Finite Group Databasebeta

← #29589942

Subgroups — #29589942

Order 15616.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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#436×D61C211yesmaximal, characteristic
2#21447620C211yesmaximal, characteristic, complemented
3#21447617C211yesmaximal, characteristic, complemented
4#21443778C211yesmaximal, characteristic, complemented
5#21443777C211yesmaximal, characteristic, complemented
6#21443776C211yesmaximal, characteristic, complemented
7C61×#1330C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C4×D4×D61C411yescharacteristic
10#16839841C2211yescharacteristic
11#16839840C411yescharacteristic
12#16839839C411yescharacteristic
13#16839838—21no—
14#16839837—21no—
15C4⋊C8×D61C411yescharacteristic
16C22⋊C8×D61—21no—
17C4×C8×D61C2211yescharacteristic
18C4⋊#11758185C2211yescharacteristic, complemented
19#16839580—21no—
20#16839541—21no—
21#16839541—21no—
22#16839538C2211yescharacteristic, complemented
23C16×Dic61—21no—
24C61×#436C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic, complemented
26C61×#346C2211yescharacteristic, complemented
27C2×D4×D61C811yescharacteristic
28C22×C4×D61—21no—
29C2×#11758194—21no—
30C2×#11758189—21no—
31C2×#11758189—21no—
32M16×D61—42no—
33M16×D61—42no—
34C2×C8×D61—21no—
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C4×D244C2×C411yescharacteristic
38D4×Dic61C811yescharacteristic
39#14519739C811yescharacteristic
40C4×C22⋊D61—21no—
41#14519737—21no—
42C4⋊C4×D61C811yescharacteristic
43C22⋊C4×D61—21no—
44C42×D61C2×C411yescharacteristic
45C2×#11758185—21no—
46C2×#11758185—21no—
47C4⋊#92418C2×C411yescharacteristic
48#14519706—21no—
49C22⋊#92418—21no—
50#14519689—21no—
51#14519689—21no—
52C4×#92418C2×C411yescharacteristic
53C8×Dic61D411yescharacteristic
54C8×Dic61D411yescharacteristic
55C2×M16×C61—21no—
56C4×D4×C61C2×C411yescharacteristic
57C2×C16×C61—21no—
58C2×C16×C61—21no—
59C4⋊C8×C61C2×C411yescharacteristic
60C22⋊C8×C61—21no—
61C4×C8×C61C2311yescharacteristic
62C23×D61—21no—
63C2×D4×C61C2×C811yescharacteristic
64C22×C4×C61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67D4×D61—42no—
68C2×D244C2×C811yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—42no—
73C2×C4×D61—42no—
74C2×C4×D61C22⋊C411yescharacteristic
75C2×C4×D61C2×C811yescharacteristic
76C2×C4×D61M1611yescharacteristic
77M16×C61—41no—
78M16×C61—41no—
79C2×C8×C61—21no—
80C2×C8×C61C2×D411yescharacteristic
81C2×C8×C61C2×D411yescharacteristic
82C4⋊C4×C61C2×C811yescharacteristic
83C22⋊C4×C61—21no—
84C42×C61C22×C411yescharacteristic
85C22⋊Dic61—21no—
86#11758198—21no—
87#11758198—21no—
88C4⋊Dic61C2×C811yescharacteristic
89#11758196—21no—
90C4×Dic61C22⋊C411yescharacteristic
91C4×Dic61C2×C811yescharacteristic
92C4×Dic61M1611yescharacteristic
93#11758194—42no—
94C2×#92418—21no—
95C2×#92418C22⋊C411yescharacteristic
96C2×#92418C22⋊C411yescharacteristic
97#11758189—42no—
98#11758189—41no—
99#11758189—41no—
100C8×D61—21no—
101C8×D61—21no—
102C8×D61—41no—
103C8×D61—42no—
104C16×C61—41no—
105C16×C61—41no—
106#11758185—41no—
107#11758185—41no—
108C23×C61—21no—
109C22×D61—21no—
110C22×D61—42no—
111C22×D61—42no—
112C22×D61—42no—
113C22×D61C22⋊C811yescharacteristic
114D4×C61—41no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61C2×C22⋊C411yescharacteristic
119C2×C4×C61C22×C811yescharacteristic
120C2×C4×C61C2×M1611yescharacteristic
121C22⋊D61—42no—
122C2×Dic61—21no—
123C2×Dic61—42no—
124C2×Dic61C22⋊C811yescharacteristic
125C2×Dic61C22⋊C811yescharacteristic
126C2×Dic61C22⋊C811yescharacteristic
127D244—41no—
128C4×D61—22no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—22no—
132C4×D61—42no—
133C4×D61—42no—
134C4×D61—41no—
135C4×D61—41no—
136C8×C61—21no—
137C8×C61—41no—
138C8×C61AGL(1,ℤ/8)11yescharacteristic
139C8×C61AGL(1,ℤ/8)11yescharacteristic
140#92418—21no—
141#92418—21no—
142#92418—41no—
143#11634—611nomaximal, Sylow
144C22×C61—41no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61C2×C22⋊C811yescharacteristic
148C2×D61—21no—
149C2×D61—21no—
150C2×D61—41no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—84no—
154C2×D61#35012yes—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—41no—
158C4×C61#41811yescharacteristic
159C4×C61#42111yescharacteristic
160Dic61—21no—
161Dic61—21no—
162Dic61—41no—
163Dic61#34912yes—
164C2×#436—611no—
165#2163—611no—
166#2162—611no—
167#1330—611no—
168#1330—611no—
169#1330—611no—
170#1330D6111yescharacteristic, complemented
171C2×C61—81no—
172C2×C61#147811yescharacteristic
173C2×C61C2×#34911yescharacteristic
174C2×C61C2×#35011yescharacteristic
175D61—22no—
176D61—81no—
177C22×M16—1221no—
178C2×C4×D4—611no—
179#436—611no—
180#436—611no—
181#436—611no—
182#436—1221no—
183#436—1221no—
184#436C2×D6111yescharacteristic
185C2×C4⋊C8—611no—
186C2×C22⋊C8—1221no—
187C2×C4×C8—611no—
188C4⋊C16—611no—
189C4⋊C16—1221no—
190C4⋊C16C2×D6111yescharacteristic, complemented
191C22⋊C16—1221no—
192C22⋊C16—1221no—
193#346—611no—
194#346C2×D6111yescharacteristic, complemented
195C4×C16—1221no—
196C61#1163411yescharacteristic, complemented, Sylow
197C22×D4—611no—
198C23×C4—1221no—
199C2×M16—21no—
200C2×M16—1221no—
201C2×M16—1221no—
202C2×M16—1221no—
203C2×M16—2442no—
204C2×M16—2442no—
205C22×C8—611no—
206C22×C8—611no—
207C22×C8—1221no—
208C4×D4—611no—
209C4×D4—611no—
210C4×D4—611no—
211C4×D4—1221no—
212C4×D4—1221no—
213C4×D4C4×D6111yescharacteristic
214C2×C4⋊C4—611no—
215C2×C22⋊C4—1221no—
216C2×C42—611no—
217C2×C16—21no—
218C2×C16—21no—
219C2×C16—1221no—
220C2×C16—1221no—
221C4⋊C8—611no—
222C4⋊C8—1221no—
223C4⋊C8C4×D6111yescharacteristic
224C22⋊C8—21no—
225C22⋊C8—1221no—
226C22⋊C8—1221no—
227C22⋊C8—1221no—
228C4×C8—611no—
229C4×C8—611no—
230C4×C8—611no—
231C4×C8C22×D6111yescharacteristic
232C24—1221no—
233C2×D4—611no—
234C2×D4—1221no—
235C2×D4—2442no—
236C2×D4C8×D6111yescharacteristic
237C22×C4—21no—
238C22×C4—611no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—1221no—
242C22×C4—1221no—
243C22×C4—1221no—
244C22×C4—1221no—
245C22×C4—2442no—
246C22×C4—2442no—
247M16—41no—
248M16—41no—
249M16—2442no—
250M16—2442no—
251M16—2441no—
252M16—2441no—
253C2×C8—21no—
254C2×C8—611no—
255C2×C8—611no—
256C2×C8—1221no—
257C2×C8—1221no—
258C2×C8—1221no—
259C2×C8—2441no—
260C2×C8—2442no—
261C2×C8D4×D6111yescharacteristic
262C2×C8D4×D6111yescharacteristic
263C4⋊C4—611no—
264C4⋊C4—1221no—
265C4⋊C4C8×D6111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—1221no—
268C22⋊C4—1221no—
269C22⋊C4—1221no—
270C42—611no—
271C42—611no—
272C42—611no—
273C42C2×C4×D6111yescharacteristic
274C16—41no—
275C16—41no—
276C16—2441no—
277C16—2441no—
278C23—21no—
279C23—611no—
280C23—1221no—
281C23—2442no—
282C23—2442no—
283C23—2442no—
284D4—41no—
285D4—2441no—
286D4—2442no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—611no—
291C2×C4—611no—
292C2×C4—611no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—2442no—
299C2×C4—2442no—
300C2×C4—2442no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4C22⋊C4×D6111yescharacteristic
304C2×C4C2×C8×D6111yescharacteristic
305C2×C4M16×D6111yescharacteristic
306C8—21no—
307C8—41no—
308C8—1221no—
309C8—1221no—
310C8—2441no—
311C8#1451980111yescharacteristic
312C8#1451980411yescharacteristic
313C22—41no—
314C22—41no—
315C22—41no—
316C22—612no—
317C22—1221no—
318C22—1221no—
319C22—4884no—
320C22—2441no—
321C22—2441no—
322C22—2441no—
323C22C22⋊C8×D6111yescharacteristic
324C4—21no—
325C4—21no—
326C4—41no—
327C4—612no—
328C4—1221no—
329C4—1221no—
330C4—2441no—
331C4#1683976511yescharacteristic
332C4#1683977711yescharacteristic
333C2—81no—
334C2—1222no—
335C2—4881no—
336C2#2144420811yescharacteristic
337C2#349×D6111yescharacteristic
338C2#350×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC4×C8C22×D61
FittingC61×#1330C2
socleC22×C61C2×C22⋊C8
prime radicalC2×D4×D61C8
cosocleC4×C8×C61C23
hypercenter#1330D61
hypocenterC61#11634
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1330

Complements

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

NH ≅ G/Ntype
2. #21447620C2semidirect
3. #21447617C2semidirect
4. #21443778C2semidirect
5. #21443777C2semidirect
6. #21443776C2semidirect
7. C61×#1330C2semidirect
18. C4⋊#11758185C22semidirect
22. #16839538C22semidirect
25. C61×C4⋊C16C22semidirect
26. C61×#346C22semidirect
170. #1330D61semidirect
190. C4⋊C16C2×D61semidirect
194. #346C2×D61semidirect
196. C61#11634semidirect

Maximal subgroups

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

subgroupindex
#436×D612
#214476202
#214476172
#214437782
#214437772
#214437762
C61×#13302
#1163461