Finite Group Databasebeta

← #29593289

Subgroups — #29593289

Order 15616.

316 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 63 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#21457171C211yesmaximal, characteristic
2#21448017C211yesmaximal, characteristic, complemented
3#21448000C211yesmaximal, characteristic
4#21447307C211yesmaximal, characteristic, complemented
5#21443832C211yesmaximal, characteristic, complemented
6#21443829C211yesmaximal, characteristic
7C61×#1322C211yesmaximal, characteristic, complemented
8#16840296—21no—
9#16840070—21no—
10#16840063—21no—
11#16840003C2211yescharacteristic
12#16839998C2211yescharacteristic
13#16839991—21no—
14#16839985—21no—
15#16839978—21no—
16C2×#14519711C2211yescharacteristic
17#16839660—21no—
18#16839590—21no—
19#16839588—21no—
20#16839567—21no—
21#16839564—21no—
22#16839525—21no—
23#16839525C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×C22⋊C16C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758190—21no—
29C2×D488D411yescharacteristic
30#14519771—41no—
31#14519769—21no—
32#14519765—21no—
33#14519760—41no—
34#14519756—21no—
35#14519751—21no—
36C4×Dic122—21no—
37C4×D244—21no—
38C4×C22⋊D61—41no—
39#14519734—41no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×#11758196—41no—
43#14519711—21no—
44#14519711—21no—
45#14519711D411yescharacteristic
46#14519711D411yescharacteristic
47#14519709—21no—
48#14519702—21no—
49#14519702—21no—
50#14519699—21no—
51#14519699—21no—
52#14519684—41no—
53C22×C8×C61D411yescharacteristic
54C22×C8×C61C2311yescharacteristic
55C2×C42×C61D411yescharacteristic
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C22×C4×C61D811yescharacteristic
61C22×C4×C61D811yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C2×C22⋊D61—41no—
64C22×Dic61—41no—
65C22×Dic61—41no—
66C2×D244—21no—
67C2×C4×D61—41no—
68C2×Dic122—21no—
69C2×C8×C61—21no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61C2×D411yescharacteristic
73C2×C8×C61C2×D411yescharacteristic
74C42×C61—21no—
75C42×C61—21no—
76C22⋊Dic61—41no—
77#11758198—41no—
78#11758198—41no—
79#11758198—41no—
80#11758198—41no—
81C4⋊Dic61—22no—
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87#11758196—41no—
88#11758196—41no—
89#11758196—41no—
90#11758196—41no—
91#11758196—82no—
92C4×Dic61—41no—
93Dic244—41no—
94D488—41no—
95#11758190—81no—
96C16×C61—41no—
97C16×C61—41no—
98C23×C61C2×D811yescharacteristic
99C22×D61—41no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61#12011yescharacteristic
108C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
109C22⋊D61—81no—
110C22⋊D61—81no—
111C2×Dic61—42no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—81no—
116C2×Dic61—81no—
117C2×Dic61—81no—
118C2×Dic61—81no—
119C2×Dic61—81no—
120D244—41no—
121D244—41no—
122C4×D61—82no—
123Dic122—41no—
124Dic122—41no—
125C8×C61—21no—
126C8×C61—21no—
127C8×C61—41no—
128#12290—611nomaximal, Sylow
129C22×C61—21no—
130C22×C61—21no—
131C22×C61#44711yescharacteristic
132C22×C61#50811yescharacteristic
133C22×C61#50911yescharacteristic
134C2×D61—81no—
135C2×D61—81no—
136C2×D61—81no—
137C4×C61—21no—
138C4×C61—41no—
139C4×C61—41no—
140C4×C61#45611yescharacteristic
141C4×C61#45811yescharacteristic
142Dic61—82no—
143Dic61—81no—
144Dic61—81no—
145Dic61—81no—
146Dic61—161no—
147#3250—611no—
148#2235—611no—
149#2232—611no—
150#2086—611no—
151#1348—611no—
152#1347—611no—
153#1322D6111yescharacteristic, complemented
154C2×C61—21no—
155C2×C61—21no—
156C2×C61#161011yescharacteristic
157C2×C61#218611yescharacteristic
158C2×C61#219111yescharacteristic
159D61—161no—
160#529—1221no—
161#479—1221no—
162#478—1221no—
163#467—611no—
164#466—611no—
165#465—1221no—
166#464—1221no—
167#463—1221no—
168C2×#107—611no—
169C2×C4⋊C8C2×D6111yescharacteristic
170#389—1221no—
171#367—1221no—
172#366—1221no—
173#358—1221no—
174#357—1221no—
175C22⋊C16C2×D6111yescharacteristic
176C22⋊C16C2×D6111yescharacteristic
177#340—611no—
178#340—1221no—
179C61#1229011yescharacteristic, complemented, Sylow
180C2×Q16—611no—
181C2×SD16—1221no—
182C2×D8—611no—
183C22×C8D24411yescharacteristic
184C22×C8C22×D6111yescharacteristic
185#126—2441no—
186#125—1221no—
187#124—1221no—
188#123—2441no—
189C22⋊Q8—1221no—
190#121—1221no—
191C4×Q8—1221no—
192C4×D4—1221no—
193C4×D4—2441no—
194#117—2441no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—2441no—
198C2×C42D24411yescharacteristic
199C2×C16—21no—
200C2×C16—21no—
201#107—611no—
202#107—611no—
203#107—1221no—
204#107—1221no—
205#106—1221no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208#103—1221no—
209#103—1221no—
210#102—1221no—
211#102—1221no—
212#95—2441no—
213C2×Q8—1221no—
214C2×D4—1221no—
215C2×D4—2441no—
216C22×C4—2441no—
217C22×C4—2441no—
218C22×C4—2441no—
219C22×C4D48811yescharacteristic
220C22×C4D48811yescharacteristic
221C22×C4C2×D24411yescharacteristic
222Q16—2441no—
223SD16—4881no—
224D8—2441no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8D4×D6111yescharacteristic
229C2×C8D4×D6111yescharacteristic
230C4⋊C4—1222no—
231C4⋊C4—1221no—
232C4⋊C4—1221no—
233C4⋊C4—4882no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C4⋊C4—2441no—
241C22⋊C4—2441no—
242C22⋊C4—2441no—
243C22⋊C4—2441no—
244C22⋊C4—2441no—
245C22⋊C4—2441no—
246C42—21no—
247C42—21no—
248C42—2441no—
249C16—41no—
250C16—41no—
251C23—2441no—
252C23C2×D48811yescharacteristic
253Q8—2441no—
254Q8—2441no—
255D4—4881no—
256D4—4881no—
257D4—2441no—
258D4—2441no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—4882no—
267C2×C4—4881no—
268C2×C4—4881no—
269C2×C4—4881no—
270C2×C4—4881no—
271C2×C4—4881no—
272C2×C4—2442no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4#1451974711yescharacteristic
277C2×C4#1451980511yescharacteristic
278C8—21no—
279C8—21no—
280C8—41no—
281C22—21no—
282C22—21no—
283C22—4881no—
284C22—4881no—
285C22—4881no—
286C22#1683989811yescharacteristic
287C22#1684019411yescharacteristic
288C22#1684020011yescharacteristic
289C4—21no—
290C4—41no—
291C4—41no—
292C4—9761no—
293C4—4882no—
294C4—4881no—
295C4—4881no—
296C4—4881no—
297C4#1683994711yescharacteristic
298C4#1683995311yescharacteristic
299C2—21no—
300C2—21no—
301C2—9761no—
302C2#2144482411yescharacteristic
303C2#2144774411yescharacteristic
304C2#2144777211yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1322C2
socleC22×C61#447
prime radical#16839998C22
hypercenter#1322D61
hypocenterC61#12290
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
2. #21448017C2semidirect
4. #21447307C2semidirect
5. #21443832C2semidirect
7. C61×#1322C2semidirect
153. #1322D61semidirect
179. C61#12290semidirect

Maximal subgroups

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

subgroupindex
#214571712
#214480172
#214480002
#214473072
#214438322
#214438292
C61×#13222
#1229061