Finite Group Databasebeta

← #16069643

Subgroups — #16069643

Order 3328.

1304 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123111C211yesmaximal, characteristic
2#13123078C214yesmaximal
3#13123076C214yesmaximal
4#13123074C214yesmaximal
5#13122904C211yesmaximal, characteristic
6#13122903C212yesmaximal
7#13118144C214yesmaximal
8#13118143C214yesmaximal
9#13118143C214yesmaximal
10C4×#88124C212yesmaximal
11C4×C13×#125C211yesmaximal, characteristic
12C2×C13×#125C2211yescharacteristic
13C2×#88124C2212yes—
14C13×#389C2212yes—
15C13×#387C2214yes—
16C13×#382C2211yescharacteristic
17C4×C13×C4⋊C4C2212yes—
18C4×C13×C4⋊C4C2214yes—
19C43×C13C2211yescharacteristic
20#11718647C2214yes—
21#11718647C2214yes—
22#11718645C2214yes—
23#11718645C2214yes—
24#11718645C2214yes—
25#11718645C2214yes—
26#11718644C2214yes—
27#11718644C2214yes—
28#11718643C2214yes—
29#11718643C2214yes—
30#11718641C2214yes—
31#11718641C2214yes—
32#11718597C2212yes—
33C4×C4⋊Dic13C2212yes—
34C4×C4⋊Dic13C2214yes—
35C4×C4⋊Dic13C2212yes—
36#11718594C2214yes—
37#11718594C2214yes—
38#11718593C2214yes—
39C4×#6101C2214yes—
40C4×#6101C2214yes—
41C4×#6101C2214yes—
42C4×#6101C2214yes—
43#11718589C2212yes—
44#11718589C2212yes—
45#11718322C2214yes—
46#11718322C2214yes—
47#11718321C2214yes—
48#11718321C2214yes—
49#11718320C2214yes—
50#11718320C2214yes—
51#11718319C2214yes—
52#11718319C2214yes—
53#11718319C2214yes—
54#11718319C2214yes—
55#11718318C2214yes—
56#11718318C2214yes—
57C13×#125—24no—
58C2×C13×C4⋊C4C2314yes—
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C4⋊C4C2312yes—
61C2×C13×C4⋊C4C2314yes—
62C2×C42×C13C2314yes—
63C2×C42×C13C2311yescharacteristic
64C2×C42×C13C2312yes—
65C2×C42×C13C2312yes—
66C2×C42×C13C2311yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×C4⋊Dic13C2312yes—
69C2×C4⋊Dic13C2312yes—
70C2×C4⋊Dic13C2312yes—
71C2×C4⋊Dic13C2314yes—
72C2×C4⋊Dic13C2314yes—
73C2×C4⋊Dic13C2312yes—
74C2×#6101C2314yes—
75C2×#6101C2314yes—
76C2×#6101C2314yes—
77C2×#6101C2314yes—
78C2×#6101C2314yes—
79C2×#6101C2314yes—
80C2×#6101C2314yes—
81C2×#6101C2314yes—
82C2×C4×Dic13C2314yes—
83C2×C4×Dic13C2314yes—
84#88124—28no—
85C13×#95C2314yes—
86C13×#95C2314yes—
87C13×#95C2314yes—
88#88071C2314yes—
89#88071C2314yes—
90#88071C2314yes—
91#88071C2314yes—
92#88071C2314yes—
93#88071C2314yes—
94#88071C2314yes—
95#88071C2314yes—
96#88071C2314yes—
97#88071C2314yes—
98#88071C2314yes—
99#88071C2314yes—
100#88071C2314yes—
101#88071C2314yes—
102#88071C2314yes—
103#88071C2314yes—
104#36701—131nomaximal, Sylow
105C22×C4×C13C2412yes—
106C22×C4×C13C2414yes—
107C22×C4×C13C2411yescharacteristic
108C22×C4×C13C2414yes—
109C22×C4×C13C2411yescharacteristic
110C22×C4×C13C2412yes—
111C22×C4×C13C2411yescharacteristic
112C22×Dic13C2414yes—
113C22×Dic13C2414yes—
114C22×Dic13C2414yes—
115C22×Dic13C2414yes—
116C13×C4⋊C4—24no—
117C13×C4⋊C4—28no—
118C13×C4⋊C4—42no—
119C13×C4⋊C4—44no—
120C42×C13—22no—
121C42×C13—24no—
122C42×C13—28no—
123C42×C13—42no—
124C42×C13—41no—
125C42×C13#4114yes—
126C4⋊Dic13—24no—
127C4⋊Dic13—24no—
128C4⋊Dic13—42no—
129C4⋊Dic13—44no—
130C4⋊Dic13—42no—
131C4⋊Dic13—44no—
132#6101—28no—
133#6101—28no—
134#6101—44no—
135#6101—44no—
136#6101—44no—
137#6101—44no—
138#6101—44no—
139#6101—44no—
140C4×Dic13—28no—
141C4×Dic13—28no—
142#2845—131no—
143#2839—134no—
144#2839—134no—
145#2839—134no—
146#2822—131no—
147#2822—132no—
148#2402—134no—
149#2402—134no—
150#2402—134no—
151C4×#125—132no—
152C4×#125D1311yescharacteristic
153C23×C13C2511yescharacteristic
154C2×C4×C13—21no—
155C2×C4×C13—22no—
156C2×C4×C13—22no—
157C2×C4×C13—21no—
158C2×C4×C13—24no—
159C2×C4×C13—24no—
160C2×C4×C13—21no—
161C2×C4×C13—22no—
162C2×C4×C13—24no—
163C2×C4×C13—22no—
164C2×C4×C13—22no—
165C2×C4×C13—24no—
166C2×C4×C13—24no—
167C2×C4×C13—24no—
168C2×C4×C13—22no—
169C2×C4×C13C2×#4112yes—
170C2×C4×C13C2×#4114yes—
171C2×C4×C132−1+412yes—
172C2×C4×C132−1+414yes—
173C2×Dic13—24no—
174C2×Dic13—24no—
175C2×Dic13—24no—
176C2×Dic13—24no—
177C2×Dic13—24no—
178C2×Dic13—24no—
179C2×Dic13—24no—
180C2×Dic13—24no—
181C2×Dic13—24no—
182C2×Dic13—24no—
183C2×Dic13—24no—
184C2×Dic13—24no—
185C2×#125—132no—
186C2×#125C2×D1311yescharacteristic
187#400—134no—
188#400—134no—
189#400—134no—
190#400—134no—
191#400—134no—
192#400—134no—
193#400—134no—
194#400—134no—
195#400—134no—
196#400—134no—
197#400—134no—
198#400—134no—
199#398—134no—
200#398—134no—
201#398—134no—
202#398—134no—
203#398—134no—
204#398—134no—
205#398—134no—
206#398—134no—
207#398—134no—
208#398—134no—
209#398—134no—
210#398—134no—
211#389—132no—
212#389—132no—
213#389C2×D1312yes—
214#387—134no—
215#387—134no—
216#387C2×D1314yes—
217#382—132no—
218#382C2×D1311yescharacteristic
219C4×C4⋊C4—134no—
220C4×C4⋊C4—134no—
221C4×C4⋊C4—132no—
222C4×C4⋊C4—132no—
223C4×C4⋊C4—134no—
224C4×C4⋊C4—134no—
225C4×C4⋊C4—134no—
226C4×C4⋊C4C2×D1314yes—
227C4×C4⋊C4C2×D1312yes—
228#376—134no—
229C43C2×D1311yescharacteristic
230C22×C13C22×#4111yescharacteristic
231C22×C13C2×2−1+411yescharacteristic
232C22×C13C2×2−1+412yes—
233C22×C13#58511yescharacteristic
234C22×C13#58512yes—
235C4×C13—24no—
236C4×C13—22no—
237C4×C13—44no—
238C4×C13—42no—
239C4×C13—44no—
240C4×C13—41no—
241C4×C13#56414yes—
242Dic13—44no—
243Dic13—44no—
244Dic13—44no—
245Dic13—44no—
246#125—24no—
247#125—268no—
248C2×C4⋊C4—134no—
249C2×C4⋊C4—134no—
250C2×C4⋊C4—132no—
251C2×C4⋊C4—132no—
252C2×C4⋊C4—134no—
253C2×C4⋊C4—134no—
254C2×C4⋊C4—134no—
255C2×C4⋊C4—134no—
256C2×C4⋊C4—134no—
257C2×C4⋊C4—134no—
258C2×C4⋊C4—132no—
259C2×C4⋊C4—132no—
260C2×C4⋊C4—134no—
261C2×C4⋊C4—134no—
262C2×C4⋊C4C22×D1314yes—
263C2×C4⋊C4C22×D1312yes—
264C2×C4⋊C4C22×D1312yes—
265C2×C4⋊C4C22×D1314yes—
266C2×C42—134no—
267C2×C42—134no—
268C2×C42C22×D1311yescharacteristic
269C2×C42C22×D1312yes—
270C2×C42C22×D1314yes—
271C2×C42C22×D1311yescharacteristic
272C2×C42C22×D1312yes—
273C2×C42C22×D1311yescharacteristic
274#95—134no—
275#95—134no—
276#95—134no—
277#95—134no—
278#95—134no—
279#95—134no—
280#95—134no—
281#95—134no—
282#95—134no—
283#95—134no—
284#95—134no—
285#95—134no—
286#95—134no—
287#95—134no—
288#95—134no—
289#95—134no—
290#95C22×D1314yes—
291#95C22×D1314yes—
292#95C22×D1314yes—
293C2×C13#346112yes—
294C2×C13#346111yescharacteristic
295C2×C13C2×#56411yescharacteristic
296C2×C13#353112yes—
297C2×C13#353111yescharacteristic
298C22×C4—134no—
299C22×C4—134no—
300C22×C4—134no—
301C22×C4—134no—
302C22×C4C23×D1312yes—
303C22×C4C23×D1314yes—
304C22×C4C23×D1311yescharacteristic
305C22×C4C23×D1314yes—
306C22×C4C23×D1311yescharacteristic
307C22×C4C23×D1312yes—
308C22×C4C23×D1311yescharacteristic
309C4⋊C4—28no—
310C4⋊C4—24no—
311C4⋊C4—42no—
312C4⋊C4—44no—
313C4⋊C4—268no—
314C4⋊C4—268no—
315C4⋊C4—264no—
316C4⋊C4—264no—
317C4⋊C4—524no—
318C4⋊C4—524no—
319C4⋊C4—524no—
320C4⋊C4—524no—
321C4⋊C4—524no—
322C4⋊C4—524no—
323C4⋊C4—522no—
324C4⋊C4—522no—
325C4⋊C4—524no—
326C4⋊C4—524no—
327C42—22no—
328C42—24no—
329C42—28no—
330C42—41no—
331C42—42no—
332C42—268no—
333C42—268no—
334C42#612714yes—
335C13#3670111yescharacteristic, complemented, Sylow
336C23C24×D1311yescharacteristic
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—264no—
353C2×C4—264no—
354C2×C4—264no—
355C2×C4—264no—
356C2×C4—264no—
357C2×C4—264no—
358C2×C4—264no—
359C2×C4—264no—
360C2×C4—264no—
361C2×C4—264no—
362C2×C4—264no—
363C2×C4—264no—
364C2×C4C2×#612714yes—
365C2×C4C2×#612712yes—
366C2×C4#8825412yes—
367C2×C4#8825714yes—
368C22C22×#612711yescharacteristic
369C22C2×#8825411yescharacteristic
370C22C2×#8825712yes—
371C22#1171964811yescharacteristic
372C22#1171964812yes—
373C4—24no—
374C4—22no—
375C4—42no—
376C4—44no—
377C4—41no—
378C4—44no—
379C4—524no—
380C4—524no—
381C4—524no—
382C4—524no—
383C4C13⋊#56414yes—
384C2#1312826312yes—
385C2#1312826911yescharacteristic
386C2C2×C13⋊#56411yescharacteristic
387C2#1312898112yes—
388C2#1312898311yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutator, socle, prime radical, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC4×C13×#125C2
hypercenterC4×#125D13
hypocenterC13#36701
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
335. C13#36701semidirect

Maximal subgroups

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

subgroupindex
#131231112
#131230782
#131230762
#131230742
#131229042
#131229032
#131181442
#131181432
C4×#881242
C4×C13×#1252
#3670113