Finite Group Databasebeta

← #13125107

Subgroups — #13125107

Order 1664.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#542C211yesmaximal, characteristic, complemented
2#11719228C211yesmaximal, characteristic, complemented
3#11718755C211yesmaximal, characteristic, complemented
4#11718745C211yesmaximal, characteristic, complemented
5#11718718C211yesmaximal, characteristic, complemented
6#11718715C211yesmaximal, characteristic, complemented
7#11718708C211yesmaximal, characteristic, complemented
8#11718704C211yesmaximal, characteristic, complemented
9#11718698C211yesmaximal, characteristic
10#11718695C211yesmaximal, characteristic, complemented
11#11718691C211yesmaximal, characteristic, complemented
12C4×#6106C211yesmaximal, characteristic, complemented
13C4×#6105C211yesmaximal, characteristic, complemented
14#11718675C211yesmaximal, characteristic, complemented
15#11718661C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C13×C4⋊Q8C2211yescharacteristic
18C13×#126—21no—
19C13×#124—21no—
20C13×#124C2211yescharacteristic
21C13×#123—21no—
22C13×C22⋊Q8—21no—
23C13×C22⋊Q8C2211yescharacteristic
24C13×#121C2211yescharacteristic
25C4×Q8×C13C2211yescharacteristic
26C4×D4×C13C2211yescharacteristic
27C13×#117C2211yescharacteristic
28C2×#6107C2211yescharacteristic
29C2×#6106C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31C2×#6104C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33#88146—21no—
34C4⋊C4×D13—21no—
35#88135—21no—
36#88135—21no—
37C4×D52C2211yescharacteristic
38C4×D52C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41#88075C2211yescharacteristic
42#88075C2211yescharacteristic
43#88072C2211yescharacteristic
44#88072C2211yescharacteristic
45C22⋊#1055C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic
47#88050C2211yescharacteristic
48#88050C2211yescharacteristic
49#88049C2211yescharacteristic
50#88049C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88048C2211yescharacteristic
54#88048C2211yescharacteristic
55C4⋊#1055C2211yescharacteristic
56C4⋊#1055C2211yescharacteristic
57#88043C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13C2311yescharacteristic
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67#6127—22no—
68#6127—22no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×Dic26C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4D411yescharacteristic
78C13×C4⋊C4D411yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C22⋊C4—21no—
82C13×C22⋊C4—21no—
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C13×C22⋊C4—21no—
86C13×C22⋊C4D411yescharacteristic
87C13×C22⋊C4D411yescharacteristic
88C42×C13—21no—
89C42×C13C2311yescharacteristic
90C42×C13C2311yescharacteristic
91#6107—22no—
92#6106—22no—
93#6105—22no—
94#6104—22no—
95#6103—21no—
96#6103—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100#6101—21no—
101#6101—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3125—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111C22×D13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13—81no—
115D4×C13—21no—
116D4×C13—21no—
117D4×C13—81no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—81no—
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2411yescharacteristic
130C22⋊D13—24no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—81no—
135D52—21no—
136D52#4112yes—
137C4×D13—24no—
138C4×D13—81no—
139C4×D13—81no—
140Dic26—21no—
141Dic26#4112yes—
142#1055—21no—
143#1055—21no—
144#1055—21no—
145#1055—21no—
146#542D1311yescharacteristic, complemented
147#520—131no—
148#483—131no—
149#481—131no—
150#476—131no—
151#475—131no—
152#464—131no—
153#463—131no—
154#452—131no—
155#449—131no—
156#442—131no—
157#441—131no—
158C4×SD16—131no—
159C4×SD16—131no—
160#433—131no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13C22×D411yescharacteristic
168C2×D13—22no—
169C2×D13—41no—
170C2×D13—41no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13C2×#4111yescharacteristic
180C4×C13C2×#4111yescharacteristic
181Dic13—22no—
182Dic13—41no—
183Dic13—41no—
184C2×#41—131no—
185C2×Q16—131no—
186C2×SD16—131no—
187C2×SD16—131no—
188C2×D8—131no—
189C4⋊Q8C2×D1311yescharacteristic
190#126—21no—
191#124—21no—
192#124C2×D1311yescharacteristic
193#123—21no—
194C22⋊Q8—21no—
195C22⋊Q8C2×D1311yescharacteristic
196#121C2×D1311yescharacteristic
197C4×Q8—131no—
198C4×Q8—131no—
199C4×Q8C2×D1311yescharacteristic
200C4×D4—131no—
201C4×D4—131no—
202C4×D4—261no—
203C4×D4—261no—
204C4×D4C2×D1311yescharacteristic
205#117—261no—
206#117C2×D1311yescharacteristic
207C2×C4⋊C4—131no—
208C2×C4⋊C4—261no—
209#106—131no—
210#106—131no—
211#106—131no—
212#106—131no—
213C4⋊C8—131no—
214C4⋊C8—131no—
215#103—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#102—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223C22⋊C8—131no—
224C22⋊C8—131no—
225#97—131no—
226C4×C8—131no—
227C2×C13—41no—
228C2×C13—81no—
229C2×C13#52511yescharacteristic
230C2×C13#57711yescharacteristic
231C2×C13#57711yescharacteristic
232D13—42no—
233#41—262no—
234#41—262no—
235C2×Q8—21no—
236C2×Q8—131no—
237C2×Q8C22×D1311yescharacteristic
238C2×D4—21no—
239C2×D4—131no—
240C2×D4—261no—
241C2×D4C22×D1311yescharacteristic
242C22×C4—21no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4C22×D1311yescharacteristic
248Q16—262no—
249SD16—262no—
250SD16—262no—
251D8—262no—
252C2×C8—131no—
253C2×C8—131no—
254C2×C8—131no—
255C2×C8—131no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—131no—
260C4⋊C4—131no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4C22⋊D1311yescharacteristic
265C4⋊C4C22⋊D1311yescharacteristic
266C4⋊C4C22×D1311yescharacteristic
267C4⋊C4C22×D1311yescharacteristic
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4C22⋊D1311yescharacteristic
276C22⋊C4C22⋊D1311yescharacteristic
277C42—21no—
278C42—261no—
279C42—261no—
280C42C22×D1311yescharacteristic
281C42C22×D1311yescharacteristic
282C13#312511yescharacteristic, complemented, Sylow
283C23—21no—
284C23—261no—
285C23C2×C22⋊D1311yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—132no—
290Q8—261no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—132no—
295D4—264no—
296D4—261no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—264no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—1041no—
308C2×C4—1041no—
309C2×C4—1041no—
310C2×C4C2×C22⋊D1311yescharacteristic
311C2×C4C2×C22⋊D1311yescharacteristic
312C2×C4C2×C22⋊D1311yescharacteristic
313C2×C4C2×C22⋊D1311yescharacteristic
314C2×C4C2×C22⋊D1311yescharacteristic
315C2×C4C23×D1311yescharacteristic
316C8—261no—
317C8—261no—
318C8—261no—
319C8—261no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—262no—
327C22—521no—
328C22—521no—
329C22C22×C22⋊D1311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—262no—
339C4—521no—
340C4—521no—
341C4#41×D1311yescharacteristic
342C4#41×D1311yescharacteristic
343C2—41no—
344C2—81no—
345C2—522no—
346C2#1171953311yescharacteristic
347C2#1171954111yescharacteristic
348C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#542C2
socleC22×C13C22×D4
prime radical#11718698C2
hypercenter#542D13
hypocenterC13#3125
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. C13×#542C2semidirect
2. #11719228C2semidirect
3. #11718755C2semidirect
4. #11718745C2semidirect
5. #11718718C2semidirect
6. #11718715C2semidirect
7. #11718708C2semidirect
8. #11718704C2semidirect
10. #11718695C2semidirect
11. #11718691C2semidirect
12. C4×#6106C2semidirect
13. C4×#6105C2semidirect
14. #11718675C2semidirect
15. #11718661C2semidirect
146. #542D13semidirect
282. C13#3125semidirect

Maximal subgroups

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

subgroupindex
C13×#5422
#117192282
#117187552
#117187452
#117187182
#117187152
#117187082
#117187042
#117186982
#117186952
#117186912
C4×#61062
C4×#61052
#117186752
#117186612
#312513