Finite Group Databasebeta

← #15778939

Subgroups — #15778939

Order 3328.

420 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#13116477C212yesmaximal
2#13114886C211yesmaximal, characteristic, complemented
3#13114882C211yesmaximal, characteristic, complemented
4#13112965C212yesmaximal, complemented
5C13×#2930C211yesmaximal, characteristic
6C2×C13×#131C2211yescharacteristic
7C22×C13×M16C411yescharacteristic, complemented
8C13×#525C2211yescharacteristic
9C13×#436—21no—
10C13×#436—21no—
11C13×#435—21no—
12C13×#435—21no—
13C13×#424C411yescharacteristic, complemented
14C13×#408C2211yescharacteristic
15C13×#407C411yescharacteristic, complemented
16C13×#405C411yescharacteristic, complemented
17#11718901C2212yes—
18#11718898C2212yes—
19C2×#88059—21no—
20#11718767—21no—
21#11718152—21no—
22#11718149—21no—
23#11718131—22no—
24#11718128—22no—
25C2×C13×#41C2311yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C13×#131—41no—
28C13×#131—41no—
29C2×C13×M16—21no—
30C2×C13×M16—21no—
31C2×C13×M16—41no—
32C2×C13×M16—41no—
33C2×C13×M16C2×C411yescharacteristic
34C2×C13×M16C2×C411yescharacteristic
35C2×C13×M16D411yescharacteristic
36C2×C13×M16D411yescharacteristic
37C22×C8×C13C2×C411yescharacteristic
38C22×C8×C13C2×C411yescharacteristic
39C22×C8×C13D411yescharacteristic
40C22×C8×C13D411yescharacteristic
41C13×#123D411yescharacteristic
42C13×#123Q811yescharacteristic
43C13×C22⋊Q8—21no—
44C13×#121—21no—
45C13×#120D411yescharacteristic
46C13×#120Q811yescharacteristic
47C4×D4×C13—21no—
48C4×D4×C13—21no—
49C13×#117C2×C411yescharacteristic
50#88180—22no—
51C2×#6099—22no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C22⋊C8—21no—
55C13×C22⋊C8—21no—
56C13×C22⋊C8—21no—
57C13×C22⋊C8—21no—
58C13×#97—21no—
59C4×C8×C13—21no—
60#88076—22no—
61#88074—22no—
62#88074—22no—
63#88073—22no—
64#88059—41no—
65#88059—41no—
66#88058—41no—
67#88057—41no—
68#12806—131nomaximal, Sylow
69C24×C13C4⋊C411yescharacteristic
70C13×#41—41no—
71C13×#41—41no—
72C2×Q8×C13#4111yescharacteristic
73C2×D4×C13—21no—
74C2×D4×C13—21no—
75C2×D4×C13C2×D411yescharacteristic
76C2×D4×C13C2×Q811yescharacteristic
77C2×D4×C13#4111yescharacteristic
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13C4⋊C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C13×M16—41no—
87C13×M16—41no—
88C13×M16—41no—
89C13×M16—42no—
90C13×M16—41no—
91C13×M16—41no—
92C13×M16—41no—
93C2×C8×C13—21no—
94C2×C8×C13—21no—
95C2×C8×C13—21no—
96C2×C8×C13—21no—
97C2×C8×C13—21no—
98C2×C8×C13—21no—
99C2×C8×C13—21no—
100C2×C8×C13—21no—
101C2×C8×C13—41no—
102C2×C8×C13C22⋊C411yescharacteristic
103C2×C8×C13C22⋊C411yescharacteristic
104C2×C8×C13C22⋊C411yescharacteristic
105C2×C8×C13C22⋊C411yescharacteristic
106C13×C4⋊C4—21no—
107C13×C4⋊C4—21no—
108C13×C4⋊C4—21no—
109C13×C22⋊C4—21no—
110C13×C22⋊C4—21no—
111C13×C22⋊C4—21no—
112C13×C22⋊C4—21no—
113C13×C22⋊C4C4⋊C411yescharacteristic
114C13×C22⋊C4C4⋊C411yescharacteristic
115C42×C13—21no—
116C22⋊Dic13—42no—
117C4⋊Dic13—42no—
118C4×Dic13—42no—
119#6099—42no—
120#6099—42no—
121C2×#1055—42no—
122#2930D1311yescharacteristic
123#2120—132no—
124#1813—131no—
125#1812—131no—
126#1395—132no—
127C23×C13—21no—
128C23×C13—41no—
129C23×C13—81no—
130C23×C13C2×C4⋊C411yescharacteristic
131C23×C13#12111yescharacteristic
132C23×C13C22⋊Q811yescharacteristic
133Q8×C13—41no—
134D4×C13—41no—
135D4×C13—41no—
136D4×C13—41no—
137D4×C13—81no—
138D4×C13—81no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—42no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13C2×C22⋊C411yescharacteristic
153C2×C4×C13#11711yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13C22⋊Q811yescharacteristic
156C2×Dic13—82no—
157C8×C13—21no—
158C8×C13—21no—
159C8×C13—21no—
160C8×C13—41no—
161C8×C13—41no—
162C8×C13#9911yescharacteristic
163C8×C13#9911yescharacteristic
164#1055—82no—
165C2×#131C2×D1311yescharacteristic
166C22×M16Dic1311yescharacteristic, complemented
167#525C2×D1311yescharacteristic
168#436—21no—
169#436—21no—
170#435—21no—
171#435—21no—
172C2×#108—261no—
173#427—261no—
174#424Dic1311yescharacteristic, complemented
175#413—132no—
176#410—132no—
177#408C2×D1311yescharacteristic
178#407Dic1311yescharacteristic, complemented
179#405Dic1311yescharacteristic, complemented
180#352—262no—
181AΣL(1,𝔽16)—262no—
182#338—261no—
183H(3,ℤ/4)—261no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—82no—
194C22×C13#38011yescharacteristic
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13C2×#9911yescharacteristic
202C4×C13#41011yescharacteristic
203Dic13—162no—
204C2×#41C22×D1311yescharacteristic
205C23×C4C2×Dic1311yescharacteristic
206#131—41no—
207#131—41no—
208C2×M16—21no—
209C2×M16—21no—
210C2×M16—41no—
211C2×M16—41no—
212C2×M16—262no—
213C2×M16C2×Dic1311yescharacteristic
214C2×M16C2×Dic1311yescharacteristic
215C2×M16C22⋊D1311yescharacteristic
216C2×M16C22⋊D1311yescharacteristic
217C22×C8C2×Dic1311yescharacteristic
218C22×C8C2×Dic1311yescharacteristic
219C22×C8C22⋊D1311yescharacteristic
220C22×C8C22⋊D1311yescharacteristic
221#123Dic2611yescharacteristic
222#123D5211yescharacteristic
223C22⋊Q8—21no—
224#121—21no—
225#120Dic2611yescharacteristic
226#120D5211yescharacteristic
227C4×D4—21no—
228C4×D4—21no—
229#117—262no—
230#117C2×Dic1311yescharacteristic
231#108—521no—
232#108—521no—
233#107—521no—
234#106—521no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237#101—262no—
238#100—262no—
239#99—262no—
240#99—262no—
241C22⋊C8—21no—
242C22⋊C8—21no—
243C22⋊C8—21no—
244C22⋊C8—21no—
245#97—21no—
246C4×C8—21no—
247C2×C13—21no—
248C2×C13—41no—
249C2×C13—41no—
250C2×C13—41no—
251C2×C13—81no—
252C2×C13#179911yescharacteristic
253C24C4⋊Dic1311yescharacteristic
254#41—41no—
255#41—41no—
256C2×Q8#612711yescharacteristic
257C2×D4—21no—
258C2×D4—21no—
259C2×D4C2×Dic2611yescharacteristic
260C2×D4C2×D5211yescharacteristic
261C2×D4#612711yescharacteristic
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4C4⋊Dic1311yescharacteristic
267C22×C4C22×Dic1311yescharacteristic
268C22×C4C2×C22⋊D1311yescharacteristic
269C22×C4C2×C22⋊D1311yescharacteristic
270M16—41no—
271M16—41no—
272M16—41no—
273M16—42no—
274M16—41no—
275M16—41no—
276M16—41no—
277M16—522no—
278M16—522no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—41no—
288C2×C8—522no—
289C2×C8C22⋊Dic1311yescharacteristic
290C2×C8C22⋊Dic1311yescharacteristic
291C2×C8C22⋊Dic1311yescharacteristic
292C2×C8C22⋊Dic1311yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—522no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—522no—
302C22⋊C4C4⋊Dic1311yescharacteristic
303C22⋊C4C4⋊Dic1311yescharacteristic
304C42—21no—
305C42—522no—
306C13#1280611yescharacteristic, complemented, Sylow
307C23—21no—
308C23—41no—
309C23—81no—
310C23#8817811yescharacteristic
311C23C2×C4⋊Dic1311yescharacteristic
312C23#8818411yescharacteristic
313Q8—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
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—21no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—1042no—
333C2×C4#8817811yescharacteristic
334C2×C4#8818011yescharacteristic
335C2×C4#8818411yescharacteristic
336C2×C4C2×C22⋊Dic1311yescharacteristic
337C8—21no—
338C8—21no—
339C8—21no—
340C8—41no—
341C8—41no—
342C8—1042no—
343C8#8807411yescharacteristic
344C8#8807411yescharacteristic
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—82no—
355C22#1171887311yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—41no—
362C4—2082no—
363C4C2×#8807411yescharacteristic
364C4#1171890111yescharacteristic
365C2—21no—
366C2—41no—
367C2—41no—
368C2—41no—
369C2—81no—
370C2#1311482411yescharacteristic
subgroupG/H
centerC4#11718901
commutatorC22×C4×C13C22×C4
FrattiniC2×#41C22×D13
FittingC13×#2930C2
socleC2×C13#1799
prime radicalC13×#525C22
cosocleC2×C13×#41C23
hypercenter#2930D13
hypocenterC13#12806
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×#131 ◁ #2930

Complements

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

NH ≅ G/Ntype
2. #13114886C2semidirect
3. #13114882C2semidirect
4. #13112965C2semidirect
7. C22×C13×M16C4semidirect
13. C13×#424C4semidirect
15. C13×#407C4semidirect
16. C13×#405C4semidirect
166. C22×M16Dic13semidirect
174. #424Dic13semidirect
178. #407Dic13semidirect
179. #405Dic13semidirect
306. C13#12806semidirect

Maximal subgroups

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

subgroupindex
#131164772
#131148862
#131148822
#131129652
C13×#29302
#1280613