Finite Group Databasebeta

← #13125068

Subgroups — #13125068

Order 1664.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719348C211yesmaximal, characteristic
2#11719221C211yesmaximal, characteristic, complemented
3C13×#485C211yesmaximal, characteristic, complemented
4#11718711C211yesmaximal, characteristic, complemented
5#11718664C211yesmaximal, characteristic
6#11718550C211yesmaximal, characteristic, complemented
7#11718536C211yesmaximal, characteristic, complemented
8#11718515C211yesmaximal, characteristic, complemented
9#11718513C211yesmaximal, characteristic, complemented
10#11718459C211yesmaximal, characteristic, complemented
11#11718459C211yesmaximal, characteristic, complemented
12#11718451C211yesmaximal, characteristic, complemented
13#11718450C211yesmaximal, characteristic, complemented
14#11718399C211yesmaximal, characteristic
15#11718381C211yesmaximal, characteristic, complemented
16C22×Dic26C2211yescharacteristic
17C13×C22⋊Q8C2211yescharacteristic
18C13×#117C2211yescharacteristic
19#88201C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21C2×#6107C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23#88184C2211yescharacteristic
24#88180C2211yescharacteristic
25C2×#6095C2211yescharacteristic
26C2×#6095C2211yescharacteristic
27#88152—21no—
28#88151—21no—
29#88147C2211yescharacteristic
30#88142C2211yescharacteristic
31#88141C2211yescharacteristic
32#88141C2211yescharacteristic
33#88141C2211yescharacteristic
34#88141C2211yescharacteristic
35#88139—21no—
36#88137—21no—
37#88131—21no—
38#88131—21no—
39C4×Dic26—21no—
40C4×Dic26—21no—
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
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×Q8×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C2×C22⋊D13—21no—
62C22×Dic13—21no—
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×Dic26—21no—
66C2×Dic26—22no—
67C2×Dic26—22no—
68C2×Dic26—21no—
69C2×Dic26C2311yescharacteristic
70C2×Dic26C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C42×C13—21no—
80C22⋊Dic13D411yescharacteristic
81C22⋊Dic13D411yescharacteristic
82#6107—22no—
83#6107—22no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13D411yescharacteristic
90C4⋊Dic13D411yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97C4×Dic13—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#3121—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111Q8×C13—21no—
112Q8×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—81no—
122C2×Dic13—24no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130D52—21no—
131D52—21no—
132C4×D13—81no—
133Dic26—24no—
134Dic26—21no—
135Dic26—21no—
136Dic26—81no—
137Dic26#4112yes—
138Dic26#4112yes—
139C8×C13—21no—
140C8×C13—21no—
141#1055—21no—
142#1055—21no—
143#542—131no—
144#519—131no—
145#485D1311yescharacteristic, complemented
146#482—131no—
147#477—131no—
148#475—131no—
149#464—131no—
150#464—131no—
151#451—131no—
152#448—131no—
153#441—131no—
154#440—131no—
155C4×Q16—131no—
156C4×SD16—131no—
157#433—131no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13C22×D411yescharacteristic
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—41no—
165C4×C13—21no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13C2×#4111yescharacteristic
171C4×C13C2×#4111yescharacteristic
172Dic13—22no—
173Dic13—22no—
174Dic13—21no—
175Dic13—21no—
176Dic13—21no—
177Dic13—21no—
178Dic13—41no—
179C22×Q8—131no—
180C2×Q16—131no—
181C2×Q16—131no—
182C2×SD16—131no—
183C2×SD16—131no—
184C4⋊Q8—131no—
185#126—261no—
186#124—131no—
187#124—261no—
188#123—261no—
189C22⋊Q8—261no—
190C22⋊Q8C2×D1311yescharacteristic
191#121—131no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×Q8—131no—
197C4×Q8—261no—
198C4×Q8—261no—
199C4×D4—131no—
200#117—131no—
201#117—261no—
202#117—261no—
203#117C2×D1311yescharacteristic
204#107—131no—
205#107C2×D1311yescharacteristic
206#106—131no—
207#106C2×D1311yescharacteristic
208C4⋊C8—131no—
209C4⋊C8—131no—
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#103C2×D1311yescharacteristic
215#103C2×D1311yescharacteristic
216#102—131no—
217#102—131no—
218C22⋊C8—131no—
219C22⋊C8C2×D1311yescharacteristic
220#97—131no—
221C4×C8—131no—
222C2×C13—41no—
223C2×C13#52511yescharacteristic
224C2×C13#57711yescharacteristic
225C2×C13#57811yescharacteristic
226D13—81no—
227C2×Q8—131no—
228C2×Q8—131no—
229C2×Q8—261no—
230C2×Q8—262no—
231C2×Q8—262no—
232C2×Q8—261no—
233C2×Q8C22×D1311yescharacteristic
234C2×D4—131no—
235C2×D4—261no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4C22×D1311yescharacteristic
239Q16—262no—
240Q16—262no—
241SD16—262no—
242SD16—262no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4C22×D1311yescharacteristic
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—131no—
263C22⋊C4—131no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C42—21no—
269C42—131no—
270C42—131no—
271C42—261no—
272C42—261no—
273C42—261no—
274C42—261no—
275C42—261no—
276C13#312111yescharacteristic, complemented, Sylow
277C23—261no—
278C23D4×D1311yescharacteristic
279Q8—21no—
280Q8—21no—
281Q8—132no—
282Q8—132no—
283Q8—264no—
284Q8—261no—
285Q8—261no—
286Q8—1041no—
287D4—261no—
288D4—261no—
289D4—1041no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—131no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—264no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—1041no—
305C2×C4D4×D1311yescharacteristic
306C2×C4C23×D1311yescharacteristic
307C8—21no—
308C8—21no—
309C8—261no—
310C8—261no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—521no—
315C22—521no—
316C22—521no—
317C22C2×D4×D1311yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—261no—
324C4—261no—
325C4—261no—
326C4—261no—
327C4—262no—
328C4—262no—
329C4—521no—
330C4#41×D1311yescharacteristic
331C4#41×D1311yescharacteristic
332C2—41no—
333C2—1041no—
334C2#1171936111yescharacteristic
335C2#1171947511yescharacteristic
336C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#485C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#485D13
hypocenterC13#3121
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #11719221C2semidirect
3. C13×#485C2semidirect
4. #11718711C2semidirect
6. #11718550C2semidirect
7. #11718536C2semidirect
8. #11718515C2semidirect
9. #11718513C2semidirect
10. #11718459C2semidirect
11. #11718459C2semidirect
12. #11718451C2semidirect
13. #11718450C2semidirect
15. #11718381C2semidirect
145. #485D13semidirect
276. C13#3121semidirect

Maximal subgroups

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

subgroupindex
#117193482
#117192212
C13×#4852
#117187112
#117186642
#117185502
#117185362
#117185152
#117185132
#117184592
#117184512
#117184502
#117183992
#117183812
#312113