Finite Group Databasebeta

← #13125123

Subgroups — #13125123

Order 1664.

382 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#11719324C211yesmaximal, characteristic
2#11719221C211yesmaximal, characteristic, complemented
3C13×#482C211yesmaximal, characteristic, complemented
4#11718701C211yesmaximal, characteristic, complemented
5#11718664C211yesmaximal, characteristic, complemented
6#11718550C211yesmaximal, characteristic, complemented
7#11718538C211yesmaximal, characteristic, complemented
8#11718518C211yesmaximal, characteristic, complemented
9#11718513C211yesmaximal, characteristic, complemented
10#11718423C211yesmaximal, characteristic, complemented
11#11718423C211yesmaximal, characteristic, complemented
12#11718419C211yesmaximal, characteristic, complemented
13#11718418C211yesmaximal, characteristic, complemented
14#11718399C211yesmaximal, characteristic, complemented
15#11718381C211yesmaximal, characteristic, complemented
16C22×Dic26C2211yescharacteristic
17C13×#121C2211yescharacteristic
18C13×#117C2211yescharacteristic
19#88194C2211yescharacteristic
20#88193—21no—
21#88192—21no—
22D4×Dic13C2211yescharacteristic
23C2×#6105C2211yescharacteristic
24C2×#6105C2211yescharacteristic
25#88184C2211yescharacteristic
26#88180C2211yescharacteristic
27C2×#6095C2211yescharacteristic
28C2×#6095C2211yescharacteristic
29#88147C2211yescharacteristic
30#88144C2211yescharacteristic
31#88141C2211yescharacteristic
32#88141C2211yescharacteristic
33#88141C2211yescharacteristic
34#88141C2211yescharacteristic
35#88140—21no—
36#88137—21no—
37#88131—21no—
38#88131—21no—
39C4×Dic26—21no—
40C4×Dic26—21no—
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#102C2211yescharacteristic
45C13×C22⋊C8C2211yescharacteristic
46C22⋊#1055C2211yescharacteristic
47#88056C2211yescharacteristic
48#88056C2211yescharacteristic
49#88055C2211yescharacteristic
50#88054C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C2×D52C2311yescharacteristic
68C2×C4×D13—21no—
69C2×Dic26—21no—
70C2×Dic26—22no—
71C2×Dic26—22no—
72C2×Dic26C2311yescharacteristic
73C2×Dic26C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C2×C8×C13C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C42×C13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13D411yescharacteristic
84C22⋊Dic13D411yescharacteristic
85#6105—22no—
86#6105—22no—
87#6103—21no—
88#6103—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13D411yescharacteristic
91C4⋊Dic13D411yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13C2311yescharacteristic
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6095—22no—
107#6095—22no—
108#3126—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111C22×D13—21no—
112D4×C13—21no—
113D4×C13—21no—
114D4×C13—81no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C22⋊D13—81no—
123C22⋊D13—81no—
124C22⋊D13—81no—
125C2×Dic13—24no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—81no—
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134D52—21no—
135D52—21no—
136C4×D13—81no—
137Dic26—24no—
138Dic26—21no—
139Dic26—21no—
140Dic26#4112yes—
141Dic26#4112yes—
142C8×C13—21no—
143C8×C13—21no—
144#1055—21no—
145#1055—21no—
146#540—131no—
147#519—131no—
148#482—131no—
149#482D1311yescharacteristic, complemented
150#479—131no—
151#479—131no—
152#460—131no—
153#460—131no—
154#448—131no—
155#448—131no—
156#440—131no—
157#440—131no—
158C4×SD16—131no—
159C4×SD16—131no—
160#433—131no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13C22×D411yescharacteristic
168C2×D13—41no—
169C2×D13—41no—
170C2×D13—41no—
171C4×C13—21no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13C2×#4111yescharacteristic
176C4×C13C2×#4111yescharacteristic
177Dic13—22no—
178Dic13—22no—
179Dic13—21no—
180Dic13—21no—
181Dic13—21no—
182Dic13—21no—
183Dic13—41no—
184C22×Q8—131no—
185C2×SD16—131no—
186C2×SD16—131no—
187C2×SD16—131no—
188C2×SD16—131no—
189#127—131no—
190#125—131no—
191#123—261no—
192#123—261no—
193#121—131no—
194#121—261no—
195#121—261no—
196#121C2×D1311yescharacteristic
197C4×Q8—131no—
198C4×Q8—131no—
199C4×Q8—131no—
200C4×Q8—131no—
201C4×Q8—261no—
202C4×Q8—261no—
203C4×D4—131no—
204C4×D4—131no—
205#117—131no—
206#117—261no—
207#117—261no—
208#117C2×D1311yescharacteristic
209#107—131no—
210#107C2×D1311yescharacteristic
211#106—131no—
212#106C2×D1311yescharacteristic
213C4⋊C8—131no—
214C4⋊C8—131no—
215#103—131no—
216#103—131no—
217#103—131no—
218#103—131no—
219#102—131no—
220#102—131no—
221#102C2×D1311yescharacteristic
222#102C2×D1311yescharacteristic
223C22⋊C8—131no—
224C22⋊C8C2×D1311yescharacteristic
225#97—131no—
226C4×C8—131no—
227C2×C13—41no—
228C2×C13—81no—
229C2×C13#52511yescharacteristic
230C2×C13#57711yescharacteristic
231C2×C13#57711yescharacteristic
232D13—81no—
233C2×Q8—131no—
234C2×Q8—131no—
235C2×Q8—262no—
236C2×Q8—262no—
237C2×Q8—261no—
238C2×D4—21no—
239C2×D4—131no—
240C2×D4—261no—
241C2×D4—261no—
242C2×D4—261no—
243C2×D4C22×D1311yescharacteristic
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4C22×D1311yescharacteristic
248SD16—262no—
249SD16—262no—
250SD16—262no—
251SD16—262no—
252C2×C8—131no—
253C2×C8—131no—
254C2×C8C22×D1311yescharacteristic
255C2×C8C22×D1311yescharacteristic
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4C22×D1311yescharacteristic
266C4⋊C4C22×D1311yescharacteristic
267C4⋊C4C22×D1311yescharacteristic
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—131no—
271C22⋊C4—131no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C42—21no—
276C42—131no—
277C42—131no—
278C42—261no—
279C42—261no—
280C42—261no—
281C42—261no—
282C13#312611yescharacteristic, complemented, Sylow
283C23—21no—
284C23—261no—
285C23D4×D1311yescharacteristic
286Q8—132no—
287Q8—132no—
288Q8—264no—
289Q8—261no—
290Q8—261no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—261no—
295D4—261no—
296D4—1041no—
297D4—1041no—
298D4—1041no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—131no—
305C2×C4—131no—
306C2×C4—131no—
307C2×C4—131no—
308C2×C4—264no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—1041no—
313C2×C4—1041no—
314C2×C4D4×D1311yescharacteristic
315C2×C4C23×D1311yescharacteristic
316C8—21no—
317C8—21no—
318C8—261no—
319C8—261no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—521no—
327C22—521no—
328C22—521no—
329C22C2×D4×D1311yescharacteristic
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—261no—
335C4—261no—
336C4—261no—
337C4—261no—
338C4—262no—
339C4—262no—
340C4—521no—
341C4#41×D1311yescharacteristic
342C4#41×D1311yescharacteristic
343C2—41no—
344C2—81no—
345C2—1041no—
346C2#1171936111yescharacteristic
347C2#1171947511yescharacteristic
348C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#482C2
socleC22×C13C22×D4
prime radical#11719324C2
hypercenter#482D13
hypocenterC13#3126
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #11719221C2semidirect
3. C13×#482C2semidirect
4. #11718701C2semidirect
5. #11718664C2semidirect
6. #11718550C2semidirect
7. #11718538C2semidirect
8. #11718518C2semidirect
9. #11718513C2semidirect
10. #11718423C2semidirect
11. #11718423C2semidirect
12. #11718419C2semidirect
13. #11718418C2semidirect
14. #11718399C2semidirect
15. #11718381C2semidirect
149. #482D13semidirect
282. C13#3126semidirect

Maximal subgroups

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

subgroupindex
#117193242
#117192212
C13×#4822
#117187012
#117186642
#117185502
#117185382
#117185182
#117185132
#117184232
#117184192
#117184182
#117183992
#117183812
#312613