Finite Group Databasebeta

← #13125117

Subgroups — #13125117

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#11719266C211yesmaximal, characteristic, complemented
2#11719251C211yesmaximal, characteristic, complemented
3C13×#442C211yesmaximal, characteristic, complemented
4#11718819C211yesmaximal, characteristic
5#11718814C211yesmaximal, characteristic, complemented
6C4×#6105C211yesmaximal, characteristic, complemented
7C4×#6105C211yesmaximal, characteristic, complemented
8#11718523C211yesmaximal, characteristic, complemented
9#11718515C211yesmaximal, characteristic, complemented
10#11718444C211yesmaximal, characteristic, complemented
11#11718438C211yesmaximal, characteristic, complemented
12#11718428C211yesmaximal, characteristic, complemented
13#11718422C211yesmaximal, characteristic, complemented
14#11718377C211yesmaximal, characteristic, complemented
15#11718370C211yesmaximal, characteristic, complemented
16C2×#6129C2211yescharacteristic
17C2×C13×D8C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20#88192C2211yescharacteristic
21#88190C2211yescharacteristic
22D4×Dic13C2211yescharacteristic
23C2×#6105C2211yescharacteristic
24C2×#6105C2211yescharacteristic
25#88183—21no—
26C4×C22⋊D13—21no—
27#88178—21no—
28C2×#6101—21no—
29C2×Dic52C2211yescharacteristic
30#88151C2211yescharacteristic
31C4⋊C4×D13C2211yescharacteristic
32#88142C2211yescharacteristic
33#88141C2211yescharacteristic
34#88139—21no—
35#88135—21no—
36#88133—21no—
37#88131—21no—
38#88126C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C4×Dic26C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#97C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88060C2211yescharacteristic
48#88060C2211yescharacteristic
49#88057C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88054C2211yescharacteristic
53#88054C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×D4×C13C2311yescharacteristic
60C2×D4×C13C2311yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C2×C22⋊D13—21no—
64C2×C22⋊D13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67#6129—22no—
68#6129—22no—
69C2×C4×D13—21no—
70C2×C4×D13C2311yescharacteristic
71C2×Dic26—21no—
72C2×Dic26C2311yescharacteristic
73C2×Dic26C2311yescharacteristic
74C13×D8—22no—
75C2×C8×C13C2311yescharacteristic
76C2×C8×C13C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C42×C13C2311yescharacteristic
82C22⋊Dic13—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86#6105—22no—
87#6105—22no—
88#6103—21no—
89#6103D411yescharacteristic
90#6103D411yescharacteristic
91C4⋊Dic13—21no—
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101D411yescharacteristic
100#6101D411yescharacteristic
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107Dic52—22no—
108#3125—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13—21no—
111C22×D13C2×D411yescharacteristic
112D4×C13—21no—
113D4×C13—21no—
114D4×C13—21no—
115D4×C13#4112yes—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C22⋊D13—24no—
124C22⋊D13—81no—
125C2×Dic13—24no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—81no—
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134C4×D13—21no—
135C4×D13—21no—
136C4×D13—81no—
137Dic26—21no—
138Dic26—21no—
139Dic26—21no—
140Dic26—81no—
141Dic26#4112yes—
142C8×C13—21no—
143C8×C13—21no—
144#1055—21no—
145#1055—21no—
146#542—131no—
147#520—131no—
148#483—131no—
149#481—131no—
150#476—131no—
151#475—131no—
152#464—131no—
153#463—131no—
154#452—131no—
155#449—131no—
156#442D1311yescharacteristic, complemented
157#441—131no—
158C4×SD16—131no—
159C4×SD16—131no—
160#433—131no—
161C22×C13—22no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13C22×D411yescharacteristic
168C2×D13—21no—
169C2×D13—21no—
170C2×D13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13C2×#4111yescharacteristic
176C4×C13C2×#4111yescharacteristic
177Dic13—22no—
178Dic13—21no—
179Dic13—21no—
180Dic13—21no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184C2×#41—131no—
185C2×Q16—131no—
186C2×SD16—131no—
187C2×SD16—131no—
188C2×D8C2×D1311yescharacteristic
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—261no—
202C4×D4—261no—
203C4×D4C2×D1311yescharacteristic
204C4×D4C2×D1311yescharacteristic
205#117—131no—
206#117—261no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—261no—
209#106—131no—
210#106—131no—
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⋊C8—131no—
225#97C2×D1311yescharacteristic
226C4×C8—131no—
227C2×C13—42no—
228C2×C13—81no—
229C2×C13#52511yescharacteristic
230C2×C13#57711yescharacteristic
231C2×C13#57711yescharacteristic
232D13—41no—
233#41—262no—
234#41—262no—
235C2×Q8—131no—
236C2×Q8—131no—
237C2×Q8—261no—
238C2×D4—261no—
239C2×D4—261no—
240C2×D4C22×D1311yescharacteristic
241C2×D4C22×D1311yescharacteristic
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—131no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248Q16—262no—
249SD16—262no—
250SD16—262no—
251D8—22no—
252C2×C8—131no—
253C2×C8—131no—
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⋊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—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C42—131no—
278C42—261no—
279C42—261no—
280C42—261no—
281C42C22×D1311yescharacteristic
282C13#312511yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—131no—
286Q8—132no—
287Q8—261no—
288Q8—261no—
289Q8—261no—
290Q8—1041no—
291D4—21no—
292D4—21no—
293D4—21no—
294D4—264no—
295D4—1041no—
296D4#612712yes—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—264no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—1041no—
312C2×C4—1041no—
313C2×C4D4×D1311yescharacteristic
314C2×C4D4×D1311yescharacteristic
315C2×C4C23×D1311yescharacteristic
316C8—21no—
317C8—21no—
318C8—261no—
319C8—261no—
320C22—22no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—261no—
327C22—261no—
328C22—261no—
329C22C2×D4×D1311yescharacteristic
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—261no—
335C4—261no—
336C4—261no—
337C4—262no—
338C4—521no—
339C4—521no—
340C4—521no—
341C4C2×#612711yescharacteristic
342C4#41×D1311yescharacteristic
343C2—42no—
344C2—81no—
345C2—521no—
346C2#1171925211yescharacteristic
347C2#1171948011yescharacteristic
348C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#442C2
socleC22×C13C22×D4
prime radical#11718819C2
hypercenter#442D13
hypocenterC13#3125
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #11719266C2semidirect
2. #11719251C2semidirect
3. C13×#442C2semidirect
5. #11718814C2semidirect
6. C4×#6105C2semidirect
7. C4×#6105C2semidirect
8. #11718523C2semidirect
9. #11718515C2semidirect
10. #11718444C2semidirect
11. #11718438C2semidirect
12. #11718428C2semidirect
13. #11718422C2semidirect
14. #11718377C2semidirect
15. #11718370C2semidirect
156. #442D13semidirect
282. C13#3125semidirect

Maximal subgroups

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

subgroupindex
#117192662
#117192512
C13×#4422
#117188192
#117188142
C4×#61052
#117185232
#117185152
#117184442
#117184382
#117184282
#117184222
#117183772
#117183702
#312513