Finite Group Databasebeta

← #15773802

Subgroups — #15773802

Order 3328.

432 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114913C211yesmaximal, characteristic, complemented
2#13113150C211yesmaximal, characteristic, complemented
3#13112857C212yesmaximal, complemented
4#13112833C212yesmaximal
5C13×#2610C211yesmaximal, characteristic
6C2×C13×#124C411yescharacteristic, complemented
7C2×C13×#117C2211yescharacteristic
8C13×#395C411yescharacteristic, complemented
9C13×#394C411yescharacteristic, complemented
10C13×#393C2211yescharacteristic
11C13×#392C2211yescharacteristic
12C13×#390—21no—
13C13×#388—21no—
14C13×#388—21no—
15C13×#386—21no—
16C13×#376C411yescharacteristic, complemented
17#11718872—21no—
18#11718586—21no—
19#11718120—21no—
20#11718118—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×#124—41no—
28C13×#124—41no—
29C13×#117—41no—
30C13×#117—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4D411yescharacteristic
41C2×C13×C22⋊C4C2311yescharacteristic
42C2×C42×C13—21no—
43C2×C42×C13C2×C411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C22⋊Dic13—22no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95C2×C411yescharacteristic
50C13×#95C2×C411yescharacteristic
51#88071—41no—
52#88071—41no—
53C22⋊#1055—22no—
54C4⋊#1055—41no—
55C4×#1055—41no—
56#11844—131nomaximal, Sylow
57C24×C13—21no—
58C24×C13C2×D411yescharacteristic
59C2×Q8×C13—41no—
60C2×Q8×C13—81no—
61C2×D4×C13—41no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C2×D4×C13—81no—
65C2×D4×C13—81no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—41no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—81no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—81no—
91C13×C22⋊C4—81no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—42no—
97C22⋊Dic13—42no—
98C22⋊Dic13—42no—
99C2×#1055—42no—
100#2610D1311yescharacteristic
101#1820—131no—
102#1458—131no—
103#1351—132no—
104#1343—132no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13C2×C22⋊C411yescharacteristic
117C23×C13#13512yes—
118Q8×C13—82no—
119D4×C13—84no—
120D4×C13—82no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—22no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13#9911yescharacteristic
146C2×C4×C13#9911yescharacteristic
147C2×Dic13—82no—
148C2×Dic13—82no—
149C2×Dic13—82no—
150#1055—82no—
151C2×#124Dic1311yescharacteristic, complemented
152C2×#117C2×D1311yescharacteristic
153#431—261no—
154#395Dic1311yescharacteristic, complemented
155#394Dic1311yescharacteristic, complemented
156#393C2×D1311yescharacteristic
157#392C2×D1311yescharacteristic
158#390—21no—
159#388—21no—
160#388—21no—
161#386—21no—
162#381—261no—
163#376Dic1311yescharacteristic, complemented
164#342—132no—
165#342—261no—
166#324—261no—
167#323—132no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—22no—
171C22×C13—42no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—81no—
175C22×C13—81no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13C2×#9911yescharacteristic
183C22×C13#41611yescharacteristic
184C22×C13#42111yescharacteristic
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—42no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—81no—
194C4×C13—81no—
195Dic13—162no—
196C22×Q8C2×Dic1311yescharacteristic
197C22×D4—21no—
198C22×D4C2×Dic1311yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200#124—41no—
201#124—41no—
202#117—41no—
203#117—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×Dic1311yescharacteristic
206C2×C4⋊C4C22⋊D1311yescharacteristic
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—262no—
214C2×C22⋊C4C22⋊D1311yescharacteristic
215C2×C22⋊C4C22×D1311yescharacteristic
216C2×C42—21no—
217C2×C42C2×Dic1311yescharacteristic
218C2×C42C22⋊D1311yescharacteristic
219C4⋊C8—521no—
220C22⋊C8—262no—
221C4×C8—521no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—521no—
226#95—521no—
227#95C2×Dic1311yescharacteristic
228#95C2×Dic1311yescharacteristic
229C2×C13—21no—
230C2×C13—21no—
231C2×C13—42no—
232C2×C13—161no—
233C2×C13#151611yescharacteristic
234C2×C13#212211yescharacteristic
235C2×C13#212611yescharacteristic
236C24—21no—
237C24C2×C22⋊D1311yescharacteristic
238C2×Q8—41no—
239C2×Q8—81no—
240C2×D4—41no—
241C2×D4—42no—
242C2×D4—42no—
243C2×D4—81no—
244C2×D4—81no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—522no—
253C22×C4C22⋊Dic1311yescharacteristic
254C22×C4C22⋊Dic1311yescharacteristic
255C22×C4C22⋊Dic1311yescharacteristic
256C22×C4C22⋊Dic1311yescharacteristic
257C22×C4C22×Dic1311yescharacteristic
258C22×C4C2×C22⋊D1311yescharacteristic
259C2×C8—522no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—81no—
271C22⋊C4—81no—
272C22⋊C4—522no—
273C22⋊C4—522no—
274C42—21no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—42no—
279C13#1184411yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23#8820412yes—
292C23C2×C22⋊Dic1311yescharacteristic
293Q8—82no—
294D4—84no—
295D4—82no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—1042no—
321C2×C4—1042no—
322C2×C4—1042no—
323C2×C4#8807411yescharacteristic
324C2×C4#8807411yescharacteristic
325C8—1042no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22C2×#8807411yescharacteristic
341C22#1171889411yescharacteristic
342C22#1171889711yescharacteristic
343C4—21no—
344C4—21no—
345C4—42no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—2082no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—161no—
358C2#1311339211yescharacteristic
359C2#1311648611yescharacteristic
360C2#1311650111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2610C2
socleC22×C13C2×#99
prime radicalC13×#392C22
cosocleC2×C13×C22⋊C4C23
hypercenter#2610D13
hypocenterC13#11844
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. #13114913C2semidirect
2. #13113150C2semidirect
3. #13112857C2semidirect
6. C2×C13×#124C4semidirect
8. C13×#395C4semidirect
9. C13×#394C4semidirect
16. C13×#376C4semidirect
151. C2×#124Dic13semidirect
154. #395Dic13semidirect
155. #394Dic13semidirect
163. #376Dic13semidirect
279. C13#11844semidirect

Maximal subgroups

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

subgroupindex
#131149132
#131131502
#131128572
#131128332
C13×#26102
#1184413