Finite Group Databasebeta

← #29593228

Subgroups — #29593228

Order 15616.

348 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 61 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#21456613C211yesmaximal, characteristic
2#21448014C211yesmaximal, characteristic, complemented
3#21448000C211yesmaximal, characteristic, complemented
4#21447244C211yesmaximal, characteristic, complemented
5#21443827C211yesmaximal, characteristic, complemented
6#21443742C211yesmaximal, characteristic, complemented
7C61×#1348C211yesmaximal, characteristic, complemented
8#16840275—21no—
9#16840102—21no—
10#16840089—21no—
11#16839998C2211yescharacteristic
12#16839993—21no—
13#16839923—21no—
14#16839910—21no—
15C2×#14519711C2211yescharacteristic
16C2×#14519689C2211yescharacteristic
17#16839619—21no—
18#16839589—21no—
19#16839588—21no—
20#16839566—21no—
21#16839564—21no—
22C22⋊#11758185C2211yescharacteristic
23#16839524—21no—
24C61×#467C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×#340C2211yescharacteristic
27C2×#11758226—21no—
28C22×C4×D61D411yescharacteristic
29C2×#11758201—21no—
30C2×D488D411yescharacteristic
31C22×#92418D411yescharacteristic
32#14519762—41no—
33#14519753—21no—
34#14519752—21no—
35#14519751—21no—
36#14519747—41no—
37#14519739—41no—
38#14519737—41no—
39#14519735—21no—
40C2×C4⋊Dic61—21no—
41C2×#11758198—41no—
42C2×#11758185—21no—
43#14519711—21no—
44#14519711—21no—
45#14519711D411yescharacteristic
46#14519708—21no—
47#14519701—21no—
48#14519699—21no—
49#14519697—21no—
50#14519689—21no—
51#14519689—21no—
52#14519684—41no—
53C2×Q16×C61D411yescharacteristic
54C22×C8×C61C2311yescharacteristic
55C22⋊Q8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C16×C61—21no—
58#107×C61D411yescharacteristic
59#103×C61—21no—
60C23×D61D811yescharacteristic
61C2×Q8×C61—21no—
62C22×C4×C61—41no—
63C22×C4×C61C2×D411yescharacteristic
64C2×C22⋊D61—41no—
65C22×Dic61—41no—
66C22×Dic61D811yescharacteristic
67#11758226—81no—
68#11758226—81no—
69C2×D244—21no—
70C2×D244—41no—
71C2×D244—41no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77Q16×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61C2×D411yescharacteristic
80C2×C8×C61C2×D411yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86#11758201—81no—
87#11758198—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758198—82no—
92C4⋊Dic61—21no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95#11758196—41no—
96C4×Dic61—41no—
97C2×#92418—21no—
98C2×#92418—41no—
99D488—41no—
100C16×C61—41no—
101#11758185—41no—
102C23×C61C2×D811yescharacteristic
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109Q8×C61—41no—
110Q8×C61—41no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—81no—
116C2×C4×C61—81no—
117C2×C4×C61—81no—
118C2×C4×C61#12011yescharacteristic
119C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
120C22⋊D61—81no—
121C22⋊D61—81no—
122C2×Dic61—21no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—81no—
126C2×Dic61—81no—
127C2×Dic61—81no—
128D244—41no—
129D244—41no—
130D244—82no—
131D244—82no—
132C4×D61—41no—
133C4×D61—41no—
134C4×D61—81no—
135C4×D61—82no—
136C8×C61—21no—
137C8×C61—21no—
138#92418—41no—
139#12280—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61#44711yescharacteristic
143C22×C61#50811yescharacteristic
144C22×C61#50911yescharacteristic
145C2×D61—42no—
146C2×D61—41no—
147C2×D61—41no—
148C2×D61—41no—
149C2×D61—81no—
150C2×D61—81no—
151C2×D61—81no—
152C2×D61—81no—
153C4×C61—21no—
154C4×C61—81no—
155C4×C61—81no—
156C4×C61—161no—
157C4×C61#45511yescharacteristic
158C4×C61#45811yescharacteristic
159Dic61—41no—
160Dic61—81no—
161Dic61—161no—
162#3191—611no—
163#2235—611no—
164#2232—611no—
165#2075—611no—
166#1348D6111yescharacteristic, complemented
167#1347—611no—
168#1314—611no—
169C2×C61—21no—
170C2×C61—21no—
171C2×C61#160711yescharacteristic
172C2×C61#218611yescharacteristic
173C2×C61#219111yescharacteristic
174D61—81no—
175D61—161no—
176#525—1221no—
177#485—1221no—
178#482—1221no—
179#467C2×D6111yescharacteristic
180#466—611no—
181#465—1221no—
182#452—1221no—
183#449—1221no—
184C2×#107—611no—
185C2×C22⋊C8—611no—
186#380—1221no—
187#367—1221no—
188#366—1221no—
189#358—1221no—
190#357—1221no—
191C22⋊C16—611no—
192C22⋊C16C2×D6111yescharacteristic
193#340—1221no—
194#340C2×D6111yescharacteristic
195C61#1228011yescharacteristic, complemented, Sylow
196C2×#41—1221no—
197C23×C4—611no—
198C2×Q16D24411yescharacteristic
199C2×SD16—1221no—
200C2×D8—611no—
201C22×C8—611no—
202C22×C8C22×D6111yescharacteristic
203#123—2441no—
204C22⋊Q8—21no—
205C22⋊Q8—1221no—
206#121—1221no—
207#121—1221no—
208#120—2441no—
209C4×D4—2441no—
210C4×D4—2441no—
211#117—1221no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—1221no—
214C2×C22⋊C4—2441no—
215C2×C16—21no—
216C2×C16—1221no—
217#107—611no—
218#107—1221no—
219#107—1221no—
220#107D24411yescharacteristic
221#106—1221no—
222#103—21no—
223#103—1221no—
224#102—1221no—
225#102—1221no—
226C22⋊C8—1221no—
227C22⋊C8—1221no—
228#95—2441no—
229C24—611no—
230#41—4881no—
231#41—4881no—
232C2×Q8—21no—
233C2×D4—1221no—
234C2×D4—2441no—
235C2×D4—2441no—
236C2×D4—2441no—
237C22×C4—41no—
238C22×C4—611no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4—2441no—
242C22×C4—2441no—
243C22×C4—2441no—
244C22×C4—2441no—
245C22×C4D4×D6111yescharacteristic
246Q16—41no—
247SD16—4881no—
248D8—2441no—
249C2×C8—41no—
250C2×C8—1221no—
251C2×C8—2441no—
252C2×C8C2×D24411yescharacteristic
253C2×C8D4×D6111yescharacteristic
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—1221no—
259C4⋊C4—2441no—
260C4⋊C4—2441no—
261C4⋊C4—2441no—
262C22⋊C4—41no—
263C22⋊C4—4882no—
264C22⋊C4—2441no—
265C22⋊C4—2441no—
266C22⋊C4—2441no—
267C22⋊C4—2441no—
268C42—2441no—
269C16—41no—
270C16—2441no—
271C23—1221no—
272C23—1221no—
273C23—1221no—
274C23—2441no—
275C23—2441no—
276C23—2441no—
277C23D8×D6111yescharacteristic
278Q8—41no—
279Q8—41no—
280D4—4882no—
281D4—4882no—
282D4—4881no—
283D4—4881no—
284D4—2441no—
285D4—2441no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—1221no—
294C2×C4—4881no—
295C2×C4—4882no—
296C2×C4—4881no—
297C2×C4—4881no—
298C2×C4—4881no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4#1451974711yescharacteristic
304C2×C4#1451980411yescharacteristic
305C8—21no—
306C8—21no—
307C8—2441no—
308C22—21no—
309C22—21no—
310C22—4881no—
311C22—4881no—
312C22—4881no—
313C22—4881no—
314C22—2442no—
315C22—2441no—
316C22—2441no—
317C22—2441no—
318C22#1683989711yescharacteristic
319C22#1684019511yescharacteristic
320C22#1684019911yescharacteristic
321C4—21no—
322C4—81no—
323C4—81no—
324C4—161no—
325C4—9761no—
326C4—4881no—
327C4—2441no—
328C4#1683994111yescharacteristic
329C4#1683995311yescharacteristic
330C2—21no—
331C2—21no—
332C2—9761no—
333C2—4881no—
334C2#2144480611yescharacteristic
335C2#2144774511yescharacteristic
336C2#2144777111yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1348C2
socleC22×C61#447
prime radical#21456613C2
hypercenter#1348D61
hypocenterC61#12280
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1348

Complements

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

NH ≅ G/Ntype
2. #21448014C2semidirect
3. #21448000C2semidirect
4. #21447244C2semidirect
5. #21443827C2semidirect
6. #21443742C2semidirect
7. C61×#1348C2semidirect
166. #1348D61semidirect
195. C61#12280semidirect

Maximal subgroups

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

subgroupindex
#214566132
#214480142
#214480002
#214472442
#214438272
#214437422
C61×#13482
#1228061