Finite Group Databasebeta

← #13127583

Subgroups — #13127583

Order 1664.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#559C211yesmaximal, characteristic, complemented
2#11719284C211yesmaximal, characteristic, complemented
3#11718733C211yesmaximal, characteristic
4#11718732C211yesmaximal, characteristic, complemented
5#11718718C211yesmaximal, characteristic, complemented
6#11718718C211yesmaximal, characteristic, complemented
7#11718717C211yesmaximal, characteristic, complemented
8#11718716C211yesmaximal, characteristic, complemented
9#11718687C211yesmaximal, characteristic, complemented
10#11718685C211yesmaximal, characteristic, complemented
11#11718683C211yesmaximal, characteristic, complemented
12#11718675C211yesmaximal, characteristic, complemented
13C4×#6104C211yesmaximal, characteristic, complemented
14#11718670C211yesmaximal, characteristic, complemented
15#11718668C211yesmaximal, characteristic, complemented
16C13×#127C2211yescharacteristic
17C13×#124—21no—
18C13×#124C2211yescharacteristic
19C13×#124C2211yescharacteristic
20C13×#123—21no—
21C13×#123—21no—
22C4×Q8×C13C2211yescharacteristic
23C4×Q8×C13C2211yescharacteristic
24C4×D4×C13—21no—
25C4×D4×C13C2211yescharacteristic
26C4×D4×C13C2211yescharacteristic
27#88200—21no—
28C2×#6106C2211yescharacteristic
29C2×#6104C2211yescharacteristic
30C2×#6104C2211yescharacteristic
31#88150—21no—
32#88150—21no—
33C4⋊C4×D13—21no—
34C4×D52C2211yescharacteristic
35C4×D52C2211yescharacteristic
36C4×D52C2211yescharacteristic
37#88124C2211yescharacteristic
38#88124C2211yescharacteristic
39#88123C2211yescharacteristic
40#88075C2211yescharacteristic
41#88075C2211yescharacteristic
42#88075C2211yescharacteristic
43#88072C2211yescharacteristic
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88072C2211yescharacteristic
49#88049C2211yescharacteristic
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×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×Dic26—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4D411yescharacteristic
74C13×C4⋊C4D411yescharacteristic
75C13×C4⋊C4D411yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C13×C22⋊C4—21no—
82C13×C22⋊C4—21no—
83C42×C13—21no—
84C42×C13C2311yescharacteristic
85C42×C13C2311yescharacteristic
86C42×C13C2311yescharacteristic
87#6106—22no—
88#6104—22no—
89#6104—22no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3370—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13—21no—
108C22×D13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13—41no—
112D4×C13—21no—
113D4×C13—21no—
114D4×C13—21no—
115D4×C13—21no—
116D4×C13—42no—
117D4×C13—81no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—81no—
121C2×C4×C13—81no—
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2411yescharacteristic
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132D52—21no—
133D52#4112yes—
134C4×D13—42no—
135C4×D13—81no—
136C4×D13—81no—
137Dic26—81no—
138#1055—21no—
139#1055—21no—
140#1055—21no—
141#1055—21no—
142#559D1311yescharacteristic, complemented
143#554—131no—
144#490—131no—
145#489—131no—
146#488—131no—
147#479—131no—
148#478—131no—
149#474—131no—
150#463—131no—
151#463—131no—
152#459—131no—
153#446—131no—
154#442—131no—
155#440—131no—
156C4×D8—131no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13C22×D411yescharacteristic
164C2×D13—22no—
165C2×D13—41no—
166C2×D13—41no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13C2×#4111yescharacteristic
176C4×C132−1+411yescharacteristic
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180C2×SD16—131no—
181C2×D8—131no—
182C2×D8—131no—
183C4⋊Q8—131no—
184#127C2×D1311yescharacteristic
185#125—131no—
186#125—131no—
187#124—21no—
188#124C2×D1311yescharacteristic
189#124C2×D1311yescharacteristic
190#123—21no—
191#123—21no—
192C22⋊Q8—261no—
193C22⋊Q8—261no—
194C22⋊Q8—261no—
195C4×Q8C2×D1311yescharacteristic
196C4×Q8C2×D1311yescharacteristic
197C4×D4—21no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—131no—
201C4×D4C2×D1311yescharacteristic
202C4×D4C2×D1311yescharacteristic
203C2×C4⋊C4—261no—
204#107—131no—
205#107—131no—
206#106—131no—
207C4⋊C8—131no—
208C4⋊C8—131no—
209C4⋊C8—131no—
210#103—131no—
211#103—131no—
212#103—131no—
213#102—131no—
214#102—131no—
215#102—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220#97—131no—
221#97—131no—
222C4×C8—131no—
223C2×C13—81no—
224C2×C13—81no—
225C2×C13#54811yescharacteristic
226C2×C13#57511yescharacteristic
227C2×C13#57611yescharacteristic
228D13—42no—
229C2×Q8—261no—
230C2×Q8C22⋊D1311yescharacteristic
231C2×Q8C22×D1311yescharacteristic
232C2×D4—21no—
233C2×D4—21no—
234C2×D4—131no—
235C2×D4C22×D1311yescharacteristic
236C2×D4C22×D1311yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4—261no—
242SD16—262no—
243D8—262no—
244D8—262no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8—131no—
248C2×C8—131no—
249C4⋊C4—21no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4C22⋊D1311yescharacteristic
259C4⋊C4C22⋊D1311yescharacteristic
260C4⋊C4C22⋊D1311yescharacteristic
261C4⋊C4C22×D1311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C42—21no—
272C42C22×D1311yescharacteristic
273C42C22×D1311yescharacteristic
274C42C22×D1311yescharacteristic
275C13#337011yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—261no—
279Q8—21no—
280Q8—21no—
281Q8—41no—
282Q8—1041no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—81no—
289D4—132no—
290D4—261no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—522no—
299C2×C4—1041no—
300C2×C4—1041no—
301C2×C4C2×C22⋊D1311yescharacteristic
302C2×C4C2×C22⋊D1311yescharacteristic
303C2×C4C2×C22⋊D1311yescharacteristic
304C2×C4C2×C22⋊D1311yescharacteristic
305C2×C4C2×C22⋊D1311yescharacteristic
306C2×C4C2×C22⋊D1311yescharacteristic
307C2×C4C23×D1311yescharacteristic
308C8—261no—
309C8—261no—
310C8—261no—
311C8—261no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—262no—
319C22—521no—
320C22—521no—
321C22C22×C22⋊D1311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4#41×D1311yescharacteristic
334C4#8825711yescharacteristic
335C2—81no—
336C2—81no—
337C2—522no—
338C2#1171952711yescharacteristic
339C2#1171953611yescharacteristic
340C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#559C2
socleC22×C13C22×D4
prime radical#11718733C2
hypercenter#559D13
hypocenterC13#3370
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. C13×#559C2semidirect
2. #11719284C2semidirect
4. #11718732C2semidirect
5. #11718718C2semidirect
6. #11718718C2semidirect
7. #11718717C2semidirect
8. #11718716C2semidirect
9. #11718687C2semidirect
10. #11718685C2semidirect
11. #11718683C2semidirect
12. #11718675C2semidirect
13. C4×#6104C2semidirect
14. #11718670C2semidirect
15. #11718668C2semidirect
142. #559D13semidirect
275. C13#3370semidirect

Maximal subgroups

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

subgroupindex
C13×#5592
#117192842
#117187332
#117187322
#117187182
#117187172
#117187162
#117186872
#117186852
#117186832
#117186752
C4×#61042
#117186702
#117186682
#337013