Finite Group Databasebeta

← #15757235

Subgroups — #15757235

Order 3328.

438 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123404C211yesmaximal, characteristic
2#13114856C211yesmaximal, characteristic
3#13113607C211yesmaximal, characteristic, complemented
4#13113592C211yesmaximal, characteristic, complemented
5#13112738C211yesmaximal, characteristic, complemented
6#13112676C211yesmaximal, characteristic, complemented
7C13×#1476C211yesmaximal, characteristic
8C4×C13×#41C2211yescharacteristic
9C2×#88202—21no—
10C13×#431C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C2×#88077—21no—
13#11718660—22no—
14#11718660—21no—
15C4×C4⋊Dic13C2211yescharacteristic
16#11718585—21no—
17#11718585C2211yescharacteristic
18#11718585C2211yescharacteristic
19C2×C4⋊#1055—21no—
20C2×C4⋊#1055C2211yescharacteristic
21C13×Q8⋊C8C411yescharacteristic, complemented
22C13×Q8⋊C8C411yescharacteristic, complemented
23C13×D4⋊C8C411yescharacteristic, complemented
24C13×D4⋊C8C411yescharacteristic, complemented
25#11718124—21no—
26#11718049—21no—
27#11718049—21no—
28#11718049—22no—
29C2×C13×#41D411yescharacteristic
30C22×C8×C13—21no—
31C4×Q8×C13C2×C411yescharacteristic
32C4×Q8×C13Q811yescharacteristic
33C4×D4×C13—21no—
34C4×D4×C13—21no—
35C4×D4×C13C2×C411yescharacteristic
36C4×D4×C13Q811yescharacteristic
37C13×#117—21no—
38C13×#117D411yescharacteristic
39C2×C42×C13—21no—
40C2×C42×C13C2311yescharacteristic
41#88202—42no—
42#88202—42no—
43C2×C4⋊Dic13—21no—
44C2×C4×Dic13—21no—
45C2×#6099—22no—
46C2×#6099—21no—
47C2×#6099—21no—
48C22×#1055—22no—
49C22×#1055—21no—
50C13×C4⋊C8C2×C411yescharacteristic
51C13×C4⋊C8C2×C411yescharacteristic
52C13×C22⋊C8—21no—
53C4×C8×C13—21no—
54C4×C8×C13—21no—
55C4×C8×C13C2×C411yescharacteristic
56C4×C8×C13C2×C411yescharacteristic
57#88077—42no—
58#88071—21no—
59C4⋊#1055—22no—
60C4⋊#1055—22no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055D412yes—
66C4⋊#1055D411yescharacteristic
67C4⋊#1055D411yescharacteristic
68#8904—131nomaximal, Sylow
69C13×#41—21no—
70C13×#41—21no—
71C13×#41SD1612yes—
72C13×#41SD1612yes—
73C2×Q8×C13C4⋊C411yescharacteristic
74C2×D4×C13—21no—
75C2×D4×C13C4⋊C411yescharacteristic
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C22×Dic13—41no—
83C2×C8×C13—21no—
84C2×C8×C13—21no—
85C2×C8×C13—21no—
86C2×C8×C13—21no—
87C2×C8×C13—42no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4C4⋊C411yescharacteristic
91C13×C4⋊C4C4⋊C411yescharacteristic
92C13×C22⋊C4—21no—
93C13×C22⋊C4—21no—
94C13×C22⋊C4—21no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13C22×C411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13C2×Q811yescharacteristic
102C4⋊Dic13—22no—
103C4⋊Dic13—41no—
104C4×Dic13—41no—
105C4×Dic13—41no—
106#6099—44no—
107#6099—41no—
108#6099—41no—
109#6099—41no—
110#6099—41no—
111C2×#1055—21no—
112C2×#1055—22no—
113C2×#1055—21no—
114C2×#1055—44no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055—41no—
118#2906—131no—
119#1806—131no—
120#1570—131no—
121#1566—131no—
122#1476D1311yescharacteristic
123#1303—131no—
124#1279—131no—
125C23×C13—21no—
126C23×C13#12311yescharacteristic
127Q8×C13—21no—
128Q8×C13#10612yes—
129D4×C13—22no—
130D4×C13—22no—
131D4×C13—21no—
132D4×C13#10612yes—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—22no—
137C2×C4×C13—22no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—81no—
144C2×C4×C13C2×C4⋊C411yescharacteristic
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13#12011yescharacteristic
148C2×C4×C13C22⋊Q811yescharacteristic
149C2×C4×C13C22⋊Q811yescharacteristic
150C2×C4×C13C2×SD1611yescharacteristic
151C2×C4×C13C2×SD1611yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13#13711yescharacteristic
154C2×Dic13—42no—
155C2×Dic13—81no—
156C2×Dic13—81no—
157C8×C13—22no—
158C8×C13—41no—
159C8×C13—41no—
160C8×C13—41no—
161#1055—41no—
162#1055—42no—
163#1055—41no—
164#1055—81no—
165C2×#131—261no—
166C4×#41C2×D1311yescharacteristic
167#431C2×D1311yescharacteristic
168#424—262no—
169#424—261no—
170#423—131no—
171#423—131no—
172#423—261no—
173C2×C4⋊C8—131no—
174C2×C4⋊C8—261no—
175C2×#104—261no—
176C2×C4×C8C2×D1311yescharacteristic
177C4×C4⋊C4—131no—
178#339—261no—
179#334—262no—
180#334—261no—
181#334—261no—
182Q8⋊C8Dic1311yescharacteristic, complemented
183Q8⋊C8Dic1311yescharacteristic, complemented
184D4⋊C8Dic1311yescharacteristic, complemented
185D4⋊C8Dic1311yescharacteristic, complemented
186C22×C13—21no—
187C22×C13—21no—
188C22×C13—22no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13#38511yescharacteristic
192C22×C13#48111yescharacteristic
193C22×C13#48311yescharacteristic
194C4×C13—22no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13C2×#10611yescharacteristic
201C4×C13#42811yescharacteristic
202C4×C13#44311yescharacteristic
203C4×C13#44411yescharacteristic
204C4×C13#44811yescharacteristic
205C4×C13#45011yescharacteristic
206Dic13—82no—
207C2×#41D5211yescharacteristic
208#131—522no—
209#131—522no—
210C2×M16—262no—
211C2×M16—261no—
212C2×M16—261no—
213C22×C8—21no—
214C22×C8—262no—
215C22×C8—261no—
216C4×Q8Dic2611yescharacteristic
217C4×Q8C2×Dic1311yescharacteristic
218C4×D4—21no—
219C4×D4—21no—
220C4×D4Dic2611yescharacteristic
221C4×D4C2×Dic1311yescharacteristic
222#117—21no—
223#117D5211yescharacteristic
224C2×C4⋊C4—261no—
225C2×C42—21no—
226C2×C42—261no—
227C2×C42C22×D1311yescharacteristic
228C4⋊C8—131no—
229C4⋊C8—131no—
230C4⋊C8—132no—
231C4⋊C8—262no—
232C4⋊C8—262no—
233C4⋊C8—261no—
234C4⋊C8—261no—
235C4⋊C8—261no—
236C4⋊C8—261no—
237C4⋊C8C2×Dic1311yescharacteristic
238C4⋊C8C2×Dic1311yescharacteristic
239#104—522no—
240C22⋊C8—21no—
241C4×C8—21no—
242C4×C8—21no—
243C4×C8C2×Dic1311yescharacteristic
244C4×C8C2×Dic1311yescharacteristic
245#95—261no—
246C2×C13—21no—
247C2×C13—21no—
248C2×C13—42no—
249C2×C13#185311yescharacteristic
250C2×C13#186111yescharacteristic
251C2×C13#186611yescharacteristic
252#41—21no—
253#41—21no—
254#41#609512yes—
255#41#609512yes—
256C2×Q8C4⋊Dic1311yescharacteristic
257C2×D4—21no—
258C2×D4C4⋊Dic1311yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—521no—
263C22×C4C2×D5211yescharacteristic
264C22×C4#612911yescharacteristic
265C22×C4#612911yescharacteristic
266M16—524no—
267M16—521no—
268M16—521no—
269M16—521no—
270M16—521no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—42no—
276C2×C8—261no—
277C2×C8—261no—
278C2×C8—262no—
279C2×C8—524no—
280C2×C8—521no—
281C2×C8—521no—
282C2×C8—521no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—262no—
286C4⋊C4—521no—
287C4⋊C4C4⋊Dic1311yescharacteristic
288C4⋊C4C4⋊Dic1311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C42—21no—
293C42—21no—
294C42—21no—
295C42—521no—
296C42—521no—
297C42C2×Dic2611yescharacteristic
298C42D4×D1311yescharacteristic
299C42D4×D1311yescharacteristic
300C42C22×Dic1311yescharacteristic
301C13#890411yescharacteristic, complemented, Sylow
302C23—21no—
303C23#8814011yescharacteristic
304Q8—21no—
305Q8#8805712yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4#8805712yes—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—522no—
322C2×C4—1041no—
323C2×C4—1041no—
324C2×C4#8813211yescharacteristic
325C2×C4#8813211yescharacteristic
326C2×C4#8813611yescharacteristic
327C2×C4C2×#609511yescharacteristic
328C2×C4C2×#609511yescharacteristic
329C2×C4#8816211yescharacteristic
330C2×C4#8816311yescharacteristic
331C2×C4C2×C4⋊Dic1311yescharacteristic
332C2×C4D4×Dic1311yescharacteristic
333C2×C4D4×Dic1311yescharacteristic
334C8—22no—
335C8—41no—
336C8—41no—
337C8—41no—
338C8—521no—
339C8—522no—
340C8—521no—
341C8—1041no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22#1171838211yescharacteristic
348C22#1171839611yescharacteristic
349C22#1171861111yescharacteristic
350C4—22no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—1042no—
357C4#1171839211yescharacteristic
358C4#1171839911yescharacteristic
359C4C2×#8805711yescharacteristic
360C4#1171878211yescharacteristic
361C4#1171885711yescharacteristic
362C4#1171885811yescharacteristic
363C2—21no—
364C2—21no—
365C2—42no—
366C2#1311503111yescharacteristic
367C2#1311507811yescharacteristic
368C2#1311511311yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1476C2
socleC22×C13#385
prime radicalC2×C13×#41D4
cosocleC2×C42×C13C23
hypercenter#1476D13
hypocenterC13#8904
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
3. #13113607C2semidirect
4. #13113592C2semidirect
5. #13112738C2semidirect
6. #13112676C2semidirect
21. C13×Q8⋊C8C4semidirect
22. C13×Q8⋊C8C4semidirect
23. C13×D4⋊C8C4semidirect
24. C13×D4⋊C8C4semidirect
182. Q8⋊C8Dic13semidirect
183. Q8⋊C8Dic13semidirect
184. D4⋊C8Dic13semidirect
185. D4⋊C8Dic13semidirect
301. C13#8904semidirect

Maximal subgroups

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

subgroupindex
#131234042
#131148562
#131136072
#131135922
#131127382
#131126762
C13×#14762
#890413