Finite Group Databasebeta

← #13126905

Subgroups — #13126905

Order 1664.

380 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#11719303C211yesmaximal, characteristic
2#11719238C211yesmaximal, characteristic, complemented
3C13×#482C211yesmaximal, characteristic, complemented
4#11718703C211yesmaximal, characteristic, complemented
5#11718665C211yesmaximal, characteristic, complemented
6#11718548C211yesmaximal, characteristic, complemented
7#11718536C211yesmaximal, characteristic, complemented
8#11718528C211yesmaximal, characteristic, complemented
9#11718514C211yesmaximal, characteristic, complemented
10#11718444C211yesmaximal, characteristic, complemented
11#11718433C211yesmaximal, characteristic, complemented
12#11718428C211yesmaximal, characteristic, complemented
13#11718426C211yesmaximal, characteristic, complemented
14#11718400C211yesmaximal, characteristic, complemented
15#11718389C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C22×Dic26C2211yescharacteristic
18C13×#121C2211yescharacteristic
19C13×#117C2211yescharacteristic
20#88193—21no—
21#88190C2211yescharacteristic
22D4×Dic13—21no—
23C2×#6105C2211yescharacteristic
24C4×C22⋊D13C2211yescharacteristic
25#88178C2211yescharacteristic
26C2×#6099C2211yescharacteristic
27C2×Dic52C2211yescharacteristic
28C2×Dic52C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88151C2211yescharacteristic
31#88151C2211yescharacteristic
32#88146C2211yescharacteristic
33#88142C2211yescharacteristic
34#88141C2211yescharacteristic
35#88141C2211yescharacteristic
36#88139—21no—
37#88139—21no—
38#88133—21no—
39#88132—21no—
40#88130—21no—
41C4×Dic26—21no—
42C13×#107C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×#102C2211yescharacteristic
46C13×C22⋊C8C2211yescharacteristic
47#88072C2211yescharacteristic
48#88060C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88055C2211yescharacteristic
52#88054C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88050C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13D411yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
66#6129—22no—
67#6129—41no—
68C2×C4×D13C2311yescharacteristic
69C2×Dic26—22no—
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×Dic26—41no—
73C2×Dic26C2311yescharacteristic
74C2×Dic26C2311yescharacteristic
75C2×Dic26C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C22⋊C4—21no—
82C13×C22⋊C4—21no—
83C42×C13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13D411yescharacteristic
88#6105—41no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103D411yescharacteristic
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101D411yescharacteristic
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13C2311yescharacteristic
105#6099—41no—
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108Dic52—22no—
109Dic52—41no—
110C8×D13—41no—
111#3313—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115D4×C13—21no—
116D4×C13—21no—
117D4×C13—42no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2411yescharacteristic
125C22⋊D13—41no—
126C22⋊D13—42no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136C4×D13—21no—
137C4×D13—21no—
138Dic26—21no—
139Dic26—21no—
140Dic26—21no—
141Dic26—21no—
142Dic26—21no—
143Dic26—42no—
144Dic26—42no—
145Dic26#4112yes—
146C8×C13—21no—
147C8×C13—21no—
148#1055—21no—
149#1055—21no—
150#556—131no—
151#548—131no—
152#489—131no—
153#485—131no—
154#482D1311yescharacteristic, complemented
155#477—131no—
156#468—131no—
157#467—131no—
158#464—131no—
159#452—131no—
160#451—131no—
161#441—131no—
162#435—131no—
163#419—131no—
164#416—131no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—41no—
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—22no—
182Dic13—21no—
183Dic13—21no—
184Dic13—21no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188C2×#41—131no—
189C22×Q8—131no—
190C2×Q16—131no—
191C2×Q16—131no—
192C2×SD16—131no—
193C2×M16—131no—
194C22×C8—131no—
195C4⋊Q8—131no—
196#126—261no—
197#126—261no—
198#124—131no—
199#124—261no—
200#124—261no—
201C22⋊Q8—131no—
202C22⋊Q8—131no—
203C22⋊Q8—131no—
204C22⋊Q8—261no—
205#121—261no—
206#121C2×D1311yescharacteristic
207C4×Q8—131no—
208C4×Q8—131no—
209C4×Q8—261no—
210C4×D4—131no—
211C4×D4—261no—
212#117—131no—
213#117C2×D1311yescharacteristic
214#107—131no—
215#107C2×D1311yescharacteristic
216#106C2×D1311yescharacteristic
217C4⋊C8—131no—
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#102C2×D1311yescharacteristic
227#102C2×D1311yescharacteristic
228C22⋊C8—131no—
229C22⋊C8C2×D1311yescharacteristic
230#97—131no—
231C2×C13—41no—
232C2×C13—81no—
233C2×C13#54611yescharacteristic
234C2×C13#57511yescharacteristic
235C2×C13#57811yescharacteristic
236D13—41no—
237#41—262no—
238#41—521no—
239C2×Q8—131no—
240C2×Q8—131no—
241C2×Q8—131no—
242C2×Q8—261no—
243C2×Q8—262no—
244C2×Q8—261no—
245C2×Q8—521no—
246C2×D4—21no—
247C2×D4—131no—
248C2×D4—261no—
249C2×D4C22×D1311yescharacteristic
250C22×C4—131no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4C22×D1311yescharacteristic
254Q16—262no—
255Q16—521no—
256SD16—521no—
257M16—521no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—521no—
261C2×C8C22×D1311yescharacteristic
262C2×C8C22×D1311yescharacteristic
263C4⋊C4—131no—
264C4⋊C4—131no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4C22×D1311yescharacteristic
272C4⋊C4C22×D1311yescharacteristic
273C4⋊C4C22×D1311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—131no—
277C22⋊C4—131no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C42—21no—
285C42—131no—
286C42—261no—
287C42—261no—
288C42—261no—
289C13#331311yescharacteristic, complemented, Sylow
290C23—21no—
291C23—131no—
292C23D4×D1311yescharacteristic
293Q8—132no—
294Q8—261no—
295Q8—261no—
296Q8—261no—
297Q8—261no—
298Q8—261no—
299Q8—522no—
300Q8—522no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—521no—
305D4—522no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—131no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
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—41no—
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—262no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4#41×D1311yescharacteristic
350C4#8825611yescharacteristic
351C2—41no—
352C2—81no—
353C2—521no—
354C2#1171935911yescharacteristic
355C2#1171947611yescharacteristic
356C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#482C2
socleC22×C13C22×D4
prime radical#11719303C2
hypercenter#482D13
hypocenterC13#3313
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #11719238C2semidirect
3. C13×#482C2semidirect
4. #11718703C2semidirect
5. #11718665C2semidirect
6. #11718548C2semidirect
7. #11718536C2semidirect
8. #11718528C2semidirect
9. #11718514C2semidirect
10. #11718444C2semidirect
11. #11718433C2semidirect
12. #11718428C2semidirect
13. #11718426C2semidirect
14. #11718400C2semidirect
15. #11718389C2semidirect
154. #482D13semidirect
289. C13#3313semidirect

Maximal subgroups

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

subgroupindex
#117193032
#117192382
C13×#4822
#117187032
#117186652
#117185482
#117185362
#117185282
#117185142
#117184442
#117184332
#117184282
#117184262
#117184002
#117183892
#331313