Finite Group Databasebeta

← #15760313

Subgroups — #15760313

Order 3328.

514 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 109 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#13123876C211yesmaximal, characteristic
2#13120005C211yesmaximal, characteristic
3#13114825C211yesmaximal, characteristic
4#13113518C211yesmaximal, characteristic, complemented
5#13113516C211yesmaximal, characteristic, complemented
6#13112739C211yesmaximal, characteristic, complemented
7C13×#1303C211yesmaximal, characteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88063—21no—
14#11718648—22no—
15#11718600—21no—
16#11718597—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19#11718499—22no—
20#11718387—22no—
21#11718349—22no—
22#11718334C414yes—
23#11718146—21no—
24#11718073—22no—
25#11718073—22no—
26C22×D52D411yescharacteristic
27C22×C4×D13D412yes—
28C22×Dic26C2×C412yes—
29C2×C13×M16—21no—
30C2×C13×C4⋊C4—21no—
31C2×C42×C13—21no—
32C2×C42×C13C2311yescharacteristic
33C2×#6103—24no—
34C2×#6103C2×C412yes—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13D411yescharacteristic
38C2×#6099—21no—
39C2×#6094—24no—
40C4×D52—21no—
41C4×D52—21no—
42C4×D52—21no—
43C4×D52—21no—
44#88123—21no—
45#88123—21no—
46#88123—21no—
47#88123—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8D412yes—
51C13×C22⋊C8—21no—
52C4×C8×C13—21no—
53C13×#95C2×C412yes—
54#88071—24no—
55C22⋊#1055—21no—
56#88063—42no—
57#88060—24no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055D412yes—
61C4×#1055—21no—
62#9399—131nomaximal, Sylow
63C23×D13C22⋊C412yes—
64C22×C4×C13—22no—
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—22no—
69C22×Dic13C22⋊C412yes—
70C2×D52—21no—
71C2×D52—21no—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×C4×D13—22no—
77C2×C4×D13—22no—
78C2×C4×D13—44no—
79C2×Dic26—22no—
80C2×Dic26—22no—
81C2×Dic26—82no—
82C13×M16—41no—
83C13×M16—41no—
84C2×C8×C13—22no—
85C2×C8×C13—41no—
86C13×C4⋊C4—42no—
87C42×C13—41no—
88C42×C13—41no—
89C42×C13C2×D411yescharacteristic
90C42×C13C2×D411yescharacteristic
91C42×C13#4111yescharacteristic
92C42×C13#4111yescharacteristic
93#6103—22no—
94#6103—22no—
95#6103—84no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102#6099—41no—
103#6099—41no—
104C2×#1055—22no—
105C2×#1055—41no—
106#6094—84no—
107#2975—131no—
108#2563—131no—
109#1800—131no—
110#1548—131no—
111#1548—131no—
112#1303—131no—
113#1303D1311yescharacteristic, complemented
114C23×C13C2×C22⋊C411yescharacteristic
115C22×D13—22no—
116C22×D13—22no—
117C22×D13—22no—
118C22×D13—42no—
119C22×D13—42no—
120C2×C4×C13—22no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13C4×D411yescharacteristic
126C2×C4×C13C4×D411yescharacteristic
127C2×C4×C13#12011yescharacteristic
128C2×C4×C13#12111yescharacteristic
129C2×C4×C13#12111yescharacteristic
130C2×C4×C13#12311yescharacteristic
131C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C13#13711yescharacteristic
133C2×C4×C13#13711yescharacteristic
134C2×C4×C13#13711yescharacteristic
135C2×Dic13—22no—
136C2×Dic13—42no—
137C2×Dic13—44no—
138C2×Dic13—42no—
139D52—41no—
140D52—41no—
141D52—41no—
142D52—41no—
143C4×D13—44no—
144C4×D13—82no—
145Dic26—82no—
146Dic26—82no—
147C8×C13—42no—
148C8×C13—81no—
149#1055—42no—
150#1055—81no—
151C2×C4⋊Q8—131no—
152C2×C4×D4—131no—
153#436—262no—
154#436—262no—
155#431—131no—
156#431C2×D1311yescharacteristic
157#423—131no—
158#423C2×D1311yescharacteristic
159C2×#100—261no—
160#407—262no—
161#393—134no—
162#390—261no—
163#382—261no—
164#380—262no—
165C4×C4⋊C4C2×D1311yescharacteristic
166#343—261no—
167#333—262no—
168#333—262no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13#38611yescharacteristic
172C22×C13#41711yescharacteristic
173C22×C13#41911yescharacteristic
174C2×D13—44no—
175C2×D13—42no—
176C2×D13—42no—
177C2×D13—42no—
178C2×D13—82no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—82no—
183C4×C13#45512yes—
184C4×C13#46811yescharacteristic
185C4×C13#46811yescharacteristic
186C4×C13#47011yescharacteristic
187C4×C13#47011yescharacteristic
188Dic13—42no—
189Dic13—82no—
190C22×Q8—132no—
191C22×D4—131no—
192C23×C4—132no—
193C2×M16—21no—
194C2×M16—264no—
195C2×M16—261no—
196C4⋊Q8—261no—
197C4⋊Q8—261no—
198C4⋊Q8—261no—
199C4⋊Q8—261no—
200C4×D4—261no—
201C4×D4—261no—
202C4×D4—261no—
203C4×D4—261no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—131no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C22⋊C4—132no—
209C2×C22⋊C4—264no—
210C2×C42—21no—
211C2×C42C22×D1311yescharacteristic
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—132no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4⋊C8D5212yes—
218#100—522no—
219C22⋊C8—21no—
220C22⋊C8—264no—
221C22⋊C8—261no—
222C4×C8—21no—
223C4×C8—261no—
224#95—264no—
225#95C4×D1312yes—
226C2×C13—21no—
227C2×C13—21no—
228C2×C13#188511yescharacteristic
229C2×C13#189411yescharacteristic
230C2×C13#191411yescharacteristic
231D13—82no—
232C24—132no—
233C2×Q8—262no—
234C2×Q8—262no—
235C2×Q8—1042no—
236C2×D4—261no—
237C2×D4—261no—
238C2×D4—261no—
239C2×D4—261no—
240C2×D4—261no—
241C2×D4—261no—
242C22×C4—22no—
243C22×C4—132no—
244C22×C4—262no—
245C22×C4—262no—
246C22×C4—262no—
247C22×C4—524no—
248C22×C4C2×C4×D1311yescharacteristic
249C22×C4D4×D1311yescharacteristic
250C22×C4D4×D1311yescharacteristic
251M16—41no—
252M16—41no—
253M16—521no—
254M16—521no—
255M16—1044no—
256C2×C8—22no—
257C2×C8—41no—
258C2×C8—262no—
259C2×C8—521no—
260C4⋊C4—42no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C22⋊C4—262no—
268C22⋊C4—262no—
269C22⋊C4—1044no—
270C42—41no—
271C42—41no—
272C42C2×D5211yescharacteristic
273C42#612711yescharacteristic
274C42D4×D1311yescharacteristic
275C42#613111yescharacteristic
276C13#939911yescharacteristic, complemented, Sylow
277C23—262no—
278C23—262no—
279C23—262no—
280C23—522no—
281C23—522no—
282C23C22⋊C4×D1311yescharacteristic
283Q8—1042no—
284Q8—1042no—
285D4—521no—
286D4—521no—
287D4—521no—
288D4—521no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—262no—
295C2×C4—524no—
296C2×C4—522no—
297C2×C4—524no—
298C2×C4—522no—
299C2×C4—1042no—
300C2×C4C4×D5211yescharacteristic
301C2×C4#8813611yescharacteristic
302C2×C4#8813811yescharacteristic
303C2×C4#8814711yescharacteristic
304C2×C4#8814811yescharacteristic
305C2×C4#8814911yescharacteristic
306C2×C4#8816511yescharacteristic
307C2×C4#8816911yescharacteristic
308C2×C4#8816911yescharacteristic
309C2×C4#8817211yescharacteristic
310C8—42no—
311C8—81no—
312C8—522no—
313C8—1041no—
314C22—21no—
315C22—21no—
316C22—524no—
317C22—522no—
318C22—522no—
319C22—522no—
320C22—1042no—
321C22#1171832611yescharacteristic
322C22#1171843211yescharacteristic
323C22#1171846311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—522no—
329C4—1042no—
330C4#1171844111yescharacteristic
331C4#1171847711yescharacteristic
332C4#1171848612yes—
333C4#1171852911yescharacteristic
334C4#1171854711yescharacteristic
335C2—21no—
336C2—21no—
337C2—1042no—
338C2#1311522311yescharacteristic
339C2#1311526811yescharacteristic
340C2#1311538211yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1303C2
socleC22×C13#386
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1303D13
hypocenterC13#9399
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
4. #13113518C2semidirect
5. #13113516C2semidirect
6. #13112739C2semidirect
7. C13×#1303C2semidirect
113. #1303D13semidirect
276. C13#9399semidirect

Maximal subgroups

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

subgroupindex
#131238762
#131200052
#131148252
#131135182
#131135162
#131127392
C13×#13032
#939913