Finite Group Databasebeta

← #13127007

Subgroups — #13127007

Order 1664.

388 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
1D4×Q8×C13C211yesmaximal, characteristic, complemented
2#11719270C211yesmaximal, characteristic
3#11718888C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic, complemented
5#11718886C211yesmaximal, characteristic, complemented
6C2×#88075C211yesmaximal, characteristic, complemented
7#11718744C211yesmaximal, characteristic, complemented
8#11718743C211yesmaximal, characteristic, complemented
9#11718710C211yesmaximal, characteristic, complemented
10#11718709C211yesmaximal, characteristic, complemented
11#11718706C211yesmaximal, characteristic, complemented
12#11718705C211yesmaximal, characteristic, complemented
13#11718687C211yesmaximal, characteristic, complemented
14#11718683C211yesmaximal, characteristic, complemented
15#11718672C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C22×Q8×C13C2211yescharacteristic
18C13×C4⋊Q8—21no—
19C13×C4⋊Q8C2211yescharacteristic
20C13×C22⋊Q8—21no—
21C13×C22⋊Q8—21no—
22C13×C22⋊Q8C2211yescharacteristic
23C13×C22⋊Q8C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×D4×C13—21no—
26C4×D4×C13C2211yescharacteristic
27C2×#6106C2211yescharacteristic
28C2×#6106C2211yescharacteristic
29C2×#6106C2211yescharacteristic
30#88193—21no—
31#88184C2211yescharacteristic
32#88184C2211yescharacteristic
33#88180C2211yescharacteristic
34C2×C4⋊Dic13C2211yescharacteristic
35C2×#6099C2211yescharacteristic
36C22×#1055C2211yescharacteristic
37#88152—21no—
38#88137—21no—
39#88135—21no—
40C4×D52C2211yescharacteristic
41#88124C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88075C2211yescharacteristic
49#88075C2211yescharacteristic
50#88075C2211yescharacteristic
51C22⋊#1055C2211yescharacteristic
52C22⋊#1055C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—21no—
61C2×Q8×C13—22no—
62C2×Q8×C13—22no—
63C2×Q8×C13—41no—
64C2×Q8×C13—41no—
65C2×Q8×C13C2311yescharacteristic
66C2×Q8×C13C2311yescharacteristic
67C2×Q8×C13C2311yescharacteristic
68C2×D4×C13D411yescharacteristic
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13C2311yescharacteristic
72C22×C4×C13C2311yescharacteristic
73C2×C22⋊D13—21no—
74C2×C22⋊D13—21no—
75C22×Dic13—21no—
76C2×D52C2311yescharacteristic
77C2×C4×D13—21no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4D411yescharacteristic
84C13×C4⋊C4C2311yescharacteristic
85C13×C22⋊C4—21no—
86C13×C22⋊C4—21no—
87C13×C22⋊C4D411yescharacteristic
88C13×C22⋊C4D411yescharacteristic
89C42×C13—21no—
90C42×C13C2311yescharacteristic
91C22⋊Dic13—21no—
92#6106—22no—
93#6106—41no—
94#6106—41no—
95#6103—21no—
96#6103—21no—
97#6103—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13C2311yescharacteristic
100C4⋊Dic13C2311yescharacteristic
101C4⋊Dic13C2311yescharacteristic
102#6101—21no—
103#6101—21no—
104C4×Dic13—21no—
105#6099—41no—
106C2×#1055—41no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111#3320—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C23×C13C2×D411yescharacteristic
114C22×D13—21no—
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119Q8×C13—21no—
120Q8×C13—42no—
121Q8×C13—42no—
122Q8×C13#4112yes—
123D4×C13—22no—
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—21no—
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
139C22⋊D13—42no—
140C22⋊D13—81no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—81no—
145D52—21no—
146D52—21no—
147C4×D13—81no—
148#1055—21no—
149#1055—21no—
150#1055—21no—
151#1055—21no—
152#553—131no—
153D4×Q8D1311yescharacteristic, complemented
154#491—131no—
155#485—131no—
156#484—131no—
157#479—131no—
158#468—131no—
159#465—131no—
160#461—131no—
161#448—131no—
162#448—131no—
163#440—131no—
164#435—131no—
165#419—131no—
166C2×#103—131no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13#13712yes—
173C22×C13C22×D411yescharacteristic
174C2×D13—41no—
175C2×D13—41no—
176C2×D13—41no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—22no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13C2×#4111yescharacteristic
186C4×C13H(5,𝔽2)11yescharacteristic
187Dic13—41no—
188Dic13—41no—
189Dic13—41no—
190C22×Q8C2×D1311yescharacteristic
191C22×Q8C2×D1311yescharacteristic
192C2×SD16—131no—
193C2×SD16—131no—
194C2×SD16—131no—
195C2×M16—131no—
196C22×C8—131no—
197C4⋊Q8—21no—
198C4⋊Q8C2×D1311yescharacteristic
199#126—261no—
200#125—131no—
201#123—261no—
202C22⋊Q8—21no—
203C22⋊Q8—21no—
204C22⋊Q8C2×D1311yescharacteristic
205C22⋊Q8C2×D1311yescharacteristic
206#121—131no—
207#121—131no—
208#121—261no—
209C4×Q8C2×D1311yescharacteristic
210C4×D4—21no—
211C4×D4—131no—
212C4×D4—261no—
213C4×D4C2×D1311yescharacteristic
214#117—131no—
215C2×C4⋊C4—131no—
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#103—131no—
226#103—131no—
227#103—131no—
228#103—131no—
229#102—131no—
230C22⋊C8—131no—
231C22⋊C8—131no—
232#97—131no—
233C2×C13—22no—
234C2×C13—41no—
235C2×C13#54611yescharacteristic
236C2×C13C2×#13711yescharacteristic
237C2×C13#57711yescharacteristic
238D13—81no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8C22×D1311yescharacteristic
246C2×Q8C22×D1311yescharacteristic
247C2×Q8C22×D1311yescharacteristic
248C2×D4—131no—
249C2×D4—261no—
250C2×D4—261no—
251C2×D4C22⋊D1311yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4C22×D1311yescharacteristic
257C22×C4C22×D1311yescharacteristic
258SD16—262no—
259SD16—521no—
260SD16—521no—
261M16—521no—
262C2×C8—131no—
263C2×C8—131no—
264C2×C8—131no—
265C2×C8—131no—
266C2×C8—521no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—131no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4C22⋊D1311yescharacteristic
279C4⋊C4C22×D1311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4C22⋊D1311yescharacteristic
287C22⋊C4C22⋊D1311yescharacteristic
288C42—21no—
289C42—261no—
290C42C22×D1311yescharacteristic
291C13#332011yescharacteristic, complemented, Sylow
292C23—261no—
293C23C2×C22⋊D1311yescharacteristic
294C23C2×C22⋊D1311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—42no—
302Q8#612912yes—
303D4—22no—
304D4—261no—
305D4—261no—
306D4—522no—
307D4—1041no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—1041no—
322C2×C4—1041no—
323C2×C4C2×C22⋊D1311yescharacteristic
324C2×C4C2×C22⋊D1311yescharacteristic
325C2×C4C2×C22⋊D1311yescharacteristic
326C2×C4C2×C22⋊D1311yescharacteristic
327C2×C4C23×D1311yescharacteristic
328C8—261no—
329C8—261no—
330C8—261no—
331C8—261no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—521no—
338C22—521no—
339C22—521no—
340C22#8819612yes—
341C22C22×C22⋊D1311yescharacteristic
342C4—21no—
343C4—21no—
344C4—22no—
345C4—21no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—521no—
351C4—521no—
352C4—521no—
353C4C2×#612911yescharacteristic
354C4#8825111yescharacteristic
355C2—22no—
356C2—41no—
357C2—1041no—
358C2#1171951111yescharacteristic
359C2C2×#8819611yescharacteristic
360C2#1171954211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingD4×Q8×C13C2
socleC22×C13C22×D4
prime radical#11719270C2
hypercenterD4×Q8D13
hypocenterC13#3320
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. D4×Q8×C13C2semidirect
3. #11718888C2semidirect
4. #11718888C2semidirect
5. #11718886C2semidirect
6. C2×#88075C2semidirect
7. #11718744C2semidirect
8. #11718743C2semidirect
9. #11718710C2semidirect
10. #11718709C2semidirect
11. #11718706C2semidirect
12. #11718705C2semidirect
13. #11718687C2semidirect
14. #11718683C2semidirect
15. #11718672C2semidirect
153. D4×Q8D13semidirect
291. C13#3320semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×C132
#117192702
#117188882
#117188862
C2×#880752
#117187442
#117187432
#117187102
#117187092
#117187062
#117187052
#117186872
#117186832
#117186722
#332013