Finite Group Databasebeta

← #13125915

Subgroups — #13125915

Order 1664.

364 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719521C211yesmaximal, characteristic
2#11719330C211yesmaximal, characteristic, complemented
3C13×#451C211yesmaximal, characteristic, complemented
4#11718889C211yesmaximal, characteristic, complemented
5#11718851C211yesmaximal, characteristic, complemented
6#11718846C211yesmaximal, characteristic, complemented
7#11718843C211yesmaximal, characteristic, complemented
8#11718842C211yesmaximal, characteristic, complemented
9#11718708C211yesmaximal, characteristic
10#11718461C211yesmaximal, characteristic, complemented
11#11718459C211yesmaximal, characteristic, complemented
12#11718458C211yesmaximal, characteristic, complemented
13#11718454C211yesmaximal, characteristic, complemented
14#11718394C211yesmaximal, characteristic
15#11718381C211yesmaximal, characteristic, complemented
16C22×Q8×C13C2211yescharacteristic
17C2×#6127C2211yescharacteristic
18C2×C13×Q16C2211yescharacteristic
19C2×C13×Q16C2211yescharacteristic
20C13×C22⋊Q8C2211yescharacteristic
21#88201C2211yescharacteristic
22#88201C2211yescharacteristic
23#88200—21no—
24#88200—21no—
25Q8×Dic13C2211yescharacteristic
26#88198C2211yescharacteristic
27#88198C2211yescharacteristic
28#88198C2211yescharacteristic
29C2×#6107C2211yescharacteristic
30C2×#6107C2211yescharacteristic
31C2×#6107C2211yescharacteristic
32C2×#6106C2211yescharacteristic
33#88183—21no—
34#88183—21no—
35#88180C2211yescharacteristic
36#88178C2211yescharacteristic
37C2×Dic52C2211yescharacteristic
38C2×#6095C2211yescharacteristic
39#88144—21no—
40#88144C2211yescharacteristic
41#88143—21no—
42#88141C2211yescharacteristic
43#88133—21no—
44#88133—21no—
45C13×#103C2211yescharacteristic
46C13×#103C2211yescharacteristic
47C13×C22⋊C8C2211yescharacteristic
48#88075C2211yescharacteristic
49#88075C2211yescharacteristic
50C22⋊#1055C2211yescharacteristic
51#88061C2211yescharacteristic
52#88056C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56C8×Dic13C2211yescharacteristic
57#88050C2211yescharacteristic
58#88049C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13C2311yescharacteristic
63C2×Q8×C13C2311yescharacteristic
64C2×Q8×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13C2311yescharacteristic
67C2×C22⋊D13—21no—
68#6127—41no—
69#6127—41no—
70C2×D52C2311yescharacteristic
71C2×C4×D13—21no—
72C2×Dic26C2311yescharacteristic
73C2×Dic26C2311yescharacteristic
74C13×Q16—41no—
75C13×Q16—41no—
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C13×C4⋊C4—21no—
79C13×C4⋊C4C2311yescharacteristic
80C13×C22⋊C4—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13D411yescharacteristic
83C22⋊Dic13D411yescharacteristic
84#6107—41no—
85#6107—41no—
86#6107—41no—
87#6106—41no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13D411yescharacteristic
95C4⋊Dic13D411yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105#6101—21no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13C2311yescharacteristic
109C4×Dic13C2311yescharacteristic
110C2×#1055C2311yescharacteristic
111C2×#1055C2311yescharacteristic
112Dic52—41no—
113#6095—41no—
114#3223—131nomaximal, Sylow
115C23×C13C2×D411yescharacteristic
116C22×D13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119Q8×C13—21no—
120Q8×C13—21no—
121Q8×C13—21no—
122Q8×C13—21no—
123Q8×C13—42no—
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—42no—
131C2×C4×C13C2×D411yescharacteristic
132C2×C4×C13C2411yescharacteristic
133C22⋊D13—42no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13C2×D411yescharacteristic
138C2×Dic13C2×D411yescharacteristic
139C2×Dic13C2×D411yescharacteristic
140C2×Dic13C2×D411yescharacteristic
141D52—21no—
142D52—21no—
143C4×D13—42no—
144Dic26—21no—
145Dic26—21no—
146Dic26—21no—
147Dic26—21no—
148C8×C13—21no—
149C8×C13—21no—
150#1055—21no—
151#1055—21no—
152#541—131no—
153#536—131no—
154#497—131no—
155#494—131no—
156#491—131no—
157#488—131no—
158#464—131no—
159#464—131no—
160#462—131no—
161#462—131no—
162#452—131no—
163#452—131no—
164#451—131no—
165#451D1311yescharacteristic, complemented
166#433—131no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13C22×D411yescharacteristic
171C2×D13—41no—
172C2×D13—41no—
173C2×D13—41no—
174C4×C13—21no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13H(5,𝔽2)11yescharacteristic
180C4×C13H(5,𝔽2)11yescharacteristic
181Dic13—21no—
182Dic13—21no—
183Dic13—21no—
184Dic13—21no—
185Dic13—41no—
186Dic13—41no—
187Dic13—41no—
188C2×#41—131no—
189C22×Q8C2×D1311yescharacteristic
190C2×Q16—131no—
191C2×Q16—131no—
192C2×Q16—131no—
193C2×Q16—131no—
194C2×Q16C2×D1311yescharacteristic
195C2×Q16C2×D1311yescharacteristic
196C2×SD16—131no—
197C2×SD16—131no—
198C4⋊Q8—131no—
199C4⋊Q8—131no—
200C4⋊Q8—131no—
201#126—261no—
202#126—261no—
203#125—131no—
204#125—261no—
205#125—261no—
206#124—131no—
207#124—131no—
208#123—261no—
209#123—261no—
210C22⋊Q8—131no—
211C22⋊Q8—261no—
212C22⋊Q8—261no—
213C22⋊Q8C2×D1311yescharacteristic
214C4×Q8—131no—
215C4×Q8—131no—
216#117—131no—
217C4⋊C8—131no—
218C4⋊C8—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—
227C22⋊C8—131no—
228C22⋊C8C2×D1311yescharacteristic
229#97—131no—
230C4×C8—131no—
231C2×C13—41no—
232C2×C13#53511yescharacteristic
233C2×C13#57811yescharacteristic
234C2×C13#57811yescharacteristic
235D13—81no—
236#41—521no—
237#41—521no—
238C2×Q8—21no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—131no—
242C2×Q8—131no—
243C2×Q8C22×D1311yescharacteristic
244C2×Q8C22×D1311yescharacteristic
245C2×Q8C22×D1311yescharacteristic
246C2×D4—131no—
247C2×D4—261no—
248C22×C4—21no—
249C22×C4—261no—
250C22×C4C22×D1311yescharacteristic
251Q16—41no—
252Q16—41no—
253Q16—521no—
254Q16—521no—
255Q16—521no—
256Q16—521no—
257SD16—521no—
258SD16—521no—
259C2×C8—131no—
260C2×C8—131no—
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⋊C4—261no—
277C4⋊C4—261no—
278C4⋊C4C22×D1311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—131no—
281C22⋊C4—131no—
282C22⋊C4—261no—
283C22⋊C4—261no—
284C22⋊C4—261no—
285C22⋊C4—261no—
286C22⋊C4—261no—
287C42—131no—
288C42—131no—
289C42—261no—
290C42—261no—
291C13#322311yescharacteristic, complemented, Sylow
292C23—261no—
293C23D4×D1311yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—261no—
302Q8—261no—
303Q8—261no—
304Q8—261no—
305D4—261no—
306D4—261no—
307D4—522no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—131no—
316C2×C4—131no—
317C2×C4—131no—
318C2×C4—131no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—522no—
323C2×C4D4×D1311yescharacteristic
324C2×C4C23×D1311yescharacteristic
325C8—21no—
326C8—21no—
327C8—261no—
328C8—261no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—521no—
333C22—521no—
334C22—521no—
335C22C2×D4×D1311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—261no—
342C4—261no—
343C4—261no—
344C4—261no—
345C4—521no—
346C4—521no—
347C4—521no—
348C4#8825111yescharacteristic
349C4#8825111yescharacteristic
350C2—41no—
351C2—1041no—
352C2#1171929711yescharacteristic
353C2#1171947111yescharacteristic
354C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#451C2
socleC22×C13C22×D4
prime radicalC2×#6127C22
hypercenter#451D13
hypocenterC13#3223
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #11719330C2semidirect
3. C13×#451C2semidirect
4. #11718889C2semidirect
5. #11718851C2semidirect
6. #11718846C2semidirect
7. #11718843C2semidirect
8. #11718842C2semidirect
10. #11718461C2semidirect
11. #11718459C2semidirect
12. #11718458C2semidirect
13. #11718454C2semidirect
15. #11718381C2semidirect
165. #451D13semidirect
291. C13#3223semidirect

Maximal subgroups

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

subgroupindex
#117195212
#117193302
C13×#4512
#117188892
#117188512
#117188462
#117188432
#117188422
#117187082
#117184612
#117184592
#117184582
#117184542
#117183942
#117183812
#322313