Finite Group Databasebeta

← #13125063

Subgroups — #13125063

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#11719277C211yesmaximal, characteristic, complemented
2#11719266C211yesmaximal, characteristic
3C13×#440C211yesmaximal, characteristic, complemented
4#11718831C211yesmaximal, characteristic
5#11718827C211yesmaximal, characteristic, complemented
6C4×#6107C211yesmaximal, characteristic, complemented
7C4×#6105C211yesmaximal, characteristic, complemented
8#11718549C211yesmaximal, characteristic, complemented
9#11718536C211yesmaximal, characteristic, complemented
10#11718469C211yesmaximal, characteristic, complemented
11#11718452C211yesmaximal, characteristic, complemented
12#11718440C211yesmaximal, characteristic
13#11718428C211yesmaximal, characteristic, complemented
14#11718377C211yesmaximal, characteristic, complemented
15#11718370C211yesmaximal, characteristic, complemented
16C2×Q8×D13C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21C2×#6107C2211yescharacteristic
22#88192C2211yescharacteristic
23#88190C2211yescharacteristic
24C2×#6105C2211yescharacteristic
25#88183—21no—
26#88178—21no—
27C2×Dic52C2211yescharacteristic
28#88151C2211yescharacteristic
29#88146—21no—
30#88146C2211yescharacteristic
31#88142C2211yescharacteristic
32#88141—21no—
33#88141C2211yescharacteristic
34#88139—21no—
35#88133—21no—
36#88126—21no—
37#88126C2211yescharacteristic
38C4×Dic26—21no—
39C4×Dic26C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#97C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88060C2211yescharacteristic
48#88060C2211yescharacteristic
49#88057C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88054C2211yescharacteristic
53#88054C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C2×C22⋊D13—21no—
63Q8×D13—22no—
64Q8×D13—22no—
65C2×C4×D13—21no—
66C2×C4×D13C2311yescharacteristic
67C2×Dic26—21no—
68C2×Dic26—21no—
69C2×Dic26C2311yescharacteristic
70C2×Dic26C2311yescharacteristic
71C13×SD16—22no—
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C42×C13—21no—
79C42×C13C2311yescharacteristic
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83#6107—22no—
84#6105—22no—
85#6103—21no—
86#6103—21no—
87#6103D411yescharacteristic
88#6103D411yescharacteristic
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98#6101D411yescharacteristic
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107Dic52—22no—
108#3121—131nomaximal, Sylow
109C23×C13—21no—
110C22×D13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13#4112yes—
113D4×C13—21no—
114D4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—81no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2411yescharacteristic
122C22⋊D13—81no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C4×D13—24no—
131C4×D13—21no—
132C4×D13—21no—
133Dic26—24no—
134Dic26—21no—
135Dic26—21no—
136Dic26—21no—
137Dic26—81no—
138Dic26#4112yes—
139C8×C13—21no—
140C8×C13—21no—
141#1055—21no—
142#1055—21no—
143#542—131no—
144#519—131no—
145#485—131no—
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#440D1311yescharacteristic, complemented
155C4×Q16—131no—
156C4×SD16—131no—
157#433—131no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13C22×D411yescharacteristic
162C2×D13—21no—
163C2×D13—21no—
164C2×D13—21no—
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13C2×#4111yescharacteristic
171C4×C13C2×#4111yescharacteristic
172Dic13—21no—
173Dic13—22no—
174Dic13—21no—
175Dic13—21no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C22×Q8—131no—
180C2×Q16—131no—
181C2×Q16—131no—
182C2×SD16—131no—
183C2×SD16C2×D1311yescharacteristic
184C4⋊Q8—131no—
185#126—261no—
186#124—131no—
187#124—261no—
188#123—261no—
189C22⋊Q8—131no—
190C22⋊Q8—261no—
191#121—131no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×Q8—261no—
197C4×Q8—261no—
198C4×Q8C2×D1311yescharacteristic
199C4×D4C2×D1311yescharacteristic
200#117—131no—
201#117—131no—
202#117—261no—
203#117—261no—
204#107—131no—
205#107C2×D1311yescharacteristic
206#106—131no—
207#106—131no—
208C4⋊C8—131no—
209C4⋊C8—131no—
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#103—131no—
215#103C2×D1311yescharacteristic
216#102—131no—
217#102C2×D1311yescharacteristic
218C22⋊C8—131no—
219C22⋊C8—131no—
220#97C2×D1311yescharacteristic
221C4×C8—131no—
222C2×C13—81no—
223C2×C13#52511yescharacteristic
224C2×C13#57711yescharacteristic
225C2×C13#57811yescharacteristic
226D13—41no—
227C2×Q8—131no—
228C2×Q8—131no—
229C2×Q8—261no—
230C2×Q8—261no—
231C2×Q8—262no—
232C2×Q8—262no—
233C2×Q8C22×D1311yescharacteristic
234C2×D4—261no—
235C2×D4C22×D1311yescharacteristic
236C22×C4—21no—
237C22×C4—131no—
238C22×C4—261no—
239Q16—262no—
240Q16—262no—
241SD16—22no—
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—131no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—131no—
262C22⋊C4—131no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C42—21no—
269C42—131no—
270C42—261no—
271C42—261no—
272C42—261no—
273C42—261no—
274C42—261no—
275C42C22×D1311yescharacteristic
276C13#312111yescharacteristic, complemented, Sylow
277C23—21no—
278C23—131no—
279Q8—21no—
280Q8—132no—
281Q8—264no—
282Q8—261no—
283Q8—261no—
284Q8—261no—
285Q8—1041no—
286Q8#612712yes—
287D4—21no—
288D4—21no—
289D4—1041no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—131no—
297C2×C4—264no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4D4×D1311yescharacteristic
305C2×C4D4×D1311yescharacteristic
306C2×C4C23×D1311yescharacteristic
307C8—21no—
308C8—21no—
309C8—261no—
310C8—261no—
311C22—41no—
312C22—41no—
313C22—41no—
314C22—261no—
315C22—261no—
316C22—261no—
317C22C2×D4×D1311yescharacteristic
318C4—21no—
319C4—21no—
320C4—22no—
321C4—41no—
322C4—41no—
323C4—261no—
324C4—261no—
325C4—261no—
326C4—262no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4C2×#612711yescharacteristic
331C4#41×D1311yescharacteristic
332C2—81no—
333C2—521no—
334C2#1171925211yescharacteristic
335C2#1171948011yescharacteristic
336C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#440C2
socleC22×C13C22×D4
prime radical#88192C22
hypercenter#440D13
hypocenterC13#3121
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #11719277C2semidirect
3. C13×#440C2semidirect
5. #11718827C2semidirect
6. C4×#6107C2semidirect
7. C4×#6105C2semidirect
8. #11718549C2semidirect
9. #11718536C2semidirect
10. #11718469C2semidirect
11. #11718452C2semidirect
13. #11718428C2semidirect
14. #11718377C2semidirect
15. #11718370C2semidirect
154. #440D13semidirect
276. C13#3121semidirect

Maximal subgroups

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

subgroupindex
#117192772
#117192662
C13×#4402
#117188312
#117188272
C4×#61072
C4×#61052
#117185492
#117185362
#117184692
#117184522
#117184402
#117184282
#117183772
#117183702
#312113