Finite Group Databasebeta

← #15773545

Subgroups — #15773545

Order 3328.

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

normal subgroups only

This group has 462 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#13113177C211yesmaximal, characteristic
3#13112860C212yesmaximal, complemented
4#13112857C212yesmaximal, complemented
5C13×#2564C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#400C411yescharacteristic, complemented
9C13×#399C2211yescharacteristic
10C13×#395C411yescharacteristic, complemented
11C13×#393C2211yescharacteristic
12C13×#387—21no—
13C13×#386—21no—
14C13×#385—21no—
15C13×#380—21no—
16C2×C13×#95C411yescharacteristic, complemented
17C2×#88074—21no—
18C4×C22⋊Dic13—21no—
19#11718587—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13D411yescharacteristic
25C23×C4×C13—21no—
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×C22⋊Q8—41no—
29C13×C22⋊Q8—41no—
30C4×D4×C13—41no—
31C4×D4×C13—41no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
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×C13D411yescharacteristic
43C2×C22⋊Dic13—22no—
44C2×C4×Dic13—41no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52#88074—24no—
53#88071—41no—
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56#88043—41no—
57#11789—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×Q8×C13—41no—
61C2×Q8×C13—81no—
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—42no—
74C22×C4×C13—42no—
75C22×C4×C13—81no—
76C22×C4×C13—81no—
77C22×C4×C13—81no—
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×Dic13—42no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—81no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—81no—
95C42×C13—21no—
96C42×C13—21no—
97C22⋊Dic13—24no—
98C22⋊Dic13—42no—
99C4×Dic13—82no—
100C2×#1055—42no—
101#2564D1311yescharacteristic
102C4×#99—131no—
103#1466—131no—
104#1352—132no—
105#1351—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13#10412yes—
115C23×C13C2×C22⋊C411yescharacteristic
116C23×C13#13712yes—
117Q8×C13—82no—
118D4×C13—44no—
119C2×C4×C13—22no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
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—41no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—84no—
146C2×C4×C13#9911yescharacteristic
147C2×C4×C13#9911yescharacteristic
148C2×Dic13—44no—
149C2×Dic13—82no—
150C2×Dic13—82no—
151#1055—82no—
152C2×C22⋊Q8Dic1311yescharacteristic, complemented
153C2×C4×D4C2×D1311yescharacteristic
154#432—261no—
155C2×#99—261no—
156#400Dic1311yescharacteristic, complemented
157#399C2×D1311yescharacteristic
158#395Dic1311yescharacteristic, complemented
159#393C2×D1311yescharacteristic
160#387—21no—
161#386—21no—
162#385—21no—
163#380—21no—
164C4×C22⋊C4—261no—
165C2×#95Dic1311yescharacteristic, complemented
166#342—132no—
167#323—132no—
168#323—261no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—22no—
172C22×C13—22no—
173C22×C13—42no—
174C22×C13—42no—
175C22×C13—42no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—81no—
181C22×C13C2×#9911yescharacteristic
182C22×C13#41911yescharacteristic
183C22×C13C2×#10411yescharacteristic
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—42no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—81no—
192C4×C13—81no—
193C4×C13—81no—
194Dic13—84no—
195C22×Q8C2×Dic1311yescharacteristic
196C22×D4C22⋊D1311yescharacteristic
197C23×C4—21no—
198C23×C4C2×Dic1311yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200C22⋊Q8—41no—
201C22⋊Q8—41no—
202C4×D4—41no—
203C4×D4—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×Dic1311yescharacteristic
208C2×C4⋊C4C2×Dic1311yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—262no—
213C2×C22⋊C4C22⋊D1311yescharacteristic
214C2×C22⋊C4C22×D1311yescharacteristic
215C2×C42—521no—
216C2×C42C22⋊D1311yescharacteristic
217C4⋊C8—521no—
218#99—264no—
219C22⋊C8—262no—
220#97—521no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—521no—
227#95C2×Dic1311yescharacteristic
228#95C2×Dic1311yescharacteristic
229C2×C13—21no—
230C2×C13—21no—
231C2×C13—42no—
232C2×C13—42no—
233C2×C13#150811yescharacteristic
234C2×C13#212111yescharacteristic
235C2×C13#212611yescharacteristic
236C24C22⋊Dic1311yescharacteristic
237C24C2×C22⋊D1311yescharacteristic
238C2×Q8—41no—
239C2×Q8—81no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—42no—
252C22×C4—42no—
253C22×C4—81no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4—522no—
257C22×C4C22⋊Dic1311yescharacteristic
258C22×C4C22⋊Dic1311yescharacteristic
259C22×C4C22⋊Dic1311yescharacteristic
260C22×C4C22×Dic1311yescharacteristic
261C22×C4C2×C22⋊D1311yescharacteristic
262C2×C8—522no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—81no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—81no—
274C22⋊C4—264no—
275C22⋊C4—522no—
276C42—21no—
277C42—21no—
278C42—1042no—
279C13#1178911yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23#8807712yes—
289C23#8819612yes—
290C23C2×C22⋊Dic1311yescharacteristic
291Q8—82no—
292D4—44no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
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—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—84no—
320C2×C4—524no—
321C2×C4—1042no—
322C2×C4—1042no—
323C2×C4#8807411yescharacteristic
324C2×C4#8807411yescharacteristic
325C8—1042no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22C2×#8807411yescharacteristic
339C22#1171888611yescharacteristic
340C22C2×#8807711yescharacteristic
341C4—21no—
342C4—21no—
343C4—42no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—1044no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—42no—
356C2#1311335611yescharacteristic
357C2#1311648211yescharacteristic
358C2#1311650111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2564C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2564D13
hypocenterC13#11789
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2564

Complements

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

NH ≅ G/Ntype
3. #13112860C2semidirect
4. #13112857C2semidirect
6. C2×C13×C22⋊Q8C4semidirect
8. C13×#400C4semidirect
10. C13×#395C4semidirect
16. C2×C13×#95C4semidirect
152. C2×C22⋊Q8Dic13semidirect
156. #400Dic13semidirect
158. #395Dic13semidirect
165. C2×#95Dic13semidirect
279. C13#11789semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131772
#131128602
#131128572
C13×#25642
#1178913