Finite Group Databasebeta

← #29597775

Subgroups — #29597775

Order 15616.

324 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21447577C211yesmaximal, characteristic, complemented
2C2×#16839545C211yesmaximal, characteristic
3#21447432C211yesmaximal, characteristic
4#21445656C211yesmaximal, characteristic
5#21443907C211yesmaximal, characteristic, complemented
6#21443901C211yesmaximal, characteristic, complemented
7C2×C61×#346C211yesmaximal, characteristic, complemented
8C2×#14519783C2211yescharacteristic
9C2×#14519717C2211yescharacteristic
10C2×#14519717C2211yescharacteristic
11C2×#14519705C411yescharacteristic
12#16839759C411yescharacteristic
13#16839717C2211yescharacteristic
14#16839580—22no—
15#16839545—22no—
16#16839541—22no—
17#16839527C411yescharacteristic
18#16839522C411yescharacteristic
19C22×C16×C61C2211yescharacteristic
20C22×C16×C61C2211yescharacteristic
21C2×C4×C8×C61C2211yescharacteristic
22C61×#346—22no—
23C2×#11758222C2×C411yescharacteristic
24#14519783—21no—
25#14519783—21no—
26#14519783—21no—
27#14519783—21no—
28C2×#11758194C2×C411yescharacteristic
29C2×#11758194C2×C411yescharacteristic
30C2×#11758189—21no—
31C2×C8×D61—21no—
32#14519736C2×C411yescharacteristic
33#14519717—21no—
34#14519717—21no—
35#14519717—21no—
36#14519717—21no—
37C2×#11758185—21no—
38C2×#11758185—21no—
39#14519705—22no—
40#14519702C812yes—
41#14519699C812yes—
42#14519687—21no—
43C8×Dic61—21no—
44C22×C8×C61C2×C411yescharacteristic
45C22×C8×C61C2311yescharacteristic
46C2×C42×C61C2×C411yescharacteristic
47C2×C16×C61—21no—
48C2×C16×C61—21no—
49C2×C16×C61—21no—
50C2×C16×C61—21no—
51C2×C16×C61D412yes—
52C2×C16×C61D412yes—
53C4×C8×C61—21no—
54C4×C8×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61C22×C411yescharacteristic
57C2×C22⋊D61—21no—
58#11758222—21no—
59#11758222—21no—
60#11758222—21no—
61#11758222—21no—
62C2×D244C2×C811yescharacteristic
63C2×C4×D61—21no—
64C2×Dic122C2×C811yescharacteristic
65C2×C8×C61—21no—
66C2×C8×C61—21no—
67C2×C8×C61C2×C812yes—
68C2×C8×C61C2×D411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61#4111yescharacteristic
71C2×C8×C61#4111yescharacteristic
72C2×C8×C61#4111yescharacteristic
73C2×C8×C61#4111yescharacteristic
74C42×C61—21no—
75C42×C61M1612yes—
76C22⋊Dic61—21no—
77C4⋊Dic61C2×C812yes—
78C4×Dic61—21no—
79#11758194—21no—
80#11758194—21no—
81#11758194—21no—
82#11758194—21no—
83C2×#92418—21no—
84C2×#92418—21no—
85#11758189—41no—
86#11758189—41no—
87C8×D61—41no—
88C8×D61—41no—
89C16×C61—22no—
90C16×C61—22no—
91#11758185—41no—
92#11758185—41no—
93C23×C61#13111yescharacteristic
94C22×D61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—42no—
97C2×C4×C61#11711yescharacteristic
98C2×C4×C61C4×D411yescharacteristic
99C2×C4×C61C4×D411yescharacteristic
100C2×C4×C61C22×C811yescharacteristic
101C2×C4×C61C2×M1611yescharacteristic
102C2×C4×C61#13111yescharacteristic
103C22⋊D61—41no—
104C22⋊D61—41no—
105C2×Dic61—22no—
106C2×Dic61—21no—
107D244—21no—
108D244—21no—
109C4×D61—41no—
110C4×D61—41no—
111Dic122—21no—
112Dic122—21no—
113C8×C61—22no—
114C8×C61#12111yescharacteristic
115C8×C61#12311yescharacteristic
116C8×C61#12411yescharacteristic
117C8×C61#12611yescharacteristic
118#92418—41no—
119#92418—41no—
120#13125—611nomaximal, Sylow
121C22×C61—22no—
122C22×C61#43311yescharacteristic
123C22×C61C8×D411yescharacteristic
124C22×C61#43511yescharacteristic
125C2×D61—42no—
126C2×D61—41no—
127C4×C61—42no—
128C4×C61#38811yescharacteristic
129C4×C61#43111yescharacteristic
130C4×C61C8×D411yescharacteristic
131C4×C61#43611yescharacteristic
132Dic61—42no—
133Dic61—41no—
134#2151—611no—
135C2×#350—611no—
136#2113—611no—
137C2×#346D6111yescharacteristic, complemented
138#1764—611no—
139#1379—611no—
140#1376—611no—
141C2×C61—21no—
142C2×C61—21no—
143C2×C61#192311yescharacteristic
144C2×C61#217112yes—
145D61—81no—
146C2×#131—611no—
147C2×M32—611no—
148C2×M32—611no—
149C22×C16C2×D6111yescharacteristic
150C22×C16C2×D6111yescharacteristic
151C2×#104—611no—
152#416—611no—
153#405—611no—
154C2×C4×C8C2×D6111yescharacteristic
155C4⋊C16—1222no—
156#350—1222no—
157C22⋊C16—1222no—
158#346—22no—
159#341—611no—
160#339—611no—
161C61#1312511yescharacteristic, complemented, Sylow
162C2×#41—611no—
163#131—1221no—
164#131—1221no—
165#131—1221no—
166#131—1221no—
167C2×M16—611no—
168C2×M16—611no—
169C2×M16—1221no—
170C22×C8—1221no—
171C22×C8C4×D6111yescharacteristic
172C22×C8C22×D6111yescharacteristic
173#117—611no—
174C2×C42C4×D6111yescharacteristic
175M32—1221no—
176M32—1221no—
177M32—1221no—
178M32—1221no—
179C2×C16—21no—
180C2×C16—21no—
181C2×C16—21no—
182C2×C16—21no—
183C2×C16—1221no—
184C2×C16—1221no—
185C2×C16D24412yes—
186C2×C16C22⋊D6112yes—
187#104—1222no—
188#103—612no—
189#102—612no—
190#97—1221no—
191C4×C8—21no—
192C4×C8—21no—
193C4×C8—1221no—
194#41—1221no—
195#41—1221no—
196#41—1221no—
197#41—1221no—
198C2×Q8—611no—
199C2×D4—611no—
200C2×D4—1221no—
201C22×C4—21no—
202C22×C4—1221no—
203C22×C4C2×C4×D6111yescharacteristic
204M16—1221no—
205M16—1221no—
206M16—1221no—
207M16—1221no—
208M16—2441no—
209M16—2441no—
210C2×C8—21no—
211C2×C8—21no—
212C2×C8—1221no—
213C2×C8—1221no—
214C2×C8—2441no—
215C2×C8—2441no—
216C2×C8C8×D6112yes—
217C2×C8C2×D24411yescharacteristic
218C2×C8#1175822211yescharacteristic
219C2×C8#1175822211yescharacteristic
220C2×C8#1175822211yescharacteristic
221C2×C8#1175822211yescharacteristic
222C2×C8C2×C22⋊D6111yescharacteristic
223C4⋊C4—612no—
224C22⋊C4—1221no—
225C42—21no—
226C42—1221no—
227C42#1175818912yes—
228C16—22no—
229C16—22no—
230C16—2441no—
231C16—2441no—
232C23—1221no—
233C23#1451978311yescharacteristic
234Q8—1221no—
235Q8—1221no—
236D4—1221no—
237D4—1221no—
238D4—2441no—
239D4—2441no—
240C2×C4—22no—
241C2×C4—42no—
242C2×C4—1222no—
243C2×C4—1221no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4#1451973411yescharacteristic
247C2×C4C4×C22⋊D6111yescharacteristic
248C2×C4C4×D24411yescharacteristic
249C2×C4C2×C8×D6111yescharacteristic
250C2×C4C2×#1175818911yescharacteristic
251C2×C4#1451978311yescharacteristic
252C8—22no—
253C8—2441no—
254C8—2441no—
255C8#1451975111yescharacteristic
256C8#1451976011yescharacteristic
257C8#1451976511yescharacteristic
258C8#1451977111yescharacteristic
259C22—22no—
260C22—2441no—
261C22—2442no—
262C22#1683982111yescharacteristic
263C22C8×D24411yescharacteristic
264C22#1683983311yescharacteristic
265C4—42no—
266C4—2441no—
267C4—2442no—
268C4#1683965311yescharacteristic
269C4#1683981311yescharacteristic
270C4C8×C22⋊D6111yescharacteristic
271C4#1683984111yescharacteristic
272C2—21no—
273C2—21no—
274C2—4881no—
275C2#2144642511yescharacteristic
276C2#2144766212yes—
subgroupG/H
centerC2×C8C2×D244
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC2×C61×#346C2
socleC22×C61C8×D4
prime radicalC2×#11758222C2×C4
cosocleC22×C8×C61C23
hypercenterC2×#346D61
hypocenterC61#13125
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ C2×#346

Complements

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

NH ≅ G/Ntype
1. #21447577C2semidirect
5. #21443907C2semidirect
6. #21443901C2semidirect
7. C2×C61×#346C2semidirect
137. C2×#346D61semidirect
161. C61#13125semidirect

Maximal subgroups

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

subgroupindex
#214475772
C2×#168395452
#214474322
#214456562
#214439072
#214439012
C2×C61×#3462
#1312561