Finite Group Databasebeta

← #29593943

Subgroups — #29593943

Order 15616.

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

normal subgroups only

This group has 284 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#21448056C211yesmaximal, characteristic
3#21447961C211yesmaximal, characteristic, complemented
4#21445348C211yesmaximal, characteristic, complemented
5#21443861C211yesmaximal, characteristic
6#21443802C211yesmaximal, characteristic, complemented
7C61×#1334C211yesmaximal, characteristic, complemented
8#16840484—21no—
9#16840167C2211yescharacteristic
10#16840155—21no—
11#16840146C2211yescharacteristic
12#16840058—21no—
13#16839984—21no—
14#16839980—21no—
15#16839971—21no—
16#16839892C2211yescharacteristic
17#16839861—21no—
18#16839589—21no—
19C4⋊#11758185C2211yescharacteristic
20#16839567—21no—
21#16839566—21no—
22#16839564—21no—
23#16839510—21no—
24C4×Q16×C61C2211yescharacteristic
25C61×#346C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758202—21no—
29C2×#11758190—21no—
30C2×#11758201—21no—
31C2×D488D411yescharacteristic
32#14519777—21no—
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—
44#14519711—21no—
45#14519711—21no—
46#14519711—41no—
47C4⋊#92418D411yescharacteristic
48#14519706—21no—
49#14519702—41no—
50#14519700—21no—
51#14519697—21no—
52#14519687—21no—
53C2×Q16×C61D411yescharacteristic
54C4×Q8×C61—21no—
55C2×C16×C61—21no—
56#107×C61D411yescharacteristic
57C4⋊C8×C61—21no—
58#103×C61—21no—
59C4×C8×C61C2311yescharacteristic
60C2×Q8×C61—21no—
61C2×D244—21no—
62C2×C4×D61—41no—
63C2×Dic122—21no—
64C2×Dic122—41no—
65C2×Dic122D811yescharacteristic
66Q16×C61—21no—
67Q16×C61—21no—
68C2×C8×C61—41no—
69C2×C8×C61C2×D411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C42×C61—41no—
74C42×C61C2×D411yescharacteristic
75#11758202—81no—
76#11758201—81no—
77#11758198—41no—
78#11758198—41no—
79#11758198—41no—
80#11758198—41no—
81#11758198—41no—
82C4⋊Dic61—41no—
83C4⋊Dic61—41no—
84C4⋊Dic61D811yescharacteristic
85#11758196—21no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—21no—
90C4×Dic61—41no—
91C2×#92418—21no—
92Dic244—41no—
93D488—41no—
94#11758190—41no—
95#11758190—41no—
96C16×C61—41no—
97#11758185—41no—
98C22×D61—41no—
99Q8×C61—41no—
100Q8×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61#12011yescharacteristic
104C2×C4×C61C2×D811yescharacteristic
105C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—41no—
109C2×Dic61—81no—
110D244—41no—
111D244—41no—
112C4×D61—82no—
113Dic122—41no—
114Dic122—41no—
115Dic122—41no—
116Dic122—161no—
117C8×C61—21no—
118C8×C61—81no—
119C8×C61#13511yescharacteristic
120C8×C61#13711yescharacteristic
121#92418—41no—
122#12389—611nomaximal, Sylow
123C22×C61#44711yescharacteristic
124C2×D61—81no—
125C2×D61—81no—
126C2×D61—81no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—81no—
130C4×C61—81no—
131C4×C61#45211yescharacteristic
132C4×C61#45511yescharacteristic
133Dic61—41no—
134Dic61—41no—
135Dic61—81no—
136Dic61—161no—
137#3402—611no—
138#2243—611no—
139#2225—611no—
140#1696—611no—
141#1360—611no—
142#1338—611no—
143#1334D6111yescharacteristic, complemented
144C2×C61#164111yescharacteristic
145C2×C61#219111yescharacteristic
146C2×C61#219311yescharacteristic
147D61—161no—
148#556—1221no—
149#500—611no—
150#497—1221no—
151#495—611no—
152#477—1221no—
153#464—1221no—
154#463—1221no—
155#462—1221no—
156#446—611no—
157#440—1221no—
158C4×Q16C2×D6111yescharacteristic
159#367—1221no—
160C4⋊C16—611no—
161#358—1221no—
162#358—1221no—
163#357—1221no—
164#346C2×D6111yescharacteristic
165#334C2×D6111yescharacteristic
166#333—1221no—
167C61#1238911yescharacteristic, complemented, Sylow
168C2×Q16—611no—
169C2×Q16—1221no—
170C2×Q16D24411yescharacteristic
171C2×SD16—1221no—
172C2×SD16—1221no—
173C2×D8—611no—
174C4⋊Q8—1221no—
175C4⋊Q8—1221no—
176#126—2441no—
177#126—2441no—
178#124—1221no—
179#124—1221no—
180C22⋊Q8—2441no—
181C4×Q8—21no—
182C4×Q8—611no—
183C4×Q8—1221no—
184C4×D4—1221no—
185#117—2441no—
186C2×C16—21no—
187C2×C16—1221no—
188#107—1221no—
189#107—1221no—
190#107—2441no—
191#107D24411yescharacteristic
192C4⋊C8—21no—
193C4⋊C8—611no—
194C4⋊C8—1221no—
195#103—21no—
196#103—1221no—
197#103—2441no—
198#102—1221no—
199#97—1221no—
200C4×C8C22×D6111yescharacteristic
201C2×Q8—21no—
202C2×Q8—611no—
203C2×Q8—1221no—
204C2×Q8—2441no—
205C2×D4—1221no—
206C22×C4—2441no—
207Q16—21no—
208Q16—21no—
209Q16—4881no—
210Q16—2441no—
211SD16—4881no—
212SD16—2441no—
213SD16—2441no—
214D8—2441no—
215C2×C8—41no—
216C2×C8—1221no—
217C2×C8C2×D24411yescharacteristic
218C2×C8D4×D6111yescharacteristic
219C4⋊C4—21no—
220C4⋊C4—41no—
221C4⋊C4—611no—
222C4⋊C4—1221no—
223C4⋊C4—2441no—
224C4⋊C4—2441no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C22⋊C4—2441no—
229C22⋊C4—2441no—
230C22⋊C4—2441no—
231C22⋊C4—2441no—
232C22⋊C4—2441no—
233C42—41no—
234C42—1221no—
235C42—2441no—
236C42D4×D6111yescharacteristic
237C16—41no—
238C16—2441no—
239C23—2441no—
240Q8—41no—
241Q8—41no—
242Q8—9761no—
243Q8—2441no—
244Q8—2441no—
245Q8—2441no—
246D4—2441no—
247D4—2441no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—4882no—
253C2×C4—4881no—
254C2×C4—2441no—
255C2×C4#1451974711yescharacteristic
256C2×C4D8×D6111yescharacteristic
257C2×C4#1451980411yescharacteristic
258C8—21no—
259C8—81no—
260C8—2441no—
261C8#1451979911yescharacteristic
262C8#1451981011yescharacteristic
263C22—4881no—
264C22—4881no—
265C22—4881no—
266C22#1683989711yescharacteristic
267C4—21no—
268C4—21no—
269C4—81no—
270C4—81no—
271C4—9761no—
272C4—4881no—
273C4—2441no—
274C4—2441no—
275C4#1683992611yescharacteristic
276C4#1683994111yescharacteristic
277C2—9761no—
278C2#2144501511yescharacteristic
279C2#2144777111yescharacteristic
280C2#2144778611yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1334C2
socleC22×C61#447
prime radicalC2×D488D4
hypercenter#1334D61
hypocenterC61#12389
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1334

Complements

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

NH ≅ G/Ntype
3. #21447961C2semidirect
4. #21445348C2semidirect
6. #21443802C2semidirect
7. C61×#1334C2semidirect
143. #1334D61semidirect
167. C61#12389semidirect

Maximal subgroups

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

subgroupindex
#214588962
#214480562
#214479612
#214453482
#214438612
#214438022
C61×#13342
#1238961