Finite Group Databasebeta

← #15832140

Subgroups — #15832140

Order 3328.

702 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
1C8×#6127C211yesmaximal, characteristic
2#13123401C212yesmaximal
3#13113606C212yesmaximal, complemented
4#13113605C214yesmaximal, complemented
5#13113592C211yesmaximal, characteristic, complemented
6#13113590C212yesmaximal, complemented
7D13×#334C212yesmaximal, complemented
8C2×C13×#334C211yesmaximal, characteristic, complemented
9C2×#88155—22no—
10C4×#6127C2211yescharacteristic
11C2×C13×C4⋊C8C2212yes—
12C2×C4×C8×C13C2211yescharacteristic
13C8×C22⋊D13C412yes—
14C8×C22⋊D13C412yes—
15#11718763—22no—
16#11718586C2211yescharacteristic
17#11718585C2212yes—
18#11718500—24no—
19#11718498C2214yes—
20D13×C4⋊C8C2214yes—
21C8×D52C411yescharacteristic
22C8×D52C411yescharacteristic
23#11718346C2212yes—
24C4×C8×D13C2212yes—
25C8×Dic26C411yescharacteristic
26C8×Dic26C411yescharacteristic
27C13×#334C2212yes—
28C13×#334C2211yescharacteristic
29C13×#334C2211yescharacteristic
30#11718072C2214yes—
31#11718072C2214yes—
32#11718049C2212yes—
33#11718049C2212yes—
34C2×#6127D411yescharacteristic
35C22×C8×C13—22no—
36C22×C8×C13C2×C411yescharacteristic
37C22×C8×C13C2×C411yescharacteristic
38C2×C42×C13C2311yescharacteristic
39C4×C22⋊D13C2×C412yes—
40C4×C22⋊D13Q812yes—
41#88180D411yescharacteristic
42C2×#6099—22no—
43#88155—48no—
44C2×#6094—24no—
45C2×C8×D13—24no—
46C2×C8×D13C2×C412yes—
47C2×C8×D13C2×C412yes—
48C4×D52C2×C411yescharacteristic
49C4×D52Q811yescharacteristic
50#88126D412yes—
51C42×D13C2312yes—
52C4×Dic26C2×C411yescharacteristic
53C4×Dic26Q811yescharacteristic
54C13×C4⋊C8—22no—
55C13×C4⋊C8C2312yes—
56C13×C4⋊C8C2312yes—
57C4×C8×C13C2×C411yescharacteristic
58C4×C8×C13C2×C411yescharacteristic
59C4×C8×C13C2311yescharacteristic
60C4×C8×C13C2311yescharacteristic
61C22⋊#1055C2×C412yes—
62#88060C2×C412yes—
63#88060C2×C412yes—
64#88054—24no—
65#88054—24no—
66#88054C2×C412yes—
67#88054C2×C412yes—
68C8×Dic13C2×C412yes—
69C8×Dic13C2×C412yes—
70C4⋊#1055—22no—
71C4⋊#1055C2×C411yescharacteristic
72C4⋊#1055C2×C411yescharacteristic
73C4⋊#1055C2314yes—
74C4×#1055C2312yes—
75#17826—131nomaximal, Sylow
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×Q811yescharacteristic
79C2×C22⋊D13C4⋊C412yes—
80#6127SD1618yes—
81C2×D52C4⋊C411yescharacteristic
82C2×C4×D13C22×C412yes—
83C2×C4×D13C2×D412yes—
84C2×C4×D13C2×Q812yes—
85C2×Dic26C4⋊C411yescharacteristic
86C2×C8×C13—22no—
87C2×C8×C13—22no—
88C2×C8×C13—22no—
89C2×C8×C13—41no—
90C2×C8×C13—44no—
91C2×C8×C13C22×C411yescharacteristic
92C2×C8×C13C22×C411yescharacteristic
93C2×C8×C13C22×C411yescharacteristic
94C2×C8×C13C22×C411yescharacteristic
95C42×C13C22×C411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13C2×Q811yescharacteristic
98C42×C13C2411yescharacteristic
99C22⋊Dic13C4⋊C412yes—
100#6103C4⋊C412yes—
101#6103C4⋊C412yes—
102C4⋊Dic13C4⋊C411yescharacteristic
103C4⋊Dic13C4⋊C411yescharacteristic
104#6101C4⋊C412yes—
105#6101C4⋊C412yes—
106C4×Dic13C22×C412yes—
107C4×Dic13C2×D412yes—
108C4×Dic13C2×Q812yes—
109#6099—44no—
110C2×#1055—24no—
111C2×#1055C22×C412yes—
112C2×#1055C22×C412yes—
113#6094—48no—
114C8×D13—24no—
115C8×D13—42no—
116C8×D13—48no—
117C8×#41—131no—
118#2906—132no—
119#1570—132no—
120#1570—134no—
121#1566—131no—
122#1566—132no—
123C2×#334—132no—
124C2×#334D1311yescharacteristic, complemented
125C23×C13C2×C4⋊C411yescharacteristic
126C22×D13C2×C4⋊C412yes—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—41no—
130C2×C4×C13C2×C4⋊C411yescharacteristic
131C2×C4×C13C2×C4⋊C411yescharacteristic
132C2×C4×C13C2×C4⋊C411yescharacteristic
133C2×C4×C13C2×SD1614yes—
134C2×C4×C13C23×C411yescharacteristic
135C2×C4×C13C22×D411yescharacteristic
136C2×C4×C13C22×Q811yescharacteristic
137C22⋊D13#10618yes—
138C2×Dic13C2×C4⋊C412yes—
139C2×Dic13C2×C4⋊C412yes—
140C2×Dic13C2×C4⋊C412yes—
141D52#10614yes—
142C4×D13—22no—
143C4×D13—22no—
144C4×D13—42no—
145C4×D13C2×SD1618yes—
146Dic26#10614yes—
147C8×C13—21no—
148C8×C13—21no—
149C8×C13—21no—
150C8×C13—42no—
151C8×C13—42no—
152C8×C13#13112yescomplemented
153#1055—22no—
154#1055—22no—
155#1055—44no—
156C2×#131—262no—
157C4×#41—131no—
158C8×Q8—131no—
159C8×Q8—131no—
160C8×D4—132no—
161C8×D4—132no—
162C8×D4—131no—
163C8×D4—131no—
164#431—131no—
165#431—132no—
166#424—264no—
167#424—262no—
168#423—132no—
169#423—134no—
170C2×C4⋊C8—134no—
171C2×C4⋊C8C2×D1312yes—
172C2×C4×C8—132no—
173C2×C4×C8C2×D1311yescharacteristic
174#334—134no—
175#334—134no—
176#334—132no—
177#334—132no—
178#334C2×D1311yescharacteristic
179#334C2×D1311yescharacteristic
180#334C2×D1312yes—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13C2×#10612yes—
184C22×C13C22×C4⋊C411yescharacteristic
185C2×D13—22no—
186C2×D13—22no—
187C2×D13C2×#10614yes—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13C2×#10612yes—
192C4×C13C2×#13111yescharacteristic
193C4×C13#56811yescharacteristic
194C4×C13C22×SD1612yes—
195Dic13—22no—
196Dic13—22no—
197Dic13C2×#10614yes—
198C2×#41—131no—
199#131—528no—
200C2×M16—264no—
201C2×M16—262no—
202C22×C8—22no—
203C22×C8—132no—
204C22×C8—132no—
205C22×C8—264no—
206C22×C8C4×D1311yescharacteristic
207C22×C8C4×D1311yescharacteristic
208C4×Q8—131no—
209C4×Q8—131no—
210C4×D4—132no—
211C4×D4—132no—
212C4×D4—131no—
213C4×D4—131no—
214#117—131no—
215#117—132no—
216C2×C42—132no—
217C2×C42C22×D1311yescharacteristic
218C4⋊C8—22no—
219C4⋊C8—132no—
220C4⋊C8—132no—
221C4⋊C8—131no—
222C4⋊C8—131no—
223C4⋊C8—134no—
224C4⋊C8—264no—
225C4⋊C8—264no—
226C4⋊C8—262no—
227C4⋊C8C22×D1312yes—
228C4⋊C8C22×D1312yes—
229C22⋊C8—132no—
230C22⋊C8—132no—
231C22⋊C8—132no—
232C4×C8—132no—
233C4×C8—132no—
234C4×C8—132no—
235C4×C8C4×D1311yescharacteristic
236C4×C8C4×D1311yescharacteristic
237C4×C8C22×D1311yescharacteristic
238C4×C8C22×D1311yescharacteristic
239C2×C13—22no—
240C2×C13#290611yescharacteristic
241C2×C13C22×#10611yescharacteristic
242C2×C13#291611yescharacteristic
243D13—24no—
244#41—138no—
245C2×Q8—131no—
246C2×D4—132no—
247C2×D4—131no—
248C22×C4—132no—
249C22×C4—132no—
250C22×C4—132no—
251C22×C4C2×C4×D1311yescharacteristic
252C22×C4D4×D1311yescharacteristic
253C22×C4Q8×D1311yescharacteristic
254M16—528no—
255M16—524no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—44no—
261C2×C8—132no—
262C2×C8—132no—
263C2×C8—264no—
264C2×C8—264no—
265C2×C8—522no—
266C2×C8—528no—
267C2×C8C2×C4×D1311yescharacteristic
268C2×C8C2×C4×D1311yescharacteristic
269C2×C8C2×C4×D1311yescharacteristic
270C2×C8C2×C4×D1311yescharacteristic
271C4⋊C4—132no—
272C4⋊C4—132no—
273C4⋊C4—131no—
274C4⋊C4—131no—
275C22⋊C4—132no—
276C22⋊C4—132no—
277C22⋊C4—132no—
278C42—132no—
279C42—132no—
280C42—132no—
281C42C2×C4×D1311yescharacteristic
282C42D4×D1311yescharacteristic
283C42Q8×D1311yescharacteristic
284C42C23×D1311yescharacteristic
285C13#1782611yescharacteristic, complemented, Sylow
286C23—132no—
287C23C4⋊C4×D1311yescharacteristic
288Q8—134no—
289D4—138no—
290D4—134no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—132no—
295C2×C4—138no—
296C2×C4—132no—
297C2×C4—132no—
298C2×C4—262no—
299C2×C4—262no—
300C2×C4—522no—
301C2×C4C4⋊C4×D1311yescharacteristic
302C2×C4C4⋊C4×D1311yescharacteristic
303C2×C4C4⋊C4×D1311yescharacteristic
304C2×C4SD16×D1314yes—
305C2×C4C22×C4×D1311yescharacteristic
306C2×C4C2×D4×D1311yescharacteristic
307C2×C4C2×Q8×D1311yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—42no—
312C8—42no—
313C8—262no—
314C8—262no—
315C8—524no—
316C8#8815512yescomplemented
317C22—21no—
318C22—21no—
319C22—134no—
320C22—262no—
321C22—262no—
322C22D13×#10612yes—
323C22C2×C4⋊C4×D1311yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—134no—
328C4—262no—
329C4—262no—
330C4D13×#10612yes—
331C4C2×#8815511yescharacteristic
332C4#1171945011yescharacteristic
333C4C2×SD16×D1312yes—
334C2—22no—
335C2—264no—
336C2#1312340111yescharacteristic
337C2C2×D13×#10611yescharacteristic
338C2#1312344411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C13×#334C2
socleC22×C13C22×C4⋊C4
prime radicalC2×#6127D4
cosocleC42×C13C24
hypercenterC2×#334D13
hypocenterC13#17826
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
3. #13113606C2semidirect
4. #13113605C2semidirect
5. #13113592C2semidirect
6. #13113590C2semidirect
7. D13×#334C2semidirect
8. C2×C13×#334C2semidirect
124. C2×#334D13semidirect
152. C8×C13#131semidirect
285. C13#17826semidirect
316. C8#88155semidirect

Maximal subgroups

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

subgroupindex
C8×#61272
#131234012
#131136062
#131136052
#131135922
#131135902
D13×#3342
C2×C13×#3342
#1782613