Finite Group Databasebeta

← #15758888

Subgroups — #15758888

Order 3328.

530 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 107 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#13123877C211yesmaximal, characteristic
2C4×#88074C211yesmaximal, characteristic
3#13113356C212yesmaximal, complemented
4#13112688C212yesmaximal, complemented
5C13×#2638C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2211yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#398C411yescharacteristic, complemented
9C13×#397—21no—
10C13×#397C411yescharacteristic, complemented
11C13×#395C411yescharacteristic, complemented
12C13×#394—21no—
13C13×#393C411yescharacteristic, complemented
14C13×#387—21no—
15C13×#385—21no—
16C13×#381C2211yescharacteristic
17C2×#88074—21no—
18C4×C22⋊Dic13C2212yes—
19#11718868—21no—
20#11718868C2212yes—
21#11718673—24no—
22#11718586—21no—
23#11718130—24no—
24#11718118—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C13×C22⋊Q8—22no—
30C13×C22⋊Q8—22no—
31C4×D4×C13—22no—
32C4×D4×C13—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4C2×C411yescharacteristic
43C2×C13×C22⋊C4D411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C22⋊Dic13—22no—
46C2×C4×Dic13—22no—
47C2×#6099—22no—
48C2×#6099—22no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95C2×C411yescharacteristic
55C13×#95C2×C411yescharacteristic
56#88074—24no—
57#88071—22no—
58C22⋊#1055—22no—
59C22⋊#1055—22no—
60C22⋊#1055D414yes—
61C4⋊#1055—22no—
62C4×#1055—22no—
63#9184—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—81no—
68C2×D4×C13—22no—
69C2×D4×C13—22no—
70C2×D4×C13—41no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—81no—
78C22×C4×C13—81no—
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C2×D412yes—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13#4112yes—
86C22×Dic13—42no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—81no—
93C13×C22⋊C4—22no—
94C13×C22⋊C4—22no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—81no—
98C13×C22⋊C4—81no—
99C42×C13—21no—
100C42×C13—21no—
101C22⋊Dic13—24no—
102C22⋊Dic13—42no—
103C4×Dic13—82no—
104#6099—82no—
105#6099—82no—
106C2×#1055—24no—
107#2975—131no—
108#2638D1311yescharacteristic
109C4×#99—131no—
110#1508—132no—
111#1284—132no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13C2×C22⋊C411yescharacteristic
122C23×C13#12112yes—
123Q8×C13—82no—
124D4×C13—44no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—42no—
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—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—81no—
149C2×C4×C13#10412yes—
150C2×C4×C13C4×D412yes—
151C2×C4×C13#12011yescharacteristic
152C2×C4×C13#12311yescharacteristic
153C2×Dic13—44no—
154C2×Dic13—82no—
155C2×Dic13—82no—
156#1055—44no—
157C2×C22⋊Q8C2×D1311yescharacteristic
158C2×C4×D4C2×D1311yescharacteristic
159#436—264no—
160#431—261no—
161C2×#99—261no—
162#407—132no—
163#407—261no—
164#398Dic1311yescharacteristic, complemented
165#397—21no—
166#397Dic1311yescharacteristic, complemented
167#395Dic1311yescharacteristic, complemented
168#394—21no—
169#393Dic1311yescharacteristic, complemented
170#387—21no—
171#385—21no—
172#381C2×D1311yescharacteristic
173C4×C22⋊C4—132no—
174#342—261no—
175#328—264no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—42no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—41no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13#38611yescharacteristic
189C22×C13C2×#10411yescharacteristic
190C22×C13#42111yescharacteristic
191C4×C13—22no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—22no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—81no—
198C4×C13—81no—
199C4×C13—81no—
200C4×C13—81no—
201Dic13—84no—
202C22×Q8C2×Dic1311yescharacteristic
203C22×D4C22⋊D1311yescharacteristic
204C23×C4C22⋊D1311yescharacteristic
205C23×C4C22×D1311yescharacteristic
206C2×M16—262no—
207C2×M16—262no—
208C22⋊Q8—22no—
209C22⋊Q8—22no—
210C4×D4—22no—
211C4×D4—22no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×Dic1311yescharacteristic
216C2×C4⋊C4C2×Dic1311yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—262no—
222C2×C22⋊C4C2×Dic1311yescharacteristic
223C2×C22⋊C4C22⋊D1311yescharacteristic
224C2×C42—262no—
225C2×C42C22⋊D1311yescharacteristic
226C4⋊C8—262no—
227#99—264no—
228C22⋊C8—134no—
229C22⋊C8—262no—
230C22⋊C8—262no—
231C4×C8—262no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—262no—
238#95C2×Dic1311yescharacteristic
239#95C2×Dic1311yescharacteristic
240C2×C13—21no—
241C2×C13—21no—
242C2×C13—42no—
243C2×C13—81no—
244C2×C13#187111yescharacteristic
245C2×C13#190911yescharacteristic
246C2×C13#191311yescharacteristic
247C24C22⋊Dic1311yescharacteristic
248C24C2×C22⋊D1311yescharacteristic
249C2×Q8—22no—
250C2×Q8—81no—
251C2×D4—22no—
252C2×D4—22no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—81no—
261C22×C4—81no—
262C22×C4—522no—
263C22×C4C22⋊Dic1311yescharacteristic
264C22×C4C22⋊Dic1311yescharacteristic
265C22×C4C22⋊Dic1311yescharacteristic
266C22×C4D4×D1312yes—
267C22×C4#612912yes—
268C22×C4C22×Dic1311yescharacteristic
269C22×C4C2×C22⋊D1311yescharacteristic
270M16—1042no—
271M16—1042no—
272C2×C8—264no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—81no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C22⋊C4—81no—
284C22⋊C4—81no—
285C22⋊C4—264no—
286C22⋊C4—522no—
287C42—21no—
288C42—21no—
289C42—1042no—
290C13#918411yescharacteristic, complemented, Sylow
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23#8819312yes—
301C23C2×C22⋊Dic1311yescharacteristic
302Q8—82no—
303D4—44no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—524no—
329C2×C4—1042no—
330C2×C4—1042no—
331C2×C4#8807712yes—
332C2×C4D4×Dic1312yes—
333C2×C4#8818911yescharacteristic
334C2×C4#8819111yescharacteristic
335C8—524no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22#1171888111yescharacteristic
349C22C2×#8807711yescharacteristic
350C22#1171889711yescharacteristic
351C4—22no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—1044no—
362C2—21no—
363C2—21no—
364C2—42no—
365C2—81no—
366C2#1311513911yescharacteristic
367C2#1311535911yescharacteristic
368C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2638C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2638D13
hypocenterC13#9184
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2638

Complements

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

NH ≅ G/Ntype
3. #13113356C2semidirect
4. #13112688C2semidirect
8. C13×#398C4semidirect
10. C13×#397C4semidirect
11. C13×#395C4semidirect
13. C13×#393C4semidirect
164. #398Dic13semidirect
166. #397Dic13semidirect
167. #395Dic13semidirect
169. #393Dic13semidirect
290. C13#9184semidirect

Maximal subgroups

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

subgroupindex
#131238772
C4×#880742
#131133562
#131126882
C13×#26382
#918413