Finite Group Databasebeta

← #15781564

Subgroups — #15781564

Order 3328.

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

normal subgroups only

This group has 484 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
1#13114824C211yesmaximal, characteristic
2C4×#88073C211yesmaximal, characteristic
3#13112954C214yesmaximal
4C13×#2487C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic, complemented
7C13×#400—21no—
8C13×#399—21no—
9C13×#389—21no—
10C13×#386C2212yes—
11C13×#385C412yescomplemented
12C13×#380—21no—
13C13×#380C411yescharacteristic, complemented
14C2×#88074C2212yes—
15C2×#88073C2212yes—
16#11718873—21no—
17C4×#6099—21no—
18#11718122—21no—
19#11718118—21no—
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13C2×C412yes—
23C23×C4×C13D411yescharacteristic
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4—41no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4C2×C412yes—
35C2×C13×C22⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C22⋊Dic13—22no—
39C2×C4⋊Dic13—41no—
40C2×#6099—22no—
41C13×#95—22no—
42C13×#95—21no—
43C13×#95—22no—
44#88074—24no—
45#88073—22no—
46#88073Q814yes—
47#88071—41no—
48#88043—41no—
49C4×#1055—41no—
50#13292—131nomaximal, Sylow
51C24×C13C22×C411yescharacteristic
52C24×C13C2×D411yescharacteristic
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13C2×Q812yes—
56C2×D4×C13#4112yes—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—82no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—42no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—42no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—82no—
79C13×C22⋊C4—41no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—42no—
82C13×C22⋊C4—82no—
83C42×C13—21no—
84C42×C13—21no—
85C22⋊Dic13—42no—
86C22⋊Dic13—42no—
87C4⋊Dic13—82no—
88#6099—24no—
89#6099—42no—
90C2×#1055—42no—
91#2487D1311yescharacteristic
92#1799—131no—
93C4×#100—131no—
94#1390—134no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13C4×Q812yes—
105C23×C13#12411yescharacteristic
106C23×C13C4⋊Q811yescharacteristic
107D4×C13—42no—
108D4×C13—42no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—81no—
128C2×C4×C13—84no—
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13#9911yescharacteristic
131C2×C4×C13C22⋊Q812yes—
132C2×Dic13—82no—
133C2×Dic13—82no—
134C2×Dic13—82no—
135#1055—44no—
136C2×C4×D4C2×D1311yescharacteristic
137C22×C4⋊C4Dic1311yescharacteristic, complemented
138C2×#100—132no—
139C2×#99—132no—
140C4×M16—261no—
141#400—21no—
142#399—21no—
143#389—21no—
144#386C2×D1312yes—
145#385Dic1312yescomplemented
146#380—21no—
147#380—261no—
148#380Dic1311yescharacteristic, complemented
149#343—261no—
150#342—261no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—22no—
155C22×C13—21no—
156C22×C13—42no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—81no—
165C22×C13#39111yescharacteristic
166C22×C13C2×#9911yescharacteristic
167C22×C13#41011yescharacteristic
168C4×C13—21no—
169C4×C13—22no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—82no—
174C4×C13—82no—
175C4×C13#35212yes—
176Dic13—162no—
177C22×D4C22×D1311yescharacteristic
178C23×C4C2×Dic1311yescharacteristic
179C23×C4C2×Dic1312yes—
180C23×C4C22⋊D1311yescharacteristic
181C2×M16—262no—
182C4×D4—41no—
183C4×D4—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4—41no—
190C2×C4⋊C4—521no—
191C2×C4⋊C4C22⋊D1311yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—262no—
194C2×C22⋊C4C2×Dic1312yes—
195C2×C22⋊C4C2×Dic1311yescharacteristic
196C2×C22⋊C4C22⋊D1311yescharacteristic
197C2×C42C22⋊D1311yescharacteristic
198#100—134no—
199#100—262no—
200#99—264no—
201#97—521no—
202C4×C8—521no—
203#95—22no—
204#95—21no—
205#95—22no—
206#95—521no—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—41no—
210C2×C13—42no—
211C2×C13—41no—
212C2×C13#199611yescharacteristic
213C2×C13C2×#35211yescharacteristic
214C2×C13#212211yescharacteristic
215C24C22×Dic1311yescharacteristic
216C24C2×C22⋊D1311yescharacteristic
217C2×D4—41no—
218C2×D4—41no—
219C2×D4Q8×D1312yes—
220C2×D4#613112yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—82no—
231C22×C4—522no—
232C22×C4C22⋊Dic1311yescharacteristic
233C22×C4C22⋊Dic1311yescharacteristic
234C22×C4C22⋊Dic1311yescharacteristic
235C22×C4C22⋊Dic1311yescharacteristic
236C22×C4C2×C22⋊D1311yescharacteristic
237M16—264no—
238M16—522no—
239C2×C8—522no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—82no—
246C4⋊C4—1042no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—42no—
250C22⋊C4—82no—
251C22⋊C4—522no—
252C22⋊C4—522no—
253C42—21no—
254C42—21no—
255C13#1329211yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23#8819811yescharacteristic
265C23Q8×Dic1312yes—
266C23#8820111yescharacteristic
267C23C2×C22⋊Dic1311yescharacteristic
268D4—42no—
269D4—42no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—81no—
289C2×C4—84no—
290C2×C4—1042no—
291C2×C4—1042no—
292C2×C4—1042no—
293C2×C4#8807411yescharacteristic
294C2×C4#8807411yescharacteristic
295C2×C4#8820012yes—
296C8—524no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—22no—
302C22—41no—
303C22—42no—
304C22—41no—
305C22—42no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22C2×#8807411yescharacteristic
312C22#1171889111yescharacteristic
313C22#1171890111yescharacteristic
314C4—21no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—82no—
320C4—82no—
321C4—2082no—
322C4#1171813112yes—
323C2—21no—
324C2—21no—
325C2—41no—
326C2—42no—
327C2—41no—
328C2#1311582211yescharacteristic
329C2C2×#1171813111yescharacteristic
330C2#1311648611yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2487C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#2487D13
hypocenterC13#13292
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2487

Complements

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

NH ≅ G/Ntype
6. C22×C13×C4⋊C4C4semidirect
11. C13×#385C4semidirect
13. C13×#380C4semidirect
137. C22×C4⋊C4Dic13semidirect
145. #385Dic13semidirect
148. #380Dic13semidirect
255. C13#13292semidirect

Maximal subgroups

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

subgroupindex
#131148242
C4×#880732
#131129542
C13×#24872
#1329213