Finite Group Databasebeta

← #13126887

Subgroups — #13126887

Order 1664.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Q8×C13C211yesmaximal, characteristic
2#11719246C211yesmaximal, characteristic
3#11718889C211yesmaximal, characteristic, complemented
4#11718889C211yesmaximal, characteristic, complemented
5#11718886C211yesmaximal, characteristic, complemented
6C2×#88075C211yesmaximal, characteristic, complemented
7#11718751C211yesmaximal, characteristic, complemented
8#11718743C211yesmaximal, characteristic, complemented
9#11718713C211yesmaximal, characteristic, complemented
10#11718712C211yesmaximal, characteristic, complemented
11#11718706C211yesmaximal, characteristic, complemented
12#11718704C211yesmaximal, characteristic, complemented
13#11718691C211yesmaximal, characteristic, complemented
14#11718683C211yesmaximal, characteristic, complemented
15#11718672C211yesmaximal, characteristic
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×#6107C2211yescharacteristic
28C2×#6107C2211yescharacteristic
29C2×#6107C2211yescharacteristic
30#88189—21no—
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#88075C2211yescharacteristic
49#88075C2211yescharacteristic
50#88075C2211yescharacteristic
51C22⋊#1055C2211yescharacteristic
52C22⋊#1055C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
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
73C22×Dic13—21no—
74C2×Dic26C2311yescharacteristic
75C13×C4⋊C4—21no—
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⋊C4D411yescharacteristic
85C13×C22⋊C4D411yescharacteristic
86C42×C13—21no—
87C42×C13C2311yescharacteristic
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91#6107—22no—
92#6107—41no—
93#6107—41no—
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#3312—131nomaximal, Sylow
112C23×C13C2×D411yescharacteristic
113C23×C13C2×D411yescharacteristic
114Q8×C13—21no—
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119Q8×C13—42no—
120Q8×C13—42no—
121Q8×C13#4112yes—
122D4×C13—22no—
123C2×C4×C13—21no—
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×C13C2×D411yescharacteristic
134C2×C4×C13C2×D411yescharacteristic
135C2×C4×C13C2×D411yescharacteristic
136C2×C4×C13C2×D411yescharacteristic
137C2×C4×C13C2411yescharacteristic
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—42no—
143Dic26—21no—
144Dic26—21no—
145#1055—21no—
146#1055—21no—
147#1055—21no—
148#1055—21no—
149#552—131no—
150D4×Q8D1311yescharacteristic
151#491—131no—
152#485—131no—
153#483—131no—
154#479—131no—
155#470—131no—
156#467—131no—
157#462—131no—
158#451—131no—
159#451—131no—
160#441—131no—
161#435—131no—
162#419—131no—
163C2×#103—131no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#13712yes—
170C22×C13C22×D411yescharacteristic
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—22no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13C2×#4111yescharacteristic
180C4×C13H(5,𝔽2)11yescharacteristic
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185C22×Q8C2×D1311yescharacteristic
186C22×Q8C2×D1311yescharacteristic
187C2×Q16—131no—
188C2×Q16—131no—
189C2×Q16—131no—
190C2×M16—131no—
191C22×C8—131no—
192C4⋊Q8—21no—
193C4⋊Q8C2×D1311yescharacteristic
194#126—261no—
195#125—131no—
196#125—261no—
197#123—261no—
198C22⋊Q8—21no—
199C22⋊Q8—21no—
200C22⋊Q8—131no—
201C22⋊Q8—131no—
202C22⋊Q8C2×D1311yescharacteristic
203C22⋊Q8C2×D1311yescharacteristic
204C4×Q8—131no—
205C4×Q8C2×D1311yescharacteristic
206C4×D4—21no—
207C4×D4C2×D1311yescharacteristic
208#117—131no—
209#117—261no—
210C2×C4⋊C4—131no—
211#107—131no—
212#106—131no—
213#106—131no—
214C4⋊C8—131no—
215#103—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103—131no—
224#103—131no—
225C22⋊C8—131no—
226C22⋊C8—131no—
227#97—131no—
228C2×C13—22no—
229C2×C13—41no—
230C2×C13#54611yescharacteristic
231C2×C13C2×#13711yescharacteristic
232C2×C13#57811yescharacteristic
233C2×Q8—21no—
234C2×Q8—21no—
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—131no—
240C2×Q8C22×D1311yescharacteristic
241C2×Q8C22×D1311yescharacteristic
242C2×Q8C22×D1311yescharacteristic
243C2×D4C22⋊D1311yescharacteristic
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—261no—
247C22×C4C22×D1311yescharacteristic
248C22×C4C22×D1311yescharacteristic
249Q16—262no—
250Q16—521no—
251Q16—521no—
252M16—521no—
253C2×C8—131no—
254C2×C8—131no—
255C2×C8—131no—
256C2×C8—131no—
257C2×C8—521no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—131no—
264C4⋊C4—131no—
265C4⋊C4—131no—
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⋊C4C22⋊D1311yescharacteristic
280C22⋊C4C22⋊D1311yescharacteristic
281C42—21no—
282C42—261no—
283C42—261no—
284C42C22×D1311yescharacteristic
285C13#331211yescharacteristic, complemented, Sylow
286C23C2×C22⋊D1311yescharacteristic
287C23C2×C22⋊D1311yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—42no—
295Q8—261no—
296Q8—261no—
297Q8#612912yes—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—522no—
314C2×C4C2×C22⋊D1311yescharacteristic
315C2×C4C2×C22⋊D1311yescharacteristic
316C2×C4C2×C22⋊D1311yescharacteristic
317C2×C4C2×C22⋊D1311yescharacteristic
318C2×C4C23×D1311yescharacteristic
319C8—261no—
320C8—261no—
321C8—261no—
322C8—261no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#8819612yes—
329C22C22×C22⋊D1311yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—521no—
339C4—521no—
340C4—521no—
341C4—521no—
342C4C2×#612911yescharacteristic
343C4#8825111yescharacteristic
344C2—22no—
345C2—41no—
346C2#1171951111yescharacteristic
347C2C2×#8819611yescharacteristic
348C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingD4×Q8×C13C2
socleC22×C13C22×D4
prime radicalC2×D4×C13D4
hypercenterD4×Q8D13
hypocenterC13#3312
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
3. #11718889C2semidirect
4. #11718889C2semidirect
5. #11718886C2semidirect
6. C2×#88075C2semidirect
7. #11718751C2semidirect
8. #11718743C2semidirect
9. #11718713C2semidirect
10. #11718712C2semidirect
11. #11718706C2semidirect
12. #11718704C2semidirect
13. #11718691C2semidirect
14. #11718683C2semidirect
285. C13#3312semidirect

Maximal subgroups

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

subgroupindex
D4×Q8×C132
#117192462
#117188892
#117188862
C2×#880752
#117187512
#117187432
#117187132
#117187122
#117187062
#117187042
#117186912
#117186832
#117186722
#331213