Finite Group Databasebeta

← #15779511

Subgroups — #15779511

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×#11718081C211yesmaximal, characteristic, complemented
2C2×#11718154C211yesmaximal, characteristic
3C2×#11718154C211yesmaximal, characteristic
4#13115569C211yesmaximal, characteristic, complemented
5#13112927C211yesmaximal, characteristic, complemented
6#13112914C211yesmaximal, characteristic, complemented
7C2×C4×C13×D8C211yesmaximal, characteristic
8C22×C13×D8C2211yescharacteristic
9C2×C4×D4×C13—21no—
10C4×C13×D8—22no—
11C4×C13×D8—22no—
12C2×C13×#107C2211yescharacteristic
13C2×C13×#102—21no—
14C2×C4×C8×C13C2211yescharacteristic
15C2×#88058C2211yescharacteristic
16C2×#88058C2211yescharacteristic
17C22×#6090C2211yescharacteristic
18C22×#6090C2211yescharacteristic
19#11718589—21no—
20#11718154—22no—
21#11718154C414yescomplemented
22#11718143—21no—
23#11718081—22no—
24C22×D4×C13—21no—
25C23×C4×C13—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×C13D411yescharacteristic
33C22×C8×C13C2311yescharacteristic
34C4×D4×C13—24no—
35C4×D4×C13—42no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C22⋊C4—41no—
38C2×C42×C13D411yescharacteristic
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×#6101—41no—
42C13×#107—21no—
43C13×#107D412yes—
44C13×#102—24no—
45C4×C8×C13—21no—
46C4×C8×C13—21no—
47#88071—41no—
48#88058—21no—
49#88058—21no—
50#88058—21no—
51#88058C2×C412yescomplemented
52C2×#6090—21no—
53C2×#6090—21no—
54C2×#6090—21no—
55C2×#6090—21no—
56C2×#6090—21no—
57C2×#6090C2×C412yescomplemented
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—44no—
67C22×C4×C13—41no—
68C22×C4×C13—82no—
69C22×C4×C13—82no—
70C22×C4×C13D811yescharacteristic
71C22×C4×C13D811yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—41no—
74C22×Dic13—41no—
75C13×D8—22no—
76C13×D8—22no—
77C13×D8—22no—
78C13×D8C4⋊C414yescomplemented
79C2×C8×C13—21no—
80C2×C8×C13—21no—
81C2×C8×C13—21no—
82C2×C8×C13C22×C411yescharacteristic
83C2×C8×C13C2×D411yescharacteristic
84C2×C8×C13C2×D411yescharacteristic
85C2×C8×C13C2×Q811yescharacteristic
86C2×C8×C13#4111yescharacteristic
87C2×C8×C13#4111yescharacteristic
88C13×C4⋊C4—22no—
89C13×C4⋊C4—41no—
90C13×C22⋊C4—44no—
91C42×C13—21no—
92C42×C13—21no—
93C4⋊Dic13—22no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97#6101—82no—
98#6090—22no—
99#6090—41no—
100C2×C4×D8D1311yescharacteristic
101C2×#366—131no—
102C2×#357—131no—
103C2×#357—131no—
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—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—42no—
125C2×C4×C13—88no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13D1612yes—
129C2×C4×C13C4×D411yescharacteristic
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13C22⋊Q811yescharacteristic
132C2×C4×C13#13511yescharacteristic
133C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C13#13711yescharacteristic
135C2×Dic13—42no—
136C2×Dic13—81no—
137C2×Dic13—81no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140C2×Dic13—81no—
141C8×C13—41no—
142C8×C13C2×C4⋊C411yescharacteristic
143C8×C13C4×D411yescharacteristic
144C8×C13C22⋊Q811yescharacteristic
145C8×C13#12311yescharacteristic
146C22×D8C2×D1311yescharacteristic
147C2×C4×D4—21no—
148C22×C16—131no—
149C22×C16—131no—
150C4×D8—22no—
151C4×D8—22no—
152C2×#107—131no—
153C2×#107—131no—
154C2×#107C2×D1311yescharacteristic
155C2×#102—21no—
156C2×C4×C8C2×D1311yescharacteristic
157#389—261no—
158#366—262no—
159#357—134no—
160#357—262no—
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—22no—
177C4×C13—41no—
178C4×C13—82no—
179C4×C13#38511yescharacteristic
180C4×C13#44011yescharacteristic
181C4×C13#45211yescharacteristic
182C4×C13#47811yescharacteristic
183Dic13—82no—
184Dic13—161no—
185C22×D4—21no—
186C23×C4—41no—
187C2×D8—21no—
188C2×D8—21no—
189C2×D8—21no—
190C2×D8Dic2612yes—
191C2×D8C4×D1312yes—
192C2×D8C22⋊D1312yes—
193C22×C8C22⋊D1311yescharacteristic
194C22×C8C22×D1311yescharacteristic
195C4×D4—24no—
196C4×D4—42no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—521no—
201C2×C22⋊C4—41no—
202C2×C42C22⋊D1311yescharacteristic
203C2×C16—132no—
204C2×C16—261no—
205C2×C16—261no—
206C2×C16—261no—
207C2×C16—261no—
208C2×C16—261no—
209#107—21no—
210#107—132no—
211#107—261no—
212#107—261no—
213#107—261no—
214#107C22⋊D1312yes—
215#102—24no—
216C4×C8—21no—
217C4×C8—21no—
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—44no—
235C22×C4—41no—
236C22×C4—82no—
237C22×C4—82no—
238C22×C4—521no—
239C22×C4—521no—
240C22×C4#610411yescharacteristic
241C22×C4#610411yescharacteristic
242C22×C4C2×C22⋊D1311yescharacteristic
243D8—22no—
244D8—22no—
245D8—22no—
246D8#610114yescomplemented
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8C2×Dic2611yescharacteristic
251C2×C8C2×C4×D1311yescharacteristic
252C2×C8#612711yescharacteristic
253C2×C8#612711yescharacteristic
254C2×C8C2×C22⋊D1311yescharacteristic
255C2×C8C2×C22⋊D1311yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—41no—
258C4⋊C4—262no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—1042no—
263C22⋊C4—44no—
264C42—21no—
265C42—21no—
266C16—262no—
267C16—521no—
268C13#1293511yescharacteristic, complemented, Sylow
269C23—42no—
270C23—42no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23C2×#610411yescharacteristic
277D4—24no—
278D4—42no—
279D4—42no—
280D4—42no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—88no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—522no—
291C2×C4—1041no—
292C2×C4—1041no—
293C2×C4—1041no—
294C2×C4—1041no—
295C2×C4—1041no—
296C2×C4#8806612yes—
297C2×C4#8817811yescharacteristic
298C2×C4C4×C22⋊D1311yescharacteristic
299C2×C4#8818611yescharacteristic
300C2×C4#8820411yescharacteristic
301C2×C4#8820511yescharacteristic
302C2×C4#8820711yescharacteristic
303C8—41no—
304C8C2×#610111yescharacteristic
305C8#8817811yescharacteristic
306C8C4×C22⋊D1311yescharacteristic
307C8#8818311yescharacteristic
308C22—44no—
309C22—82no—
310C22—82no—
311C22—82no—
312C22—82no—
313C22—82no—
314C22—82no—
315C22#1171866811yescharacteristic
316C22C4×#610411yescharacteristic
317C22C2×#8806611yescharacteristic
318C22#1171880811yescharacteristic
319C22#1171885511yescharacteristic
320C22#1171885611yescharacteristic
321C22#1171887811yescharacteristic
322C4—22no—
323C4—41no—
324C4—82no—
325C4—1042no—
326C4—2081no—
327C4#1171867011yescharacteristic
328C4#1171867911yescharacteristic
329C4#1171887111yescharacteristic
330C4#1171890011yescharacteristic
331C2—84no—
332C2#1311508311yescharacteristic
333C2C4×#8806611yescharacteristic
334C2#1311670011yescharacteristic
335C2#1311674811yescharacteristic
336C2#1311677611yescharacteristic
337C2#1311697311yescharacteristic
338C2#1311699311yescharacteristic
subgroupG/H
centerC23C2×#6104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC2×C4×C13×D8C2
socleC23×C13C2×D8
prime radicalC22×C13×D8C22
cosocleC22×C8×C13C23
hypercenterC2×C4×D8D13
hypocenterC13#12935
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#11718081C2semidirect
4. #13115569C2semidirect
5. #13112927C2semidirect
6. #13112914C2semidirect
21. #11718154C4semidirect
51. #88058C2×C4semidirect
57. C2×#6090C2×C4semidirect
78. C13×D8C4⋊C4semidirect
246. D8#6101semidirect
268. C13#12935semidirect

Maximal subgroups

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

subgroupindex
C2×#117180812
C2×#117181542
#131155692
#131129272
#131129142
C2×C4×C13×D82
#1293513