Finite Group Databasebeta

← #15757397

Subgroups — #15757397

Order 3328.

426 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123580C211yesmaximal, characteristic
2#13115612C211yesmaximal, characteristic, complemented
3#13113611C211yesmaximal, characteristic, complemented
4#13113287C211yesmaximal, characteristic
5#13112672C211yesmaximal, characteristic, complemented
6#13112670C211yesmaximal, characteristic, complemented
7C13×#1540C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C2×#88202—21no—
10C13×#431C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12#11718895—21no—
13C2×#88059—21no—
14#11718673—21no—
15#11718672—22no—
16D4×#1055—21no—
17#11718585C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C4×#6099C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21C13×#332C411yescharacteristic
22C13×#332C411yescharacteristic
23C13×#331C411yescharacteristic
24C13×#331C411yescharacteristic
25#11718144—21no—
26D4⋊#1055—22no—
27#11718050—21no—
28#11718050—21no—
29C2×C13×#41—21no—
30C22×C8×C13—21no—
31C13×C4⋊Q8C2×C411yescharacteristic
32C13×#127C2×C411yescharacteristic
33C13×#124—21no—
34C13×#121—21no—
35C13×#121Q812yes—
36C4×D4×C13—21no—
37C4×D4×C13D412yes—
38C2×C42×C13C2311yescharacteristic
39#88202—42no—
40#88202—42no—
41C2×#6099—22no—
42C2×#6099—21no—
43C2×#6099D411yescharacteristic
44C2×#6099D411yescharacteristic
45C22×#1055—22no—
46C22×#1055—21no—
47C22×#1055—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8C2×C411yescharacteristic
50C13×C4⋊C8C2×C411yescharacteristic
51C13×C4⋊C8C2×C411yescharacteristic
52C13×C4⋊C8C2×C411yescharacteristic
53C13×C22⋊C8—21no—
54C4×C8×C13—21no—
55C22⋊#1055—22no—
56C22⋊#1055—22no—
57#88059—42no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055D411yescharacteristic
62C4⋊#1055D411yescharacteristic
63#88043—21no—
64C4×#1055—21no—
65C4×#1055—21no—
66C4×#1055—21no—
67#8930—131nomaximal, Sylow
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—41no—
71C13×#41—41no—
72C2×Q8×C13—21no—
73C2×D4×C13—22no—
74C2×D4×C13—21no—
75C2×D4×C13—21no—
76C2×D4×C13C4⋊C412yes—
77C22×C4×C13—22no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×Q811yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C2×C8×C13—21no—
82C2×C8×C13—21no—
83C2×C8×C13—21no—
84C2×C8×C13—21no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4C4⋊C412yes—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—22no—
91C42×C13C22×C411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13#4111yescharacteristic
95#6099—21no—
96#6099—21no—
97#6099—21no—
98#6099—44no—
99#6099—41no—
100#6099—41no—
101#6099D812yes—
102C2×#1055—21no—
103C2×#1055—22no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055—44no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055—41no—
113#2935—131no—
114#1950—131no—
115#1571—131no—
116#1540D1311yescharacteristic
117#1492—131no—
118#1278—131no—
119#1277—131no—
120C23×C13—22no—
121C23×C13C22⋊Q811yescharacteristic
122Q8×C13—41no—
123Q8×C13—41no—
124D4×C13—42no—
125D4×C13—42no—
126D4×C13—42no—
127D4×C13—41no—
128D4×C13—41no—
129D4×C13—41no—
130D4×C13—41no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—22no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13C2×C4⋊C411yescharacteristic
138C2×C4×C13C4×D411yescharacteristic
139C2×C4×C13C4×D411yescharacteristic
140C2×C4×C13#12011yescharacteristic
141C2×C4×C13C22⋊Q811yescharacteristic
142C2×C4×C13#12311yescharacteristic
143C2×C4×C13C2×D811yescharacteristic
144C2×C4×C13#13511yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13#13711yescharacteristic
147C8×C13—41no—
148C8×C13—41no—
149C8×C13—41no—
150C8×C13—41no—
151#1055—22no—
152#1055—42no—
153#1055—41no—
154#1055—41no—
155#1055—41no—
156#1055—81no—
157C2×#131—261no—
158#532C2×D1311yescharacteristic
159#436—261no—
160#435—262no—
161C8×D4—261no—
162#431C2×D1311yescharacteristic
163C2×#108—261no—
164#423—131no—
165C2×C4⋊C8—131no—
166C2×C4⋊C8C2×D1311yescharacteristic
167#408—261no—
168C4×M16—131no—
169C2×C4×C8—131no—
170#341—261no—
171#335—261no—
172#335—261no—
173#332Dic1311yescharacteristic
174#332Dic1311yescharacteristic
175#331Dic1311yescharacteristic
176#331Dic1311yescharacteristic
177D4⋊C8—262no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—42no—
181C22×C13—42no—
182C22×C13—42no—
183C22×C13#38511yescharacteristic
184C22×C13#47411yescharacteristic
185C22×C13#47811yescharacteristic
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—42no—
190C4×C13C4×D811yescharacteristic
191C4×C13#44011yescharacteristic
192C4×C13#44311yescharacteristic
193C4×C13#44411yescharacteristic
194C4×C13#44711yescharacteristic
195C4×C13#45211yescharacteristic
196C2×#41—21no—
197#131—522no—
198#131—522no—
199C2×M16—131no—
200C2×M16—131no—
201C2×M16—262no—
202C2×M16—261no—
203C22×C8—21no—
204C22×C8—262no—
205C22×C8—261no—
206C22×C8—261no—
207C4⋊Q8C2×Dic1311yescharacteristic
208#127C2×Dic1311yescharacteristic
209#124—21no—
210#121—21no—
211#121Dic2612yes—
212C4×D4—21no—
213C4×D4D5212yes—
214C2×C42C22×D1311yescharacteristic
215#108—522no—
216C4⋊C8—21no—
217C4⋊C8—131no—
218C4⋊C8—131no—
219C4⋊C8—261no—
220C4⋊C8—261no—
221C4⋊C8—261no—
222C4⋊C8C2×Dic1311yescharacteristic
223C4⋊C8C2×Dic1311yescharacteristic
224C4⋊C8C2×Dic1311yescharacteristic
225C4⋊C8C2×Dic1311yescharacteristic
226C22⋊C8—21no—
227C22⋊C8—262no—
228C22⋊C8—262no—
229#97—261no—
230C4×C8—21no—
231C4×C8—261no—
232C4×C8—261no—
233C4×C8—261no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—82no—
237C2×C13#185811yescharacteristic
238C2×C13#186211yescharacteristic
239C2×C13#186611yescharacteristic
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C4⋊Dic1312yes—
249C22×C4—22no—
250C22×C4C2×Dic2611yescharacteristic
251C22×C4D4×D1311yescharacteristic
252C22×C4#612911yescharacteristic
253M16—132no—
254M16—261no—
255M16—261no—
256M16—261no—
257M16—524no—
258M16—521no—
259M16—521no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—261no—
267C2×C8—262no—
268C2×C8—261no—
269C2×C8—261no—
270C2×C8—261no—
271C2×C8—524no—
272C2×C8—521no—
273C2×C8—521no—
274C2×C8—521no—
275C2×C8—521no—
276C2×C8—521no—
277C4⋊C4—21no—
278C4⋊C4C4⋊Dic1312yes—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C42C2×D5211yescharacteristic
282C42D4×D1311yescharacteristic
283C42#612911yescharacteristic
284C42C22×Dic1311yescharacteristic
285C13#893011yescharacteristic, complemented, Sylow
286C23—22no—
287C23#8813211yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—42no—
291D4—42no—
292D4—42no—
293D4—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4#8813211yescharacteristic
304C2×C4#8813611yescharacteristic
305C2×C4#8814011yescharacteristic
306C2×C4D8×D1311yescharacteristic
307C2×C4#8816611yescharacteristic
308C2×C4#8816811yescharacteristic
309C2×C4#8816911yescharacteristic
310C2×C4C2×C4⋊Dic1311yescharacteristic
311C2×C4D4×Dic1311yescharacteristic
312C2×C4D4×Dic1311yescharacteristic
313C8—41no—
314C8—41no—
315C8—41no—
316C8—41no—
317C8—262no—
318C8—522no—
319C8—521no—
320C8—521no—
321C8—521no—
322C8—1041no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22#1171842011yescharacteristic
329C22#1171842711yescharacteristic
330C22#1171861111yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4#1171843411yescharacteristic
336C4#1171844411yescharacteristic
337C4D8×Dic1311yescharacteristic
338C4#1171882511yescharacteristic
339C4#1171885711yescharacteristic
340C4#1171885811yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1311505811yescharacteristic
345C2#1311508511yescharacteristic
346C2#1311511311yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1540C2
socleC22×C13#385
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#1540D13
hypocenterC13#8930
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1540

Complements

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

NH ≅ G/Ntype
2. #13115612C2semidirect
3. #13113611C2semidirect
5. #13112672C2semidirect
6. #13112670C2semidirect
285. C13#8930semidirect

Maximal subgroups

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

subgroupindex
#131235802
#131156122
#131136112
#131132872
#131126722
#131126702
C13×#15402
#893013