Finite Group Databasebeta

← #29593321

Subgroups — #29593321

Order 15616.

290 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 57 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#21457281C211yesmaximal, characteristic
2#21448014C211yesmaximal, characteristic, complemented
3#21448005C211yesmaximal, characteristic
4#21447326C211yesmaximal, characteristic, complemented
5#21443833C211yesmaximal, characteristic
6#21443760C211yesmaximal, characteristic, complemented
7C61×#1350C211yesmaximal, characteristic, complemented
8#16840385—21no—
9#16840055—21no—
10#16840041—21no—
11#16840010—21no—
12#16839998C2211yescharacteristic
13#16839986—21no—
14#16839980—21no—
15#16839804—21no—
16C2×#14519711C2211yescharacteristic
17#16839788C2211yescharacteristic
18#16839590—21no—
19#16839589—21no—
20#16839566—21no—
21#16839564—21no—
22C22⋊#11758185C2211yescharacteristic
23#16839530—21no—
24C61×#467C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×#341C2211yescharacteristic
27C2×#11758201—21no—
28C2×D488D411yescharacteristic
29C2×#11758194D411yescharacteristic
30#14519776—21no—
31#14519772—41no—
32#14519766—21no—
33#14519763—41no—
34#14519759—41no—
35#14519757—41no—
36#14519751—21no—
37Q8×Dic61—21no—
38#14519739—21no—
39#14519736D411yescharacteristic
40C2×C4⋊Dic61—21no—
41C2×#11758185—21no—
42#14519711—21no—
43#14519711—21no—
44#14519711—41no—
45#14519711D411yescharacteristic
46#14519710—21no—
47#14519709—41no—
48#14519706—21no—
49#14519706—21no—
50#14519701—21no—
51#14519699—21no—
52#14519697—21no—
53C2×Q16×C61D411yescharacteristic
54C2×M16×C61—21no—
55C22×C8×C61C2311yescharacteristic
56C22⋊Q8×C61—21no—
57C2×C16×C61—21no—
58#107×C61D411yescharacteristic
59#103×C61—21no—
60C2×Q8×C61—21no—
61C22×C4×C61C2×D411yescharacteristic
62C2×C22⋊D61—41no—
63C22×Dic61—41no—
64C2×D244—21no—
65C2×C4×D61—41no—
66C2×Dic122—41no—
67Q16×C61—41no—
68M16×C61—22no—
69M16×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61C2×D411yescharacteristic
73C2×C8×C61C2×D411yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C22⋊Dic61—21no—
78#11758201—81no—
79#11758198—41no—
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61D811yescharacteristic
88C4⋊Dic61D811yescharacteristic
89#11758196—41no—
90C4×Dic61—21no—
91C4×Dic61—41no—
92#11758194—41no—
93C2×#92418—21no—
94D488—41no—
95C16×C61—41no—
96#11758185—41no—
97C23×C61AGL(1,ℤ/8)11yescharacteristic
98C22×D61—41no—
99Q8×C61—41no—
100Q8×C61—41no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61#12011yescharacteristic
106C2×C4×C61C2×D811yescharacteristic
107C22⋊D61—161no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—41no—
111C2×Dic61—81no—
112C2×Dic61—161no—
113D244—41no—
114D244—41no—
115C4×D61—161no—
116Dic122—161no—
117C8×C61—21no—
118C8×C61—21no—
119C8×C61—42no—
120#92418—41no—
121#12295—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—21no—
125C22×C61#44711yescharacteristic
126C2×D61—81no—
127C2×D61—81no—
128C2×D61—81no—
129C4×C61—21no—
130C4×C61—81no—
131C4×C61—81no—
132C4×C61#45611yescharacteristic
133C4×C61#45811yescharacteristic
134Dic61—41no—
135Dic61—41no—
136Dic61—81no—
137Dic61—161no—
138#3262—611no—
139#2235—611no—
140#2233—611no—
141#2089—611no—
142#1350D6111yescharacteristic, complemented
143#1349—611no—
144#1323—611no—
145C2×C61—41no—
146C2×C61#161011yescharacteristic
147C2×C61#219311yescharacteristic
148C2×C61#219411yescharacteristic
149D61—161no—
150#542—1221no—
151#477—1221no—
152#474—1221no—
153#468—1221no—
154#467C2×D6111yescharacteristic
155#466—611no—
156#464—1221no—
157#463—1221no—
158#428—1221no—
159C2×#107—611no—
160#424—611no—
161#367—1221no—
162#367—1221no—
163#358—1221no—
164#357—1221no—
165C22⋊C16—611no—
166C22⋊C16C2×D6111yescharacteristic
167#343—1221no—
168#341C2×D6111yescharacteristic
169C61#1229511yescharacteristic, complemented, Sylow
170C2×Q16D24411yescharacteristic
171C2×SD16—1221no—
172C2×D8—611no—
173C2×M16—21no—
174C2×M16—611no—
175C22×C8C22×D6111yescharacteristic
176C4⋊Q8—1221no—
177#126—2441no—
178#124—1221no—
179#124—2441no—
180#123—2441no—
181C22⋊Q8—21no—
182C22⋊Q8—2441no—
183#121—1221no—
184C4×Q8—1221no—
185C4×D4—1221no—
186#117—611no—
187C2×C4⋊C4—1221no—
188C2×C16—21no—
189C2×C16—1221no—
190#107—611no—
191#107—1221no—
192#107—1221no—
193#107—1221no—
194#107—2441no—
195#107D24411yescharacteristic
196#106—2441no—
197C4⋊C8—1221no—
198C4⋊C8—1221no—
199#103—21no—
200#103—1221no—
201#102—1221no—
202#102—1221no—
203C2×Q8—21no—
204C2×Q8—2441no—
205C2×D4—1221no—
206C2×D4—2441no—
207C22×C4—2441no—
208C22×C4—2441no—
209C22×C4D4×D6111yescharacteristic
210Q16—41no—
211SD16—4881no—
212D8—2441no—
213M16—22no—
214M16—41no—
215M16—2441no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—1221no—
219C2×C8C2×D24411yescharacteristic
220C2×C8D4×D6111yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—611no—
224C4⋊C4—611no—
225C4⋊C4—1221no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C22⋊C4—41no—
231C22⋊C4—1221no—
232C22⋊C4—2441no—
233C22⋊C4—2441no—
234C22⋊C4—2441no—
235C22⋊C4—2441no—
236C42—1221no—
237C42—2441no—
238C16—41no—
239C16—2441no—
240C23—2441no—
241C23#1451980411yescharacteristic
242Q8—41no—
243Q8—41no—
244Q8—9761no—
245D4—9761no—
246D4—2441no—
247D4—2441no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—9761no—
255C2×C4—9761no—
256C2×C4—4881no—
257C2×C4—2441no—
258C2×C4#1451974711yescharacteristic
259C2×C4D8×D6111yescharacteristic
260C8—21no—
261C8—21no—
262C8—42no—
263C8—2441no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—4881no—
268C22—4881no—
269C22—4881no—
270C22#1683989711yescharacteristic
271C4—21no—
272C4—81no—
273C4—81no—
274C4—9761no—
275C4—4881no—
276C4—2441no—
277C4—2441no—
278C4#1683994611yescharacteristic
279C4#1683995311yescharacteristic
280C2—41no—
281C2—9761no—
282C2#2144482311yescharacteristic
283C2#2144778611yescharacteristic
284C2#2144779111yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1350C2
socleC22×C61#447
prime radical#16839998C22
hypercenter#1350D61
hypocenterC61#12295
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1350

Complements

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

NH ≅ G/Ntype
2. #21448014C2semidirect
4. #21447326C2semidirect
6. #21443760C2semidirect
7. C61×#1350C2semidirect
142. #1350D61semidirect
169. C61#12295semidirect

Maximal subgroups

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

subgroupindex
#214572812
#214480142
#214480052
#214473262
#214438332
#214437602
C61×#13502
#1229561