Finite Group Databasebeta

← #15759633

Subgroups — #15759633

Order 3328.

454 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 107 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#13125786C211yesmaximal, characteristic
2#13117582C211yesmaximal, characteristic
3#13115816C211yesmaximal, characteristic
4#13113518C211yesmaximal, characteristic
5#13113399C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic
7C13×#1286C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C13×#382C2211yescharacteristic
13C4⋊C4×Dic13—21no—
14#11718634—21no—
15#11718593C2211yescharacteristic
16#11718586C2211yescharacteristic
17#11718510—22no—
18#11718400—22no—
19#11718360C412yescomplemented
20#11718342C412yescomplemented
21#11718314—22no—
22#11718307—22no—
23#11718147—21no—
24#11718147—21no—
25#11718073—22no—
26#11718044—22no—
27C22×Dic26D412yes—
28C2×C13×M16—21no—
29C2×C13×C4⋊C4—21no—
30C2×C42×C13C2311yescharacteristic
31#88180—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34#88178—21no—
35#88178—21no—
36C2×#6101—22no—
37C2×C4×Dic13—22no—
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×Dic52—24no—
41#88124—21no—
42#88123—21no—
43#88123—21no—
44#88123C2×C411yescharacteristic
45#88123C2×C411yescharacteristic
46#88123C2×C412yes—
47#88123D412yes—
48C4×Dic26—21no—
49C4×Dic26—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C22⋊C8—21no—
54C4×C8×C13C2×C412yes—
55C13×#95—21no—
56C13×#95D412yes—
57#88071—22no—
58#88071—22no—
59#88071—21no—
60#88071—21no—
61C22⋊#1055—21no—
62#88056—24no—
63C4⋊#1055—21no—
64C4×#1055—21no—
65#9297—131nomaximal, Sylow
66C22×C4×C13—22no—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—22no—
72C22×Dic13—21no—
73C2×Dic26—21no—
74C2×Dic26—22no—
75C2×Dic26—21no—
76C2×Dic26—82no—
77C2×Dic26C22⋊C414yes—
78C13×M16—41no—
79C13×M16—41no—
80C2×C8×C13—22no—
81C2×C8×C13—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C42×C13C22×C411yescharacteristic
85C42×C13C2×D411yescharacteristic
86C42×C13#4111yescharacteristic
87C42×C13#4111yescharacteristic
88C22⋊Dic13—41no—
89C4⋊Dic13—22no—
90C4⋊Dic13—22no—
91C4⋊Dic13—22no—
92C4⋊Dic13—22no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97#6101—41no—
98#6101—41no—
99#6101—82no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—41no—
104C4×Dic13—82no—
105C4×Dic13Q1612yescomplemented
106C2×#1055—41no—
107Dic52—84no—
108#3209—131no—
109#2331—131no—
110#1995—131no—
111#1548—131no—
112#1518—131no—
113#1286D1311yescharacteristic
114#1274—131no—
115C23×C13#12011yescharacteristic
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13C2×C22⋊C411yescharacteristic
122C2×C4×C13C4×D411yescharacteristic
123C2×C4×C13C4×D411yescharacteristic
124C2×C4×C13#12111yescharacteristic
125C2×C4×C13#12111yescharacteristic
126C2×C4×C13#12311yescharacteristic
127C2×C4×C13C2×Q1611yescharacteristic
128C2×C4×C13#13511yescharacteristic
129C2×C4×C13#13711yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×Dic13—24no—
132C2×Dic13—22no—
133C2×Dic13—41no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142Dic26—44no—
143Dic26—42no—
144Dic26—82no—
145Dic26—81no—
146C8×C13—42no—
147C8×C13—81no—
148#1055—81no—
149#533—131no—
150C2×C4⋊Q8—131no—
151#494—132no—
152#487—132no—
153#462—262no—
154#451—262no—
155#431—131no—
156#431C2×D1311yescharacteristic
157#423C2×D1311yescharacteristic
158#391—262no—
159#389—261no—
160#387—262no—
161#382C2×D1311yescharacteristic
162C4×C4⋊C4—261no—
163#376—131no—
164#339—261no—
165#339—261no—
166#333—262no—
167#328—262no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13#38611yescharacteristic
171C22×C13#45111yescharacteristic
172C22×C13#45211yescharacteristic
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—82no—
178C4×C13C4×Q1611yescharacteristic
179C4×C13#44111yescharacteristic
180C4×C13#46211yescharacteristic
181C4×C13#46411yescharacteristic
182Dic13—42no—
183Dic13—44no—
184Dic13—81no—
185Dic13—81no—
186Dic13—81no—
187C22×Q8—132no—
188C2×Q16—264no—
189C2×M16—21no—
190C4⋊Q8—132no—
191C4⋊Q8—131no—
192C4⋊Q8—131no—
193C4⋊Q8—132no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196#125—261no—
197C22⋊Q8—261no—
198C22⋊Q8—261no—
199C4×Q8—261no—
200C4×Q8—261no—
201#117—261no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—261no—
205C2×C4⋊C4—262no—
206C2×C42—131no—
207C2×C42—131no—
208C2×C42—262no—
209C2×C42C22×D1311yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—261no—
214#103—264no—
215C22⋊C8—21no—
216C22⋊C8—261no—
217C4×C8—261no—
218C4×C8C4×D1312yes—
219#95—21no—
220#95—262no—
221#95—262no—
222#95—261no—
223#95—261no—
224#95D5212yes—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13#187811yescharacteristic
228C2×C13#190511yescharacteristic
229C2×C13#191111yescharacteristic
230C2×Q8—134no—
231C2×Q8—262no—
232C2×Q8—261no—
233C2×Q8—261no—
234C2×Q8—1042no—
235C22×C4—22no—
236C22×C4—261no—
237C22×C4—262no—
238C22×C4—261no—
239C22×C4C2×D5211yescharacteristic
240C22×C4D4×D1311yescharacteristic
241C22×C4D4×D1311yescharacteristic
242Q16—1044no—
243M16—41no—
244M16—41no—
245C2×C8—22no—
246C2×C8—41no—
247C2×C8—521no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—262no—
251C4⋊C4—262no—
252C4⋊C4—262no—
253C4⋊C4—262no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—1042no—
261C22⋊C4—521no—
262C42—132no—
263C42—261no—
264C42—261no—
265C42—261no—
266C42—521no—
267C42—1042no—
268C42C2×C4×D1311yescharacteristic
269C42#612711yescharacteristic
270C42D4×D1311yescharacteristic
271C42#613111yescharacteristic
272C13#929711yescharacteristic, complemented, Sylow
273C23#8813611yescharacteristic
274Q8—524no—
275Q8—522no—
276Q8—1042no—
277Q8—1041no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—262no—
284C2×C4—264no—
285C2×C4—521no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4C4×D5211yescharacteristic
295C2×C4C22⋊C4×D1311yescharacteristic
296C2×C4#8813811yescharacteristic
297C2×C4#8814711yescharacteristic
298C2×C4#8814811yescharacteristic
299C2×C4#8814911yescharacteristic
300C2×C4#8816611yescharacteristic
301C2×C4#8816911yescharacteristic
302C2×C4#8816911yescharacteristic
303C2×C4Q16×D1311yescharacteristic
304C8—42no—
305C8—81no—
306C8—1041no—
307C22—21no—
308C22—21no—
309C22#1171832611yescharacteristic
310C22#1171844411yescharacteristic
311C22#1171846911yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—82no—
317C4—522no—
318C4—524no—
319C4—1041no—
320C4—1041no—
321C4—1041no—
322C4#1171842811yescharacteristic
323C4#1171845411yescharacteristic
324C4#1171851411yescharacteristic
325C4#1171853411yescharacteristic
326C2—21no—
327C2—21no—
328C2#1311517811yescharacteristic
329C2#1311532911yescharacteristic
330C2#1311536711yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1286C2
socleC22×C13#386
prime radicalC23×C13#120
cosocleC2×C42×C13C23
hypercenter#1286D13
hypocenterC13#9297
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1286

Complements

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

NH ≅ G/Ntype
19. #11718360C4semidirect
20. #11718342C4semidirect
105. C4×Dic13Q16semidirect
272. C13#9297semidirect

Maximal subgroups

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

subgroupindex
#131257862
#131175822
#131158162
#131135182
#131133992
#131126642
C13×#12862
#929713