Finite Group Databasebeta

← #13125006

Subgroups — #13125006

Order 1664.

386 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
1#11719385C211yesmaximal, characteristic
2C4×Q8×D13C211yesmaximal, characteristic, complemented
3C13×#464C211yesmaximal, characteristic, complemented
4#11718847C211yesmaximal, characteristic, complemented
5#11718845C211yesmaximal, characteristic, complemented
6#11718831C211yesmaximal, characteristic
7#11718825C211yesmaximal, characteristic, complemented
8#11718715C211yesmaximal, characteristic, complemented
9#11718683C211yesmaximal, characteristic, complemented
10#11718496C211yesmaximal, characteristic, complemented
11#11718490C211yesmaximal, characteristic, complemented
12#11718470C211yesmaximal, characteristic, complemented
13#11718450C211yesmaximal, characteristic, complemented
14#11718438C211yesmaximal, characteristic
15#11718418C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×C13×Q16C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C13×#124C2211yescharacteristic
20C4×Q8×C13C2211yescharacteristic
21#88200C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24C2×#6107C2211yescharacteristic
25#88192C2211yescharacteristic
26D4×Dic13C2211yescharacteristic
27C2×#6105C2211yescharacteristic
28C4⋊C4×D13—21no—
29C4⋊C4×D13C2211yescharacteristic
30#88141—21no—
31#88141C2211yescharacteristic
32#88137—21no—
33#88135—21no—
34#88133—21no—
35#88131—21no—
36C42×D13—21no—
37C42×D13C2211yescharacteristic
38#88124C2211yescharacteristic
39C4×Dic26—21no—
40C4×Dic26C2211yescharacteristic
41C13×C4⋊C8C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#102C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88055C2211yescharacteristic
55#88055C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C22×Dic13—21no—
64Q8×D13—22no—
65Q8×D13—22no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13D411yescharacteristic
69C2×C4×D13D411yescharacteristic
70C2×C4×D13C2311yescharacteristic
71C2×Dic26—21no—
72C2×Dic26C2311yescharacteristic
73C13×Q16—22no—
74C13×SD16—22no—
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C13×C4⋊C4—21no—
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C42×C13—21no—
82C42×C13C2311yescharacteristic
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85#6107—22no—
86#6105—22no—
87#6103—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13D411yescharacteristic
104C4×Dic13D411yescharacteristic
105C4×Dic13C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3117—131nomaximal, Sylow
109C23×C13—21no—
110C22×D13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13#4112yes—
115D4×C13—21no—
116D4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C22⋊D13—42no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—42no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C4×D13—24no—
133C4×D13—22no—
134C4×D13—21no—
135C4×D13—21no—
136C4×D13—41no—
137C4×D13—42no—
138Dic26—24no—
139Dic26—21no—
140Dic26#4112yes—
141C8×C13—21no—
142C8×C13—21no—
143#1055—21no—
144#1055—21no—
145#529—131no—
146C2×C4×Q8—131no—
147#484—131no—
148#481—131no—
149#479—131no—
150#479—131no—
151#464—131no—
152#464D1311yescharacteristic, complemented
153#451—131no—
154#448—131no—
155#441—131no—
156#441—131no—
157#440—131no—
158#440—131no—
159#432—131no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13C22×D411yescharacteristic
164C2×D13—21no—
165C2×D13—21no—
166C2×D13#13712yes—
167C4×C13—22no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13C2×#4111yescharacteristic
173C4×C13C2×#4111yescharacteristic
174Dic13—21no—
175Dic13—22no—
176Dic13—21no—
177Dic13—21no—
178Dic13—41no—
179Dic13—41no—
180Dic13—41no—
181C22×Q8—131no—
182C2×Q16—131no—
183C2×Q16C2×D1311yescharacteristic
184C2×SD16—131no—
185C2×SD16C2×D1311yescharacteristic
186#126—261no—
187#125—131no—
188#124C2×D1311yescharacteristic
189#123—261no—
190C22⋊Q8—131no—
191#121—131no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×Q8—261no—
197C4×Q8—261no—
198C4×Q8C2×D1311yescharacteristic
199C4×D4—131no—
200C4×D4—261no—
201#117—261no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—261no—
204C2×C42—131no—
205C2×C42—261no—
206#107—131no—
207#107—131no—
208#106—131no—
209#106—131no—
210C4⋊C8—131no—
211C4⋊C8C2×D1311yescharacteristic
212#103—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#103—131no—
217#103C2×D1311yescharacteristic
218#102—131no—
219#102C2×D1311yescharacteristic
220C22⋊C8—131no—
221C22⋊C8—131no—
222#97—131no—
223#97—131no—
224C2×C13—81no—
225C2×C13#52511yescharacteristic
226C2×C13C2×#13711yescharacteristic
227C2×C13#57511yescharacteristic
228D13—22no—
229C2×Q8—131no—
230C2×Q8—261no—
231C2×Q8—262no—
232C2×Q8—262no—
233C2×Q8C22×D1311yescharacteristic
234C2×Q8C22×D1311yescharacteristic
235C2×D4—261no—
236C2×D4C22×D1311yescharacteristic
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—261no—
243Q16—22no—
244Q16—262no—
245SD16—22no—
246SD16—262no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8C22×D1311yescharacteristic
250C2×C8C22×D1311yescharacteristic
251C4⋊C4—21no—
252C4⋊C4—131no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4C22×D1311yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C42—21no—
270C42—131no—
271C42—131no—
272C42—131no—
273C42—261no—
274C42—261no—
275C42—261no—
276C42—261no—
277C42C22×D1311yescharacteristic
278C13#311711yescharacteristic, complemented, Sylow
279C23—21no—
280C23—131no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—132no—
285Q8—264no—
286Q8—261no—
287Q8#612912yes—
288D4—21no—
289D4—21no—
290D4—522no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—262no—
298C2×C4—264no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—521no—
306C2×C4—522no—
307C2×C4—522no—
308C2×C4D4×D1311yescharacteristic
309C2×C4D4×D1311yescharacteristic
310C2×C4C23×D1311yescharacteristic
311C8—21no—
312C8—21no—
313C8—261no—
314C8—261no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—132no—
319C22—261no—
320C22—261no—
321C22C2×D4×D1311yescharacteristic
322C4—21no—
323C4—21no—
324C4—22no—
325C4—41no—
326C4—41no—
327C4—261no—
328C4—261no—
329C4—261no—
330C4—262no—
331C4—521no—
332C4—521no—
333C4—521no—
334C4C2×#612911yescharacteristic
335C4#41×D1311yescharacteristic
336C2—81no—
337C2—262no—
338C2#1171931111yescharacteristic
339C2#1171947311yescharacteristic
340C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#464C2
socleC22×C13C22×D4
prime radical#88192C22
hypercenter#464D13
hypocenterC13#3117
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D13C2semidirect
3. C13×#464C2semidirect
4. #11718847C2semidirect
5. #11718845C2semidirect
7. #11718825C2semidirect
8. #11718715C2semidirect
9. #11718683C2semidirect
10. #11718496C2semidirect
11. #11718490C2semidirect
12. #11718470C2semidirect
13. #11718450C2semidirect
15. #11718418C2semidirect
152. #464D13semidirect
278. C13#3117semidirect

Maximal subgroups

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

subgroupindex
#117193852
C4×Q8×D132
C13×#4642
#117188472
#117188452
#117188312
#117188252
#117187152
#117186832
#117184962
#117184902
#117184702
#117184502
#117184382
#117184182
#311713