Finite Group Databasebeta

← #13126934

Subgroups — #13126934

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#11719256C211yesmaximal, characteristic
2#11719246C211yesmaximal, characteristic, complemented
3C13×#435C211yesmaximal, characteristic, complemented
4#11718798C211yesmaximal, characteristic, complemented
5#11718794C211yesmaximal, characteristic, complemented
6#11718777C211yesmaximal, characteristic, complemented
7#11718774C211yesmaximal, characteristic, complemented
8#11718510C211yesmaximal, characteristic, complemented
9#11718508C211yesmaximal, characteristic, complemented
10#11718394C211yesmaximal, characteristic, complemented
11#11718394C211yesmaximal, characteristic, complemented
12#11718384C211yesmaximal, characteristic, complemented
13#11718383C211yesmaximal, characteristic, complemented
14#11718371C211yesmaximal, characteristic, complemented
15#11718364C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C2×#6127C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C22×C8×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21#88192—21no—
22#88189—21no—
23#88180C2211yescharacteristic
24C2×C4⋊Dic13C2211yescharacteristic
25#88178C2211yescharacteristic
26#88178C2211yescharacteristic
27#88178C2211yescharacteristic
28#88178C2211yescharacteristic
29C2×Dic52C2211yescharacteristic
30C2×Dic52C2211yescharacteristic
31C2×#6095C2211yescharacteristic
32C4⋊C4×D13—21no—
33#88143—21no—
34#88137—21no—
35#88137—21no—
36#88133—21no—
37#88131—21no—
38C4×D52C2211yescharacteristic
39#88124C2211yescharacteristic
40#88123C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45C13×#97C2211yescharacteristic
46#88061C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88056C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C2×D4×C13D411yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C22×Dic13—21no—
65#6127—22no—
66#6127—22no—
67#6127—41no—
68#6127—41no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×Dic26C2311yescharacteristic
74C2×Dic26C2311yescharacteristic
75C2×Dic26C2311yescharacteristic
76C13×M16—41no—
77C2×C8×C13—41no—
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C2×C8×C13C2311yescharacteristic
82C13×C4⋊C4D411yescharacteristic
83C13×C22⋊C4D411yescharacteristic
84C13×C22⋊C4D411yescharacteristic
85C42×C13C2311yescharacteristic
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101—21no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108Dic52—41no—
109Dic52—41no—
110#6095—22no—
111#3315—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115D4×C13—41no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C22⋊D13—42no—
126C22⋊D13—42no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—42no—
135D52—21no—
136D52#4112yes—
137C4×D13—42no—
138C4×D13—42no—
139C4×D13—42no—
140Dic26—21no—
141Dic26—21no—
142Dic26—21no—
143Dic26—21no—
144Dic26—21no—
145Dic26—21no—
146C8×C13—21no—
147C8×C13—21no—
148C8×C13—21no—
149C8×C13—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#452—131no—
161#440—131no—
162#435D1311yescharacteristic, complemented
163#417—131no—
164#416—131no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13C22×D411yescharacteristic
172C2×D13—22no—
173C2×D13—41no—
174C2×D13—41no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13C2×#4111yescharacteristic
180C4×C13H(5,𝔽2)11yescharacteristic
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188C2×#41—131no—
189C2×#41—131no—
190C2×Q16—131no—
191C2×Q16—131no—
192C2×SD16—131no—
193C2×M16C2×D1311yescharacteristic
194C22×C8C2×D1311yescharacteristic
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⋊Q8—131no—
206#121—261no—
207C4×Q8—131no—
208C4×D4—131no—
209C4×D4C2×D1311yescharacteristic
210#117—131no—
211#117—261no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214#107—131no—
215#107—131no—
216#106—131no—
217C4⋊C8C2×D1311yescharacteristic
218#103—131no—
219#103—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225#102—131no—
226#102—131no—
227#102—131no—
228C22⋊C8C2×D1311yescharacteristic
229C22⋊C8C2×D1311yescharacteristic
230#97C2×D1311yescharacteristic
231C2×C13—41no—
232C2×C13—41no—
233C2×C13#54611yescharacteristic
234C2×C13#57511yescharacteristic
235C2×C13#57811yescharacteristic
236D13—42no—
237#41—262no—
238#41—262no—
239#41—521no—
240#41—521no—
241C2×Q8—131no—
242C2×Q8—131no—
243C2×Q8—131no—
244C2×D4—131no—
245C2×D4—261no—
246C2×D4—261no—
247C2×D4D5211yescharacteristic
248C22×C4—261no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4C22×D1311yescharacteristic
253C22×C4C22×D1311yescharacteristic
254Q16—521no—
255Q16—521no—
256SD16—262no—
257M16—41no—
258C2×C8—41no—
259C2×C8C22×D1311yescharacteristic
260C2×C8C22×D1311yescharacteristic
261C2×C8C22×D1311yescharacteristic
262C2×C8C22×D1311yescharacteristic
263C4⋊C4—131no—
264C4⋊C4—131no—
265C4⋊C4—131no—
266C4⋊C4—131no—
267C4⋊C4—261no—
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⋊C4D5211yescharacteristic
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4D5211yescharacteristic
285C22⋊C4D5211yescharacteristic
286C42—261no—
287C42—261no—
288C42C22×D1311yescharacteristic
289C13#331511yescharacteristic, complemented, Sylow
290C23—261no—
291C23C2×D5211yescharacteristic
292C23C2×D5211yescharacteristic
293Q8—261no—
294Q8—261no—
295Q8—261no—
296Q8—261no—
297Q8—261no—
298Q8—261no—
299D4—41no—
300D4—132no—
301D4—261no—
302D4—522no—
303D4—522no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—522no—
316C2×C4—522no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4C2×D5211yescharacteristic
320C2×C4C2×D5211yescharacteristic
321C2×C4C2×D5211yescharacteristic
322C2×C4C2×D5211yescharacteristic
323C2×C4C23×D1311yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—262no—
335C22—521no—
336C22—521no—
337C22C22×D5211yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—521no—
343C4—521no—
344C4—521no—
345C4—521no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4#8825111yescharacteristic
350C4#41×D1311yescharacteristic
351C2—41no—
352C2—41no—
353C2—522no—
354C2#1171925911yescharacteristic
355C2#1171945311yescharacteristic
356C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#435C2
socleC22×C13C22×D4
prime radical#11719256C2
hypercenter#435D13
hypocenterC13#3315
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #11719246C2semidirect
3. C13×#435C2semidirect
4. #11718798C2semidirect
5. #11718794C2semidirect
6. #11718777C2semidirect
7. #11718774C2semidirect
8. #11718510C2semidirect
9. #11718508C2semidirect
10. #11718394C2semidirect
11. #11718394C2semidirect
12. #11718384C2semidirect
13. #11718383C2semidirect
14. #11718371C2semidirect
15. #11718364C2semidirect
162. #435D13semidirect
289. C13#3315semidirect

Maximal subgroups

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

subgroupindex
#117192562
#117192462
C13×#4352
#117187982
#117187942
#117187772
#117187742
#117185102
#117185082
#117183942
#117183842
#117183832
#117183712
#117183642
#331513