C42—261no—
270C42—261no—
271C42—261no—
272C42—521no—
273C42—521no—
274C42C2×Dic2611yescharacteristic
275C42#612711yescharacteristic
276C42#612911yescharacteristic
277C42#612911yescharacteristic
278C13#1037311yescharacteristic, complemented, Sylow
279C23#8819111yescharacteristic
280Q8—81no—
281Q8—81no—
282C2×C4—22no—
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—262no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4#8813211yescharacteristic
305C2×C4#8813211yescharacteristic
306C2×C4#8813911yescharacteristic
307C2×C4#8813911yescharacteristic
308C2×C4#8816911yescharacteristic
309C2×C4#8817011yescharacteristic
310C2×C4#8817211yescharacteristic
311C2×C4#8817311yescharacteristic
312C2×C4#8817811yescharacteristic
313C2×C4#8819011yescharacteristic
314C8—81no—
315C8—1041no—
316C8—1041no—
317C22—21no—
318C22—21no—
319C22#1171860811yescharacteristic
320C22#1171883411yescharacteristic
321C22#1171884811yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—42no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—522no—
331C4—1041no—
332C4—1041no—
333C4—1041no—
334C4#1171845711yescharacteristic
335C4#1171845811yescharacteristic
336C4#1171846011yescharacteristic
337C4#1171846111yescharacteristic
338C2—21no—
339C2—21no—
340C2#1311598511yescharacteristic
341C2#1311600811yescharacteristic
342C2#1311601011yescharacteristic
subgroupG/H
centerC2×C4#88139
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1503C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#1503D13
hypocenterC13#10373
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
278. C13#10373semidirect

Maximal subgroups

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

subgroupindex
#131181442
#131158182
#131133352
#131127392
#131127382
#131126642
C13×#15032
#1037313