Finite Group Databasebeta

← #13126932

Subgroups — #13126932

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
1C13×#547C211yesmaximal, characteristic
2#11719246C211yesmaximal, characteristic, complemented
3#11718900C211yesmaximal, characteristic, complemented
4#11718900C211yesmaximal, characteristic, complemented
5#11718894C211yesmaximal, characteristic, complemented
6#11718893C211yesmaximal, characteristic, complemented
7#11718751C211yesmaximal, characteristic, complemented
8#11718743C211yesmaximal, characteristic, complemented
9#11718713C211yesmaximal, characteristic, complemented
10#11718712C211yesmaximal, characteristic, complemented
11#11718706C211yesmaximal, characteristic, complemented
12#11718705C211yesmaximal, characteristic, complemented
13#11718679C211yesmaximal, characteristic, complemented
14#11718672C211yesmaximal, characteristic, complemented
15#11718670C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×C13×#41C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C13×#123—21no—
20C13×#123—21no—
21C13×C22⋊Q8C2211yescharacteristic
22C13×C22⋊Q8C2211yescharacteristic
23C13×#121—21no—
24C4×D4×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C2×C13×C4⋊C4—21no—
27C2×#6107C2211yescharacteristic
28C2×#6107C2211yescharacteristic
29#88189—21no—
30C2×#6105C2211yescharacteristic
31#88180C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33#88178C2211yescharacteristic
34#88178C2211yescharacteristic
35C2×#6099C2211yescharacteristic
36C22×#1055C2211yescharacteristic
37#88143—21no—
38#88133—21no—
39#88131—21no—
40#88124C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88072C2211yescharacteristic
49#88072C2211yescharacteristic
50#88072C2211yescharacteristic
51C22⋊#1055C2211yescharacteristic
52C22⋊#1055C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C13×#41—22no—
60C13×#41—22no—
61C13×#41—41no—
62C13×#41—41no—
63C2×Q8×C13C2311yescharacteristic
64C2×Q8×C13C2311yescharacteristic
65C2×D4×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13D411yescharacteristic
68C2×D4×C13C2311yescharacteristic
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13C2311yescharacteristic
73C22×C4×C13C2311yescharacteristic
74C22×Dic13—21no—
75C2×Dic26C2311yescharacteristic
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4D411yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C13×C22⋊C4D411yescharacteristic
86C13×C22⋊C4D411yescharacteristic
87C42×C13C2311yescharacteristic
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91#6107—41no—
92#6107—41no—
93#6105—22no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105#6099—41no—
106C2×#1055—41no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#3315—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C23×C13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119D4×C13—21no—
120D4×C13—41no—
121D4×C13—42no—
122D4×C13—42no—
123D4×C13#4112yes—
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×C13—21no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13C2×D411yescharacteristic
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2×D411yescharacteristic
138C2×C4×C13C2411yescharacteristic
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—42no—
144Dic26—21no—
145Dic26—21no—
146#1055—21no—
147#1055—21no—
148#1055—21no—
149#1055—21no—
150#552—131no—
151#547D1311yescharacteristic
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#435—131no—
163#417—131no—
164#416—131no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—22no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13C22×D411yescharacteristic
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13C2×#4111yescharacteristic
183C4×C13H(5,𝔽2)11yescharacteristic
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188C2×#41C2×D1311yescharacteristic
189C2×#41C2×D1311yescharacteristic
190C2×Q16—131no—
191C2×Q16—131no—
192C2×SD16—131no—
193C2×M16—131no—
194C22×C8—131no—
195C4⋊Q8C2×D1311yescharacteristic
196#126—261no—
197#125—131no—
198#125—261no—
199#123—21no—
200#123—21no—
201#123—261no—
202C22⋊Q8—131no—
203C22⋊Q8—131no—
204C22⋊Q8C2×D1311yescharacteristic
205C22⋊Q8C2×D1311yescharacteristic
206#121—21no—
207C4×Q8—131no—
208C4×D4C2×D1311yescharacteristic
209C4×D4C2×D1311yescharacteristic
210#117—131no—
211#117—261no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—131no—
214#107—131no—
215#107—131no—
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#103—131no—
225#102—131no—
226#102—131no—
227#102—131no—
228C22⋊C8—131no—
229C22⋊C8—131no—
230#97—131no—
231C2×C13—41no—
232C2×C13—41no—
233C2×C13—42no—
234C2×C13#54611yescharacteristic
235C2×C13#57511yescharacteristic
236C2×C13#57811yescharacteristic
237#41—22no—
238#41—22no—
239#41—41no—
240#41—41no—
241C2×Q8—131no—
242C2×Q8C22×D1311yescharacteristic
243C2×Q8C22×D1311yescharacteristic
244C2×D4—21no—
245C2×D4—21no—
246C2×D4C22⋊D1311yescharacteristic
247C2×D4C22×D1311yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—261no—
252C22×C4C22×D1311yescharacteristic
253C22×C4C22×D1311yescharacteristic
254Q16—521no—
255Q16—521no—
256SD16—262no—
257M16—521no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—131no—
261C2×C8—131no—
262C2×C8—521no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—131no—
268C4⋊C4—131no—
269C4⋊C4—131no—
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—21no—
280C22⋊C4—21no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4C22⋊D1311yescharacteristic
285C22⋊C4C22⋊D1311yescharacteristic
286C42—261no—
287C42—261no—
288C42C22×D1311yescharacteristic
289C13#331511yescharacteristic, complemented, Sylow
290C23—21no—
291C23C2×C22⋊D1311yescharacteristic
292C23C2×C22⋊D1311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—261no—
298Q8—261no—
299D4—21no—
300D4—41no—
301D4—42no—
302D4—42no—
303D4#612912yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—522no—
319C2×C4C2×C22⋊D1311yescharacteristic
320C2×C4C2×C22⋊D1311yescharacteristic
321C2×C4C2×C22⋊D1311yescharacteristic
322C2×C4C2×C22⋊D1311yescharacteristic
323C2×C4C23×D1311yescharacteristic
324C8—261no—
325C8—261no—
326C8—261no—
327C8—261no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22C22×C22⋊D1311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—521no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4C2×#612911yescharacteristic
350C4#8825111yescharacteristic
351C2—41no—
352C2—41no—
353C2—42no—
354C2#1171951111yescharacteristic
355C2#1171952711yescharacteristic
356C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#547C2
socleC22×C13C22×D4
hypercenter#547D13
hypocenterC13#3315
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
2. #11719246C2semidirect
3. #11718900C2semidirect
4. #11718900C2semidirect
5. #11718894C2semidirect
6. #11718893C2semidirect
7. #11718751C2semidirect
8. #11718743C2semidirect
9. #11718713C2semidirect
10. #11718712C2semidirect
11. #11718706C2semidirect
12. #11718705C2semidirect
13. #11718679C2semidirect
14. #11718672C2semidirect
15. #11718670C2semidirect
289. C13#3315semidirect

Maximal subgroups

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

subgroupindex
C13×#5472
#117192462
#117189002
#117188942
#117188932
#117187512
#117187432
#117187132
#117187122
#117187062
#117187052
#117186792
#117186722
#117186702
#331513