Finite Group Databasebeta

← #15759454

Subgroups — #15759454

Order 3328.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125980C211yesmaximal, characteristic
2#13123779C211yesmaximal, characteristic
3#13115681C211yesmaximal, characteristic
4#13113524C211yesmaximal, characteristic
5#13112733C211yesmaximal, characteristic
6#13112686C211yesmaximal, characteristic
7C2×C13×#332C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9#11719175C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88076—21no—
13C2×#88076—21no—
14#11718763—21no—
15#11718762—21no—
16#11718755—22no—
17#11718754—21no—
18#11718740—21no—
19#11718632C414yes—
20#11718586C2211yescharacteristic
21#11718585C2211yescharacteristic
22C4×#6099C2211yescharacteristic
23#11718492—21no—
24#11718491—21no—
25#11718489—22no—
26C13×#332—21no—
27C13×#332—21no—
28#11718074—21no—
29#11718073—21no—
30C22×Q8×C13—21no—
31C22×C8×C13—21no—
32C22×C8×C13—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4C2×C412yes—
39C2×C42×C13C2311yescharacteristic
40#88180—21no—
41#88178—21no—
42#88178C2×C412yes—
43C2×#6099—21no—
44C2×#6099D411yescharacteristic
45C2×#6099D411yescharacteristic
46#88124—21no—
47#88123D411yescharacteristic
48#88123D411yescharacteristic
49C4×Dic26—21no—
50C4×Dic26D412yes—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8D411yescharacteristic
55C13×C4⋊C8D411yescharacteristic
56#88076—42no—
57#88076—42no—
58C22⋊#1055C2×C412yes—
59#88055—22no—
60#88054—22no—
61#88054—22no—
62C8×Dic13—22no—
63#88050—24no—
64#88048—24no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68#88043—21no—
69C4×#1055—21no—
70C4×#1055—21no—
71#9272—131nomaximal, Sylow
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C2×Q8×C13—41no—
76C2×Q8×C13—41no—
77C2×Q8×C13—41no—
78C22×C4×C13—22no—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13#4111yescharacteristic
82C2×Dic26—21no—
83C2×Dic26C22⋊C412yes—
84C2×C8×C13—21no—
85C2×C8×C13—21no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C2×C8×C13—81no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—22no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13#4111yescharacteristic
98C22⋊Dic13—22no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13C22⋊C412yes—
103#6101—22no—
104#6101—22no—
105C4×Dic13—22no—
106#6099—21no—
107#6099—21no—
108#6099—21no—
109#6099—41no—
110#6099—41no—
111#6099SD1612yes—
112C2×#1055—21no—
113C2×#1055—22no—
114C2×#1055—21no—
115C2×#1055—41no—
116#3229—131no—
117#2962—131no—
118#1966—131no—
119#1550—131no—
120C2×#332D1311yescharacteristic
121#1301—131no—
122#1283—131no—
123C23×C13C4×D411yescharacteristic
124Q8×C13—81no—
125Q8×C13—81no—
126Q8×C13—81no—
127Q8×C13—81no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13C2×C22⋊C411yescharacteristic
135C2×C4×C13C4×D411yescharacteristic
136C2×C4×C13#12011yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#12311yescharacteristic
140C2×C4×C13C2×SD1611yescharacteristic
141C2×C4×C13#13511yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C2×Dic13—22no—
145C2×Dic13—22no—
146Dic26—41no—
147Dic26—41no—
148Dic26—42no—
149C8×C13—41no—
150C8×C13—41no—
151C8×C13—81no—
152#1055—22no—
153#1055—42no—
154#1055—41no—
155#1055—81no—
156#533—131no—
157C2×C4⋊Q8C2×D1311yescharacteristic
158#498—261no—
159#487—261no—
160#483—134no—
161#475—262no—
162#446—262no—
163#446—261no—
164C8×Q8—261no—
165#431—131no—
166#424—261no—
167#423—131no—
168C2×C4⋊C8C2×D1311yescharacteristic
169C2×C4⋊C8C2×D1311yescharacteristic
170C2×#101—261no—
171C2×#101—261no—
172#405—261no—
173C4×M16—131no—
174#333—261no—
175#332—21no—
176#332—21no—
177#332—261no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13#38611yescharacteristic
181C22×C13C4×SD1611yescharacteristic
182C22×C13#44011yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—82no—
187C4×C13#44811yescharacteristic
188C4×C13#44911yescharacteristic
189C4×C13#46011yescharacteristic
190C4×C13#46411yescharacteristic
191C4×C13#47111yescharacteristic
192C4×C13#47311yescharacteristic
193Dic13—42no—
194Dic13—42no—
195C22×Q8—21no—
196C2×M16—131no—
197C2×M16—131no—
198C2×M16—261no—
199C22×C8—21no—
200C22×C8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—131no—
206C4⋊Q8—131no—
207#125—261no—
208C22⋊Q8—132no—
209C22⋊Q8—261no—
210C4×Q8—132no—
211C4×Q8—261no—
212#117—261no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4C4×D1312yes—
215C2×C42C22×D1311yescharacteristic
216#106—264no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—262no—
221C4⋊C8—262no—
222C4⋊C8—261no—
223C4⋊C8—261no—
224C4⋊C8—261no—
225C4⋊C8C22⋊D1311yescharacteristic
226C4⋊C8C22⋊D1311yescharacteristic
227#103—264no—
228#101—522no—
229#101—522no—
230C22⋊C8—132no—
231#97—262no—
232#97—261no—
233C4×C8—262no—
234C4×C8—261no—
235C4×C8—261no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13#188011yescharacteristic
239C2×C13#190811yescharacteristic
240C2×C13#191511yescharacteristic
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—132no—
248C2×Q8—261no—
249C22×C4—22no—
250C22×C4C2×C4×D1311yescharacteristic
251C22×C4D4×D1311yescharacteristic
252C22×C4#612911yescharacteristic
253M16—132no—
254M16—261no—
255M16—261no—
256M16—261no—
257M16—521no—
258M16—521no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—81no—
265C2×C8—261no—
266C2×C8—262no—
267C2×C8—261no—
268C2×C8—521no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—132no—
274C4⋊C4—262no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—262no—
278C4⋊C4—261no—
279C22⋊C4—262no—
280C42—262no—
281C42#612711yescharacteristic
282C42D4×D1311yescharacteristic
283C42D4×D1311yescharacteristic
284C42C2×C22⋊D1311yescharacteristic
285C13#927211yescharacteristic, complemented, Sylow
286C23#8813511yescharacteristic
287Q8—81no—
288Q8—81no—
289Q8—81no—
290Q8—81no—
291Q8—522no—
292Q8—521no—
293Q8—521no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—262no—
301C2×C4—262no—
302C2×C4C22⋊C4×D1311yescharacteristic
303C2×C4#8813711yescharacteristic
304C2×C4#8813811yescharacteristic
305C2×C4#8816511yescharacteristic
306C2×C4#8816611yescharacteristic
307C2×C4SD16×D1311yescharacteristic
308C2×C4#8816911yescharacteristic
309C2×C4C4×C22⋊D1311yescharacteristic
310C2×C4#8819111yescharacteristic
311C2×C4#8819211yescharacteristic
312C8—41no—
313C8—41no—
314C8—81no—
315C8—262no—
316C8—522no—
317C8—521no—
318C8—1041no—
319C22—21no—
320C22—21no—
321C22#1171841811yescharacteristic
322C22#1171841911yescharacteristic
323C22#1171861711yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—522no—
329C4—522no—
330C4#1171842311yescharacteristic
331C4#1171842811yescharacteristic
332C4#1171881911yescharacteristic
333C4#1171883111yescharacteristic
334C4#1171883811yescharacteristic
335C4#1171885311yescharacteristic
336C2—21no—
337C2—21no—
338C2#1311518811yescharacteristic
339C2#1311535411yescharacteristic
340C2#1311538511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#332C2
socleC22×C13#386
prime radicalC23×C13C4×D4
cosocleC2×C42×C13C23
hypercenterC2×#332D13
hypocenterC13#9272
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
285. C13#9272semidirect

Maximal subgroups

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

subgroupindex
#131259802
#131237792
#131156812
#131135242
#131127332
#131126862
C2×C13×#3322
#927213