Finite Group Databasebeta

← #15756584

Subgroups — #15756584

Order 3328.

378 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114987C211yesmaximal, characteristic
2#13114952C211yesmaximal, characteristic
3C4×#88055C211yesmaximal, characteristic
4#13112671C211yesmaximal, characteristic
5#13112670C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic
7C13×#1277C211yesmaximal, characteristic
8C2×C13×C4⋊C8C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C13C2211yescharacteristic
11C2×#88055C411yescharacteristic
12C2×#88055C411yescharacteristic
13C2×#88055C411yescharacteristic
14C2×#88055C411yescharacteristic
15C2×#88054—21no—
16C2×#88054—21no—
17C42×Dic13C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21#11718142—21no—
22#11718142—21no—
23C22×C8×C13—21no—
24C22×C8×C13—21no—
25C22×C8×C13C2×C411yescharacteristic
26C22×C8×C13C2×C411yescharacteristic
27C2×C42×C13C2311yescharacteristic
28C2×C4×Dic13C2×C411yescharacteristic
29C2×C4×Dic13C2×C411yescharacteristic
30C2×C4×Dic13D411yescharacteristic
31C2×C4×Dic13D411yescharacteristic
32C2×C4×Dic13Q811yescharacteristic
33C2×C4×Dic13Q811yescharacteristic
34C22×#1055—21no—
35C22×#1055—21no—
36C22×#1055C2×C411yescharacteristic
37C22×#1055C2×C411yescharacteristic
38C13×C4⋊C8—21no—
39C13×C4⋊C8—21no—
40C13×C4⋊C8—21no—
41C13×C4⋊C8—21no—
42C4×C8×C13—21no—
43C4×C8×C13—21no—
44#88055—22no—
45#88055—22no—
46#88055—22no—
47#88055C814yescomplemented
48#88054—42no—
49#88054—42no—
50C4⋊#1055—21no—
51C4⋊#1055—21no—
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54C4×#1055—21no—
55C4×#1055—21no—
56#8786—131nomaximal, Sylow
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×Q811yescharacteristic
60C22×Dic13C4⋊C411yescharacteristic
61C22×Dic13C4⋊C411yescharacteristic
62C22×Dic13C4⋊C411yescharacteristic
63C22×Dic13C4⋊C411yescharacteristic
64C2×C8×C13—21no—
65C2×C8×C13—21no—
66C2×C8×C13—21no—
67C2×C8×C13—21no—
68C2×C8×C13—41no—
69C2×C8×C13—41no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13C2×C812yes—
75C2×C8×C13M1612yes—
76C42×C13#4111yescharacteristic
77C42×C13#4111yescharacteristic
78C42×C13#4111yescharacteristic
79C42×C13#4111yescharacteristic
80C4×Dic13—21no—
81C4×Dic13—21no—
82C4×Dic13—21no—
83C4×Dic13—21no—
84C4×Dic13—21no—
85C4×Dic13—21no—
86C4×Dic13—41no—
87C4×Dic13—41no—
88C4×Dic13C2×C812yes—
89C4×Dic13M1612yes—
90C2×#1055—21no—
91C2×#1055—21no—
92C2×#1055—21no—
93C2×#1055—21no—
94C2×#1055—41no—
95C2×#1055—41no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#1055C2×C812yes—
101C2×#1055M1612yes—
102#1842—131no—
103#1831—131no—
104C4×#97—131no—
105#1277—131no—
106#1277—131no—
107#1277—131no—
108#1277D1311yescharacteristic
109C23×C13C2×C4⋊C411yescharacteristic
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13#11711yescharacteristic
113C2×C4×C13#11711yescharacteristic
114C2×C4×C13#12411yescharacteristic
115C2×C4×C13#12411yescharacteristic
116C2×C4×C13#12511yescharacteristic
117C2×C4×C13#12511yescharacteristic
118C2×C4×C13C22×C811yescharacteristic
119C2×C4×C13C2×M1611yescharacteristic
120C2×C4×C13C2×M1611yescharacteristic
121C2×C4×C13C2×M1611yescharacteristic
122C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C13#13711yescharacteristic
125C2×C4×C13#13711yescharacteristic
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13C4⋊C812yes—
137C2×Dic13C4⋊C812yes—
138C8×C13—22no—
139C8×C13—22no—
140C8×C13—81no—
141C8×C13—81no—
142#1055—22no—
143#1055—22no—
144#1055—81no—
145#1055—81no—
146C2×C4⋊C8—131no—
147C2×C4⋊C8—131no—
148C2×C4⋊C8—261no—
149C2×C4⋊C8—261no—
150C2×C4⋊C8C2×D1311yescharacteristic
151C2×C4⋊C8C2×D1311yescharacteristic
152C2×#97—131no—
153C2×#97—131no—
154C2×#97—131no—
155C2×#97—131no—
156C2×C4×C8—131no—
157C2×C4×C8C2×D1311yescharacteristic
158C43—131no—
159#336—261no—
160#336—261no—
161C22×C13#38211yescharacteristic
162C22×C13C2×C4⋊C811yescharacteristic
163C22×C13#42311yescharacteristic
164C22×C13#42811yescharacteristic
165C22×C13#42811yescharacteristic
166C22×C13#43011yescharacteristic
167C22×C13#43011yescharacteristic
168C4×C13—21no—
169C4×C13—21no—
170C4×C13#43111yescharacteristic
171C4×C13#43111yescharacteristic
172C4×C13#43211yescharacteristic
173C4×C13#43211yescharacteristic
174C4×C13#48911yescharacteristic
175C4×C13#48911yescharacteristic
176C4×C13#49011yescharacteristic
177C4×C13#49111yescharacteristic
178Dic13—22no—
179Dic13—22no—
180Dic13—41no—
181Dic13—41no—
182C22×C8—21no—
183C22×C8—21no—
184C22×C8—131no—
185C22×C8—131no—
186C22×C8—261no—
187C22×C8—261no—
188C22×C8C4×D1311yescharacteristic
189C22×C8C4×D1311yescharacteristic
190C2×C42—131no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42C22×D1311yescharacteristic
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—261no—
202C4⋊C8—261no—
203C4⋊C8—261no—
204C4⋊C8—261no—
205C4⋊C8—522no—
206C4⋊C8—522no—
207#97—134no—
208#97—262no—
209#97—262no—
210#97—262no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—261no—
214C4×C8—261no—
215C2×C13#156511yescharacteristic
216C2×C13#156511yescharacteristic
217C2×C13#156911yescharacteristic
218C2×C13#156911yescharacteristic
219C2×C13#183111yescharacteristic
220C2×C13#183611yescharacteristic
221C2×C13#183811yescharacteristic
222C22×C4—131no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4C2×C4×D1311yescharacteristic
227C22×C4D4×D1311yescharacteristic
228C22×C4Q8×D1311yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—132no—
240C2×C8—132no—
241C2×C8—261no—
242C2×C8—261no—
243C2×C8—261no—
244C2×C8—261no—
245C2×C8—521no—
246C2×C8—521no—
247C2×C8—521no—
248C2×C8—521no—
249C2×C8—521no—
250C2×C8—521no—
251C2×C8C8×D1312yes—
252C2×C8#609412yes—
253C42—132no—
254C42—132no—
255C42—261no—
256C42—261no—
257C42—261no—
258C42—261no—
259C42—261no—
260C42—261no—
261C42—521no—
262C42—521no—
263C42#612711yescharacteristic
264C42#612711yescharacteristic
265C42#612911yescharacteristic
266C42#612911yescharacteristic
267C13#878611yescharacteristic, complemented, Sylow
268C23C4⋊C4×D1311yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—132no—
272C2×C4—132no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4#8812611yescharacteristic
284C2×C4#8813111yescharacteristic
285C2×C4#8813911yescharacteristic
286C2×C4#8813911yescharacteristic
287C2×C4#8814311yescharacteristic
288C2×C4#8814311yescharacteristic
289C2×C4C2×C8×D1311yescharacteristic
290C2×C4C2×#609411yescharacteristic
291C2×C4M16×D1311yescharacteristic
292C2×C4M16×D1311yescharacteristic
293C2×C4#8816511yescharacteristic
294C2×C4#8816811yescharacteristic
295C2×C4#8816911yescharacteristic
296C2×C4#8817211yescharacteristic
297C8—22no—
298C8—22no—
299C8—81no—
300C8—81no—
301C8—262no—
302C8—262no—
303C8—1041no—
304C8—1041no—
305C22#1171831111yescharacteristic
306C22D13×C4⋊C811yescharacteristic
307C22#1171849811yescharacteristic
308C22#1171852211yescharacteristic
309C22#1171854211yescharacteristic
310C22#1171855411yescharacteristic
311C22#1171855411yescharacteristic
312C4—21no—
313C4—21no—
314C4—262no—
315C4—262no—
316C4—521no—
317C4—521no—
318C4#1171834611yescharacteristic
319C4#1171836611yescharacteristic
320C4#1171837911yescharacteristic
321C4#1171838011yescharacteristic
322C4#1171842511yescharacteristic
323C4#1171842611yescharacteristic
324C4#1171845611yescharacteristic
325C4#1171845811yescharacteristic
326C2#1311358511yescharacteristic
327C2#1311358711yescharacteristic
328C2#1311360011yescharacteristic
329C2#1311360211yescharacteristic
330C2#1311495111yescharacteristic
331C2#1311496811yescharacteristic
332C2#1311497511yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1277C2
socle, prime radicalC23×C13C2×C4⋊C4
cosocleC2×C42×C13C23
hypercenter#1277D13
hypocenterC13#8786
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
47. #88055C8semidirect
267. C13#8786semidirect

Maximal subgroups

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

subgroupindex
#131149872
#131149522
C4×#880552
#131126712
#131126702
C13×#12772
#878613