Finite Group Databasebeta

← #15759821

Subgroups — #15759821

Order 3328.

536 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 111 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#13124966C211yesmaximal, characteristic
2#13115779C211yesmaximal, characteristic
3#13113347C211yesmaximal, characteristic
4#13113283C211yesmaximal, characteristic
5#13112729C211yesmaximal, characteristic
6#13112692C211yesmaximal, characteristic
7C13×#2276C211yesmaximal, characteristic
8C2×C4×Q8×C13—21no—
9C2×C4×Q8×C13C2211yescharacteristic
10#11719175C2211yescharacteristic
11C4×C13×C4⋊C4—21no—
12C4×C13×C4⋊C4—22no—
13C4×C13×C4⋊C4—21no—
14C4×C13×C4⋊C4C2211yescharacteristic
15C13×#376—21no—
16C13×#376C2211yescharacteristic
17#11718889—21no—
18#11718692C412yescomplemented
19#11718691—22no—
20#11718681C412yescomplemented
21#11718632—21no—
22#11718587C2211yescharacteristic
23#11718587C2211yescharacteristic
24C4×#6099C2211yescharacteristic
25Q8⋊#1055—22no—
26#11718115—22no—
27#11718044—21no—
28#11718044—21no—
29C22×Q8×C13D411yescharacteristic
30C4×Q8×C13—28no—
31C4×Q8×C13—21no—
32C4×Q8×C13—21no—
33C4×Q8×C13C2×C412yes—
34C4×Q8×C13D412yes—
35C2×C13×C4⋊C4—22no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C42×C13—22no—
40C2×C42×C13—21no—
41C2×C42×C13—21no—
42C2×C42×C13—22no—
43C2×C42×C13D412yes—
44C2×C42×C13C2311yescharacteristic
45C2×#6107—22no—
46#88180—21no—
47#88178—21no—
48#88178—21no—
49C2×#6099—21no—
50#88124—21no—
51#88123C2×C411yescharacteristic
52#88123C2×C411yescharacteristic
53C4×Dic26—21no—
54C4×Dic26—21no—
55C13×#95—22no—
56C13×#95—21no—
57C13×#95—21no—
58C13×#95D411yescharacteristic
59C13×#95D411yescharacteristic
60#88075—22no—
61C22⋊#1055—21no—
62C22⋊#1055—21no—
63#88050—22no—
64#88048—22no—
65C4⋊#1055—21no—
66C4⋊#1055C2×C412yes—
67#88043—21no—
68#88043—21no—
69#88043—21no—
70C4×#1055—21no—
71#9324—131nomaximal, Sylow
72C2×Q8×C13—24no—
73C2×Q8×C13—21no—
74C2×Q8×C13C22⋊C412yes—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—22no—
79C22×C4×C13—21no—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C2×Dic26—21no—
84C2×Dic26—21no—
85C13×C4⋊C4—28no—
86C13×C4⋊C4—24no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4C22⋊C412yes—
91C42×C13—28no—
92C42×C13—24no—
93C42×C13—22no—
94C42×C13—22no—
95C42×C13—42no—
96C42×C13—82no—
97C42×C13C22×C411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C42×C13#4111yescharacteristic
100C42×C13#4111yescharacteristic
101C22⋊Dic13—41no—
102#6107—44no—
103C4⋊Dic13—21no—
104C4⋊Dic13—21no—
105C4⋊Dic13—21no—
106C4⋊Dic13—21no—
107#6101—41no—
108#6101—41no—
109C4×Dic13—41no—
110#6099—22no—
111#6099—41no—
112C2×#1055—22no—
113C2×#1055—41no—
114C2×#1055—41no—
115#3113—131no—
116#2276D1311yescharacteristic
117#1986—131no—
118#1506—131no—
119#1491—131no—
120#1300—131no—
121#1285—131no—
122C23×C13#12011yescharacteristic
123Q8×C13—24no—
124Q8×C13—22no—
125Q8×C13#10414yes—
126C2×C4×C13—24no—
127C2×C4×C13—22no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—24no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13C2×C22⋊C411yescharacteristic
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12311yescharacteristic
150C2×Dic13—41no—
151C2×Dic13—41no—
152Dic26—42no—
153Dic26—81no—
154#1055—42no—
155#1055—42no—
156#1055—81no—
157#533—131no—
158C2×C4×Q8—21no—
159C2×C4×Q8C2×D1311yescharacteristic
160#483—261no—
161#475—132no—
162#462—132no—
163#451—261no—
164#441—262no—
165#432—131no—
166#432—131no—
167C4×M16—131no—
168C4×C4⋊C4—21no—
169C4×C4⋊C4—22no—
170C4×C4⋊C4—21no—
171C4×C4⋊C4C2×D1311yescharacteristic
172#376—21no—
173#376C2×D1311yescharacteristic
174#339—262no—
175#328—261no—
176#328—261no—
177Q8⋊C8—262no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13#38611yescharacteristic
181C22×C13#45511yescharacteristic
182C22×C13#45611yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—24no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—44no—
190C4×C13—42no—
191C4×C13—42no—
192C4×C13—42no—
193C4×C13C2×#10412yes—
194Dic13—81no—
195Dic13—81no—
196C22×Q8C22⋊D1311yescharacteristic
197C2×Q16—262no—
198C2×M16—261no—
199C4⋊Q8—131no—
200C4⋊Q8—131no—
201#125—261no—
202C22⋊Q8—261no—
203C22⋊Q8—261no—
204C4×Q8—28no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8—261no—
208C4×Q8—261no—
209C4×Q8C4×D1312yes—
210C4×Q8D5212yes—
211#117—261no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C22⋊D1311yescharacteristic
216C2×C42—22no—
217C2×C42—21no—
218C2×C42—21no—
219C2×C42—22no—
220C2×C42C22⋊D1312yes—
221C2×C42C22×D1311yescharacteristic
222#106—262no—
223C4⋊C8—132no—
224C4⋊C8—261no—
225#103—262no—
226#103—262no—
227C22⋊C8—261no—
228C22⋊C8—261no—
229#97—261no—
230#97—261no—
231#97—261no—
232C4×C8—261no—
233#95—22no—
234#95—21no—
235#95—21no—
236#95C22⋊D1311yescharacteristic
237#95C22⋊D1311yescharacteristic
238C2×C13—21no—
239C2×C13—21no—
240C2×C13#188211yescharacteristic
241C2×C13#189611yescharacteristic
242C2×C13#190511yescharacteristic
243C2×Q8—24no—
244C2×Q8—21no—
245C2×Q8—261no—
246C2×Q8—261no—
247C2×Q8#610312yes—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4C2×C22⋊D1311yescharacteristic
254C22×C4C2×C22⋊D1311yescharacteristic
255C22×C4C2×C22⋊D1311yescharacteristic
256Q16—524no—
257M16—262no—
258M16—521no—
259C2×C8—262no—
260C2×C8—521no—
261C2×C8—521no—
262C4⋊C4—28no—
263C4⋊C4—24no—
264C4⋊C4—22no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—261no—
270C4⋊C4—261no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C4⋊C4#610312yes—
274C22⋊C4—521no—
275C42—28no—
276C42—24no—
277C42—22no—
278C42—22no—
279C42—42no—
280C42—82no—
281C42—521no—
282C42C2×C4×D1311yescharacteristic
283C42C2×D5211yescharacteristic
284C42#612711yescharacteristic
285C42#612711yescharacteristic
286C13#932411yescharacteristic, complemented, Sylow
287C23#8820711yescharacteristic
288Q8—24no—
289Q8—22no—
290Q8—522no—
291Q8—1041no—
292Q8#8804514yes—
293C2×C4—24no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—24no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4C2×#610311yescharacteristic
314C2×C4C4×C22⋊D1311yescharacteristic
315C2×C4C4×C22⋊D1311yescharacteristic
316C2×C4#8818311yescharacteristic
317C2×C4#8818411yescharacteristic
318C2×C4#8818411yescharacteristic
319C8—522no—
320C8—522no—
321C8—1041no—
322C22—21no—
323C22—21no—
324C22#1171887411yescharacteristic
325C22#1171890311yescharacteristic
326C22#1171890711yescharacteristic
327C4—21no—
328C4—21no—
329C4—24no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—44no—
334C4—42no—
335C4—42no—
336C4—42no—
337C4—1041no—
338C4—1041no—
339C4C2×#8804512yes—
340C2—21no—
341C2—21no—
342C2#1311520511yescharacteristic
343C2#1311527911yescharacteristic
344C2#1311533011yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2276C2
socleC22×C13#386
prime radicalC23×C13#120
cosocleC2×C42×C13C23
hypercenter#2276D13
hypocenterC13#9324
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2276

Complements

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

NH ≅ G/Ntype
18. #11718692C4semidirect
20. #11718681C4semidirect
286. C13#9324semidirect

Maximal subgroups

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

subgroupindex
#131249662
#131157792
#131133472
#131132832
#131127292
#131126922
C13×#22762
#932413