Finite Group Databasebeta

← #15830922

Subgroups — #15830922

Order 3328.

960 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
1#13123856C211yesmaximal, characteristic, complemented
2#13123264C211yesmaximal, characteristic, complemented
3#13113451C213yesmaximal, complemented
4#13113443C213yesmaximal, complemented
5#13113431C213yesmaximal, complemented
6#13113424C213yesmaximal, complemented
7C13×#3518C211yesmaximal, characteristic
8Q82×C13C411yescharacteristic
9C13×#556—23no—
10C13×#556C413yes—
11C13×#555C413yes—
12D4×Q8×C13C411yescharacteristic
13C13×#548—21no—
14C13×#542—23no—
15C13×#533C2213yes—
16C13×#529C2213yes—
17C13×#519—21no—
18C4×C13×#41C2211yescharacteristic
19C2×#88202—21no—
20Q8×#1055—21no—
21#11718673—23no—
22#11718658—23no—
23#11718587C2213yes—
24C4×#6099C2213yes—
25C4×#6099C2213yes—
26C2×#88043C2213yes—
27#11718135C2213yes—
28#11718135C2213yes—
29#11718135C2216yes—
30#11718132C2211yescharacteristic
31#11718132C2213yes—
32C2×C13×#41D411yescharacteristic
33C22×Q8×C13—21no—
34C13×C4⋊Q8—23no—
35C13×C4⋊Q8C2×C413yes—
36C13×C4⋊Q8C2×C413yes—
37C13×#126—26no—
38C13×#126—23no—
39C13×#125C2313yes—
40C13×#124—23no—
41C13×#124—26no—
42C13×#124C2311yescharacteristic
43C13×#123—23no—
44C13×C22⋊Q8—23no—
45C13×C22⋊Q8—23no—
46C13×C22⋊Q8—23no—
47C13×C22⋊Q8C2×C413yes—
48C13×#121—23no—
49C13×#121C2×C413yes—
50C4×Q8×C13—21no—
51C4×Q8×C13—23no—
52C4×Q8×C13—23no—
53C4×Q8×C13—23no—
54C4×Q8×C13C2×C413yes—
55C4×Q8×C13C2×C411yescharacteristic
56C4×Q8×C13D411yescharacteristic
57C4×D4×C13—23no—
58C4×D4×C13C2×C413yes—
59C4×D4×C13C2×C413yes—
60C4×D4×C13D413yes—
61C13×#117—23no—
62C13×#117—23no—
63C13×#117C2×C416yes—
64C13×#117D413yes—
65C2×C42×C13C2313yes—
66#88202—28no—
67C2×#6099—23no—
68C2×#6099—23no—
69C22×#1055—23no—
70C22⋊#1055—23no—
71C4⋊#1055—23no—
72#88043—23no—
73#88043C2311yescharacteristic
74#88043C2313yes—
75#88043C2311yescharacteristic
76#88043C2313yes—
77C4×#1055—23no—
78C4×#1055—23no—
79#17654—131nomaximal, Sylow
80C13×#41—24no—
81C2×Q8×C13—23no—
82C2×Q8×C13—23no—
83C2×Q8×C13—44no—
84C2×Q8×C13C22⋊C411yescharacteristic
85C2×Q8×C13C22×C411yescharacteristic
86C2×D4×C13—23no—
87C2×D4×C13C22⋊C413yes—
88C2×D4×C13C22×C411yescharacteristic
89C22×C4×C13—23no—
90C22×C4×C13C22×C413yes—
91C22×C4×C13C2×D413yes—
92C22×C4×C13C2×D413yes—
93C13×C4⋊C4—23no—
94C13×C4⋊C4—23no—
95C13×C4⋊C4—23no—
96C13×C4⋊C4—23no—
97C13×C4⋊C4—23no—
98C13×C4⋊C4—23no—
99C13×C4⋊C4C22⋊C413yes—
100C13×C4⋊C4C22⋊C413yes—
101C13×C4⋊C4C22×C413yes—
102C13×C4⋊C4C22×C413yes—
103C13×C22⋊C4—26no—
104C13×C22⋊C4—23no—
105C13×C22⋊C4—23no—
106C13×C22⋊C4—23no—
107C13×C22⋊C4—21no—
108C13×C22⋊C4—21no—
109C13×C22⋊C4C22⋊C416yes—
110C42×C13—26no—
111C42×C13—23no—
112C42×C13C22×C413yes—
113C42×C13C2×D413yes—
114C42×C13C2×D413yes—
115C42×C13C2411yescharacteristic
116#6099—212no—
117#6099—46no—
118C2×#1055—212no—
119C2×#1055—21no—
120C2×#1055—23no—
121C2×#1055—21no—
122C2×#1055—23no—
123#3518D1311yescharacteristic
124#2971—131no—
125#2875—131no—
126#1531—133no—
127#1529—133no—
128#1526—133no—
129#1524—133no—
130C23×C13—21no—
131C23×C13C2×C22⋊C413yes—
132Q8×C13—41no—
133Q8×C13—46no—
134Q8×C13—83no—
135Q8×C13#10414yes—
136D4×C13—26no—
137D4×C13—41no—
138D4×C13—83no—
139C2×C4×C13—26no—
140C2×C4×C13—21no—
141C2×C4×C13—23no—
142C2×C4×C13—23no—
143C2×C4×C13—43no—
144C2×C4×C13—43no—
145C2×C4×C13—46no—
146C2×C4×C13C2×C22⋊C413yes—
147C2×C4×C13C2×C22⋊C413yes—
148C2×C4×C13C2×C22⋊C413yes—
149C2×C4×C13C23×C411yescharacteristic
150C2×C4×C13C22×D411yescharacteristic
151C2×C4×C13C22×D411yescharacteristic
152#1055—22no—
153#1055—26no—
154#1055—22no—
155#1055—43no—
156C2×#131—261no—
157Q82Dic1311yescharacteristic
158#556—23no—
159#556Dic1313yes—
160#555Dic1313yes—
161D4×Q8Dic1311yescharacteristic
162#548—21no—
163#542—23no—
164#533C2×D1313yes—
165#529C2×D1313yes—
166#519—21no—
167C4×#41C2×D1311yescharacteristic
168C8×Q8—261no—
169#436—263no—
170#432—133no—
171#405—263no—
172C4×M16—133no—
173C4×M16—133no—
174C2×#97—133no—
175#330—133no—
176#330—133no—
177#330—136no—
178#329—131no—
179#329—133no—
180C22×C13—23no—
181C22×C13—23no—
182C22×C13—23no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—41no—
186C22×C13C22×C22⋊C411yescharacteristic
187C4×C13—21no—
188C4×C13—23no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—23no—
192C4×C13—41no—
193C4×C13—43no—
194C4×C13—43no—
195C4×C13C2×#10416yes—
196C2×#41C22⋊D1311yescharacteristic
197C22×Q8—21no—
198#131—268no—
199C2×M16—263no—
200C2×M16—263no—
201C22×C8—263no—
202C4⋊Q8—23no—
203C4⋊Q8C2×Dic1313yes—
204C4⋊Q8C2×Dic1313yes—
205#126—26no—
206#126—23no—
207#125C22×D1313yes—
208#124—23no—
209#124—26no—
210#124C22×D1311yescharacteristic
211#123—23no—
212C22⋊Q8—23no—
213C22⋊Q8—23no—
214C22⋊Q8—23no—
215C22⋊Q8C2×Dic1313yes—
216#121—23no—
217#121C2×Dic1313yes—
218C4×Q8—21no—
219C4×Q8—23no—
220C4×Q8—23no—
221C4×Q8—23no—
222C4×Q8C2×Dic1313yes—
223C4×Q8C2×Dic1311yescharacteristic
224C4×Q8C22⋊D1311yescharacteristic
225C4×D4—23no—
226C4×D4C2×Dic1313yes—
227C4×D4C2×Dic1313yes—
228C4×D4C22⋊D1313yes—
229#117—23no—
230#117—23no—
231#117C2×Dic1316yes—
232#117C22⋊D1313yes—
233C2×C42C22×D1313yes—
234C4⋊C8—263no—
235C22⋊C8—263no—
236#97—131no—
237#97—133no—
238#97—131no—
239#97—133no—
240#97—263no—
241C4×C8—263no—
242C4×C8—263no—
243C2×C13—43no—
244C2×C13—81no—
245C2×C13#288911yescharacteristic
246C2×C13C22×#10411yescharacteristic
247C2×C13#290111yescharacteristic
248#41—24no—
249C2×Q8—23no—
250C2×Q8—23no—
251C2×Q8—44no—
252C2×Q8C22⋊Dic1311yescharacteristic
253C2×Q8C22×Dic1311yescharacteristic
254C2×D4—23no—
255C2×D4C22⋊Dic1313yes—
256C2×D4C22×Dic1311yescharacteristic
257C22×C4—23no—
258C22×C4C22×Dic1313yes—
259C22×C4C2×C22⋊D1313yes—
260C22×C4C2×C22⋊D1313yes—
261M16—2612no—
262M16—526no—
263C2×C8—2612no—
264C2×C8—261no—
265C2×C8—263no—
266C2×C8—261no—
267C2×C8—263no—
268C4⋊C4—23no—
269C4⋊C4—23no—
270C4⋊C4—23no—
271C4⋊C4—23no—
272C4⋊C4—23no—
273C4⋊C4—23no—
274C4⋊C4C22⋊Dic1313yes—
275C4⋊C4C22⋊Dic1313yes—
276C4⋊C4C22×Dic1313yes—
277C4⋊C4C22×Dic1313yes—
278C22⋊C4—26no—
279C22⋊C4—23no—
280C22⋊C4—23no—
281C22⋊C4—23no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4C22⋊Dic1316yes—
285C42—26no—
286C42—23no—
287C42C22×Dic1313yes—
288C42C2×C22⋊D1313yes—
289C42C2×C22⋊D1313yes—
290C42C23×D1311yescharacteristic
291C13#1765411yescharacteristic, complemented, Sylow
292C23—21no—
293C23C2×C22⋊Dic1313yes—
294Q8—41no—
295Q8—46no—
296Q8—83no—
297Q8#8807714yes—
298D4—26no—
299D4—41no—
300D4—83no—
301C2×C4—26no—
302C2×C4—21no—
303C2×C4—23no—
304C2×C4—23no—
305C2×C4—43no—
306C2×C4—43no—
307C2×C4—46no—
308C2×C4C2×C22⋊Dic1313yes—
309C2×C4C2×C22⋊Dic1313yes—
310C2×C4C2×C22⋊Dic1313yes—
311C2×C4C23×Dic1311yescharacteristic
312C2×C4C22×C22⋊D1311yescharacteristic
313C2×C4C22×C22⋊D1311yescharacteristic
314C8—262no—
315C8—266no—
316C8—262no—
317C8—523no—
318C22—23no—
319C22—23no—
320C22—23no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22C22×C22⋊Dic1311yescharacteristic
325C4—21no—
326C4—21no—
327C4—23no—
328C4—21no—
329C4—23no—
330C4—43no—
331C4—43no—
332C4—41no—
333C4C2×#8807716yes—
334C2—43no—
335C2—81no—
336C2#1312331911yescharacteristic
337C2C22×#8807711yescharacteristic
338C2#1312338311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
Fitting, prime radicalC13×#3518C2
socleC22×C13C22×C22⋊C4
cosocleC42×C13C24
hypercenter#3518D13
hypocenterC13#17654
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3518

Complements

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

NH ≅ G/Ntype
1. #13123856C2semidirect
2. #13123264C2semidirect
3. #13113451C2semidirect
4. #13113443C2semidirect
5. #13113431C2semidirect
6. #13113424C2semidirect
291. C13#17654semidirect

Maximal subgroups

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

subgroupindex
#131238562
#131232642
#131134512
#131134432
#131134312
#131134242
C13×#35182
#1765413