Finite Group Databasebeta

← #29593670

Subgroups — #29593670

Order 15616.

302 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 63 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#21458393C211yesmaximal, characteristic, complemented
2#21448061C211yesmaximal, characteristic, complemented
3#21447860C211yesmaximal, characteristic, complemented
4#21445298C211yesmaximal, characteristic
5#21443870C211yesmaximal, characteristic, complemented
6#21443790C211yesmaximal, characteristic, complemented
7C61×#1330C211yesmaximal, characteristic, complemented
8#16840452—21no—
9C2×#14519722—21no—
10#16840164C2211yescharacteristic
11#16840139C2211yescharacteristic
12#16840104—21no—
13#16840098—21no—
14#16840070—21no—
15#16840020—21no—
16#16839957—21no—
17C4×Dic244C2211yescharacteristic
18#16839804—21no—
19#16839564—21no—
20#16839564—21no—
21#16839564—21no—
22#16839513C2211yescharacteristic
23#16839505—21no—
24C61×#436C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#346C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×D488—21no—
29C2×D488—21no—
30C2×#11758199—41no—
31#14519774—21no—
32#14519770—41no—
33#14519769—21no—
34#14519767—41no—
35#14519758—41no—
36#14519756—21no—
37#14519756—21no—
38C4×Dic122—21no—
39#14519736—21no—
40#14519733—41no—
41C2×C4⋊Dic61—21no—
42#14519722—42no—
43#14519711—21no—
44#14519711D411yescharacteristic
45#14519711D411yescharacteristic
46#14519711D411yescharacteristic
47#14519709—21no—
48#14519709—21no—
49C4⋊#92418—21no—
50#14519702—21no—
51#14519702—21no—
52#14519702—21no—
53#14519697—41no—
54C2×M16×C61—21no—
55C4×D4×C61D411yescharacteristic
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C4⋊C8×C61D411yescharacteristic
59C22⋊C8×C61—21no—
60C4×C8×C61C2311yescharacteristic
61C2×D4×C61D811yescharacteristic
62C22×C4×C61—21no—
63C22×Dic61—41no—
64C2×D244—41no—
65C2×D244—41no—
66C2×D244—41no—
67C2×Dic122—21no—
68M16×C61—41no—
69M16×C61—41no—
70C2×C8×C61—21no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61D811yescharacteristic
74C22⋊C4×C61—21no—
75C42×C61C2×D411yescharacteristic
76C22⋊Dic61—41no—
77C22⋊Dic61—41no—
78C22⋊Dic61—41no—
79#11758199—82no—
80C4⋊Dic61—21no—
81C4⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—41no—
90C4×Dic61—41no—
91C2×#92418—41no—
92Dic244—21no—
93Dic244—21no—
94D488—42no—
95D488—41no—
96D488—41no—
97C16×C61—41no—
98C16×C61—41no—
99C23×C61—21no—
100C22×D61—81no—
101D4×C61—41no—
102C2×C4×C61—21no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61#12011yescharacteristic
106C2×C4×C61C2×D811yescharacteristic
107C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—82no—
113D244—81no—
114D244—81no—
115D244—81no—
116D244—81no—
117D244—161no—
118Dic122—41no—
119Dic122—41no—
120C8×C61—21no—
121C8×C61—41no—
122C8×C61#13511yescharacteristic
123C8×C61AGL(1,ℤ/8)11yescharacteristic
124#92418—81no—
125#12349—611nomaximal, Sylow
126C22×C61—41no—
127C22×C61—41no—
128C22×C61—41no—
129C22×C61#44711yescharacteristic
130C2×D61—161no—
131C2×D61—161no—
132C2×D61—161no—
133C4×C61—21no—
134C4×C61—21no—
135C4×C61—41no—
136C4×C61#44911yescharacteristic
137C4×C61#45411yescharacteristic
138Dic61—81no—
139Dic61—81no—
140Dic61—81no—
141Dic61—81no—
142#3352—611no—
143#2244—611no—
144#2207—611no—
145#1687—611no—
146#1363—611no—
147#1334—611no—
148#1330D6111yescharacteristic, complemented
149C2×C61—81no—
150C2×C61#162511yescharacteristic
151C2×C61#219011yescharacteristic
152C2×C61#219311yescharacteristic
153D61—321no—
154#552—1221no—
155C2×SD32—1221no—
156#499—611no—
157#493—611no—
158#485—1221no—
159#484—1221no—
160#479—1221no—
161#470—1221no—
162#459—1221no—
163C4×Q16—611no—
164#436C2×D6111yescharacteristic
165#428—1221no—
166C4⋊C16C2×D6111yescharacteristic
167#357—1221no—
168#357—1221no—
169#357—1221no—
170#346C2×D6111yescharacteristic
171#334—611no—
172#331—1221no—
173C61#1234911yescharacteristic, complemented, Sylow
174C2×Q16—611no—
175C2×D8—1221no—
176C2×D8—1221no—
177C2×D8—2441no—
178C2×M16—21no—
179#127—1221no—
180#126—2441no—
181#125—1221no—
182#125—2441no—
183#123—2441no—
184C22⋊Q8—1221no—
185C22⋊Q8—1221no—
186C4×Q8—1221no—
187C4×D4D24411yescharacteristic
188#117—1221no—
189#117—2441no—
190C2×C4⋊C4—1221no—
191SD32—2442no—
192C2×C16—21no—
193C2×C16—21no—
194#107—611no—
195#107—611no—
196#107—611no—
197#107—1221no—
198#106—1221no—
199#106—1221no—
200C4⋊C8—1221no—
201C4⋊C8D24411yescharacteristic
202#103—1221no—
203#103—1221no—
204#103—1221no—
205#102—2441no—
206C22⋊C8—21no—
207C4×C8C22×D6111yescharacteristic
208C2×Q8—1221no—
209C2×D4—2441no—
210C2×D4—2441no—
211C2×D4—2441no—
212C2×D4D48811yescharacteristic
213C22×C4—21no—
214C22×C4—2441no—
215Q16—1221no—
216Q16—1221no—
217D8—4882no—
218D8—2442no—
219D8—2441no—
220D8—2441no—
221M16—41no—
222M16—41no—
223C2×C8—21no—
224C2×C8—2441no—
225C2×C8D4×D6111yescharacteristic
226C2×C8D4×D6111yescharacteristic
227C4⋊C4—1221no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C4⋊C4—2441no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4D48811yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—2441no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C42—2441no—
242C42—2441no—
243C42C2×D24411yescharacteristic
244C16—41no—
245C16—41no—
246C23—21no—
247C23—4881no—
248Q8—2441no—
249Q8—2441no—
250D4—41no—
251D4—9761no—
252D4—4881no—
253D4—4881no—
254D4—4881no—
255D4—4881no—
256C2×C4—21no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—4882no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4#1451974711yescharacteristic
265C2×C4C2×D48811yescharacteristic
266C2×C4#1451980511yescharacteristic
267C8—21no—
268C8—41no—
269C8—4881no—
270C8#1451979811yescharacteristic
271C8#1451980111yescharacteristic
272C22—41no—
273C22—41no—
274C22—41no—
275C22—9761no—
276C22—9761no—
277C22—9761no—
278C22#1683989811yescharacteristic
279C4—21no—
280C4—21no—
281C4—41no—
282C4—4881no—
283C4—4881no—
284C4—4881no—
285C4—4881no—
286C4#1683990811yescharacteristic
287C4#1683993611yescharacteristic
288C2—81no—
289C2—19521no—
290C2#2144491011yescharacteristic
291C2#2144776711yescharacteristic
292C2#2144778511yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1330C2
socleC22×C61#447
prime radical#21445298C2
hypercenter#1330D61
hypocenterC61#12349
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #436 ◁ #1330

Complements

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

NH ≅ G/Ntype
1. #21458393C2semidirect
2. #21448061C2semidirect
3. #21447860C2semidirect
5. #21443870C2semidirect
6. #21443790C2semidirect
7. C61×#1330C2semidirect
148. #1330D61semidirect
173. C61#12349semidirect

Maximal subgroups

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

subgroupindex
#214583932
#214480612
#214478602
#214452982
#214438702
#214437902
C61×#13302
#1234961