Finite Group Databasebeta

← #13127126

Subgroups — #13127126

Order 1664.

386 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C22⋊D13C211yesmaximal, characteristic, complemented
2#11719237C211yesmaximal, characteristic
3C13×#419C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic, complemented
5#11718795C211yesmaximal, characteristic, complemented
6#11718789C211yesmaximal, characteristic, complemented
7#11718657C211yesmaximal, characteristic, complemented
8#11718479C211yesmaximal, characteristic, complemented
9#11718475C211yesmaximal, characteristic, complemented
10#11718473C211yesmaximal, characteristic, complemented
11#11718467C211yesmaximal, characteristic, complemented
12#11718463C211yesmaximal, characteristic, complemented
13#11718455C211yesmaximal, characteristic, complemented
14#11718453C211yesmaximal, characteristic, complemented
15#11718449C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C2×Q8×D13C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C13×#117C2211yescharacteristic
20#88200—21no—
21#88200C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23#88198—21no—
24#88198C2211yescharacteristic
25C2×#6106C2211yescharacteristic
26C2×#6106C2211yescharacteristic
27#88184C2211yescharacteristic
28C4×C22⋊D13—21no—
29C4×C22⋊D13C2211yescharacteristic
30#88178—21no—
31#88178C2211yescharacteristic
32C2×#6095C2211yescharacteristic
33C2×#6094C2211yescharacteristic
34#88149C2211yescharacteristic
35#88147C2211yescharacteristic
36#88146C2211yescharacteristic
37#88142C2211yescharacteristic
38#88139—21no—
39#88138—21no—
40#88129—21no—
41#88126—21no—
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88061C2211yescharacteristic
50#88060C2211yescharacteristic
51#88058C2211yescharacteristic
52#88056C2211yescharacteristic
53#88054C2211yescharacteristic
54C8×Dic13C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×Q8×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13C2311yescharacteristic
66C2×C22⋊D13—21no—
67C2×C22⋊D13D411yescharacteristic
68Q8×D13—22no—
69Q8×D13—41no—
70C2×D52—21no—
71C2×D52C2311yescharacteristic
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13C2311yescharacteristic
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26C2311yescharacteristic
78C13×M16—41no—
79C2×C8×C13C2311yescharacteristic
80C2×C8×C13C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C4⋊C4C2311yescharacteristic
83C13×C22⋊C4—21no—
84C42×C13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13D411yescharacteristic
87#6106—22no—
88#6106—41no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94#6103D411yescharacteristic
95C4⋊Dic13—21no—
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101D411yescharacteristic
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109#6095—41no—
110#6094—41no—
111#3329—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C22×D13—21no—
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—42no—
119Q8×C13#4112yes—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—42no—
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2411yescharacteristic
129C22⋊D13—22no—
130C22⋊D13—81no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136C2×Dic13C2×D411yescharacteristic
137D52—21no—
138D52—21no—
139D52—81no—
140C4×D13—21no—
141C4×D13—21no—
142C4×D13—42no—
143C4×D13—42no—
144Dic26—21no—
145Dic26—21no—
146Dic26—42no—
147Dic26—81no—
148C8×C13—21no—
149C8×C13—21no—
150#1055—21no—
151#1055—21no—
152#555—131no—
153D4×Q8—131no—
154#487—131no—
155#485—131no—
156#485—131no—
157#477—131no—
158#468—131no—
159#468—131no—
160#461—131no—
161#448—131no—
162#448—131no—
163C4×SD16—131no—
164#436—131no—
165#419—131no—
166#419D1311yescharacteristic, complemented
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13C22×D411yescharacteristic
171C2×D13—21no—
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—41no—
175C2×D13—41no—
176C2×D13—41no—
177C4×C13—22no—
178C4×C13—21no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13C2×#4111yescharacteristic
183C4×C13H(5,𝔽2)11yescharacteristic
184Dic13—21no—
185Dic13—21no—
186Dic13—41no—
187Dic13—41no—
188Dic13—41no—
189Dic13#13712yes—
190C22×Q8—131no—
191C22×Q8C2×D1311yescharacteristic
192C2×SD16—131no—
193C2×SD16—131no—
194C2×SD16—131no—
195C2×M16—131no—
196C2×M16C2×D1311yescharacteristic
197C4⋊Q8—131no—
198C4⋊Q8—131no—
199C4⋊Q8—261no—
200#124—261no—
201#124—261no—
202C22⋊Q8—131no—
203C22⋊Q8—131no—
204C22⋊Q8—261no—
205C22⋊Q8—261no—
206#121—131no—
207#121—131no—
208#121—261no—
209C4×Q8—131no—
210C4×D4—131no—
211C4×D4—131no—
212C4×D4—261no—
213#117—131no—
214#117—261no—
215#117C2×D1311yescharacteristic
216#107—131no—
217#107—131no—
218#106—131no—
219C4⋊C8—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225#103C2×D1311yescharacteristic
226#103C2×D1311yescharacteristic
227#103C2×D1311yescharacteristic
228#103C2×D1311yescharacteristic
229#102—131no—
230C22⋊C8—131no—
231C22⋊C8—131no—
232C4×C8—131no—
233C2×C13—41no—
234C2×C13#54611yescharacteristic
235C2×C13C2×#13711yescharacteristic
236C2×C13#57711yescharacteristic
237D13—41no—
238D13—81no—
239C2×Q8—21no—
240C2×Q8—22no—
241C2×Q8—41no—
242C2×Q8—131no—
243C2×Q8—261no—
244C2×Q8—261no—
245C2×Q8—262no—
246C2×Q8—521no—
247C2×Q8C22×D1311yescharacteristic
248C2×Q8C22×D1311yescharacteristic
249C2×D4—131no—
250C2×D4—131no—
251C2×D4—261no—
252C2×D4—261no—
253C22×C4—21no—
254C22×C4—131no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4C22×D1311yescharacteristic
258SD16—262no—
259SD16—521no—
260SD16—521no—
261M16—41no—
262M16—521no—
263C2×C8—131no—
264C2×C8—131no—
265C2×C8C22×D1311yescharacteristic
266C2×C8C22×D1311yescharacteristic
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—131no—
280C22⋊C4—131no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C42—21no—
288C42—131no—
289C42—261no—
290C42—261no—
291C13#332911yescharacteristic, complemented, Sylow
292C23—131no—
293C23—261no—
294C23D4×D1311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—261no—
300Q8—261no—
301Q8—522no—
302Q8—1041no—
303Q8#612712yes—
304D4—262no—
305D4—261no—
306D4—261no—
307D4—1041no—
308D4—1041no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—42no—
316C2×C4—131no—
317C2×C4—131no—
318C2×C4—131no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4D4×D1311yescharacteristic
327C2×C4C23×D1311yescharacteristic
328C8—21no—
329C8—21no—
330C8—261no—
331C8—261no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—261no—
336C22—261no—
337C22—261no—
338C22—521no—
339C22—521no—
340C22—521no—
341C22C2×D4×D1311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—132no—
348C4—261no—
349C4—261no—
350C4—521no—
351C4—521no—
352C4—521no—
353C4C2×#612711yescharacteristic
354C4#8825111yescharacteristic
355C2—41no—
356C2—521no—
357C2—1041no—
358C2#1171919511yescharacteristic
359C2D13×#13711yescharacteristic
360C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#419C2
socleC22×C13C22×D4
prime radical#11719237C2
hypercenter#419D13
hypocenterC13#3329
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. Q8×C22⋊D13C2semidirect
3. C13×#419C2semidirect
4. #11718888C2semidirect
5. #11718795C2semidirect
6. #11718789C2semidirect
7. #11718657C2semidirect
8. #11718479C2semidirect
9. #11718475C2semidirect
10. #11718473C2semidirect
11. #11718467C2semidirect
12. #11718463C2semidirect
13. #11718455C2semidirect
14. #11718453C2semidirect
15. #11718449C2semidirect
166. #419D13semidirect
291. C13#3329semidirect

Maximal subgroups

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

subgroupindex
Q8×C22⋊D132
#117192372
C13×#4192
#117188882
#117187952
#117187892
#117186572
#117184792
#117184752
#117184732
#117184672
#117184632
#117184552
#117184532
#117184492
#332913