Finite Group Databasebeta

← #13123909

Subgroups — #13123909

Order 1664.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719537C211yesmaximal, characteristic
2C13×#408C211yesmaximal, characteristic, complemented
3#11718895C211yesmaximal, characteristic, complemented
4#11718789C211yesmaximal, characteristic, complemented
5#11718788C211yesmaximal, characteristic, complemented
6#11718772C211yesmaximal, characteristic, complemented
7C8×C22⋊D13C211yesmaximal, characteristic, complemented
8#11718391C211yesmaximal, characteristic, complemented
9#11718390C211yesmaximal, characteristic, complemented
10#11718389C211yesmaximal, characteristic, complemented
11#11718388C211yesmaximal, characteristic, complemented
12#11718388C211yesmaximal, characteristic, complemented
13#11718386C211yesmaximal, characteristic, complemented
14#11718380C211yesmaximal, characteristic, complemented
15#11718379C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6127C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C22×C8×C13C2211yescharacteristic
20#88201C411yescharacteristic
21#88198C411yescharacteristic
22#88194C411yescharacteristic
23#88193C411yescharacteristic
24#88193C411yescharacteristic
25#88193C411yescharacteristic
26#88193C411yescharacteristic
27#88190C411yescharacteristic
28C4×C22⋊D13C2211yescharacteristic
29C4×C22⋊D13C2211yescharacteristic
30C4×C22⋊D13C2211yescharacteristic
31C4×C22⋊D13C2211yescharacteristic
32C2×C4×Dic13C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35C2×#6094C2211yescharacteristic
36C2×#6094C2211yescharacteristic
37C2×C8×D13C2211yescharacteristic
38C2×C8×D13C2211yescharacteristic
39C13×C22⋊C8C2211yescharacteristic
40C13×C22⋊C8C2211yescharacteristic
41C13×C22⋊C8C2211yescharacteristic
42C13×C22⋊C8C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45C22⋊#1055C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic
47#88060C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88060C2211yescharacteristic
51#88055C2211yescharacteristic
52#88055C2211yescharacteristic
53#88054C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56#88054C2211yescharacteristic
57C8×Dic13C2211yescharacteristic
58C8×Dic13C2211yescharacteristic
59C13×#41—41no—
60C13×#41—41no—
61C2×Q8×C13C2×C411yescharacteristic
62C2×D4×C13C2×C411yescharacteristic
63C2×D4×C13C2×C411yescharacteristic
64C2×D4×C13C2×C411yescharacteristic
65C22×C4×C13C2311yescharacteristic
66C22×C4×C13C2311yescharacteristic
67C22×C4×C13C2311yescharacteristic
68C2×C22⋊D13C2×C411yescharacteristic
69C2×C22⋊D13C2×C411yescharacteristic
70C2×C22⋊D13C2×C411yescharacteristic
71C2×C22⋊D13C2×C411yescharacteristic
72C2×C22⋊D13C2×C411yescharacteristic
73C2×C22⋊D13C2×C411yescharacteristic
74C22×Dic13C2×C411yescharacteristic
75C22×Dic13C2×C411yescharacteristic
76#6127—41no—
77#6127—41no—
78C2×D52C2×C411yescharacteristic
79C2×C4×D13C2311yescharacteristic
80C2×C4×D13C2311yescharacteristic
81C2×Dic26C2×C411yescharacteristic
82C13×M16—41no—
83C2×C8×C13—41no—
84C2×C8×C13C2311yescharacteristic
85C2×C8×C13C2311yescharacteristic
86C2×C8×C13C2311yescharacteristic
87C2×C8×C13C2311yescharacteristic
88C22⋊Dic13C2×C411yescharacteristic
89C22⋊Dic13C2×C411yescharacteristic
90C22⋊Dic13C2×C411yescharacteristic
91C22⋊Dic13C2×C411yescharacteristic
92#6103C2×C411yescharacteristic
93#6103C2×C411yescharacteristic
94#6103C2×C411yescharacteristic
95#6103C2×C411yescharacteristic
96#6101C2×C411yescharacteristic
97#6101C2×C411yescharacteristic
98#6101C2×C411yescharacteristic
99#6101C2×C411yescharacteristic
100C4×Dic13C2×C411yescharacteristic
101C4×Dic13C2×C411yescharacteristic
102C4×Dic13C2311yescharacteristic
103C4×Dic13C2311yescharacteristic
104#6099—41no—
105C2×#1055—41no—
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110#6094—41no—
111#6094—41no—
112C8×D13—41no—
113C8×D13—41no—
114#2981—131nomaximal, Sylow
115C23×C13C22×C411yescharacteristic
116C23×C13C22×C411yescharacteristic
117C23×C13C22×C411yescharacteristic
118C22×D13C22×C411yescharacteristic
119C22×D13C22×C411yescharacteristic
120Q8×C13—41no—
121D4×C13—41no—
122D4×C13—41no—
123D4×C13—41no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13C22×C411yescharacteristic
131C2×C4×C13C22×C411yescharacteristic
132C2×C4×C13C22×C411yescharacteristic
133C2×C4×C13C2411yescharacteristic
134C22⋊D13—22no—
135C22⋊D13—22no—
136C22⋊D13—41no—
137C22⋊D13—41no—
138C22⋊D13—41no—
139C22⋊D13—41no—
140C2×Dic13—22no—
141C2×Dic13—41no—
142C2×Dic13C22×C411yescharacteristic
143C2×Dic13C22×C411yescharacteristic
144C2×Dic13C22×C411yescharacteristic
145C2×Dic13C22×C411yescharacteristic
146C2×Dic13C22×C411yescharacteristic
147C2×Dic13C22×C411yescharacteristic
148D52—41no—
149C4×D13—21no—
150C4×D13—21no—
151C4×D13—21no—
152C4×D13—21no—
153Dic26—41no—
154C8×C13—21no—
155C8×C13—21no—
156C8×C13—21no—
157C8×C13—21no—
158#1055—21no—
159#1055—21no—
160#1055—21no—
161#1055—21no—
162#532—131no—
163#436—131no—
164#436—131no—
165#435—131no—
166#435—131no—
167#435—131no—
168#435—131no—
169C8×D4—131no—
170C8×D4—131no—
171#432—131no—
172#431—131no—
173#408—131no—
174#408—131no—
175#408—131no—
176#408D1311yescharacteristic, complemented
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13C23×C411yescharacteristic
187C2×D13—21no—
188C2×D13—21no—
189C2×D13—21no—
190C2×D13—21no—
191C2×D13—21no—
192C2×D13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13H(5,𝔽2)11yescharacteristic
197C4×C13H(5,𝔽2)11yescharacteristic
198Dic13—21no—
199Dic13—21no—
200Dic13—21no—
201Dic13—21no—
202Dic13—21no—
203Dic13#13112yes—
204C2×#41—131no—
205C2×#41C2×D1311yescharacteristic
206C2×M16—131no—
207C2×M16—131no—
208C2×M16—131no—
209C2×M16C2×D1311yescharacteristic
210C22×C8—131no—
211C22×C8—131no—
212C22×C8—131no—
213C22×C8C2×D1311yescharacteristic
214C4⋊Q8—131no—
215#127—131no—
216#124—131no—
217#124—131no—
218#121—131no—
219#121—131no—
220#121—131no—
221#121—131no—
222C4×D4—131no—
223C4×D4—131no—
224C4×D4—131no—
225C4×D4—131no—
226C2×C42—131no—
227C4⋊C8—131no—
228C4⋊C8—131no—
229C4⋊C8—131no—
230C4⋊C8—131no—
231C22⋊C8—131no—
232C22⋊C8—131no—
233C22⋊C8—131no—
234C22⋊C8—131no—
235C22⋊C8—131no—
236C22⋊C8—131no—
237C22⋊C8—131no—
238C22⋊C8—131no—
239C22⋊C8C2×D1311yescharacteristic
240C22⋊C8C2×D1311yescharacteristic
241C22⋊C8C2×D1311yescharacteristic
242C22⋊C8C2×D1311yescharacteristic
243#97—131no—
244#97—131no—
245C4×C8—131no—
246C4×C8—131no—
247C2×C13—41no—
248C2×C13—41no—
249C2×C13—41no—
250C2×C13#51811yescharacteristic
251C2×C13C2×#13111yescharacteristic
252C2×C13#56811yescharacteristic
253D13—41no—
254D13—41no—
255#41—41no—
256#41—41no—
257#41—521no—
258#41—521no—
259C2×Q8—131no—
260C2×Q8C4×D1311yescharacteristic
261C2×D4—131no—
262C2×D4—131no—
263C2×D4—131no—
264C2×D4—131no—
265C2×D4—131no—
266C2×D4—131no—
267C2×D4—131no—
268C2×D4C4×D1311yescharacteristic
269C2×D4C4×D1311yescharacteristic
270C2×D4C4×D1311yescharacteristic
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4C22×D1311yescharacteristic
276C22×C4C22×D1311yescharacteristic
277C22×C4C22×D1311yescharacteristic
278M16—41no—
279M16—521no—
280M16—521no—
281M16—521no—
282C2×C8—41no—
283C2×C8—131no—
284C2×C8—131no—
285C2×C8—131no—
286C2×C8—131no—
287C2×C8—521no—
288C2×C8—521no—
289C2×C8—521no—
290C2×C8C22×D1311yescharacteristic
291C2×C8C22×D1311yescharacteristic
292C2×C8C22×D1311yescharacteristic
293C2×C8C22×D1311yescharacteristic
294C4⋊C4—131no—
295C4⋊C4—131no—
296C4⋊C4—131no—
297C4⋊C4—131no—
298C22⋊C4—131no—
299C22⋊C4—131no—
300C22⋊C4—131no—
301C22⋊C4—131no—
302C22⋊C4—131no—
303C22⋊C4—131no—
304C22⋊C4—131no—
305C22⋊C4—131no—
306C42—131no—
307C42—131no—
308C42—131no—
309C42—131no—
310C13#298111yescharacteristic, complemented, Sylow
311C23—131no—
312C23—131no—
313C23C2×C4×D1311yescharacteristic
314C23C2×C4×D1311yescharacteristic
315C23C2×C4×D1311yescharacteristic
316Q8—41no—
317Q8—521no—
318D4—41no—
319D4—41no—
320D4—41no—
321D4—262no—
322D4—262no—
323D4—521no—
324D4—521no—
325D4—521no—
326D4—521no—
327D4—521no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—131no—
335C2×C4—131no—
336C2×C4—131no—
337C2×C4—131no—
338C2×C4—131no—
339C2×C4—131no—
340C2×C4—262no—
341C2×C4—261no—
342C2×C4—261no—
343C2×C4—261no—
344C2×C4—261no—
345C2×C4—521no—
346C2×C4C2×C4×D1311yescharacteristic
347C2×C4C2×C4×D1311yescharacteristic
348C2×C4C2×C4×D1311yescharacteristic
349C2×C4C23×D1311yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—261no—
355C8—261no—
356C8—261no—
357C8—261no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—261no—
368C22—261no—
369C22—261no—
370C22—261no—
371C22—261no—
372C22—261no—
373C22C22×C4×D1311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—132no—
378C4—261no—
379C4—261no—
380C4—261no—
381C4—261no—
382C4—261no—
383C4#8825111yescharacteristic
384C4#8825111yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—521no—
389C2—521no—
390C2#1171919111yescharacteristic
391C2D13×#13111yescharacteristic
392C2#1171945511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D13
commutator, socleC22×C13C23×C4
FittingC13×#408C2
prime radical#11719537C2
cosocleC2×C4×C13C24
hypercenter#408D13
hypocenterC13#2981
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
2. C13×#408C2semidirect
3. #11718895C2semidirect
4. #11718789C2semidirect
5. #11718788C2semidirect
6. #11718772C2semidirect
7. C8×C22⋊D13C2semidirect
8. #11718391C2semidirect
9. #11718390C2semidirect
10. #11718389C2semidirect
11. #11718388C2semidirect
12. #11718388C2semidirect
13. #11718386C2semidirect
14. #11718380C2semidirect
15. #11718379C2semidirect
176. #408D13semidirect
310. C13#2981semidirect

Maximal subgroups

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

subgroupindex
#117195372
C13×#4082
#117188952
#117187892
#117187882
#117187722
C8×C22⋊D132
#117183912
#117183902
#117183892
#117183882
#117183862
#117183802
#117183792
#298113