Finite Group Databasebeta

← #29593322

Subgroups — #29593322

Order 15616.

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

normal subgroups only

This group has 278 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#21457268C211yesmaximal, characteristic
2#21448016C211yesmaximal, characteristic
3#21447325C211yesmaximal, characteristic
4#21443838C211yesmaximal, characteristic
5#21443837C211yesmaximal, characteristic
6#21443760C211yesmaximal, characteristic
7C61×#2236C211yesmaximal, characteristic
8#16840372—21no—
9#16840071—21no—
10#16840068—21no—
11#16840018—21no—
12#16840003C2211yescharacteristic
13#16839971—21no—
14#16839970—21no—
15#16839802—21no—
16#16839788C2211yescharacteristic
17#16839589—21no—
18#16839565—21no—
19C22⋊#11758185C2211yescharacteristic
20#16839531—21no—
21#16839527C2211yescharacteristic
22C61×#467C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#366—21no—
25C61×#358—21no—
26C61×C22⋊C16C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758202—21no—
29C2×#11758194—21no—
30C2×#11758194D411yescharacteristic
31#14519775—21no—
32#14519770—41no—
33#14519770—41no—
34#14519768—21no—
35#14519768—41no—
36#14519767—41no—
37#14519756—21no—
38Q8×Dic61—21no—
39#14519742—21no—
40#14519736D411yescharacteristic
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519710—41no—
44#14519708—21no—
45#14519708—41no—
46#14519706—21no—
47#14519706—21no—
48#14519702—21no—
49#14519701—21no—
50#14519700—21no—
51C2×Q16×C61D411yescharacteristic
52C22×C8×C61C2311yescharacteristic
53C22⋊Q8×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C16×C61—21no—
56#107×C61—21no—
57#107×C61—21no—
58#107×C61D411yescharacteristic
59#103×C61—21no—
60C2×Q8×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61C2×D411yescharacteristic
63C2×Dic122—21no—
64Q16×C61—41no—
65C2×C8×C61—41no—
66C2×C8×C61C2×D411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C22⋊C4×C61—41no—
73C22⋊Dic61—21no—
74C22⋊Dic61—41no—
75#11758202—81no—
76C4⋊Dic61—21no—
77C4⋊Dic61—41no—
78C4⋊Dic61—41no—
79C4⋊Dic61D811yescharacteristic
80C4⋊Dic61D811yescharacteristic
81#11758196—41no—
82#11758196—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86C4×Dic61—21no—
87C4×Dic61—41no—
88C4×Dic61—41no—
89#11758194—22no—
90#11758194—41no—
91#11758194—41no—
92C2×#92418—21no—
93C2×#92418—41no—
94Dic244—41no—
95C16×C61—41no—
96#11758185—41no—
97C23×C61AGL(1,ℤ/8)11yescharacteristic
98Q8×C61—41no—
99Q8×C61—41no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—81no—
105C2×C4×C61—161no—
106C2×C4×C61#12011yescharacteristic
107C2×C4×C61C2×D811yescharacteristic
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112Dic122—41no—
113Dic122—41no—
114C8×C61—21no—
115C8×C61—21no—
116#92418—42no—
117#92418—41no—
118#12296—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—21no—
122C22×C61#44711yescharacteristic
123C4×C61—21no—
124C4×C61—81no—
125C4×C61—81no—
126C4×C61—161no—
127C4×C61#45611yescharacteristic
128C4×C61#45811yescharacteristic
129Dic61—41no—
130Dic61—41no—
131Dic61—81no—
132Dic61—81no—
133#3261—611no—
134#2236D6111yescharacteristic
135#2235—611no—
136#2089—611no—
137#1350—611no—
138#1350—611no—
139#1323—611no—
140C2×C61—41no—
141C2×C61#161011yescharacteristic
142C2×C61#219311yescharacteristic
143C2×C61#219511yescharacteristic
144#541—1221no—
145#479—1221no—
146#479—1221no—
147#470—1221no—
148#467—611no—
149#467C2×D6111yescharacteristic
150#462—1221no—
151#462—1221no—
152#428—1221no—
153C2×#107C2×D6111yescharacteristic
154#424—611no—
155#367—1221no—
156#366—21no—
157#358—21no—
158#358—1221no—
159C22⋊C16—611no—
160C22⋊C16C2×D6111yescharacteristic
161#343—1221no—
162#341—611no—
163C61#1229611yescharacteristic, complemented, Sylow
164C2×Q16—611no—
165C2×Q16—1221no—
166C2×Q16C22⋊D6111yescharacteristic
167C2×M16—611no—
168C2×M16—1221no—
169C22×C8C22×D6111yescharacteristic
170C4⋊Q8—1221no—
171#126—2441no—
172#126—2441no—
173#125—1221no—
174#125—2441no—
175#125—2441no—
176C22⋊Q8—21no—
177C22⋊Q8—1221no—
178C4×Q8—1221no—
179C4×Q8—1221no—
180#117—611no—
181C2×C4⋊C4—21no—
182C2×C16—21no—
183C2×C16—1221no—
184#107—21no—
185#107—21no—
186#107—611no—
187#107—2441no—
188#107C22⋊D6111yescharacteristic
189#106—1221no—
190#106—2441no—
191C4⋊C8—1221no—
192C4⋊C8—1221no—
193#103—21no—
194#103—1221no—
195#103—1221no—
196#103—1221no—
197C2×Q8—21no—
198C2×Q8—1221no—
199C22×C4—41no—
200C22×C4D4×D6111yescharacteristic
201Q16—41no—
202Q16—4881no—
203Q16—2441no—
204M16—1222no—
205M16—2441no—
206M16—2441no—
207C2×C8—41no—
208C2×C8—1221no—
209C2×C8—2441no—
210C2×C8D4×D6111yescharacteristic
211C2×C8C2×C22⋊D6111yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—611no—
217C4⋊C4—611no—
218C4⋊C4—1221no—
219C4⋊C4—2441no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C22⋊C4—41no—
227C22⋊C4—1221no—
228C22⋊C4—2441no—
229C42—1221no—
230C42—2441no—
231C42—2441no—
232C16—41no—
233C16—2441no—
234C23#1451980111yescharacteristic
235Q8—41no—
236Q8—41no—
237Q8—2441no—
238Q8—2441no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—81no—
244C2×C4—161no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—2441no—
248C2×C4—2441no—
249C2×C4#1451974511yescharacteristic
250C2×C4D8×D6111yescharacteristic
251C8—21no—
252C8—21no—
253C8—2442no—
254C8—2441no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22#1683989411yescharacteristic
259C4—21no—
260C4—81no—
261C4—81no—
262C4—161no—
263C4—4881no—
264C4—4881no—
265C4—2441no—
266C4—2441no—
267C4#1683994311yescharacteristic
268C4#1683995111yescharacteristic
269C2—41no—
270C2#2144482011yescharacteristic
271C2#2144778011yescharacteristic
272C2#2144779611yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2236C2
socleC22×C61#447
prime radicalC23×C61AGL(1,ℤ/8)
hypercenter#2236D61
hypocenterC61#12296
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
163. C61#12296semidirect

Maximal subgroups

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

subgroupindex
#214572682
#214480162
#214473252
#214438382
#214438372
#214437602
C61×#22362
#1229661