Finite Group Databasebeta

← #13127455

Subgroups — #13127455

Order 1664.

354 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
1#11719321C211yesmaximal, characteristic
2#11719216C211yesmaximal, characteristic, complemented
3C13×#480C211yesmaximal, characteristic, complemented
4#11718703C211yesmaximal, characteristic, complemented
5#11718625C211yesmaximal, characteristic, complemented
6#11718549C211yesmaximal, characteristic, complemented
7#11718542C211yesmaximal, characteristic, complemented
8#11718536C211yesmaximal, characteristic, complemented
9#11718535C211yesmaximal, characteristic, complemented
10#11718441C211yesmaximal, characteristic, complemented
11#11718435C211yesmaximal, characteristic, complemented
12#11718422C211yesmaximal, characteristic, complemented
13#11718419C211yesmaximal, characteristic, complemented
14#11718390C211yesmaximal, characteristic, complemented
15#11718384C211yesmaximal, characteristic, complemented
16C13×#121C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18#88193—21no—
19#88192C2211yescharacteristic
20#88190—21no—
21D4×Dic13C2211yescharacteristic
22C2×#6105C2211yescharacteristic
23C4×C22⋊D13—21no—
24C4×C22⋊D13C2211yescharacteristic
25#88180C2211yescharacteristic
26#88178—21no—
27#88178C2211yescharacteristic
28C2×#6099C2211yescharacteristic
29C2×#6094C2211yescharacteristic
30#88151C2211yescharacteristic
31#88150—21no—
32#88146C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34#88143—21no—
35#88142C2211yescharacteristic
36#88142C2211yescharacteristic
37#88141C2211yescharacteristic
38#88139—21no—
39#88131—21no—
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88072C2211yescharacteristic
46#88060C2211yescharacteristic
47#88058C2211yescharacteristic
48#88057C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13D411yescharacteristic
65C22×Dic13—21no—
66C2×C4×D13—21no—
67C2×C4×D13C2311yescharacteristic
68C2×Dic26—21no—
69C2×Dic26—21no—
70C2×Dic26C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13D411yescharacteristic
83#6105—22no—
84#6103—21no—
85#6103—21no—
86#6103D411yescharacteristic
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#6101D411yescharacteristic
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101#6099—22no—
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6094—22no—
105#3357—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13C2×D411yescharacteristic
108C22×D13C2×D411yescharacteristic
109D4×C13—21no—
110D4×C13—21no—
111D4×C13—81no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—81no—
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C22⋊D13—22no—
121C22⋊D13—81no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—42no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C4×D13—21no—
131C4×D13—21no—
132C4×D13—81no—
133Dic26—21no—
134Dic26—21no—
135Dic26—81no—
136Dic26—81no—
137C8×C13—21no—
138C8×C13—21no—
139#1055—21no—
140#1055#4112yes—
141#555—131no—
142#554—131no—
143#500—131no—
144#485—131no—
145#485—131no—
146#480—131no—
147#480D1311yescharacteristic, complemented
148#477—131no—
149#476—131no—
150#468—131no—
151#468—131no—
152C4×SD16—131no—
153#436—131no—
154#428—131no—
155#428—131no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13C22×D411yescharacteristic
163C2×D13—21no—
164C2×D13—21no—
165C2×D13—21no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13C2×#4111yescharacteristic
171C4×C132−1+411yescharacteristic
172Dic13—21no—
173Dic13—21no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13#13712yes—
179C2×SD16—131no—
180C2×M16—131no—
181C2×M16—131no—
182C4⋊Q8—131no—
183C4⋊Q8—131no—
184#125—261no—
185#124—261no—
186#124—261no—
187C22⋊Q8—131no—
188C22⋊Q8—131no—
189C22⋊Q8—261no—
190C22⋊Q8—261no—
191#121—131no—
192#121—261no—
193#121C2×D1311yescharacteristic
194C4×Q8—131no—
195C4×D4—131no—
196C4×D4—131no—
197C4×D4—261no—
198#117—131no—
199#117—131no—
200#117—261no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4C2×D1311yescharacteristic
203#107—131no—
204#107—131no—
205#107—131no—
206#107—131no—
207#107C2×D1311yescharacteristic
208#107C2×D1311yescharacteristic
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#102C2×D1311yescharacteristic
218#102C2×D1311yescharacteristic
219C22⋊C8—131no—
220C22⋊C8C2×D1311yescharacteristic
221C4×C8—131no—
222C2×C13—41no—
223C2×C13—81no—
224C2×C13#54711yescharacteristic
225C2×C13C2×#13711yescharacteristic
226C2×C13#57611yescharacteristic
227D13—41no—
228C2×Q8—131no—
229C2×Q8—261no—
230C2×Q8—261no—
231C2×D4—21no—
232C2×D4—131no—
233C2×D4—261no—
234C2×D4C22×D1311yescharacteristic
235C22×C4—21no—
236C22×C4—131no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4C22×D1311yescharacteristic
240SD16—262no—
241M16—262no—
242M16—262no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C4⋊C4C22×D1311yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—131no—
263C22⋊C4—131no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C42—131no—
271C42—261no—
272C42—261no—
273C42—261no—
274C13#335711yescharacteristic, complemented, Sylow
275C23—21no—
276C23—131no—
277C23D4×D1311yescharacteristic
278Q8—261no—
279Q8—261no—
280Q8—1041no—
281Q8—1041no—
282D4—21no—
283D4—21no—
284D4—81no—
285D4—262no—
286D4—1041no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—81no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—522no—
303C2×C4—1041no—
304C2×C4D4×D1311yescharacteristic
305C2×C4C23×D1311yescharacteristic
306C8—21no—
307C8—21no—
308C8—132no—
309C8—261no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—261no—
317C22—261no—
318C22—261no—
319C22C2×D4×D1311yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—132no—
325C4—261no—
326C4—261no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4—521no—
331C4#41×D1311yescharacteristic
332C4#8825711yescharacteristic
333C2—41no—
334C2—81no—
335C2—521no—
336C2#1171936011yescharacteristic
337C2#1171946211yescharacteristic
338C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#480C2
socleC22×C13C22×D4
prime radical#11719321C2
hypercenter#480D13
hypocenterC13#3357
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #11719216C2semidirect
3. C13×#480C2semidirect
4. #11718703C2semidirect
5. #11718625C2semidirect
6. #11718549C2semidirect
7. #11718542C2semidirect
8. #11718536C2semidirect
9. #11718535C2semidirect
10. #11718441C2semidirect
11. #11718435C2semidirect
12. #11718422C2semidirect
13. #11718419C2semidirect
14. #11718390C2semidirect
15. #11718384C2semidirect
147. #480D13semidirect
274. C13#3357semidirect

Maximal subgroups

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

subgroupindex
#117193212
#117192162
C13×#4802
#117187032
#117186252
#117185492
#117185422
#117185362
#117185352
#117184412
#117184352
#117184222
#117184192
#117183902
#117183842
#335713