Finite Group Databasebeta

← #13126170

Subgroups — #13126170

Order 1664.

354 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#11719385C211yesmaximal, characteristic
2#11719283C211yesmaximal, characteristic, complemented
3C13×#464C211yesmaximal, characteristic, complemented
4#11718849C211yesmaximal, characteristic, complemented
5#11718843C211yesmaximal, characteristic, complemented
6#11718832C211yesmaximal, characteristic
7#11718823C211yesmaximal, characteristic, complemented
8#11718715C211yesmaximal, characteristic, complemented
9#11718683C211yesmaximal, characteristic, complemented
10D13×C4⋊C8C211yesmaximal, characteristic, complemented
11#11718490C211yesmaximal, characteristic, complemented
12#11718474C211yesmaximal, characteristic, complemented
13#11718452C211yesmaximal, characteristic, complemented
14#11718439C211yesmaximal, characteristic
15#11718420C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C13×#124C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20#88200C2211yescharacteristic
21#88200C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23#88198C2211yescharacteristic
24C2×#6107C2211yescharacteristic
25#88192C2211yescharacteristic
26D4×Dic13C2211yescharacteristic
27C2×#6105C2211yescharacteristic
28C2×C8×D13C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88151C2211yescharacteristic
31#88150—21no—
32#88143—21no—
33#88142C2211yescharacteristic
34#88137—21no—
35#88135—21no—
36#88133—21no—
37#88131—21no—
38#88126—21no—
39C42×D13C2211yescharacteristic
40#88124C2211yescharacteristic
41C4×Dic26—21no—
42C4×Dic26C2211yescharacteristic
43C13×C4⋊C8C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88075C2211yescharacteristic
49#88072C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C22×Dic13—21no—
64C2×C4×D13D411yescharacteristic
65C2×C4×D13D411yescharacteristic
66C2×C4×D13C2311yescharacteristic
67C2×Dic26—21no—
68C2×Dic26C2311yescharacteristic
69C13×Q16—41no—
70C13×SD16—41no—
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C22⋊C4—21no—
76C13×C22⋊C4—21no—
77C42×C13—21no—
78C42×C13C2311yescharacteristic
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81#6107—41no—
82#6105—41no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86C4⋊Dic13—21no—
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#6101—21no—
97#6101—21no—
98#6101—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13D411yescharacteristic
102C4×Dic13D411yescharacteristic
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C8×D13—41no—
107C8×D13—41no—
108#3248—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—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—22no—
133C4×D13—21no—
134C4×D13—21no—
135C4×D13—22no—
136Dic26—21no—
137Dic26—21no—
138Dic26—42no—
139C8×C13—21no—
140C8×C13—21no—
141#1055—21no—
142#1055—21no—
143#533—131no—
144#529—131no—
145#479—131no—
146#479—131no—
147#475—131no—
148#474—131no—
149#467—131no—
150#467—131no—
151#465—131no—
152#465—131no—
153#464—131no—
154#464D1311yescharacteristic, complemented
155#462—131no—
156#461—131no—
157C2×C4⋊C8—131no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13C22×D411yescharacteristic
162C2×D13—21no—
163C2×D13—21no—
164C2×D13#13712yes—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13H(5,𝔽2)11yescharacteristic
171C4×C132−1+411yescharacteristic
172Dic13—21no—
173Dic13—21no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13#13512yes—
179C2×Q16—131no—
180C2×Q16C2×D1311yescharacteristic
181C2×SD16—131no—
182C2×SD16C2×D1311yescharacteristic
183C22×C8—131no—
184C22×C8—131no—
185C4⋊Q8—131no—
186C4⋊Q8—131no—
187#126—261no—
188#125—131no—
189#125—261no—
190#124C2×D1311yescharacteristic
191#123—261no—
192C22⋊Q8—131no—
193C22⋊Q8—131no—
194C22⋊Q8—131no—
195C22⋊Q8—261no—
196#121—131no—
197C4×Q8—131no—
198C4×Q8—131no—
199C4×Q8—261no—
200C4×Q8C2×D1311yescharacteristic
201C4×D4—131no—
202C4×D4—261no—
203#117—261no—
204#117—261no—
205C2×C42—131no—
206#107—131no—
207#107—131no—
208#106—131no—
209#106—131no—
210C4⋊C8—131no—
211C4⋊C8—131no—
212C4⋊C8—131no—
213C4⋊C8C2×D1311yescharacteristic
214#103—131no—
215#103—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#103C2×D1311yescharacteristic
220#102—131no—
221#102C2×D1311yescharacteristic
222C2×C13—81no—
223C2×C13#53711yescharacteristic
224C2×C13C2×#13511yescharacteristic
225C2×C13C2×#13711yescharacteristic
226D13—22no—
227C2×Q8—131no—
228C2×Q8—261no—
229C2×Q8C22×D1311yescharacteristic
230C2×Q8C22×D1311yescharacteristic
231C2×D4—261no—
232C2×D4C22×D1311yescharacteristic
233C22×C4—131no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—261no—
237Q16—41no—
238Q16—521no—
239SD16—41no—
240SD16—521no—
241C2×C8—131no—
242C2×C8—131no—
243C2×C8—521no—
244C2×C8—521no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4C22×D1311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C42—21no—
270C42—131no—
271C42—131no—
272C42—131no—
273C42—261no—
274C42—261no—
275C42C22×D1311yescharacteristic
276C13#324811yescharacteristic, complemented, Sylow
277C23—21no—
278C23—131no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—261no—
284Q8—261no—
285Q8—522no—
286D4—21no—
287D4—21no—
288D4—522no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—262no—
296C2×C4—262no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—522no—
304C2×C4D4×D1311yescharacteristic
305C2×C4D4×D1311yescharacteristic
306C2×C4C23×D1311yescharacteristic
307C8—21no—
308C8—21no—
309C8—261no—
310C8—261no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—132no—
315C22—261no—
316C22—261no—
317C22C2×D4×D1311yescharacteristic
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—132no—
324C4—261no—
325C4—261no—
326C4—521no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4#8825111yescharacteristic
331C4#8825711yescharacteristic
332C2—81no—
333C2—262no—
334C2#1171931311yescharacteristic
335C2D13×#13511yescharacteristic
336C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#464C2
socleC22×C13C22×D4
prime radical#88192C22
hypercenter#464D13
hypocenterC13#3248
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. #11719283C2semidirect
3. C13×#464C2semidirect
4. #11718849C2semidirect
5. #11718843C2semidirect
7. #11718823C2semidirect
8. #11718715C2semidirect
9. #11718683C2semidirect
10. D13×C4⋊C8C2semidirect
11. #11718490C2semidirect
12. #11718474C2semidirect
13. #11718452C2semidirect
15. #11718420C2semidirect
154. #464D13semidirect
276. C13#3248semidirect

Maximal subgroups

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

subgroupindex
#117193852
#117192832
C13×#4642
#117188492
#117188432
#117188322
#117188232
#117187152
#117186832
D13×C4⋊C82
#117184902
#117184742
#117184522
#117184392
#117184202
#324813