Finite Group Databasebeta

← #15755896

Subgroups — #15755896

Order 3328.

456 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114874C211yesmaximal, characteristic, complemented
2#13114865C211yesmaximal, characteristic, complemented
3#13113379C212yesmaximal
4#13112741C212yesmaximal, complemented
5C13×#2929C211yesmaximal, characteristic
6C2×C13×#131C411yescharacteristic, complemented
7C23×C8×C13C2211yescharacteristic
8C13×#525C2211yescharacteristic
9C13×#435—21no—
10C13×#435—21no—
11C8×D4×C13—21no—
12C8×D4×C13—21no—
13C13×#424C411yescharacteristic, complemented
14C13×#408C411yescharacteristic, complemented
15C13×#407C2211yescharacteristic
16C13×#405C411yescharacteristic, complemented
17#11718873C2212yes—
18#11718868C2212yes—
19C2×#88059—21no—
20C2×#88058—21no—
21#11718144—21no—
22#11718143—21no—
23#11718130—22no—
24#11718129—22no—
25C2×C13×#41C2×C411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C13×#131—42no—
28C2×C13×M16—21no—
29C2×C13×M16C2×C411yescharacteristic
30C2×C13×M16C2×C411yescharacteristic
31C22×C8×C13—21no—
32C22×C8×C13—42no—
33C22×C8×C13C2×C411yescharacteristic
34C22×C8×C13C2×C411yescharacteristic
35C22×C8×C13D411yescharacteristic
36C22×C8×C13D411yescharacteristic
37C22×C8×C13D411yescharacteristic
38C22×C8×C13D411yescharacteristic
39C13×#123—21no—
40C13×C22⋊Q8D411yescharacteristic
41C13×C22⋊Q8Q811yescharacteristic
42C13×#121D411yescharacteristic
43C13×#121Q811yescharacteristic
44C13×#120—21no—
45C4×D4×C13—21no—
46C4×D4×C13—21no—
47C13×#117C2×C411yescharacteristic
48C2×C22⋊Dic13—22no—
49C2×C4⋊Dic13—22no—
50C2×#6099—22no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C22⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×C22⋊C8—21no—
57C13×#97—21no—
58C4×C8×C13—21no—
59#88071—22no—
60C22⋊#1055—22no—
61C22⋊#1055—22no—
62#88059—42no—
63#88058—42no—
64#8627—131nomaximal, Sylow
65C24×C13#4111yescharacteristic
66C13×#41—41no—
67C13×#41—41no—
68C2×Q8×C13C4⋊C411yescharacteristic
69C2×D4×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13—21no—
72C2×D4×C13C4⋊C411yescharacteristic
73C22×C4×C13—21no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×Q811yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C22×Dic13—42no—
83C13×M16—42no—
84C13×M16—41no—
85C13×M16—41no—
86C2×C8×C13—22no—
87C2×C8×C13—22no—
88C2×C8×C13—22no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—41no—
92C2×C8×C13—41no—
93C2×C8×C13—41no—
94C2×C8×C13—42no—
95C2×C8×C13C22⋊C411yescharacteristic
96C2×C8×C13C22⋊C411yescharacteristic
97C2×C8×C13C22⋊C411yescharacteristic
98C2×C8×C13C22⋊C411yescharacteristic
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4C4⋊C411yescharacteristic
102C13×C4⋊C4C4⋊C411yescharacteristic
103C13×C22⋊C4—21no—
104C13×C22⋊C4—21no—
105C13×C22⋊C4—21no—
106C13×C22⋊C4—21no—
107C13×C22⋊C4—21no—
108C42×C13—21no—
109C22⋊Dic13—82no—
110C4⋊Dic13—42no—
111C4⋊Dic13—42no—
112#6099—42no—
113#6099—42no—
114C2×#1055—42no—
115#2929D1311yescharacteristic
116#1810—131no—
117#1808—131no—
118#1513—132no—
119#1305—132no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13#11711yescharacteristic
126C23×C13#12111yescharacteristic
127C23×C13C22⋊Q811yescharacteristic
128Q8×C13—41no—
129D4×C13—41no—
130D4×C13—42no—
131D4×C13—42no—
132D4×C13—41no—
133D4×C13—41no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13C2×C22⋊C411yescharacteristic
149C2×C4×C13C2×C4⋊C411yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13C22⋊Q811yescharacteristic
152C2×Dic13—82no—
153C2×Dic13—82no—
154C2×Dic13—82no—
155C8×C13—21no—
156C8×C13—21no—
157C8×C13—21no—
158C8×C13—41no—
159C8×C13—41no—
160C8×C13#9912yes—
161#1055—82no—
162C2×#131Dic1311yescharacteristic, complemented
163C23×C8C2×D1311yescharacteristic
164#525C2×D1311yescharacteristic
165#435—21no—
166#435—21no—
167C8×D4—21no—
168C8×D4—21no—
169C2×#108—261no—
170C2×#107—261no—
171#424Dic1311yescharacteristic, complemented
172#408Dic1311yescharacteristic, complemented
173#407—132no—
174#407C2×D1311yescharacteristic
175#405Dic1311yescharacteristic, complemented
176#380—132no—
177#341—261no—
178#340—261no—
179#328—262no—
180#327—262no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—42no—
190C22×C13—42no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13#38011yescharacteristic
195C22×C13#47211yescharacteristic
196C22×C13#47311yescharacteristic
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13—41no—
203C4×C13C2×#9911yescharacteristic
204C4×C13#41011yescharacteristic
205Dic13—162no—
206C2×#41C2×Dic1311yescharacteristic
207C23×C4C22×D1311yescharacteristic
208#131—42no—
209C2×M16—21no—
210C2×M16—262no—
211C2×M16C2×Dic1311yescharacteristic
212C2×M16C2×Dic1311yescharacteristic
213C22×C8—21no—
214C22×C8—42no—
215C22×C8C2×Dic1311yescharacteristic
216C22×C8C2×Dic1311yescharacteristic
217C22×C8C22⋊D1311yescharacteristic
218C22×C8C22⋊D1311yescharacteristic
219C22×C8C22⋊D1311yescharacteristic
220C22×C8C22⋊D1311yescharacteristic
221#123—21no—
222C22⋊Q8Dic2611yescharacteristic
223C22⋊Q8D5211yescharacteristic
224#121Dic2611yescharacteristic
225#121D5211yescharacteristic
226#120—21no—
227C4×D4—21no—
228C4×D4—21no—
229#117C2×Dic1311yescharacteristic
230C2×C4⋊C4—262no—
231C2×C22⋊C4—262no—
232#108—522no—
233#107—522no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8—21no—
239C22⋊C8—21no—
240C22⋊C8—262no—
241C22⋊C8—262no—
242#97—21no—
243C4×C8—21no—
244#95—262no—
245C2×C13—21no—
246C2×C13—21no—
247C2×C13—41no—
248C2×C13—41no—
249C2×C13—81no—
250C2×C13#179911yescharacteristic
251C2×C13#181411yescharacteristic
252C2×C13#181611yescharacteristic
253C24#612711yescharacteristic
254#41—41no—
255#41—41no—
256C2×Q8C4⋊Dic1311yescharacteristic
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4C4⋊Dic1311yescharacteristic
261C22×C4—21no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—522no—
265C22×C4C2×Dic2611yescharacteristic
266C22×C4C2×D5211yescharacteristic
267C22×C4#612711yescharacteristic
268C22×C4C22×Dic1311yescharacteristic
269C22×C4C2×C22⋊D1311yescharacteristic
270C22×C4C2×C22⋊D1311yescharacteristic
271M16—42no—
272M16—41no—
273M16—41no—
274M16—522no—
275M16—522no—
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—42no—
285C2×C8—522no—
286C2×C8C22⋊Dic1311yescharacteristic
287C2×C8C22⋊Dic1311yescharacteristic
288C2×C8C22⋊Dic1311yescharacteristic
289C2×C8C22⋊Dic1311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—522no—
293C4⋊C4—522no—
294C4⋊C4C4⋊Dic1311yescharacteristic
295C4⋊C4C4⋊Dic1311yescharacteristic
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1042no—
302C42—21no—
303C13#862711yescharacteristic, complemented, Sylow
304C23—21no—
305C23—21no—
306C23—21no—
307C23—41no—
308C23—41no—
309C23#8817811yescharacteristic
310C23#8818011yescharacteristic
311C23#8818411yescharacteristic
312Q8—41no—
313D4—41no—
314D4—42no—
315D4—42no—
316D4—41no—
317D4—41no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—1042no—
333C2×C4—1042no—
334C2×C4—1042no—
335C2×C4#8817811yescharacteristic
336C2×C4C2×C4⋊Dic1311yescharacteristic
337C2×C4#8818411yescharacteristic
338C2×C4C2×C22⋊Dic1311yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—41no—
343C8—41no—
344C8—1042no—
345C8#8807412yes—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—42no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22#1171880311yescharacteristic
360C22#1171880411yescharacteristic
361C22#1171887311yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—2082no—
369C4C2×#8807411yescharacteristic
370C4#1171890111yescharacteristic
371C2—21no—
372C2—21no—
373C2—41no—
374C2—41no—
375C2—81no—
376C2#1311482411yescharacteristic
377C2#1311489011yescharacteristic
378C2#1311490011yescharacteristic
subgroupG/H
centerC22#11718873
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2929C2
socleC22×C13#380
prime radicalC13×#525C22
cosocleC23×C4×C13C23
hypercenter#2929D13
hypocenterC13#8627
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. #13114874C2semidirect
2. #13114865C2semidirect
4. #13112741C2semidirect
6. C2×C13×#131C4semidirect
13. C13×#424C4semidirect
14. C13×#408C4semidirect
16. C13×#405C4semidirect
162. C2×#131Dic13semidirect
171. #424Dic13semidirect
172. #408Dic13semidirect
175. #405Dic13semidirect
303. C13#8627semidirect

Maximal subgroups

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

subgroupindex
#131148742
#131148652
#131133792
#131127412
C13×#29292
#862713