Finite Group Databasebeta

← #13125047

Subgroups — #13125047

Order 1664.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719436C211yesmaximal, characteristic, complemented
2#11719251C211yesmaximal, characteristic
3C13×#461C211yesmaximal, characteristic, complemented
4#11718834C211yesmaximal, characteristic
5#11718834C211yesmaximal, characteristic
6#11718825C211yesmaximal, characteristic, complemented
7SD16×Dic13C211yesmaximal, characteristic, complemented
8#11718751C211yesmaximal, characteristic, complemented
9#11718670C211yesmaximal, characteristic, complemented
10#11718501C211yesmaximal, characteristic, complemented
11#11718490C211yesmaximal, characteristic, complemented
12#11718470C211yesmaximal, characteristic, complemented
13#11718466C211yesmaximal, characteristic, complemented
14#11718451C211yesmaximal, characteristic, complemented
15#11718450C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C13×C4⋊Q8C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21#88200C2211yescharacteristic
22#88200C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24Q8×Dic13C2211yescharacteristic
25C2×#6107C2211yescharacteristic
26C2×#6107C2211yescharacteristic
27D4×Dic13C2211yescharacteristic
28C4×C22⋊D13—21no—
29C2×#6101—21no—
30#88152—21no—
31#88152—21no—
32C4⋊C4×D13C2211yescharacteristic
33#88143—21no—
34#88143—21no—
35#88141C2211yescharacteristic
36#88135—21no—
37#88131—21no—
38#88126C2211yescharacteristic
39#88124C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C13×C4⋊C8C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88055C2211yescharacteristic
55C8×Dic13C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C2×C22⋊D13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66#6129—22no—
67#6129—22no—
68C2×C4×D13—21no—
69C2×C4×D13C2311yescharacteristic
70C2×Dic26C2311yescharacteristic
71C13×SD16—22no—
72C13×SD16—22no—
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C42×C13C2311yescharacteristic
80C22⋊Dic13—21no—
81#6107—22no—
82#6107—22no—
83#6103—21no—
84#6103—21no—
85#6103D411yescharacteristic
86#6103D411yescharacteristic
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101D411yescharacteristic
100#6101D411yescharacteristic
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3120—131nomaximal, Sylow
109C23×C13—21no—
110C22×D13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
115D4×C13—21no—
116D4×C13#4112yes—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—81no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2411yescharacteristic
124C22⋊D13—24no—
125C2×Dic13—24no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—81no—
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134C4×D13—21no—
135C4×D13—21no—
136C4×D13—81no—
137Dic26—21no—
138Dic26#4112yes—
139C8×C13—21no—
140C8×C13—21no—
141#1055—21no—
142#1055—21no—
143#541—131no—
144#520—131no—
145#484—131no—
146#483—131no—
147#479—131no—
148#478—131no—
149#462—131no—
150#461D1311yescharacteristic, complemented
151#452—131no—
152#452—131no—
153#441—131no—
154#440—131no—
155C4×Q16—131no—
156C4×SD16—131no—
157#433—131no—
158C22×C13—22no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13C22×D411yescharacteristic
162C2×D13—21no—
163C2×D13—21no—
164C2×D13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13C2×#4111yescharacteristic
171C4×C13C2×#4111yescharacteristic
172Dic13—22no—
173Dic13—21no—
174Dic13—21no—
175Dic13—21no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C2×#41—131no—
180C2×Q16—131no—
181C2×Q16—131no—
182C2×SD16C2×D1311yescharacteristic
183C2×SD16C2×D1311yescharacteristic
184C4⋊Q8C2×D1311yescharacteristic
185#126—261no—
186#126—261no—
187#125—131no—
188#125—261no—
189#125—261no—
190C22⋊Q8—131no—
191C22⋊Q8—131no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×D4—131no—
197C4×D4—261no—
198C4×D4—261no—
199C4×D4C2×D1311yescharacteristic
200#117—131no—
201#117—261no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—261no—
204#107—131no—
205#107—131no—
206#106—131no—
207#106—131no—
208C4⋊C8—131no—
209C4⋊C8C2×D1311yescharacteristic
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#103C2×D1311yescharacteristic
215#103C2×D1311yescharacteristic
216#102—131no—
217#102—131no—
218C22⋊C8—131no—
219C22⋊C8—131no—
220#97—131no—
221C4×C8—131no—
222C2×C13—42no—
223C2×C13#52511yescharacteristic
224C2×C13#57711yescharacteristic
225C2×C13#57811yescharacteristic
226D13—41no—
227#41—262no—
228#41—262no—
229C2×Q8—131no—
230C2×Q8C22×D1311yescharacteristic
231C2×Q8C22×D1311yescharacteristic
232C2×D4—261no—
233C2×D4C22×D1311yescharacteristic
234C22×C4—21no—
235C22×C4—131no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239Q16—262no—
240Q16—262no—
241SD16—22no—
242SD16—22no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—131no—
254C4⋊C4—261no—
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—131no—
266C22⋊C4—131no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C42—131no—
271C42—261no—
272C42—261no—
273C42—261no—
274C42—261no—
275C42C22×D1311yescharacteristic
276C13#312011yescharacteristic, complemented, Sylow
277C23—21no—
278C23—131no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—132no—
284Q8—261no—
285D4—21no—
286D4—264no—
287D4#612912yes—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—264no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—1041no—
303C2×C4—1041no—
304C2×C4D4×D1311yescharacteristic
305C2×C4D4×D1311yescharacteristic
306C2×C4C23×D1311yescharacteristic
307C8—21no—
308C8—21no—
309C8—261no—
310C8—261no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—261no—
315C22—261no—
316C22—261no—
317C22C2×D4×D1311yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—261no—
324C4—261no—
325C4—261no—
326C4—262no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4C2×#612911yescharacteristic
331C4#41×D1311yescharacteristic
332C2—42no—
333C2—521no—
334C2#1171931111yescharacteristic
335C2#1171946711yescharacteristic
336C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radicalC2×#6129C22
hypercenter#461D13
hypocenterC13#3120
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #11719436C2semidirect
3. C13×#461C2semidirect
6. #11718825C2semidirect
7. SD16×Dic13C2semidirect
8. #11718751C2semidirect
9. #11718670C2semidirect
10. #11718501C2semidirect
11. #11718490C2semidirect
12. #11718470C2semidirect
13. #11718466C2semidirect
14. #11718451C2semidirect
15. #11718450C2semidirect
150. #461D13semidirect
276. C13#3120semidirect

Maximal subgroups

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

subgroupindex
#117194362
#117192512
C13×#4612
#117188342
#117188252
SD16×Dic132
#117187512
#117186702
#117185012
#117184902
#117184702
#117184662
#117184512
#117184502
#312013