Finite Group Databasebeta

← #15767437

Subgroups — #15767437

Order 3328.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115762C211yesmaximal, characteristic
2#13115641C211yesmaximal, characteristic
3#13115592C211yesmaximal, characteristic, complemented
4#13115552C211yesmaximal, characteristic, complemented
5C2×#11718072C211yesmaximal, characteristic, complemented
6C2×#11718077C211yesmaximal, characteristic
7C13×#1296C211yesmaximal, characteristic, complemented
8C2×#88128C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C2×#88061—21no—
13C2×#88061—21no—
14C2×#88054—21no—
15C2×#88049—21no—
16C2×#88049—21no—
17C2×#88047—21no—
18C4×C4⋊Dic13C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21#11718142—21no—
22#11718121—21no—
23#11718077—22no—
24#11718072—22no—
25C22×D52—21no—
26C22×D52—21no—
27C22×D52—21no—
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13D411yescharacteristic
35C2×C4⋊Dic13D411yescharacteristic
36C2×C4×Dic13—21no—
37C22×#1055—21no—
38C22×#1055D411yescharacteristic
39C22×#1055D411yescharacteristic
40#88128—21no—
41#88128—21no—
42#88128—21no—
43#88128Q812yes—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48#88071—21no—
49#88061—42no—
50#88061—42no—
51#88054—42no—
52#88049—42no—
53#88049—42no—
54#88047—42no—
55C4⋊#1055—21no—
56C4⋊#1055D412yes—
57C4×#1055—21no—
58C4×#1055—21no—
59#10587—131nomaximal, Sylow
60C23×D13—41no—
61C22×C4×C13—41no—
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13#4111yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C2×D52—22no—
68C2×D52—22no—
69C2×D52—22no—
70C2×D52—41no—
71C2×D52—41no—
72C2×D52—41no—
73C2×D52—41no—
74C2×D52—41no—
75C2×D52—41no—
76C2×D52—41no—
77C2×D52—41no—
78C2×D52—41no—
79C2×D52—41no—
80C2×D52—41no—
81C2×D52—81no—
82C2×D52—81no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—81no—
94C42×C13C2×D411yescharacteristic
95C42×C13C2×Q811yescharacteristic
96C42×C13#4111yescharacteristic
97C42×C13#4111yescharacteristic
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13SD1612yes—
102C4×Dic13—41no—
103C4×Dic13—41no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—22no—
107C2×#1055—21no—
108C2×#1055—21no—
109C2×#1055—21no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055D812yes—
113#1982—131no—
114#1957—131no—
115#1947—131no—
116#1939—131no—
117C2×#334—131no—
118C2×#331—131no—
119#1296D1311yescharacteristic, complemented
120C23×C13#12111yescharacteristic
121C22×D13—42no—
122C22×D13—81no—
123C22×D13—81no—
124C22×D13—81no—
125C22×D13—81no—
126C22×D13—81no—
127C22×D13—81no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13C22⋊Q811yescharacteristic
136C2×C4×C13C22⋊Q811yescharacteristic
137C2×C4×C13C22⋊Q811yescharacteristic
138C2×C4×C13#12611yescharacteristic
139C2×C4×C13C2×D811yescharacteristic
140C2×C4×C13C2×SD1611yescharacteristic
141C2×C4×C13#13511yescharacteristic
142C2×C4×C13#13511yescharacteristic
143C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13#13711yescharacteristic
147C2×Dic13—22no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153D52—42no—
154D52—42no—
155D52—42no—
156D52—42no—
157D52—82no—
158D52—82no—
159D52—81no—
160D52—81no—
161D52—81no—
162D52—81no—
163C8×C13—81no—
164C8×C13—81no—
165#1055—22no—
166#1055—42no—
167#1055—41no—
168C2×#127—131no—
169C2×#107—261no—
170C2×C4⋊C8—131no—
171C2×C4⋊C8—261no—
172C2×C4⋊C8C2×D1311yescharacteristic
173C2×C4⋊C8C2×D1311yescharacteristic
174C2×#102—261no—
175C2×#102—261no—
176C2×#102—261no—
177C2×#102—261no—
178C2×C4×C8—131no—
179#384C2×D1311yescharacteristic
180C4×C4⋊C4—131no—
181#340—261no—
182#336—261no—
183#334—262no—
184#331—262no—
185C22×C13#39611yescharacteristic
186C22×C13#45911yescharacteristic
187C22×C13#46411yescharacteristic
188C22×C13#46511yescharacteristic
189C22×C13#46911yescharacteristic
190C22×C13#47111yescharacteristic
191C22×C13#47211yescharacteristic
192C2×D13—82no—
193C2×D13—82no—
194C2×D13—82no—
195C2×D13—161no—
196C2×D13—161no—
197C2×D13—161no—
198C2×D13—161no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—161no—
202C4×C13#46011yescharacteristic
203C4×C13#46311yescharacteristic
204C4×C13#46611yescharacteristic
205C4×C13#46811yescharacteristic
206C4×C13#47411yescharacteristic
207C4×C13#47611yescharacteristic
208C4×C13#47811yescharacteristic
209C4×C13#47811yescharacteristic
210Dic13—42no—
211Dic13—81no—
212C22×D4—261no—
213C22×D4—261no—
214C22×D4—261no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—131no—
218C22×C8—131no—
219C22×C8—261no—
220#127—132no—
221#127—261no—
222#127—261no—
223#127—261no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—131no—
228C2×C4⋊C4—131no—
229C2×C42—261no—
230C2×C42C22×D1311yescharacteristic
231#107—522no—
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—132no—
237C4⋊C8—261no—
238C4⋊C8—522no—
239#102—522no—
240#102—522no—
241#102—522no—
242#102—522no—
243C4×C8—261no—
244C4×C8—261no—
245#95—261no—
246C2×C13#166511yescharacteristic
247C2×C13#167811yescharacteristic
248C2×C13#168711yescharacteristic
249C2×C13#170211yescharacteristic
250C2×C13#206311yescharacteristic
251C2×C13#206511yescharacteristic
252C2×C13#206711yescharacteristic
253D13—162no—
254C24—521no—
255C2×D4—262no—
256C2×D4—262no—
257C2×D4—262no—
258C2×D4—521no—
259C2×D4—521no—
260C2×D4—521no—
261C2×D4—521no—
262C2×D4—521no—
263C2×D4—521no—
264C2×D4—521no—
265C2×D4—521no—
266C2×D4—521no—
267C2×D4—521no—
268C2×D4—521no—
269C2×D4—1041no—
270C2×D4—1041no—
271C22×C4—41no—
272C22×C4—261no—
273C22×C4—261no—
274C22×C4#612711yescharacteristic
275C22×C4D4×D1311yescharacteristic
276C22×C4D4×D1311yescharacteristic
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—132no—
284C2×C8—261no—
285C2×C8—261no—
286C2×C8—261no—
287C2×C8—262no—
288C2×C8—261no—
289C2×C8—261no—
290C2×C8—521no—
291C2×C8—521no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—81no—
297C4⋊C4—132no—
298C4⋊C4—261no—
299C4⋊C4—261no—
300C4⋊C4—261no—
301C42—521no—
302C42—521no—
303C42#612711yescharacteristic
304C42#612711yescharacteristic
305C42D4×D1311yescharacteristic
306C42Q8×D1311yescharacteristic
307C13#1058711yescharacteristic, complemented, Sylow
308C23—522no—
309C23—1041no—
310C23—1041no—
311C23—1041no—
312C23—1041no—
313C23—1041no—
314C23—1041no—
315C23#8813811yescharacteristic
316D4—522no—
317D4—522no—
318D4—522no—
319D4—522no—
320D4—1042no—
321D4—1042no—
322D4—1041no—
323D4—1041no—
324D4—1041no—
325D4—1041no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—262no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4#8813011yescharacteristic
338C2×C4#8813811yescharacteristic
339C2×C4#8813811yescharacteristic
340C2×C4#8815011yescharacteristic
341C2×C4#8815011yescharacteristic
342C2×C4#8815011yescharacteristic
343C2×C4D8×D1311yescharacteristic
344C2×C4#8816511yescharacteristic
345C2×C4SD16×D1311yescharacteristic
346C2×C4#8816811yescharacteristic
347C2×C4#8816811yescharacteristic
348C2×C4#8817011yescharacteristic
349C2×C4#8817211yescharacteristic
350C2×C4#8817311yescharacteristic
351C8—81no—
352C8—81no—
353C8—262no—
354C8—521no—
355C8—522no—
356C22—1042no—
357C22—1042no—
358C22—1042no—
359C22—2081no—
360C22—2081no—
361C22—2081no—
362C22—2081no—
363C22#1171833711yescharacteristic
364C22#1171841011yescharacteristic
365C22#1171841511yescharacteristic
366C22#1171844311yescharacteristic
367C22#1171844711yescharacteristic
368C22#1171845911yescharacteristic
369C22#1171846811yescharacteristic
370C4—21no—
371C4—21no—
372C4—161no—
373C4—522no—
374C4—1041no—
375C4#1171842311yescharacteristic
376C4#1171843611yescharacteristic
377C4#1171847311yescharacteristic
378C4#1171848011yescharacteristic
379C4#1171853111yescharacteristic
380C4#1171853211yescharacteristic
381C4#1171855111yescharacteristic
382C4#1171855211yescharacteristic
383C2—2082no—
384C2#1311418011yescharacteristic
385C2#1311425511yescharacteristic
386C2#1311431411yescharacteristic
387C2#1311440711yescharacteristic
388C2#1311619711yescharacteristic
389C2#1311621111yescharacteristic
390C2#1311622511yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socleC23×C13#121
prime radicalC2×#88128C22
hypercenter#1296D13
hypocenterC13#10587
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
3. #13115592C2semidirect
4. #13115552C2semidirect
5. C2×#11718072C2semidirect
7. C13×#1296C2semidirect
119. #1296D13semidirect
307. C13#10587semidirect

Maximal subgroups

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

subgroupindex
#131157622
#131156412
#131155922
#131155522
C2×#117180722
C2×#117180772
C13×#12962
#1058713