Finite Group Databasebeta

← #13127781

Subgroups — #13127781

Order 1664.

334 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#554C211yesmaximal, characteristic
2#11719272C211yesmaximal, characteristic, complemented
3#11718755C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718726C211yesmaximal, characteristic, complemented
6#11718725C211yesmaximal, characteristic, complemented
7#11718724C211yesmaximal, characteristic, complemented
8#11718724C211yesmaximal, characteristic, complemented
9#11718685C211yesmaximal, characteristic, complemented
10#11718679C211yesmaximal, characteristic
11#11718679C211yesmaximal, characteristic
12C4×#6105C211yesmaximal, characteristic
13#11718670C211yesmaximal, characteristic
14#11718670C211yesmaximal, characteristic
15#11718669C211yesmaximal, characteristic
16C13×C4⋊Q8C2211yescharacteristic
17C13×#125C2211yescharacteristic
18C13×#125C2211yescharacteristic
19C13×C22⋊Q8—21no—
20C13×C22⋊Q8—21no—
21C13×C22⋊Q8—21no—
22C4×Q8×C13C2211yescharacteristic
23C4×D4×C13C2211yescharacteristic
24C4×D4×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C2×C13×C4⋊C4—21no—
27#88198—21no—
28C2×#6105C2211yescharacteristic
29#88143—21no—
30#88143—21no—
31#88141—21no—
32#88124C2211yescharacteristic
33#88124C2211yescharacteristic
34#88123C2211yescharacteristic
35C4×Dic26C2211yescharacteristic
36C4×Dic26C2211yescharacteristic
37C4×Dic26C2211yescharacteristic
38#88072C2211yescharacteristic
39#88072C2211yescharacteristic
40#88072C2211yescharacteristic
41#88050C2211yescharacteristic
42#88050C2211yescharacteristic
43#88050C2211yescharacteristic
44#88048C2211yescharacteristic
45#88048C2211yescharacteristic
46#88048C2211yescharacteristic
47#88048C2211yescharacteristic
48#88048C2211yescharacteristic
49#88047C2211yescharacteristic
50#88047C2211yescharacteristic
51#88047C2211yescharacteristic
52#88047C2211yescharacteristic
53C4⋊#1055C2211yescharacteristic
54C4⋊#1055C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56#88043C2211yescharacteristic
57#88043C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13D411yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C2×Dic26—21no—
66C2×Dic26C2311yescharacteristic
67C13×C4⋊C4—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4D411yescharacteristic
73C13×C4⋊C4D411yescharacteristic
74C13×C4⋊C4D411yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C42×C13C2311yescharacteristic
82C42×C13C2311yescharacteristic
83C42×C13C2311yescharacteristic
84#6105Q814yescomplemented
85C4⋊Dic13—21no—
86C4⋊Dic13C2311yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C2×#1055C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103#3388—131nomaximal, Sylow
104C23×C13—21no—
105Q8×C13—41no—
106Q8×C13—81no—
107D4×C13—21no—
108D4×C13C2×Q812yes—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—42no—
113C2×C4×C13—81no—
114C2×C4×C13—81no—
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126Dic26—21no—
127Dic26—42no—
128Dic26C2×Q812yes—
129#1055—21no—
130#1055—21no—
131#1055—21no—
132#1055C2×Q812yes—
133#557—131no—
134#554D1311yescharacteristic
135#501—131no—
136#501—131no—
137#499—131no—
138#479—131no—
139#479—131no—
140#478—131no—
141#478—131no—
142#476—131no—
143#475—131no—
144#446—131no—
145#440—131no—
146#440—131no—
147C4×SD16—131no—
148C22×C13—22no—
149C22×C13—41no—
150C22×C13—41no—
151C22×C13C22×D411yescharacteristic
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13C22×Q811yescharacteristic
162C4×C132−1+411yescharacteristic
163Dic13—22no—
164Dic13—41no—
165Dic13—41no—
166Dic13—41no—
167C2×SD16—131no—
168C4⋊Q8—131no—
169C4⋊Q8—261no—
170C4⋊Q8C2×D1311yescharacteristic
171#125—131no—
172#125—131no—
173#125—261no—
174#125—261no—
175#125C2×D1311yescharacteristic
176#125C2×D1311yescharacteristic
177C22⋊Q8—21no—
178C22⋊Q8—21no—
179C22⋊Q8—21no—
180C4×Q8—131no—
181C4×Q8—131no—
182C4×Q8—131no—
183C4×Q8—261no—
184C4×Q8C2×D1311yescharacteristic
185C4×D4C2×D1311yescharacteristic
186C4×D4C2×D1311yescharacteristic
187C4×D4C2×D1311yescharacteristic
188C2×C4⋊C4—21no—
189#107—131no—
190#107—131no—
191#107—131no—
192#107—131no—
193#106—131no—
194#106—131no—
195#106—131no—
196#106—131no—
197#106—131no—
198C4⋊C8—131no—
199C4⋊C8—131no—
200C4⋊C8—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204#102—131no—
205#102—131no—
206#102—131no—
207#97—131no—
208#97—131no—
209C4×C8—131no—
210C2×C13—42no—
211C2×C13D4×Q811yescharacteristic
212C2×C13#57511yescharacteristic
213C2×C13#57711yescharacteristic
214C2×Q8—21no—
215C2×Q8—131no—
216C2×Q8—261no—
217C2×Q8C22⋊D1311yescharacteristic
218C2×D4C22×D1311yescharacteristic
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222SD16—134no—
223C2×C8—131no—
224C2×C8—131no—
225C2×C8—131no—
226C2×C8—131no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—131no—
233C4⋊C4—131no—
234C4⋊C4—131no—
235C4⋊C4—261no—
236C4⋊C4—261no—
237C4⋊C4—261no—
238C4⋊C4—261no—
239C4⋊C4—261no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4C22⋊D1311yescharacteristic
244C4⋊C4C22⋊D1311yescharacteristic
245C4⋊C4C22⋊D1311yescharacteristic
246C4⋊C4C22×D1311yescharacteristic
247C4⋊C4C22×D1311yescharacteristic
248C4⋊C4C22×D1311yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—21no—
251C22⋊C4—21no—
252C42—261no—
253C42—261no—
254C42—261no—
255C42C22×D1311yescharacteristic
256C42C22×D1311yescharacteristic
257C42C22×D1311yescharacteristic
258C13#338811yescharacteristic, complemented, Sylow
259C23—21no—
260Q8—41no—
261Q8—81no—
262Q8—132no—
263Q8—261no—
264Q8—522no—
265D4—21no—
266D4Q8×D1312yes—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4C2×C22⋊D1311yescharacteristic
278C2×C4C2×C22⋊D1311yescharacteristic
279C2×C4C2×C22⋊D1311yescharacteristic
280C2×C4C2×C22⋊D1311yescharacteristic
281C2×C4C2×C22⋊D1311yescharacteristic
282C2×C4C2×C22⋊D1311yescharacteristic
283C2×C4C23×D1311yescharacteristic
284C8—132no—
285C8—261no—
286C8—261no—
287C8—261no—
288C22—22no—
289C22—41no—
290C22—41no—
291C22C22×C22⋊D1311yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—262no—
302C4—521no—
303C4—521no—
304C4—521no—
305C4C2×Q8×D1311yescharacteristic
306C4#8825411yescharacteristic
307C2—42no—
308C2Q8×C22⋊D1311yescharacteristic
309C2#1171952711yescharacteristic
310C2#1171954111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#554C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#554D13
hypocenterC13#3388
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #11719272C2semidirect
3. #11718755C2semidirect
4. #11718741C2semidirect
5. #11718726C2semidirect
6. #11718725C2semidirect
7. #11718724C2semidirect
8. #11718724C2semidirect
9. #11718685C2semidirect
84. #6105Q8semidirect
258. C13#3388semidirect

Maximal subgroups

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

subgroupindex
C13×#5542
#117192722
#117187552
#117187412
#117187262
#117187252
#117187242
#117186852
#117186792
C4×#61052
#117186702
#117186692
#338813