Finite Group Databasebeta

← #29593286

Subgroups — #29593286

Order 15616.

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

normal subgroups only

This group has 316 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#21457172C211yesmaximal, characteristic
2#21447999C211yesmaximal, characteristic
3#21447308C211yesmaximal, characteristic, complemented
4#21443831C211yesmaximal, characteristic, complemented
5#21443829C211yesmaximal, characteristic
6#21443758C211yesmaximal, characteristic, complemented
7C61×#2235C211yesmaximal, characteristic, complemented
8#16840298—21no—
9#16840071—21no—
10#16840065—21no—
11#16839998C2211yescharacteristic
12#16839993—21no—
13#16839986—21no—
14#16839980—21no—
15C2×#14519706C2211yescharacteristic
16#16839658—21no—
17#16839587—21no—
18#16839562—21no—
19C22⋊#11758185C2211yescharacteristic
20#16839525C2211yescharacteristic
21#16839524—21no—
22C61×#467C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#367—21no—
25C61×#358—21no—
26C61×C22⋊C16C2211yescharacteristic
27C2×#11758201—21no—
28C2×D488D411yescharacteristic
29C22×#92418D411yescharacteristic
30#14519772—41no—
31#14519768—21no—
32#14519766—21no—
33#14519761—41no—
34#14519751—21no—
35Q8×Dic61—21no—
36#14519739—21no—
37#14519737—41no—
38#14519735—41no—
39C2×C4⋊Dic61—21no—
40C2×#11758196—41no—
41C2×C4×Dic61D411yescharacteristic
42C2×#11758185—21no—
43#14519711D411yescharacteristic
44#14519708—21no—
45#14519706—21no—
46#14519706—21no—
47#14519701—21no—
48#14519699—21no—
49#14519697—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
63C2×C22⋊D61—41no—
64C22×Dic61—41no—
65C22×Dic61D811yescharacteristic
66C22×Dic61D811yescharacteristic
67C2×D244—21no—
68C2×C4×D61—41no—
69Q16×C61—41no—
70C2×C8×C61—41no—
71C2×C8×C61C2×D411yescharacteristic
72C2×C8×C61C2×D411yescharacteristic
73C4⋊C4×C61—21no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C22⋊C4×C61—41no—
78#11758201—81no—
79#11758198—41no—
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—22no—
84C4⋊Dic61—21no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88#11758196—41no—
89#11758196—82no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—41no—
93C2×#92418—21no—
94C2×#92418—41no—
95D488—41no—
96C16×C61—41no—
97#11758185—41no—
98C23×C61C2×D811yescharacteristic
99C22×D61—41no—
100Q8×C61—41no—
101Q8×C61—41no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—81no—
107C2×C4×C61—81no—
108C2×C4×C61—81no—
109C2×C4×C61#12011yescharacteristic
110C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
111C22⋊D61—81no—
112C22⋊D61—81no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—41no—
118C2×Dic61—42no—
119C2×Dic61—41no—
120C2×Dic61—81no—
121C2×Dic61—81no—
122D244—41no—
123D244—41no—
124C4×D61—82no—
125C8×C61—21no—
126C8×C61—21no—
127#92418—41no—
128#12290—611nomaximal, Sylow
129C22×C61—21no—
130C22×C61—21no—
131C22×C61#44711yescharacteristic
132C22×C61#50811yescharacteristic
133C22×C61#50911yescharacteristic
134C2×D61—81no—
135C2×D61—81no—
136C2×D61—81no—
137C4×C61—21no—
138C4×C61—81no—
139C4×C61—81no—
140C4×C61—161no—
141C4×C61#45611yescharacteristic
142C4×C61#45811yescharacteristic
143Dic61—41no—
144Dic61—41no—
145Dic61—82no—
146Dic61—81no—
147#3250—611no—
148#2235D6111yescharacteristic, complemented
149#2232—611no—
150#2086—611no—
151#1348—611no—
152#1347—611no—
153#1322—611no—
154C2×C61—21no—
155C2×C61—21no—
156C2×C61#161011yescharacteristic
157C2×C61#218611yescharacteristic
158C2×C61#219111yescharacteristic
159D61—161no—
160#529—1221no—
161#479—1221no—
162#478—1221no—
163#467C2×D6111yescharacteristic
164#466—611no—
165#465—1221no—
166#464—1221no—
167#463—1221no—
168C2×#107C2×D6111yescharacteristic
169C2×C4⋊C8—611no—
170#389—1221no—
171#367—21no—
172#366—1221no—
173#358—21no—
174#357—1221no—
175C22⋊C16—611no—
176C22⋊C16C2×D6111yescharacteristic
177#340—611no—
178#340—1221no—
179C61#1229011yescharacteristic, complemented, Sylow
180C2×Q16C22⋊D6111yescharacteristic
181C2×SD16—1221no—
182C2×D8—611no—
183C22×C8—611no—
184C22×C8C22×D6111yescharacteristic
185#126—2441no—
186#125—1221no—
187#124—1221no—
188#123—2441no—
189C22⋊Q8—21no—
190#121—1221no—
191C4×Q8—1221no—
192C4×D4—1221no—
193C4×D4—2441no—
194#117—2441no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—2441no—
198C2×C42—611no—
199C2×C16—21no—
200C2×C16—1221no—
201#107—21no—
202#107—21no—
203#107—611no—
204#107C22⋊D6111yescharacteristic
205#106—1221no—
206C4⋊C8—1221no—
207C4⋊C8—1221no—
208#103—21no—
209#103—1221no—
210#102—1221no—
211#102—1221no—
212#95—2441no—
213C2×Q8—21no—
214C2×D4—1221no—
215C2×D4—2441no—
216C22×C4—41no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—2441no—
220C22×C4—2441no—
221C22×C4D4×D6111yescharacteristic
222Q16—41no—
223SD16—4881no—
224D8—2441no—
225C2×C8—41no—
226C2×C8—1221no—
227C2×C8—2441no—
228C2×C8D4×D6111yescharacteristic
229C2×C8C2×C22⋊D6111yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—1222no—
235C4⋊C4—1221no—
236C4⋊C4—4882no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C4⋊C4—2441no—
241C22⋊C4—41no—
242C22⋊C4—2441no—
243C22⋊C4—2441no—
244C22⋊C4—2441no—
245C22⋊C4—2441no—
246C42—1221no—
247C42—1221no—
248C42—2441no—
249C16—41no—
250C16—2441no—
251C23—2441no—
252C23D8×D6111yescharacteristic
253Q8—41no—
254Q8—41no—
255D4—4881no—
256D4—4881no—
257D4—2441no—
258D4—2441no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—4882no—
271C2×C4—4881no—
272C2×C4—4881no—
273C2×C4—2442no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4#1451974511yescharacteristic
277C2×C4#1451980111yescharacteristic
278C8—21no—
279C8—21no—
280C8—2441no—
281C22—21no—
282C22—21no—
283C22—4881no—
284C22—4881no—
285C22—4881no—
286C22#1683989411yescharacteristic
287C22#1684019311yescharacteristic
288C22#1684019911yescharacteristic
289C4—21no—
290C4—81no—
291C4—81no—
292C4—161no—
293C4—4882no—
294C4—4881no—
295C4—2441no—
296C4—2441no—
297C4#1683994311yescharacteristic
298C4#1683995111yescharacteristic
299C2—21no—
300C2—21no—
301C2—9761no—
302C2#2144482011yescharacteristic
303C2#2144774111yescharacteristic
304C2#2144776811yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2235C2
socleC22×C61#447
prime radical#16839998C22
hypercenter#2235D61
hypocenterC61#12290
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
3. #21447308C2semidirect
4. #21443831C2semidirect
6. #21443758C2semidirect
7. C61×#2235C2semidirect
148. #2235D61semidirect
179. C61#12290semidirect

Maximal subgroups

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

subgroupindex
#214571722
#214479992
#214473082
#214438312
#214438292
#214437582
C61×#22352
#1229061