Finite Group Databasebeta

← #30604983

Subgroups — #30604983

Order 15616.

484 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461524C211yesmaximal, characteristic, complemented
2#21461072C211yesmaximal, characteristic, complemented
3#21460818C212yesmaximal, complemented
4#21460801C212yesmaximal, complemented
5#21451379C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7#16840782—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840606—21no—
12C2×#14519734C2211yescharacteristic
13#16839700C2211yescharacteristic
14#16839697C411yescharacteristic
15#16839676C2211yescharacteristic
16#16839670C411yescharacteristic
17#16839650—21no—
18#16839641—21no—
19#16839638—21no—
20#16839635—21no—
21#16839630C411yescharacteristic
22C2×C4×D4×C61C411yescharacteristic
23C2×#11758213—41no—
24D61⋊M16—24no—
25D61⋊M16—42no—
26C2×#11758217—22no—
27C2×D61⋊C8—41no—
28#14519844—41no—
29C22⋊#92420—22no—
30#14519832—41no—
31C22×C22⋊D61—21no—
32C22×C4×D61D411yescharacteristic
33#14519734—41no—
34#14519734—41no—
35C2×#11758196—21no—
36C2×#11758196D411yescharacteristic
37C2×#11758196C2311yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×#11758198—21no—
42C2×#11758198C2×C411yescharacteristic
43C2×#11758198D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684C2×C411yescharacteristic
50#14519684C2×C411yescharacteristic
51C22×D4×C61C2×C411yescharacteristic
52C23×C4×C61—21no—
53C4×D4×C61—41no—
54C4×D4×C61—41no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61—21no—
57C2×C42×C61C2×C411yescharacteristic
58C24×C61—21no—
59C23×D61C22⋊C411yescharacteristic
60C2×D4×C61—41no—
61C2×D4×C61—42no—
62C22×C4×C61—21no—
63C22×C4×C61—42no—
64C22×C4×C61—81no—
65C22×C4×C61—81no—
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22×C411yescharacteristic
69C2×C22⋊D61—42no—
70C2×C22⋊D61—42no—
71C2×C22⋊D61—81no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61C22⋊C411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C2×C4×D61—22no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82#11758217—24no—
83#11758217—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86#11758213—44no—
87D61⋊C8—44no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C42×C61—21no—
92C42×C61—21no—
93C22⋊Dic61—42no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—81no—
97#11758198—41no—
98#11758198—41no—
99#11758198—81no—
100#11758196—41no—
101#11758196—41no—
102#11758196—81no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C23×C61—22no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61C2×C22⋊C411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—41no—
116C22×D61—41no—
117C22×D61#10412yes—
118D4×C61—42no—
119D4×C61—42no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—84no—
130C2×C4×C61#9911yescharacteristic
131C2×C4×C61#9911yescharacteristic
132C22⋊D61—84no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61AGL(1,ℤ/8)11yescharacteristic
146C2×Dic61#13711yescharacteristic
147C4×D61—22no—
148C4×D61—22no—
149C4×D61—22no—
150C4×D61—22no—
151#92420—44no—
152#92420—82no—
153#11761—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—42no—
157C22×C61—42no—
158C22×C61—42no—
159C22×C61—81no—
160C22×C61—81no—
161C22×C61—81no—
162C22×C61—81no—
163C22×C61C2×#9911yescharacteristic
164C22×C61#41711yescharacteristic
165C22×C61C2×#10411yescharacteristic
166C2×D61—22no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—42no—
170C2×D61—81no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—81no—
176Dic61—21no—
177Dic61—21no—
178Dic61—41no—
179Dic61—41no—
180Dic61—81no—
181Dic61—81no—
182#2598—611no—
183#1742—611no—
184#1464—611no—
185#1353—612no—
186#1345—612no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61—82no—
190C2×C61#150411yescharacteristic
191C2×C61#212011yescharacteristic
192C2×C61#213411yescharacteristic
193D61—42no—
194C22×M16—1221no—
195C2×C4×D4#692311yescharacteristic
196C2×#117—611no—
197#432—1221no—
198#400—611no—
199#399—611no—
200#394—611no—
201#392—611no—
202#388—1221no—
203#386—1221no—
204#386—1221no—
205#385—1221no—
206#383—611no—
207#343—612no—
208#343—1221no—
209#324—612no—
210#323—1221no—
211C61#1176111yescharacteristic, complemented, Sylow
212C22×D4—1221no—
213C22×D4C2×#692311yescharacteristic
214C23×C4—21no—
215C23×C4—611no—
216C2×M16—1222no—
217C2×M16—1224no—
218C2×M16—2442no—
219C2×M16—2441no—
220C22×C8—2441no—
221C4×D4—41no—
222C4×D4—41no—
223#117—2441no—
224#117—2441no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4C2×#692311yescharacteristic
229C2×C22⋊C4—21no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—1221no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1221no—
235C2×C22⋊C4—1221no—
236C2×C42—611no—
237C2×C42C2×#692311yescharacteristic
238C4⋊C8—2441no—
239C22⋊C8—1222no—
240#97—2441no—
241#95—611no—
242#95—611no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247C24—21no—
248C24—611no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—4881no—
252C2×D4—2442no—
253C2×D4—2442no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1222no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4C22⋊#692311yescharacteristic
269C22×C4C22⋊#692311yescharacteristic
270C22×C4C22×#692311yescharacteristic
271M16—1224no—
272M16—2442no—
273M16—2444no—
274C2×C8—2442no—
275C2×C8—2444no—
276C2×C8—2442no—
277C4⋊C4—41no—
278C4⋊C4—4881no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—4881no—
284C22⋊C4—4881no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C22⋊C4—2441no—
288C22⋊C4—2441no—
289C22⋊C4—2442no—
290C42—21no—
291C42—21no—
292C42—1221no—
293C42—1221no—
294C23—22no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—612no—
302C23—1221no—
303C23—1221no—
304C23—2441no—
305C23—2441no—
306C23C2×C22⋊#692311yescharacteristic
307D4—42no—
308D4—42no—
309D4—4884no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—84no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—1222no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4#1451983511yescharacteristic
339C2×C4#1451983511yescharacteristic
340C8—4882no—
341C8—2444no—
342C22—21no—
343C22—21no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—1222no—
352C22—4881no—
353C22—2442no—
354C22—2441no—
355C22—2441no—
356C22C2×#1451983511yescharacteristic
357C22#1684075311yescharacteristic
358C22D61⋊#10411yescharacteristic
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—81no—
364C4—1221no—
365C4—1221no—
366C4—4881no—
367C4—4881no—
368C4—2441no—
369C4—2441no—
370C2—21no—
371C2—21no—
372C2—82no—
373C2—2442no—
374C2#2146120511yescharacteristic
375C2#2146207011yescharacteristic
376C2#2146211811yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C2×#99
prime radical#16839670C4
cosocleC2×#11758196C23
hypercenterC2×C4×D4#6923
hypocenterC61#11761
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21461524C2semidirect
2. #21461072C2semidirect
3. #21460818C2semidirect
4. #21460801C2semidirect
211. C61#11761semidirect

Maximal subgroups

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

subgroupindex
#214615242
#214610722
#214608182
#214608012
#214513792
#1176161