Finite Group Databasebeta

← #29593953

Subgroups — #29593953

Order 15616.

290 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 61 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#21458896C211yesmaximal, characteristic
2#21448058C211yesmaximal, characteristic
3#21445334C211yesmaximal, characteristic, complemented
4#21443863C211yesmaximal, characteristic
5#21443800C211yesmaximal, characteristic, complemented
6#21443789C211yesmaximal, characteristic, complemented
7C61×#2227C211yesmaximal, characteristic, complemented
8#16840484—21no—
9#16840155—21no—
10#16840146C2211yescharacteristic
11#16839984—21no—
12#16839980—21no—
13#16839971—21no—
14#16839969—21no—
15#16839892C2211yescharacteristic
16#16839861—21no—
17#16839565—21no—
18#16839562—21no—
19#16839538C2211yescharacteristic
20#16839513C2211yescharacteristic
21#16839508—21no—
22C61×#500C2211yescharacteristic
23C4×Q16×C61C2211yescharacteristic
24C61×#366—21no—
25C61×C4⋊C16C2211yescharacteristic
26C61×#358—21no—
27C2×Dic244D411yescharacteristic
28C2×#11758202—21no—
29C2×#11758202—41no—
30C2×#11758190—21no—
31C2×#11758201—21no—
32C2×D488D411yescharacteristic
33#14519775—21no—
34#14519772—41no—
35#14519771—41no—
36#14519766—21no—
37#14519765—21no—
38#14519755—41no—
39C4×Dic122D411yescharacteristic
40#14519742—21no—
41#14519739—21no—
42#14519734—41no—
43C2×#11758185—21no—
44C4⋊#92418—21no—
45C4⋊#92418D411yescharacteristic
46#14519706—21no—
47#14519701—41no—
48#14519700—21no—
49#14519697—21no—
50#14519687—21no—
51C2×Q16×C61D411yescharacteristic
52C4⋊Q8×C61—21no—
53C4×Q8×C61—21no—
54C2×C16×C61—21no—
55#107×C61—21no—
56#107×C61—21no—
57#107×C61D411yescharacteristic
58#103×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×Q8×C61—21no—
61C2×Q8×C61—41no—
62C2×D244—21no—
63C2×C4×D61—41no—
64C2×Dic122—21no—
65C2×Dic122D811yescharacteristic
66Q16×C61—21no—
67Q16×C61—21no—
68C2×C8×C61C2×D411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C4⋊C4×C61—21no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C42×C61—41no—
75C42×C61C2×D411yescharacteristic
76#11758202—81no—
77#11758202—82no—
78#11758201—81no—
79#11758198—41no—
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83#11758198—41no—
84C4⋊Dic61D811yescharacteristic
85#11758196—21no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—21no—
90C4×Dic61—41no—
91C2×#92418—21no—
92C2×#92418—41no—
93Dic244—41no—
94D488—41no—
95#11758190—41no—
96#11758190—41no—
97C16×C61—41no—
98#11758185—41no—
99C22×D61—41no—
100Q8×C61—41no—
101Q8×C61—41no—
102Q8×C61—81no—
103Q8×C61—81no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—81no—
107C2×C4×C61#12011yescharacteristic
108C2×C4×C61C2×D811yescharacteristic
109C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—41no—
113D244—41no—
114D244—41no—
115C4×D61—82no—
116Dic122—41no—
117Dic122—41no—
118Dic122—41no—
119C8×C61—21no—
120C8×C61#13511yescharacteristic
121C8×C61#13711yescharacteristic
122#92418—41no—
123#92418—81no—
124#12391—611nomaximal, Sylow
125C22×C61#44711yescharacteristic
126C2×D61—81no—
127C2×D61—81no—
128C2×D61—81no—
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—81no—
132C4×C61—81no—
133C4×C61—161no—
134C4×C61#45211yescharacteristic
135C4×C61#45511yescharacteristic
136Dic61—41no—
137Dic61—41no—
138Dic61—81no—
139#3402—611no—
140#2243—611no—
141#2227D6111yescharacteristic, complemented
142#1694—611no—
143#1360—611no—
144#1338—611no—
145#1334—611no—
146C2×C61#164111yescharacteristic
147C2×C61#219011yescharacteristic
148C2×C61#219511yescharacteristic
149D61—161no—
150#556—1221no—
151#500C2×D6111yescharacteristic
152#497—1221no—
153#495—611no—
154#464—1221no—
155#463—1221no—
156#462—1221no—
157#462—1221no—
158#446—611no—
159#440—1221no—
160C4×Q16C2×D6111yescharacteristic
161#366—21no—
162C4⋊C16C2×D6111yescharacteristic
163#358—21no—
164#358—1221no—
165#357—1221no—
166#346—611no—
167#334—611no—
168#332—1221no—
169C61#1239111yescharacteristic, complemented, Sylow
170C2×Q16—611no—
171C2×Q16—1221no—
172C2×Q16—2441no—
173C2×Q16C22⋊D6111yescharacteristic
174C2×SD16—1221no—
175C2×SD16—1221no—
176C2×D8—611no—
177C4⋊Q8—21no—
178C4⋊Q8—1221no—
179#126—2441no—
180#126—2441no—
181#124—1221no—
182#124—1221no—
183C22⋊Q8—2441no—
184C4×Q8—21no—
185C4×Q8—611no—
186C4×Q8—1221no—
187C4×D4—1221no—
188#117—2441no—
189C2×C16—21no—
190C2×C16—1221no—
191#107—21no—
192#107—21no—
193#107C22⋊D6111yescharacteristic
194C4⋊C8—611no—
195C4⋊C8—1221no—
196C4⋊C8—1221no—
197#103—21no—
198#103—1221no—
199#103—2441no—
200#102—1221no—
201#97—1221no—
202C4×C8C22×D6111yescharacteristic
203C2×Q8—21no—
204C2×Q8—41no—
205C2×Q8—611no—
206C2×Q8—1221no—
207C2×D4—1221no—
208C22×C4—2441no—
209Q16—21no—
210Q16—21no—
211Q16—4882no—
212Q16—4881no—
213Q16—2441no—
214SD16—4881no—
215SD16—2441no—
216SD16—2441no—
217D8—2441no—
218C2×C8—1221no—
219C2×C8—2441no—
220C2×C8D4×D6111yescharacteristic
221C2×C8C2×C22⋊D6111yescharacteristic
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—611no—
227C4⋊C4—1221no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C22⋊C4—2441no—
232C22⋊C4—2441no—
233C22⋊C4—2441no—
234C22⋊C4—2441no—
235C22⋊C4—2441no—
236C42—41no—
237C42—1221no—
238C42—2441no—
239C42D4×D6111yescharacteristic
240C16—41no—
241C16—2441no—
242C23—2441no—
243Q8—41no—
244Q8—41no—
245Q8—81no—
246Q8—81no—
247Q8—2441no—
248Q8—2441no—
249Q8—2441no—
250D4—2441no—
251D4—2441no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—81no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—4882no—
258C2×C4—2441no—
259C2×C4#1451974511yescharacteristic
260C2×C4D8×D6111yescharacteristic
261C2×C4#1451980111yescharacteristic
262C8—21no—
263C8—4881no—
264C8—2441no—
265C8#1451979711yescharacteristic
266C8#1451980811yescharacteristic
267C22—4881no—
268C22—4881no—
269C22—4881no—
270C22#1683989411yescharacteristic
271C4—21no—
272C4—21no—
273C4—81no—
274C4—81no—
275C4—161no—
276C4—4881no—
277C4—2441no—
278C4—2441no—
279C4#1683992211yescharacteristic
280C4#1683993811yescharacteristic
281C2—9761no—
282C2#2144501111yescharacteristic
283C2#2144776311yescharacteristic
284C2#2144779611yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2227C2
socleC22×C61#447
prime radicalC2×D488D4
hypercenter#2227D61
hypocenterC61#12391
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
3. #21445334C2semidirect
5. #21443800C2semidirect
6. #21443789C2semidirect
7. C61×#2227C2semidirect
141. #2227D61semidirect
169. C61#12391semidirect

Maximal subgroups

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

subgroupindex
#214588962
#214480582
#214453342
#214438632
#214438002
#214437892
C61×#22272
#1239161