Finite Group Databasebeta

← #15766640

Subgroups — #15766640

Order 3328.

374 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124641C211yesmaximal, characteristic
2#13114832C211yesmaximal, characteristic
3#13113592C211yesmaximal, characteristic
4#13113524C211yesmaximal, characteristic
5#13113292C211yesmaximal, characteristic
6#13112711C211yesmaximal, characteristic
7C2×C13×Q8⋊C8C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9#11719175C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C2×#88076—21no—
13#11718886—21no—
14#11718683—22no—
15#11718682—21no—
16#11718681—21no—
17#11718625—21no—
18#11718585C2211yescharacteristic
19#11718585C2211yescharacteristic
20#11718585C2211yescharacteristic
21C13×Q8⋊C8—21no—
22C13×Q8⋊C8—21no—
23#11718122—21no—
24#11718074—21no—
25#11718073—21no—
26#11718049—22no—
27#11718048—21no—
28#11718048—21no—
29C22×Q8×C13D411yescharacteristic
30C22×C8×C13—21no—
31C22×C8×C13—21no—
32C4×Q8×C13—21no—
33C4×Q8×C13—21no—
34C4×Q8×C13—21no—
35C4×Q8×C13—21no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C42×C13—21no—
39C2×C42×C13C2311yescharacteristic
40#88180—21no—
41#88178—21no—
42#88178—21no—
43C2×#6099—21no—
44C2×#6099—21no—
45C2×#6099—21no—
46#88124—21no—
47#88123D411yescharacteristic
48#88123D411yescharacteristic
49C4×Dic26—21no—
50C4×Dic26—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C4×C8×C13—21no—
54C4×C8×C13D411yescharacteristic
55C4×C8×C13D411yescharacteristic
56#88076—42no—
57#88075—22no—
58#88075—22no—
59#88048—22no—
60#88047—22no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055D412yes—
67#10462—131nomaximal, Sylow
68C2×Q8×C13—21no—
69C2×Q8×C13—21no—
70C2×Q8×C13—21no—
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13SD1612yes—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13#4111yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C2×Dic26—21no—
80C2×Dic26—21no—
81C2×C8×C13—21no—
82C2×C8×C13—21no—
83C2×C8×C13—42no—
84C2×C8×C13—41no—
85C2×C8×C13—81no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C42×C13—41no—
91C42×C13—41no—
92C42×C13C2×D411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13#4111yescharacteristic
96C22⋊Dic13—41no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101#6101—41no—
102#6101—41no—
103C4×Dic13—41no—
104#6099—41no—
105#6099—41no—
106#6099—41no—
107#6099—41no—
108#6099—41no—
109#6099—41no—
110C2×#1055—22no—
111C2×#1055—41no—
112C2×#1055—41no—
113#3078—131no—
114#1801—131no—
115#1566—131no—
116#1550—131no—
117#1493—131no—
118C2×Q8⋊C8D1311yescharacteristic
119#1292—131no—
120C23×C13#12311yescharacteristic
121Q8×C13—22no—
122Q8×C13—22no—
123Q8×C13—41no—
124Q8×C13—41no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—22no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—81no—
133C2×C4×C13#12011yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12311yescharacteristic
138C2×C4×C13#12411yescharacteristic
139C2×C4×C13C2×SD1611yescharacteristic
140C2×C4×C13#13511yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C2×C4×C13#13711yescharacteristic
143C2×Dic13—41no—
144C2×Dic13—41no—
145Dic26—41no—
146Dic26—41no—
147Dic26—81no—
148C8×C13—22no—
149C8×C13—41no—
150C8×C13—81no—
151#1055—42no—
152#1055—81no—
153#1055—81no—
154#533—131no—
155C2×C4×Q8C2×D1311yescharacteristic
156#479—262no—
157#477—261no—
158#475—261no—
159#428—261no—
160#423—131no—
161#423—131no—
162#423—131no—
163C2×C4⋊C8C2×D1311yescharacteristic
164#419—261no—
165C2×#101—261no—
166C2×C4×C8C2×D1311yescharacteristic
167#343—261no—
168#334—262no—
169#333—261no—
170#332—261no—
171Q8⋊C8—21no—
172Q8⋊C8—21no—
173Q8⋊C8—261no—
174Q8⋊C8—261no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13#39411yescharacteristic
178C22×C13#48311yescharacteristic
179C22×C13#48511yescharacteristic
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—42no—
184C4×C13—81no—
185C4×C13#44811yescharacteristic
186C4×C13#45211yescharacteristic
187C4×C13#46511yescharacteristic
188C4×C13#47011yescharacteristic
189C4×C13#47111yescharacteristic
190C4×C13#47311yescharacteristic
191Dic13—81no—
192Dic13—81no—
193C22×Q8D5211yescharacteristic
194C2×M16—261no—
195C2×M16—261no—
196C2×M16—261no—
197C22×C8—21no—
198C22×C8—21no—
199C4⋊Q8—131no—
200C4⋊Q8—131no—
201#125—261no—
202C22⋊Q8—261no—
203C22⋊Q8—261no—
204C4×Q8—21no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208C4×Q8—261no—
209C4×Q8—261no—
210#117—261no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4D5211yescharacteristic
213C2×C42—21no—
214C2×C42C22×D1311yescharacteristic
215#107—262no—
216#106—262no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—132no—
220C4⋊C8—261no—
221C4⋊C8—261no—
222C4⋊C8—261no—
223C4⋊C8—261no—
224C4⋊C8—261no—
225#103—262no—
226#103—262no—
227#101—522no—
228C4×C8—21no—
229C4×C8C22⋊D1311yescharacteristic
230C4×C8C22⋊D1311yescharacteristic
231C2×C13—21no—
232C2×C13—21no—
233C2×C13#203511yescharacteristic
234C2×C13#205011yescharacteristic
235C2×C13#205211yescharacteristic
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—261no—
242C2×Q8—261no—
243C2×Q8#609512yes—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4C2×D5211yescharacteristic
247C22×C4#612911yescharacteristic
248C22×C4#612911yescharacteristic
249M16—521no—
250M16—521no—
251M16—521no—
252M16—521no—
253M16—521no—
254M16—521no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—42no—
258C2×C8—41no—
259C2×C8—81no—
260C2×C8—262no—
261C2×C8—521no—
262C2×C8—521no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C22⋊C4—521no—
274C42—41no—
275C42—41no—
276C42—521no—
277C42#612711yescharacteristic
278C42D4×D1311yescharacteristic
279C42D4×D1311yescharacteristic
280C42C2×C22⋊D1311yescharacteristic
281C13#1046211yescharacteristic, complemented, Sylow
282C23#8814011yescharacteristic
283Q8—22no—
284Q8—22no—
285Q8—41no—
286Q8—41no—
287Q8—521no—
288Q8—521no—
289Q8—1041no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4#8813611yescharacteristic
301C2×C4#8813711yescharacteristic
302C2×C4#8813911yescharacteristic
303C2×C4C2×#609511yescharacteristic
304C2×C4#8815811yescharacteristic
305C2×C4#8816311yescharacteristic
306C2×C4#8816311yescharacteristic
307C2×C4#8818411yescharacteristic
308C2×C4#8819211yescharacteristic
309C2×C4#8819311yescharacteristic
310C8—22no—
311C8—41no—
312C8—81no—
313C8—522no—
314C8—1041no—
315C8—1041no—
316C22—21no—
317C22—21no—
318C22#1171838211yescharacteristic
319C22#1171838411yescharacteristic
320C22#1171862211yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—81no—
326C4—1041no—
327C4—1041no—
328C4#1171839411yescharacteristic
329C4#1171839911yescharacteristic
330C4#1171877511yescharacteristic
331C4#1171879811yescharacteristic
332C4#1171883811yescharacteristic
333C4#1171885311yescharacteristic
334C2—21no—
335C2—21no—
336C2#1311603311yescharacteristic
337C2#1311612211yescharacteristic
338C2#1311613611yescharacteristic
subgroupG/H
centerC22#11718622
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×Q8⋊C8C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenterC2×Q8⋊C8D13
hypocenterC13#10462
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
281. C13#10462semidirect

Maximal subgroups

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

subgroupindex
#131246412
#131148322
#131135922
#131135242
#131132922
#131127112
C2×C13×Q8⋊C82
#1046213