Finite Group Databasebeta

← #15761512

Subgroups — #15761512

Order 3328.

388 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114987C211yesmaximal, characteristic
2#13114691C211yesmaximal, characteristic
3C4×#88054C211yesmaximal, characteristic
4C2×#11718050C211yesmaximal, characteristic
5C2×#11718071C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic
7C13×#1277C211yesmaximal, characteristic
8C2×C13×C4⋊C8C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C13C2211yescharacteristic
11C2×#88055—21no—
12C2×#88054—21no—
13C2×#88054—21no—
14C2×#88054C411yescharacteristic
15C2×#88054C411yescharacteristic
16C42×Dic13C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C2×C4×#1055C2211yescharacteristic
20#11718142—21no—
21#11718142C411yescharacteristic
22#11718142C411yescharacteristic
23#11718071—22no—
24#11718050—22no—
25C22×C8×C13—21no—
26C22×C8×C13—21no—
27C22×C8×C13C2×C411yescharacteristic
28C22×C8×C13C2×C411yescharacteristic
29C2×C42×C13C2311yescharacteristic
30C2×C4×Dic13C2×C411yescharacteristic
31C2×C4×Dic13C2×C411yescharacteristic
32C2×C4×Dic13D411yescharacteristic
33C2×C4×Dic13D411yescharacteristic
34C2×C4×Dic13Q811yescharacteristic
35C2×C4×Dic13Q811yescharacteristic
36C22×#1055—21no—
37C22×#1055—21no—
38C22×#1055C2×C411yescharacteristic
39C22×#1055C2×C411yescharacteristic
40C13×C4⋊C8—21no—
41C13×C4⋊C8—21no—
42C13×C4⋊C8—21no—
43C13×C4⋊C8Q812yes—
44C4×C8×C13—21no—
45C4×C8×C13—21no—
46#88055—42no—
47#88054—22no—
48#88054—22no—
49#88054—42no—
50#88054—42no—
51C4⋊#1055—21no—
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055D412yes—
55C4×#1055—21no—
56C4×#1055—21no—
57#9604—131nomaximal, Sylow
58C22×C4×C13C22×C411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13C2×Q811yescharacteristic
61C22×Dic13C4⋊C411yescharacteristic
62C22×Dic13C4⋊C411yescharacteristic
63C22×Dic13C4⋊C411yescharacteristic
64C22×Dic13C4⋊C411yescharacteristic
65C2×C8×C13—21no—
66C2×C8×C13—21no—
67C2×C8×C13—21no—
68C2×C8×C13—22no—
69C2×C8×C13—21no—
70C2×C8×C13—21no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C2×C8×C13M1612yes—
77C42×C13C2×D411yescharacteristic
78C42×C13C2×Q811yescharacteristic
79C42×C13#4111yescharacteristic
80C42×C13#4111yescharacteristic
81C4×Dic13—21no—
82C4×Dic13—21no—
83C4×Dic13—21no—
84C4×Dic13—21no—
85C4×Dic13—21no—
86C4×Dic13—21no—
87C4×Dic13—22no—
88C4×Dic13—41no—
89C4×Dic13D812yes—
90C4×Dic13Q1612yes—
91C2×#1055—21no—
92C2×#1055—21no—
93C2×#1055—21no—
94C2×#1055—22no—
95C2×#1055—21no—
96C2×#1055—21no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055M1612yes—
103#1842—131no—
104#1767—131no—
105C4×C4⋊C8—131no—
106C2×#335—131no—
107C2×#335—131no—
108#1277—131no—
109#1277D1311yescharacteristic
110C23×C13C2×C4⋊C411yescharacteristic
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13C4×D411yescharacteristic
114C2×C4×C13C4×Q811yescharacteristic
115C2×C4×C13#12111yescharacteristic
116C2×C4×C13C22⋊Q811yescharacteristic
117C2×C4×C13#12511yescharacteristic
118C2×C4×C13C4⋊Q811yescharacteristic
119C2×C4×C13C2×M1611yescharacteristic
120C2×C4×C13C2×M1611yescharacteristic
121C2×C4×C13#13111yescharacteristic
122C2×C4×C13#13111yescharacteristic
123C2×C4×C13C2×D811yescharacteristic
124C2×C4×C13C2×Q1611yescharacteristic
125C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C13#13711yescharacteristic
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×Dic13#10712yes—
137C2×Dic13#10712yes—
138C2×Dic13#10812yes—
139C8×C13—22no—
140C8×C13—41no—
141C8×C13—42no—
142C8×C13—81no—
143#1055—22no—
144#1055—41no—
145#1055—42no—
146#1055—81no—
147C2×C4⋊C8—131no—
148C2×C4⋊C8—131no—
149C2×C4⋊C8—131no—
150C2×C4⋊C8—131no—
151C2×C4⋊C8—261no—
152C2×C4⋊C8—261no—
153C2×C4⋊C8C2×D1311yescharacteristic
154C2×C4⋊C8C2×D1311yescharacteristic
155C2×#97—261no—
156C2×C4×C8—131no—
157C2×C4×C8C2×D1311yescharacteristic
158C43—131no—
159#336—131no—
160#336—131no—
161#336—261no—
162#335—262no—
163#335—262no—
164C22×C13#38911yescharacteristic
165C22×C13#42311yescharacteristic
166C22×C13#42411yescharacteristic
167C22×C13C2×#10711yescharacteristic
168C22×C13#42811yescharacteristic
169C22×C13C2×#10811yescharacteristic
170C22×C13#43011yescharacteristic
171C4×C13—21no—
172C4×C13—21no—
173C4×C13#43511yescharacteristic
174C4×C13#43511yescharacteristic
175C4×C13#44611yescharacteristic
176C4×C13#44611yescharacteristic
177C4×C13#45911yescharacteristic
178C4×C13#46211yescharacteristic
179C4×C13#47411yescharacteristic
180C4×C13#47711yescharacteristic
181Dic13—22no—
182Dic13—22no—
183Dic13—22no—
184Dic13—41no—
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—131no—
188C22×C8—131no—
189C22×C8—261no—
190C22×C8—261no—
191C22×C8C4×D1311yescharacteristic
192C22×C8C4×D1311yescharacteristic
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42C22×D1311yescharacteristic
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—132no—
204C4⋊C8—262no—
205C4⋊C8—262no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208C4⋊C8—261no—
209C4⋊C8—522no—
210C4⋊C8—522no—
211C4⋊C8Dic2612yes—
212#97—522no—
213C4×C8—21no—
214C4×C8—21no—
215C4×C8—261no—
216C4×C8—261no—
217C2×C13#156711yescharacteristic
218C2×C13#156911yescharacteristic
219C2×C13#157111yescharacteristic
220C2×C13#157311yescharacteristic
221C2×C13#194011yescharacteristic
222C2×C13#194711yescharacteristic
223C2×C13#195011yescharacteristic
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4C2×C4×D1311yescharacteristic
229C22×C4D4×D1311yescharacteristic
230C22×C4Q8×D1311yescharacteristic
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—22no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—132no—
243C2×C8—261no—
244C2×C8—261no—
245C2×C8—261no—
246C2×C8—262no—
247C2×C8—261no—
248C2×C8—261no—
249C2×C8—521no—
250C2×C8—521no—
251C2×C8—521no—
252C2×C8—521no—
253C2×C8—521no—
254C2×C8#609412yes—
255C42—132no—
256C42—132no—
257C42—262no—
258C42—261no—
259C42—261no—
260C42—261no—
261C42—261no—
262C42—261no—
263C42—261no—
264C42—521no—
265C42C2×Dic2611yescharacteristic
266C42#612711yescharacteristic
267C42D4×D1311yescharacteristic
268C42#612911yescharacteristic
269C13#960411yescharacteristic, complemented, Sylow
270C23C4⋊C4×D1311yescharacteristic
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—132no—
274C2×C4—132no—
275C2×C4—132no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4C4×Dic2611yescharacteristic
286C2×C4#8813211yescharacteristic
287C2×C4#8813511yescharacteristic
288C2×C4#8813811yescharacteristic
289C2×C4#8814211yescharacteristic
290C2×C4#8814311yescharacteristic
291C2×C4C2×#609411yescharacteristic
292C2×C4#8815511yescharacteristic
293C2×C4M16×D1311yescharacteristic
294C2×C4#8816111yescharacteristic
295C2×C4D8×D1311yescharacteristic
296C2×C4#8816811yescharacteristic
297C2×C4#8816911yescharacteristic
298C2×C4Q16×D1311yescharacteristic
299C8—22no—
300C8—42no—
301C8—41no—
302C8—81no—
303C8—262no—
304C8—522no—
305C8—521no—
306C8—1041no—
307C22#1171830811yescharacteristic
308C22#1171849811yescharacteristic
309C22#1171850011yescharacteristic
310C22#1171852211yescharacteristic
311C22D13×#10711yescharacteristic
312C22D13×#10811yescharacteristic
313C22#1171855411yescharacteristic
314C4—21no—
315C4—21no—
316C4—262no—
317C4—262no—
318C4—262no—
319C4—521no—
320C4#1171834011yescharacteristic
321C4#1171836211yescharacteristic
322C4#1171838911yescharacteristic
323C4#1171839111yescharacteristic
324C4#1171842011yescharacteristic
325C4#1171844711yescharacteristic
326C4#1171845411yescharacteristic
327C4#1171845511yescharacteristic
328C2#1311359311yescharacteristic
329C2#1311360011yescharacteristic
330C2#1311360911yescharacteristic
331C2#1311361811yescharacteristic
332C2#1311555811yescharacteristic
333C2#1311559311yescharacteristic
334C2#1311561011yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1277C2
socle, prime radicalC23×C13C2×C4⋊C4
cosocleC2×C42×C13C23
hypercenter#1277D13
hypocenterC13#9604
LCSG ▷ C22×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
269. C13#9604semidirect

Maximal subgroups

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

subgroupindex
#131149872
#131146912
C4×#880542
C2×#117180502
C2×#117180712
#131126702
C13×#12772
#960413