Finite Group Databasebeta

← #29569315

Subgroups — #29569315

Order 15616.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#21452850C211yesmaximal, characteristic
2#21447383C211yesmaximal, characteristic
3#21447382C211yesmaximal, characteristic
4#21447356C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443643C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519776—21no—
9C2×#14519711—21no—
10C2×#14519702—21no—
11#16839695—21no—
12#16839683—21no—
13#16839682—21no—
14#16839668C2211yescharacteristic
15#16839660C2211yescharacteristic
16#16839648—21no—
17#16839645—21no—
18#16839632C2211yescharacteristic
19#16839525—21no—
20#16839525—21no—
21#16839524—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122D411yescharacteristic
29C22×#92418—21no—
30#14519776—42no—
31#14519776—42no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×C4×Dic61—21no—
43#14519711—42no—
44#14519702—42no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×C8×C61—21no—
52C22×C8×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57#95×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—41no—
68C2×Dic122—21no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×Dic122—42no—
72C2×Dic122—81no—
73C2×Dic122—81no—
74C2×Dic122SD1612yes—
75C2×C8×C61—22no—
76C2×C8×C61—41no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61Q1612yes—
86C42×C61—41no—
87C4⋊Dic61—21no—
88C4⋊Dic61—42no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C4⋊Dic61—42no—
94C4⋊Dic61—42no—
95C4⋊Dic61Q1612yes—
96#11758196—42no—
97#11758196—41no—
98#11758196—41no—
99#11758196—81no—
100C4×Dic61—42no—
101C2×#92418—41no—
102C2×#92418—41no—
103C2×#92418—41no—
104C23×C61#12011yescharacteristic
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—22no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61C2×SD1611yescharacteristic
118C2×C4×C61C2×Q1611yescharacteristic
119C2×C4×C61C2×Q1611yescharacteristic
120C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C61#13711yescharacteristic
122C2×C4×C61#13711yescharacteristic
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137C2×Dic61—81no—
138Dic122—42no—
139Dic122—81no—
140Dic122—84no—
141C8×C61—42no—
142C8×C61—81no—
143#92418—81no—
144#7829—611nomaximal, Sylow
145C22×C61#45011yescharacteristic
146C22×C61#45111yescharacteristic
147C22×C61#45111yescharacteristic
148C22×C61#45311yescharacteristic
149C22×C61#45411yescharacteristic
150C22×C61#45411yescharacteristic
151C22×C61#45811yescharacteristic
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—42no—
159C4×C61—81no—
160Dic61—42no—
161Dic61—42no—
162Dic61—81no—
163Dic61—81no—
164Dic61—161no—
165#2734—611no—
166#2100—611no—
167#2100—611no—
168#2095—611no—
169#1272—611no—
170#1271—611no—
171#1271D6111yescharacteristic
172C2×C61#161311yescharacteristic
173C2×C61#161711yescharacteristic
174C2×C61#161711yescharacteristic
175C2×C61#163311yescharacteristic
176C2×C61#163711yescharacteristic
177C2×C61#163711yescharacteristic
178C2×C61#165711yescharacteristic
179C2×C4⋊Q8—1221no—
180C2×#107—1221no—
181C2×#103—1221no—
182#398—1221no—
183#395—1221no—
184#395—1221no—
185#391—611no—
186#389—611no—
187#389C2×D6111yescharacteristic
188#387—1221no—
189#387—1221no—
190#384—611no—
191#340—1221no—
192#340—1221no—
193#340—1221no—
194#340—1221no—
195#336—611no—
196#336C2×D6111yescharacteristic
197#336C2×D6111yescharacteristic
198C61#782911yescharacteristic, complemented, Sylow
199C22×Q8—611no—
200C22×Q8—1221no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—1221no—
204C4⋊Q8—2442no—
205C4⋊Q8—2442no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4—1221no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4D24411yescharacteristic
218C2×C4⋊C4D24411yescharacteristic
219C2×C42—1221no—
220C2×C42C22×D6111yescharacteristic
221#107—2442no—
222#103—2442no—
223#95—21no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230C2×Q8—612no—
231C2×Q8—1221no—
232C2×Q8—4881no—
233C2×Q8—4881no—
234C2×Q8—2441no—
235C2×Q8—2441no—
236C2×Q8—2442no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—2441no—
244C22×C4C2×D24411yescharacteristic
245C22×C4D4×D6111yescharacteristic
246C22×C4D4×D6111yescharacteristic
247C2×C8—22no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—2441no—
254C2×C8—2441no—
255C2×C8—2441no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—612no—
261C4⋊C4—1221no—
262C4⋊C4—4881no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C4⋊C4—2442no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C4⋊C4—2442no—
270C4⋊C4—2442no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4Dic24412yes—
274C42—41no—
275C42—2442no—
276C23#1451974711yescharacteristic
277Q8—4881no—
278Q8—4884no—
279Q8—2442no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—1222no—
293C2×C4—1222no—
294C2×C4—4881no—
295C2×C4—4881no—
296C2×C4—4881no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4SD16×D6111yescharacteristic
308C2×C4Q16×D6111yescharacteristic
309C2×C4C2×Dic24411yescharacteristic
310C2×C4#1451980111yescharacteristic
311C2×C4#1451980611yescharacteristic
312C2×C4#1451981011yescharacteristic
313C8—42no—
314C8—81no—
315C8—4881no—
316C22#1683991411yescharacteristic
317C22#1683991911yescharacteristic
318C22#1683992011yescharacteristic
319C22#1683993111yescharacteristic
320C22#1683993611yescharacteristic
321C22#1683993711yescharacteristic
322C22#1683995311yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4—81no—
331C4—9761no—
332C4—4881no—
333C4—4881no—
334C4—2442no—
335C4—2442no—
336C2#2144484011yescharacteristic
337C2#2144486211yescharacteristic
338C2#2144486311yescharacteristic
339C2#2144496111yescharacteristic
340C2#2144498511yescharacteristic
341C2#2144498711yescharacteristic
342C2#2144511911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7829
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
198. C61#7829semidirect

Maximal subgroups

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

subgroupindex
#214528502
#214473832
#214473822
#214473562
#214436442
#214436432
C61×#12712
#782961