Finite Group Databasebeta

← #29584095

Subgroups — #29584095

Order 15616.

386 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 79 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#21457136C211yesmaximal, characteristic
2#21444517C211yesmaximal, characteristic, complemented
3#21444512C211yesmaximal, characteristic
4#21444330C211yesmaximal, characteristic, complemented
5#21444326C211yesmaximal, characteristic
6#21443689C211yesmaximal, characteristic, complemented
7C61×#1843C211yesmaximal, characteristic, complemented
8#16840319C2211yescharacteristic
9#16840312C2211yescharacteristic
10#16840053—21no—
11#16840048—21no—
12#16839991—22no—
13#16839968—21no—
14#16839963—21no—
15#16839819C2211yescharacteristic
16#16839819C2211yescharacteristic
17#16839510—21no—
18#16839509—21no—
19#16839507—21no—
20#16839505—21no—
21#16839498—22no—
22#16839495—22no—
23C2×C4⋊C8×C61—22no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#376C2211yescharacteristic
27C2×#11758222—21no—
28C2×#11758190—22no—
29#14519777D411yescharacteristic
30#14519777D411yescharacteristic
31#14519777D411yescharacteristic
32#14519774D411yescharacteristic
33#14519769—21no—
34#14519765—21no—
35#14519756—21no—
36#14519756—21no—
37#14519751—21no—
38#14519751—21no—
39C4×Dic122—21no—
40C4×Dic122—21no—
41C4×D244—21no—
42C4×D244—21no—
43#14519736—21no—
44#14519709—22no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47#14519702—22no—
48#14519699—22no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519688—21no—
52#14519688—21no—
53C22×C8×C61—21no—
54C22×C8×C61D412yes—
55C2×C42×C61—21no—
56C2×C42×C61C2311yescharacteristic
57C4⋊C8×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61—44no—
62#95×C61—21no—
63#95×C61D412yes—
64C22×C4×C61—22no—
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61#4111yescharacteristic
68C2×C22⋊D61—41no—
69#11758222—82no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244—21no—
73C2×C4×D61—41no—
74C2×Dic122—21no—
75C2×Dic122—21no—
76C2×Dic122—21no—
77C2×C8×C61—22no—
78C2×C8×C61—42no—
79C2×C8×C61—42no—
80C2×C8×C61—41no—
81C42×C61—22no—
82C42×C61—22no—
83C42×C61C2×D411yescharacteristic
84C42×C61C2×D411yescharacteristic
85C42×C61#4111yescharacteristic
86C42×C61#4111yescharacteristic
87C22⋊Dic61—41no—
88#11758198—41no—
89#11758198—41no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—41no—
99C2×#92418—41no—
100C2×#92418—41no—
101#11758190—82no—
102C23×C61#12111yescharacteristic
103C22×D61—41no—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—24no—
108C2×C4×C61—41no—
109C2×C4×C61—42no—
110C2×C4×C61—42no—
111C2×C4×C61#12011yescharacteristic
112C2×C4×C61#12111yescharacteristic
113C2×C4×C61#12111yescharacteristic
114C2×C4×C61#12311yescharacteristic
115C2×C4×C61#12311yescharacteristic
116C2×C4×C61#12411yescharacteristic
117C22⋊D61—82no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121D244—41no—
122D244—41no—
123D244—81no—
124D244—81no—
125C4×D61—82no—
126Dic122—41no—
127Dic122—41no—
128Dic122—81no—
129Dic122—81no—
130C8×C61—42no—
131C8×C61—81no—
132#92418—81no—
133#92418—81no—
134#10514—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61#39411yescharacteristic
138C22×C61#47112yes—
139C2×D61—81no—
140C2×D61—81no—
141C2×D61—81no—
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—44no—
148C4×C61#45311yescharacteristic
149C4×C61#45611yescharacteristic
150Dic61—81no—
151Dic61—81no—
152Dic61—81no—
153#3246—611no—
154#1843D6111yescharacteristic, complemented
155#1552—611no—
156#1551—611no—
157#1506—611no—
158#1505—611no—
159#1290—611no—
160C2×C61—22no—
161C2×C61#203911yescharacteristic
162C2×C61#204611yescharacteristic
163C2×C61#205311yescharacteristic
164D61—161no—
165#533—611no—
166#532—611no—
167#476—1221no—
168#475—1221no—
169#465—1222no—
170#461—1221no—
171#460—1221no—
172#432—611no—
173#432—611no—
174C2×C4⋊C8—22no—
175C2×C4⋊C8C2×D6111yescharacteristic
176C2×C4⋊C8C2×D6111yescharacteristic
177#376C2×D6111yescharacteristic
178#333—1221no—
179#332—1221no—
180#332—1221no—
181#331—1221no—
182#328—1222no—
183#327—1222no—
184C61#1051411yescharacteristic, complemented, Sylow
185C2×#41—1221no—
186C2×SD16—1222no—
187C22×C8—21no—
188C22×C8C22⋊D6112yes—
189C4⋊Q8—611no—
190C4⋊Q8—611no—
191C4⋊Q8—611no—
192#127—611no—
193#125—1221no—
194#124—1221no—
195C22⋊Q8—1221no—
196C22⋊Q8—1221no—
197#121—1221no—
198#121—1221no—
199C4×Q8—1221no—
200C4×Q8—1221no—
201C4×D4—1221no—
202C4×D4—1221no—
203#117—1221no—
204C2×C42—21no—
205C2×C42C22×D6111yescharacteristic
206#106—1222no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—44no—
212C4⋊C8—1221no—
213C4⋊C8—1221no—
214#103—1222no—
215#102—1222no—
216C22⋊C8—1221no—
217C22⋊C8—1221no—
218#97—1221no—
219#97—1221no—
220#95—21no—
221#95D24412yes—
222#41—4882no—
223C2×Q8—1221no—
224C2×Q8—1221no—
225C2×Q8—1221no—
226C2×D4—1221no—
227C2×D4—1221no—
228C2×D4—1221no—
229C2×D4—2441no—
230C22×C4—22no—
231C22×C4—2441no—
232C22×C4C2×D24411yescharacteristic
233C22×C4#1175822211yescharacteristic
234C22×C4C2×C22⋊D6111yescharacteristic
235SD16—4882no—
236C2×C8—22no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—41no—
240C2×C8—2441no—
241C2×C8—2441no—
242C4⋊C4—1221no—
243C4⋊C4—1221no—
244C4⋊C4—1221no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—2441no—
249C4⋊C4—2441no—
250C22⋊C4—2441no—
251C22⋊C4—2441no—
252C22⋊C4—2441no—
253C42—22no—
254C42—22no—
255C42—2441no—
256C42D4×D6111yescharacteristic
257C42D4×D6111yescharacteristic
258C42#1175822611yescharacteristic
259C42#1175822611yescharacteristic
260C23—2441no—
261C23#1451975111yescharacteristic
262Q8—4881no—
263Q8—4881no—
264Q8—2441no—
265Q8—2441no—
266D4—4881no—
267D4—4881no—
268D4—4882no—
269D4—2441no—
270D4—2441no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—4882no—
279C2×C4—2441no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4#1451974511yescharacteristic
283C2×C4#1451975211yescharacteristic
284C2×C4#1451975211yescharacteristic
285C2×C4#1451976211yescharacteristic
286C2×C4#1451976211yescharacteristic
287C2×C4#1451976611yescharacteristic
288C8—42no—
289C8—81no—
290C8—4881no—
291C8—4881no—
292C22—21no—
293C22—21no—
294C22—4881no—
295C22—4881no—
296C22—4881no—
297C22#1683967911yescharacteristic
298C22#1684002512yes—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—44no—
305C4—4881no—
306C4—4881no—
307C4—4881no—
308C4#1683992911yescharacteristic
309C4#1683994411yescharacteristic
310C2—22no—
311C2—9761no—
312C2#2144704311yescharacteristic
313C2#2144708211yescharacteristic
314C2#2144712511yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1843C2
socleC22×C61#394
prime radical#16840312C22
hypercenter#1843D61
hypocenterC61#10514
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1843

Complements

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

NH ≅ G/Ntype
2. #21444517C2semidirect
4. #21444330C2semidirect
6. #21443689C2semidirect
7. C61×#1843C2semidirect
154. #1843D61semidirect
184. C61#10514semidirect

Maximal subgroups

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

subgroupindex
#214571362
#214445172
#214445122
#214443302
#214443262
#214436892
C61×#18432
#1051461