Finite Group Databasebeta

← #15756873

Subgroups — #15756873

Order 3328.

516 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718499C211yesmaximal, characteristic
2#13115555C211yesmaximal, characteristic, complemented
3C4×#88049C211yesmaximal, characteristic
4C2×#11718072C211yesmaximal, characteristic, complemented
5C2×#11718051C211yesmaximal, characteristic
6#13112663C211yesmaximal, characteristic, complemented
7C13×#1279C211yesmaximal, characteristic, complemented
8C22×#6094—21no—
9C2×C4×D52C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88060—21no—
14C2×#88049C411yescharacteristic
15C2×#88049C411yescharacteristic
16C2×C4⋊#1055—21no—
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19C2×C4×#1055C2211yescharacteristic
20#11718499—22no—
21#11718499—22no—
22#11718121C411yescharacteristic
23#11718121C411yescharacteristic
24#11718116—21no—
25#11718072—22no—
26#11718051—22no—
27C22×D52C2×C411yescharacteristic
28C22×C4×D13—21no—
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C42×C13—21no—
34C2×C42×C13C2311yescharacteristic
35C2×#6103—21no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C22×#1055—21no—
38C22×#1055C2×C411yescharacteristic
39C22×#1055C2×C411yescharacteristic
40C22×#1055D411yescharacteristic
41C22×#1055D411yescharacteristic
42C2×#6094—24no—
43C2×#6094—42no—
44C2×#6094—42no—
45C4×D52—21no—
46C4×D52—21no—
47C4×D52D412yes—
48C4×D52Q812yes—
49C13×C4⋊C8—21no—
50C13×C4⋊C8D412yes—
51C4×C8×C13—21no—
52C4×C8×C13—21no—
53C13×#95—21no—
54#88060—24no—
55#88049—22no—
56#88049—22no—
57C4⋊#1055—21no—
58C4⋊#1055—21no—
59C4⋊#1055—42no—
60C4×#1055—21no—
61C4×#1055—21no—
62C4×#1055—21no—
63C4×#1055—21no—
64#8849—131nomaximal, Sylow
65C23×D13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13#4111yescharacteristic
71C22×Dic13—21no—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52C4⋊C412yes—
78C2×C4×D13—22no—
79C2×C4×D13—22no—
80C2×C4×D13—41no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C8×C13—22no—
85C2×C8×C13—22no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C2×C8×C13—41no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4M1612yescomplemented
94C42×C13—41no—
95C42×C13—41no—
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13C2×Q811yescharacteristic
99C42×C13#4111yescharacteristic
100#6103—22no—
101#6103—22no—
102C4⋊Dic13—21no—
103C4⋊Dic13C4⋊C412yes—
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—21no—
113C2×#1055—21no—
114C2×#1055—41no—
115C2×#1055—41no—
116C2×#1055—41no—
117C2×#1055M1612yescomplemented
118C2×#1055SD1612yes—
119#6094—48no—
120C2×#436—131no—
121#1939—131no—
122C4×#102—131no—
123C2×#334—131no—
124C2×D4⋊C8—131no—
125#1279D1311yescharacteristic, complemented
126#1273—131no—
127C23×C13C4×D411yescharacteristic
128C22×D13—22no—
129C22×D13—41no—
130C22×D13—41no—
131C22×D13—41no—
132C22×D13—41no—
133C22×D13—41no—
134C22×D13—41no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—22no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13C2×C4⋊C411yescharacteristic
144C2×C4×C13C4×D411yescharacteristic
145C2×C4×C13#12011yescharacteristic
146C2×C4×C13C22⋊Q811yescharacteristic
147C2×C4×C13C22⋊Q811yescharacteristic
148C2×C4×C13#12311yescharacteristic
149C2×C4×C13C2×M1611yescharacteristic
150C2×C4×C13C2×M1611yescharacteristic
151C2×C4×C13#13111yescharacteristic
152C2×C4×C13#13111yescharacteristic
153C2×C4×C13C2×SD1611yescharacteristic
154C2×C4×C13#13511yescharacteristic
155C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
157C2×Dic13—22no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160D52—22no—
161D52—22no—
162D52—41no—
163D52—41no—
164C4×D13—42no—
165C4×D13—42no—
166C4×D13—42no—
167C4×D13—42no—
168C8×C13—42no—
169C8×C13—42no—
170#1055—22no—
171#1055—22no—
172#1055—41no—
173#1055—41no—
174#1055—81no—
175C22×M16—261no—
176C2×C4×D4—131no—
177#436—262no—
178#436—262no—
179C2×C4⋊C8—131no—
180C2×C4⋊C8—261no—
181C2×C4⋊C8C2×D1311yescharacteristic
182C2×#102—131no—
183C2×#102—131no—
184C2×C22⋊C8—261no—
185C2×C4×C8—131no—
186C2×C4×C8—131no—
187C2×C4×C8C2×D1311yescharacteristic
188C4×C4⋊C4C2×D1311yescharacteristic
189#340—131no—
190#340—131no—
191#336—261no—
192#334—262no—
193D4⋊C8—262no—
194C22×C13#38511yescharacteristic
195C22×C13#43511yescharacteristic
196C22×C13#43611yescharacteristic
197C22×C13C4×SD1611yescharacteristic
198C22×C13#44211yescharacteristic
199C22×C13#44311yescharacteristic
200C22×C13#44411yescharacteristic
201C2×D13—42no—
202C2×D13—42no—
203C2×D13—42no—
204C2×D13—81no—
205C2×D13—81no—
206C2×D13—81no—
207C2×D13—81no—
208C4×C13—21no—
209C4×C13—21no—
210C4×C13—42no—
211C4×C13—81no—
212C4×C13#42311yescharacteristic
213C4×C13#42411yescharacteristic
214C4×C13#43511yescharacteristic
215C4×C13#43611yescharacteristic
216C4×C13#44911yescharacteristic
217C4×C13#45011yescharacteristic
218C4×C13#47611yescharacteristic
219C4×C13#47811yescharacteristic
220Dic13—42no—
221C22×D4—131no—
222C23×C4—261no—
223C2×M16—264no—
224C2×M16—522no—
225C2×M16—522no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—131no—
229C22×C8—131no—
230C22×C8—131no—
231C22×C8—131no—
232C22×C8—261no—
233C4×D4—132no—
234C4×D4—132no—
235C4×D4—261no—
236C4×D4—261no—
237C2×C4⋊C4—131no—
238C2×C4⋊C4C4×D1311yescharacteristic
239C2×C4⋊C4C4×D1311yescharacteristic
240C2×C22⋊C4—261no—
241C2×C42—21no—
242C2×C42C22×D1311yescharacteristic
243C4⋊C8—21no—
244C4⋊C8—261no—
245C4⋊C8—261no—
246C4⋊C8—522no—
247C4⋊C8D5212yes—
248#102—262no—
249#102—262no—
250C22⋊C8—264no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—261no—
254C4×C8—261no—
255C4×C8—261no—
256C4×C8—261no—
257#95—21no—
258C2×C13#158311yescharacteristic
259C2×C13#158611yescharacteristic
260C2×C13#159011yescharacteristic
261C2×C13#159411yescharacteristic
262C2×C13#185111yescharacteristic
263C2×C13#186411yescharacteristic
264C2×C13#186611yescharacteristic
265D13—82no—
266C24—261no—
267C2×D4—132no—
268C2×D4—261no—
269C2×D4—261no—
270C2×D4—261no—
271C2×D4—261no—
272C2×D4—261no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—261no—
276C22×C4—262no—
277C22×C4—262no—
278C22×C4—521no—
279C22×C4—521no—
280C22×C4—521no—
281C22×C4—521no—
282C22×C4C2×C4×D1311yescharacteristic
283C22×C4D4×D1311yescharacteristic
284C22×C4#612911yescharacteristic
285M16—528no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—132no—
293C2×C8—132no—
294C2×C8—261no—
295C2×C8—261no—
296C2×C8—261no—
297C2×C8—261no—
298C2×C8—261no—
299C2×C8—261no—
300C2×C8—261no—
301C2×C8—261no—
302C2×C8—261no—
303C2×C8—261no—
304C2×C8—521no—
305C2×C8—521no—
306C2×C8—521no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—132no—
311C4⋊C4—261no—
312C4⋊C4#609412yescomplemented
313C22⋊C4—262no—
314C22⋊C4—262no—
315C42—41no—
316C42—41no—
317C42C2×D5211yescharacteristic
318C42#612711yescharacteristic
319C42D4×D1311yescharacteristic
320C42Q8×D1311yescharacteristic
321C13#884911yescharacteristic, complemented, Sylow
322C23—262no—
323C23—521no—
324C23—521no—
325C23—521no—
326C23—521no—
327C23—521no—
328C23—521no—
329C23#8813511yescharacteristic
330D4—262no—
331D4—262no—
332D4—521no—
333D4—521no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—262no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—522no—
346C2×C4—522no—
347C2×C4—522no—
348C2×C4—522no—
349C2×C4C4×D5211yescharacteristic
350C2×C4#8813611yescharacteristic
351C2×C4#8813711yescharacteristic
352C2×C4C4⋊C4×D1311yescharacteristic
353C2×C4#8815011yescharacteristic
354C2×C4#8815111yescharacteristic
355C2×C4C2×#609411yescharacteristic
356C2×C4#8815511yescharacteristic
357C2×C4M16×D1311yescharacteristic
358C2×C4#8816111yescharacteristic
359C2×C4#8816511yescharacteristic
360C2×C4SD16×D1311yescharacteristic
361C2×C4#8816811yescharacteristic
362C2×C4#8817311yescharacteristic
363C8—42no—
364C8—42no—
365C8—262no—
366C8—262no—
367C8—521no—
368C8—521no—
369C8—1041no—
370C22—522no—
371C22—522no—
372C22—522no—
373C22—1041no—
374C22—1041no—
375C22—1041no—
376C22—1041no—
377C22#1171832911yescharacteristic
378C22#1171839011yescharacteristic
379C22#1171839111yescharacteristic
380C22#1171844611yescharacteristic
381C22#1171844911yescharacteristic
382C22#1171848411yescharacteristic
383C22#1171848511yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—81no—
388C4—522no—
389C4#1171834911yescharacteristic
390C4#1171836711yescharacteristic
391C4#1171843711yescharacteristic
392C4#1171847211yescharacteristic
393C4#1171849811yescharacteristic
394C4#1171850011yescharacteristic
395C4#1171853111yescharacteristic
396C4#1171855211yescharacteristic
397C2—1042no—
398C2#1311367611yescharacteristic
399C2#1311369711yescharacteristic
400C2#1311372311yescharacteristic
401C2#1311374711yescharacteristic
402C2#1311502011yescharacteristic
403C2#1311509811yescharacteristic
404C2#1311511211yescharacteristic
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#8849
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
4. C2×#11718072C2semidirect
6. #13112663C2semidirect
7. C13×#1279C2semidirect
93. C13×C4⋊C4M16semidirect
117. C2×#1055M16semidirect
125. #1279D13semidirect
312. C4⋊C4#6094semidirect
321. C13#8849semidirect

Maximal subgroups

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

subgroupindex
C2×#117184992
#131155552
C4×#880492
C2×#117180722
C2×#117180512
#131126632
C13×#12792
#884913