Finite Group Databasebeta

← #16780474

Subgroups — #16780474

Order 3328.

542 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130622C211yesmaximal, characteristic
2C42×#1057C211yesmaximal, characteristic
3C2×Q8⋊#1057C212yesmaximal
4#13129672C212yesmaximal
5#13117311C211yesmaximal, characteristic
6C2×Q8×Dic13C2211yescharacteristic
7C2×#88110—21no—
8C2×C4⋊#1057C2212yes—
9C2×C4×#1057—21no—
10C2×C4×#1057—21no—
11C2×C4×#1057C2212yes—
12C13×#391C411yescharacteristic
13#11718891C411yescharacteristic
14C4⋊C4×Dic13C2211yescharacteristic
15#11718634C411yescharacteristic
16C42×Dic13C2211yescharacteristic
17#11718589C411yescharacteristic
18#11718315—21no—
19#11718314—21no—
20#11718310—21no—
21#11718309—21no—
22Q8⋊#1057C418yescomplemented
23#11718290—21no—
24C22×Q8×C13C2×C411yescharacteristic
25C22×#1057—22no—
26C22×#1057—22no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29Q8×Dic13—22no—
30Q8×Dic13C2×C414yes—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×#6101—21no—
35C2×#6101—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44#88110—42no—
45C4⋊#1057—22no—
46C4⋊#1057C2×C414yes—
47C4×#1057—24no—
48C4×#1057—24no—
49C4×#1057—22no—
50C4×#1057C2×C414yes—
51C13×#95—21no—
52C13×#95—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#8176—131nomaximal, Sylow
59C2×Q8×C13—21no—
60C2×Q8×C13—22no—
61C2×Q8×C13—22no—
62C2×Q8×C13C4212yes—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22×C411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C2×D411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74C2×#1057—24no—
75C2×#1057—24no—
76C2×#1057—24no—
77C2×#1057—24no—
78C2×#1057—42no—
79C2×#1057—42no—
80C13×C4⋊C4—22no—
81C42×C13—22no—
82C4⋊Dic13—21no—
83C4⋊Dic13—24no—
84C4⋊Dic13—22no—
85C4⋊Dic13C4212yes—
86#6101—42no—
87#6101—42no—
88C4×Dic13—22no—
89C4×Dic13—22no—
90C4×Dic13—22no—
91C4×Dic13—24no—
92C4×Dic13—22no—
93C4×Dic13—42no—
94C4×Dic13SD1612yes—
95C4×Dic13Q1612yes—
96C4×Dic13C22×C412yes—
97C4×Dic13#4112yes—
98#2295—131no—
99#1767—131no—
100C42×C8—131no—
101C2×Q8⋊C8—132no—
102#1279—132no—
103C23×C13C2×C22⋊C411yescharacteristic
104Q8×C13—24no—
105Q8×C13—42no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13#10312yes—
117C2×C4×C13#10412yes—
118C2×C4×C13C2×C4211yescharacteristic
119C2×C4×C13#11711yescharacteristic
120C2×C4×C13#13112yes—
121C2×C4×C13#13112yes—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—22no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13#10312yes—
135C2×Dic13#10412yes—
136C2×Dic13C4×D412yes—
137C2×Dic13C4×D412yes—
138C2×Dic13C2×SD1611yescharacteristic
139C2×Dic13C2×Q1611yescharacteristic
140C2×Dic13#13512yes—
141#1057—28no—
142#1057—44no—
143C2×C4×Q8—131no—
144C2×C4⋊C8—132no—
145C2×#97—261no—
146C2×C4×C8—132no—
147C2×C4×C8—261no—
148C2×C4×C8—261no—
149#391—131no—
150#391#26111yescharacteristic
151#389—131no—
152#389—131no—
153#387—261no—
154#387—261no—
155C4×C4⋊C4—131no—
156C4×C4⋊C4—261no—
157#376—261no—
158C43—131no—
159#336—261no—
160Q8⋊C8—138no—
161C22×C13C4×C22⋊C411yescharacteristic
162C22×C13#40811yescharacteristic
163C22×C13#40811yescharacteristic
164C22×C13C2×#10311yescharacteristic
165C22×C13#41611yescharacteristic
166C22×C13C2×#10411yescharacteristic
167C22×C13C2×#10411yescharacteristic
168C4×C13—22no—
169C4×C13—22no—
170C4×C13—42no—
171C4×C13—81no—
172C4×C13#40512yes—
173C4×C13#43312yes—
174Dic13—22no—
175Dic13—22no—
176Dic13—22no—
177Dic13—42no—
178Dic13—81no—
179Dic13C4×SD1612yes—
180Dic13C4×Q1612yes—
181C22×Q8C2×#26111yescharacteristic
182C22×C8—262no—
183C22×C8—262no—
184C4×Q8—134no—
185C4×Q8—262no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4C2×#26111yescharacteristic
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—261no—
199C2×C42—261no—
200C2×C42C2×#26111yescharacteristic
201C4⋊C8—134no—
202C4⋊C8—262no—
203#97—522no—
204C4×C8—134no—
205C4×C8—262no—
206C4×C8—264no—
207C4×C8—264no—
208#95—21no—
209#95—21no—
210#95—261no—
211#95—261no—
212#95—261no—
213#95—261no—
214#95—261no—
215C2×C13#149311yescharacteristic
216C2×C13#149311yescharacteristic
217C2×C13#149411yescharacteristic
218C2×C13#149411yescharacteristic
219C2×C13#175011yescharacteristic
220C2×C13C4×#10411yescharacteristic
221C2×C13C4×#10311yescharacteristic
222C2×Q8—21no—
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8C4×#26112yes—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4C22⋊#26111yescharacteristic
235C22×C4C22⋊#26111yescharacteristic
236C22×C4C22×#26111yescharacteristic
237C2×C8—264no—
238C2×C8—264no—
239C2×C8—264no—
240C2×C8—264no—
241C2×C8—522no—
242C2×C8—522no—
243C4⋊C4—22no—
244C4⋊C4—132no—
245C4⋊C4—264no—
246C4⋊C4—261no—
247C4⋊C4—262no—
248C4⋊C4—522no—
249C4⋊C4—522no—
250C42—22no—
251C42—132no—
252C42—132no—
253C42—132no—
254C42—132no—
255C42—262no—
256C42—262no—
257C42—264no—
258C42—262no—
259C42—262no—
260C42—522no—
261C13#817611yescharacteristic, complemented, Sylow
262C23C2×C22⋊#26111yescharacteristic
263Q8—24no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—132no—
276C2×C4—131no—
277C2×C4—131no—
278C2×C4—132no—
279C2×C4—132no—
280C2×C4—132no—
281C2×C4—132no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—262no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4#8811712yes—
295C2×C4#8811812yes—
296C2×C4C2×C4×#26111yescharacteristic
297C2×C4#8823711yescharacteristic
298C2×C4#8823812yes—
299C2×C4#8823812yes—
300C8—268no—
301C8—524no—
302C22C4×C22⋊#26111yescharacteristic
303C22#1171914611yescharacteristic
304C22#1171914711yescharacteristic
305C22C2×#8811711yescharacteristic
306C22C2×#8811811yescharacteristic
307C22D13⋊#10411yescharacteristic
308C22#1171916511yescharacteristic
309C4—22no—
310C4—22no—
311C4—42no—
312C4—81no—
313C4—132no—
314C4—132no—
315C4—262no—
316C4—262no—
317C4—262no—
318C4—522no—
319C4—1041no—
320C4#1171906212yes—
321C4#1171906812yes—
322C2#1313018411yescharacteristic
323C2#1313018511yescharacteristic
324C2#1313018811yescharacteristic
325C2#1313018911yescharacteristic
326C2#1313056611yescharacteristic
327C2C4×#8811811yescharacteristic
328C2C4×#8811711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#391C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#391#261
hypocenterC13#8176
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
22. Q8⋊#1057C4semidirect
261. C13#8176semidirect

Maximal subgroups

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

subgroupindex
#131306222
C42×#10572
C2×Q8⋊#10572
#131296722
#131173112
#817613