Finite Group Databasebeta

← #13126931

Subgroups — #13126931

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
1#11719431C211yesmaximal, characteristic
2#11719399C211yesmaximal, characteristic, complemented
3C13×#491C211yesmaximal, characteristic, complemented
4#11718751C211yesmaximal, characteristic, complemented
5#11718727C211yesmaximal, characteristic, complemented
6#11718477C211yesmaximal, characteristic, complemented
7#11718475C211yesmaximal, characteristic, complemented
8#11718474C211yesmaximal, characteristic, complemented
9#11718471C211yesmaximal, characteristic, complemented
10#11718471C211yesmaximal, characteristic, complemented
11#11718470C211yesmaximal, characteristic, complemented
12#11718465C211yesmaximal, characteristic, complemented
13#11718464C211yesmaximal, characteristic, complemented
14#11718371C211yesmaximal, characteristic, complemented
15#11718367C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×#6131C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C13×#125C2211yescharacteristic
20#88200C2211yescharacteristic
21#88200C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23C2×#6107C2211yescharacteristic
24C2×#6095C2211yescharacteristic
25C2×#6094C2211yescharacteristic
26C2×C8×D13C2211yescharacteristic
27#88152—21no—
28#88151C2211yescharacteristic
29#88151C2211yescharacteristic
30#88149—21no—
31#88148—21no—
32#88148—21no—
33#88148—21no—
34#88146—21no—
35#88146C2211yescharacteristic
36C4⋊C4×D13—21no—
37C4⋊C4×D13C2211yescharacteristic
38#88144—21no—
39C4×D52C2211yescharacteristic
40C4×D52C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46C13×#97C2211yescharacteristic
47#88075C2211yescharacteristic
48#88075C2211yescharacteristic
49#88061C2211yescharacteristic
50#88060C2211yescharacteristic
51#88060C2211yescharacteristic
52#88058C2211yescharacteristic
53#88056C2211yescharacteristic
54#88049C2211yescharacteristic
55#88049C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61#6131—22no—
62#6131—22no—
63#6131—41no—
64#6131—41no—
65C2×D52—21no—
66C2×D52—21no—
67C2×D52D411yescharacteristic
68C2×D52C2311yescharacteristic
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13C2311yescharacteristic
74C2×C4×D13C2311yescharacteristic
75C2×Dic26C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C13×C4⋊C4—21no—
79C13×C4⋊C4—21no—
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4C2311yescharacteristic
83C13×C4⋊C4C2311yescharacteristic
84C42×C13C2311yescharacteristic
85#6107—41no—
86#6107—41no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103D411yescharacteristic
94#6103D411yescharacteristic
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13D411yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#6095—22no—
109#6094—41no—
110C8×D13—41no—
111#3315—131nomaximal, Sylow
112C22×D13—21no—
113C22×D13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2411yescharacteristic
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131D52—21no—
132D52—41no—
133D52—42no—
134D52—42no—
135D52#4112yes—
136C4×D13—21no—
137C4×D13—21no—
138C4×D13—21no—
139C4×D13—21no—
140C4×D13—42no—
141C4×D13—42no—
142C4×D13—42no—
143C4×D13—42no—
144Dic26—21no—
145Dic26—21no—
146C8×C13—21no—
147C8×C13—21no—
148#1055—21no—
149#1055—21no—
150#552—131no—
151#547—131no—
152#491D1311yescharacteristic, complemented
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×C13C22×D411yescharacteristic
166C2×D13—21no—
167C2×D13—21no—
168C2×D13—22no—
169C2×D13—21no—
170C2×D13—21no—
171C2×D13—21no—
172C2×D13—21no—
173C2×D13—41no—
174C2×D13—41no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13C2×#4111yescharacteristic
182C4×C13H(5,𝔽2)11yescharacteristic
183Dic13—21no—
184Dic13—21no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188C2×#41—131no—
189C2×#41—131no—
190C2×Q16—131no—
191C2×Q16—131no—
192C2×SD16—131no—
193C2×M16—131no—
194C22×C8—131no—
195C4⋊Q8C2×D1311yescharacteristic
196#126—261no—
197#125—261no—
198#125C2×D1311yescharacteristic
199#123—261no—
200#123—261no—
201#123—261no—
202C22⋊Q8—131no—
203C22⋊Q8—131no—
204C22⋊Q8—131no—
205C22⋊Q8—131no—
206#121—261no—
207C4×Q8—131no—
208C4×D4—131no—
209C4×D4—131no—
210#117—131no—
211#117—261no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—261no—
214#107—131no—
215#107—131no—
216#106—131no—
217C4⋊C8—131no—
218#103—131no—
219#103—131no—
220#103—131no—
221#103C2×D1311yescharacteristic
222#103C2×D1311yescharacteristic
223#103C2×D1311yescharacteristic
224#103C2×D1311yescharacteristic
225#102—131no—
226#102—131no—
227#102—131no—
228C22⋊C8—131no—
229C22⋊C8—131no—
230#97C2×D1311yescharacteristic
231C2×C13#54611yescharacteristic
232C2×C13#57511yescharacteristic
233C2×C13#57811yescharacteristic
234D13—41no—
235D13—41no—
236D13—42no—
237#41—262no—
238#41—262no—
239#41—521no—
240#41—521no—
241C2×Q8—131no—
242C2×Q8C22×D1311yescharacteristic
243C2×Q8C22×D1311yescharacteristic
244C2×D4—131no—
245C2×D4—131no—
246C2×D4—261no—
247C2×D4—261no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254Q16—521no—
255Q16—521no—
256SD16—262no—
257M16—521no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—521no—
261C2×C8C22×D1311yescharacteristic
262C2×C8C22×D1311yescharacteristic
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—131no—
279C22⋊C4—131no—
280C22⋊C4—261no—
281C22⋊C4—261no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C42—261no—
287C42—261no—
288C42C22×D1311yescharacteristic
289C13#331511yescharacteristic, complemented, Sylow
290C23—131no—
291C23—131no—
292C23—261no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—261no—
298Q8—261no—
299D4—132no—
300D4—261no—
301D4—521no—
302D4—522no—
303D4—522no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—131no—
309C2×C4—131no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—522no—
318C2×C4—522no—
319C2×C4—522no—
320C2×C4—522no—
321C2×C4D4×D1311yescharacteristic
322C2×C4D4×D1311yescharacteristic
323C2×C4C23×D1311yescharacteristic
324C8—21no—
325C8—21no—
326C8—261no—
327C8—261no—
328C22—261no—
329C22—261no—
330C22—261no—
331C22—261no—
332C22—261no—
333C22—261no—
334C22—262no—
335C22—521no—
336C22—521no—
337C22C2×D4×D1311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—261no—
345C4—261no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4#41×D1311yescharacteristic
350C4#8825611yescharacteristic
351C2—521no—
352C2—521no—
353C2—522no—
354C2#1171938111yescharacteristic
355C2#1171948211yescharacteristic
356C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#491C2
socleC22×C13C22×D4
prime radical#11719431C2
hypercenter#491D13
hypocenterC13#3315
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #11719399C2semidirect
3. C13×#491C2semidirect
4. #11718751C2semidirect
5. #11718727C2semidirect
6. #11718477C2semidirect
7. #11718475C2semidirect
8. #11718474C2semidirect
9. #11718471C2semidirect
10. #11718471C2semidirect
11. #11718470C2semidirect
12. #11718465C2semidirect
13. #11718464C2semidirect
14. #11718371C2semidirect
15. #11718367C2semidirect
152. #491D13semidirect
289. C13#3315semidirect

Maximal subgroups

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

subgroupindex
#117194312
#117193992
C13×#4912
#117187512
#117187272
#117184772
#117184752
#117184742
#117184712
#117184702
#117184652
#117184642
#117183712
#117183672
#331513