Finite Group Databasebeta

← #13127321

Subgroups — #13127321

Order 1664.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#553C211yesmaximal, characteristic
2#11719248C211yesmaximal, characteristic, complemented
3#11718726C211yesmaximal, characteristic, complemented
4#11718724C211yesmaximal, characteristic, complemented
5#11718703C211yesmaximal, characteristic, complemented
6#11718702C211yesmaximal, characteristic, complemented
7#11718695C211yesmaximal, characteristic, complemented
8#11718694C211yesmaximal, characteristic, complemented
9#11718679C211yesmaximal, characteristic, complemented
10#11718672C211yesmaximal, characteristic, complemented
11#11718668C211yesmaximal, characteristic, complemented
12#11718657C211yesmaximal, characteristic, complemented
13#11718656C211yesmaximal, characteristic, complemented
14#11718631C211yesmaximal, characteristic, complemented
15C2×#88047C211yesmaximal, characteristic, complemented
16C13×#126—21no—
17C13×#125C2211yescharacteristic
18C13×#123—21no—
19C13×#121—21no—
20C13×#121C2211yescharacteristic
21C13×#121C2211yescharacteristic
22C4×D4×C13—21no—
23C4×D4×C13C2211yescharacteristic
24C4×D4×C13C2211yescharacteristic
25C13×#117C2211yescharacteristic
26C2×C13×C4⋊C4C2211yescharacteristic
27D4×Dic13—21no—
28C2×#6105C2211yescharacteristic
29C2×C4⋊Dic13C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31#88178C2211yescharacteristic
32#88178C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35#88144—21no—
36#88132—21no—
37#88132—21no—
38#88123C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40#88072C2211yescharacteristic
41#88072C2211yescharacteristic
42#88072C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88050C2211yescharacteristic
46#88050C2211yescharacteristic
47#88050C2211yescharacteristic
48#88048C2211yescharacteristic
49#88048C2211yescharacteristic
50#88048C2211yescharacteristic
51#88047C2211yescharacteristic
52#88047C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13D411yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×Dic13—21no—
68C22×Dic13—21no—
69C2×Dic26—21no—
70C2×Dic26C2311yescharacteristic
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4D411yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C13×C22⋊C4—21no—
82C13×C22⋊C4D411yescharacteristic
83C13×C22⋊C4D411yescharacteristic
84C42×C13—21no—
85C42×C13C2311yescharacteristic
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88#6105—22no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95#6101—21no—
96#6101—21no—
97#6101—21no—
98C4×Dic13—21no—
99#6099—22no—
100C2×#1055—22no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3346—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13C2×D411yescharacteristic
108C23×C13C2×D411yescharacteristic
109D4×C13—22no—
110D4×C13—21no—
111D4×C13—21no—
112D4×C13—42no—
113D4×C13—81no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—81no—
122C2×C4×C13—81no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2411yescharacteristic
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—81no—
133C2×Dic13—81no—
134Dic26—21no—
135Dic26—21no—
136Dic26—81no—
137#1055—21no—
138#1055—21no—
139#1055—21no—
140#1055#4112yes—
141#554—131no—
142#553D1311yescharacteristic
143#501—131no—
144#485—131no—
145#484—131no—
146#481—131no—
147#480—131no—
148#479—131no—
149#474—131no—
150#468—131no—
151#465—131no—
152#440—131no—
153#435—131no—
154#428—131no—
155C2×#107—131no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13#13712yes—
165C22×C13C22×D411yescharacteristic
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13C2×#4111yescharacteristic
174C4×C132−1+411yescharacteristic
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C2×SD16—131no—
180C2×M16—131no—
181C22×C8—131no—
182C4⋊Q8—131no—
183#126—21no—
184#125—261no—
185#125C2×D1311yescharacteristic
186#123—21no—
187C22⋊Q8—131no—
188C22⋊Q8—131no—
189C22⋊Q8—261no—
190C22⋊Q8—261no—
191#121—21no—
192#121C2×D1311yescharacteristic
193#121C2×D1311yescharacteristic
194C4×Q8—131no—
195C4×D4—21no—
196C4×D4—261no—
197C4×D4C2×D1311yescharacteristic
198C4×D4C2×D1311yescharacteristic
199#117C2×D1311yescharacteristic
200C2×C4⋊C4—131no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4C2×D1311yescharacteristic
203#107—131no—
204#107—131no—
205#107—131no—
206#107—131no—
207#107—131no—
208#107—131no—
209#106—131no—
210#106—131no—
211#106—131no—
212C4⋊C8—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#102—131no—
217#102—131no—
218#102—131no—
219C22⋊C8—131no—
220C22⋊C8—131no—
221#97—131no—
222C2×C13—22no—
223C2×C13—41no—
224C2×C13—81no—
225C2×C13#54711yescharacteristic
226C2×C13C2×#13711yescharacteristic
227C2×C13#57611yescharacteristic
228C2×Q8—131no—
229C2×Q8—261no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4C22⋊D1311yescharacteristic
233C2×D4C22×D1311yescharacteristic
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4C22×D1311yescharacteristic
239C22×C4C22×D1311yescharacteristic
240SD16—262no—
241M16—262no—
242C2×C8—131no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8—131no—
246C2×C8—262no—
247C4⋊C4—21no—
248C4⋊C4—21no—
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⋊C4—261no—
259C4⋊C4C22⋊D1311yescharacteristic
260C4⋊C4C22×D1311yescharacteristic
261C4⋊C4C22×D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4C22⋊D1311yescharacteristic
270C22⋊C4C22⋊D1311yescharacteristic
271C42—21no—
272C42—261no—
273C42C22×D1311yescharacteristic
274C13#334611yescharacteristic, complemented, Sylow
275C23—21no—
276C23C2×C22⋊D1311yescharacteristic
277C23C2×C22⋊D1311yescharacteristic
278Q8—261no—
279Q8—261no—
280Q8—1041no—
281D4—22no—
282D4—21no—
283D4—21no—
284D4—42no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—1041no—
300C2×C4—1041no—
301C2×C4C2×C22⋊D1311yescharacteristic
302C2×C4C2×C22⋊D1311yescharacteristic
303C2×C4C2×C22⋊D1311yescharacteristic
304C2×C4C2×C22⋊D1311yescharacteristic
305C2×C4C23×D1311yescharacteristic
306C8—132no—
307C8—261no—
308C8—261no—
309C8—261no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22#8820512yes—
319C22C22×C22⋊D1311yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4—521no—
331C4#41×D1311yescharacteristic
332C4#8825711yescharacteristic
333C2—22no—
334C2—41no—
335C2—81no—
336C2C2×#8820511yescharacteristic
337C2#1171952911yescharacteristic
338C2#1171954011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#553C2
socleC22×C13C22×D4
hypercenter#553D13
hypocenterC13#3346
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
2. #11719248C2semidirect
3. #11718726C2semidirect
4. #11718724C2semidirect
5. #11718703C2semidirect
6. #11718702C2semidirect
7. #11718695C2semidirect
8. #11718694C2semidirect
9. #11718679C2semidirect
10. #11718672C2semidirect
11. #11718668C2semidirect
12. #11718657C2semidirect
13. #11718656C2semidirect
14. #11718631C2semidirect
15. C2×#88047C2semidirect
274. C13#3346semidirect

Maximal subgroups

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

subgroupindex
C13×#5532
#117192482
#117187262
#117187242
#117187032
#117187022
#117186952
#117186942
#117186792
#117186722
#117186682
#117186572
#117186562
#117186312
C2×#880472
#334613