Finite Group Databasebeta

← #29593296

Subgroups — #29593296

Order 15616.

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

normal subgroups only

This group has 310 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#21457160C211yesmaximal, characteristic
2#21448021C211yesmaximal, characteristic
3#21447313C211yesmaximal, characteristic
4#21443832C211yesmaximal, characteristic
5#21443831C211yesmaximal, characteristic
6#21443758C211yesmaximal, characteristic
7C61×#2236C211yesmaximal, characteristic
8#16840314—21no—
9#16840056—21no—
10#16840055—21no—
11#16840003C2211yescharacteristic
12#16840001—21no—
13#16839971—21no—
14#16839970—21no—
15C2×#14519706C2211yescharacteristic
16#16839658—21no—
17#16839587—21no—
18#16839565—21no—
19C22⋊#11758185C2211yescharacteristic
20#16839525C2211yescharacteristic
21#16839524—21no—
22C61×#467C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#366—21no—
25C61×#358—21no—
26C61×C22⋊C16C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758202—21no—
29C22×#92418D411yescharacteristic
30#14519776—21no—
31#14519775—21no—
32#14519767—41no—
33#14519756—21no—
34#14519754—41no—
35Q8×Dic61—21no—
36#14519742—21no—
37#14519742—41no—
38#14519733—41no—
39C2×C4⋊Dic61—21no—
40C2×#11758196—41no—
41C2×C4×Dic61D411yescharacteristic
42C2×#11758185—21no—
43#14519711D411yescharacteristic
44#14519710—21no—
45#14519706—21no—
46#14519706—21no—
47#14519702—21no—
48#14519701—21no—
49#14519700—21no—
50#14519684—41no—
51C2×Q16×C61D411yescharacteristic
52C22×C8×C61C2311yescharacteristic
53C22⋊Q8×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C16×C61—21no—
56#107×C61—21no—
57#107×C61—21no—
58#107×C61D411yescharacteristic
59#103×C61—21no—
60C2×Q8×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—41no—
64C22×Dic61D811yescharacteristic
65C22×Dic61D811yescharacteristic
66C2×Dic122—21no—
67C2×Dic122—41no—
68Q16×C61—41no—
69C2×C8×C61—41no—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C4⋊C4×C61—21no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C22⋊Dic61—41no—
78#11758202—81no—
79C4⋊Dic61—22no—
80C4⋊Dic61—21no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83#11758196—41no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—82no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—41no—
92C4×Dic61—41no—
93C2×#92418—21no—
94C2×#92418—41no—
95Dic244—41no—
96C16×C61—41no—
97#11758185—41no—
98C23×C61C2×D811yescharacteristic
99Q8×C61—41no—
100Q8×C61—41no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—81no—
106C2×C4×C61—81no—
107C2×C4×C61—81no—
108C2×C4×C61#12011yescharacteristic
109C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—41no—
114C2×Dic61—42no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—81no—
118C2×Dic61—81no—
119C2×Dic61Q3212yes—
120Dic122—41no—
121Dic122—41no—
122Dic122—82no—
123C8×C61—21no—
124C8×C61—21no—
125#92418—41no—
126#12292—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—21no—
129C22×C61#44711yescharacteristic
130C22×C61C2×Q3211yescharacteristic
131C22×C61#51011yescharacteristic
132C4×C61—21no—
133C4×C61—81no—
134C4×C61—81no—
135C4×C61—161no—
136C4×C61#45611yescharacteristic
137C4×C61#45811yescharacteristic
138Dic61—22no—
139Dic61—41no—
140Dic61—82no—
141Dic61—81no—
142Dic61—81no—
143#3249—611no—
144#2236—611no—
145#2236D6111yescharacteristic
146#2087—611no—
147#1348—611no—
148#1348—611no—
149#1322—611no—
150C2×C61—21no—
151C2×C61—21no—
152C2×C61#161011yescharacteristic
153C2×C61#218811yescharacteristic
154C2×C61#219011yescharacteristic
155#533—1221no—
156#477—1221no—
157#477—1221no—
158#467—611no—
159#467—1221no—
160#467C2×D6111yescharacteristic
161#462—1221no—
162#462—1221no—
163C2×#107C2×D6111yescharacteristic
164C2×C4⋊C8—611no—
165#389—1221no—
166#366—21no—
167#366—1221no—
168#358—21no—
169#358—1221no—
170C22⋊C16—611no—
171C22⋊C16C2×D6111yescharacteristic
172#340—611no—
173#340—1221no—
174C61#1229211yescharacteristic, complemented, Sylow
175C2×Q16—611no—
176C2×Q16—1221no—
177C2×Q16C22⋊D6111yescharacteristic
178C22×C8—611no—
179C22×C8C22×D6111yescharacteristic
180C4⋊Q8—1221no—
181C4⋊Q8—1221no—
182#125—2441no—
183C22⋊Q8—21no—
184C22⋊Q8—1221no—
185C22⋊Q8—2441no—
186C4×Q8—1221no—
187C4×Q8—1221no—
188C4×Q8—2441no—
189#117—2441no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—2441no—
193C2×C42—611no—
194C2×C16—21no—
195C2×C16—1221no—
196#107—21no—
197#107—21no—
198#107—611no—
199#107—1221no—
200#107C22⋊D6111yescharacteristic
201C4⋊C8—1221no—
202C4⋊C8—1221no—
203#103—21no—
204#103—1221no—
205#103—1221no—
206#103—1221no—
207#95—2441no—
208C2×Q8—21no—
209C2×Q8—1221no—
210C2×Q8—2441no—
211C22×C4—41no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—2441no—
215C22×C4D4×D6111yescharacteristic
216Q16—41no—
217Q16—4881no—
218Q16—2441no—
219C2×C8—41no—
220C2×C8—1221no—
221C2×C8—2441no—
222C2×C8D4×D6111yescharacteristic
223C2×C8C2×C22⋊D6111yescharacteristic
224C4⋊C4—21no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—1222no—
229C4⋊C4—1221no—
230C4⋊C4—4882no—
231C4⋊C4—2441no—
232C4⋊C4—2441no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C22⋊C4—41no—
239C22⋊C4—2441no—
240C42—1221no—
241C42—1221no—
242C42—2441no—
243C42—2441no—
244C16—41no—
245C16—2441no—
246C23D8×D6111yescharacteristic
247Q8—41no—
248Q8—41no—
249Q8—4882no—
250Q8—2441no—
251Q8—2441no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—612no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—4881no—
264C2×C4—4881no—
265C2×C4—2442no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4#1451974511yescharacteristic
270C2×C4#1451980111yescharacteristic
271C8—21no—
272C8—21no—
273C8—2441no—
274C22—21no—
275C22—21no—
276C22#1683989411yescharacteristic
277C22Q32×D6111yescharacteristic
278C22#1684020411yescharacteristic
279C4—21no—
280C4—81no—
281C4—81no—
282C4—161no—
283C4—1222no—
284C4—4882no—
285C4—4881no—
286C4—4881no—
287C4—2441no—
288C4#1683994311yescharacteristic
289C4#1683995111yescharacteristic
290C2—21no—
291C2—21no—
292C2#2144482011yescharacteristic
293C2#2144775111yescharacteristic
294C2#2144776311yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2236C2
socleC22×C61#447
prime radicalC23×C61C2×D8
hypercenter#2236D61
hypocenterC61#12292
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
174. C61#12292semidirect

Maximal subgroups

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

subgroupindex
#214571602
#214480212
#214473132
#214438322
#214438312
#214437582
C61×#22362
#1229261