Finite Group Databasebeta

← #15751235

Subgroups — #15751235

Order 3328.

384 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 99 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#13117395C211yesmaximal, characteristic
2#13114978C211yesmaximal, characteristic
3#13114978C211yesmaximal, characteristic
4#13112660C211yesmaximal, characteristic
5#13112659C211yesmaximal, characteristic
6#13112658C211yesmaximal, characteristic
7C13×#1271C211yesmaximal, characteristic
8C2×#88144C411yescharacteristic
9C13×#389C2211yescharacteristic
10#11718639—21no—
11#11718638C411yescharacteristic
12C4⋊C4×Dic13—21no—
13C4⋊C4×Dic13C411yescharacteristic
14C4⋊C4×Dic13C411yescharacteristic
15C42×Dic13C2211yescharacteristic
16#11718589C2211yescharacteristic
17#11718314—21no—
18#11718310—21no—
19C13×#336C2211yescharacteristic
20C13×#336C2211yescharacteristic
21#11718142—21no—
22#11718142—21no—
23#11718142—21no—
24#11718142—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×C8×C13—21no—
28C22×C8×C13—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C22×#1055—21no—
47C22×#1055—21no—
48#88144—22no—
49#88144—22no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#7650—131nomaximal, Sylow
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C22⋊C411yescharacteristic
68C2×C8×C13—41no—
69C2×C8×C13—41no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4M1612yes—
79C42×C13—41no—
80C4⋊Dic13—24no—
81C4⋊Dic13—21no—
82C4⋊Dic13—41no—
83C4⋊Dic13M1612yes—
84#6101—24no—
85#6101—41no—
86#6101—41no—
87C4×Dic13—21no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—22no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96C4×Dic13—42no—
97C4×Dic13—42no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C4×#125—131no—
105#1839—131no—
106#1839—131no—
107#1271—131no—
108#1271—131no—
109#1271—131no—
110#1271D1311yescharacteristic
111C23×C13C2×C22⋊C411yescharacteristic
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
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×C13C2×M1611yescharacteristic
125C2×C4×C13C2×M1611yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13#13511yescharacteristic
128C2×C4×C13#13511yescharacteristic
129C2×C4×C13#13511yescharacteristic
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—22no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13#10112yes—
148C8×C13—81no—
149C8×C13—81no—
150#1055—81no—
151#1055—81no—
152C2×#125—131no—
153#389—131no—
154#389C2×D1311yescharacteristic
155#387—261no—
156#387—261no—
157#382—131no—
158C4×C4⋊C4—131no—
159C4×C4⋊C4—131no—
160C4×C4⋊C4—261no—
161C4×C4⋊C4—261no—
162C43—131no—
163#336—131no—
164#336—131no—
165#336—261no—
166#336—261no—
167#336—261no—
168#336—261no—
169#336C2×D1311yescharacteristic
170#336C2×D1311yescharacteristic
171C22×C13#40711yescharacteristic
172C22×C13#41011yescharacteristic
173C22×C13C2×#10111yescharacteristic
174C22×C13#41611yescharacteristic
175C22×C13#41611yescharacteristic
176C22×C13#42111yescharacteristic
177C22×C13#42111yescharacteristic
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—42no—
185C4×C13—81no—
186Dic13—22no—
187Dic13—41no—
188Dic13—41no—
189Dic13—41no—
190Dic13—42no—
191Dic13—81no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—261no—
195C22×C8—261no—
196#125—262no—
197#125—262no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4C4×D1311yescharacteristic
205C2×C4⋊C4C4×D1311yescharacteristic
206C2×C42—131no—
207C2×C42—131no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—261no—
213C2×C42—261no—
214C2×C42C22×D1311yescharacteristic
215#95—21no—
216#95—261no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221C2×C13#146711yescharacteristic
222C2×C13#148811yescharacteristic
223C2×C13#148811yescharacteristic
224C2×C13#152111yescharacteristic
225C2×C13#152111yescharacteristic
226C2×C13#153411yescharacteristic
227C2×C13#154411yescharacteristic
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4C2×C4×D1311yescharacteristic
237C22×C4D4×D1311yescharacteristic
238C22×C4D4×D1311yescharacteristic
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—
248C2×C8—521no—
249C2×C8—521no—
250C2×C8—521no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—132no—
256C4⋊C4—264no—
257C4⋊C4—264no—
258C4⋊C4—261no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4#609412yes—
263C42—41no—
264C42—262no—
265C42—261no—
266C42—261no—
267C42—261no—
268C42—261no—
269C42—261no—
270C42—261no—
271C42—521no—
272C42—521no—
273C42—522no—
274C42—522no—
275C13#765011yescharacteristic, complemented, Sylow
276C23C22⋊C4×D1311yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—132no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—262no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4C2×#609411yescharacteristic
308C2×C4M16×D1311yescharacteristic
309C2×C4#8816611yescharacteristic
310C2×C4#8817011yescharacteristic
311C2×C4#8817011yescharacteristic
312C2×C4#8817311yescharacteristic
313C8—81no—
314C8—81no—
315C8—1041no—
316C8—1041no—
317C22#1171838711yescharacteristic
318C22#1171840111yescharacteristic
319C22D13×#10111yescharacteristic
320C22#1171843311yescharacteristic
321C22#1171846511yescharacteristic
322C22#1171848211yescharacteristic
323C22#1171848211yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—42no—
331C4—81no—
332C4—262no—
333C4—521no—
334C4—521no—
335C4—521no—
336C4—522no—
337C4—1041no—
338C2#1311317811yescharacteristic
339C2#1311326711yescharacteristic
340C2#1311326911yescharacteristic
341C2#1311341011yescharacteristic
342C2#1311341211yescharacteristic
343C2#1311346111yescharacteristic
344C2#1311349911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1271C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1271D13
hypocenterC13#7650
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
275. C13#7650semidirect

Maximal subgroups

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

subgroupindex
#131173952
#131149782
#131126602
#131126592
#131126582
C13×#12712
#765013