Finite Group Databasebeta

← #29593951

Subgroups — #29593951

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#21458901C211yesmaximal, characteristic
2#21447968C211yesmaximal, characteristic, complemented
3#21445334C211yesmaximal, characteristic, complemented
4#21443862C211yesmaximal, characteristic
5#21443802C211yesmaximal, characteristic, complemented
6#21443790C211yesmaximal, characteristic, complemented
7C61×#2243C211yesmaximal, characteristic
8#16840481—21no—
9#16840153—21no—
10#16839981—21no—
11#16839975—21no—
12#16839970—21no—
13#16839969—21no—
14#16839892C2211yescharacteristic
15#16839863—21no—
16C4×Dic244C2211yescharacteristic
17#16839587—21no—
18C4⋊#11758185C2211yescharacteristic
19#16839565—21no—
20#16839513C2211yescharacteristic
21#16839508—21no—
22C61×#500C2211yescharacteristic
23C61×#495C2211yescharacteristic
24C61×#358—21no—
25C61×#357—21no—
26C61×#346C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758202—21no—
29C2×#11758202—41no—
30C2×#11758200—21no—
31#14519775—21no—
32#14519770—41no—
33#14519770—41no—
34#14519764—21no—
35#14519754—41no—
36Q8×Dic61—21no—
37C4×Dic122—21no—
38C4×Dic122D411yescharacteristic
39D4×Dic61—21no—
40#14519733—41no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43C4⋊#92418—21no—
44C4⋊#92418D411yescharacteristic
45#14519706—21no—
46#14519702—21no—
47#14519701—21no—
48#14519701—41no—
49#14519698—21no—
50#14519687—21no—
51C2×Q16×C61D411yescharacteristic
52C2×SD16×C61—21no—
53C2×D8×C61D411yescharacteristic
54C4⋊Q8×C61—21no—
55#124×C61—21no—
56C2×C16×C61—21no—
57#107×C61—21no—
58#107×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×Q8×C61—21no—
61C2×Q8×C61—41no—
62C2×D4×C61—21no—
63C22×Dic61—41no—
64C2×Dic122—21no—
65C2×Dic122D811yescharacteristic
66Q16×C61—41no—
67SD16×C61—41no—
68SD16×C61—41no—
69D8×C61—41no—
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C22⋊C4×C61—41no—
75C22⋊C4×C61—41no—
76C42×C61C2×D411yescharacteristic
77C22⋊Dic61—41no—
78C22⋊Dic61—41no—
79C22⋊Dic61—41no—
80#11758202—81no—
81#11758202—82no—
82#11758200—81no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61D811yescharacteristic
86#11758196—21no—
87#11758196—41no—
88#11758196—41no—
89#11758196—41no—
90C4×Dic61—21no—
91C4×Dic61—41no—
92C4×Dic61—41no—
93C2×#92418—21no—
94C2×#92418—41no—
95Dic244—21no—
96Dic244—21no—
97C16×C61—41no—
98#11758185—41no—
99C23×C61—41no—
100Q8×C61—41no—
101Q8×C61—41no—
102Q8×C61—81no—
103Q8×C61—81no—
104D4×C61—41no—
105D4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—81no—
108C2×C4×C61#12011yescharacteristic
109C2×C4×C61C2×D811yescharacteristic
110C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—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—81no—
126C22×C61—81no—
127C22×C61—81no—
128C22×C61#44711yescharacteristic
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—81no—
132C4×C61—161no—
133C4×C61#45211yescharacteristic
134C4×C61#45511yescharacteristic
135Dic61—41no—
136Dic61—41no—
137Dic61—81no—
138Dic61—81no—
139#3402—611no—
140#2243D6111yescharacteristic
141#2227—611no—
142#1694—611no—
143#1360—611no—
144#1338—611no—
145#1334—611no—
146C2×C61—161no—
147C2×C61#164111yescharacteristic
148C2×C61#219011yescharacteristic
149C2×C61#219511yescharacteristic
150#556—1221no—
151#500C2×D6111yescharacteristic
152#497—1221no—
153#495C2×D6111yescharacteristic
154#464—1221no—
155#463—1221no—
156#462—1221no—
157#462—1221no—
158#446—611no—
159#440—1221no—
160C4×Q16—611no—
161#366—1221no—
162C4⋊C16—611no—
163#358—21no—
164#358—1221no—
165#357—21no—
166#346C2×D6111yescharacteristic
167#334—611no—
168#332—1221no—
169C61#1239111yescharacteristic, complemented, Sylow
170C2×Q16—611no—
171C2×Q16—1221no—
172C2×Q16—2441no—
173C2×Q16C22⋊D6111yescharacteristic
174C2×SD16—21no—
175C2×SD16—1221no—
176C2×D8C22⋊D6111yescharacteristic
177C4⋊Q8—21no—
178C4⋊Q8—1221no—
179#126—2441no—
180#126—2441no—
181#124—21no—
182#124—1221no—
183C22⋊Q8—2441no—
184C4×Q8—611no—
185C4×Q8—1221no—
186C4×Q8—1221no—
187C4×D4—1221no—
188#117—2441no—
189C2×C16—21no—
190C2×C16—1221no—
191#107—21no—
192#107—21no—
193#107—611no—
194C4⋊C8—611no—
195C4⋊C8—1221no—
196C4⋊C8—1221no—
197#103—1221no—
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—21no—
208C22×C4—2441no—
209Q16—41no—
210Q16—1221no—
211Q16—1221no—
212Q16—4882no—
213Q16—4881no—
214SD16—41no—
215SD16—41no—
216SD16—4881no—
217D8—41no—
218C2×C8—1221no—
219C2×C8—2441no—
220C2×C8D4×D6111yescharacteristic
221C2×C8C2×C22⋊D6111yescharacteristic
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—611no—
225C4⋊C4—1221no—
226C4⋊C4—1221no—
227C4⋊C4—2441no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—2441no—
234C22⋊C4—2441no—
235C22⋊C4—2441no—
236C42—1221no—
237C42—2441no—
238C42—2441no—
239C42D4×D6111yescharacteristic
240C16—41no—
241C16—2441no—
242C23—41no—
243Q8—41no—
244Q8—41no—
245Q8—81no—
246Q8—81no—
247Q8—2441no—
248Q8—2441no—
249Q8—2441no—
250D4—41no—
251D4—41no—
252C2×C4—41no—
253C2×C4—81no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—4882no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4#1451974511yescharacteristic
260C2×C4D8×D6111yescharacteristic
261C2×C4#1451980111yescharacteristic
262C8—21no—
263C8—4881no—
264C8—2441no—
265C8#1451979811yescharacteristic
266C8#1451980611yescharacteristic
267C22—81no—
268C22—81no—
269C22—81no—
270C22#1683989411yescharacteristic
271C4—21no—
272C4—21no—
273C4—81no—
274C4—161no—
275C4—4881no—
276C4—4881no—
277C4—2441no—
278C4—2441no—
279C4#1683992111yescharacteristic
280C4#1683993911yescharacteristic
281C2—161no—
282C2#2144500911yescharacteristic
283C2#2144776311yescharacteristic
284C2#2144779411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2243C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#2243D61
hypocenterC61#12391
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

Complements

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

NH ≅ G/Ntype
2. #21447968C2semidirect
3. #21445334C2semidirect
5. #21443802C2semidirect
6. #21443790C2semidirect
169. C61#12391semidirect

Maximal subgroups

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

subgroupindex
#214589012
#214479682
#214453342
#214438622
#214438022
#214437902
C61×#22432
#1239161