Finite Group Databasebeta

← #15848280

Subgroups — #15848280

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125989C211yesmaximal, characteristic
2#13124641C211yesmaximal, characteristic
3C2×#11718682C211yesmaximal, characteristic
4#13114294C214yesmaximal, complemented
5#13114240C214yesmaximal, complemented
6#13113611C211yesmaximal, characteristic
7#13113516C211yesmaximal, characteristic
8#13113491C211yesmaximal, characteristic
9C13×#2982C211yesmaximal, characteristic
10C2×C4×Q8×C13C2211yescharacteristic
11#11719175C2211yescharacteristic
12C2×#88123C2211yescharacteristic
13C8×Q8×C13—22no—
14C8×Q8×C13C2214yes—
15C13×#431—22no—
16C13×#431C2211yescharacteristic
17C13×#431C2211yescharacteristic
18#11718886—21no—
19C2×#88075—21no—
20#11718683—22no—
21#11718682—22no—
22#11718682C2212yes—
23#11718682C2214yes—
24#11718681C2212yes—
25#11718625—21no—
26C2×#88047—21no—
27#11718585C2211yescharacteristic
28C2×C4⋊#1055C2211yescharacteristic
29#11718511—22no—
30#11718383—22no—
31#11718343C2212yes—
32#11718342C2212yes—
33#11718074C2212yes—
34#11718073C2212yes—
35#11718073C2214yes—
36#11718050C2214yes—
37C22×Q8×C13D411yescharacteristic
38C22×Dic26—21no—
39C4×Q8×C13—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13D412yes—
42C4×Q8×C13C2312yes—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4D411yescharacteristic
45C2×C42×C13—21no—
46C2×C42×C13C2311yescharacteristic
47#88180—21no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13—21no—
50#88178—21no—
51#88178—21no—
52C2×#6099—21no—
53C22×#1055—21no—
54#88124—21no—
55#88123—21no—
56#88123—21no—
57#88123—21no—
58#88123C2312yes—
59#88123C2311yescharacteristic
60#88123C2311yescharacteristic
61C4×Dic26—21no—
62C4×Dic26—21no—
63C13×C4⋊C8—24no—
64C13×C4⋊C8D412yes—
65C13×C4⋊C8C2312yes—
66C13×C22⋊C8—21no—
67C13×C22⋊C8D412yes—
68C4×C8×C13—24no—
69C4×C8×C13—21no—
70C4×C8×C13C2312yes—
71#88075—22no—
72#88075—24no—
73#88075—22no—
74#88058—24no—
75#88056—24no—
76#88048—22no—
77#88047—24no—
78#88047—22no—
79C4⋊#1055—21no—
80C4⋊#1055—21no—
81C4⋊#1055C2312yes—
82C4⋊#1055C2312yes—
83#19405—131nomaximal, Sylow
84C2×Q8×C13—21no—
85C2×Q8×C13—22no—
86C2×Q8×C13Q1614yes—
87C2×Q8×C13C2×D412yes—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13#4111yescharacteristic
93C22×Dic13—41no—
94C2×Dic26—21no—
95C2×Dic26—21no—
96C2×Dic26—22no—
97C2×Dic26—41no—
98C2×Dic26—82no—
99C2×C8×C13—22no—
100C2×C8×C13C2×D414yes—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4C2×D412yes—
105C42×C13—22no—
106C42×C13—22no—
107C42×C13C2×D411yescharacteristic
108C42×C13C2×D411yescharacteristic
109C42×C13#4111yescharacteristic
110C42×C13C2411yescharacteristic
111C22⋊Dic13—41no—
112C4⋊Dic13—22no—
113C4⋊Dic13—21no—
114C4⋊Dic13—21no—
115C4⋊Dic13—21no—
116C4⋊Dic13—22no—
117C4⋊Dic13—21no—
118C4⋊Dic13—41no—
119C4⋊Dic13—41no—
120#6101—41no—
121#6101—41no—
122C4×Dic13—41no—
123#6099—42no—
124C2×#1055—22no—
125C2×#1055—22no—
126C2×#1055—42no—
127#3230—131no—
128#3078—131no—
129C2×#477—131no—
130#2982D1311yescharacteristic
131#1684—134no—
132#1676—134no—
133#1571—131no—
134#1548—131no—
135#1542—131no—
136C23×C13#12111yescharacteristic
137Q8×C13—22no—
138Q8×C13—24no—
139Q8×C13C2×Q1614yes—
140C2×C4×C13—22no—
141C2×C4×C13—24no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
144C2×C4×C13—41no—
145C2×C4×C13—81no—
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13C2×Q1612yes—
150C2×C4×C13#13512yes—
151C2×C4×C13C22×D411yescharacteristic
152C2×C4×C13C22×D411yescharacteristic
153C2×C4×C13C2×#4111yescharacteristic
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—42no—
157C2×Dic13—82no—
158Dic26—42no—
159Dic26—82no—
160Dic26—81no—
161Dic26—82no—
162C8×C13—24no—
163C8×C13—42no—
164#1055—42no—
165#1055—42no—
166#533—131no—
167C2×C4⋊Q8—131no—
168C2×C4×Q8C2×D1311yescharacteristic
169#500—132no—
170#487—132no—
171#484—262no—
172#479—262no—
173#477—134no—
174#477—132no—
175#477—262no—
176#477—262no—
177#475—132no—
178C8×Q8—22no—
179C8×Q8C2×D1314yes—
180#431—22no—
181#431C2×D1311yescharacteristic
182#431C2×D1311yescharacteristic
183#428—261no—
184C2×#107—261no—
185#423—131no—
186C2×C4⋊C8—131no—
187#419—261no—
188C2×#103—261no—
189#335—134no—
190#333—132no—
191#333—134no—
192#332—132no—
193C22×C13—21no—
194C22×C13—21no—
195C22×C13#46712yes—
196C22×C13C2×#12111yescharacteristic
197C4×C13—21no—
198C4×C13—24no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—42no—
202C4×C13#46712yes—
203C4×C13C22×Q1611yescharacteristic
204C4×C13C2×#13511yescharacteristic
205C4×C13#57812yes—
206Dic13—81no—
207Dic13—82no—
208Dic13—81no—
209C22×Q8—261no—
210C22×Q8D5211yescharacteristic
211C2×M16—261no—
212C22×C8—261no—
213C4⋊Q8—132no—
214C4⋊Q8—131no—
215C4⋊Q8—131no—
216C4⋊Q8—261no—
217C4⋊Q8—261no—
218C4⋊Q8—261no—
219#125—261no—
220C22⋊Q8—261no—
221C22⋊Q8—261no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—261no—
225C4×Q8—261no—
226C4×Q8D5212yes—
227C4×Q8C22×D1312yes—
228#117—261no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4D5211yescharacteristic
233C2×C42—21no—
234C2×C42C22×D1311yescharacteristic
235#107—264no—
236#107—264no—
237#107—262no—
238#106—262no—
239C4⋊C8—24no—
240C4⋊C8—132no—
241C4⋊C8—132no—
242C4⋊C8—261no—
243C4⋊C8—261no—
244C4⋊C8C22⋊D1312yes—
245C4⋊C8C22×D1312yes—
246#103—264no—
247#103—262no—
248#103—262no—
249#103—264no—
250C22⋊C8—21no—
251C22⋊C8C22⋊D1312yes—
252C4×C8—24no—
253C4×C8—21no—
254C4×C8C22×D1312yes—
255C2×C13—22no—
256C2×C13#304411yescharacteristic
257C2×C13C2×#46711yescharacteristic
258C2×C13#306811yescharacteristic
259C2×Q8—22no—
260C2×Q8—21no—
261C2×Q8—261no—
262C2×Q8—262no—
263C2×Q8—261no—
264C2×Q8—521no—
265C2×Q8—1042no—
266C2×Q8Dic5214yes—
267C2×Q8C2×D5212yes—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—521no—
271C22×C4C2×D5211yescharacteristic
272C22×C4#612711yescharacteristic
273C22×C4C2×C22⋊D1311yescharacteristic
274M16—522no—
275C2×C8—22no—
276C2×C8—262no—
277C2×C8—262no—
278C2×C8—522no—
279C2×C8C2×C22⋊D1314yes—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—261no—
284C4⋊C4—262no—
285C4⋊C4—261no—
286C4⋊C4—261no—
287C4⋊C4—262no—
288C4⋊C4—261no—
289C4⋊C4—521no—
290C4⋊C4—521no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4C2×D5212yes—
294C22⋊C4—521no—
295C42—22no—
296C42—22no—
297C42—521no—
298C42C2×D5211yescharacteristic
299C42#612711yescharacteristic
300C42C2×C22⋊D1311yescharacteristic
301C42C23×D1311yescharacteristic
302C13#1940511yescharacteristic, complemented, Sylow
303C23#8818411yescharacteristic
304Q8—22no—
305Q8—24no—
306Q8—522no—
307Q8—1041no—
308Q8—1042no—
309Q8—1042no—
310Q8C2×Dic5214yes—
311C2×C4—22no—
312C2×C4—24no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—522no—
320C2×C4—1042no—
321C2×C4#8815812yes—
322C2×C4C2×Dic5212yes—
323C2×C4#8818411yescharacteristic
324C2×C4#8818411yescharacteristic
325C2×C4#8818411yescharacteristic
326C2×C4C22×D5211yescharacteristic
327C2×C4C2×#612711yescharacteristic
328C2×C4C22×C22⋊D1311yescharacteristic
329C8—24no—
330C8—42no—
331C8—522no—
332C8—522no—
333C22—21no—
334C22—21no—
335C22#1171877712yes—
336C22C2×#8818411yescharacteristic
337C4—21no—
338C4—24no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—1041no—
343C4—1042no—
344C4—1041no—
345C4#1171877712yes—
346C4C2×#8815811yescharacteristic
347C4C22×Dic5211yescharacteristic
348C4#1171954312yes—
349C2—22no—
350C2#1312436611yescharacteristic
351C2C2×#1171877711yescharacteristic
352C2#1312456411yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#2982C2
socleC22×C13C2×#121
prime radicalC23×C13#121
hypercenter#2982D13
hypocenterC13#19405
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
4. #13114294C2semidirect
5. #13114240C2semidirect
302. C13#19405semidirect

Maximal subgroups

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

subgroupindex
#131259892
#131246412
C2×#117186822
#131142942
#131142402
#131136112
#131135162
#131134912
C13×#29822
#1940513