Finite Group Databasebeta

← #15779424

Subgroups — #15779424

Order 3328.

486 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×D13×#107C211yesmaximal, characteristic
2C2×#11718097C211yesmaximal, characteristic, complemented
3C2×#11718082C211yesmaximal, characteristic, complemented
4C2×#11718099C211yesmaximal, characteristic
5#13114862C211yesmaximal, characteristic
6#13112927C211yesmaximal, characteristic, complemented
7C13×#1380C211yesmaximal, characteristic, complemented
8C22×C8×D13C2211yescharacteristic
9C2×C4⋊C4×D13—21no—
10C22×C13×C16C2211yescharacteristic
11C2×C13×#107C2211yescharacteristic
12C2×C13×#107C2211yescharacteristic
13C2×#88058C2211yescharacteristic
14C2×#88058C2211yescharacteristic
15C22×#6090C2211yescharacteristic
16#11718648—21no—
17C2×#88047—21no—
18D13×#107—22no—
19D13×#107—22no—
20#11718121—21no—
21#11718099C414yescomplemented
22#11718097—22no—
23#11718082—22no—
24C22×C4×D13—41no—
25C22×C4×D13D411yescharacteristic
26C22×C8×C13C2311yescharacteristic
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×#6103—41no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×#6101—41no—
33C22×#1055D411yescharacteristic
34C2×C8×D13—21no—
35C2×C8×D13—21no—
36C2×C8×D13—21no—
37C2×C8×D13—21no—
38C2×C8×D13C2×C412yes—
39C2×C8×D13Q812yes—
40C4⋊C4×D13—24no—
41C4⋊C4×D13—42no—
42C2×C13×C16—21no—
43C2×C13×C16—21no—
44C2×C13×C16C2×C412yescomplemented
45C13×#107—21no—
46C13×#107—21no—
47C13×#107—21no—
48C13×#107D412yes—
49#88071—41no—
50#88058—21no—
51#88058—21no—
52#88058—21no—
53#88058D412yes—
54C2×#6090—21no—
55C2×#6090—21no—
56C2×#6090C2×C412yescomplemented
57#88047—24no—
58#12920—131nomaximal, Sylow
59C23×D13D811yescharacteristic
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—41no—
64C22×Dic13—41no—
65C22×Dic13D811yescharacteristic
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13—44no—
71C2×C4×D13—82no—
72C2×C4×D13—82no—
73C2×C4×D13C4⋊C412yes—
74C2×C4×D13Q1612yes—
75C2×C8×C13C22×C411yescharacteristic
76C2×C8×C13C2×D411yescharacteristic
77C2×C8×C13C2×D411yescharacteristic
78C2×C8×C13C2×Q811yescharacteristic
79C2×C8×C13#4111yescharacteristic
80C2×C8×C13#4111yescharacteristic
81C13×C4⋊C4—22no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85#6103—82no—
86C4⋊Dic13—22no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89C4⋊Dic13—41no—
90#6101—44no—
91C2×#1055—21no—
92C2×#1055—21no—
93C2×#1055C4⋊C412yes—
94C8×D13—22no—
95C8×D13—22no—
96C8×D13—22no—
97C8×D13—22no—
98C13×C16—22no—
99#6090—22no—
100C22×#107—131no—
101C2×#367—131no—
102C2×#367—131no—
103C2×C22⋊C16—131no—
104#1808—131no—
105#1380—131no—
106#1380D1311yescharacteristic, complemented
107C23×C13C2×D811yescharacteristic
108C22×D13—21no—
109C22×D13—21no—
110C22×D13—21no—
111C22×D13—21no—
112C22×D13#10712yes—
113C22×D13SD3212yes—
114C22×D13SD3212yes—
115C2×C4×C13—42no—
116C2×C4×C13—81no—
117C2×C4×C13—81no—
118C2×C4×C13—81no—
119C2×C4×C13—81no—
120C2×C4×C13—81no—
121C2×C4×C13C2×C4⋊C411yescharacteristic
122C2×C4×C13#12011yescharacteristic
123C2×C4×C13#12311yescharacteristic
124C2×C4×C13C2×Q1611yescharacteristic
125C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C13#13711yescharacteristic
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—42no—
130C2×Dic13—81no—
131C2×Dic13—81no—
132C2×Dic13—81no—
133C2×Dic13—81no—
134C2×Dic13—81no—
135C2×Dic13#10712yes—
136C4×D13—22no—
137C4×D13—22no—
138C4×D13—22no—
139C4×D13—22no—
140C4×D13—88no—
141C8×C13C4×D411yescharacteristic
142C8×C13C4×D411yescharacteristic
143C8×C13C22⋊Q811yescharacteristic
144C8×C13C22⋊Q811yescharacteristic
145#1055—22no—
146C23×C8—131no—
147C22×C4⋊C4—261no—
148C22×C16—131no—
149C22×C16C2×D1311yescharacteristic
150C2×#107—131no—
151C2×#107—131no—
152C2×#107—262no—
153C2×#107—261no—
154C2×#107—262no—
155C2×#107C2×D1311yescharacteristic
156C2×#107C2×D1311yescharacteristic
157#380—261no—
158#367—262no—
159#367—262no—
160C22⋊C16—134no—
161#340—261no—
162C22×C13C2×#10711yescharacteristic
163C22×C13#44711yescharacteristic
164C22×C13#48011yescharacteristic
165C22×C13C2×SD3211yescharacteristic
166C22×C13C2×SD3211yescharacteristic
167C22×C13#50911yescharacteristic
168C22×C13#51011yescharacteristic
169C2×D13—22no—
170C2×D13—22no—
171C2×D13—22no—
172C2×D13—22no—
173C2×D13—22no—
174C2×D13—22no—
175C2×D13#36714yescomplemented
176C4×C13—82no—
177C4×C13—161no—
178C4×C13#38511yescharacteristic
179C4×C13#42811yescharacteristic
180C4×C13#45111yescharacteristic
181C4×C13#48411yescharacteristic
182Dic13—22no—
183Dic13—82no—
184Dic13—161no—
185C23×C4—131no—
186C23×C4—521no—
187C22×C8—131no—
188C22×C8—132no—
189C22×C8—132no—
190C22×C8—261no—
191C22×C8—261no—
192C22×C8—261no—
193C22×C8—261no—
194C22×C8C22×D1311yescharacteristic
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—264no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—522no—
201C2×C4⋊C4—521no—
202C2×C22⋊C4—521no—
203C2×C16—21no—
204C2×C16—21no—
205C2×C16—132no—
206C2×C16—261no—
207C2×C16—261no—
208C2×C16C4×D1312yescomplemented
209#107—21no—
210#107—21no—
211#107—21no—
212#107—132no—
213#107—264no—
214#107—261no—
215#107—261no—
216#107—261no—
217#107D5212yes—
218#95—521no—
219C2×C13#185211yescharacteristic
220C2×C13C2×#36711yescharacteristic
221C2×C13#215911yescharacteristic
222C2×C13#218511yescharacteristic
223C2×C13#218711yescharacteristic
224C2×C13#223311yescharacteristic
225C2×C13#223511yescharacteristic
226D13—24no—
227C24—131no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—131no—
231C22×C4—132no—
232C22×C4—132no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—524no—
238C22×C4—521no—
239C22×C4—521no—
240C22×C4—1042no—
241C22×C4—1042no—
242C22×C4D4×D1311yescharacteristic
243C2×C8—132no—
244C2×C8—261no—
245C2×C8—261no—
246C2×C8—262no—
247C2×C8—262no—
248C2×C8—262no—
249C2×C8—262no—
250C2×C8C2×C4×D1311yescharacteristic
251C2×C8C2×D5211yescharacteristic
252C2×C8#612711yescharacteristic
253C2×C8D4×D1311yescharacteristic
254C2×C8#612911yescharacteristic
255C2×C8Q8×D1311yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—262no—
261C4⋊C4—524no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C22⋊C4—1042no—
266C16—22no—
267C16—262no—
268C13#1292011yescharacteristic, complemented, Sylow
269C23—132no—
270C23—132no—
271C23—132no—
272C23—261no—
273C23—261no—
274C23—261no—
275C23—261no—
276C23D8×D1311yescharacteristic
277C2×C4—42no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—132no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—262no—
287C2×C4—262no—
288C2×C4—262no—
289C2×C4—262no—
290C2×C4—522no—
291C2×C4—1048no—
292C2×C4—1041no—
293C2×C4—1041no—
294C2×C4—1041no—
295C2×C4—1041no—
296C2×C4—1041no—
297C2×C4#8813611yescharacteristic
298C2×C4#8813711yescharacteristic
299C2×C4C4⋊C4×D1311yescharacteristic
300C2×C4#8816811yescharacteristic
301C2×C4#8816911yescharacteristic
302C2×C4Q16×D1311yescharacteristic
303C8—262no—
304C8C4×D5211yescharacteristic
305C8#8813511yescharacteristic
306C8#8815011yescharacteristic
307C8#8815111yescharacteristic
308C22—134no—
309C22—262no—
310C22—262no—
311C22—262no—
312C22—262no—
313C22—262no—
314C22—262no—
315C22#1171843411yescharacteristic
316C22#1171843511yescharacteristic
317C22D13×#10711yescharacteristic
318C22#1171857211yescharacteristic
319C22D13×SD3211yescharacteristic
320C22D13×SD3211yescharacteristic
321C22#1171857911yescharacteristic
322C4—82no—
323C4—161no—
324C4—262no—
325C4—1042no—
326C4—2081no—
327C4#1171832911yescharacteristic
328C4#1171846911yescharacteristic
329C4#1171847011yescharacteristic
330C4#1171852211yescharacteristic
331C2—264no—
332C2#1311502511yescharacteristic
333C2D13×#36711yescharacteristic
334C2#1311662111yescharacteristic
335C2#1311675411yescharacteristic
336C2#1311676611yescharacteristic
337C2#1311702011yescharacteristic
338C2#1311703211yescharacteristic
subgroupG/H
centerC23D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1380C2
socleC23×C13C2×D8
prime radicalC23×D13D8
cosocleC22×C8×C13C23
hypercenter#1380D13
hypocenterC13#12920
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#11718097C2semidirect
3. C2×#11718082C2semidirect
6. #13112927C2semidirect
7. C13×#1380C2semidirect
21. #11718099C4semidirect
44. C2×C13×C16C2×C4semidirect
56. C2×#6090C2×C4semidirect
106. #1380D13semidirect
175. C2×D13#367semidirect
208. C2×C16C4×D13semidirect
268. C13#12920semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1072
C2×#117180972
C2×#117180822
C2×#117180992
#131148622
#131129272
C13×#13802
#1292013