Finite Group Databasebeta

← #16018418

Subgroups — #16018418

Order 3328.

482 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125349C211yesmaximal, characteristic
2#13125347C211yesmaximal, characteristic
3#13117123C211yesmaximal, characteristic, complemented
4#13117122C211yesmaximal, characteristic, complemented
5#13117121C212yesmaximal, complemented
6#13117120C212yesmaximal, complemented
7#13117119C211yesmaximal, characteristic, complemented
8#13116619C212yesmaximal
9#13116617C212yesmaximal
10D13×#346C211yesmaximal, characteristic
11C13×#2255C211yesmaximal, characteristic, complemented
12#11719433—21no—
13#11719393—21no—
14C13×#500C2211yescharacteristic
15C13×#499C2211yescharacteristic
16#11718740—21no—
17#11718725—21no—
18C2×C16×D13C2212yes—
19#11718541—21no—
20#11718541C2211yescharacteristic
21#11718541C2212yes—
22#11718541C2211yescharacteristic
23#11718539—21no—
24#11718539C2212yes—
25#11718535C2211yescharacteristic
26#11718535C2211yescharacteristic
27#11718521—21no—
28#11718516—21no—
29C4×C8×D13C2211yescharacteristic
30#11718344C2211yescharacteristic
31#11718343C2211yescharacteristic
32C13×#367C2212yes—
33C13×#366C2212yes—
34C13×#346C2211yescharacteristic
35#11718097C2212yes—
36#11718096C2212yes—
37#11718094C2212yes—
38#11718082C2212yes—
39#11718082C2212yes—
40#11718081C2212yes—
41#11718081C2212yes—
42#11718053C2211yescharacteristic
43C13×C4⋊Q8—21no—
44C13×#125—21no—
45#88200—41no—
46Q8×Dic13—41no—
47C2×C8×D13D411yescharacteristic
48C2×C8×D13C2311yescharacteristic
49#88151—41no—
50#88150—41no—
51#88150—41no—
52#88146—22no—
53#88146—21no—
54#88146—21no—
55#88144—22no—
56#88142—21no—
57#88142—21no—
58#88141—41no—
59#88141—41no—
60#88141—41no—
61C42×D13D411yescharacteristic
62#88124—21no—
63#88123—21no—
64C2×C13×C16C2312yes—
65C13×#107—21no—
66C13×#107C2311yescharacteristic
67C13×#107C2312yes—
68C13×#107C2311yescharacteristic
69C13×#106—21no—
70C4×C8×C13C2311yescharacteristic
71#88058—21no—
72#88058C2311yescharacteristic
73#88058C2311yescharacteristic
74#88058C2312yes—
75#88057—21no—
76C8×Dic13D411yescharacteristic
77C8×Dic13C2311yescharacteristic
78C2×#6090C2312yes—
79#88048—21no—
80#88048—21no—
81#88048—22no—
82#88048—22no—
83#88047—21no—
84#88047—21no—
85C4×#1055D411yescharacteristic
86C16×D13Q818yescomplemented
87#33728—131nomaximal, Sylow
88C2×Q8×C13—41no—
89C2×C4×D13D811yescharacteristic
90C2×C4×D13D811yescharacteristic
91C2×C4×D13C2×D411yescharacteristic
92C2×Dic26—41no—
93C2×Dic26—41no—
94C2×Dic26—41no—
95C2×C8×C13C2×D411yescharacteristic
96C2×C8×C13C2411yescharacteristic
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C13×C4⋊C4—41no—
103C42×C13C2×D411yescharacteristic
104#6103—41no—
105#6103—41no—
106#6103—42no—
107C4⋊Dic13—22no—
108C4⋊Dic13—21no—
109C4⋊Dic13—21no—
110C4⋊Dic13—41no—
111C4⋊Dic13—42no—
112#6101—41no—
113#6101—41no—
114#6101—41no—
115#6101—41no—
116#6101—42no—
117C4×Dic13—41no—
118C4×Dic13—41no—
119C4×Dic13—42no—
120C4×Dic13D811yescharacteristic
121C4×Dic13D811yescharacteristic
122C4×Dic13C2×D411yescharacteristic
123C2×#1055C2×D411yescharacteristic
124C2×#1055C2×D411yescharacteristic
125C8×D13Q1614yes—
126C8×D13C2×Q814yes—
127C13×C16C2×Q814yes—
128#6090C2×Q814yes—
129#3160—131no—
130#3160—131no—
131#2255—131no—
132#2255—131no—
133#2255—132no—
134#2255—132no—
135#2255—131no—
136#2255D1311yescharacteristic, complemented
137#2158—132no—
138#2158—132no—
139C2×#346—131no—
140C22×D13C2×D811yescharacteristic
141Q8×C13—82no—
142C2×C4×C13—42no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13C2×D811yescharacteristic
146C2×C4×C13C2×D811yescharacteristic
147C2×C4×C13C22×D411yescharacteristic
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—42no—
151C2×Dic13C2×D811yescharacteristic
152C2×Dic13C2×D811yescharacteristic
153C2×Dic13C2×D811yescharacteristic
154C4×D13—41no—
155C4×D13—41no—
156C4×D13C4⋊Q812yes—
157C4×D13C2×Q1612yes—
158Dic26—82no—
159Dic26—82no—
160Dic26—82no—
161C8×C13C2×Q1612yes—
162C8×C13C22×Q812yes—
163#1055C4⋊Q812yes—
164#1055C2×Q1612yes—
165#533—261no—
166#533—261no—
167C22×C16—132no—
168#500—131no—
169#500—131no—
170#500—131no—
171#500C2×D1311yescharacteristic
172#499—132no—
173#499—131no—
174#499—261no—
175#499—261no—
176#499C2×D1311yescharacteristic
177#498—261no—
178#498—261no—
179#427—131no—
180#427—132no—
181#427—131no—
182#427—261no—
183#427—261no—
184C2×C4×C8—131no—
185#367—132no—
186#367—132no—
187#367—132no—
188#367C2×D1312yes—
189#366—132no—
190#366—132no—
191#366—132no—
192#366C2×D1312yes—
193#346—132no—
194#346—131no—
195#346C2×D1311yescharacteristic
196C22×C13C22×D811yescharacteristic
197C2×D13—21no—
198C2×D13—21no—
199C2×D13#50012yes—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—81no—
203C4×C13—81no—
204C4×C13—82no—
205C4×C13C2×C4⋊Q811yescharacteristic
206C4×C13C22×Q1611yescharacteristic
207Dic13—21no—
208Dic13—21no—
209Dic13—81no—
210Dic13—81no—
211Dic13—82no—
212Dic13#50012yes—
213C22×C8—131no—
214C22×C8—131no—
215C4⋊Q8—21no—
216C4⋊Q8—261no—
217C4⋊Q8—261no—
218C4⋊Q8—261no—
219#125—21no—
220#125—262no—
221#125—261no—
222C22⋊Q8—521no—
223C22⋊Q8—521no—
224C22⋊Q8—521no—
225C22⋊Q8—521no—
226C4×Q8—521no—
227C4×Q8—521no—
228C4×Q8—521no—
229C4×Q8—521no—
230#117—261no—
231#117—261no—
232#117—262no—
233C2×C42—131no—
234C2×C16—132no—
235C2×C16—138no—
236C2×C16C22×D1312yes—
237#107—21no—
238#107—131no—
239#107—132no—
240#107—131no—
241#107—261no—
242#107—261no—
243#107—261no—
244#107C22×D1311yescharacteristic
245#107C22×D1312yes—
246#107C22×D1311yescharacteristic
247#106—21no—
248#106—261no—
249#106—261no—
250#106—262no—
251#106—262no—
252#106—261no—
253C4×C8—131no—
254C4×C8—131no—
255C4×C8—131no—
256C4×C8C22×D1311yescharacteristic
257C2×C13C2×#50011yescharacteristic
258C2×C13#341411yescharacteristic
259C2×C13#341411yescharacteristic
260D13—22no—
261C2×Q8—41no—
262C2×Q8—521no—
263C2×Q8—521no—
264C2×Q8—521no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C2×C8—131no—
269C2×C8—131no—
270C2×C8—134no—
271C2×C8—134no—
272C2×C8D4×D1311yescharacteristic
273C2×C8C23×D1311yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—262no—
281C4⋊C4—261no—
282C4⋊C4—261no—
283C4⋊C4—522no—
284C4⋊C4—522no—
285C4⋊C4—521no—
286C4⋊C4—521no—
287C4⋊C4—521no—
288C4⋊C4—521no—
289C4⋊C4—521no—
290C22⋊C4—521no—
291C22⋊C4—521no—
292C22⋊C4—522no—
293C42—131no—
294C42—131no—
295C42—131no—
296C42—521no—
297C42—521no—
298C42—522no—
299C42D4×D1311yescharacteristic
300C16—134no—
301C16Q8×D1314yes—
302C13#3372811yescharacteristic, complemented, Sylow
303C23—131no—
304Q8—82no—
305Q8—1042no—
306Q8—1042no—
307Q8—1042no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—131no—
312C2×C4—132no—
313C2×C4—132no—
314C2×C4—131no—
315C2×C4—131no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—522no—
320C2×C4—521no—
321C2×C4D8×D1311yescharacteristic
322C2×C4D8×D1311yescharacteristic
323C2×C4C2×D4×D1311yescharacteristic
324C8—132no—
325C8—132no—
326C8Q16×D1312yes—
327C8C2×Q8×D1312yes—
328C22—132no—
329C22—261no—
330C22—261no—
331C22C2×D8×D1311yescharacteristic
332C4—21no—
333C4—21no—
334C4—82no—
335C4—81no—
336C4—81no—
337C4—132no—
338C4—261no—
339C4—261no—
340C4—1041no—
341C4—1042no—
342C4—1041no—
343C4D13×C4⋊Q811yescharacteristic
344C4C2×Q16×D1311yescharacteristic
345C2—262no—
346C2D13×#50011yescharacteristic
347C2#1312796811yescharacteristic
348C2#1312797111yescharacteristic
subgroupG/H
centerC22C2×D8×D13
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2255C2
socleC22×C13C22×D8
prime radicalC22×D13C2×D8
hypercenter#2255D13
hypocenterC13#33728
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2255

Complements

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

NH ≅ G/Ntype
3. #13117123C2semidirect
4. #13117122C2semidirect
5. #13117121C2semidirect
6. #13117120C2semidirect
7. #13117119C2semidirect
11. C13×#2255C2semidirect
86. C16×D13Q8semidirect
136. #2255D13semidirect
302. C13#33728semidirect

Maximal subgroups

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

subgroupindex
#131253492
#131253472
#131171232
#131171222
#131171212
#131171202
#131171192
#131166192
#131166172
D13×#3462
C13×#22552
#3372813