Finite Group Databasebeta

← #15767168

Subgroups — #15767168

Order 3328.

422 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
1C2×#11718739C211yesmaximal, characteristic
2#13115785C211yesmaximal, characteristic
3#13115783C211yesmaximal, characteristic
4#13115552C211yesmaximal, characteristic
5C2×#11718073C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic
7C2×C13×#333C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88054—21no—
13#11718739—22no—
14#11718739—22no—
15C2×#88047—21no—
16C2×#88047—21no—
17C4×C4⋊Dic13C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C2×C4×#1055C2211yescharacteristic
20C13×#333—22no—
21#11718143—21no—
22#11718143—21no—
23#11718142—21no—
24#11718121—21no—
25#11718121—21no—
26#11718073—22no—
27C22×Q8×C13—21no—
28C22×Dic26—21no—
29C22×C8×C13—21no—
30C22×C8×C13—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8D412yes—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—21no—
37C2×C42×C13C2311yescharacteristic
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13D411yescharacteristic
41C2×C4⋊Dic13D411yescharacteristic
42C2×C4×Dic13—21no—
43C22×#1055—21no—
44C22×#1055D411yescharacteristic
45C22×#1055D411yescharacteristic
46#88123—21no—
47#88123—21no—
48#88123—21no—
49#88123D412yes—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54#88071—21no—
55#88054—42no—
56#88047—24no—
57#88047—24no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4×#1055—21no—
61C4×#1055—21no—
62#10543—131nomaximal, Sylow
63C2×Q8×C13—22no—
64C2×Q8×C13—41no—
65C2×Q8×C13—81no—
66C2×Q8×C13—81no—
67C22×C4×C13—41no—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13#4111yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13—41no—
74C2×Dic26—22no—
75C2×Dic26—41no—
76C2×Dic26—81no—
77C2×Dic26—81no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C42×C13C2×D411yescharacteristic
89C42×C13C2×D411yescharacteristic
90C42×C13#4111yescharacteristic
91C42×C13#4111yescharacteristic
92C4⋊Dic13—21no—
93C4⋊Dic13—22no—
94C4⋊Dic13—22no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—41no—
98C4⋊Dic13—41no—
99C4⋊Dic13Q1612yes—
100C4×Dic13—41no—
101C4×Dic13—41no—
102C2×#1055—21no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—41no—
107C2×#1055—41no—
108C2×#1055—41no—
109C2×#1055SD1612yes—
110C2×#1055Q1612yes—
111C2×#500—131no—
112#1987—131no—
113#1987—131no—
114#1939—131no—
115C2×#333—131no—
116C2×#333D1311yescharacteristic
117#1277—131no—
118C23×C13#12111yescharacteristic
119Q8×C13—82no—
120Q8×C13—82no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—42no—
124C2×C4×C13—81no—
125C2×C4×C13—81no—
126C2×C4×C13#12011yescharacteristic
127C2×C4×C13#12111yescharacteristic
128C2×C4×C13#12111yescharacteristic
129C2×C4×C13#12311yescharacteristic
130C2×C4×C13#12311yescharacteristic
131C2×C4×C13#12411yescharacteristic
132C2×C4×C13C2×SD1611yescharacteristic
133C2×C4×C13C2×Q1611yescharacteristic
134C2×C4×C13C2×Q1611yescharacteristic
135C2×C4×C13#13511yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C2×C4×C13#13711yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C2×C4×C13#13711yescharacteristic
140C2×Dic13—22no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—42no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149Dic26—82no—
150Dic26—82no—
151C8×C13—81no—
152C8×C13—81no—
153#1055—22no—
154#1055—22no—
155#1055—81no—
156C2×C4⋊Q8—131no—
157C2×C4⋊Q8C2×D1311yescharacteristic
158#500—262no—
159#500—262no—
160C2×#107—261no—
161C2×#107—261no—
162C2×C4⋊C8—131no—
163C2×C4⋊C8—261no—
164C2×C4⋊C8C2×D1311yescharacteristic
165C2×C4⋊C8C2×D1311yescharacteristic
166C2×C4×C8—131no—
167C4×C4⋊C4—131no—
168#340—261no—
169#340—261no—
170#340—261no—
171#340—261no—
172#336—261no—
173#333—22no—
174#333—262no—
175C22×C13#39411yescharacteristic
176C22×C13#46111yescharacteristic
177C22×C13#46211yescharacteristic
178C22×C13#46711yescharacteristic
179C22×C13#47011yescharacteristic
180C22×C13#47211yescharacteristic
181C22×C13#47211yescharacteristic
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—82no—
185C4×C13#44811yescharacteristic
186C4×C13#45111yescharacteristic
187C4×C13#46211yescharacteristic
188C4×C13#46211yescharacteristic
189C4×C13#46411yescharacteristic
190C4×C13#46411yescharacteristic
191C4×C13#48711yescharacteristic
192C4×C13#49111yescharacteristic
193Dic13—42no—
194Dic13—81no—
195Dic13—82no—
196C22×Q8—21no—
197C22×Q8—261no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—131no—
201C22×C8—131no—
202C22×C8—261no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—132no—
207C4⋊Q8—261no—
208C4⋊Q8—261no—
209C4⋊Q8—261no—
210C4⋊Q8C22⋊D1312yes—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C42—261no—
218C2×C42C22×D1311yescharacteristic
219#107—264no—
220#107—264no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—261no—
226C4⋊C8—261no—
227C4⋊C8—522no—
228C4×C8—261no—
229C4×C8—261no—
230#95—261no—
231C2×C13#167511yescharacteristic
232C2×C13#167611yescharacteristic
233C2×C13#169511yescharacteristic
234C2×C13#169611yescharacteristic
235C2×C13#204311yescharacteristic
236C2×C13#204511yescharacteristic
237C2×C13#205611yescharacteristic
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—81no—
241C2×Q8—81no—
242C2×Q8—262no—
243C2×Q8—521no—
244C2×Q8—1041no—
245C2×Q8—1041no—
246C22×C4—41no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4—521no—
250C22×C4#612711yescharacteristic
251C22×C4D4×D1311yescharacteristic
252C22×C4D4×D1311yescharacteristic
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—132no—
260C2×C8—132no—
261C2×C8—261no—
262C2×C8—261no—
263C2×C8—261no—
264C2×C8—261no—
265C2×C8—521no—
266C2×C8—521no—
267C2×C8—521no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—132no—
273C4⋊C4—261no—
274C4⋊C4—262no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—262no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C42—521no—
281C42—521no—
282C42#612711yescharacteristic
283C42D4×D1311yescharacteristic
284C42#612911yescharacteristic
285C42C2×C22⋊D1311yescharacteristic
286C13#1054311yescharacteristic, complemented, Sylow
287C23#8813811yescharacteristic
288Q8—82no—
289Q8—82no—
290Q8—1042no—
291Q8—1042no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—262no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—522no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4#8813711yescharacteristic
307C2×C4#8813811yescharacteristic
308C2×C4#8813911yescharacteristic
309C2×C4SD16×D1311yescharacteristic
310C2×C4#8816911yescharacteristic
311C2×C4#8816911yescharacteristic
312C2×C4#8817011yescharacteristic
313C2×C4Q16×D1311yescharacteristic
314C2×C4Q16×D1311yescharacteristic
315C2×C4#8817211yescharacteristic
316C2×C4#8817211yescharacteristic
317C2×C4#8818311yescharacteristic
318C2×C4#8819111yescharacteristic
319C2×C4#8819311yescharacteristic
320C8—81no—
321C8—81no—
322C8—262no—
323C8—262no—
324C8—1041no—
325C22#1171841011yescharacteristic
326C22#1171841011yescharacteristic
327C22#1171845411yescharacteristic
328C22#1171847411yescharacteristic
329C22#1171847711yescharacteristic
330C22#1171847911yescharacteristic
331C22#1171862011yescharacteristic
332C4—21no—
333C4—21no—
334C4—82no—
335C4—522no—
336C4—1042no—
337C4—1041no—
338C4#1171845311yescharacteristic
339C4#1171845411yescharacteristic
340C4#1171845811yescharacteristic
341C4#1171845911yescharacteristic
342C4#1171882711yescharacteristic
343C4#1171883111yescharacteristic
344C4#1171884311yescharacteristic
345C4#1171884711yescharacteristic
346C2#1311423411yescharacteristic
347C2#1311423911yescharacteristic
348C2#1311435811yescharacteristic
349C2#1311436311yescharacteristic
350C2#1311608011yescharacteristic
351C2#1311609011yescharacteristic
352C2#1311615711yescharacteristic
subgroupG/H
centerC23#88138
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#333C2
socle, prime radicalC23×C13#121
hypercenterC2×#333D13
hypocenterC13#10543
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
286. C13#10543semidirect

Maximal subgroups

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

subgroupindex
C2×#117187392
#131157852
#131157832
#131155522
C2×#117180732
#131126702
C2×C13×#3332
#1054313