Finite Group Databasebeta

← #15789691

Subgroups — #15789691

Order 3328.

1830 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic13C211yesmaximal, characteristic, complemented
2C2×#11718612C213yesmaximal
3#13113107C211yesmaximal, characteristic, complemented
4#13113101C213yesmaximal, complemented
5#13113081C213yesmaximal
6#13113061C213yesmaximal, complemented
7C2×C13×#393C211yesmaximal, characteristic
8C23×Q8×C13C2211yescharacteristic
9C22×C13×C22⋊C4C2213yes—
10C22×C22⋊Dic13C2211yescharacteristic
11C22×C22⋊Dic13C2213yes—
12C2×Q8×Dic13—212no—
13C22×C4⋊Dic13C2213yes—
14C22×C4⋊Dic13C2213yes—
15C22×C4×Dic13C2213yes—
16C13×#393C418yescomplemented
17C2×C13×#95C2213yes—
18C2×#88071C2213yes—
19C2×#88071C2213yes—
20C2×#88071C2213yes—
21C2×#88071C2216yes—
22#11718612—212no—
23C25×C13C2311yescharacteristic
24C22×Q8×C13—26no—
25C22×Q8×C13—26no—
26C22×Q8×C13C2×C414yes—
27C23×C4×C13C2313yes—
28C23×C4×C13C2313yes—
29C23×Dic13C2311yescharacteristic
30C23×Dic13C2313yes—
31C23×Dic13C2313yes—
32C23×Dic13C2311yescharacteristic
33C2×C13×C22⋊C4—26no—
34C2×C13×C22⋊C4—26no—
35C2×C13×C22⋊C4C2×C4112yes—
36C2×C22⋊Dic13—26no—
37C2×C22⋊Dic13—26no—
38C2×C22⋊Dic13—46no—
39Q8×Dic13—232no—
40C2×C4⋊Dic13—26no—
41C2×C4⋊Dic13—212no—
42C2×C4⋊Dic13—26no—
43C2×C4⋊Dic13—46no—
44C2×C4×Dic13—212no—
45C2×C4×Dic13D4112yes—
46C13×#95C2×C4112yes—
47#88071—26no—
48#88071—26no—
49#88071—26no—
50#88071—46no—
51#14301—131nomaximal, Sylow
52C24×C13—23no—
53C24×C13—23no—
54C24×C13—23no—
55C24×C13—21no—
56C24×C13—21no—
57C24×C13—23no—
58C24×C13C22×C412yes—
59C24×C13C2411yescharacteristic
60C2×Q8×C13—28no—
61C2×Q8×C13—224no—
62C2×Q8×C13—224no—
63C22×C4×C13—26no—
64C22×C4×C13—26no—
65C22×C4×C13—23no—
66C22×C4×C13—23no—
67C22×C4×C13—26no—
68C22×C4×C13—26no—
69C22×C4×C13C22×C416yes—
70C22×C4×C13C22×C416yes—
71C22×C4×C13C2×D416yes—
72C22×C4×C13#4116yes—
73C22×Dic13—21no—
74C22×Dic13—23no—
75C22×Dic13—26no—
76C22×Dic13—23no—
77C22×Dic13—26no—
78C22×Dic13—23no—
79C22×Dic13—23no—
80C22×Dic13—23no—
81C22×Dic13—26no—
82C22×Dic13—26no—
83C22×Dic13—23no—
84C22×Dic13—23no—
85C22×Dic13—23no—
86C22×Dic13—21no—
87C22×Dic13C2×D416yes—
88C22×Dic13C2×D416yes—
89C13×C22⋊C4—224no—
90C22⋊Dic13—412no—
91C22⋊Dic13—44no—
92C4⋊Dic13—224no—
93C4⋊Dic13—412no—
94C4×Dic13—224no—
95C22×C4×Q8—131no—
96C2×#393D1311yescharacteristic
97C2×#388—133no—
98#1446—131no—
99#1444—133no—
100#1439—133no—
101#1434—133no—
102C23×C13—26no—
103C23×C13—22no—
104C23×C13—26no—
105C23×C13—41no—
106C23×C13—43no—
107C23×C13—43no—
108C23×C13—43no—
109C23×C13—43no—
110C23×C13—43no—
111C23×C13—43no—
112C23×C13—43no—
113C23×C13—46no—
114C23×C13C23×C411yescharacteristic
115C23×C13C22×D413yes—
116C23×C13C2×#4113yes—
117C23×C13H(5,𝔽2)13yes—
118C23×C132−1+411yescharacteristic
119C23×C132−1+411yescharacteristic
120C23×C132−1+413yes—
121Q8×C13—232no—
122C2×C4×C13—212no—
123C2×C4×C13—26no—
124C2×C4×C13—26no—
125C2×C4×C13—212no—
126C2×C4×C13—26no—
127C2×C4×C13—212no—
128C2×C4×C13—43no—
129C2×C4×C13—43no—
130C2×C4×C13—46no—
131C2×C4×C13C4×D4112yes—
132C2×Dic13—26no—
133C2×Dic13—26no—
134C2×Dic13—26no—
135C2×Dic13—26no—
136C2×Dic13—26no—
137C2×Dic13—46no—
138C2×Dic13—46no—
139C2×Dic13—41no—
140C2×Dic13—43no—
141C2×Dic13—43no—
142C2×Dic13—43no—
143C2×Dic13—43no—
144C2×Dic13—43no—
145C2×Dic13—46no—
146C2×Dic13—46no—
147C2×Dic13#12014yes—
148C23×Q8C2×D1311yescharacteristic
149C2×C4×Q8—2612no—
150C22×C4⋊C4—133no—
151C22×C4⋊C4—133no—
152C22×C22⋊C4—131no—
153C22×C22⋊C4—133no—
154C22×C22⋊C4C2×D1313yes—
155C22×C42—133no—
156#393Dic1318yescomplemented
157#388—2612no—
158C2×#95—133no—
159C2×#95—133no—
160C2×#95—133no—
161C2×#95—136no—
162C2×#95C2×D1313yes—
163C22×C13—46no—
164C22×C13—46no—
165C22×C13—42no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13—83no—
169C22×C13—83no—
170C22×C13C2×C4×D413yes—
171C22×C13#51911yescharacteristic
172C22×C13#52013yes—
173C22×C13C2×#12011yescharacteristic
174C22×C13#52513yes—
175C22×C13#53513yes—
176C22×C13#53613yes—
177C22×C13#53613yes—
178C22×C13#53713yes—
179C22×C13#54113yes—
180C22×C13#54213yes—
181C22×C13#54216yes—
182C4×C13—212no—
183C4×C13—46no—
184Dic13—24no—
185Dic13—46no—
186Dic13—81no—
187Dic13—83no—
188C25C22×D1311yescharacteristic
189C22×Q8—26no—
190C22×Q8—26no—
191C22×Q8C2×Dic1314yes—
192C23×C4—131no—
193C23×C4—133no—
194C23×C4—131no—
195C23×C4—133no—
196C23×C4C22×D1313yes—
197C23×C4C22×D1313yes—
198C4×Q8—2632no—
199C2×C4⋊C4—2612no—
200C2×C4⋊C4—266no—
201C2×C4⋊C4—266no—
202C2×C4⋊C4—526no—
203C2×C22⋊C4—26no—
204C2×C22⋊C4—26no—
205C2×C22⋊C4—266no—
206C2×C22⋊C4—266no—
207C2×C22⋊C4—526no—
208C2×C22⋊C4C2×Dic13112yes—
209C2×C42—1312no—
210C2×C42—2612no—
211#95—266no—
212#95—266no—
213#95—266no—
214#95—526no—
215#95C2×Dic13112yes—
216C2×C13—82no—
217C2×C13C4×#12011yescharacteristic
218C2×C13#232313yes—
219C2×C13#232613yes—
220C2×C13#261411yescharacteristic
221C2×C13#261511yescharacteristic
222C2×C13#263213yes—
223C2×C13#263713yes—
224C24—23no—
225C24—23no—
226C24—21no—
227C24—21no—
228C24—23no—
229C24—23no—
230C24C22×Dic1312yes—
231C24C23×D1311yescharacteristic
232C2×Q8—28no—
233C2×Q8—224no—
234C2×Q8—224no—
235C22×C4—26no—
236C22×C4—26no—
237C22×C4—23no—
238C22×C4—23no—
239C22×C4—26no—
240C22×C4—26no—
241C22×C4—136no—
242C22×C4—136no—
243C22×C4—261no—
244C22×C4—263no—
245C22×C4—266no—
246C22×C4—263no—
247C22×C4—263no—
248C22×C4—266no—
249C22×C4—263no—
250C22×C4—263no—
251C22×C4—266no—
252C22×C4—263no—
253C22×C4—261no—
254C22×C4—266no—
255C22×C4—263no—
256C22×C4—263no—
257C22×C4D4×D1316yes—
258C22×C4#612916yes—
259C22×C4C22×Dic1316yes—
260C22×C4C22×Dic1316yes—
261C4⋊C4—2624no—
262C4⋊C4—5212no—
263C22⋊C4—224no—
264C22⋊C4—524no—
265C22⋊C4—5212no—
266C42—2624no—
267C13#1430111yescharacteristic, complemented, Sylow
268C23—26no—
269C23—22no—
270C23—26no—
271C23—43no—
272C23—41no—
273C23—43no—
274C23—43no—
275C23—43no—
276C23—43no—
277C23—43no—
278C23—43no—
279C23—46no—
280C23C2×D4×D1313yes—
281C23C2×#612913yes—
282C23#8825411yescharacteristic
283C23#8825411yescharacteristic
284C23#8825613yes—
285C23#8825713yes—
286C23C23×Dic1311yescharacteristic
287Q8—232no—
288C2×C4—212no—
289C2×C4—26no—
290C2×C4—212no—
291C2×C4—26no—
292C2×C4—26no—
293C2×C4—212no—
294C2×C4—43no—
295C2×C4—43no—
296C2×C4—46no—
297C2×C4—134no—
298C2×C4—266no—
299C2×C4—266no—
300C2×C4—266no—
301C2×C4—266no—
302C2×C4—266no—
303C2×C4—526no—
304C2×C4—526no—
305C2×C4—523no—
306C2×C4—521no—
307C2×C4—523no—
308C2×C4—523no—
309C2×C4—526no—
310C2×C4—523no—
311C2×C4—523no—
312C2×C4—526no—
313C2×C4D4×Dic13112yes—
314C22—46no—
315C22—46no—
316C22—42no—
317C22—81no—
318C22—81no—
319C22—83no—
320C22—83no—
321C22#1171929113yes—
322C22D13×#12011yescharacteristic
323C22#1171933013yes—
324C22#1171933313yes—
325C22#1171933413yes—
326C22#1171934813yes—
327C22#1171937913yes—
328C22#1171938013yes—
329C22#1171938716yes—
330C22C2×D4×Dic1313yes—
331C22#1171951711yescharacteristic
332C22#1171953213yes—
333C4—212no—
334C4—46no—
335C4—264no—
336C4—526no—
337C4—1041no—
338C4—1043no—
339C2—82no—
340C2#120×Dic1311yescharacteristic
341C2#1311752013yes—
342C2#1311754913yes—
343C2#1312055411yescharacteristic
344C2#1312056311yescharacteristic
345C2#1312069513yes—
346C2#1312074113yes—
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#393C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#393D13
hypocenterC13#14301
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic13C2semidirect
3. #13113107C2semidirect
4. #13113101C2semidirect
6. #13113061C2semidirect
16. C13×#393C4semidirect
156. #393Dic13semidirect
267. C13#14301semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic132
C2×#117186122
#131131072
#131131012
#131130812
#131130612
C2×C13×#3932
#1430113