Finite Group Databasebeta

← #15848249

Subgroups — #15848249

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124637C211yesmaximal, characteristic
2C2×#11718751C211yesmaximal, characteristic
3#13123916C211yesmaximal, characteristic
4#13114263C214yesmaximal, complemented
5#13114215C214yesmaximal, complemented
6#13113607C211yesmaximal, characteristic
7#13113508C211yesmaximal, characteristic
8#13113493C211yesmaximal, characteristic
9C13×#3229C211yesmaximal, characteristic
10C13×#533C2211yescharacteristic
11C2×C13×C4⋊Q8C2211yescharacteristic
12C22×#6107—21no—
13C2×C4×Dic26C2211yescharacteristic
14C13×#498C2212yes—
15C13×#487C2212yes—
16C13×#483—22no—
17C13×#475—22no—
18C13×#431C2211yescharacteristic
19C2×#88075—21no—
20#11718755C2212yes—
21#11718752C2212yes—
22#11718751—22no—
23#11718751C2214yes—
24#11718724—22no—
25#11718665—21no—
26#11718656—21no—
27#11718586C2211yescharacteristic
28#11718585C2211yescharacteristic
29C2×C4⋊#1055C2211yescharacteristic
30#11718491—22no—
31#11718379—22no—
32C8×Dic26C2214yes—
33#11718139C2214yes—
34#11718139C2212yes—
35#11718138C2212yes—
36#11718049C2214yes—
37C22×Q8×C13—21no—
38C22×Dic26D411yescharacteristic
39C13×C4⋊Q8—21no—
40C13×C4⋊Q8—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8C2312yes—
43C13×C4⋊Q8C2311yescharacteristic
44C13×C4⋊Q8C2311yescharacteristic
45C13×#125—21no—
46C13×C22⋊Q8—21no—
47C13×C22⋊Q8—21no—
48C4×Q8×C13—21no—
49C4×Q8×C13—21no—
50C13×#117—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C42×C13C2311yescharacteristic
54C2×#6107—24no—
55C2×#6107—44no—
56C2×C4⋊Dic13D411yescharacteristic
57C2×#6101—21no—
58C2×C4×Dic13—21no—
59C2×#6099—21no—
60C22×#1055—21no—
61C4×Dic26—21no—
62C4×Dic26—21no—
63C4×Dic26D412yes—
64C4×Dic26C2312yes—
65C13×#106—24no—
66C13×C4⋊C8D412yes—
67C13×#103—24no—
68C13×C22⋊C8D412yes—
69C4×C8×C13C2312yes—
70#88075—24no—
71C22⋊#1055—21no—
72#88054—24no—
73C8×Dic13—24no—
74#88050—22no—
75#88050—22no—
76#88048—22no—
77#88047—22no—
78C4⋊#1055—21no—
79C4⋊#1055—21no—
80C4⋊#1055C2312yes—
81C4⋊#1055C2312yes—
82C4⋊#1055C2312yes—
83C4×#1055—21no—
84#19402—131nomaximal, Sylow
85C2×Q8×C13—22no—
86C2×Q8×C13—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—41no—
89C2×Q8×C13—42no—
90C2×Q8×C13—42no—
91C22×C4×C13—41no—
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13#4111yescharacteristic
95C22×Dic13—21no—
96C22×Dic13—21no—
97C2×Dic26—21no—
98C2×Dic26—22no—
99C2×Dic26SD1614yes—
100C2×Dic26C2×D412yes—
101C2×C8×C13C2×D414yes—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—21no—
106C13×C4⋊C4—22no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—41no—
109C13×C4⋊C4—41no—
110C13×C4⋊C4—41no—
111C13×C4⋊C4—41no—
112C13×C22⋊C4—41no—
113C42×C13—41no—
114C42×C13C2×D411yescharacteristic
115C42×C13C2×D411yescharacteristic
116C42×C13#4111yescharacteristic
117C42×C13C2411yescharacteristic
118#6107—48no—
119C4⋊Dic13—21no—
120C4⋊Dic13C2×D412yes—
121#6101—22no—
122#6101—22no—
123C4×Dic13—22no—
124C4×Dic13—22no—
125#6099—42no—
126C2×#1055—22no—
127C2×#1055—22no—
128C2×#1055—22no—
129C2×#1055—42no—
130#3229D1311yescharacteristic
131#3078—131no—
132C2×#462—131no—
133#2982—131no—
134#1680—134no—
135#1672—134no—
136#1570—131no—
137#1546—131no—
138#1542—131no—
139C23×C13#12111yescharacteristic
140Q8×C13—42no—
141Q8×C13—42no—
142Q8×C13—42no—
143Q8×C13—81no—
144Q8×C13—82no—
145C2×C4×C13—22no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—42no—
150C2×C4×C13—82no—
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12111yescharacteristic
154C2×C4×C13C2×SD1612yes—
155C2×C4×C13#13512yes—
156C2×C4×C13C22×D411yescharacteristic
157C2×C4×C13C22×D411yescharacteristic
158C2×C4×C13C2×#4111yescharacteristic
159C2×Dic13—22no—
160C2×Dic13—24no—
161C2×Dic13—22no—
162C2×Dic13—81no—
163Dic26—22no—
164Dic26—24no—
165Dic26C2×SD1614yes—
166C8×C13—24no—
167#1055—42no—
168#1055—42no—
169#1055—42no—
170C22×Q16—261no—
171#533C2×D1311yescharacteristic
172C2×C4⋊Q8C2×D1311yescharacteristic
173C2×C4×Q8—131no—
174#498C2×D1312yes—
175#487C2×D1312yes—
176#483—22no—
177#479—262no—
178#477—132no—
179#475—22no—
180#475—132no—
181#462—134no—
182#462—262no—
183C8×Q8—134no—
184C8×Q8—262no—
185#431—131no—
186#431—262no—
187#431C2×D1311yescharacteristic
188#428—261no—
189#423—131no—
190C2×C4⋊C8—131no—
191#419—261no—
192C2×#103—261no—
193#334—134no—
194#333—132no—
195#332—132no—
196#332—134no—
197C22×C13—21no—
198C22×C13—21no—
199C22×C13#46512yes—
200C22×C13C2×#12111yescharacteristic
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—81no—
205C4×C13—82no—
206C4×C13—81no—
207C4×C13#46512yes—
208C4×C13C22×SD1611yescharacteristic
209C4×C13C2×#13511yescharacteristic
210C4×C13#57812yes—
211Dic13—24no—
212Dic13—42no—
213C22×Q8—21no—
214C22×Q8—131no—
215C2×Q16—264no—
216C2×Q16—524no—
217C2×M16—261no—
218C22×C8—261no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8C22×D1312yes—
223C4⋊Q8C22×D1311yescharacteristic
224C4⋊Q8C22×D1311yescharacteristic
225#125—21no—
226C22⋊Q8—21no—
227C22⋊Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—132no—
231C4×Q8—132no—
232C4×Q8—261no—
233C4×Q8—261no—
234#117—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—131no—
238C2×C4⋊C4—261no—
239C2×C42—261no—
240C2×C42C22×D1311yescharacteristic
241#107—262no—
242#106—24no—
243#106—262no—
244C4⋊C8—132no—
245C4⋊C8—132no—
246C4⋊C8—132no—
247C4⋊C8—264no—
248C4⋊C8—261no—
249C4⋊C8—261no—
250C4⋊C8C22⋊D1312yes—
251#103—24no—
252#103—262no—
253#103—262no—
254#103—264no—
255C22⋊C8—261no—
256C22⋊C8C22⋊D1312yes—
257C4×C8—264no—
258C4×C8—261no—
259C4×C8C22×D1312yes—
260C2×C13—22no—
261C2×C13#304411yescharacteristic
262C2×C13C2×#46511yescharacteristic
263C2×C13#306911yescharacteristic
264C2×Q8—22no—
265C2×Q8—21no—
266C2×Q8—21no—
267C2×Q8—41no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8—134no—
271C2×Q8—132no—
272C2×Q8—262no—
273C2×Q8—261no—
274C22×C4—41no—
275C22×C4—261no—
276C22×C4—261no—
277C22×C4D4×D1311yescharacteristic
278C22×C4#612911yescharacteristic
279C22×C4C2×C22⋊D1311yescharacteristic
280Q16—528no—
281M16—522no—
282C2×C8—262no—
283C2×C8—262no—
284C2×C8—262no—
285C2×C8—522no—
286C2×C8C2×C22⋊D1314yes—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—22no—
290C4⋊C4—21no—
291C4⋊C4—22no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—132no—
298C4⋊C4—261no—
299C4⋊C4—262no—
300C4⋊C4—262no—
301C22⋊C4—41no—
302C42—41no—
303C42—262no—
304C42—262no—
305C42D4×D1311yescharacteristic
306C42#612911yescharacteristic
307C42C2×C22⋊D1311yescharacteristic
308C42C23×D1311yescharacteristic
309C13#1940211yescharacteristic, complemented, Sylow
310C23#8819211yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—42no—
314Q8—81no—
315Q8—82no—
316Q8—134no—
317Q8—262no—
318Q8—264no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—262no—
326C2×C4—264no—
327C2×C4—262no—
328C2×C4—1041no—
329C2×C4SD16×D1312yes—
330C2×C4#8817012yes—
331C2×C4#8819211yescharacteristic
332C2×C4#8819211yescharacteristic
333C2×C4#8819211yescharacteristic
334C2×C4C2×D4×D1311yescharacteristic
335C2×C4C2×#612911yescharacteristic
336C2×C4C22×C22⋊D1311yescharacteristic
337C8—24no—
338C8—522no—
339C8—522no—
340C8—522no—
341C22—21no—
342C22—21no—
343C22#1171883212yes—
344C22C2×#8819211yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—81no—
349C4—82no—
350C4—81no—
351C4—264no—
352C4—522no—
353C4#1171883212yes—
354C4C2×SD16×D1311yescharacteristic
355C4C2×#8817011yescharacteristic
356C4#1171954312yes—
357C2—22no—
358C2#1312436211yescharacteristic
359C2C2×#1171883211yescharacteristic
360C2#1312456911yescharacteristic
subgroupG/H
centerC22C2×#88192
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#3229C2
socleC22×C13C2×#121
prime radicalC23×C13#121
hypercenter#3229D13
hypocenterC13#19402
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
4. #13114263C2semidirect
5. #13114215C2semidirect
309. C13#19402semidirect

Maximal subgroups

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

subgroupindex
#131246372
C2×#117187512
#131239162
#131142632
#131142152
#131136072
#131135082
#131134932
C13×#32292
#1940213