Finite Group Databasebeta

← #15767489

Subgroups — #15767489

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#13115763C211yesmaximal, characteristic
2#13115641C211yesmaximal, characteristic
3#13115555C211yesmaximal, characteristic, complemented
4C2×#11718072C211yesmaximal, characteristic, complemented
5C2×#11718077C211yesmaximal, characteristic
6#13112719C211yesmaximal, characteristic, complemented
7C13×#1948C211yesmaximal, characteristic, complemented
8C2×#88128C2211yescharacteristic
9C2×C13×#106—21no—
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88049—21no—
14C2×#88049—21no—
15C2×#88049—21no—
16C2×#88049—21no—
17C2×C4⋊#1055—21no—
18C2×C4⋊#1055C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21C13×#340—21no—
22#11718116—21no—
23#11718077—22no—
24#11718072—22no—
25C22×D52—21no—
26C22×D52—21no—
27C22×D52—21no—
28C22×C8×C13—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C42×C13—21no—
35C2×C42×C13C2311yescharacteristic
36C22×#1055—21no—
37C22×#1055—21no—
38C22×#1055D411yescharacteristic
39C22×#1055D411yescharacteristic
40#88128—21no—
41#88128—21no—
42#88128—21no—
43#88128Q812yes—
44C13×#106—42no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8D412yes—
47C13×#95—21no—
48#88049—42no—
49#88049—42no—
50#88049—42no—
51#88049—42no—
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055—21no—
56C4⋊#1055—42no—
57C4×#1055—21no—
58C4×#1055—21no—
59#10595—131nomaximal, Sylow
60C23×D13—41no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—41no—
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4111yescharacteristic
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—22no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—81no—
94C13×C4⋊C4SD1612yes—
95C42×C13—41no—
96C42×C13—41no—
97C42×C13C2×D411yescharacteristic
98C42×C13C2×Q811yescharacteristic
99C42×C13#4111yescharacteristic
100C42×C13#4111yescharacteristic
101C2×#1055—21no—
102C2×#1055—21no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—41no—
107C2×#1055—41no—
108C2×#1055—41no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055SD1612yes—
113#1982—131no—
114#1957—131no—
115#1948D1311yescharacteristic, complemented
116#1939—131no—
117C2×#334—131no—
118C2×#331—131no—
119#1296—131no—
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—22no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—81no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13C22⋊Q811yescharacteristic
142C2×C4×C13C22⋊Q811yescharacteristic
143C2×C4×C13C22⋊Q811yescharacteristic
144C2×C4×C13#12611yescharacteristic
145C2×C4×C13C2×SD1611yescharacteristic
146C2×C4×C13C2×SD1611yescharacteristic
147C2×C4×C13#13511yescharacteristic
148C2×C4×C13#13511yescharacteristic
149C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153D52—42no—
154D52—42no—
155D52—42no—
156D52—42no—
157D52—82no—
158D52—82no—
159D52—81no—
160D52—81no—
161D52—81no—
162D52—81no—
163C8×C13—42no—
164#1055—22no—
165#1055—41no—
166#1055—81no—
167#1055—81no—
168C2×#127—131no—
169C2×#106—21no—
170C2×C4⋊C8—131no—
171C2×C4⋊C8—131no—
172C2×C4⋊C8—261no—
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⋊C4C2×D1311yescharacteristic
181#340—21no—
182#336—261no—
183#334—262no—
184#331—262no—
185C22×C13#39611yescharacteristic
186C22×C13#46011yescharacteristic
187C22×C13#46311yescharacteristic
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—42no—
202C4×C13—81no—
203C4×C13—161no—
204C4×C13#46011yescharacteristic
205C4×C13#46311yescharacteristic
206C4×C13#46511yescharacteristic
207C4×C13#46911yescharacteristic
208C4×C13#47611yescharacteristic
209C4×C13#47611yescharacteristic
210C4×C13#47811yescharacteristic
211C4×C13#47811yescharacteristic
212C22×D4—261no—
213C22×D4—261no—
214C22×D4—261no—
215C22×C8—21no—
216C22×C8—131no—
217C22×C8—131no—
218C22×C8—261no—
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⋊C4C22⋊D1311yescharacteristic
228C2×C4⋊C4C22⋊D1311yescharacteristic
229C2×C42—21no—
230C2×C42C22×D1311yescharacteristic
231#106—42no—
232C4⋊C8—21no—
233C4⋊C8—261no—
234C4⋊C8—261no—
235C4⋊C8—261no—
236C4⋊C8—261no—
237C4⋊C8—522no—
238C4⋊C8D5212yes—
239#102—522no—
240#102—522no—
241#102—522no—
242#102—522no—
243C4×C8—261no—
244C4×C8—261no—
245#95—21no—
246C2×C13#166611yescharacteristic
247C2×C13#167711yescharacteristic
248C2×C13#168811yescharacteristic
249C2×C13#170111yescharacteristic
250C2×C13#206311yescharacteristic
251C2×C13#206511yescharacteristic
252C2×C13#206511yescharacteristic
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—21no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4D4×D1311yescharacteristic
275C22×C4#612911yescharacteristic
276C22×C4C2×C22⋊D1311yescharacteristic
277C2×C8—22no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—132no—
281C2×C8—261no—
282C2×C8—261no—
283C2×C8—261no—
284C2×C8—261no—
285C2×C8—261no—
286C2×C8—521no—
287C2×C8—521no—
288C2×C8—521no—
289C2×C8—521no—
290C2×C8—521no—
291C2×C8—521no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—81no—
300C4⋊C4#610612yes—
301C42—41no—
302C42—41no—
303C42C2×D5211yescharacteristic
304C42#612711yescharacteristic
305C42Q8×D1311yescharacteristic
306C42#613111yescharacteristic
307C13#1059511yescharacteristic, complemented, Sylow
308C23—522no—
309C23—1041no—
310C23—1041no—
311C23—1041no—
312C23—1041no—
313C23—1041no—
314C23—1041no—
315C23#8819311yescharacteristic
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—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#8814911yescharacteristic
338C2×C4#8815011yescharacteristic
339C2×C4#8815111yescharacteristic
340C2×C4#8815211yescharacteristic
341C2×C4SD16×D1311yescharacteristic
342C2×C4#8816811yescharacteristic
343C2×C4#8816811yescharacteristic
344C2×C4#8817011yescharacteristic
345C2×C4#8818411yescharacteristic
346C2×C4#8818611yescharacteristic
347C2×C4C2×#610611yescharacteristic
348C2×C4#8820011yescharacteristic
349C2×C4#8820311yescharacteristic
350C2×C4#8820411yescharacteristic
351C8—42no—
352C8—262no—
353C8—521no—
354C8—1041no—
355C8—1041no—
356C22—1042no—
357C22—1042no—
358C22—1042no—
359C22—2081no—
360C22—2081no—
361C22—2081no—
362C22—2081no—
363C22#1171865511yescharacteristic
364C22#1171870011yescharacteristic
365C22#1171870911yescharacteristic
366C22#1171882411yescharacteristic
367C22#1171882611yescharacteristic
368C22#1171886011yescharacteristic
369C22#1171886411yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—161no—
375C4#1171852511yescharacteristic
376C4#1171852611yescharacteristic
377C4#1171853111yescharacteristic
378C4#1171853211yescharacteristic
379C4#1171867711yescharacteristic
380C4#1171868811yescharacteristic
381C4#1171872711yescharacteristic
382C4#1171874511yescharacteristic
383C2—2082no—
384C2#1311418611yescharacteristic
385C2#1311424711yescharacteristic
386C2#1311431811yescharacteristic
387C2#1311439911yescharacteristic
388C2#1311619311yescharacteristic
389C2#1311620511yescharacteristic
390C2#1311620711yescharacteristic
subgroupG/H
centerC23#88193
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1948C2
socleC23×C13#121
prime radicalC2×#88128C22
hypercenter#1948D13
hypocenterC13#10595
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #13115555C2semidirect
4. C2×#11718072C2semidirect
6. #13112719C2semidirect
7. C13×#1948C2semidirect
115. #1948D13semidirect
307. C13#10595semidirect

Maximal subgroups

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

subgroupindex
#131157632
#131156412
#131155552
C2×#117180722
C2×#117180772
#131127192
C13×#19482
#1059513