Finite Group Databasebeta

← #29593756

Subgroups — #29593756

Order 15616.

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

normal subgroups only

This group has 292 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#21458780C211yesmaximal, characteristic
2#21447861C211yesmaximal, characteristic
3#21445310C211yesmaximal, characteristic, complemented
4#21443871C211yesmaximal, characteristic, complemented
5#21443802C211yesmaximal, characteristic, complemented
6#21443787C211yesmaximal, characteristic
7C61×#2245C211yesmaximal, characteristic, complemented
8#16840468—21no—
9C2×#14519720—21no—
10#16840169—21no—
11#16840065—21no—
12#16840059—21no—
13#16840044—21no—
14#16840041—21no—
15#16839892C2211yescharacteristic
16#16839873—21no—
17C4×D488C2211yescharacteristic
18C4⋊#11758185C2211yescharacteristic
19#16839566—21no—
20#16839513C2211yescharacteristic
21#16839508—21no—
22C61×#499C2211yescharacteristic
23C61×#494C2211yescharacteristic
24C61×#358—21no—
25C61×#358—21no—
26C61×#346C2211yescharacteristic
27C2×D488D411yescharacteristic
28#14519776—21no—
29#14519768—21no—
30#14519757—41no—
31#14519755—41no—
32#14519755—41no—
33C4×Dic122D411yescharacteristic
34C4×D244—21no—
35#14519739—21no—
36#14519739—21no—
37C4⋊C4×D61—41no—
38#14519720—42no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519710—21no—
42#14519708—21no—
43#14519708—41no—
44C4⋊#92418—21no—
45C4⋊#92418D411yescharacteristic
46#14519706—21no—
47#14519700—41no—
48#14519699—21no—
49#14519697—21no—
50#14519697—21no—
51#14519687—21no—
52C2×Q16×C61—21no—
53C2×Q16×C61—21no—
54C4⋊Q8×C61—21no—
55#125×C61—21no—
56C2×C16×C61—21no—
57#107×C61D411yescharacteristic
58#107×C61D411yescharacteristic
59#106×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×Q8×C61—41no—
62C2×D244—21no—
63C2×C4×D61—41no—
64C2×C4×D61—41no—
65C2×C4×D61—41no—
66C2×Dic122—41no—
67C2×Dic122D811yescharacteristic
68Q16×C61—42no—
69Q16×C61—41no—
70Q16×C61—41no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C42×C61C2×D411yescharacteristic
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61D811yescharacteristic
86#11758196—21no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—21no—
90C2×#92418—21no—
91C2×#92418—41no—
92D488—21no—
93D488SD1612yes—
94C16×C61—41no—
95#11758185—41no—
96C22×D61—41no—
97Q8×C61—81no—
98Q8×C61—81no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—81no—
102C2×C4×C61#12011yescharacteristic
103C2×C4×C61C2×D811yescharacteristic
104C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—41no—
108D244—22no—
109D244—41no—
110C4×D61—82no—
111C4×D61—161no—
112C4×D61—161no—
113Dic122—41no—
114Dic122—161no—
115C8×C61—21no—
116C8×C61C2×SD1611yescharacteristic
117C8×C61#13711yescharacteristic
118#92418—41no—
119#92418—81no—
120#12362—611nomaximal, Sylow
121C22×C61#44711yescharacteristic
122C2×D61—42no—
123C2×D61—81no—
124C2×D61—81no—
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—81no—
128C4×C61—81no—
129C4×C61—161no—
130C4×C61#44811yescharacteristic
131C4×C61#45411yescharacteristic
132Dic61—41no—
133Dic61—41no—
134Dic61—81no—
135#3389—611no—
136#2245D6111yescharacteristic, complemented
137#2208—611no—
138#1690—611no—
139#1363—611no—
140#1338—611no—
141#1333—611no—
142C2×C61#162711yescharacteristic
143C2×C61#219111yescharacteristic
144C2×C61#219411yescharacteristic
145D61—82no—
146#554—1221no—
147C2×SD32—1221no—
148#501—1221no—
149#499C2×D6111yescharacteristic
150#494C2×D6111yescharacteristic
151#478—1221no—
152#478—1221no—
153#475—1221no—
154#474—1221no—
155#446—611no—
156#442—1221no—
157C4×D8—611no—
158C4⋊C16—611no—
159#358—21no—
160#358—21no—
161#358—1221no—
162#346C2×D6111yescharacteristic
163#334—611no—
164#332—1221no—
165C61#1236211yescharacteristic, complemented, Sylow
166C2×Q16—21no—
167C2×Q16—21no—
168C2×D8—611no—
169C4⋊Q8—21no—
170C4⋊Q8—1221no—
171#125—21no—
172#125—1221no—
173C22⋊Q8—2441no—
174C22⋊Q8—2441no—
175C22⋊Q8—2441no—
176C4×Q8—611no—
177C4×D4—1221no—
178C4×D4—1221no—
179C4×D4—1221no—
180C2×C4⋊C4—2441no—
181SD32—2442no—
182C2×C16—21no—
183C2×C16—1221no—
184#107—611no—
185#107—1221no—
186#107C22⋊D6111yescharacteristic
187#107C22⋊D6111yescharacteristic
188#106—21no—
189#106—1221no—
190#106—2441no—
191C4⋊C8—611no—
192C4⋊C8—1221no—
193C4⋊C8—1221no—
194#103—2441no—
195#102—1221no—
196#102—1221no—
197#102—1221no—
198#97—1221no—
199C4×C8C22×D6111yescharacteristic
200C2×Q8—41no—
201C2×Q8—611no—
202C2×Q8—2441no—
203C2×D4—1221no—
204C22×C4—2441no—
205C22×C4—2441no—
206C22×C4—2441no—
207Q16—42no—
208Q16—41no—
209Q16—41no—
210D8—612no—
211D8—1221no—
212C2×C8—1221no—
213C2×C8—2441no—
214C2×C8D4×D6111yescharacteristic
215C2×C8C2×C22⋊D6111yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—611no—
223C4⋊C4—1221no—
224C4⋊C4—1221no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C22⋊C4—2441no—
229C22⋊C4—2441no—
230C22⋊C4—2441no—
231C42—1221no—
232C42D4×D6111yescharacteristic
233C16—41no—
234C16—2441no—
235C23—2441no—
236Q8—81no—
237Q8—81no—
238Q8—9761no—
239Q8—2441no—
240D4—1222no—
241D4—2441no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—81no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—9761no—
248C2×C4—9761no—
249C2×C4—4882no—
250C2×C4—2441no—
251C2×C4#1451974511yescharacteristic
252C2×C4D8×D6111yescharacteristic
253C2×C4#1451980111yescharacteristic
254C8—21no—
255C8—4881no—
256C8—2441no—
257C8SD16×D6111yescharacteristic
258C8#1451980611yescharacteristic
259C22—4881no—
260C22—4881no—
261C22—2442no—
262C22#1683989411yescharacteristic
263C4—21no—
264C4—21no—
265C4—81no—
266C4—81no—
267C4—161no—
268C4—4881no—
269C4—2441no—
270C4—2441no—
271C4#1683989911yescharacteristic
272C4#1683993411yescharacteristic
273C2—4882no—
274C2#2144491911yescharacteristic
275C2#2144776811yescharacteristic
276C2#2144778711yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2245C2
socleC22×C61#447
prime radicalC2×D488D4
hypercenter#2245D61
hypocenterC61#12362
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2245

Complements

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

NH ≅ G/Ntype
3. #21445310C2semidirect
4. #21443871C2semidirect
5. #21443802C2semidirect
7. C61×#2245C2semidirect
136. #2245D61semidirect
165. C61#12362semidirect

Maximal subgroups

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

subgroupindex
#214587802
#214478612
#214453102
#214438712
#214438022
#214437872
C61×#22452
#1236261