Finite Group Databasebeta

← #29593832

Subgroups — #29593832

Order 15616.

344 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 69 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#21457569C211yesmaximal, characteristic
2#21447968C211yesmaximal, characteristic, complemented
3#21445215C211yesmaximal, characteristic
4#21443868C211yesmaximal, characteristic, complemented
5#21443784C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic
7C61×#2241C211yesmaximal, characteristic, complemented
8C2×Q16×D61—21no—
9#16840427—21no—
10#16840049—21no—
11#16840000—21no—
12#16839969—21no—
13#16839916—22no—
14C4×Dic244C2211yescharacteristic
15C8×D244C2211yescharacteristic
16#16839587—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839565—21no—
19#16839515C2211yescharacteristic
20#16839511—21no—
21C61×#500C2211yescharacteristic
22C61×#494C2211yescharacteristic
23C61×#358—22no—
24C4×C16×C61C2211yescharacteristic
25C2×Q8×D61—22no—
26C2×Dic244D411yescharacteristic
27C2×#11758202—22no—
28Q16×D61—42no—
29Q16×D61—42no—
30C2×C8×D61—21no—
31#14519776—41no—
32#14519755—42no—
33#14519753—22no—
34C4×Dic122—21no—
35C4×D244D411yescharacteristic
36#14519739—41no—
37C2×#11758185—21no—
38#14519711D411yescharacteristic
39#14519708—41no—
40C4⋊#92418—21no—
41C4⋊#92418D411yescharacteristic
42#14519702—21no—
43#14519701—22no—
44#14519697—41no—
45#14519689—21no—
46C2×Q16×C61—21no—
47C2×Q16×C61D412yes—
48C4⋊Q8×C61—21no—
49C4⋊Q8×C61—21no—
50C2×C16×C61—21no—
51#107×C61—21no—
52#107×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—22no—
55C2×Q8×C61—41no—
56Q8×D61—44no—
57Q8×D61—82no—
58C2×D244D811yescharacteristic
59C2×C4×D61—21no—
60C2×C4×D61—42no—
61C2×Dic122—21no—
62C2×Dic122—42no—
63Q16×C61—42no—
64Q16×C61—41no—
65Q16×C61—41no—
66C2×C8×C61C2×D411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C42×C61C2×D411yescharacteristic
73#11758202—44no—
74#11758198—21no—
75#11758198—42no—
76C4⋊Dic61—21no—
77C4⋊Dic61D811yescharacteristic
78#11758196—42no—
79#11758196—41no—
80C4×Dic61—41no—
81C2×#92418—21no—
82C2×#92418—41no—
83Dic244—21no—
84Dic244SD1612yes—
85C8×D61—41no—
86C8×D61—41no—
87C16×C61—41no—
88#11758185—41no—
89C22×D61—21no—
90Q8×C61—42no—
91Q8×C61—42no—
92Q8×C61—161no—
93C2×C4×C61—42no—
94C2×C4×C61—81no—
95C2×C4×C61#12011yescharacteristic
96C2×C4×C61C2×D811yescharacteristic
97C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101D244—21no—
102D244Q3212yes—
103C4×D61—41no—
104C4×D61—41no—
105C4×D61—84no—
106Dic122—22no—
107Dic122—41no—
108Dic122—84no—
109C8×C61—21no—
110C8×C61C2×SD1611yescharacteristic
111C8×C61AGL(1,ℤ/8)11yescharacteristic
112#92418—41no—
113#92418—81no—
114#12374—611nomaximal, Sylow
115C22×C61#44711yescharacteristic
116C2×D61—22no—
117C2×D61—41no—
118C2×D61—41no—
119C4×C61—21no—
120C4×C61—82no—
121C4×C61—161no—
122C4×C61#45011yescharacteristic
123C4×C61#45511yescharacteristic
124C4×C61C2×Q3211yescharacteristic
125C4×C61#51011yescharacteristic
126Dic61—42no—
127Dic61—41no—
128Dic61—81no—
129D4×Q16—611no—
130#2241D6111yescharacteristic, complemented
131#2227—611no—
132#1675—611no—
133#1362—611no—
134#1332—611no—
135D4⋊C16—611no—
136C2×C61#163911yescharacteristic
137C2×C61#218811yescharacteristic
138C2×C61#219311yescharacteristic
139D61—42no—
140C22×Q16—1221no—
141D4×Q8—1221no—
142#500C2×D6111yescharacteristic
143#494C2×D6111yescharacteristic
144#476—1221no—
145#467—1221no—
146#462—1221no—
147#451—1222no—
148C4×Q16—611no—
149C8×D4—611no—
150#366—1221no—
151C4⋊C16—611no—
152#358—22no—
153#358—1221no—
154C4×C16C2×D6111yescharacteristic
155#335—611no—
156#333—1221no—
157C61#1237411yescharacteristic, complemented, Sylow
158C22×Q8—1222no—
159C2×Q16—21no—
160C2×Q16—611no—
161C2×Q16—1222no—
162C2×Q16—2442no—
163C2×Q16—2442no—
164C2×Q16C22⋊D6112yes—
165C22×C8—1221no—
166C4⋊Q8—21no—
167C4⋊Q8—21no—
168C4⋊Q8—2441no—
169C22⋊Q8—1222no—
170C22⋊Q8—2442no—
171C4×Q8—1221no—
172C4×D4—611no—
173C4×D4—2441no—
174C2×C16—21no—
175C2×C16—1221no—
176#107—21no—
177#107—21no—
178#107—611no—
179#106—2441no—
180C4⋊C8—611no—
181C4⋊C8—1221no—
182#103—1222no—
183#103—1221no—
184#102—2441no—
185C22⋊C8—1221no—
186C4×C8C22×D6111yescharacteristic
187C2×Q8—22no—
188C2×Q8—41no—
189C2×Q8—1221no—
190C2×Q8—4882no—
191C2×Q8—2442no—
192C2×Q8—2444no—
193C2×D4—611no—
194C22×C4—1221no—
195C22×C4—2442no—
196Q16—42no—
197Q16—41no—
198Q16—41no—
199Q16—612no—
200Q16—1221no—
201Q16—2444no—
202C2×C8—1221no—
203C2×C8—2441no—
204C2×C8—2441no—
205C2×C8—2441no—
206C2×C8D4×D6111yescharacteristic
207C2×C8C2×C22⋊D6111yescharacteristic
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—611no—
213C4⋊C4—1221no—
214C4⋊C4—2442no—
215C4⋊C4—2441no—
216C22⋊C4—1221no—
217C22⋊C4—2442no—
218C42—2441no—
219C42D4×D6111yescharacteristic
220C16—41no—
221C16—2441no—
222C23—1221no—
223Q8—42no—
224Q8—42no—
225Q8—161no—
226Q8—1222no—
227Q8—4884no—
228Q8—2441no—
229D4—612no—
230D4—1221no—
231C2×C4—42no—
232C2×C4—81no—
233C2×C4—1221no—
234C2×C4—4884no—
235C2×C4—2441no—
236C2×C4—2441no—
237C2×C4—2441no—
238C2×C4—2441no—
239C2×C4#1451974511yescharacteristic
240C2×C4D8×D6111yescharacteristic
241C2×C4#1451980111yescharacteristic
242C8—21no—
243C8—4881no—
244C8—2441no—
245C8SD16×D6111yescharacteristic
246C8#1451980411yescharacteristic
247C22—1222no—
248C22—2441no—
249C22—2441no—
250C22#1683989411yescharacteristic
251C4—21no—
252C4—82no—
253C4—161no—
254C4—4881no—
255C4—2441no—
256C4—2442no—
257C4#1683991111yescharacteristic
258C4#1683993911yescharacteristic
259C4Q32×D6111yescharacteristic
260C4#1684020411yescharacteristic
261C2—2442no—
262C2#2144499511yescharacteristic
263C2#2144775111yescharacteristic
264C2#2144778211yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2241C2
socleC22×C61#447
prime radicalC2×D244D8
hypercenter#2241D61
hypocenterC61#12374
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
2. #21447968C2semidirect
4. #21443868C2semidirect
5. #21443784C2semidirect
7. C61×#2241C2semidirect
130. #2241D61semidirect
157. C61#12374semidirect

Maximal subgroups

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

subgroupindex
#214575692
#214479682
#214452152
#214438682
#214437842
#214437752
C61×#22412
#1237461