Finite Group Databasebeta

← #29593808

Subgroups — #29593808

Order 15616.

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

normal subgroups only

This group has 350 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#21448046C211yesmaximal, characteristic, complemented
3#21447962C211yesmaximal, characteristic, complemented
4#21445209C211yesmaximal, characteristic
5#21443782C211yesmaximal, characteristic, complemented
6#21443773C211yesmaximal, characteristic
7C61×#1362C211yesmaximal, characteristic, complemented
8C2×Q16×D61—21no—
9#16840427—21no—
10#16840167C2211yescharacteristic
11#16840000—21no—
12#16839969—21no—
13#16839968—21no—
14#16839916—22no—
15C4×Dic244C2211yescharacteristic
16C8×D244C2211yescharacteristic
17#16839590—21no—
18#16839567—21no—
19#16839566—22no—
20C4×#11758185C2211yescharacteristic
21#16839509—21no—
22C61×#494C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Q8×D61—22no—
26C2×Dic244D411yescharacteristic
27C2×#11758202—22no—
28Q16×D61—42no—
29Q16×D61—42no—
30C2×#11758190—41no—
31C2×C8×D61—21no—
32#14519777—21no—
33#14519776—41no—
34#14519755—42no—
35#14519753—22no—
36C4×Dic122—21no—
37C4×D244D411yescharacteristic
38#14519739—41no—
39C2×#11758185—21no—
40#14519711—21no—
41#14519711—21no—
42#14519711D411yescharacteristic
43C4⋊#92418D411yescharacteristic
44#14519702—21no—
45#14519702—41no—
46#14519701—22no—
47#14519689—21no—
48C2×Q16×C61—21no—
49C2×Q16×C61D412yes—
50C4⋊Q8×C61—21no—
51C2×C16×C61—21no—
52C4⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—22no—
55Q8×D61—44no—
56Q8×D61—82no—
57C2×D244D811yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61—42no—
60C2×Dic122—21no—
61C2×Dic122—42no—
62C2×Dic122—41no—
63Q16×C61—42no—
64Q16×C61—41no—
65Q16×C61—41no—
66C2×C8×C61—41no—
67C2×C8×C61C2×D411yescharacteristic
68C2×C8×C61C2×D411yescharacteristic
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C42×C61C2×D411yescharacteristic
72#11758202—44no—
73#11758198—21no—
74#11758198—42no—
75C4⋊Dic61—21no—
76C4⋊Dic61—41no—
77C4⋊Dic61—41no—
78C4⋊Dic61D811yescharacteristic
79#11758196—42no—
80#11758196—41no—
81C4×Dic61—41no—
82C2×#92418—21no—
83Dic244—21no—
84Dic244SD1612yescomplemented
85#11758190—82no—
86C8×D61—41no—
87C8×D61—41no—
88C16×C61—41no—
89#11758185—41no—
90C22×D61—21no—
91Q8×C61—42no—
92Q8×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61#12011yescharacteristic
95C2×C4×C61C2×D811yescharacteristic
96C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
97C2×Dic61—21no—
98C2×Dic61—41no—
99C2×Dic61—41no—
100C2×Dic61—81no—
101D244—21no—
102D244SD3212yes—
103C4×D61—41no—
104C4×D61—41no—
105C4×D61—84no—
106Dic122—22no—
107Dic122—41no—
108Dic122—84no—
109Dic122—81no—
110Dic122—81no—
111C8×C61—21no—
112C8×C61—81no—
113C8×C61C2×SD1611yescharacteristic
114C8×C61AGL(1,ℤ/8)11yescharacteristic
115#92418—41no—
116#12370—611nomaximal, Sylow
117C22×C61#44711yescharacteristic
118C2×D61—22no—
119C2×D61—41no—
120C2×D61—41no—
121C4×C61—21no—
122C4×C61—82no—
123C4×C61#45011yescharacteristic
124C4×C61#45511yescharacteristic
125C4×C61C2×SD3211yescharacteristic
126C4×C61#51011yescharacteristic
127Dic61—42no—
128Dic61—41no—
129Dic61—81no—
130Dic61—161no—
131D4×Q16—611no—
132#2241—611no—
133#2225—611no—
134#1673—611no—
135#1362D6111yescharacteristic, complemented
136#1332—611no—
137D4⋊C16—611no—
138C2×C61#163911yescharacteristic
139C2×C61#218511yescharacteristic
140C2×C61#219511yescharacteristic
141D61—42no—
142C22×Q16—1221no—
143D4×Q8—1221no—
144#500—611no—
145#494C2×D6111yescharacteristic
146#467—1221no—
147#462—1221no—
148#461—1221no—
149#451—1222no—
150C4×Q16—611no—
151C8×D4—611no—
152#367—1221no—
153C4⋊C16C2×D6111yescharacteristic
154#358—1221no—
155#358—1222no—
156C4×C16—611no—
157#335C2×D6111yescharacteristic
158#332—1221no—
159C61#1237011yescharacteristic, complemented, Sylow
160C22×Q8—1222no—
161C2×Q16—21no—
162C2×Q16—611no—
163C2×Q16—1222no—
164C2×Q16—2442no—
165C2×Q16—2442no—
166C2×Q16D24412yes—
167C2×SD16—2441no—
168C22×C8—1221no—
169C4⋊Q8—21no—
170C4⋊Q8—1221no—
171C4⋊Q8—2441no—
172C22⋊Q8—1222no—
173C22⋊Q8—2442no—
174C4×Q8—1221no—
175C4×D4—611no—
176C4×D4—2441no—
177C2×C16—21no—
178C2×C16—1221no—
179#107—611no—
180#107—1221no—
181#107—1221no—
182C4⋊C8—21no—
183C4⋊C8—611no—
184#103—1222no—
185#103—1221no—
186#103—2441no—
187C22⋊C8—1221no—
188C4×C8C22×D6111yescharacteristic
189C2×Q8—22no—
190C2×Q8—1221no—
191C2×Q8—4882no—
192C2×Q8—2442no—
193C2×Q8—2444no—
194C2×Q8—2441no—
195C2×D4—611no—
196C22×C4—1221no—
197C22×C4—2442no—
198Q16—42no—
199Q16—41no—
200Q16—41no—
201Q16—612no—
202Q16—1221no—
203Q16—2444no—
204SD16—4882no—
205C2×C8—41no—
206C2×C8—1221no—
207C2×C8—2441no—
208C2×C8—2441no—
209C2×C8C2×D24411yescharacteristic
210C2×C8D4×D6111yescharacteristic
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—611no—
214C4⋊C4—1221no—
215C4⋊C4—2442no—
216C4⋊C4—2441no—
217C4⋊C4—2441no—
218C4⋊C4—2441no—
219C22⋊C4—1221no—
220C22⋊C4—2442no—
221C42—2441no—
222C42D4×D6111yescharacteristic
223C16—41no—
224C16—2441no—
225C23—1221no—
226Q8—42no—
227Q8—42no—
228Q8—1222no—
229Q8—4884no—
230Q8—4881no—
231Q8—4881no—
232Q8—2441no—
233D4—612no—
234D4—1221no—
235C2×C4—42no—
236C2×C4—1221no—
237C2×C4—4884no—
238C2×C4—4881no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4#1451974711yescharacteristic
244C2×C4D8×D6111yescharacteristic
245C2×C4#1451980411yescharacteristic
246C8—21no—
247C8—81no—
248C8—2441no—
249C8SD16×D6111yescharacteristic
250C8#1451980111yescharacteristic
251C22—1222no—
252C22—2441no—
253C22—2441no—
254C22#1683989711yescharacteristic
255C4—21no—
256C4—82no—
257C4—9761no—
258C4—4881no—
259C4—2441no—
260C4—2442no—
261C4#1683991411yescharacteristic
262C4#1683994211yescharacteristic
263C4SD32×D6111yescharacteristic
264C4#1684020411yescharacteristic
265C2—2442no—
266C2#2144499911yescharacteristic
267C2#2144773711yescharacteristic
268C2#2144780011yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61#447
prime radicalC2×D244D8
hypercenter#1362D61
hypocenterC61#12370
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
2. #21448046C2semidirect
3. #21447962C2semidirect
5. #21443782C2semidirect
7. C61×#1362C2semidirect
84. Dic244SD16semidirect
135. #1362D61semidirect
159. C61#12370semidirect

Maximal subgroups

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

subgroupindex
#214575692
#214480462
#214479622
#214452092
#214437822
#214437732
C61×#13622
#1237061