Finite Group Databasebeta

← #13126939

Subgroups — #13126939

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#11719286C211yesmaximal, characteristic, complemented
3C13×#462C211yesmaximal, characteristic, complemented
4#11718850C211yesmaximal, characteristic, complemented
5#11718849C211yesmaximal, characteristic, complemented
6#11718848C211yesmaximal, characteristic, complemented
7#11718848C211yesmaximal, characteristic, complemented
8#11718743C211yesmaximal, characteristic, complemented
9#11718687C211yesmaximal, characteristic, complemented
10#11718508C211yesmaximal, characteristic, complemented
11#11718497C211yesmaximal, characteristic, complemented
12#11718476C211yesmaximal, characteristic, complemented
13#11718470C211yesmaximal, characteristic, complemented
14#11718465C211yesmaximal, characteristic, complemented
15#11718464C211yesmaximal, characteristic, complemented
16C2×#6131C2211yescharacteristic
17C2×#6131C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic
19C2×C13×Q16C2211yescharacteristic
20C13×C4⋊Q8C2211yescharacteristic
21C4×Q8×C13C2211yescharacteristic
22#88200C2211yescharacteristic
23#88200C2211yescharacteristic
24#88200C2211yescharacteristic
25#88200C2211yescharacteristic
26C2×#6106C2211yescharacteristic
27C2×#6094C2211yescharacteristic
28C2×C8×D13C2211yescharacteristic
29#88149—21no—
30#88148—21no—
31#88148—21no—
32#88148—21no—
33#88146C2211yescharacteristic
34C4⋊C4×D13—21no—
35C4⋊C4×D13C2211yescharacteristic
36#88143—21no—
37#88130—21no—
38C4×D52C2211yescharacteristic
39C4×D52C2211yescharacteristic
40#88126—21no—
41#88124C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88075C2211yescharacteristic
49#88075C2211yescharacteristic
50#88061C2211yescharacteristic
51#88061C2211yescharacteristic
52#88060C2211yescharacteristic
53#88060C2211yescharacteristic
54#88058C2211yescharacteristic
55#88057C2211yescharacteristic
56#88049C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62#6131—22no—
63#6131—22no—
64#6131—41no—
65#6131—41no—
66C2×D52—21no—
67C2×D52—21no—
68C2×D52D411yescharacteristic
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13C2311yescharacteristic
75C2×C4×D13C2311yescharacteristic
76C13×Q16—41no—
77C13×Q16—41no—
78C2×C8×C13C2311yescharacteristic
79C2×C8×C13C2311yescharacteristic
80C13×C4⋊C4—21no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4C2311yescharacteristic
84C42×C13—21no—
85C42×C13C2311yescharacteristic
86#6106—22no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93#6103D411yescharacteristic
94#6103D411yescharacteristic
95C4⋊Dic13D411yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101—21no—
106C4×Dic13—21no—
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
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—
119Q8×C13—21no—
120Q8×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2411yescharacteristic
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133D52—21no—
134D52—41no—
135D52—42no—
136D52—42no—
137D52#4112yes—
138C4×D13—21no—
139C4×D13—21no—
140C4×D13—21no—
141C4×D13—21no—
142C4×D13—42no—
143C4×D13—42no—
144C4×D13—42no—
145C4×D13—42no—
146C8×C13—21no—
147C8×C13—21no—
148#1055—21no—
149#1055—21no—
150#552—131no—
151#547—131no—
152#491—131no—
153#485—131no—
154#484—131no—
155#478—131no—
156#470—131no—
157#467—131no—
158#462D1311yescharacteristic, complemented
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×Q16C2×D1311yescharacteristic
191C2×Q16C2×D1311yescharacteristic
192C2×SD16—131no—
193C2×M16—131no—
194C22×C8—131no—
195C4⋊Q8C2×D1311yescharacteristic
196#126—261no—
197#125—131no—
198#125—261no—
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×Q8C2×D1311yescharacteristic
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⋊C8C2×D1311yescharacteristic
218#103—131no—
219#103—131no—
220#103—131no—
221#103—131no—
222#103—131no—
223#103C2×D1311yescharacteristic
224#103C2×D1311yescharacteristic
225#102—131no—
226#102—131no—
227#102—131no—
228C22⋊C8—131no—
229C22⋊C8—131no—
230#97—131no—
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×Q8C22×D1311yescharacteristic
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—41no—
255Q16—41no—
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—131no—
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⋊C4—261no—
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—21no—
287C42—261no—
288C42C22×D1311yescharacteristic
289C13#331511yescharacteristic, complemented, Sylow
290C23—131no—
291C23—131no—
292C23—261no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
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#8825111yescharacteristic
350C4#41×D1311yescharacteristic
351C2—521no—
352C2—521no—
353C2—522no—
354C2#1171931711yescharacteristic
355C2#1171947111yescharacteristic
356C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#462C2
socleC22×C13C22×D4
prime radical#11719431C2
hypercenter#462D13
hypocenterC13#3315
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #11719286C2semidirect
3. C13×#462C2semidirect
4. #11718850C2semidirect
5. #11718849C2semidirect
6. #11718848C2semidirect
7. #11718848C2semidirect
8. #11718743C2semidirect
9. #11718687C2semidirect
10. #11718508C2semidirect
11. #11718497C2semidirect
12. #11718476C2semidirect
13. #11718470C2semidirect
14. #11718465C2semidirect
15. #11718464C2semidirect
158. #462D13semidirect
289. C13#3315semidirect

Maximal subgroups

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

subgroupindex
#117194312
#117192862
C13×#4622
#117188502
#117188492
#117188482
#117187432
#117186872
#117185082
#117184972
#117184762
#117184702
#117184652
#117184642
#331513