Finite Group Databasebeta

← #13125100

Subgroups — #13125100

Order 1664.

384 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
1#11719239C211yesmaximal, characteristic, complemented
2#11719228C211yesmaximal, characteristic, complemented
3C13×#433C211yesmaximal, characteristic, complemented
4#11718511C211yesmaximal, characteristic, complemented
5#11718507C211yesmaximal, characteristic, complemented
6#11718506C211yesmaximal, characteristic, complemented
7#11718505C211yesmaximal, characteristic, complemented
8#11718397C211yesmaximal, characteristic, complemented
9#11718395C211yesmaximal, characteristic
10#11718394C211yesmaximal, characteristic, complemented
11#11718383C211yesmaximal, characteristic, complemented
12#11718371C211yesmaximal, characteristic, complemented
13#11718371C211yesmaximal, characteristic, complemented
14C4×Dic52C211yesmaximal, characteristic, complemented
15C4×D104C211yesmaximal, characteristic, complemented
16C2×#6127C2211yescharacteristic
17C13×#117C2211yescharacteristic
18#88184C2211yescharacteristic
19C2×C4⋊Dic13C2211yescharacteristic
20#88178C2211yescharacteristic
21C2×Dic52C2211yescharacteristic
22C2×D104C2211yescharacteristic
23C2×#6095C2211yescharacteristic
24C2×#6095C2211yescharacteristic
25#88152—21no—
26#88150—21no—
27#88146—21no—
28C4⋊C4×D13—21no—
29#88139—21no—
30#88137—21no—
31#88135—21no—
32#88135—21no—
33#88129C2211yescharacteristic
34C4×D52C2211yescharacteristic
35C4×D52C2211yescharacteristic
36C4×D52C2211yescharacteristic
37#88123C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C13×C4⋊C8C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×C22⋊C8C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45C13×#97C2211yescharacteristic
46C4×C8×C13C2211yescharacteristic
47#88061C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88061C2211yescharacteristic
51#88058C2211yescharacteristic
52#88058C2211yescharacteristic
53#88058C2211yescharacteristic
54#88058C2211yescharacteristic
55#88056C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C22×C4×C13C2311yescharacteristic
60C2×C22⋊D13—21no—
61C2×C22⋊D13—21no—
62C22×Dic13—21no—
63#6127—22no—
64#6127—22no—
65C2×D52C2311yescharacteristic
66C2×D52C2311yescharacteristic
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×Dic26—21no—
72C2×Dic26C2311yescharacteristic
73C2×Dic26C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C2×C8×C13C2311yescharacteristic
78C13×C4⋊C4D411yescharacteristic
79C13×C4⋊C4D411yescharacteristic
80C13×C22⋊C4D411yescharacteristic
81C13×C22⋊C4D411yescharacteristic
82C42×C13C2311yescharacteristic
83C42×C13C2311yescharacteristic
84C22⋊Dic13—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104Dic52—22no—
105D104—22no—
106#6095—22no—
107#6095—22no—
108#3124—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111C22×D13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C22⋊D13—24no—
121C22⋊D13—81no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—81no—
129D52—21no—
130D52—21no—
131D52—21no—
132D52#4112yes—
133C4×D13—24no—
134C4×D13—81no—
135C4×D13—81no—
136C4×D13—81no—
137Dic26—21no—
138Dic26—21no—
139Dic26—21no—
140Dic26—81no—
141Dic26#4112yes—
142C8×C13—21no—
143C8×C13—21no—
144C8×C13—21no—
145C8×C13—21no—
146#542—131no—
147#520—131no—
148#484—131no—
149#480—131no—
150#477—131no—
151#474—131no—
152#464—131no—
153#463—131no—
154#452—131no—
155#449—131no—
156#440—131no—
157#440—131no—
158C4×Q16—131no—
159C4×D8—131no—
160#433D1311yescharacteristic, complemented
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13C22×D411yescharacteristic
165C2×D13—22no—
166C2×D13—41no—
167C2×D13—41no—
168C2×D13—41no—
169C2×D13—41no—
170C2×D13—41no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13C2×#4111yescharacteristic
177C4×C13C2×#4111yescharacteristic
178Dic13—22no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184C2×#41—131no—
185C2×Q16—131no—
186C2×SD16—131no—
187C2×SD16—131no—
188C2×D8—131no—
189C4⋊Q8—131no—
190#126—261no—
191#124—131no—
192#124—261no—
193#123—261no—
194C22⋊Q8—131no—
195C22⋊Q8—261no—
196#121—131no—
197C4×Q8—131no—
198C4×Q8—131no—
199C4×Q8—131no—
200C4×D4—131no—
201C4×D4—131no—
202C4×D4—131no—
203C4×D4—261no—
204C4×D4—261no—
205#117—261no—
206#117C2×D1311yescharacteristic
207C2×C4⋊C4—131no—
208C2×C4⋊C4—261no—
209#107—131no—
210#107—131no—
211#107—131no—
212#107—131no—
213C4⋊C8C2×D1311yescharacteristic
214C4⋊C8C2×D1311yescharacteristic
215#103—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#102—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223C22⋊C8C2×D1311yescharacteristic
224C22⋊C8C2×D1311yescharacteristic
225#97C2×D1311yescharacteristic
226C4×C8C2×D1311yescharacteristic
227C2×C13—41no—
228C2×C13#52511yescharacteristic
229C2×C13#57611yescharacteristic
230C2×C13#57811yescharacteristic
231D13—42no—
232D13—81no—
233#41—262no—
234#41—262no—
235C2×Q8—131no—
236C2×Q8—131no—
237C2×Q8—261no—
238C2×D4—131no—
239C2×D4—131no—
240C2×D4—261no—
241C2×D4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4C22×D1311yescharacteristic
248Q16—262no—
249SD16—262no—
250SD16—262no—
251D8—262no—
252C2×C8C22×D1311yescharacteristic
253C2×C8C22×D1311yescharacteristic
254C2×C8C22×D1311yescharacteristic
255C2×C8C22×D1311yescharacteristic
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4D5211yescharacteristic
267C4⋊C4D5211yescharacteristic
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C22⋊C4D5211yescharacteristic
276C22⋊C4D5211yescharacteristic
277C42—261no—
278C42—261no—
279C42—261no—
280C42C22×D1311yescharacteristic
281C42C22×D1311yescharacteristic
282C13#312411yescharacteristic, complemented, Sylow
283C23—261no—
284C23—261no—
285C23C2×D5211yescharacteristic
286Q8—132no—
287Q8—261no—
288Q8—261no—
289Q8—261no—
290Q8—1041no—
291D4—132no—
292D4—264no—
293D4—261no—
294D4—261no—
295D4—261no—
296D4—1041no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—264no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—1041no—
307C2×C4—1041no—
308C2×C4—1041no—
309C2×C4—1041no—
310C2×C4C2×D5211yescharacteristic
311C2×C4C2×D5211yescharacteristic
312C2×C4C2×D5211yescharacteristic
313C2×C4C2×D5211yescharacteristic
314C2×C4C2×D5211yescharacteristic
315C2×C4C23×D1311yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—262no—
324C22—521no—
325C22—521no—
326C22—521no—
327C22—521no—
328C22—521no—
329C22C22×D5211yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—262no—
336C4—521no—
337C4—521no—
338C4—521no—
339C4—521no—
340C4—521no—
341C4#41×D1311yescharacteristic
342C4#41×D1311yescharacteristic
343C2—41no—
344C2—522no—
345C2—1041no—
346C2#1171922911yescharacteristic
347C2#1171945711yescharacteristic
348C2#1171945811yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#433C2
socleC22×C13C22×D4
prime radical#11718395C2
hypercenter#433D13
hypocenterC13#3124
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #11719239C2semidirect
2. #11719228C2semidirect
3. C13×#433C2semidirect
4. #11718511C2semidirect
5. #11718507C2semidirect
6. #11718506C2semidirect
7. #11718505C2semidirect
8. #11718397C2semidirect
10. #11718394C2semidirect
11. #11718383C2semidirect
12. #11718371C2semidirect
13. #11718371C2semidirect
14. C4×Dic52C2semidirect
15. C4×D104C2semidirect
160. #433D13semidirect
282. C13#3124semidirect

Maximal subgroups

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

subgroupindex
#117192392
#117192282
C13×#4332
#117185112
#117185072
#117185062
#117185052
#117183972
#117183952
#117183942
#117183832
#117183712
C4×Dic522
C4×D1042
#312413