Finite Group Databasebeta

← #29593315

Subgroups — #29593315

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#21457274C211yesmaximal, characteristic
2#21448016C211yesmaximal, characteristic, complemented
3#21447325C211yesmaximal, characteristic, complemented
4#21443838C211yesmaximal, characteristic, complemented
5#21443834C211yesmaximal, characteristic
6#21443760C211yesmaximal, characteristic, complemented
7C61×#2233C211yesmaximal, characteristic
8#16840379—21no—
9#16840056—21no—
10#16840040—21no—
11#16840006—21no—
12#16840003C2211yescharacteristic
13#16839983—21no—
14#16839975—21no—
15#16839802—21no—
16#16839788C2211yescharacteristic
17#16839589—21no—
18#16839565—21no—
19C22⋊#11758185C2211yescharacteristic
20#16839531—21no—
21#16839527C2211yescharacteristic
22C61×#466C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#367—21no—
25C61×#357—21no—
26C61×C22⋊C16C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758200—21no—
29C2×#11758194—21no—
30C2×#11758194D411yescharacteristic
31#14519776—21no—
32#14519770—41no—
33#14519764—21no—
34#14519764—41no—
35#14519758—41no—
36#14519756—21no—
37#14519754—41no—
38#14519742—21no—
39D4×Dic61—21no—
40#14519736D411yescharacteristic
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519710—21no—
44#14519710—41no—
45#14519708—41no—
46#14519706—21no—
47#14519706—21no—
48#14519702—21no—
49#14519700—21no—
50#14519698—21no—
51C2×D8×C61D411yescharacteristic
52C22×C8×C61C2311yescharacteristic
53#121×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C16×C61—21no—
56#107×C61—21no—
57#107×C61—21no—
58#107×C61D411yescharacteristic
59#102×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—41no—
65C2×Dic122—21no—
66C2×Dic122—41no—
67D8×C61—41no—
68C2×C8×C61—41no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C22⋊C4×C61—41no—
75C22⋊Dic61—21no—
76C22⋊Dic61—41no—
77C22⋊Dic61—41no—
78C22⋊Dic61—41no—
79C22⋊Dic61—41no—
80#11758200—81no—
81C4⋊Dic61—21no—
82C4⋊Dic61D811yescharacteristic
83C4⋊Dic61D811yescharacteristic
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87C4×Dic61—21no—
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×C61—41no—
98C23×C61AGL(1,ℤ/8)11yescharacteristic
99D4×C61—41no—
100D4×C61—41no—
101D4×C61—161no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—41no—
105C2×C4×C61—81no—
106C2×C4×C61—161no—
107C2×C4×C61#12011yescharacteristic
108C2×C4×C61C2×D811yescharacteristic
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—161no—
114Dic122—41no—
115Dic122—41no—
116Dic122—161no—
117C8×C61—21no—
118C8×C61—21no—
119#92418—42no—
120#92418—41no—
121#12295—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—21no—
125C22×C61—81no—
126C22×C61—81no—
127C22×C61—81no—
128C22×C61#44711yescharacteristic
129C4×C61—21no—
130C4×C61—81no—
131C4×C61—161no—
132C4×C61#45611yescharacteristic
133C4×C61#45811yescharacteristic
134Dic61—41no—
135Dic61—41no—
136Dic61—81no—
137Dic61—81no—
138#3262—611no—
139#2235—611no—
140#2233D6111yescharacteristic
141#2089—611no—
142#1350—611no—
143#1349—611no—
144#1323—611no—
145C2×C61—41no—
146C2×C61—161no—
147C2×C61#161011yescharacteristic
148C2×C61#219311yescharacteristic
149C2×C61#219411yescharacteristic
150#542—1221no—
151#477—1221no—
152#474—1221no—
153#468—1221no—
154#467—611no—
155#466C2×D6111yescharacteristic
156#464—1221no—
157#463—1221no—
158#428—1221no—
159C2×#107C2×D6111yescharacteristic
160#424—611no—
161#367—21no—
162#367—1221no—
163#358—1221no—
164#357—21no—
165C22⋊C16—611no—
166C22⋊C16C2×D6111yescharacteristic
167#343—1221no—
168#341—611no—
169C61#1229511yescharacteristic, complemented, Sylow
170C2×Q16—611no—
171C2×SD16—1221no—
172C2×D8C22⋊D6111yescharacteristic
173C2×M16—611no—
174C2×M16—1221no—
175C22×C8C22×D6111yescharacteristic
176C4⋊Q8—1221no—
177#126—2441no—
178#124—1221no—
179#124—2441no—
180#123—2441no—
181C22⋊Q8—1221no—
182C22⋊Q8—2441no—
183#121—21no—
184C4×Q8—1221no—
185C4×D4—1221no—
186#117—611no—
187C2×C4⋊C4—21no—
188C2×C16—21no—
189C2×C16—1221no—
190#107—21no—
191#107—21no—
192#107—611no—
193#107—1221no—
194#107—2441no—
195#107C22⋊D6111yescharacteristic
196#106—2441no—
197C4⋊C8—1221no—
198C4⋊C8—1221no—
199#103—1221no—
200#103—1221no—
201#102—21no—
202#102—1221no—
203C2×Q8—1221no—
204C2×Q8—2441no—
205C2×D4—21no—
206C2×D4—41no—
207C22×C4—41no—
208C22×C4—2441no—
209C22×C4D4×D6111yescharacteristic
210Q16—2441no—
211SD16—4881no—
212D8—41no—
213M16—1222no—
214M16—2441no—
215M16—2441no—
216C2×C8—41no—
217C2×C8—1221no—
218C2×C8—2441no—
219C2×C8D4×D6111yescharacteristic
220C2×C8C2×C22⋊D6111yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—611no—
225C4⋊C4—611no—
226C4⋊C4—1221no—
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—41no—
241C23#1451980111yescharacteristic
242Q8—9761no—
243Q8—2441no—
244Q8—2441no—
245D4—41no—
246D4—41no—
247D4—161no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—81no—
252C2×C4—161no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—9761no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4#1451974511yescharacteristic
259C2×C4D8×D6111yescharacteristic
260C8—21no—
261C8—21no—
262C8—2442no—
263C8—2441no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—81no—
268C22—81no—
269C22—81no—
270C22#1683989411yescharacteristic
271C4—21no—
272C4—81no—
273C4—161no—
274C4—4881no—
275C4—4881no—
276C4—2441no—
277C4—2441no—
278C4#1683994311yescharacteristic
279C4#1683995111yescharacteristic
280C2—41no—
281C2—161no—
282C2#2144482011yescharacteristic
283C2#2144778011yescharacteristic
284C2#2144778911yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2233C2
socleC22×C61#447
prime radicalC61×#466C22
hypercenter#2233D61
hypocenterC61#12295
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
2. #21448016C2semidirect
3. #21447325C2semidirect
4. #21443838C2semidirect
6. #21443760C2semidirect
169. C61#12295semidirect

Maximal subgroups

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

subgroupindex
#214572742
#214480162
#214473252
#214438382
#214438342
#214437602
C61×#22332
#1229561