Finite Group Databasebeta

← #15781577

Subgroups — #15781577

Order 3328.

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

normal subgroups only

This group has 488 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#13114828C211yesmaximal, characteristic
2C4×#88074C211yesmaximal, 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—
16C4×C22⋊Dic13—21no—
17#11718585—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—22no—
45#88074Q814yes—
46#88073—24no—
47#88071—41no—
48C4⋊#1055—41no—
49C4⋊#1055—41no—
50#13295—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—24no—
86C22⋊Dic13—42no—
87C4×Dic13—82no—
88#6099—42no—
89#6099—42no—
90C2×#1055—42no—
91#2487D1311yescharacteristic
92#1800—131no—
93C4×#99—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×C13C22⋊Q812yes—
106D4×C13—42no—
107D4×C13—42no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—81no—
127C2×C4×C13—84no—
128C2×C4×C13#9911yescharacteristic
129C2×C4×C13#9911yescharacteristic
130C2×C4×C13#12411yescharacteristic
131C2×C4×C13C4⋊Q811yescharacteristic
132C2×Dic13—44no—
133C2×Dic13—82no—
134C2×Dic13—82no—
135#1055—82no—
136C2×C4×D4C2×D1311yescharacteristic
137C22×C4⋊C4Dic1311yescharacteristic, complemented
138#423—261no—
139C2×#100—132no—
140C2×#99—132no—
141#400—21no—
142#399—21no—
143#389—21no—
144#386C2×D1312yes—
145#385Dic1312yescomplemented
146#380—21no—
147#380Dic1311yescharacteristic, complemented
148C4×C22⋊C4—261no—
149#343—261no—
150#342—261no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—42no—
156C22×C13—42no—
157C22×C13—42no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—81no—
163C22×C13#39111yescharacteristic
164C22×C13C2×#9911yescharacteristic
165C22×C13#41011yescharacteristic
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—82no—
173C4×C13—82no—
174C4×C13#35212yes—
175Dic13—84no—
176C22×D4C22×D1311yescharacteristic
177C23×C4C2×Dic1311yescharacteristic
178C23×C4C2×Dic1312yes—
179C23×C4C22⋊D1311yescharacteristic
180C2×M16—262no—
181C4×D4—41no—
182C4×D4—41no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—41no—
189C2×C4⋊C4C22⋊D1311yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—262no—
192C2×C22⋊C4C2×Dic1312yes—
193C2×C22⋊C4C2×Dic1311yescharacteristic
194C2×C22⋊C4C22⋊D1311yescharacteristic
195C2×C42—521no—
196C2×C42C22⋊D1311yescharacteristic
197C4⋊C8—521no—
198C4⋊C8—521no—
199#100—264no—
200#99—134no—
201#99—262no—
202#95—22no—
203#95—21no—
204#95—22no—
205#95—521no—
206C2×C13—21no—
207C2×C13—21no—
208C2×C13—42no—
209C2×C13—42no—
210C2×C13#199611yescharacteristic
211C2×C13C2×#35211yescharacteristic
212C2×C13#212211yescharacteristic
213C24C22×Dic1311yescharacteristic
214C24C2×C22⋊D1311yescharacteristic
215C2×D4—41no—
216C2×D4—41no—
217C2×D4Q8×D1312yes—
218C2×D4#613112yes—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—42no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—82no—
229C22×C4—522no—
230C22×C4C22⋊Dic1311yescharacteristic
231C22×C4C22⋊Dic1311yescharacteristic
232C22×C4C22⋊Dic1311yescharacteristic
233C22×C4C22⋊Dic1311yescharacteristic
234C22×C4C2×C22⋊D1311yescharacteristic
235M16—522no—
236M16—522no—
237C2×C8—522no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—82no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C22⋊C4—42no—
247C22⋊C4—82no—
248C22⋊C4—264no—
249C22⋊C4—522no—
250C42—21no—
251C42—21no—
252C42—1042no—
253C13#1329511yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23Q8×Dic1312yes—
263C23#8820012yes—
264C23C2×C22⋊Dic1311yescharacteristic
265D4—42no—
266D4—42no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—81no—
286C2×C4—84no—
287C2×C4—524no—
288C2×C4—1042no—
289C2×C4—1042no—
290C2×C4#8807411yescharacteristic
291C2×C4#8807411yescharacteristic
292C2×C4#8819811yescharacteristic
293C2×C4#8820111yescharacteristic
294C8—1042no—
295C22—21no—
296C22—21no—
297C22—22no—
298C22—22no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—81no—
307C22C2×#8807411yescharacteristic
308C22#1171889111yescharacteristic
309C22#1171890111yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—82no—
317C4—82no—
318C4—1044no—
319C4#1171813112yes—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—42no—
324C2#1311582211yescharacteristic
325C2C2×#1171813111yescharacteristic
326C2#1311648611yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2487C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#2487D13
hypocenterC13#13295
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
147. #380Dic13semidirect
253. C13#13295semidirect

Maximal subgroups

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

subgroupindex
#131148282
C4×#880742
#131129542
C13×#24872
#1329513