Finite Group Databasebeta

← #13127672

Subgroups — #13127672

Order 1664.

332 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#556C211yesmaximal, characteristic
2#11719272C211yesmaximal, characteristic, complemented
3#11718751C211yesmaximal, characteristic, complemented
4#11718743C211yesmaximal, characteristic, complemented
5#11718717C211yesmaximal, characteristic
6#11718716C211yesmaximal, characteristic
7#11718715C211yesmaximal, characteristic
8#11718715C211yesmaximal, characteristic
9#11718691C211yesmaximal, characteristic, complemented
10C4×#6107C211yesmaximal, characteristic, complemented
11#11718685C211yesmaximal, characteristic, complemented
12#11718683C211yesmaximal, characteristic, complemented
13#11718682C211yesmaximal, characteristic, complemented
14#11718679C211yesmaximal, characteristic
15#11718670C211yesmaximal, characteristic
16C13×C4⋊Q8C2211yescharacteristic
17C13×#126—21no—
18C13×#126—21no—
19C13×#124C2211yescharacteristic
20C13×#124C2211yescharacteristic
21C13×C22⋊Q8—21no—
22C4×Q8×C13C2211yescharacteristic
23C4×Q8×C13C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C13×#117—21no—
27#88198—21no—
28C2×#6107C2211yescharacteristic
29C2×#6107C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31#88143—21no—
32#88143—21no—
33#88141—21no—
34#88124C2211yescharacteristic
35#88124C2211yescharacteristic
36#88123C2211yescharacteristic
37C4×Dic26C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40#88075C2211yescharacteristic
41#88075C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88050C2211yescharacteristic
50#88048C2211yescharacteristic
51#88047C2211yescharacteristic
52#88047C2211yescharacteristic
53C4⋊#1055C2211yescharacteristic
54C4⋊#1055C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56#88043C2211yescharacteristic
57#88043C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13D411yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C2×Dic26—21no—
65C2×Dic26C2311yescharacteristic
66C13×C4⋊C4—21no—
67C13×C4⋊C4—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4D411yescharacteristic
71C13×C4⋊C4D411yescharacteristic
72C13×C4⋊C4D411yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C13×C22⋊C4—21no—
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13C2311yescharacteristic
82C42×C13C2311yescharacteristic
83C42×C13C2311yescharacteristic
84#6107—22no—
85#6107—22no—
86#6105—22no—
87C4⋊Dic13—21no—
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3377—131nomaximal, Sylow
106C23×C13—21no—
107Q8×C13—21no—
108Q8×C13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13—41no—
112D4×C13—21no—
113D4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—42no—
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129Dic26—21no—
130Dic26—42no—
131Dic26#4112yes—
132#1055—21no—
133#1055—21no—
134#1055—21no—
135#1055—21no—
136#557—131no—
137#556D1311yescharacteristic
138#491—131no—
139#489—131no—
140#488—131no—
141#479—131no—
142#478—131no—
143#477—131no—
144#464—131no—
145#464—131no—
146#462—131no—
147#446—131no—
148#441—131no—
149#440—131no—
150C4×Q16—131no—
151C22×C13—41no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13C22×D411yescharacteristic
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13C2×#4111yescharacteristic
165C4×C132−1+411yescharacteristic
166Dic13—22no—
167Dic13—41no—
168Dic13—41no—
169Dic13—41no—
170C2×Q16—131no—
171C2×Q16—131no—
172C2×SD16—131no—
173C4⋊Q8—131no—
174C4⋊Q8—261no—
175C4⋊Q8C2×D1311yescharacteristic
176#126—21no—
177#126—21no—
178#125—131no—
179#125—131no—
180#125—261no—
181#125—261no—
182#124C2×D1311yescharacteristic
183#124C2×D1311yescharacteristic
184C22⋊Q8—21no—
185C4×Q8—131no—
186C4×Q8—131no—
187C4×Q8—131no—
188C4×Q8—261no—
189C4×Q8C2×D1311yescharacteristic
190C4×Q8C2×D1311yescharacteristic
191C4×Q8C2×D1311yescharacteristic
192C4×D4C2×D1311yescharacteristic
193#117—21no—
194#107—131no—
195#107—131no—
196#106—131no—
197C4⋊C8—131no—
198C4⋊C8—131no—
199C4⋊C8—131no—
200#103—131no—
201#103—131no—
202#103—131no—
203#103—131no—
204#103—131no—
205#103—131no—
206#103—131no—
207#102—131no—
208#102—131no—
209#102—131no—
210#97—131no—
211#97—131no—
212C4×C8—131no—
213C2×C13—81no—
214C2×C13#54811yescharacteristic
215C2×C13#57511yescharacteristic
216C2×C13#57811yescharacteristic
217C2×Q8—131no—
218C2×Q8—261no—
219C2×Q8C22⋊D1311yescharacteristic
220C2×Q8C22×D1311yescharacteristic
221C2×Q8C22×D1311yescharacteristic
222C2×D4C22×D1311yescharacteristic
223C22×C4—21no—
224Q16—262no—
225Q16—262no—
226SD16—262no—
227C2×C8—131no—
228C2×C8—131no—
229C2×C8—131no—
230C2×C8—131no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—131no—
236C4⋊C4—131no—
237C4⋊C4—131no—
238C4⋊C4—261no—
239C4⋊C4—261no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4C22⋊D1311yescharacteristic
247C4⋊C4C22⋊D1311yescharacteristic
248C4⋊C4C22⋊D1311yescharacteristic
249C4⋊C4C22×D1311yescharacteristic
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—21no—
255C42—21no—
256C42—21no—
257C42—261no—
258C42—261no—
259C42—261no—
260C42C22×D1311yescharacteristic
261C42C22×D1311yescharacteristic
262C42C22×D1311yescharacteristic
263C13#337711yescharacteristic, complemented, Sylow
264C23—21no—
265Q8—21no—
266Q8—21no—
267Q8—21no—
268Q8—21no—
269Q8—41no—
270Q8—132no—
271Q8—261no—
272Q8—522no—
273D4—21no—
274D4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4C2×C22⋊D1311yescharacteristic
284C2×C4C2×C22⋊D1311yescharacteristic
285C2×C4C2×C22⋊D1311yescharacteristic
286C2×C4C2×C22⋊D1311yescharacteristic
287C2×C4C2×C22⋊D1311yescharacteristic
288C2×C4C2×C22⋊D1311yescharacteristic
289C2×C4C23×D1311yescharacteristic
290C8—261no—
291C8—261no—
292C8—261no—
293C8—261no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22C22×C22⋊D1311yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—262no—
308C4—521no—
309C4—521no—
310C4—521no—
311C4#41×D1311yescharacteristic
312C4#8825711yescharacteristic
313C2—81no—
314C2#1171952711yescharacteristic
315C2#1171953611yescharacteristic
316C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#556C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#556D13
hypocenterC13#3377
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
2. #11719272C2semidirect
3. #11718751C2semidirect
4. #11718743C2semidirect
9. #11718691C2semidirect
10. C4×#6107C2semidirect
11. #11718685C2semidirect
12. #11718683C2semidirect
13. #11718682C2semidirect
263. C13#3377semidirect

Maximal subgroups

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

subgroupindex
C13×#5562
#117192722
#117187512
#117187432
#117187172
#117187162
#117187152
#117186912
C4×#61072
#117186852
#117186832
#117186822
#117186792
#117186702
#337713