Finite Group Databasebeta

← #16782133

Subgroups — #16782133

Order 3328.

680 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#13130690C211yesmaximal, characteristic
2C4×C22⋊#1057C211yesmaximal, characteristic
3#13129672C214yesmaximal, complemented
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic
7C22×C4×Dic13—21no—
8C22×C4×Dic13C2211yescharacteristic
9C2×C22⋊#1057—21no—
10C2×C22⋊#1057—21no—
11C2×C4⋊#1057C2212yes—
12C2×C4×#1057C2212yes—
13C2×#88071—21no—
14C4⋊C4×Dic13—21no—
15C4⋊C4×Dic13—21no—
16C4⋊C4×Dic13C412yes—
17C4⋊C4×Dic13C2212yes—
18#11718290—21no—
19#11718290—21no—
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C23×Dic13—21no—
23C23×Dic13D411yescharacteristic
24C23×Dic13D411yescharacteristic
25C22×#1057—22no—
26C22×#1057—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4C814yescomplemented
30C2×C13×C4⋊C4C2×C412yes—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—24no—
33C2×C4⋊Dic13C2×C412yes—
34C2×C4×Dic13—24no—
35C2×C4×Dic13—22no—
36C2×C4×Dic13—22no—
37C2×C4×Dic13—42no—
38C2×C4×Dic13—42no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13C2311yescharacteristic
43C22⋊#1057—24no—
44C22⋊#1057—42no—
45C4⋊#1057—24no—
46C4×#1057—24no—
47#88071—22no—
48#88071—22no—
49#8706—131nomaximal, Sylow
50C24×C13C22⋊C411yescharacteristic
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—24no—
54C22×C4×C13—22no—
55C22×C4×C13—42no—
56C22×C4×C13—42no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C2×C812yes—
59C22×C4×C13M1612yes—
60C22×C4×C13C22×C411yescharacteristic
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—24no—
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C22×Dic13—41no—
68C22×Dic13—42no—
69C22×Dic13—42no—
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13D812yes—
73C22×Dic13SD1612yes—
74C22×Dic13C2×D411yescharacteristic
75C22×Dic13C2×D411yescharacteristic
76C2×#1057—24no—
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C2×#1057—42no—
81C2×#1057—42no—
82C13×C4⋊C4—24no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4C2×C814yes—
85C4⋊Dic13—24no—
86C4⋊Dic13—22no—
87C4⋊Dic13M1614yes—
88C4×Dic13—22no—
89C4×Dic13—22no—
90C4×Dic13—22no—
91C4×Dic13—44no—
92C4×Dic13—42no—
93C4×Dic13—42no—
94C4×Dic13#4114yes—
95C2×C4×C4⋊C4—131no—
96#1797—131no—
97C4×C22⋊C8—131no—
98#1279—134no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13C22⋊C812yes—
104C23×C13#10212yes—
105C23×C13#10412yes—
106C23×C13C2×C22⋊C411yescharacteristic
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—24no—
110C2×C4×C13—24no—
111C2×C4×C13—24no—
112C2×C4×C13—48no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13C22⋊C812yes—
116C2×C4×C13#11712yes—
117C2×C4×C13C22×C811yescharacteristic
118C2×C4×C13C2×M1612yes—
119C2×C4×C13C2×M1611yescharacteristic
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—24no—
125C2×Dic13—24no—
126C2×Dic13—21no—
127C2×Dic13—24no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—44no—
131C2×Dic13—48no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13#10212yes—
135C2×Dic13#12312yes—
136C2×Dic13#12312yes—
137C2×Dic13C2×D811yescharacteristic
138C2×Dic13C2×SD1611yescharacteristic
139C2×Dic13#13712yes—
140#1057—44no—
141#1057—82no—
142C22×C4⋊C4—131no—
143C22×C4⋊C4#26111yescharacteristic
144C22×C42—131no—
145C22×C42—261no—
146C2×C4⋊C8—132no—
147C2×C22⋊C8—261no—
148C2×C22⋊C8—261no—
149C2×C4×C8—132no—
150C4×C4⋊C4—132no—
151C4×C4⋊C4—132no—
152C4×C4⋊C4—261no—
153C4×C4⋊C4—261no—
154C2×#95—261no—
155#336—261no—
156#336—261no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13D4⋊C814yes—
164C22×C13#38111yescharacteristic
165C22×C13C2×C22⋊C811yescharacteristic
166C22×C13#40711yescharacteristic
167C22×C13C2×#10211yescharacteristic
168C22×C13#41911yescharacteristic
169C22×C13C2×#10411yescharacteristic
170C22×C13#42111yescharacteristic
171C4×C13—22no—
172C4×C13—44no—
173C4×C13#43112yes—
174C4×C13#43212yes—
175Dic13—22no—
176Dic13—22no—
177Dic13—41no—
178Dic13—44no—
179Dic13#48012yes—
180Dic13#48312yes—
181C23×C4—21no—
182C23×C4—131no—
183C23×C4—131no—
184C23×C4—261no—
185C23×C4C2×#26111yescharacteristic
186C22×C8—262no—
187C22×C8—262no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—132no—
191C2×C4⋊C4—264no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4#105714yescomplemented
194C2×C4⋊C4C2×#26112yes—
195C2×C42—131no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—264no—
200C2×C42—262no—
201C2×C42—262no—
202C2×C42—522no—
203C2×C42—522no—
204C4⋊C8—264no—
205C22⋊C8—264no—
206C22⋊C8—522no—
207C4×C8—264no—
208#95—262no—
209#95—262no—
210C2×C13—24no—
211C2×C13C2×D4⋊C811yescharacteristic
212C2×C13#147911yescharacteristic
213C2×C13#148611yescharacteristic
214C2×C13#149111yescharacteristic
215C2×C13#181711yescharacteristic
216C2×C13#182311yescharacteristic
217C2×C13#182611yescharacteristic
218C24C22⋊#26111yescharacteristic
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—22no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—131no—
226C22×C4—132no—
227C22×C4—132no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—262no—
232C22×C4—262no—
233C22×C4—262no—
234C22×C4—264no—
235C22×C4—262no—
236C22×C4—262no—
237C22×C4—521no—
238C22×C4—522no—
239C22×C4—522no—
240C22×C4C2×#105712yes—
241C22×C4#612212yes—
242C22×C4C22⋊#26111yescharacteristic
243C22×C4C22×#26111yescharacteristic
244C2×C8—264no—
245C2×C8—522no—
246C2×C8—522no—
247C2×C8—522no—
248C2×C8—522no—
249C2×C8—522no—
250C4⋊C4—24no—
251C4⋊C4—22no—
252C4⋊C4—134no—
253C4⋊C4—264no—
254C4⋊C4—262no—
255C4⋊C4C2×#105714yes—
256C42—134no—
257C42—262no—
258C42—262no—
259C42—262no—
260C42—522no—
261C42—522no—
262C42—524no—
263C13#870611yescharacteristic, complemented, Sylow
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#8811512yes—
269C23#8811612yes—
270C23C22⋊#105712yes—
271C23C2×C22⋊#26111yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—48no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—132no—
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—132no—
284C2×C4—132no—
285C2×C4—132no—
286C2×C4—264no—
287C2×C4—264no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—264no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—524no—
297C2×C4—528no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4C22⋊#105712yes—
301C2×C4D13⋊M1612yes—
302C2×C4#8823712yes—
303C2×C4C22×#105711yescharacteristic
304C2×C4C2×#612211yescharacteristic
305C8—524no—
306C8—1042no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22D4⋊#105714yes—
314C22#1171912611yescharacteristic
315C22#1171913511yescharacteristic
316C22C2×#8811511yescharacteristic
317C22C2×#8811611yescharacteristic
318C22#1171915311yescharacteristic
319C22#1171915511yescharacteristic
320C22C2×C22⋊#105711yescharacteristic
321C4—22no—
322C4—44no—
323C4—132no—
324C4—132no—
325C4—262no—
326C4—262no—
327C4—524no—
328C4—521no—
329C4#1171911912yes—
330C4#1171912812yes—
331C2—24no—
332C2C2×D4⋊#105711yescharacteristic
333C2#1313013811yescharacteristic
334C2#1313016311yescharacteristic
335C2#1313018011yescharacteristic
336C2#1313072611yescharacteristic
337C2#1313073911yescharacteristic
338C2#1313074211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#8706
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13129672C2semidirect
29. C2×C13×C4⋊C4C8semidirect
193. C2×C4⋊C4#1057semidirect
263. C13#8706semidirect

Maximal subgroups

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

subgroupindex
#131306902
C4×C22⋊#10572
#131296722
C2×C4⋊C4×Dic132
#870613