Finite Group Databasebeta

← #15773524

Subgroups — #15773524

Order 3328.

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

normal subgroups only

This group has 460 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#13113174C211yesmaximal, characteristic
3#13112860C212yesmaximal, complemented
4#13112857C212yesmaximal, complemented
5C13×#2580C211yesmaximal, characteristic
6C2×C4×Q8×C13C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#399C411yescharacteristic, complemented
9C13×#399C2211yescharacteristic
10C13×#393C411yescharacteristic, complemented
11C13×#393C2211yescharacteristic
12C13×#390—21no—
13C13×#389—21no—
14C13×#385—21no—
15C13×#385—21no—
16C13×#382C411yescharacteristic, complemented
17C2×#88074—21no—
18C4×C22⋊Dic13—21no—
19#11718868—21no—
20#11718120—21no—
21#11718118C2212yes—
22#11718117C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C4×Q8×C13—41no—
28C4×Q8×C13—41no—
29C4×D4×C13—41no—
30C4×D4×C13—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
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×C13—21no—
44C2×C42×C13C2×C411yescharacteristic
45C2×C22⋊Dic13—22no—
46C2×C4×Dic13—41no—
47C2×#6099—41no—
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#11784—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×Q8×C13—42no—
61C2×Q8×C13—41no—
62C2×D4×C13—22no—
63C2×D4×C13—22no—
64C2×D4×C13—41no—
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—21no—
72C22×C4×C13—21no—
73C22×C4×C13—81no—
74C22×C4×C13—81no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—42no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—81no—
87C13×C4⋊C4—81no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—81no—
93C13×C22⋊C4—81no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—42no—
97C22⋊Dic13—24no—
98C22⋊Dic13—42no—
99C4×Dic13—82no—
100#6099—82no—
101C2×#1055—42no—
102#2580D1311yescharacteristic
103C4×#99—131no—
104#1465—131no—
105#1352—132no—
106#1351—132no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13C2×C22⋊C411yescharacteristic
117C23×C13#13712yes—
118Q8×C13—42no—
119Q8×C13—42no—
120D4×C13—44no—
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—41no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
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—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13#9911yescharacteristic
147C2×C4×C13#9911yescharacteristic
148C2×C4×C13#10412yes—
149C2×Dic13—44no—
150C2×Dic13—82no—
151C2×Dic13—82no—
152#1055—82no—
153C2×C4×Q8Dic1311yescharacteristic, complemented
154C2×C4×D4C2×D1311yescharacteristic
155C2×#99—261no—
156#407—261no—
157#399Dic1311yescharacteristic, complemented
158#399C2×D1311yescharacteristic
159#393Dic1311yescharacteristic, complemented
160#393C2×D1311yescharacteristic
161#390—21no—
162#389—21no—
163#385—21no—
164#385—21no—
165#382Dic1311yescharacteristic, complemented
166C4×C22⋊C4—261no—
167#342—132no—
168#324—261no—
169#323—132no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—22no—
173C22×C13—42no—
174C22×C13—42no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—81no—
181C22×C13—81no—
182C22×C13C2×#9911yescharacteristic
183C22×C13#41911yescharacteristic
184C22×C13C2×#10411yescharacteristic
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—22no—
188C4×C13—42no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—81no—
193C4×C13—81no—
194C4×C13—81no—
195Dic13—84no—
196C22×Q8C2×Dic1311yescharacteristic
197C22×D4C22⋊D1311yescharacteristic
198C23×C4C22⋊D1311yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200C2×M16—521no—
201C4×Q8—41no—
202C4×Q8—41no—
203C4×D4—41no—
204C4×D4—41no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4C2×Dic1311yescharacteristic
210C2×C4⋊C4C22⋊D1311yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—262no—
216C2×C22⋊C4C2×Dic1311yescharacteristic
217C2×C22⋊C4C22×D1311yescharacteristic
218C2×C42—21no—
219C2×C42—521no—
220C2×C42C2×Dic1311yescharacteristic
221#99—264no—
222C22⋊C8—262no—
223C22⋊C8—521no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—521no—
228#95C2×Dic1311yescharacteristic
229#95C2×Dic1311yescharacteristic
230C2×C13—21no—
231C2×C13—21no—
232C2×C13—42no—
233C2×C13—81no—
234C2×C13#150811yescharacteristic
235C2×C13#212011yescharacteristic
236C2×C13#212711yescharacteristic
237C24C22⋊Dic1311yescharacteristic
238C24C2×C22⋊D1311yescharacteristic
239C2×Q8—42no—
240C2×Q8—41no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—41no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—81no—
253C22×C4—81no—
254C22×C4—522no—
255C22×C4C22⋊Dic1311yescharacteristic
256C22×C4C22⋊Dic1311yescharacteristic
257C22×C4C22⋊Dic1311yescharacteristic
258C22×C4C22×Dic1311yescharacteristic
259C22×C4C2×C22⋊D1311yescharacteristic
260M16—1042no—
261C2×C8—522no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—42no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—81no—
274C22⋊C4—81no—
275C22⋊C4—264no—
276C22⋊C4—522no—
277C42—21no—
278C42—21no—
279C42—42no—
280C42—1042no—
281C13#1178411yescharacteristic, complemented, Sylow
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23#8819612yes—
292C23C2×C22⋊Dic1311yescharacteristic
293Q8—42no—
294Q8—42no—
295D4—44no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
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—81no—
320C2×C4—81no—
321C2×C4—524no—
322C2×C4—1042no—
323C2×C4—1042no—
324C2×C4#8807411yescharacteristic
325C2×C4#8807411yescharacteristic
326C2×C4#8807712yes—
327C8—1042no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—81no—
339C22—81no—
340C22C2×#8807411yescharacteristic
341C22#1171888611yescharacteristic
342C22C2×#8807711yescharacteristic
343C4—22no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—81no—
351C4—81no—
352C4—81no—
353C4—1044no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—81no—
358C2#1311335611yescharacteristic
359C2#1311647711yescharacteristic
360C2#1311650511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2580C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2580D13
hypocenterC13#11784
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2580

Complements

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

NH ≅ G/Ntype
3. #13112860C2semidirect
4. #13112857C2semidirect
6. C2×C4×Q8×C13C4semidirect
8. C13×#399C4semidirect
10. C13×#393C4semidirect
16. C13×#382C4semidirect
153. C2×C4×Q8Dic13semidirect
157. #399Dic13semidirect
159. #393Dic13semidirect
165. #382Dic13semidirect
281. C13#11784semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131742
#131128602
#131128572
C13×#25802
#1178413