Finite Group Databasebeta

← #13126937

Subgroups — #13126937

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#11719286C211yesmaximal, characteristic, complemented
2#11719260C211yesmaximal, characteristic
3C13×#440C211yesmaximal, characteristic, complemented
4#11718834C211yesmaximal, characteristic, complemented
5#11718834C211yesmaximal, characteristic, complemented
6#11718692C211yesmaximal, characteristic, complemented
7#11718670C211yesmaximal, characteristic, complemented
8#11718549C211yesmaximal, characteristic, complemented
9#11718545C211yesmaximal, characteristic, complemented
10#11718477C211yesmaximal, characteristic, complemented
11#11718474C211yesmaximal, characteristic, complemented
12#11718433C211yesmaximal, characteristic, complemented
13#11718432C211yesmaximal, characteristic, complemented
14#11718367C211yesmaximal, characteristic, complemented
15#11718364C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20C4×D4×C13C2211yescharacteristic
21#88200C2211yescharacteristic
22#88200C2211yescharacteristic
23C2×#6107C2211yescharacteristic
24C2×#6107C2211yescharacteristic
25#88184—21no—
26C2×C4⋊Dic13—21no—
27C2×#6094C2211yescharacteristic
28C2×C8×D13C2211yescharacteristic
29#88151C2211yescharacteristic
30#88151C2211yescharacteristic
31#88148—21no—
32#88146C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34#88143—21no—
35#88140—21no—
36#88140—21no—
37#88130—21no—
38C4×D52C2211yescharacteristic
39#88126—21no—
40#88124C2211yescharacteristic
41#88123C2211yescharacteristic
42C13×#107C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×#97C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66#6129—22no—
67#6129—22no—
68#6129—41no—
69#6129—41no—
70C2×D52D411yescharacteristic
71C2×C4×D13—21no—
72C2×C4×D13C2311yescharacteristic
73C2×C4×D13C2311yescharacteristic
74C2×Dic26C2311yescharacteristic
75C2×Dic26C2311yescharacteristic
76C13×SD16—22no—
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C42×C13—21no—
84C42×C13C2311yescharacteristic
85#6107—41no—
86#6107—41no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103D411yescharacteristic
93#6103D411yescharacteristic
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13D411yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101—21no—
106C4×Dic13—21no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109#6094—41no—
110C8×D13—41no—
111#3315—131nomaximal, Sylow
112C23×C13—21no—
113C22×D13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117D4×C13—21no—
118D4×C13#4112yes—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—42no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2411yescharacteristic
126C22⋊D13—42no—
127C22⋊D13—42no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136D52—41no—
137C4×D13—21no—
138C4×D13—21no—
139C4×D13—21no—
140C4×D13—21no—
141C4×D13—42no—
142Dic26—21no—
143Dic26—21no—
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#452—131no—
161#440D1311yescharacteristic, complemented
162#435—131no—
163#417—131no—
164#416—131no—
165C22×C13—22no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13C22×D411yescharacteristic
169C2×D13—21no—
170C2×D13—21no—
171C2×D13—21no—
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13C2×#4111yescharacteristic
181C4×C13H(5,𝔽2)11yescharacteristic
182Dic13—21no—
183Dic13—21no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188C2×#41—131no—
189C2×#41—131no—
190C2×Q16—131no—
191C2×Q16—131no—
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⋊Q8—131no—
206#121—261no—
207C4×Q8C2×D1311yescharacteristic
208C4×D4—131no—
209C4×D4C2×D1311yescharacteristic
210#117—131no—
211#117—261no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214#107—131no—
215#107C2×D1311yescharacteristic
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⋊C8—131no—
230#97C2×D1311yescharacteristic
231C2×C13—42no—
232C2×C13#54611yescharacteristic
233C2×C13#57511yescharacteristic
234C2×C13#57811yescharacteristic
235D13—41no—
236D13—41no—
237#41—262no—
238#41—262no—
239#41—521no—
240#41—521no—
241C2×Q8—131no—
242C2×Q8—131no—
243C2×Q8C22×D1311yescharacteristic
244C2×D4—131no—
245C2×D4—261no—
246C2×D4—261no—
247C2×D4C22×D1311yescharacteristic
248C22×C4—21no—
249C22×C4—131no—
250C22×C4—131no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254Q16—521no—
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—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⋊C4C22×D1311yescharacteristic
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—21no—
287C42—261no—
288C42C22×D1311yescharacteristic
289C13#331511yescharacteristic, complemented, Sylow
290C23—21no—
291C23—131no—
292C23—131no—
293Q8—21no—
294Q8—21no—
295Q8—261no—
296Q8—261no—
297Q8—261no—
298Q8—261no—
299D4—21no—
300D4—521no—
301D4—522no—
302D4—522no—
303D4#612712yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—131no—
309C2×C4—131no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—522no—
319C2×C4—522no—
320C2×C4—522no—
321C2×C4D4×D1311yescharacteristic
322C2×C4D4×D1311yescharacteristic
323C2×C4C23×D1311yescharacteristic
324C8—21no—
325C8—21no—
326C8—261no—
327C8—261no—
328C22—22no—
329C22—41no—
330C22—41no—
331C22—261no—
332C22—261no—
333C22—261no—
334C22—261no—
335C22—261no—
336C22—261no—
337C22C2×D4×D1311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—261no—
344C4—261no—
345C4—521no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4C2×#612711yescharacteristic
350C4#8825611yescharacteristic
351C2—42no—
352C2—521no—
353C2—521no—
354C2#1171925511yescharacteristic
355C2#1171947811yescharacteristic
356C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#440C2
socleC22×C13C22×D4
prime radical#11719260C2
hypercenter#440D13
hypocenterC13#3315
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #11719286C2semidirect
3. C13×#440C2semidirect
4. #11718834C2semidirect
5. #11718834C2semidirect
6. #11718692C2semidirect
7. #11718670C2semidirect
8. #11718549C2semidirect
9. #11718545C2semidirect
10. #11718477C2semidirect
11. #11718474C2semidirect
12. #11718433C2semidirect
13. #11718432C2semidirect
14. #11718367C2semidirect
15. #11718364C2semidirect
161. #440D13semidirect
289. C13#3315semidirect

Maximal subgroups

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

subgroupindex
#117192862
#117192602
C13×#4402
#117188342
#117186922
#117186702
#117185492
#117185452
#117184772
#117184742
#117184332
#117184322
#117183672
#117183642
#331513