Finite Group Databasebeta

← #15781216

Subgroups — #15781216

Order 3328.

540 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 111 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×#11718131C214yesmaximal
2#13114828C211yesmaximal, characteristic
3C4×#88074C211yesmaximal, characteristic
4C13×#2486C211yesmaximal, characteristic
5C2×C13×#123C2212yes—
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C411yescharacteristic, complemented
8C13×#398—21no—
9C13×#397—21no—
10C13×#389—21no—
11C13×#381C412yescomplemented
12C13×#380—21no—
13C13×#380C411yescharacteristic, complemented
14C2×#88074C2212yes—
15C2×#88073C2212yes—
16C4×C22⋊Dic13—21no—
17#11718585—21no—
18#11718131—28no—
19#11718122—21no—
20#11718118—21no—
21C22×D4×C13C2311yescharacteristic
22C23×C4×C13C2×C412yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C13×#123—24no—
26C13×#123—24no—
27C4×D4×C13—41no—
28C4×D4×C13—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—41no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4C2×C412yes—
38C2×C13×C22⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×C22⋊Dic13—22no—
42C2×C4×Dic13—41no—
43C2×#6099—22no—
44C13×#95—22no—
45C13×#95—21no—
46C13×#95—22no—
47#88074—22no—
48#88074D414yes—
49#88073—24no—
50#88071—41no—
51C4⋊#1055—41no—
52C4⋊#1055—41no—
53#13220—131nomaximal, Sylow
54C24×C13C22×C411yescharacteristic
55C24×C13C2×D411yescharacteristic
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13C2×D412yes—
59C2×D4×C13#4112yes—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—24no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—42no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C22⋊C4—24no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—44no—
88C42×C13—21no—
89C42×C13—21no—
90C22⋊Dic13—24no—
91C22⋊Dic13—42no—
92C4×Dic13—82no—
93#6099—42no—
94#6099—42no—
95C2×#1055—42no—
96#2486D1311yescharacteristic
97C2×#352—134no—
98#1800—131no—
99C4×#99—131no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C22⋊C411yescharacteristic
109C23×C13C4×D412yes—
110C23×C13#12112yes—
111D4×C13—42no—
112D4×C13—42no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—81no—
132C2×C4×C13—84no—
133C2×C4×C13#9911yescharacteristic
134C2×C4×C13#9911yescharacteristic
135C2×C4×C13#12411yescharacteristic
136C2×C4×C13#12711yescharacteristic
137C2×Dic13—44no—
138C2×Dic13—82no—
139C2×Dic13—82no—
140#1055—82no—
141C2×#123C2×D1312yes—
142C2×C4×D4C2×D1311yescharacteristic
143C22×C4⋊C4Dic1311yescharacteristic, complemented
144#423—261no—
145C2×#100—132no—
146C2×#99—132no—
147#398—21no—
148#397—21no—
149#389—21no—
150#381Dic1312yescomplemented
151#380—21no—
152#380Dic1311yescharacteristic, complemented
153C4×C22⋊C4—261no—
154#352—268no—
155#343—261no—
156#342—261no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—42no—
162C22×C13—42no—
163C22×C13—42no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—81no—
169C22×C13#39011yescharacteristic
170C22×C13C2×#9911yescharacteristic
171C22×C13#41011yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—82no—
179C4×C13—82no—
180C4×C13#35212yescomplemented
181Dic13—84no—
182C22×D4C22×D1311yescharacteristic
183C23×C4C2×Dic1312yes—
184C23×C4C2×Dic1311yescharacteristic
185C23×C4C22⋊D1311yescharacteristic
186C2×M16—262no—
187#123—24no—
188#123—24no—
189C4×D4—41no—
190C4×D4—41no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4C22⋊D1311yescharacteristic
198C2×C22⋊C4—22no—
199C2×C22⋊C4—262no—
200C2×C22⋊C4C2×Dic1312yes—
201C2×C22⋊C4C2×Dic1311yescharacteristic
202C2×C22⋊C4C22⋊D1311yescharacteristic
203C2×C42—521no—
204C2×C42C22⋊D1311yescharacteristic
205C4⋊C8—521no—
206C4⋊C8—521no—
207#100—264no—
208#99—134no—
209#99—262no—
210#95—22no—
211#95—21no—
212#95—22no—
213#95—521no—
214C2×C13—21no—
215C2×C13—21no—
216C2×C13—42no—
217C2×C13—42no—
218C2×C13#196411yescharacteristic
219C2×C13C2×#35211yescharacteristic
220C2×C13#212311yescharacteristic
221C24C22×Dic1311yescharacteristic
222C24C2×C22⋊D1311yescharacteristic
223C2×D4—41no—
224C2×D4—41no—
225C2×D4D4×D1312yes—
226C2×D4#612912yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—24no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—522no—
239C22×C4C22⋊Dic1311yescharacteristic
240C22×C4C22⋊Dic1311yescharacteristic
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C2×C22⋊D1311yescharacteristic
244M16—522no—
245M16—522no—
246C2×C8—522no—
247C4⋊C4—41no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C22⋊C4—24no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—44no—
258C22⋊C4—264no—
259C22⋊C4—522no—
260C42—21no—
261C42—21no—
262C42—1042no—
263C13#1322011yescharacteristic, complemented, Sylow
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23D4×Dic1312yes—
273C23#8819212yes—
274C23C2×C22⋊Dic1311yescharacteristic
275D4—42no—
276D4—42no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4—84no—
297C2×C4—524no—
298C2×C4—1042no—
299C2×C4—1042no—
300C2×C4#8807411yescharacteristic
301C2×C4#8807411yescharacteristic
302C2×C4#8819011yescharacteristic
303C2×C4#8819411yescharacteristic
304C8—1042no—
305C22—21no—
306C22—21no—
307C22—22no—
308C22—22no—
309C22—42no—
310C22—42no—
311C22—42no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22C2×#8807411yescharacteristic
318C22#1171888211yescharacteristic
319C22#1171890111yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—82no—
327C4—82no—
328C4—1044no—
329C4#1171813112yescomplemented
330C2—21no—
331C2—21no—
332C2—42no—
333C2—42no—
334C2#1311567311yescharacteristic
335C2C2×#1171813111yescharacteristic
336C2#1311649011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2486C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#2486D13
hypocenterC13#13220
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2486

Complements

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

NH ≅ G/Ntype
7. C22×C13×C4⋊C4C4semidirect
11. C13×#381C4semidirect
13. C13×#380C4semidirect
143. C22×C4⋊C4Dic13semidirect
150. #381Dic13semidirect
152. #380Dic13semidirect
180. C4×C13#352semidirect
263. C13#13220semidirect
329. C4#11718131semidirect

Maximal subgroups

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

subgroupindex
C2×#117181312
#131148282
C4×#880742
C13×#24862
#1322013