Finite Group Databasebeta

← #15751229

Subgroups — #15751229

Order 3328.

500 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114904C211yesmaximal, characteristic
2#13114816C211yesmaximal, characteristic
3#13112662C212yesmaximal, complemented
4#13112659C212yesmaximal, complemented
5C4×C13×C22⋊Q8C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C2×C4×Q8×C13C411yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C13×#391C2211yescharacteristic
10C13×#389C2211yescharacteristic
11C13×#387—21no—
12C13×#385—21no—
13C13×#380C411yescharacteristic
14C4×C13×C4⋊C4—21no—
15C4×C13×C4⋊C4C411yescharacteristic
16C4×C13×C22⋊C4—21no—
17C2×C22⋊#1055—21no—
18C2×C22⋊#1055—21no—
19C2×C4⋊#1055—21no—
20#11718116—21no—
21#11718116C2212yes—
22#11718116C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C22⋊Q8—22no—
28C13×C22⋊Q8—22no—
29C4×Q8×C13—42no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C42×C13—21no—
39C2×C42×C13—21no—
40C2×C42×C13—42no—
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×C42×C13C2311yescharacteristic
45C22×#1055—22no—
46C22×#1055—22no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C22⋊#1055—42no—
53C22⋊#1055—42no—
54C4⋊#1055—42no—
55#7648—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C2×Q8×C13—21no—
58C2×Q8×C13—41no—
59C2×Q8×C13—41no—
60C2×Q8×C13M1612yes—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13SD1612yes—
78C22×C4×C13Q1612yes—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C13×C4⋊C4—24no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4M1612yes—
89C13×C22⋊C4—24no—
90C13×C22⋊C4—42no—
91C42×C13—22no—
92C42×C13—22no—
93C42×C13—41no—
94C42×C13—41no—
95C42×C13—42no—
96C42×C13—42no—
97C2×#1055—42no—
98C2×#1055—42no—
99C2×#1055—42no—
100C2×#1055—42no—
101C2×#1055—42no—
102C2×#1055—42no—
103C4×C22⋊Q8D1311yescharacteristic
104#1817—131no—
105#1797—131no—
106#1272—132no—
107#1271—132no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13#10312yes—
115C23×C13C2×C22⋊C411yescharacteristic
116Q8×C13—42no—
117Q8×C13—42no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—44no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13#9912yes—
149C2×C4×C13#10312yes—
150C2×C4×C13C2×M1611yescharacteristic
151C2×C4×C13C2×M1611yescharacteristic
152C2×C4×C13C2×SD1611yescharacteristic
153C2×C4×C13C2×Q1611yescharacteristic
154C2×C4×C13#13512yes—
155#1055—82no—
156#1055—82no—
157C2×C22⋊Q8Dic1311yescharacteristic
158C2×C4×Q8Dic1311yescharacteristic
159C22×C42C2×D1311yescharacteristic
160C2×C4⋊C8—261no—
161C2×C22⋊C8—261no—
162C2×C22⋊C8—261no—
163#391C2×D1311yescharacteristic
164#389C2×D1311yescharacteristic
165#387—21no—
166#385—21no—
167#380Dic1311yescharacteristic
168C4×C4⋊C4—21no—
169C4×C4⋊C4Dic1311yescharacteristic
170C4×C22⋊C4—21no—
171#336—132no—
172#336—132no—
173#336—261no—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13#40711yescharacteristic
182C22×C13C2×#9911yescharacteristic
183C22×C13#41311yescharacteristic
184C22×C13C2×#10311yescharacteristic
185C22×C13#41611yescharacteristic
186C22×C13#42111yescharacteristic
187C22×C13#42111yescharacteristic
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—22no—
191C4×C13—22no—
192C4×C13—21no—
193C4×C13—22no—
194C4×C13—21no—
195C4×C13—41no—
196C4×C13—42no—
197C4×C13—42no—
198C4×C13—81no—
199C4×C13—81no—
200C22×Q8C2×Dic1311yescharacteristic
201C23×C4C2×Dic1311yescharacteristic
202C23×C4C22⋊D1311yescharacteristic
203C23×C4C22⋊D1311yescharacteristic
204C22×C8—262no—
205C22×C8—262no—
206C22⋊Q8—22no—
207C22⋊Q8—22no—
208C4×Q8—42no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4C2×Dic1311yescharacteristic
213C2×C4⋊C4C2×Dic1311yescharacteristic
214C2×C4⋊C4C2×Dic1311yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—42no—
220C2×C42C2×Dic1311yescharacteristic
221C2×C42C22⋊D1311yescharacteristic
222C2×C42C22⋊D1311yescharacteristic
223C2×C42C22×D1311yescharacteristic
224C4⋊C8—522no—
225C22⋊C8—522no—
226C22⋊C8—522no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232C2×C13—42no—
233C2×C13#146511yescharacteristic
234C2×C13#148711yescharacteristic
235C2×C13#148811yescharacteristic
236C2×C13#151611yescharacteristic
237C2×C13#152011yescharacteristic
238C2×C13#153511yescharacteristic
239C2×C13#154211yescharacteristic
240C24C22⋊Dic1311yescharacteristic
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8#609912yes—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4#610612yes—
259C22×C4#610712yes—
260C22×C4C22⋊Dic1311yescharacteristic
261C22×C4C22⋊Dic1311yescharacteristic
262C22×C4C22⋊Dic1311yescharacteristic
263C22×C4C22×Dic1311yescharacteristic
264C22×C4C2×C22⋊D1311yescharacteristic
265C22×C4C2×C22⋊D1311yescharacteristic
266C2×C8—522no—
267C2×C8—522no—
268C2×C8—522no—
269C2×C8—522no—
270C2×C8—522no—
271C2×C8—522no—
272C4⋊C4—24no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4#609912yes—
279C22⋊C4—24no—
280C22⋊C4—42no—
281C42—22no—
282C42—22no—
283C42—41no—
284C42—41no—
285C42—42no—
286C42—42no—
287C13#764811yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23#8807512yes—
295C23C2×C22⋊Dic1311yescharacteristic
296Q8—42no—
297Q8—42no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4#8807412yes—
329C2×C4#8807512yes—
330C2×C4C2×#609911yescharacteristic
331C2×C4C2×#609911yescharacteristic
332C2×C4C2×#610611yescharacteristic
333C2×C4C2×#610711yescharacteristic
334C2×C4#8820412yes—
335C8—1042no—
336C8—1042no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22#1171886811yescharacteristic
345C22C2×#8807411yescharacteristic
346C22C2×#8807511yescharacteristic
347C22#1171889411yescharacteristic
348C22#1171889711yescharacteristic
349C22#1171889711yescharacteristic
350C22#1171889811yescharacteristic
351C4—22no—
352C4—22no—
353C4—21no—
354C4—22no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—41no—
359C4—42no—
360C4—42no—
361C4—81no—
362C4—81no—
363C2—42no—
364C2#1311317411yescharacteristic
365C2#1311326511yescharacteristic
366C2#1311327011yescharacteristic
367C2#1311339211yescharacteristic
368C2#1311340811yescharacteristic
369C2#1311346711yescharacteristic
370C2#1311349311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC4×C13×C22⋊Q8C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenterC4×C22⋊Q8D13
hypocenterC13#7648
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #13112662C2semidirect
4. #13112659C2semidirect
287. C13#7648semidirect

Maximal subgroups

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

subgroupindex
#131149042
#131148162
#131126622
#131126592
C4×C13×C22⋊Q82
#764813