Finite Group Databasebeta

← #13126936

Subgroups — #13126936

Order 1664.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719529C211yesmaximal, characteristic
2#11719344C211yesmaximal, characteristic, complemented
3C13×#452C211yesmaximal, characteristic, complemented
4#11718894C211yesmaximal, characteristic, complemented
5#11718850C211yesmaximal, characteristic, complemented
6#11718843C211yesmaximal, characteristic, complemented
7#11718834C211yesmaximal, characteristic, complemented
8#11718825C211yesmaximal, characteristic, complemented
9#11718712C211yesmaximal, characteristic, complemented
10#11718470C211yesmaximal, characteristic, complemented
11#11718458C211yesmaximal, characteristic, complemented
12#11718432C211yesmaximal, characteristic, complemented
13#11718424C211yesmaximal, characteristic, complemented
14#11718391C211yesmaximal, characteristic, complemented
15#11718384C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21#88200C2211yescharacteristic
22#88200C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24#88198C2211yescharacteristic
25C2×#6107C2211yescharacteristic
26#88193—21no—
27#88189—21no—
28D4×Dic13C2211yescharacteristic
29#88183—21no—
30C4×C22⋊D13C2211yescharacteristic
31#88180C2211yescharacteristic
32#88178C2211yescharacteristic
33C2×#6101—21no—
34C22×#1055C2211yescharacteristic
35C2×#6094C2211yescharacteristic
36#88146—21no—
37C4⋊C4×D13C2211yescharacteristic
38#88144C2211yescharacteristic
39#88143—21no—
40#88137—21no—
41#88133—21no—
42C13×#103C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88060C2211yescharacteristic
51#88058C2211yescharacteristic
52#88057C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88055C2211yescharacteristic
56#88054C2211yescharacteristic
57#88050C2211yescharacteristic
58#88047C2211yescharacteristic
59C13×#41—22no—
60C13×#41—41no—
61C2×Q8×C13C2311yescharacteristic
62C2×Q8×C13C2311yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71#6129—22no—
72#6129—41no—
73C2×C4×D13—21no—
74C2×C4×D13C2311yescharacteristic
75C2×Dic26C2311yescharacteristic
76C13×Q16—41no—
77C13×SD16—22no—
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C13×C4⋊C4—21no—
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13D411yescharacteristic
87#6107—41no—
88#6103—21no—
89#6103—21no—
90#6103D411yescharacteristic
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101D411yescharacteristic
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107C2×#1055—41no—
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6094—41no—
111#3315—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119D4×C13—21no—
120D4×C13—42no—
121D4×C13#4112yes—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—42no—
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2411yescharacteristic
130C22⋊D13—41no—
131C22⋊D13—42no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140C2×Dic13C2×D411yescharacteristic
141C4×D13—21no—
142C4×D13—21no—
143C4×D13—42no—
144Dic26—21no—
145Dic26—21no—
146C8×C13—21no—
147C8×C13—21no—
148#1055—21no—
149#1055—21no—
150#552—131no—
151#547—131no—
152#491—131no—
153#485—131no—
154#484—131no—
155#478—131no—
156#470—131no—
157#467—131no—
158#462—131no—
159#452—131no—
160#452D1311yescharacteristic, complemented
161#440—131no—
162#435—131no—
163#417—131no—
164#416—131no—
165C22×C13—22no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13C22×D411yescharacteristic
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—21no—
175C4×C13—21no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13C2×#4111yescharacteristic
180C4×C13H(5,𝔽2)11yescharacteristic
181Dic13—21no—
182Dic13—21no—
183Dic13—21no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188C2×#41—131no—
189C2×#41C2×D1311yescharacteristic
190C2×Q16—131no—
191C2×Q16C2×D1311yescharacteristic
192C2×SD16C2×D1311yescharacteristic
193C2×M16—131no—
194C22×C8—131no—
195C4⋊Q8—131no—
196#126—261no—
197#125—131no—
198#125—261no—
199#123—261no—
200#123—261no—
201#123—261no—
202C22⋊Q8—131no—
203C22⋊Q8—131no—
204C22⋊Q8—131no—
205C22⋊Q8C2×D1311yescharacteristic
206#121—261no—
207C4×Q8—131no—
208C4×D4—131no—
209C4×D4—131no—
210#117—131no—
211#117—261no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214#107—131no—
215#107—131no—
216#106—131no—
217C4⋊C8—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103C2×D1311yescharacteristic
225#102—131no—
226#102—131no—
227#102C2×D1311yescharacteristic
228C22⋊C8—131no—
229C22⋊C8C2×D1311yescharacteristic
230#97—131no—
231C2×C13—41no—
232C2×C13—42no—
233C2×C13#54611yescharacteristic
234C2×C13#57511yescharacteristic
235C2×C13#57811yescharacteristic
236D13—41no—
237#41—22no—
238#41—41no—
239#41—262no—
240#41—521no—
241C2×Q8—131no—
242C2×Q8C22×D1311yescharacteristic
243C2×Q8C22×D1311yescharacteristic
244C2×D4—21no—
245C2×D4—131no—
246C2×D4—261no—
247C2×D4C22×D1311yescharacteristic
248C22×C4—21no—
249C22×C4—131no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4C22×D1311yescharacteristic
254Q16—41no—
255Q16—521no—
256SD16—22no—
257M16—521no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—521no—
261C2×C8C22×D1311yescharacteristic
262C2×C8C22×D1311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—131no—
265C4⋊C4—131no—
266C4⋊C4—131no—
267C4⋊C4—131no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—261no—
272C4⋊C4—261no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4C22×D1311yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—131no—
280C22⋊C4—131no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C42—131no—
287C42—261no—
288C42—261no—
289C13#331511yescharacteristic, complemented, Sylow
290C23—21no—
291C23—131no—
292C23D4×D1311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—261no—
298Q8—261no—
299D4—21no—
300D4—42no—
301D4—521no—
302D4—522no—
303D4#612912yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—131no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—522no—
320C2×C4—522no—
321C2×C4—522no—
322C2×C4D4×D1311yescharacteristic
323C2×C4C23×D1311yescharacteristic
324C8—21no—
325C8—21no—
326C8—261no—
327C8—261no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—22no—
332C22—41no—
333C22—41no—
334C22—261no—
335C22—261no—
336C22—261no—
337C22C2×D4×D1311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—261no—
343C4—261no—
344C4—261no—
345C4—521no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4C2×#612911yescharacteristic
350C4#8825111yescharacteristic
351C2—41no—
352C2—42no—
353C2—521no—
354C2#1171929611yescharacteristic
355C2#1171947311yescharacteristic
356C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#452C2
socleC22×C13C22×D4
prime radical#11719529C2
hypercenter#452D13
hypocenterC13#3315
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
2. #11719344C2semidirect
3. C13×#452C2semidirect
4. #11718894C2semidirect
5. #11718850C2semidirect
6. #11718843C2semidirect
7. #11718834C2semidirect
8. #11718825C2semidirect
9. #11718712C2semidirect
10. #11718470C2semidirect
11. #11718458C2semidirect
12. #11718432C2semidirect
13. #11718424C2semidirect
14. #11718391C2semidirect
15. #11718384C2semidirect
160. #452D13semidirect
289. C13#3315semidirect

Maximal subgroups

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

subgroupindex
#117195292
#117193442
C13×#4522
#117188942
#117188502
#117188432
#117188342
#117188252
#117187122
#117184702
#117184582
#117184322
#117184242
#117183912
#117183842
#331513