Finite Group Databasebeta

← #15772211

Subgroups — #15772211

Order 3328.

460 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 103 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#13117548C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112781C212yesmaximal, complemented
4#13112769C212yesmaximal, complemented
5C13×#1459C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88190C411yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9C2×C13×C22⋊C8—21no—
10#11718882C411yescharacteristic
11#11718871—21no—
12#11718871—21no—
13C2×C22⋊#1055—21no—
14#11718637C2211yescharacteristic
15#11718635C2211yescharacteristic
16#11718605—21no—
17#11718605—21no—
18#11718593C411yescharacteristic
19C13×#324C2212yes—
20C13×#323—21no—
21#11718120C2212yes—
22#11718117—21no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C22×C8×C13—41no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4C2311yescharacteristic
31C2×C13×C22⋊C4D411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C42×C13C2×C411yescharacteristic
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38#88190—22no—
39#88190C814yescomplemented
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×C4×Dic13—21no—
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C22×#1055—41no—
48C4×Dic26—41no—
49C4×Dic26—41no—
50C13×C22⋊C8—22no—
51C13×C22⋊C8—41no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11481—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C24×C13C22⋊C411yescharacteristic
61C2×D4×C13—41no—
62C2×D4×C13—41no—
63C2×D4×C13C2×C812yes—
64C2×D4×C13M1612yes—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—81no—
70C22×C4×C13—81no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C2×Dic26—21no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26C2×C812yescomplemented
84C2×C8×C13—42no—
85C2×C8×C13—82no—
86C13×C4⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C42×C13—21no—
90C42×C13—21no—
91C22⋊Dic13—24no—
92C22⋊Dic13—24no—
93C22⋊Dic13—81no—
94C22⋊Dic13—81no—
95C4⋊Dic13—41no—
96#6101—41no—
97#6101—41no—
98#6101—81no—
99#6101—81no—
100C4×Dic13—21no—
101C4×Dic13—42no—
102C4×Dic13—41no—
103C4×Dic13C2×C812yescomplemented
104C2×#1055—42no—
105C2×#1055—82no—
106#2326—131no—
107#1459—131no—
108#1459D1311yescharacteristic
109#1325—132no—
110#1319—132no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13C22⋊C812yes—
120C23×C13C22⋊C812yes—
121C23×C13C2×C22⋊C411yescharacteristic
122D4×C13—42no—
123D4×C13—42no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13#9911yescharacteristic
138C2×C4×C13#9911yescharacteristic
139C2×C4×C13C22×C811yescharacteristic
140C2×C4×C13C2×M1611yescharacteristic
141C2×Dic13—22no—
142C2×Dic13—22no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153Dic26—42no—
154Dic26—42no—
155C8×C13—82no—
156#1055—82no—
157C2×#124—131no—
158C2×C4×Q8—131no—
159C2×C4×D4C2×D1311yescharacteristic
160C2×C22⋊C8—21no—
161C2×C22⋊C8—261no—
162#391—131no—
163#390—131no—
164#388—261no—
165#388—261no—
166#385—261no—
167#385—261no—
168#384—131no—
169#376—131no—
170#324—132no—
171#324C2×D1312yes—
172#323—21no—
173#323—261no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—42no—
179C22×C13—42no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13C2×C22⋊C811yescharacteristic
187C22×C13C2×#9911yescharacteristic
188C22×C13#41311yescharacteristic
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13—41no—
196Dic13—42no—
197Dic13—42no—
198Dic13—81no—
199Dic13—81no—
200C22×Q8—131no—
201C22×D4C4×D1311yescharacteristic
202C23×C4D5211yescharacteristic
203C23×C4C22⋊D1311yescharacteristic
204C22×C8—41no—
205C22×C8—521no—
206#124—134no—
207#124—262no—
208C4×Q8—521no—
209C4×Q8—521no—
210C4×D4—41no—
211C4×D4—41no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4C22×D1311yescharacteristic
217C2×C22⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4—261no—
220C2×C22⋊C4—261no—
221C2×C22⋊C4D5211yescharacteristic
222C2×C22⋊C4C22⋊D1311yescharacteristic
223C2×C42—131no—
224C2×C42—131no—
225C2×C42—261no—
226C2×C42C4×D1311yescharacteristic
227C22⋊C8—22no—
228C22⋊C8—41no—
229C22⋊C8—262no—
230C22⋊C8—521no—
231#95—261no—
232#95—261no—
233#95—261no—
234#95—261no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13—42no—
238C2×C13—42no—
239C2×C13#145911yescharacteristic
240C2×C13#212711yescharacteristic
241C2×C13#213511yescharacteristic
242C24#610311yescharacteristic
243C24#610311yescharacteristic
244C2×Q8—132no—
245C2×Q8—261no—
246C2×Q8—521no—
247C2×Q8—521no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4C8×D1312yes—
251C2×D4#609412yes—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4#610311yescharacteristic
263C22×C4#610311yescharacteristic
264C22×C4C2×C4×D1311yescharacteristic
265C22×C4C2×D5211yescharacteristic
266C22×C4C2×C22⋊D1311yescharacteristic
267C2×C8—42no—
268C2×C8—82no—
269C2×C8—522no—
270C2×C8—1042no—
271C4⋊C4—41no—
272C4⋊C4—521no—
273C4⋊C4—521no—
274C4⋊C4—521no—
275C4⋊C4—1041no—
276C4⋊C4—1041no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—264no—
280C22⋊C4—264no—
281C22⋊C4—1041no—
282C22⋊C4—1041no—
283C42—21no—
284C42—21no—
285C42—132no—
286C42—261no—
287C42—521no—
288C42—522no—
289C13#1148111yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23#8806012yes—
299C23#8806012yes—
300C23C2×#610311yescharacteristic
301Q8—522no—
302Q8—522no—
303D4—42no—
304D4—42no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—262no—
319C2×C4—262no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4#8804611yescharacteristic
331C2×C4#8804611yescharacteristic
332C2×C4C2×C8×D1311yescharacteristic
333C2×C4C2×#609411yescharacteristic
334C8—82no—
335C8—1042no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—81no—
348C22C2×#8804611yescharacteristic
349C22C2×#8806011yescharacteristic
350C22#1171879311yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—522no—
359C4—522no—
360C4—1041no—
361C4—1041no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—42no—
366C2#1311315211yescharacteristic
367C2#1311650311yescharacteristic
368C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC2×C4×C13C22×C8
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1459C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1459D13
hypocenterC13#11481
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13112781C2semidirect
4. #13112769C2semidirect
39. #88190C8semidirect
83. C2×Dic26C2×C8semidirect
103. C4×Dic13C2×C8semidirect
289. C13#11481semidirect

Maximal subgroups

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

subgroupindex
#131175482
#131131542
#131127812
#131127692
C13×#14592
#1148113