Finite Group Databasebeta

← #16784313

Subgroups — #16784313

Order 3328.

414 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131006C211yesmaximal, characteristic
2#13130934C211yesmaximal, characteristic
3C2×#11718244C211yesmaximal, characteristic
4C2×C8×#1057C211yesmaximal, characteristic
5#13129672C211yesmaximal, characteristic
6#13129666C211yesmaximal, characteristic
7#13114655C211yesmaximal, characteristic
8C2×#88141C2211yescharacteristic
9C2×#88112—21no—
10C2×C4⋊#1057C2211yescharacteristic
11C2×C4⋊#1057C2211yescharacteristic
12C2×C4×#1057C2211yescharacteristic
13C2×C4×#1057C2211yescharacteristic
14C2×#88056C411yescharacteristic
15C2×C8×Dic13C2211yescharacteristic
16C4⋊C4×Dic13C2211yescharacteristic
17C2×#88050C411yescharacteristic
18#11718290—21no—
19#11718290—21no—
20#11718290—21no—
21C8×#1057—22no—
22#11718244—22no—
23C13×#340C411yescharacteristic
24#11718121C411yescharacteristic
25C22×Dic26C2×C411yescharacteristic
26C22×#1057—21no—
27C22×#1057—21no—
28C22×#1057—21no—
29C22×#1057D411yescharacteristic
30C22×#1057D411yescharacteristic
31C22×C8×C13C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2311yescharacteristic
39C22×#1055C2×C411yescharacteristic
40#88141—21no—
41#88141—21no—
42#88141—21no—
43#88141—21no—
44#88112—42no—
45C4⋊#1057—21no—
46C4⋊#1057—21no—
47C4⋊#1057—21no—
48C4⋊#1057—21no—
49C4×#1057—21no—
50C4×#1057—21no—
51C4×#1057—21no—
52C4×#1057D412yes—
53#88071—21no—
54#88056C814yescomplemented
55C8×Dic13—21no—
56C8×Dic13—21no—
57#88050—22no—
58#9553—131nomaximal, Sylow
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13C2×D411yescharacteristic
65C22×Dic13#4111yescharacteristic
66C2×Dic26—21no—
67C2×Dic26—21no—
68C2×Dic26—21no—
69C2×Dic26—21no—
70C2×Dic26—21no—
71C2×Dic26C2×C812yes—
72C2×#1057—22no—
73C2×#1057—22no—
74C2×#1057—21no—
75C2×#1057—21no—
76C2×#1057—22no—
77C2×#1057—21no—
78C2×#1057—21no—
79C2×#1057—41no—
80C2×#1057—41no—
81C2×#1057—41no—
82C2×#1057—41no—
83C2×#1057—41no—
84C2×#1057—41no—
85C2×#1057SD1612yes—
86C2×#1057Q1612yes—
87C2×C8×C13—21no—
88C2×C8×C13—21no—
89C2×C8×C13C2×C812yes—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—21no—
93C13×C4⋊C4—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13C2×C812yes—
96#6101—41no—
97#6101—41no—
98C4×Dic13—41no—
99C4×Dic13—41no—
100C4×Dic13—41no—
101C4×Dic13—41no—
102C4×Dic13C2×D411yescharacteristic
103C4×Dic13#4111yescharacteristic
104C4×Dic13#4111yescharacteristic
105C4×Dic13#4111yescharacteristic
106C2×#1055—21no—
107C2×#1055—21no—
108C2×#1055M1612yes—
109#1984—131no—
110#1939—131no—
111C4×#103—131no—
112C2×Q8⋊C8—131no—
113C2×C82—131no—
114#1279—131no—
115#1277—131no—
116C23×C13C4×D411yescharacteristic
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13#11711yescharacteristic
124C2×C4×C13C4×D411yescharacteristic
125C2×C4×C13C22×C811yescharacteristic
126C2×C4×C13C2×M1611yescharacteristic
127C2×C4×C13#13111yescharacteristic
128C2×C4×C13#13111yescharacteristic
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—22no—
132C2×Dic13—22no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13#12111yescharacteristic
138C2×Dic13#12311yescharacteristic
139C2×Dic13#12411yescharacteristic
140C2×Dic13#12611yescharacteristic
141C2×Dic13C2×SD1611yescharacteristic
142C2×Dic13C2×Q1611yescharacteristic
143C2×Dic13#13511yescharacteristic
144C2×Dic13#13511yescharacteristic
145Dic26—22no—
146Dic26—22no—
147Dic26—41no—
148Dic26—41no—
149#1057—24no—
150#1057—22no—
151#1057—22no—
152#1057—81no—
153#1057—81no—
154C8×C13—22no—
155#1055—22no—
156C2×C4×Q8—131no—
157C2×C4⋊C8—131no—
158C2×C4⋊C8—131no—
159C2×C4⋊C8—261no—
160C2×#103—131no—
161C2×#103—131no—
162C2×C4×C8—131no—
163C2×C4×C8—131no—
164C2×C4×C8—131no—
165C4×C4⋊C4—131no—
166#340—131no—
167#340#26111yescharacteristic
168#336—261no—
169#336—261no—
170#336—261no—
171Q8⋊C8—262no—
172C82—262no—
173C22×C13#38811yescharacteristic
174C22×C13C8×D411yescharacteristic
175C22×C13#43611yescharacteristic
176C22×C13C4×SD1611yescharacteristic
177C22×C13C4×Q1611yescharacteristic
178C22×C13#44311yescharacteristic
179C22×C13#44311yescharacteristic
180C4×C13—81no—
181C4×C13—81no—
182C4×C13#43111yescharacteristic
183C4×C13#43311yescharacteristic
184C4×C13C8×D411yescharacteristic
185C4×C13#43511yescharacteristic
186Dic13—21no—
187Dic13—21no—
188Dic13—42no—
189Dic13—42no—
190Dic13#46511yescharacteristic
191Dic13#46711yescharacteristic
192Dic13#48711yescharacteristic
193Dic13#48811yescharacteristic
194C22×Q8—131no—
195C22×C8—131no—
196C22×C8—131no—
197C22×C8—131no—
198C22×C8—261no—
199C22×C8—261no—
200C22×C8—261no—
201C22×C8C2×#26111yescharacteristic
202C4×Q8—261no—
203C4×Q8—261no—
204C4×Q8—261no—
205C4×Q8—261no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4C2×#26111yescharacteristic
209C2×C4⋊C4C2×#26111yescharacteristic
210C2×C42—131no—
211C2×C42—261no—
212C2×C42—261no—
213C4⋊C8—261no—
214C4⋊C8—261no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4⋊C8—522no—
218#103—134no—
219#103—262no—
220C4×C8—132no—
221C4×C8—261no—
222C4×C8—261no—
223C4×C8—261no—
224C4×C8—261no—
225C4×C8—261no—
226#95—261no—
227C2×C13C8×SD1611yescharacteristic
228C2×C13C8×Q1611yescharacteristic
229C2×C13#159011yescharacteristic
230C2×C13#159111yescharacteristic
231C2×C13#192311yescharacteristic
232C2×C13#193311yescharacteristic
233C2×C13#193711yescharacteristic
234C2×Q8—132no—
235C2×Q8—261no—
236C2×Q8—261no—
237C2×Q8—261no—
238C2×Q8—261no—
239C2×Q8—261no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4C22×#26111yescharacteristic
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—132no—
250C2×C8—132no—
251C2×C8—132no—
252C2×C8—262no—
253C2×C8—261no—
254C2×C8—261no—
255C2×C8—261no—
256C2×C8—261no—
257C2×C8—262no—
258C2×C8—262no—
259C2×C8—261no—
260C2×C8—261no—
261C2×C8—521no—
262C2×C8—521no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8—521no—
266C2×C8—521no—
267C2×C8D13⋊C812yes—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—132no—
273C4⋊C4—261no—
274C4⋊C4—521no—
275C4⋊C4—521no—
276C42—131no—
277C42—131no—
278C42—131no—
279C42—131no—
280C42—521no—
281C42—521no—
282C42—521no—
283C42—521no—
284C13#955311yescharacteristic, complemented, Sylow
285C23D4×#26111yescharacteristic
286Q8—262no—
287Q8—262no—
288Q8—521no—
289Q8—521no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—131no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—131no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—262no—
307C2×C4—262no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4C2×D13⋊C811yescharacteristic
313C2×C4D13⋊M1611yescharacteristic
314C2×C4#8823711yescharacteristic
315C2×C4#8823811yescharacteristic
316C2×C4D4×#26111yescharacteristic
317C2×C4#8824011yescharacteristic
318C8—22no—
319C8—262no—
320C8—262no—
321C8—264no—
322C8—262no—
323C8—1041no—
324C8—1041no—
325C22#1171906611yescharacteristic
326C22#1171907111yescharacteristic
327C22#1171907311yescharacteristic
328C22#1171910311yescharacteristic
329C22SD16×#26111yescharacteristic
330C22#1171910711yescharacteristic
331C22Q16×#26111yescharacteristic
332C4—81no—
333C4—81no—
334C4—131no—
335C4—131no—
336C4—131no—
337C4—131no—
338C4—261no—
339C4—261no—
340C4—522no—
341C4—522no—
342C4#1171904911yescharacteristic
343C4#1171906311yescharacteristic
344C4#1171907511yescharacteristic
345C4#1171907711yescharacteristic
346C2#1313042111yescharacteristic
347C2#1313042411yescharacteristic
348C2#1313047311yescharacteristic
349C2#1313047411yescharacteristic
350C2#1313090711yescharacteristic
351C2#1313092511yescharacteristic
352C2#1313093011yescharacteristic
subgroupG/H
centerC23D4×#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#340C4
socle, prime radicalC23×C13C4×D4
cosocleC2×C4×Dic13C23
hypercenter#340#261
hypocenterC13#9553
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
54. #88056C8semidirect
284. C13#9553semidirect

Maximal subgroups

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

subgroupindex
#131310062
#131309342
C2×#117182442
C2×C8×#10572
#131296722
#131296662
#131146552
#955313