Finite Group Databasebeta

← #29590905

Subgroups — #29590905

Order 15616.

382 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 69 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#21451510C211yesmaximal, characteristic
2#21445895C211yesmaximal, characteristic
3#21444130C211yesmaximal, characteristic
4#21443843C211yesmaximal, characteristic
5#21443820C211yesmaximal, characteristic
6#21443818C211yesmaximal, characteristic
7C61×#1352C211yesmaximal, characteristic
8C2×#14519768C411yescharacteristic, complemented
9C2×#14519733C2211yescharacteristic
10#16839812—21no—
11#16839700C411yescharacteristic, complemented
12#16839694C411yescharacteristic, complemented
13#16839687C2211yescharacteristic
14#16839658—21no—
15#16839650—21no—
16#16839648—21no—
17#16839637—21no—
18#16839623—21no—
19#16839607C411yescharacteristic, complemented
20#16839529C2211yescharacteristic
21#16839528—21no—
22#16839487—21no—
23#16839486C2211yescharacteristic
24C61×#399C2211yescharacteristic
25C61×#342C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C23×Dic61D411yescharacteristic
28#14519768—41no—
29#14519768—41no—
30#14519733—41no—
31#14519733—41no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196C2×C411yescharacteristic
37C2×#11758196D411yescharacteristic
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61D411yescharacteristic
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44#14519706—41no—
45C22⋊#92418—21no—
46C8×Dic61—41no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—41no—
53#14519684—41no—
54#14519684C2×C411yescharacteristic
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61C2×C411yescharacteristic
62C24×C61C2×D411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—41no—
66C22×C4×C61C22×C411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C22⋊C411yescharacteristic
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C2×C8×C61—41no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—42no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊Dic61—41no—
88C22⋊Dic61—41no—
89C22⋊Dic61—41no—
90C22⋊Dic61—41no—
91C22⋊Dic61—41no—
92C4⋊Dic61—42no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96#11758196—41no—
97#11758196—41no—
98#11758196—42no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C4×Dic61—21no—
103C4×Dic61—42no—
104C2×#92418—41no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61C2×C22⋊C411yescharacteristic
110C23×C61#13511yescharacteristic
111C23×C61#13511yescharacteristic
112C2×C4×C61—22no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—81no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61#9911yescharacteristic
148C2×Dic61#9911yescharacteristic
149C8×C61—81no—
150#92418—81no—
151#11846—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—81no—
161C22×C61C2×#9911yescharacteristic
162C22×C61#41611yescharacteristic
163C22×C61#42111yescharacteristic
164C4×C61—42no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—81no—
168C4×C61—161no—
169Dic61—21no—
170Dic61—21no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174Dic61—81no—
175Dic61—81no—
176Dic61—161no—
177#2611—611no—
178#1820—611no—
179#1458—611no—
180#1352—611no—
181#1352D6111yescharacteristic
182#1344—611no—
183#1344—611no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—41no—
187C2×C61—41no—
188C2×C61#151611yescharacteristic
189C2×C61#212311yescharacteristic
190C2×C61#212611yescharacteristic
191C2×#125—611no—
192C2×#117—611no—
193#431—1221no—
194#400—611no—
195#399C2×D6111yescharacteristic
196#398—611no—
197#397—611no—
198#389—1221no—
199#388—1221no—
200#387—1221no—
201#385—1221no—
202#381—1221no—
203#376—611no—
204#342—611no—
205#342—1221no—
206#342C2×D6111yescharacteristic
207#324—1221no—
208#323—611no—
209#323C2×D6111yescharacteristic
210C61#1184611yescharacteristic, complemented, Sylow
211C23×C4—611no—
212#125—2441no—
213#125—2441no—
214#117—2441no—
215#117—2441no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4C4×D6111yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—611no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4C22×D6111yescharacteristic
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—1221no—
233C4⋊C8—2441no—
234C22⋊C8—21no—
235C22⋊C8—1221no—
236C4×C8—2441no—
237#95—611no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—2441no—
244#95—2441no—
245#95C4×D6111yescharacteristic
246C24D4×D6111yescharacteristic
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4C2×C4×D6111yescharacteristic
263C22×C4D4×D6111yescharacteristic
264C2×C8—41no—
265C2×C8—2441no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C22⋊C4—41no—
276C22⋊C4—42no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—2441no—
280C22⋊C4—2441no—
281C22⋊C4—2441no—
282C22⋊C4—2441no—
283C22⋊C4—2441no—
284C42—1221no—
285C42—1221no—
286C42—1221no—
287C42—1221no—
288C42—2442no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23C22⋊C4×D6111yescharacteristic
294C23#1451979811yescharacteristic
295C23#1451980011yescharacteristic
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—611no—
310C2×C4—611no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—4881no—
319C2×C4—4881no—
320C2×C4—4881no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C8—81no—
334C8—4881no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22#99×D6111yescharacteristic
345C22#1683975711yescharacteristic
346C22#1683977711yescharacteristic
347C4—42no—
348C4—41no—
349C4—41no—
350C4—81no—
351C4—161no—
352C4—1221no—
353C4—1221no—
354C4—9761no—
355C4—4881no—
356C4—4881no—
357C4—2441no—
358C4—2441no—
359C4—2441no—
360C2—21no—
361C2—21no—
362C2—41no—
363C2—41no—
364C2#2144437411yescharacteristic
365C2#2144747111yescharacteristic
366C2#2144748111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1352C2
socleC22×C61C2×#99
prime radicalC24×C61C2×D4
cosocleC2×C22⋊C4×C61C23
hypercenter#1352D61
hypocenterC61#11846
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1352

Complements

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

NH ≅ G/Ntype
8. C2×#14519768C4semidirect
11. #16839700C4semidirect
12. #16839694C4semidirect
19. #16839607C4semidirect
210. C61#11846semidirect

Maximal subgroups

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

subgroupindex
#214515102
#214458952
#214441302
#214438432
#214438202
#214438182
C61×#13522
#1184661