Finite Group Databasebeta

← #29589561

Subgroups — #29589561

Order 15616.

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

normal subgroups only

This group has 380 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#21450103C211yesmaximal, characteristic
2#21444150C211yesmaximal, characteristic
3#21444130C211yesmaximal, characteristic
4#21443768C211yesmaximal, characteristic
5#21443766C211yesmaximal, characteristic
6#21443749C211yesmaximal, characteristic
7C61×#1317C211yesmaximal, characteristic
8C2×#14519733C2211yescharacteristic
9C22×#11758196C411yescharacteristic
10#16839816—21no—
11#16839812—21no—
12#16839703—21no—
13#16839696—21no—
14#16839645—21no—
15#16839644—21no—
16#16839637C411yescharacteristic
17#16839634C2211yescharacteristic
18#16839625C411yescharacteristic
19#16839623C411yescharacteristic
20#16839487—21no—
21#16839487—21no—
22#16839486C2211yescharacteristic
23#16839486C2211yescharacteristic
24C61×#381C2211yescharacteristic
25C61×#323C2211yescharacteristic
26C61×#323C2211yescharacteristic
27C23×Dic61C2×C411yescharacteristic
28C23×Dic61C2×C411yescharacteristic
29#14519733—41no—
30#14519733—41no—
31C2×C4⋊Dic61—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—41no—
36C2×#11758196—41no—
37C2×#11758196D411yescharacteristic
38C2×#11758196D411yescharacteristic
39C2×C22⋊Dic61C2×C411yescharacteristic
40C2×C22⋊Dic61C2×C411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43#14519706—41no—
44#14519706—41no—
45C22⋊#92418—21no—
46C22⋊#92418—21no—
47#14519687—41no—
48C8×Dic61—41no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55C23×C4×C61C2×C411yescharacteristic
56C2×C22⋊C4×C61C2×C411yescharacteristic
57C2×C22⋊C4×C61C2311yescharacteristic
58C22⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60#95×C61—21no—
61#95×C61—21no—
62C24×C61C22×C411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—41no—
78C22×Dic61—42no—
79C22×Dic61—41no—
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—41no—
91C4⋊Dic61—42no—
92#11758196—41no—
93#11758196—41no—
94#11758196—42no—
95#11758196—42no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—21no—
102C2×#92418—41no—
103C2×#92418—41no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61C2×C22⋊C411yescharacteristic
109C23×C61#13111yescharacteristic
110C23×C61#13111yescharacteristic
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
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—81no—
122C2×C4×C61—81no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—22no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—42no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61#9911yescharacteristic
145C2×Dic61#9911yescharacteristic
146C8×C61—81no—
147C8×C61—81no—
148#92418—81no—
149#92418—81no—
150#11548—611nomaximal, Sylow
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—42no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61#40811yescharacteristic
161C22×C61C2×#9911yescharacteristic
162C22×C61#41311yescharacteristic
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—81no—
166C4×C61—81no—
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170Dic61—42no—
171Dic61—41no—
172Dic61—41no—
173Dic61—81no—
174#2484—611no—
175#1464—611no—
176#1458—611no—
177#1326—611no—
178#1326—611no—
179#1317—611no—
180#1317D6111yescharacteristic
181C2×C61—21no—
182C2×C61—21no—
183C2×C61—41no—
184C2×C61—41no—
185C2×C61#146811yescharacteristic
186C2×C61#212011yescharacteristic
187C2×C61#212311yescharacteristic
188C2×#117—611no—
189C22×C4⋊C4—611no—
190#432—1221no—
191#431—1221no—
192#400—1221no—
193#398—1221no—
194#387—1221no—
195#387—1221no—
196#385—611no—
197#385—611no—
198#381—611no—
199#381—611no—
200#381C2×D6111yescharacteristic
201#324—1221no—
202#324—1221no—
203#323—611no—
204#323—611no—
205#323C2×D6111yescharacteristic
206#323C2×D6111yescharacteristic
207C61#1154811yescharacteristic, complemented, Sylow
208C23×C4—611no—
209C23×C4—611no—
210C23×C4C4×D6111yescharacteristic
211#117—2441no—
212#117—2441no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—2441no—
220C2×C4⋊C4—2441no—
221C2×C22⋊C4—611no—
222C2×C22⋊C4—611no—
223C2×C22⋊C4C4×D6111yescharacteristic
224C2×C22⋊C4C22×D6111yescharacteristic
225C2×C42—611no—
226C2×C42—611no—
227C4⋊C8—2441no—
228C4⋊C8—2441no—
229C22⋊C8—21no—
230C22⋊C8—21no—
231C22⋊C8—1221no—
232C22⋊C8—1221no—
233#97—2441no—
234C4×C8—2441no—
235#95—21no—
236#95—21no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243C24C2×C4×D6111yescharacteristic
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—41no—
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—2442no—
262C22×C4—2441no—
263C22×C4D4×D6111yescharacteristic
264C22×C4D4×D6111yescharacteristic
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—2441no—
268C2×C8—2441no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C4⋊C4—2442no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—2441no—
281C42—1221no—
282C42—1221no—
283C42—1221no—
284C42—1221no—
285C23—21no—
286C23—21no—
287C23—41no—
288C23—41no—
289C23C22⋊C4×D6111yescharacteristic
290C23#1451978311yescharacteristic
291C23#1451978511yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1222no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2442no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2442no—
327C8—81no—
328C8—81no—
329C8—4881no—
330C8—4881no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22#1683972711yescharacteristic
341C22#99×D6111yescharacteristic
342C22#1683974311yescharacteristic
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—1221no—
348C4—1221no—
349C4—4881no—
350C4—2441no—
351C4—2442no—
352C4—2441no—
353C4—2441no—
354C2—21no—
355C2—21no—
356C2—41no—
357C2—41no—
358C2#2144416411yescharacteristic
359C2#2144745911yescharacteristic
360C2#2144747111yescharacteristic
subgroupG/H
centerC22#99×D61
commutator, prime radicalC24×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1317C2
socleC22×C61C2×#99
cosocleC2×C22⋊C4×C61C23
hypercenter#1317D61
hypocenterC61#11548
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1317

Complements

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

NH ≅ G/Ntype
207. C61#11548semidirect

Maximal subgroups

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

subgroupindex
#214501032
#214441502
#214441302
#214437682
#214437662
#214437492
C61×#13172
#1154861