Finite Group Databasebeta

← #15848282

Subgroups — #15848282

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#13125984C211yesmaximal, characteristic
2C2×#11718682C211yesmaximal, characteristic
3#13123917C211yesmaximal, characteristic
4#13114292C214yesmaximal, complemented
5#13114238C214yesmaximal, complemented
6#13113612C211yesmaximal, characteristic
7#13113518C211yesmaximal, characteristic
8#13113493C211yesmaximal, characteristic
9C13×#3078C211yesmaximal, characteristic
10C13×#533C2211yescharacteristic
11C2×C4×Q8×C13C2211yescharacteristic
12C2×#88123C2211yescharacteristic
13C13×#479—22no—
14C13×#477C2212yes—
15C13×#475C2212yes—
16C13×#428—21no—
17C13×#423C2211yescharacteristic
18C13×#419—21no—
19C2×#88075—21no—
20#11718742C2212yes—
21#11718739C2212yes—
22#11718705—22no—
23Q8×#1055—22no—
24Q8×#1055C2214yes—
25#11718682—22no—
26#11718682—22no—
27#11718682C2214yes—
28C2×#88047—21no—
29#11718586—22no—
30#11718586C2211yescharacteristic
31#11718586C2211yescharacteristic
32C2×C4⋊#1055C2211yescharacteristic
33#11718139C2212yes—
34#11718138C2212yes—
35#11718073C2214yes—
36#11718071C2214yes—
37C22×Q8×C13D411yescharacteristic
38C22×Dic26—21no—
39C2×C13×M16—21no—
40C13×C4⋊Q8C2311yescharacteristic
41C13×C4⋊Q8C2311yescharacteristic
42C13×#125—21no—
43C13×C22⋊Q8—21no—
44C13×C22⋊Q8—21no—
45C4×Q8×C13—21no—
46C4×Q8×C13—21no—
47C4×Q8×C13—21no—
48C4×Q8×C13—21no—
49C4×Q8×C13D412yes—
50C4×Q8×C13C2312yes—
51C13×#117—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4D411yescharacteristic
54C2×C42×C13—21no—
55C2×C42×C13C2311yescharacteristic
56C2×C4⋊Dic13—21no—
57C2×C4⋊Dic13—21no—
58C22×#1055—21no—
59#88123—21no—
60#88123—21no—
61#88123—21no—
62#88123C2312yes—
63C13×#107—22no—
64C13×#106—22no—
65C13×C4⋊C8—21no—
66C13×C4⋊C8C2312yes—
67C13×#103—22no—
68C13×#103—22no—
69#88075—24no—
70#88075—24no—
71C22⋊#1055—21no—
72C22⋊#1055D412yes—
73#88047—24no—
74#88047—24no—
75C4⋊#1055—21no—
76C4⋊#1055—24no—
77C4⋊#1055D412yes—
78C4⋊#1055C2312yes—
79C4⋊#1055C2312yes—
80C4×#1055—21no—
81C4×#1055—24no—
82C4×#1055C2312yes—
83#19405—131nomaximal, Sylow
84C2×Q8×C13—21no—
85C2×Q8×C13—22no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13Q1614yes—
89C2×Q8×C13C2×D412yes—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13#4111yescharacteristic
95C22×Dic13—41no—
96C2×Dic26—22no—
97C2×Dic26—41no—
98C2×Dic26—82no—
99C13×M16—42no—
100C2×C8×C13—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4C2×D412yes—
111C13×C22⋊C4—41no—
112C42×C13—22no—
113C42×C13—22no—
114C42×C13—41no—
115C42×C13C2×D411yescharacteristic
116C42×C13C2×D411yescharacteristic
117C42×C13#4111yescharacteristic
118C42×C13C2411yescharacteristic
119C4⋊Dic13—22no—
120C4⋊Dic13—22no—
121C4⋊Dic13—41no—
122C4⋊Dic13—41no—
123C2×#1055—22no—
124C2×#1055—22no—
125C2×#1055—42no—
126C2×#1055C2×D414yes—
127#3230—131no—
128#3078D1311yescharacteristic
129C2×#477—131no—
130#2982—131no—
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×C13—42no—
140Q8×C13—81no—
141Q8×C13C2×Q1614yes—
142C2×C4×C13—22no—
143C2×C4×C13—24no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—81no—
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13C2×Q1612yes—
154C2×C4×C13#13512yes—
155C2×C4×C13C22×D411yescharacteristic
156C2×C4×C13C22×D411yescharacteristic
157C2×C4×C13C2×#4111yescharacteristic
158C2×Dic13—42no—
159C2×Dic13—82no—
160Dic26—82no—
161Dic26—82no—
162C8×C13—42no—
163#1055—24no—
164#1055—42no—
165#1055—42no—
166#533C2×D1311yescharacteristic
167C2×C4⋊Q8—131no—
168C2×C4×Q8C2×D1311yescharacteristic
169#500—132no—
170#487—132no—
171#484—262no—
172#479—22no—
173#477—134no—
174#477—262no—
175#477—262no—
176#477C2×D1312yes—
177#475C2×D1312yes—
178C8×Q8—134no—
179C8×Q8—262no—
180#431—131no—
181#431—131no—
182#431—262no—
183#428—21no—
184C2×#107—261no—
185#423C2×D1311yescharacteristic
186C2×C4⋊C8—131no—
187#419—21no—
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—81no—
203C4×C13—81no—
204C4×C13#46712yes—
205C4×C13C22×Q1611yescharacteristic
206C4×C13C2×#13511yescharacteristic
207C4×C13#57812yes—
208Dic13—82no—
209C22×Q8—261no—
210C22×Q8C22⋊D1311yescharacteristic
211C2×M16—21no—
212C22×C8—261no—
213C4⋊Q8—132no—
214C4⋊Q8—261no—
215C4⋊Q8—261no—
216C4⋊Q8—261no—
217C4⋊Q8C22×D1311yescharacteristic
218C4⋊Q8C22×D1311yescharacteristic
219#125—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8—21no—
225C4×Q8—21no—
226C4×Q8C22⋊D1312yes—
227C4×Q8C22×D1312yes—
228#117—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4—261no—
232C2×C4⋊C4C22⋊D1311yescharacteristic
233C2×C42—21no—
234C2×C42C22×D1311yescharacteristic
235#107—22no—
236#107—264no—
237#107—264no—
238#106—22no—
239C4⋊C8—21no—
240C4⋊C8—132no—
241C4⋊C8—132no—
242C4⋊C8—132no—
243C4⋊C8—264no—
244C4⋊C8—261no—
245C4⋊C8C22×D1312yes—
246#103—22no—
247#103—22no—
248#103—264no—
249#103—264no—
250C22⋊C8—132no—
251C22⋊C8—261no—
252C4×C8—132no—
253C4×C8—264no—
254C4×C8—261no—
255C2×C13—22no—
256C2×C13#304411yescharacteristic
257C2×C13C2×#46711yescharacteristic
258C2×C13#306811yescharacteristic
259C2×Q8—21no—
260C2×Q8—22no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—262no—
264C2×Q8—521no—
265C2×Q8—1042no—
266C2×Q8#610714yes—
267C2×Q8C2×C22⋊D1312yes—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—521no—
271C22×C4D4×D1311yescharacteristic
272C22×C4#612911yescharacteristic
273C22×C4C2×C22⋊D1311yescharacteristic
274M16—42no—
275C2×C8—22no—
276C2×C8—134no—
277C2×C8—262no—
278C2×C8—262no—
279C2×C8—522no—
280C4⋊C4—22no—
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—262no—
290C4⋊C4—262no—
291C4⋊C4—521no—
292C4⋊C4—521no—
293C4⋊C4C2×C22⋊D1312yes—
294C22⋊C4—41no—
295C42—22no—
296C42—22no—
297C42—41no—
298C42D4×D1311yescharacteristic
299C42#612911yescharacteristic
300C42C2×C22⋊D1311yescharacteristic
301C42C23×D1311yescharacteristic
302C13#1940511yescharacteristic, complemented, Sylow
303C23#8819311yescharacteristic
304Q8—24no—
305Q8—22no—
306Q8—42no—
307Q8—81no—
308Q8—1042no—
309Q8—1042no—
310Q8C2×#610714yes—
311C2×C4—24no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—522no—
320C2×C4—1042no—
321C2×C4#8819311yescharacteristic
322C2×C4#8819311yescharacteristic
323C2×C4#8819311yescharacteristic
324C2×C4C2×#610712yes—
325C2×C4#8820412yes—
326C2×C4C2×D4×D1311yescharacteristic
327C2×C4C2×#612911yescharacteristic
328C2×C4C22×C22⋊D1311yescharacteristic
329C8—42no—
330C8—264no—
331C8—522no—
332C8—522no—
333C22—21no—
334C22—21no—
335C22#1171871212yes—
336C22C2×#8819311yescharacteristic
337C4—21no—
338C4—24no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—81no—
343C4—81no—
344C4—1042no—
345C4#1171871212yes—
346C4#1171948412yes—
347C4C22×#610711yescharacteristic
348C4C2×#8820411yescharacteristic
349C2—22no—
350C2#1312436811yescharacteristic
351C2C2×#1171871211yescharacteristic
352C2#1312456611yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#3078C2
socleC22×C13C2×#121
prime radicalC23×C13#121
hypercenter#3078D13
hypocenterC13#19405
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
4. #13114292C2semidirect
5. #13114238C2semidirect
302. C13#19405semidirect

Maximal subgroups

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

subgroupindex
#131259842
C2×#117186822
#131239172
#131142922
#131142382
#131136122
#131135182
#131134932
C13×#30782
#1940513