Finite Group Databasebeta

← #15778910

Subgroups — #15778910

Order 3328.

588 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 119 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
1C2×#11718137C212yesmaximal
2#13114824C212yesmaximal, complemented
3#13112961C212yesmaximal, complemented
4C13×#2328C211yesmaximal, characteristic
5C2×C13×#127C2211yescharacteristic
6C2×C4×D4×C13C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#390C411yescharacteristic, complemented
9C13×#390C2211yescharacteristic
10C13×#386—22no—
11C13×#386—22no—
12C13×#382C411yescharacteristic, complemented
13C13×#376C411yescharacteristic, complemented
14C2×#88074C2214yes—
15#11718873—22no—
16#11718137—24no—
17#11718118—22no—
18C22×D4×C13—22no—
19C22×D4×C13C2×C411yescharacteristic
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13D412yes—
23C13×#127—22no—
24C13×#127D412yes—
25C13×#127Q812yes—
26C4×D4×C13—42no—
27C4×D4×C13—42no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4—21no—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4D412yes—
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13C2×C411yescharacteristic
37C2×C22⋊Dic13—24no—
38C2×C4⋊Dic13—42no—
39C13×#95—22no—
40C13×#95—21no—
41C13×#95—21no—
42#88074—24no—
43#88074—24no—
44#88071—42no—
45#12799—131nomaximal, Sylow
46C24×C13—21no—
47C24×C13C2×D412yes—
48C2×D4×C13—24no—
49C2×D4×C13—24no—
50C2×D4×C13—21no—
51C2×D4×C13—41no—
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13—82no—
56C2×D4×C13—82no—
57C2×D4×C13C4⋊C412yescomplemented
58C2×D4×C13C2×D411yescharacteristic
59C2×D4×C13C2×Q811yescharacteristic
60C2×D4×C13#4112yes—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—42no—
67C22×C4×C13—82no—
68C22×C4×C13—82no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C412yes—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×Dic13—44no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—42no—
78C13×C22⋊C4—82no—
79C13×C22⋊C4—82no—
80C42×C13—22no—
81C42×C13—21no—
82C42×C13—41no—
83C42×C13C4⋊C412yescomplemented
84C22⋊Dic13—44no—
85C22⋊Dic13—44no—
86C4⋊Dic13—84no—
87#2328D1311yescharacteristic
88C2×#353—132no—
89#1799—132no—
90#1393—132no—
91C23×C13—22no—
92C23×C13—22no—
93C23×C13—22no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13—42no—
98C23×C13—41no—
99C23×C13—41no—
100C23×C13C2×C22⋊C411yescharacteristic
101C23×C13#12112yes—
102C23×C13C22⋊Q812yes—
103D4×C13—41no—
104D4×C13—41no—
105D4×C13—42no—
106D4×C13—42no—
107D4×C13—42no—
108D4×C13—84no—
109D4×C13—84no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13—44no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—82no—
127C2×C4×C13—84no—
128C2×C4×C13#9912yes—
129C2×C4×C13C2×C4⋊C411yescharacteristic
130C2×C4×C13#11711yescharacteristic
131C2×Dic13—84no—
132C2×Dic13—84no—
133C2×Dic13—84no—
134C2×#127C2×D1311yescharacteristic
135C2×C4×D4Dic1311yescharacteristic, complemented
136C2×C4×D4C2×D1311yescharacteristic
137C2×#99—134no—
138#390Dic1311yescharacteristic, complemented
139#390C2×D1311yescharacteristic
140#386—22no—
141#386—22no—
142#382Dic1311yescharacteristic, complemented
143#380—262no—
144#376Dic1311yescharacteristic, complemented
145#353—264no—
146#342—262no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—22no—
150C22×C13—22no—
151C22×C13—42no—
152C22×C13—42no—
153C22×C13—44no—
154C22×C13—42no—
155C22×C13—42no—
156C22×C13—42no—
157C22×C13—82no—
158C22×C13—82no—
159C22×C13—81no—
160C22×C13—81no—
161C22×C13#38011yescharacteristic
162C22×C13C2×#9911yescharacteristic
163C22×C13#41011yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—42no—
168C4×C13—42no—
169C4×C13—41no—
170C4×C13—81no—
171C4×C13—81no—
172Dic13—164no—
173C22×D4—22no—
174C22×D4C2×Dic1311yescharacteristic
175C22×D4C22×D1311yescharacteristic
176C23×C4—21no—
177C23×C4C22⋊D1312yes—
178#127—22no—
179#127Dic2612yes—
180#127D5212yes—
181C4×D4—42no—
182C4×D4—42no—
183C2×C4⋊C4—522no—
184C2×C4⋊C4C2×Dic1311yescharacteristic
185C2×C4⋊C4C2×Dic1311yescharacteristic
186C2×C22⋊C4—21no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—264no—
190C2×C22⋊C4C22⋊D1312yes—
191C2×C42C2×Dic1311yescharacteristic
192C2×C42C2×Dic1311yescharacteristic
193C2×C42C2×Dic1311yescharacteristic
194#99—264no—
195#99—264no—
196#95—21no—
197#95—22no—
198#95—21no—
199#95—522no—
200C2×C13—21no—
201C2×C13—21no—
202C2×C13—42no—
203C2×C13—42no—
204C2×C13—82no—
205C2×C13#179911yescharacteristic
206C2×C13#212711yescharacteristic
207C2×C13#212811yescharacteristic
208C24—21no—
209C24C2×C22⋊D1312yes—
210C2×D4—24no—
211C2×D4—24no—
212C2×D4—21no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—82no—
218C2×D4—82no—
219C2×D4C4⋊Dic1312yescomplemented
220C2×D4C2×Dic2611yescharacteristic
221C2×D4C2×D5211yescharacteristic
222C2×D4#612712yes—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—42no—
229C22×C4—82no—
230C22×C4—82no—
231C22×C4—524no—
232C22×C4C22⋊Dic1311yescharacteristic
233C22×C4C22⋊Dic1312yes—
234C22×C4C22⋊Dic1311yescharacteristic
235C22×C4C22×Dic1311yescharacteristic
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—1044no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—82no—
242C22⋊C4—82no—
243C22⋊C4—524no—
244C22⋊C4—524no—
245C42—22no—
246C42—21no—
247C42—41no—
248C42C4⋊Dic1312yescomplemented
249C13#1279911yescharacteristic, complemented, Sylow
250C23—22no—
251C23—22no—
252C23—22no—
253C23—42no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—41no—
258C23—41no—
259C23#8817812yes—
260C23#8818412yes—
261C23C2×C22⋊Dic1311yescharacteristic
262D4—41no—
263D4—41no—
264D4—42no—
265D4—42no—
266D4—42no—
267D4—84no—
268D4—84no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—82no—
286C2×C4—84no—
287C2×C4—1044no—
288C2×C4—1044no—
289C2×C4—1044no—
290C2×C4#8807412yes—
291C2×C4C2×C4⋊Dic1311yescharacteristic
292C2×C4#8818011yescharacteristic
293C22—21no—
294C22—21no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—44no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—82no—
304C22—82no—
305C22—81no—
306C22—81no—
307C22#1171887311yescharacteristic
308C22C2×#8807411yescharacteristic
309C22#1171890111yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—42no—
315C4—41no—
316C4—81no—
317C4—81no—
318C4—2084no—
319C2—21no—
320C2—21no—
321C2—42no—
322C2—42no—
323C2—82no—
324C2#1311482411yescharacteristic
325C2#1311650511yescharacteristic
326C2#1311650811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2328C2
socleC22×C13C2×#99
prime radicalC2×C13×#127C22
cosocleC22×D4×C13C23
hypercenter#2328D13
hypocenterC13#12799
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2328

Complements

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

NH ≅ G/Ntype
2. #13114824C2semidirect
3. #13112961C2semidirect
6. C2×C4×D4×C13C4semidirect
8. C13×#390C4semidirect
12. C13×#382C4semidirect
13. C13×#376C4semidirect
57. C2×D4×C13C4⋊C4semidirect
83. C42×C13C4⋊C4semidirect
135. C2×C4×D4Dic13semidirect
138. #390Dic13semidirect
142. #382Dic13semidirect
144. #376Dic13semidirect
219. C2×D4C4⋊Dic13semidirect
248. C42C4⋊Dic13semidirect
249. C13#12799semidirect

Maximal subgroups

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

subgroupindex
C2×#117181372
#131148242
#131129612
C13×#23282
#1279913