Finite Group Databasebeta

← #29593681

Subgroups — #29593681

Order 15616.

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

normal subgroups only

This group has 286 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#21458395C211yesmaximal, characteristic
2#21448064C211yesmaximal, characteristic, complemented
3#21445305C211yesmaximal, characteristic
4#21443870C211yesmaximal, characteristic, complemented
5#21443789C211yesmaximal, characteristic, complemented
6#21443776C211yesmaximal, characteristic
7C61×#2209C211yesmaximal, characteristic, complemented
8#16840453—21no—
9#16840164C2211yescharacteristic
10#16840102—21no—
11#16840096—21no—
12#16840069—21no—
13#16840039—21no—
14#16840017—21no—
15#16839841C2211yescharacteristic
16#16839803—21no—
17#16839566—21no—
18#16839566—21no—
19#16839538C2211yescharacteristic
20#16839513C2211yescharacteristic
21#16839508—21no—
22C2×Q32×C61—21no—
23C61×#494C2211yescharacteristic
24C4×Q16×C61C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#358—21no—
27C2×#11758189—21no—
28#14519771—41no—
29#14519769—21no—
30#14519767—41no—
31#14519762—41no—
32#14519753—21no—
33#14519753—21no—
34C4×D244D411yescharacteristic
35#14519735—21no—
36#14519734—41no—
37C4⋊C4×D61—21no—
38C2×#11758185—21no—
39#14519711D411yescharacteristic
40#14519711D411yescharacteristic
41#14519710—21no—
42#14519710—41no—
43#14519709—21no—
44#14519708—21no—
45C4⋊#92418—21no—
46C4⋊#92418D411yescharacteristic
47#14519701—21no—
48#14519701—21no—
49#14519697—41no—
50#14519689—21no—
51C2×Q16×C61—21no—
52C2×Q16×C61—21no—
53C2×Q16×C61D411yescharacteristic
54C4⋊Q8×C61—21no—
55C4×Q8×C61—21no—
56Q32×C61—42no—
57C2×C16×C61—21no—
58#107×C61D411yescharacteristic
59#103×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×Q8×C61—21no—
62C2×Q8×C61—41no—
63C2×D244D811yescharacteristic
64C2×C4×D61—21no—
65C2×C4×D61—41no—
66Q16×C61—21no—
67Q16×C61—21no—
68Q16×C61—42no—
69Q16×C61—41no—
70Q16×C61—41no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C42×C61—41no—
78C42×C61C2×D411yescharacteristic
79#11758198—21no—
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61D811yescharacteristic
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89#11758196—41no—
90#11758196—41no—
91C4×Dic61—41no—
92C2×#92418—21no—
93C2×#92418—41no—
94#11758189—41no—
95#11758189—41no—
96C16×C61—41no—
97#11758185—41no—
98C22×D61—21no—
99Q8×C61—41no—
100Q8×C61—41no—
101Q8×C61—81no—
102Q8×C61—81no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—81no—
106C2×C4×C61#12011yescharacteristic
107C2×C4×C61C2×D811yescharacteristic
108C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
109C2×Dic61—21no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112D244—41no—
113C4×D61—41no—
114C4×D61—41no—
115C4×D61—82no—
116C8×C61—21no—
117C8×C61#13511yescharacteristic
118C8×C61AGL(1,ℤ/8)11yescharacteristic
119#92418—41no—
120#92418—81no—
121#12351—611nomaximal, Sylow
122C22×C61#44711yescharacteristic
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—41no—
126C4×C61—21no—
127C4×C61—21no—
128C4×C61—81no—
129C4×C61—81no—
130C4×C61—161no—
131C4×C61#44911yescharacteristic
132C4×C61#45411yescharacteristic
133Dic61—41no—
134Dic61—81no—
135Dic61—81no—
136#3352—611no—
137#2245—611no—
138#2209D6111yescharacteristic, complemented
139#1689—611no—
140#1363—611no—
141#1334—611no—
142#1330—611no—
143C2×C61#162511yescharacteristic
144C2×C61#219111yescharacteristic
145C2×C61#219511yescharacteristic
146D61—81no—
147#552—1221no—
148C2×Q32—21no—
149#499—611no—
150#494C2×D6111yescharacteristic
151#485—1221no—
152#484—1221no—
153#479—1221no—
154#474—1221no—
155#470—1221no—
156C4×Q16C2×D6111yescharacteristic
157#436—611no—
158#428—1221no—
159C4⋊C16C2×D6111yescharacteristic
160#358—21no—
161#358—1221no—
162#358—1221no—
163#346—611no—
164#334—611no—
165#332—1221no—
166C61#1235111yescharacteristic, complemented, Sylow
167C2×Q16—21no—
168C2×Q16—21no—
169C2×Q16C22⋊D6111yescharacteristic
170C2×M16—1221no—
171C4⋊Q8—21no—
172#126—2441no—
173#125—1221no—
174#125—2441no—
175#123—2441no—
176C22⋊Q8—1221no—
177C22⋊Q8—1221no—
178C4×Q8—21no—
179C4×D4—611no—
180#117—1221no—
181#117—2441no—
182C2×C4⋊C4—1221no—
183Q32—42no—
184C2×C16—21no—
185C2×C16—1221no—
186#107—611no—
187#107—611no—
188#107—1221no—
189#107—2441no—
190#107C22⋊D6111yescharacteristic
191#106—1221no—
192#106—1221no—
193C4⋊C8—611no—
194C4⋊C8—1221no—
195#103—21no—
196#103—1221no—
197#103—1221no—
198#102—2441no—
199C22⋊C8—1221no—
200C4×C8C22×D6111yescharacteristic
201C2×Q8—21no—
202C2×Q8—41no—
203C2×D4—611no—
204C22×C4—1221no—
205C22×C4—2441no—
206Q16—21no—
207Q16—21no—
208Q16—42no—
209Q16—41no—
210Q16—41no—
211M16—2441no—
212M16—2441no—
213C2×C8—1221no—
214C2×C8—2441no—
215C2×C8D4×D6111yescharacteristic
216C2×C8C2×C22⋊D6111yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—611no—
222C4⋊C4—1221no—
223C4⋊C4—1221no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4—2441no—
229C22⋊C4—1221no—
230C22⋊C4—2441no—
231C22⋊C4—2441no—
232C22⋊C4—2441no—
233C42—41no—
234C42—2441no—
235C42D4×D6111yescharacteristic
236C16—41no—
237C16—2441no—
238C23—1221no—
239Q8—41no—
240Q8—41no—
241Q8—81no—
242Q8—81no—
243D4—2441no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—81no—
247C2×C4—1221no—
248C2×C4—4882no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4#1451974511yescharacteristic
254C2×C4D8×D6111yescharacteristic
255C2×C4#1451980111yescharacteristic
256C8—21no—
257C8—4881no—
258C8—2441no—
259C8#1451979711yescharacteristic
260C8#1451980311yescharacteristic
261C22—2441no—
262C22—2441no—
263C22—2441no—
264C22#1683989411yescharacteristic
265C4—21no—
266C4—21no—
267C4—81no—
268C4—81no—
269C4—161no—
270C4—4881no—
271C4—4881no—
272C4—2441no—
273C4#1683990511yescharacteristic
274C4#1683993311yescharacteristic
275C2—4881no—
276C2#2144490711yescharacteristic
277C2#2144776811yescharacteristic
278C2#2144779611yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2209C2
socleC22×C61#447
prime radicalC2×D244D8
hypercenter#2209D61
hypocenterC61#12351
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

Complements

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

NH ≅ G/Ntype
2. #21448064C2semidirect
4. #21443870C2semidirect
5. #21443789C2semidirect
7. C61×#2209C2semidirect
138. #2209D61semidirect
166. C61#12351semidirect

Maximal subgroups

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

subgroupindex
#214583952
#214480642
#214453052
#214438702
#214437892
#214437762
C61×#22092
#1235161