Finite Group Databasebeta

← #15779513

Subgroups — #15779513

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic13C211yesmaximal, characteristic
2C2×#11718096C211yesmaximal, characteristic, complemented
3C2×#11718154C211yesmaximal, characteristic
4#13115570C211yesmaximal, characteristic, complemented
5#13112927C211yesmaximal, characteristic, complemented
6#13112913C211yesmaximal, characteristic, complemented
7C2×C13×#357C211yesmaximal, characteristic
8C22×C13×D8C2211yescharacteristic
9C2×D4×Dic13—21no—
10C22×C13×C16C2211yescharacteristic
11C2×C13×#107C2211yescharacteristic
12C2×#88072—21no—
13D8×Dic13—22no—
14D8×Dic13—22no—
15C2×#88058C2211yescharacteristic
16C2×#88058C2211yescharacteristic
17C2×C8×Dic13C2211yescharacteristic
18C22×#6090C2211yescharacteristic
19#11718646—21no—
20C13×#357C414yescomplemented
21#11718154—22no—
22#11718121—21no—
23#11718096—22no—
24C22×D4×C13—21no—
25C23×Dic13—41no—
26C2×C13×D8—21no—
27C2×C13×D8—21no—
28C2×C13×D8—21no—
29C2×C13×D8C2×C412yes—
30C2×C13×D8D412yes—
31C2×C13×D8Q812yes—
32C22×C8×C13C2311yescharacteristic
33C2×C13×C4⋊C4—21no—
34C2×C22⋊Dic13—41no—
35D4×Dic13—24no—
36D4×Dic13—42no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—41no—
40C2×C4×Dic13D411yescharacteristic
41C22×#1055D411yescharacteristic
42C2×C13×C16—21no—
43C2×C13×C16—21no—
44C2×C13×C16C2×C412yescomplemented
45C13×#107—21no—
46C13×#107C2×C412yescomplemented
47#88072—24no—
48#88071—41no—
49#88058—21no—
50#88058—21no—
51#88058—21no—
52#88058D412yes—
53C8×Dic13—21no—
54C8×Dic13—21no—
55C2×#6090—21no—
56C2×#6090—21no—
57C2×#6090—21no—
58#12935—131nomaximal, Sylow
59C24×C13—41no—
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C22×C4×C13—41no—
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—44no—
69C22×Dic13—41no—
70C22×Dic13—41no—
71C22×Dic13—82no—
72C22×Dic13—82no—
73C22×Dic13D811yescharacteristic
74C22×Dic13D811yescharacteristic
75C13×D8—22no—
76C13×D8—22no—
77C13×D8—22no—
78C13×D8C4⋊C414yescomplemented
79C2×C8×C13C22×C411yescharacteristic
80C2×C8×C13C2×D411yescharacteristic
81C2×C8×C13C2×D411yescharacteristic
82C2×C8×C13C2×Q811yescharacteristic
83C2×C8×C13#4111yescharacteristic
84C2×C8×C13#4111yescharacteristic
85C13×C4⋊C4—22no—
86C13×C4⋊C4—41no—
87C22⋊Dic13—44no—
88C4⋊Dic13—22no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—82no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C2×#1055—21no—
96C2×#1055—21no—
97C2×#1055—21no—
98C13×C16—22no—
99#6090—41no—
100C2×C4×D8—131no—
101C2×#366—131no—
102C2×#357—131no—
103C2×#357D1311yescharacteristic
104#1942—131no—
105#1380—131no—
106#1374—131no—
107C23×C13—42no—
108C23×C13—42no—
109C23×C13—42no—
110C23×C13—81no—
111C23×C13—81no—
112C23×C13—81no—
113C23×C13—81no—
114C23×C13C2×D811yescharacteristic
115D4×C13—24no—
116D4×C13—42no—
117D4×C13—42no—
118D4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—81no—
121C2×C4×C13—81no—
122C2×C4×C13C4×D411yescharacteristic
123C2×C4×C13#12011yescharacteristic
124C2×C4×C13C22⋊Q811yescharacteristic
125C2×C4×C13#13511yescharacteristic
126C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C13#13711yescharacteristic
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—42no—
134C2×Dic13—88no—
135C2×Dic13—81no—
136C2×Dic13—81no—
137C2×Dic13—81no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140C2×Dic13D1612yes—
141C8×C13C2×C4⋊C411yescharacteristic
142C8×C13C4×D411yescharacteristic
143C8×C13C22⋊Q811yescharacteristic
144C8×C13#12311yescharacteristic
145#1055—41no—
146C22×D8C2×D1311yescharacteristic
147C2×C4×D4—261no—
148C22×C16—131no—
149C22×C16C2×D1311yescharacteristic
150C4×D8—262no—
151C4×D8—262no—
152C2×#107—131no—
153C2×#107—131no—
154C2×#107C2×D1311yescharacteristic
155C2×#102—261no—
156C2×C4×C8—131no—
157#389—261no—
158#366—262no—
159#357—262no—
160#357Dic1314yescomplemented
161#340—261no—
162C22×C13—44no—
163C22×C13—82no—
164C22×C13—82no—
165C22×C13—82no—
166C22×C13—82no—
167C22×C13—82no—
168C22×C13—82no—
169C22×C13C4×D811yescharacteristic
170C22×C13#44711yescharacteristic
171C22×C13#47411yescharacteristic
172C22×C13C2×D1611yescharacteristic
173C22×C13#50811yescharacteristic
174C22×C13#50911yescharacteristic
175C22×C13#51011yescharacteristic
176C4×C13—82no—
177C4×C13#38511yescharacteristic
178C4×C13#44011yescharacteristic
179C4×C13#45211yescharacteristic
180C4×C13#47811yescharacteristic
181Dic13—22no—
182Dic13—41no—
183Dic13—82no—
184Dic13—161no—
185C22×D4—21no—
186C23×C4—521no—
187C2×D8—21no—
188C2×D8—21no—
189C2×D8—21no—
190C2×D8Dic2612yes—
191C2×D8D5212yes—
192C2×D8C2×Dic1312yes—
193C22×C8—131no—
194C22×C8C22×D1311yescharacteristic
195C4×D4—264no—
196C4×D4—522no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—521no—
201C2×C22⋊C4—521no—
202C2×C42—131no—
203C2×C16—21no—
204C2×C16—21no—
205C2×C16—261no—
206C2×C16—261no—
207C2×C16—261no—
208C2×C16C2×Dic1312yescomplemented
209#107—21no—
210#107—132no—
211#107—261no—
212#107—261no—
213#107—261no—
214#107C2×Dic1312yescomplemented
215#102—264no—
216C4×C8—261no—
217C4×C8—261no—
218#95—521no—
219C2×C13—84no—
220C2×C13#186211yescharacteristic
221C2×C13C4×D1611yescharacteristic
222C2×C13#217511yescharacteristic
223C2×C13#218411yescharacteristic
224C2×C13#218911yescharacteristic
225C2×C13#222411yescharacteristic
226C2×C13#222811yescharacteristic
227C24—41no—
228C2×D4—22no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C22×C4—41no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—524no—
238C22×C4—521no—
239C22×C4—521no—
240C22×C4—1042no—
241C22×C4—1042no—
242C22×C4D4×D1311yescharacteristic
243D8—22no—
244D8—22no—
245D8—22no—
246D8C4⋊Dic1314yescomplemented
247C2×C8—261no—
248C2×C8—261no—
249C2×C8—261no—
250C2×C8C2×Dic2611yescharacteristic
251C2×C8C2×D5211yescharacteristic
252C2×C8D4×D1311yescharacteristic
253C2×C8#612911yescharacteristic
254C2×C8#612911yescharacteristic
255C2×C8C22×Dic1311yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—262no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—1042no—
263C22⋊C4—524no—
264C42—261no—
265C42—261no—
266C16—22no—
267C16—521no—
268C13#1293511yescharacteristic, complemented, Sylow
269C23—42no—
270C23—42no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23D8×D1311yescharacteristic
277D4—24no—
278D4—42no—
279D4—42no—
280D4—42no—
281C2×C4—42no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—132no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—522no—
291C2×C4—1048no—
292C2×C4—1041no—
293C2×C4—1041no—
294C2×C4—1041no—
295C2×C4—1041no—
296C2×C4—1041no—
297C2×C4#8813211yescharacteristic
298C2×C4#8813611yescharacteristic
299C2×C4#8816611yescharacteristic
300C2×C4#8816811yescharacteristic
301C2×C4#8816911yescharacteristic
302C2×C4D4×Dic1311yescharacteristic
303C8—521no—
304C8#8813211yescharacteristic
305C8#8814011yescharacteristic
306C8C2×C4⋊Dic1311yescharacteristic
307C8D4×Dic1311yescharacteristic
308C22—44no—
309C22—82no—
310C22—82no—
311C22—82no—
312C22—82no—
313C22—82no—
314C22—82no—
315C22#1171842011yescharacteristic
316C22#1171843411yescharacteristic
317C22D13×D1611yescharacteristic
318C22#1171857311yescharacteristic
319C22#1171857511yescharacteristic
320C22#1171857611yescharacteristic
321C22D8×Dic1311yescharacteristic
322C4—82no—
323C4—262no—
324C4—521no—
325C4—1042no—
326C4—2081no—
327C4#1171842711yescharacteristic
328C4#1171844411yescharacteristic
329C4#1171861111yescharacteristic
330C4#1171882511yescharacteristic
331C2—84no—
332C2#1311508511yescharacteristic
333C2D16×Dic1311yescharacteristic
334C2#1311670111yescharacteristic
335C2#1311674911yescharacteristic
336C2#1311677711yescharacteristic
337C2#1311697111yescharacteristic
338C2#1311699111yescharacteristic
subgroupG/H
centerC23D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×#357C2
socleC23×C13C2×D8
prime radicalC22×C13×D8C22
cosocleC22×C8×C13C23
hypercenterC2×#357D13
hypocenterC13#12935
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#11718096C2semidirect
4. #13115570C2semidirect
5. #13112927C2semidirect
6. #13112913C2semidirect
20. C13×#357C4semidirect
44. C2×C13×C16C2×C4semidirect
46. C13×#107C2×C4semidirect
78. C13×D8C4⋊C4semidirect
160. #357Dic13semidirect
208. C2×C16C2×Dic13semidirect
214. #107C2×Dic13semidirect
246. D8C4⋊Dic13semidirect
268. C13#12935semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic132
C2×#117180962
C2×#117181542
#131155702
#131129272
#131129132
C2×C13×#3572
#1293513