Finite Group Databasebeta

← #13126218

Subgroups — #13126218

Order 1664.

386 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719327C211yesmaximal, characteristic, complemented
2#11719301C211yesmaximal, characteristic
3C13×#468C211yesmaximal, characteristic, complemented
4#11718824C211yesmaximal, characteristic, complemented
5#11718823C211yesmaximal, characteristic, complemented
6#11718795C211yesmaximal, characteristic, complemented
7#11718779C211yesmaximal, characteristic, complemented
8#11718710C211yesmaximal, characteristic, complemented
9#11718703C211yesmaximal, characteristic, complemented
10#11718551C211yesmaximal, characteristic, complemented
11#11718536C211yesmaximal, characteristic, complemented
12#11718479C211yesmaximal, characteristic, complemented
13#11718455C211yesmaximal, characteristic, complemented
14#11718423C211yesmaximal, characteristic, complemented
15#11718420C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C2×C13×SD16C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C13×C22⋊Q8C2211yescharacteristic
20C13×#121C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22#88198C2211yescharacteristic
23C2×#6106C2211yescharacteristic
24#88194C2211yescharacteristic
25#88193—21no—
26D4×Dic13C2211yescharacteristic
27C2×#6105C2211yescharacteristic
28#88184C2211yescharacteristic
29#88178C2211yescharacteristic
30C2×C4×Dic13C2211yescharacteristic
31C2×#6099C2211yescharacteristic
32C2×#6095C2211yescharacteristic
33#88147C2211yescharacteristic
34#88143—21no—
35#88142C2211yescharacteristic
36#88142C2211yescharacteristic
37#88141—21no—
38#88141C2211yescharacteristic
39#88139—21no—
40#88135—21no—
41#88132—21no—
42#88131—21no—
43C13×#107C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48#88061C2211yescharacteristic
49#88058C2211yescharacteristic
50#88056C2211yescharacteristic
51#88054C2211yescharacteristic
52#88054C2211yescharacteristic
53#88054C2211yescharacteristic
54#88054C2211yescharacteristic
55#88050C2211yescharacteristic
56#88049C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67C22×Dic13D411yescharacteristic
68C22×Dic13D411yescharacteristic
69#6129—44no—
70C2×D52C2311yescharacteristic
71C2×C4×D13—21no—
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×Dic26C2311yescharacteristic
75C13×SD16—41no—
76C13×M16—41no—
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C13×C22⋊C4—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86#6106—41no—
87#6105—41no—
88#6103—21no—
89#6103—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13D411yescharacteristic
102C4×Dic13D411yescharacteristic
103C4×Dic13C2311yescharacteristic
104C4×Dic13C2311yescharacteristic
105#6099—41no—
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#6095—41no—
109#3254—131nomaximal, Sylow
110C23×C13—21no—
111C23×C13C2×D411yescharacteristic
112C22×D13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
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—42no—
126C22⋊D13—42no—
127C22⋊D13—42no—
128C2×Dic13—22no—
129C2×Dic13—22no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—42no—
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136C2×Dic13C2×D411yescharacteristic
137C2×Dic13C2×D411yescharacteristic
138D52—21no—
139D52—21no—
140C4×D13—42no—
141Dic26—21no—
142Dic26—21no—
143Dic26—42no—
144Dic26—42no—
145C8×C13—21no—
146C8×C13—21no—
147#1055—21no—
148#1055—21no—
149#533—131no—
150#532—131no—
151#477—131no—
152#477—131no—
153#474—131no—
154#474—131no—
155#468—131no—
156#468—131no—
157#468—131no—
158#468D1311yescharacteristic, complemented
159#461—131no—
160#461—131no—
161#460—131no—
162#460—131no—
163#423—131no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13C22×D411yescharacteristic
171C2×D13—41no—
172C2×D13—41no—
173C2×D13—41no—
174C4×C13—21no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13H(5,𝔽2)11yescharacteristic
179C4×C132−1+411yescharacteristic
180Dic13—21no—
181Dic13—21no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185Dic13AGL(1,ℤ/8)12yes—
186Dic13#13712yes—
187C2×#41—261no—
188C2×SD16—131no—
189C2×SD16—131no—
190C2×SD16—131no—
191C2×SD16C2×D1311yescharacteristic
192C2×M16—131no—
193C2×M16C2×D1311yescharacteristic
194C4⋊Q8—131no—
195C4⋊Q8—131no—
196C4⋊Q8—131no—
197#127—131no—
198#125—261no—
199#124—261no—
200C22⋊Q8—131no—
201C22⋊Q8—261no—
202C22⋊Q8C2×D1311yescharacteristic
203#121—131no—
204#121—261no—
205#121C2×D1311yescharacteristic
206C4×Q8—131no—
207C4×Q8—131no—
208C4×Q8—261no—
209C4×D4—131no—
210C4×D4—131no—
211C4×D4—261no—
212#117—261no—
213C2×C42—131no—
214#107—131no—
215#107—131no—
216#107—131no—
217#107C2×D1311yescharacteristic
218C4⋊C8—131no—
219C4⋊C8—131no—
220C4⋊C8—131no—
221C4⋊C8—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225#103C2×D1311yescharacteristic
226#102—131no—
227#102—131no—
228#102—131no—
229#102C2×D1311yescharacteristic
230C2×C13—41no—
231C2×C13—81no—
232C2×C13#53711yescharacteristic
233C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
234C2×C13C2×#13711yescharacteristic
235D13—81no—
236#41—524no—
237C2×Q8—131no—
238C2×Q8—261no—
239C2×Q8—261no—
240C2×Q8C22×D1311yescharacteristic
241C2×D4—21no—
242C2×D4—131no—
243C2×D4—261no—
244C2×D4—261no—
245C2×D4—261no—
246C2×D4C22×D1311yescharacteristic
247C22×C4—131no—
248C22×C4—131no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4C22×D1311yescharacteristic
252SD16—41no—
253SD16—521no—
254SD16—521no—
255SD16—521no—
256M16—41no—
257M16—521no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8C22×D1311yescharacteristic
261C2×C8C22×D1311yescharacteristic
262C4⋊C4—21no—
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⋊C4—261no—
272C4⋊C4C22×D1311yescharacteristic
273C4⋊C4C22×D1311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C42—131no—
281C42—131no—
282C42—131no—
283C42—131no—
284C42—261no—
285C42—261no—
286C13#325411yescharacteristic, complemented, Sylow
287C23—21no—
288C23—261no—
289C23D4×D1311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—261no—
293Q8—261no—
294Q8—522no—
295Q8—522no—
296D4—21no—
297D4—21no—
298D4—42no—
299D4—261no—
300D4—261no—
301D4—522no—
302D4—522no—
303D4—522no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—131no—
310C2×C4—131no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—262no—
314C2×C4—262no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—522no—
319C2×C4—522no—
320C2×C4D4×D1311yescharacteristic
321C2×C4C23×D1311yescharacteristic
322C8—21no—
323C8—21no—
324C8—261no—
325C8—261no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—521no—
333C22—521no—
334C22—521no—
335C22C2×D4×D1311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—132no—
341C4—132no—
342C4—261no—
343C4—261no—
344C4—521no—
345C4—521no—
346C4—521no—
347C4#8825111yescharacteristic
348C4#8825711yescharacteristic
349C2—41no—
350C2—81no—
351C2—1041no—
352C2#1171930211yescharacteristic
353C2D13×AGL(1,ℤ/8)11yescharacteristic
354C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#468C2
socleC22×C13C22×D4
prime radical#11719301C2
hypercenter#468D13
hypocenterC13#3254
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #11719327C2semidirect
3. C13×#468C2semidirect
4. #11718824C2semidirect
5. #11718823C2semidirect
6. #11718795C2semidirect
7. #11718779C2semidirect
8. #11718710C2semidirect
9. #11718703C2semidirect
10. #11718551C2semidirect
11. #11718536C2semidirect
12. #11718479C2semidirect
13. #11718455C2semidirect
14. #11718423C2semidirect
15. #11718420C2semidirect
158. #468D13semidirect
286. C13#3254semidirect

Maximal subgroups

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

subgroupindex
#117193272
#117193012
C13×#4682
#117188242
#117188232
#117187952
#117187792
#117187102
#117187032
#117185512
#117185362
#117184792
#117184552
#117184232
#117184202
#325413