Finite Group Databasebeta

← #29568543

Subgroups — #29568543

Order 15616.

378 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 95 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#21454205C211yesmaximal, characteristic
2#21445934C211yesmaximal, characteristic
3#21445671C211yesmaximal, characteristic
4#21443643C211yesmaximal, characteristic
5#21443642C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519706—21no—
9C2×#14519706—21no—
10C2×#14519687—21no—
11#16839661C411yescharacteristic
12#16839660C2211yescharacteristic
13#16839658C411yescharacteristic
14#16839648—21no—
15#16839647—21no—
16#16839644—21no—
17#16839643—21no—
18#16839627C411yescharacteristic
19#16839627C411yescharacteristic
20C42×Dic61C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839517C2211yescharacteristic
23#16839516—21no—
24C61×#389C2211yescharacteristic
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#14519706—24no—
41#14519706—42no—
42#14519687—42no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C22×C8×C61—21no—
51C22×C8×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#95×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22×C411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C2×C8×C61—22no—
69C2×C8×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C42×C61—41no—
80C4⋊Dic61—21no—
81C4⋊Dic61—21no—
82C4⋊Dic61—42no—
83C4⋊Dic61—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—42no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—21no—
93C4×Dic61—22no—
94C4×Dic61—22no—
95C4×Dic61—41no—
96C2×#92418—22no—
97C2×#92418—41no—
98C2×#92418—41no—
99C2×#92418—41no—
100C2×#92418—41no—
101C2×#92418—41no—
102C23×C61C2×C22⋊C411yescharacteristic
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61#13111yescharacteristic
116C2×C4×C61#13111yescharacteristic
117C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C61#13711yescharacteristic
120C2×C4×C61#13711yescharacteristic
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—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61#10112yes—
138C2×Dic61#10412yes—
139C8×C61—42no—
140C8×C61—81no—
141#92418—42no—
142#92418—81no—
143#7697—611nomaximal, Sylow
144C22×C61#40811yescharacteristic
145C22×C61#41011yescharacteristic
146C22×C61C2×#10111yescharacteristic
147C22×C61#41711yescharacteristic
148C22×C61#41711yescharacteristic
149C22×C61C2×#10411yescharacteristic
150C22×C61#42111yescharacteristic
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—81no—
158C4×C61—81no—
159Dic61—22no—
160Dic61—22no—
161Dic61—41no—
162Dic61—41no—
163Dic61—81no—
164Dic61—81no—
165#2864—611no—
166#1831—611no—
167#1767—611no—
168#1271—611no—
169#1271—611no—
170#1271—611no—
171#1271D6111yescharacteristic
172C2×C61#147011yescharacteristic
173C2×C61#148311yescharacteristic
174C2×C61#149511yescharacteristic
175C2×C61#150911yescharacteristic
176C2×C61#151211yescharacteristic
177C2×C61#153111yescharacteristic
178C2×C61#156111yescharacteristic
179C2×C4⋊C8—1221no—
180C2×C4⋊C8—1221no—
181C2×#97—1221no—
182#389—611no—
183#389—611no—
184#389—611no—
185#389C2×D6111yescharacteristic
186#387—1221no—
187#387—1221no—
188#387—1221no—
189#387—1221no—
190#382—611no—
191#382—611no—
192C43—611no—
193#336—611no—
194#336—611no—
195#336—1221no—
196#336C2×D6111yescharacteristic
197#336C2×D6111yescharacteristic
198C61#769711yescharacteristic, complemented, Sylow
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—1221no—
202C22×C8—1221no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4C4×D6111yescharacteristic
210C2×C4⋊C4C4×D6111yescharacteristic
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42C22×D6111yescharacteristic
218C4⋊C8—1224no—
219C4⋊C8—2442no—
220#97—2442no—
221#95—21no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
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—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—1222no—
247C2×C8—2441no—
248C2×C8—2441no—
249C2×C8—2441no—
250C2×C8—2441no—
251C2×C8—2441no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—1221no—
258C4⋊C4—1221no—
259C4⋊C4—2441no—
260C4⋊C4—2442no—
261C4⋊C4—2442no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C42—41no—
265C42—1222no—
266C42—1222no—
267C42—1221no—
268C42—1221no—
269C42—1221no—
270C42—1221no—
271C42—1221no—
272C42—1221no—
273C42—2441no—
274C23C22⋊C4×D6111yescharacteristic
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—612no—
288C2×C4—612no—
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—1221no—
298C2×C4—1221no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4#1451978311yescharacteristic
306C2×C4#1451978511yescharacteristic
307C2×C4#1451980111yescharacteristic
308C2×C4#1451980411yescharacteristic
309C2×C4#1451980611yescharacteristic
310C2×C4#1451980911yescharacteristic
311C8—42no—
312C8—81no—
313C8—4881no—
314C8—2442no—
315C22#1683972711yescharacteristic
316C22#1683973411yescharacteristic
317C22#101×D6111yescharacteristic
318C22#1683976011yescharacteristic
319C22#1683976211yescharacteristic
320C22#104×D6111yescharacteristic
321C22#1683977711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—81no—
329C4—81no—
330C4—1222no—
331C4—1222no—
332C4—4881no—
333C4—4881no—
334C4—2441no—
335C4—2441no—
336C2#2144417311yescharacteristic
337C2#2144422911yescharacteristic
338C2#2144428311yescharacteristic
339C2#2144434311yescharacteristic
340C2#2144435411yescharacteristic
341C2#2144443211yescharacteristic
342C2#2144455511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7697
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
198. C61#7697semidirect

Maximal subgroups

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

subgroupindex
#214542052
#214459342
#214456712
#214436432
#214436422
#214436412
C61×#12712
#769761