Finite Group Databasebeta

← #29568685

Subgroups — #29568685

Order 15616.

346 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 91 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#21454198C211yesmaximal, characteristic
2#21445961C211yesmaximal, characteristic
3#21445961C211yesmaximal, characteristic
4#21443645C211yesmaximal, characteristic
5#21443643C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#1272C211yesmaximal, characteristic
8#16839669C411yescharacteristic
9#16839669C411yescharacteristic
10#16839661C411yescharacteristic
11#16839660C2211yescharacteristic
12#16839658C411yescharacteristic
13#16839649—21no—
14#16839647—21no—
15#16839644—21no—
16#16839629—21no—
17C42×Dic61C2211yescharacteristic
18#16839517C2211yescharacteristic
19#16839517C2211yescharacteristic
20#16839516—21no—
21#16839516—21no—
22#16839516—21no—
23#16839516—21no—
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×#92418—21no—
28C22×#92418—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47C22×Q8×C61C2×C411yescharacteristic
48C22×C8×C61—21no—
49C22×C8×C61—21no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C42×C61C2311yescharacteristic
52#95×C61—21no—
53#95×C61—21no—
54C2×Q8×C61—21no—
55C2×Q8×C61—21no—
56C2×Q8×C61—41no—
57C2×Q8×C61—41no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C22×C411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C22⋊C411yescharacteristic
69C2×C8×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C2×C8×C61—41no—
75C4⋊C4×C61—41no—
76C42×C61—41no—
77C4⋊Dic61—21no—
78C4⋊Dic61—21no—
79C4⋊Dic61—42no—
80C4⋊Dic61—41no—
81#11758196—42no—
82#11758196—41no—
83#11758196—41no—
84C4×Dic61—21no—
85C4×Dic61—21no—
86C4×Dic61—21no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—41no—
91C4×Dic61—41no—
92C4×Dic61—41no—
93C2×#92418—41no—
94C2×#92418—41no—
95C2×#92418—41no—
96C2×#92418—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C23×C61C2×C22⋊C411yescharacteristic
100Q8×C61—81no—
101Q8×C61—81no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61#13111yescharacteristic
115C2×C4×C61#13111yescharacteristic
116C2×C4×C61#13511yescharacteristic
117C2×C4×C61#13511yescharacteristic
118C2×C4×C61#13711yescharacteristic
119C2×C4×C61#13711yescharacteristic
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
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—
138C8×C61—81no—
139C8×C61—81no—
140#92418—81no—
141#92418—81no—
142#7729—611nomaximal, Sylow
143C22×C61#40811yescharacteristic
144C22×C61#41011yescharacteristic
145C22×C61#41311yescharacteristic
146C22×C61#41611yescharacteristic
147C22×C61#41911yescharacteristic
148C22×C61#42111yescharacteristic
149C22×C61#42111yescharacteristic
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—81no—
157C4×C61—81no—
158Dic61—41no—
159Dic61—41no—
160Dic61—41no—
161Dic61—41no—
162Dic61—81no—
163Dic61—81no—
164#2863—611no—
165#1839—611no—
166#1839—611no—
167#1272—611no—
168#1272D6111yescharacteristic
169#1271—611no—
170#1271—611no—
171C2×C61#147311yescharacteristic
172C2×C61#148211yescharacteristic
173C2×C61#149711yescharacteristic
174C2×C61#151511yescharacteristic
175C2×C61#152111yescharacteristic
176C2×C61#153511yescharacteristic
177C2×C61#155411yescharacteristic
178#391—611no—
179#391—611no—
180#391C2×D6111yescharacteristic
181#389—611no—
182#389—611no—
183#389—611no—
184#387—1221no—
185#387—1221no—
186#387—1221no—
187#383—1221no—
188C43—611no—
189#336—611no—
190#336—611no—
191#336—1221no—
192#336—1221no—
193#336—1221no—
194#336—1221no—
195#336C2×D6111yescharacteristic
196#336C2×D6111yescharacteristic
197C61#772911yescharacteristic, complemented, Sylow
198C22×Q8C4×D6111yescharacteristic
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—1221no—
202C22×C8—1221no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4C4×D6111yescharacteristic
209C2×C42—611no—
210C2×C42—611no—
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—611no—
215C2×C42C22×D6111yescharacteristic
216#95—21no—
217#95—21no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—41no—
228C2×Q8—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4C2×C4×D6111yescharacteristic
238C22×C4D4×D6111yescharacteristic
239C22×C4D4×D6111yescharacteristic
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—2441no—
247C2×C8—2441no—
248C2×C8—2441no—
249C2×C8—2441no—
250C2×C8—2441no—
251C2×C8—2441no—
252C4⋊C4—41no—
253C4⋊C4—1221no—
254C4⋊C4—1221no—
255C4⋊C4—2441no—
256C4⋊C4—2442no—
257C4⋊C4—2442no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C42—41no—
261C42—1221no—
262C42—1221no—
263C42—1221no—
264C42—1221no—
265C42—1221no—
266C42—1221no—
267C42—2441no—
268C42—2441no—
269C42—2441no—
270C23C22⋊C4×D6111yescharacteristic
271Q8—81no—
272Q8—81no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4#1451978311yescharacteristic
304C2×C4#1451978511yescharacteristic
305C2×C4#1451979811yescharacteristic
306C2×C4#1451980011yescharacteristic
307C2×C4#1451980611yescharacteristic
308C2×C4#1451980911yescharacteristic
309C8—81no—
310C8—81no—
311C8—4881no—
312C8—4881no—
313C22#1683972711yescharacteristic
314C22#1683973411yescharacteristic
315C22#1683974311yescharacteristic
316C22#1683975711yescharacteristic
317C22#1683976911yescharacteristic
318C22#1683977711yescharacteristic
319C22#1683977711yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—81no—
327C4—81no—
328C4—4881no—
329C4—4881no—
330C4—2441no—
331C4—2441no—
332C4—2441no—
333C4—2441no—
334C2#2144418511yescharacteristic
335C2#2144422611yescharacteristic
336C2#2144429011yescharacteristic
337C2#2144436811yescharacteristic
338C2#2144439511yescharacteristic
339C2#2144444711yescharacteristic
340C2#2144452811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1272D61
hypocenterC61#7729
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
197. C61#7729semidirect

Maximal subgroups

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

subgroupindex
#214541982
#214459612
#214436452
#214436432
#214436412
C61×#12722
#772961