Finite Group Databasebeta

← #15761226

Subgroups — #15761226

Order 3328.

446 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115629C211yesmaximal, characteristic
2#13115555C211yesmaximal, characteristic, complemented
3C4×#88049C211yesmaximal, characteristic
4C2×#11718051C211yesmaximal, characteristic
5C2×#11718047C211yesmaximal, characteristic, complemented
6#13112670C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C2×C4×D52C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C4×C8×C13C2211yescharacteristic
11C4×C13×C4⋊C4C2211yescharacteristic
12C2×#88060—21no—
13C2×#88060—21no—
14C2×#88049C411yescharacteristic
15C2×#88049C411yescharacteristic
16C2×C4⋊#1055—21no—
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19C2×C4×#1055C2211yescharacteristic
20#11718121C411yescharacteristic
21#11718121C411yescharacteristic
22#11718116—21no—
23#11718051—22no—
24#11718047—22no—
25C22×D52C2×C411yescharacteristic
26C22×C4×D13—21no—
27C22×C8×C13—21no—
28C22×C8×C13—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C42×C13—21no—
32C2×C42×C13C2311yescharacteristic
33C2×#6103—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C22×#1055—21no—
36C22×#1055C2×C411yescharacteristic
37C22×#1055C2×C411yescharacteristic
38C22×#1055D411yescharacteristic
39C22×#1055D411yescharacteristic
40C4×D52—21no—
41C4×D52—21no—
42C4×D52—21no—
43C4×D52—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C4×C8×C13—21no—
47C4×C8×C13D412yes—
48C13×#95—21no—
49#88060—42no—
50#88060—42no—
51#88049—22no—
52#88049—22no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055—42no—
56C4×#1055—21no—
57C4×#1055—21no—
58C4×#1055—21no—
59C4×#1055—21no—
60#9560—131nomaximal, Sylow
61C23×D13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C22×Dic13—21no—
68C2×D52—21no—
69C2×D52—21no—
70C2×D52—21no—
71C2×D52—21no—
72C2×D52—21no—
73C2×D52M1612yes—
74C2×C4×D13—41no—
75C2×C4×D13—41no—
76C2×C4×D13—41no—
77C2×C4×D13—41no—
78C2×C4×D13—41no—
79C2×C4×D13—41no—
80C2×C8×C13—22no—
81C2×C8×C13—22no—
82C2×C8×C13—22no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4M1612yes—
90C42×C13—41no—
91C42×C13—41no—
92C42×C13C2×D411yescharacteristic
93C42×C13#4111yescharacteristic
94C42×C13#4111yescharacteristic
95C42×C13#4111yescharacteristic
96#6103—41no—
97#6103—41no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C2×#1055—21no—
101C2×#1055—21no—
102C2×#1055—21no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—21no—
107C2×#1055—21no—
108C2×#1055—21no—
109C2×#1055—21no—
110C2×#1055—21no—
111C2×#1055—21no—
112C2×#1055—41no—
113C2×#1055—41no—
114C2×#1055—41no—
115#1954—131no—
116#1939—131no—
117C4×#102—131no—
118C2×D4⋊C8—131no—
119C2×#322—131no—
120#1279D1311yescharacteristic, complemented
121#1277—131no—
122C23×C13C4×D411yescharacteristic
123C22×D13—22no—
124C22×D13—41no—
125C22×D13—41no—
126C22×D13—41no—
127C22×D13—41no—
128C22×D13—41no—
129C22×D13—41no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—22no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13#11711yescharacteristic
139C2×C4×C13C4×D411yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12311yescharacteristic
142C2×C4×C13#12411yescharacteristic
143C2×C4×C13#12611yescharacteristic
144C2×C4×C13C2×M1611yescharacteristic
145C2×C4×C13C2×M1611yescharacteristic
146C2×C4×C13#13111yescharacteristic
147C2×C4×C13#13111yescharacteristic
148C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C13#13711yescharacteristic
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155D52—22no—
156D52—22no—
157D52—41no—
158D52—41no—
159C4×D13—81no—
160C4×D13—81no—
161C4×D13—81no—
162C4×D13—81no—
163C8×C13—24no—
164C8×C13—81no—
165#1055—41no—
166#1055—41no—
167#1055—41no—
168#1055—41no—
169#1055—81no—
170C2×C4×D4—131no—
171C2×C4⋊C8—131no—
172C2×C4⋊C8—261no—
173C2×C4⋊C8C2×D1311yescharacteristic
174C2×#102—131no—
175C2×#102—131no—
176C2×C22⋊C8—261no—
177C2×C22⋊C8—261no—
178C2×C4×C8—131no—
179C2×C4×C8—131no—
180C2×C4×C8C2×D1311yescharacteristic
181C4×C4⋊C4C2×D1311yescharacteristic
182#340—131no—
183#340—131no—
184#336—261no—
185D4⋊C8—262no—
186#322—262no—
187C22×C13#38811yescharacteristic
188C22×C13#43511yescharacteristic
189C22×C13#43511yescharacteristic
190C22×C13#44011yescharacteristic
191C22×C13#44211yescharacteristic
192C22×C13#44311yescharacteristic
193C22×C13#44311yescharacteristic
194C2×D13—42no—
195C2×D13—42no—
196C2×D13—42no—
197C2×D13—81no—
198C2×D13—81no—
199C2×D13—81no—
200C2×D13—81no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—42no—
204C4×C13—81no—
205C4×C13#43211yescharacteristic
206C4×C13#43311yescharacteristic
207C4×C13#43511yescharacteristic
208C4×C13#43611yescharacteristic
209C4×C13#46811yescharacteristic
210C4×C13#46911yescharacteristic
211C4×C13#48911yescharacteristic
212C4×C13#49011yescharacteristic
213Dic13—81no—
214C22×D4—131no—
215C23×C4—261no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—131no—
219C22×C8—131no—
220C22×C8—131no—
221C22×C8—131no—
222C22×C8—261no—
223C4×D4—261no—
224C4×D4—261no—
225C4×D4—261no—
226C4×D4—261no—
227C2×C4⋊C4—131no—
228C2×C4⋊C4C4×D1311yescharacteristic
229C2×C4⋊C4C4×D1311yescharacteristic
230C2×C22⋊C4—261no—
231C2×C42—21no—
232C2×C42C22×D1311yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—261no—
236C4⋊C8—261no—
237C4⋊C8—522no—
238#102—262no—
239#102—262no—
240C22⋊C8—522no—
241C22⋊C8—522no—
242C4×C8—21no—
243C4×C8—261no—
244C4×C8—261no—
245C4×C8—261no—
246C4×C8—261no—
247C4×C8D5212yes—
248#95—21no—
249C2×C13#158511yescharacteristic
250C2×C13#158611yescharacteristic
251C2×C13#158611yescharacteristic
252C2×C13#158811yescharacteristic
253C2×C13#192411yescharacteristic
254C2×C13#193611yescharacteristic
255C2×C13#193711yescharacteristic
256D13—82no—
257C24—261no—
258C2×D4—132no—
259C2×D4—261no—
260C2×D4—261no—
261C2×D4—261no—
262C2×D4—261no—
263C2×D4—261no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—261no—
267C22×C4—521no—
268C22×C4—521no—
269C22×C4—521no—
270C22×C4—521no—
271C22×C4—521no—
272C22×C4—521no—
273C22×C4C2×C4×D1311yescharacteristic
274C22×C4D4×D1311yescharacteristic
275C22×C4#612911yescharacteristic
276C2×C8—22no—
277C2×C8—22no—
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—261no—
283C2×C8—261no—
284C2×C8—261no—
285C2×C8—261no—
286C2×C8—261no—
287C2×C8—261no—
288C2×C8—261no—
289C2×C8—261no—
290C2×C8—261no—
291C2×C8—261no—
292C2×C8—261no—
293C2×C8—261no—
294C2×C8—521no—
295C2×C8—521no—
296C2×C8—521no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—261no—
301C4⋊C4—261no—
302C4⋊C4#609412yes—
303C22⋊C4—521no—
304C22⋊C4—521no—
305C42—41no—
306C42—41no—
307C42C2×D5211yescharacteristic
308C42#612711yescharacteristic
309C42#612911yescharacteristic
310C42#613111yescharacteristic
311C13#956011yescharacteristic, complemented, Sylow
312C23—262no—
313C23—521no—
314C23—521no—
315C23—521no—
316C23—521no—
317C23—521no—
318C23—521no—
319C23#8813511yescharacteristic
320D4—262no—
321D4—262no—
322D4—521no—
323D4—521no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—1041no—
336C2×C4—1041no—
337C2×C4—1041no—
338C2×C4—1041no—
339C2×C4C4×D5211yescharacteristic
340C2×C4#8813911yescharacteristic
341C2×C4#8814011yescharacteristic
342C2×C4#8814611yescharacteristic
343C2×C4#8814911yescharacteristic
344C2×C4#8815211yescharacteristic
345C2×C4C2×#609411yescharacteristic
346C2×C4#8815511yescharacteristic
347C2×C4M16×D1311yescharacteristic
348C2×C4#8816111yescharacteristic
349C2×C4#8816511yescharacteristic
350C2×C4#8816811yescharacteristic
351C2×C4#8816811yescharacteristic
352C2×C4#8817211yescharacteristic
353C8—24no—
354C8—81no—
355C8—521no—
356C8—521no—
357C8—521no—
358C8—521no—
359C8—1041no—
360C22—522no—
361C22—522no—
362C22—522no—
363C22—1041no—
364C22—1041no—
365C22—1041no—
366C22—1041no—
367C22#1171833111yescharacteristic
368C22#1171838911yescharacteristic
369C22#1171839111yescharacteristic
370C22#1171844611yescharacteristic
371C22#1171847811yescharacteristic
372C22#1171848511yescharacteristic
373C22#1171848511yescharacteristic
374C4—21no—
375C4—21no—
376C4—42no—
377C4—81no—
378C4—1041no—
379C4#1171834911yescharacteristic
380C4#1171836711yescharacteristic
381C4#1171842511yescharacteristic
382C4#1171845611yescharacteristic
383C4#1171849611yescharacteristic
384C4#1171850111yescharacteristic
385C4#1171852611yescharacteristic
386C4#1171854711yescharacteristic
387C2—1042no—
388C2#1311369611yescharacteristic
389C2#1311369711yescharacteristic
390C2#1311370311yescharacteristic
391C2#1311371111yescharacteristic
392C2#1311545011yescharacteristic
393C2#1311553411yescharacteristic
394C2#1311554111yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1279C2
socleC23×C13C4×D4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1279D13
hypocenterC13#9560
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #13115555C2semidirect
5. C2×#11718047C2semidirect
6. #13112670C2semidirect
7. C13×#1279C2semidirect
120. #1279D13semidirect
311. C13#9560semidirect

Maximal subgroups

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

subgroupindex
#131156292
#131155552
C4×#880492
C2×#117180512
C2×#117180472
#131126702
C13×#12792
#956013