Finite Group Databasebeta

← #15779855

Subgroups — #15779855

Order 3328.

626 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718776C211yesmaximal, characteristic
2C22×#88058C211yesmaximal, characteristic, complemented
3C2×#11718101C212yesmaximal, complemented
4#13112928C212yesmaximal, complemented
5C2×C13×C22⋊C16C211yesmaximal, characteristic, complemented
6C23×C8×C13C2211yescharacteristic
7C2×#88184—21no—
8C22×C4⋊Dic13—21no—
9C22×D104C2211yescharacteristic
10C22×C13×C16C2212yes—
11#11718776—22no—
12#11718776C414yescomplemented
13C2×#88061—21no—
14C2×#88058—24no—
15C2×#88058—21no—
16C2×#88058C2211yescharacteristic
17C2×#88058C2212yes—
18C13×C22⋊C16—22no—
19#11718101—24no—
20C23×C4×C13D411yescharacteristic
21C22×C22⋊D13—41no—
22C23×Dic13—41no—
23C22×D52—21no—
24C22×C8×C13—22no—
25C22×C8×C13—22no—
26C22×C8×C13C2×C412yes—
27C22×C8×C13D411yescharacteristic
28C22×C8×C13D412yes—
29C22×C8×C13C2311yescharacteristic
30#88184—24no—
31#88184—42no—
32C2×#6103—41no—
33C2×C4⋊Dic13—24no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—42no—
37C2×C4⋊Dic13—41no—
38C2×D104—22no—
39C2×D104—22no—
40C2×D104—21no—
41C2×D104C2×C412yescomplemented
42C2×C13×C16—22no—
43C2×C13×C16—22no—
44C2×C13×C16—22no—
45#88061—24no—
46#88058—24no—
47#88058—22no—
48#88058—21no—
49#88058C2×C412yescomplemented
50#88058D414yescomplemented
51#12991—131nomaximal, Sylow
52C24×C13D811yescharacteristic
53C23×D13—41no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13D811yescharacteristic
60C22×C4×C13SD1612yes—
61C22×C4×C13C2×D411yescharacteristic
62C2×C22⋊D13—44no—
63C2×C22⋊D13—82no—
64C2×C22⋊D13—82no—
65C22×Dic13—44no—
66C22×Dic13—42no—
67C22×Dic13—41no—
68C22×Dic13—82no—
69C22×Dic13—82no—
70C2×D52—22no—
71C2×D52—41no—
72C2×D52—41no—
73C2×D52—41no—
74C2×D52—41no—
75C2×D52—41no—
76C2×C8×C13—21no—
77C2×C8×C13—21no—
78C2×C8×C13—24no—
79C2×C8×C13—24no—
80C2×C8×C13C22⋊C412yes—
81C2×C8×C13C22×C411yescharacteristic
82C2×C8×C13C2×D412yes—
83C2×C8×C13C2×D411yescharacteristic
84C2×C8×C13#4112yes—
85#6103—44no—
86C4⋊Dic13—22no—
87C4⋊Dic13—24no—
88C4⋊Dic13—44no—
89C4⋊Dic13—41no—
90C4⋊Dic13—42no—
91D104—24no—
92D104—42no—
93C13×C16—42no—
94C2×#466—131no—
95C22×#107—131no—
96C2×#357—132no—
97C2×C22⋊C16D1311yescharacteristic, complemented
98#1380—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13#10212yes—
104C23×C13D1612yes—
105C23×C13SD3212yes—
106C23×C13C2×D811yescharacteristic
107C22×D13—42no—
108C22×D13—81no—
109C22×D13—81no—
110C22×D13—81no—
111C22×D13—81no—
112C22×D13—81no—
113C22×D13—81no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13#10212yes—
121C2×C4×C13C2×C22⋊C411yescharacteristic
122C2×C4×C13#12011yescharacteristic
123C2×C4×C13#12311yescharacteristic
124C2×C4×C13C2×SD1611yescharacteristic
125C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C13#13711yescharacteristic
127C22⋊D13—88no—
128C2×Dic13—42no—
129C2×Dic13—44no—
130C2×Dic13—88no—
131C2×Dic13—82no—
132C2×Dic13—81no—
133C2×Dic13—81no—
134C2×Dic13—82no—
135D52—42no—
136D52—42no—
137D52—81no—
138D52—81no—
139C8×C13—22no—
140C8×C13C4×D412yes—
141C8×C13#12112yes—
142C22×D8—131no—
143C23×C8C2×D1311yescharacteristic
144C2×#121—261no—
145C22×C4⋊C4—261no—
146C22×C16C2×D1312yes—
147#466—134no—
148#466—262no—
149C2×#107—132no—
150C2×#107—131no—
151C2×#107—264no—
152C2×#107—261no—
153C2×#102—261no—
154#357—264no—
155C22⋊C16—22no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13#35714yescomplemented
163C22×C13C2×#10211yescharacteristic
164C22×C13#44711yescharacteristic
165C22×C13#48011yescharacteristic
166C22×C13C2×D1611yescharacteristic
167C22×C13C2×SD3211yescharacteristic
168C22×C13#50911yescharacteristic
169C22×C13#51011yescharacteristic
170C2×D13—82no—
171C2×D13—82no—
172C2×D13—82no—
173C2×D13—161no—
174C2×D13—161no—
175C2×D13—161no—
176C2×D13—161no—
177C4×C13—22no—
178C4×C13#38611yescharacteristic
179C4×C13#41711yescharacteristic
180C4×C13#44811yescharacteristic
181C4×C13#48111yescharacteristic
182Dic13—82no—
183Dic13—84no—
184C22×D4—261no—
185C22×D4—521no—
186C23×C4—521no—
187C23×C4D5211yescharacteristic
188C2×D8—132no—
189C2×D8—262no—
190C2×D8—262no—
191C2×D8—261no—
192C22×C8—22no—
193C22×C8—22no—
194C22×C8C4×D1312yes—
195C22×C8D5211yescharacteristic
196C22×C8C22⋊D1312yes—
197C22×C8C22×D1311yescharacteristic
198#121—264no—
199#121—522no—
200C2×C4⋊C4—264no—
201C2×C4⋊C4—262no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—522no—
204C2×C4⋊C4—521no—
205C2×C22⋊C4—521no—
206C2×C16—22no—
207C2×C16—22no—
208C2×C16—22no—
209#107—132no—
210#107—134no—
211#107—264no—
212#107—262no—
213#107—261no—
214#102—264no—
215C2×C13—24no—
216C2×C13#187411yescharacteristic
217C2×C13C2×#35711yescharacteristic
218C2×C13#213911yescharacteristic
219C2×C13#218411yescharacteristic
220C2×C13#218511yescharacteristic
221C2×C13#223211yescharacteristic
222C2×C13#223311yescharacteristic
223D13—162no—
224C24—521no—
225C24D10411yescharacteristic
226C2×D4—262no—
227C2×D4—524no—
228C2×D4—521no—
229C2×D4—521no—
230C2×D4—521no—
231C2×D4—521no—
232C2×D4—521no—
233C2×D4—1042no—
234C2×D4—1042no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—524no—
240C22×C4—521no—
241C22×C4—522no—
242C22×C4—1042no—
243C22×C4—1042no—
244C22×C4#609512yes—
245C22×C4D10411yescharacteristic
246C22×C4#610312yes—
247C22×C4C2×D5211yescharacteristic
248D8—264no—
249D8—522no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—24no—
253C2×C8—24no—
254C2×C8#610312yes—
255C2×C8C2×C4×D1311yescharacteristic
256C2×C8D4×D1312yes—
257C2×C8#612912yes—
258C2×C8C2×C22⋊D1311yescharacteristic
259C4⋊C4—264no—
260C4⋊C4—262no—
261C4⋊C4—524no—
262C4⋊C4—521no—
263C4⋊C4—522no—
264C22⋊C4—524no—
265C16—42no—
266C13#1299111yescharacteristic, complemented, Sylow
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—522no—
272C23—1041no—
273C23—1041no—
274C23—1041no—
275C23—1041no—
276C23—1041no—
277C23—1041no—
278C23D20812yes—
279C23#8804012yes—
280C23#8806112yes—
281C23C2×D10411yescharacteristic
282D4—522no—
283D4—522no—
284D4—1048no—
285D4—1041no—
286D4—1041no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—522no—
294C2×C4—524no—
295C2×C4—1048no—
296C2×C4—1042no—
297C2×C4—1041no—
298C2×C4—1041no—
299C2×C4—1042no—
300C2×C4#8806112yes—
301C2×C4#8813611yescharacteristic
302C2×C4#8814011yescharacteristic
303C2×C4C2×#609511yescharacteristic
304C2×C4#8816211yescharacteristic
305C2×C4#8816311yescharacteristic
306C2×C4C2×#610311yescharacteristic
307C8—22no—
308C8#8813512yes—
309C8#8819312yes—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—1042no—
317C22—1042no—
318C22—1042no—
319C22—2081no—
320C22—2081no—
321C22—2081no—
322C22—2081no—
323C22#1171810114yescomplemented
324C22#1171839311yescharacteristic
325C22#1171839711yescharacteristic
326C22C2×D20811yescharacteristic
327C22C2×#8804011yescharacteristic
328C22#1171856911yescharacteristic
329C22#1171857011yescharacteristic
330C22C2×#8806111yescharacteristic
331C4—22no—
332C4—1044no—
333C4—1042no—
334C4#1171839611yescharacteristic
335C4#1171839911yescharacteristic
336C4#1171861911yescharacteristic
337C4#1171879411yescharacteristic
338C2—24no—
339C2—2082no—
340C2#1311515111yescharacteristic
341C2C2×#1171810111yescharacteristic
342C2#1311654911yescharacteristic
343C2#1311675011yescharacteristic
344C2#1311675511yescharacteristic
345C2#1311701711yescharacteristic
346C2#1311702211yescharacteristic
subgroupG/H
centerC23C2×D104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C13×C22⋊C16C2
socleC23×C13C2×D8
prime radicalC2×#11718776C2
cosocleC22×C8×C13C23
hypercenterC2×C22⋊C16D13
hypocenterC13#12991
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C22×#88058C2semidirect
3. C2×#11718101C2semidirect
4. #13112928C2semidirect
5. C2×C13×C22⋊C16C2semidirect
12. #11718776C4semidirect
41. C2×D104C2×C4semidirect
49. #88058C2×C4semidirect
50. #88058D4semidirect
97. C2×C22⋊C16D13semidirect
162. C22×C13#357semidirect
266. C13#12991semidirect
323. C22#11718101semidirect

Maximal subgroups

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

subgroupindex
C2×#117187762
C22×#880582
C2×#117181012
#131129282
C2×C13×C22⋊C162
#1299113