Finite Group Databasebeta

← #15762055

Subgroups — #15762055

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114816C211yesmaximal, characteristic
2C2×#11718130C214yesmaximal
3#13113063C211yesmaximal, characteristic
4C13×#2857C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×C13×C22⋊Q8C2212yes—
7C22×C42×C13C2211yescharacteristic
8C13×#391C412yescomplemented
9C13×#389—21no—
10C13×#389—21no—
11C13×#384C411yescharacteristic, complemented
12C13×#380—21no—
13C13×#380—21no—
14C2×#88071—21no—
15C2×#88071—21no—
16C2×#88071C2212yes—
17C2×C22⋊#1055C2212yes—
18C2×C4⋊#1055—21no—
19#11718130—28no—
20#11718116—21no—
21C22×Q8×C13C2×C412yes—
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C23×Dic13—22no—
26C13×C4⋊Q8—42no—
27C13×C22⋊Q8—24no—
28C13×C22⋊Q8—24no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4C2×C412yes—
35C2×C13×C22⋊C4—22no—
36C2×C42×C13—42no—
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13C2×C411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C22×#1055—22no—
42C13×#95—22no—
43C13×#95—22no—
44#88071—22no—
45#88071—42no—
46#88071—42no—
47#88071D414yes—
48C22⋊#1055—24no—
49C4⋊#1055—42no—
50#9714—131nomaximal, Sylow
51C24×C13C2×D411yescharacteristic
52C2×Q8×C13—24no—
53C2×Q8×C13—42no—
54C2×Q8×C13—42no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13SD1612yes—
69C22×C4×C13Q1612yes—
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D412yes—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13#4112yes—
74C22×Dic13—24no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C22×Dic13—42no—
78C22×Dic13—42no—
79C22×Dic13—42no—
80C22×Dic13—42no—
81C13×C4⋊C4—24no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—42no—
88C13×C22⋊C4—44no—
89C42×C13—22no—
90C42×C13—22no—
91C42×C13—41no—
92C42×C13—41no—
93C2×#1055—42no—
94C2×#1055—42no—
95C2×#1055—42no—
96#2857D1311yescharacteristic
97#1797—131no—
98C2×#328—134no—
99#1434—131no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13#12112yes—
106C23×C13C2×SD1611yescharacteristic
107C23×C13C2×Q1611yescharacteristic
108C23×C13#13712yes—
109Q8×C13—84no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—44no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13#9912yes—
135C2×C4×C13#10312yes—
136C2×C4×C13#10312yes—
137C2×C4×C13C4×D412yes—
138C2×C4×C13#12411yescharacteristic
139C2×C4×C13#12711yescharacteristic
140C2×Dic13—44no—
141C2×Dic13—44no—
142C2×Dic13—44no—
143C2×Dic13—82no—
144C2×Dic13—82no—
145C2×Dic13—82no—
146C2×Dic13—82no—
147#1055—82no—
148C2×C4⋊Q8Dic1311yescharacteristic, complemented
149C2×C22⋊Q8C2×D1312yes—
150C22×C42C2×D1311yescharacteristic
151C2×C4⋊C8—261no—
152C2×C22⋊C8—132no—
153#391Dic1312yescomplemented
154#389—21no—
155#389—21no—
156#384Dic1311yescharacteristic, complemented
157#380—21no—
158#380—21no—
159C2×#95—132no—
160C2×#95—261no—
161C2×#95—261no—
162#336—261no—
163#328—268no—
164C22×C13—22no—
165C22×C13—22no—
166C22×C13—22no—
167C22×C13—22no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13#39011yescharacteristic
173C22×C13C2×#9911yescharacteristic
174C22×C13#41011yescharacteristic
175C22×C13C2×#10311yescharacteristic
176C22×C13#41911yescharacteristic
177C22×C13#42111yescharacteristic
178C22×C13#42111yescharacteristic
179C22×C13#46112yes—
180C22×C13#46212yes—
181C4×C13—21no—
182C4×C13—22no—
183C4×C13—21no—
184C4×C13—22no—
185C4×C13—22no—
186C4×C13—22no—
187C4×C13—41no—
188C4×C13—82no—
189C4×C13—82no—
190Dic13—84no—
191C22×Q8C2×Dic1312yes—
192C23×C4—262no—
193C23×C4C22⋊D1311yescharacteristic
194C23×C4C22⋊D1311yescharacteristic
195C23×C4C22×D1311yescharacteristic
196C22×C8—262no—
197C4⋊Q8—42no—
198C22⋊Q8—24no—
199C22⋊Q8—24no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4C2×Dic1312yes—
206C2×C22⋊C4—22no—
207C2×C42—42no—
208C2×C42C2×Dic1311yescharacteristic
209C2×C42C2×Dic1311yescharacteristic
210C2×C42C22⋊D1311yescharacteristic
211C2×C42C22⋊D1311yescharacteristic
212C4⋊C8—522no—
213C22⋊C8—264no—
214#95—22no—
215#95—22no—
216#95—134no—
217#95—262no—
218#95—522no—
219#95—522no—
220C2×C13—22no—
221C2×C13—22no—
222C2×C13#151111yescharacteristic
223C2×C13#151511yescharacteristic
224C2×C13#151811yescharacteristic
225C2×C13#152011yescharacteristic
226C2×C13#196311yescharacteristic
227C2×C13#196411yescharacteristic
228C2×C13#198111yescharacteristic
229C24C2×C22⋊D1311yescharacteristic
230C2×Q8—24no—
231C2×Q8—42no—
232C2×Q8—42no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—264no—
243C22×C4—522no—
244C22×C4—522no—
245C22×C4—522no—
246C22×C4—522no—
247C22×C4—522no—
248C22×C4—522no—
249C22×C4#610612yes—
250C22×C4#610712yes—
251C22×C4C22⋊Dic1311yescharacteristic
252C22×C4C22⋊Dic1311yescharacteristic
253C22×C4C22⋊Dic1311yescharacteristic
254C22×C4C22⋊Dic1311yescharacteristic
255C22×C4D4×D1312yes—
256C22×C4#612912yes—
257C22×C4C22×Dic1311yescharacteristic
258C22×C4C2×C22⋊D1311yescharacteristic
259C2×C8—522no—
260C2×C8—522no—
261C2×C8—522no—
262C4⋊C4—24no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C22⋊C4—44no—
270C42—22no—
271C42—22no—
272C42—41no—
273C42—41no—
274C13#971411yescharacteristic, complemented, Sylow
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23#8819212yes—
280C23C2×#610611yescharacteristic
281C23#8819612yes—
282C23C2×#610711yescharacteristic
283C23C2×C22⋊Dic1311yescharacteristic
284Q8—84no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—44no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—524no—
310C2×C4—524no—
311C2×C4—524no—
312C2×C4—1042no—
313C2×C4—1042no—
314C2×C4—1042no—
315C2×C4—1042no—
316C2×C4#8807412yes—
317C2×C4#8807512yes—
318C2×C4#8807512yes—
319C2×C4D4×Dic1312yes—
320C2×C4#8819011yescharacteristic
321C2×C4#8819411yescharacteristic
322C8—1042no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—22no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22#1171874412yes—
332C22#1171875112yes—
333C22C2×#8807411yescharacteristic
334C22#1171888211yescharacteristic
335C22C2×#8807511yescharacteristic
336C22#1171888611yescharacteristic
337C22#1171889711yescharacteristic
338C22#1171889711yescharacteristic
339C22#1171890111yescharacteristic
340C4—22no—
341C4—21no—
342C4—22no—
343C4—21no—
344C4—22no—
345C4—22no—
346C4—41no—
347C4—82no—
348C4—82no—
349C4—1044no—
350C2—22no—
351C2—22no—
352C2#1311336911yescharacteristic
353C2#1311338711yescharacteristic
354C2#1311340011yescharacteristic
355C2#1311340811yescharacteristic
356C2#1311566911yescharacteristic
357C2#1311567311yescharacteristic
358C2#1311576011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2857C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2857D13
hypocenterC13#9714
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
5. C2×C13×C4⋊Q8C4semidirect
8. C13×#391C4semidirect
11. C13×#384C4semidirect
148. C2×C4⋊Q8Dic13semidirect
153. #391Dic13semidirect
156. #384Dic13semidirect
274. C13#9714semidirect

Maximal subgroups

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

subgroupindex
#131148162
C2×#117181302
#131130632
C13×#28572
#971413