Finite Group Databasebeta

← #15773278

Subgroups — #15773278

Order 3328.

442 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#88074C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112860C212yesmaximal, complemented
4#13112836C212yesmaximal, complemented
5C13×#2633C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#399C411yescharacteristic, complemented
9C13×#399C2211yescharacteristic
10C13×#398—21no—
11C13×#397C411yescharacteristic, complemented
12C13×#397C2211yescharacteristic
13C13×#394—21no—
14C13×#385—21no—
15C13×#385—21no—
16C13×#383C411yescharacteristic, complemented
17C2×#88074—21no—
18C4×C22⋊Dic13—21no—
19C2×C22⋊#1055—21no—
20#11718120—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C13×#125—41no—
27C13×#125—41no—
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4C2311yescharacteristic
43C2×C42×C13C2×C411yescharacteristic
44C2×C22⋊Dic13—22no—
45C2×C4×Dic13—41no—
46C22×#1055—41no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95C2×C411yescharacteristic
52C13×#95C2×C411yescharacteristic
53#88074—24no—
54#88071—41no—
55C22⋊#1055—22no—
56C22⋊#1055—41no—
57#11732—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—41no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—81no—
72C22×C4×C13—81no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×Dic13—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—81no—
86C13×C4⋊C4—81no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—81no—
92C13×C22⋊C4—81no—
93C42×C13—21no—
94C42×C13—21no—
95C22⋊Dic13—24no—
96C22⋊Dic13—42no—
97C4×Dic13—82no—
98C2×#1055—42no—
99C2×#1055—82no—
100#2633D1311yescharacteristic
101C4×#99—131no—
102#1459—131no—
103#1352—132no—
104#1344—132no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13#10412yes—
114C23×C13C2×C22⋊C411yescharacteristic
115C23×C13#13512yes—
116D4×C13—44no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
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—81no—
142C2×C4×C13—81no—
143C2×C4×C13#9911yescharacteristic
144C2×C4×C13#9911yescharacteristic
145C2×Dic13—44no—
146C2×Dic13—82no—
147C2×Dic13—82no—
148#1055—82no—
149C2×#125Dic1311yescharacteristic, complemented
150C2×C4×D4C2×D1311yescharacteristic
151C2×#99—261no—
152C2×C22⋊C8—261no—
153#399Dic1311yescharacteristic, complemented
154#399C2×D1311yescharacteristic
155#398—21no—
156#397Dic1311yescharacteristic, complemented
157#397C2×D1311yescharacteristic
158#394—21no—
159#385—21no—
160#385—21no—
161#383Dic1311yescharacteristic, complemented
162C4×C22⋊C4—261no—
163#342—132no—
164#324—261no—
165#323—132no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13C2×#9911yescharacteristic
179C22×C13#41611yescharacteristic
180C22×C13C2×#10411yescharacteristic
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—81no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13—81no—
191Dic13—84no—
192C22×D4C22⋊D1311yescharacteristic
193C23×C4C22⋊D1311yescharacteristic
194C23×C4C22⋊D1311yescharacteristic
195C22×C8—521no—
196#125—41no—
197#125—41no—
198C4×D4—41no—
199C4×D4—41no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×Dic1311yescharacteristic
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—262no—
212C2×C22⋊C4C2×Dic1311yescharacteristic
213C2×C22⋊C4C22×D1311yescharacteristic
214C2×C42—521no—
215C2×C42C2×Dic1311yescharacteristic
216#99—264no—
217C22⋊C8—262no—
218C22⋊C8—521no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—521no—
224#95C2×Dic1311yescharacteristic
225#95C2×Dic1311yescharacteristic
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—42no—
229C2×C13—42no—
230C2×C13#150111yescharacteristic
231C2×C13#212311yescharacteristic
232C2×C13#212711yescharacteristic
233C24C22⋊Dic1311yescharacteristic
234C24C2×C22⋊D1311yescharacteristic
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4—522no—
249C22×C4C22⋊Dic1311yescharacteristic
250C22×C4C22⋊Dic1311yescharacteristic
251C22×C4C22⋊Dic1311yescharacteristic
252C22×C4C22×Dic1311yescharacteristic
253C22×C4C2×C22⋊D1311yescharacteristic
254C2×C8—522no—
255C2×C8—1042no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—81no—
269C22⋊C4—81no—
270C22⋊C4—264no—
271C22⋊C4—522no—
272C42—21no—
273C42—21no—
274C42—1042no—
275C13#1173211yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23#8807712yes—
285C23#8820412yes—
286C23C2×C22⋊Dic1311yescharacteristic
287D4—44no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—524no—
315C2×C4—1042no—
316C2×C4—1042no—
317C2×C4#8807411yescharacteristic
318C2×C4#8807411yescharacteristic
319C8—1042no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22—81no—
332C22C2×#8807411yescharacteristic
333C22#1171889411yescharacteristic
334C22C2×#8807711yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—1044no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—42no—
350C2#1311332711yescharacteristic
351C2#1311649011yescharacteristic
352C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2633C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2633D13
hypocenterC13#11732
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2633

Complements

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

NH ≅ G/Ntype
3. #13112860C2semidirect
4. #13112836C2semidirect
6. C2×C13×#125C4semidirect
8. C13×#399C4semidirect
11. C13×#397C4semidirect
16. C13×#383C4semidirect
149. C2×#125Dic13semidirect
153. #399Dic13semidirect
156. #397Dic13semidirect
161. #383Dic13semidirect
275. C13#11732semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131542
#131128602
#131128362
C13×#26332
#1173213