Finite Group Databasebeta

← #13126933

Subgroups — #13126933

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#11719529C211yesmaximal, characteristic
2#11719218C211yesmaximal, characteristic, complemented
3C13×#417C211yesmaximal, characteristic, complemented
4#11718900C211yesmaximal, characteristic, complemented
5#11718798C211yesmaximal, characteristic, complemented
6#11718788C211yesmaximal, characteristic, complemented
7#11718631C211yesmaximal, characteristic, complemented
8#11718476C211yesmaximal, characteristic, complemented
9#11718474C211yesmaximal, characteristic, complemented
10#11718458C211yesmaximal, characteristic, complemented
11#11718454C211yesmaximal, characteristic, complemented
12#11718444C211yesmaximal, characteristic, complemented
13#11718433C211yesmaximal, characteristic, complemented
14#11718424C211yesmaximal, characteristic, complemented
15#11718418C211yesmaximal, characteristic, complemented
16C2×C13×#41C2211yescharacteristic
17C2×#6129C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C2×C13×C4⋊C4C2211yescharacteristic
20#88200C2211yescharacteristic
21#88198C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23#88193—21no—
24#88189—21no—
25D4×Dic13C2211yescharacteristic
26C2×#6105C2211yescharacteristic
27#88183—21no—
28#88183—21no—
29C4×C22⋊D13C2211yescharacteristic
30#88180—21no—
31#88178C2211yescharacteristic
32#88178C2211yescharacteristic
33C2×#6101—21no—
34C2×Dic52C2211yescharacteristic
35C2×C8×D13C2211yescharacteristic
36#88152—21no—
37#88151C2211yescharacteristic
38#88146C2211yescharacteristic
39#88144C2211yescharacteristic
40#88143—21no—
41#88141C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×#102C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48C22⋊#1055C2211yescharacteristic
49#88060C2211yescharacteristic
50#88057C2211yescharacteristic
51#88056C2211yescharacteristic
52#88056C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88050C2211yescharacteristic
56#88050C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C13×#41—22no—
60C13×#41—41no—
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13—21no—
63C2×D4×C13C2311yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68C2×C22⋊D13D411yescharacteristic
69C22×Dic13—21no—
70C22×Dic13—21no—
71#6129—22no—
72#6129—41no—
73C2×C4×D13C2311yescharacteristic
74C2×Dic26C2311yescharacteristic
75C2×Dic26C2311yescharacteristic
76C13×M16—41no—
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4—21no—
80C13×C4⋊C4C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13D411yescharacteristic
86#6107—41no—
87#6105—22no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103D411yescharacteristic
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
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
109Dic52—41no—
110C8×D13—41no—
111#3315—131nomaximal, Sylow
112C23×C13—21no—
113C23×C13C2×D411yescharacteristic
114C22×D13C2×D411yescharacteristic
115Q8×C13—21no—
116Q8×C13—21no—
117D4×C13—21no—
118D4×C13—42no—
119D4×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—42no—
126C2×C4×C13—42no—
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2411yescharacteristic
129C22⋊D13—41no—
130C22⋊D13—42no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140C4×D13—21no—
141C4×D13—21no—
142Dic26—21no—
143Dic26—21no—
144Dic26—21no—
145Dic26—21no—
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#462—131no—
159#452—131no—
160#452—131no—
161#440—131no—
162#435—131no—
163#417D1311yescharacteristic, complemented
164#416—131no—
165C22×C13—22no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13C22×D411yescharacteristic
172C2×D13—21no—
173C2×D13—21no—
174C2×D13—21no—
175C4×C13—21no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13C2×#4111yescharacteristic
180C4×C13H(5,𝔽2)11yescharacteristic
181Dic13—21no—
182Dic13—21no—
183Dic13—21no—
184Dic13—41no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188C2×#41—131no—
189C2×#41C2×D1311yescharacteristic
190C2×Q16—131no—
191C2×Q16—131no—
192C2×SD16—131no—
193C2×M16C2×D1311yescharacteristic
194C22×C8—131no—
195C4⋊Q8—131no—
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×Q8—131no—
208C4×D4—131no—
209C4×D4—131no—
210#117—131no—
211#117—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4C2×D1311yescharacteristic
214#107—131no—
215#107—131no—
216#106—131no—
217C4⋊C8—131no—
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#102C2×D1311yescharacteristic
227#102C2×D1311yescharacteristic
228C22⋊C8—131no—
229C22⋊C8—131no—
230#97—131no—
231C2×C13—41no—
232C2×C13—42no—
233C2×C13#54611yescharacteristic
234C2×C13#57511yescharacteristic
235C2×C13#57811yescharacteristic
236D13—41no—
237#41—22no—
238#41—41no—
239#41—262no—
240#41—521no—
241C2×Q8—131no—
242C2×Q8—131no—
243C2×Q8C22×D1311yescharacteristic
244C2×D4—21no—
245C2×D4—131no—
246C2×D4—261no—
247C2×D4C22×D1311yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—131no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4C22×D1311yescharacteristic
254Q16—521no—
255Q16—521no—
256SD16—262no—
257M16—41no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—521no—
261C2×C8C22×D1311yescharacteristic
262C2×C8C22×D1311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—131no—
265C4⋊C4—131no—
266C4⋊C4—131no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
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—131no—
287C42—261no—
288C42—261no—
289C13#331511yescharacteristic, complemented, Sylow
290C23—21no—
291C23—131no—
292C23D4×D1311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—261no—
296Q8—261no—
297Q8—261no—
298Q8—261no—
299D4—21no—
300D4—42no—
301D4—521no—
302D4—522no—
303D4#612712yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—131no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—522no—
321C2×C4—522no—
322C2×C4D4×D1311yescharacteristic
323C2×C4C23×D1311yescharacteristic
324C8—21no—
325C8—21no—
326C8—261no—
327C8—261no—
328C22—21no—
329C22—22no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—261no—
335C22—261no—
336C22—261no—
337C22C2×D4×D1311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—261no—
343C4—261no—
344C4—261no—
345C4—521no—
346C4—521no—
347C4—521no—
348C4—521no—
349C4C2×#612711yescharacteristic
350C4#8825111yescharacteristic
351C2—41no—
352C2—42no—
353C2—521no—
354C2#1171919511yescharacteristic
355C2#1171947811yescharacteristic
356C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#417C2
socleC22×C13C22×D4
prime radical#11719529C2
hypercenter#417D13
hypocenterC13#3315
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. #11719218C2semidirect
3. C13×#417C2semidirect
4. #11718900C2semidirect
5. #11718798C2semidirect
6. #11718788C2semidirect
7. #11718631C2semidirect
8. #11718476C2semidirect
9. #11718474C2semidirect
10. #11718458C2semidirect
11. #11718454C2semidirect
12. #11718444C2semidirect
13. #11718433C2semidirect
14. #11718424C2semidirect
15. #11718418C2semidirect
163. #417D13semidirect
289. C13#3315semidirect

Maximal subgroups

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

subgroupindex
#117195292
#117192182
C13×#4172
#117189002
#117187982
#117187882
#117186312
#117184762
#117184742
#117184582
#117184542
#117184442
#117184332
#117184242
#117184182
#331513