Finite Group Databasebeta

← #29593588

Subgroups — #29593588

Order 15616.

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

normal subgroups only

This group has 320 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#21458910C211yesmaximal, characteristic
2#21447861C211yesmaximal, characteristic, complemented
3#21445310C211yesmaximal, characteristic, complemented
4#21443862C211yesmaximal, characteristic, complemented
5#21443802C211yesmaximal, characteristic, complemented
6#21443787C211yesmaximal, characteristic, complemented
7C61×#2251C211yesmaximal, characteristic, complemented
8#16840494—21no—
9C2×#14519720—21no—
10#16840148—21no—
11#16840044—21no—
12#16839986—21no—
13#16839974—21no—
14#16839955—21no—
15#16839892C2211yescharacteristic
16#16839863—21no—
17C4×D488C2211yescharacteristic
18C4⋊#11758185C2211yescharacteristic
19#16839566—21no—
20#16839513C2211yescharacteristic
21#16839508—21no—
22C2×Q32×C61—21no—
23C2×SD32×C61—21no—
24C61×#495C2211yescharacteristic
25C61×#494C2211yescharacteristic
26C61×#346C2211yescharacteristic
27C2×#11758201—21no—
28C2×D488D411yescharacteristic
29C2×#11758199—21no—
30#14519773—21no—
31#14519766—21no—
32#14519763—41no—
33#14519761—41no—
34#14519759—41no—
35Q8×Dic61—21no—
36C4×Dic122D411yescharacteristic
37C4×D244—21no—
38D4×Dic61—21no—
39#14519737—41no—
40#14519720—42no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519708—41no—
44C4⋊#92418—21no—
45C4⋊#92418D411yescharacteristic
46#14519706—21no—
47#14519701—21no—
48#14519700—41no—
49#14519699—21no—
50#14519698—21no—
51#14519687—21no—
52C2×Q16×C61—21no—
53C2×Q16×C61—21no—
54C2×Q16×C61D411yescharacteristic
55C2×SD16×C61—21no—
56C2×D8×C61D411yescharacteristic
57C4⋊Q8×C61—21no—
58#124×C61—21no—
59Q32×C61—42no—
60SD32×C61—42no—
61C2×C16×C61—21no—
62C4×C8×C61C2311yescharacteristic
63C2×Q8×C61—21no—
64C2×Q8×C61—41no—
65C2×D4×C61—21no—
66C2×C22⋊D61—41no—
67C2×C22⋊D61—41no—
68C22×Dic61—41no—
69C2×D244—21no—
70C2×C4×D61—41no—
71C2×Dic122D811yescharacteristic
72Q16×C61—41no—
73Q16×C61—41no—
74Q16×C61—41no—
75Q16×C61—41no—
76Q16×C61—41no—
77SD16×C61—41no—
78SD16×C61—41no—
79D8×C61—41no—
80C2×C8×C61C2×D411yescharacteristic
81C2×C8×C61C2×D411yescharacteristic
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C42×C61C2×D411yescharacteristic
87C22⋊Dic61—41no—
88#11758201—81no—
89#11758199—81no—
90#11758198—41no—
91#11758198—41no—
92#11758198—41no—
93C4⋊Dic61—21no—
94C4⋊Dic61—41no—
95C4⋊Dic61D811yescharacteristic
96#11758196—21no—
97C4×Dic61—21no—
98C4×Dic61—41no—
99C2×#92418—21no—
100C2×#92418—41no—
101D488—21no—
102D488—21no—
103C16×C61—22no—
104#11758185—41no—
105C23×C61—41no—
106C22×D61—41no—
107Q8×C61—41no—
108Q8×C61—41no—
109Q8×C61—81no—
110Q8×C61—81no—
111D4×C61—41no—
112D4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—81no—
115C2×C4×C61#12011yescharacteristic
116C2×C4×C61C2×D811yescharacteristic
117C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
118C22⋊D61—82no—
119C22⋊D61—161no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—41no—
123C2×Dic61—161no—
124D244—41no—
125D244—41no—
126C4×D61—161no—
127Dic122—41no—
128C8×C61—21no—
129C8×C61#13511yescharacteristic
130C8×C61AGL(1,ℤ/8)11yescharacteristic
131#92418—41no—
132#92418—81no—
133#12338—611nomaximal, Sylow
134C22×C61—81no—
135C22×C61—81no—
136C22×C61—81no—
137C22×C61#44711yescharacteristic
138C2×D61—81no—
139C2×D61—81no—
140C2×D61—81no—
141C4×C61—21no—
142C4×C61—21no—
143C4×C61—81no—
144C4×C61—161no—
145C4×C61#44911yescharacteristic
146C4×C61#45311yescharacteristic
147Dic61—41no—
148Dic61—41no—
149Dic61—81no—
150#3403—611no—
151#2251D6111yescharacteristic, complemented
152#2208—611no—
153#1690—611no—
154#1360—611no—
155#1338—611no—
156#1333—611no—
157C2×C61—161no—
158C2×C61#162111yescharacteristic
159C2×C61#219111yescharacteristic
160C2×C61#219411yescharacteristic
161D61—161no—
162#559—1221no—
163C2×Q32—21no—
164C2×SD32—21no—
165C2×SD32—1221no—
166#496—1221no—
167#495C2×D6111yescharacteristic
168#494C2×D6111yescharacteristic
169#475—1221no—
170#464—1221no—
171#463—1221no—
172#459—1221no—
173#446—611no—
174#440—1221no—
175C4×D8—611no—
176C4⋊C16—611no—
177#358—1221no—
178#346C2×D6111yescharacteristic
179#334—611no—
180#332—1221no—
181C61#1233811yescharacteristic, complemented, Sylow
182C2×Q16—21no—
183C2×Q16—21no—
184C2×Q16C22⋊D6111yescharacteristic
185C2×SD16—21no—
186C2×SD16—1221no—
187C2×D8—611no—
188C2×D8—1221no—
189C2×D8C22⋊D6111yescharacteristic
190C4⋊Q8—21no—
191#127—1221no—
192#124—21no—
193#124—1221no—
194#124—2441no—
195#123—2441no—
196#123—2441no—
197C4×Q8—611no—
198C4×Q8—1221no—
199C4×D4—1221no—
200C4×D4—1221no—
201C4×D4—2441no—
202Q32—42no—
203SD32—42no—
204SD32—2442no—
205C2×C16—21no—
206C2×C16—1221no—
207#107—611no—
208#106—2441no—
209C4⋊C8—611no—
210C4⋊C8—1221no—
211C4⋊C8—1221no—
212#103—1221no—
213#103—2441no—
214#102—1221no—
215#102—1221no—
216#97—1221no—
217C4×C8C22×D6111yescharacteristic
218C2×Q8—21no—
219C2×Q8—41no—
220C2×Q8—611no—
221C2×D4—21no—
222C2×D4—1221no—
223C2×D4—2441no—
224C2×D4—2441no—
225C22×C4—2441no—
226C22×C4—2441no—
227Q16—41no—
228Q16—41no—
229Q16—41no—
230Q16—41no—
231Q16—41no—
232SD16—41no—
233SD16—41no—
234SD16—4881no—
235D8—41no—
236D8—1221no—
237D8—1221no—
238D8—4881no—
239C2×C8—1221no—
240C2×C8—2441no—
241C2×C8D4×D6111yescharacteristic
242C2×C8C2×C22⋊D6111yescharacteristic
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—611no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—2441no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—2441no—
252C22⋊C4—2441no—
253C22⋊C4—2441no—
254C22⋊C4—2441no—
255C42—1221no—
256C42—2441no—
257C42D4×D6111yescharacteristic
258C16—22no—
259C16—2441no—
260C23—41no—
261C23—2441no—
262Q8—41no—
263Q8—41no—
264Q8—81no—
265Q8—81no—
266Q8—2441no—
267D4—41no—
268D4—41no—
269D4—9761no—
270D4—4882no—
271D4—2441no—
272D4—2441no—
273C2×C4—41no—
274C2×C4—81no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—9761no—
278C2×C4—9761no—
279C2×C4—2441no—
280C2×C4#1451974511yescharacteristic
281C2×C4D8×D6111yescharacteristic
282C2×C4#1451980111yescharacteristic
283C8—21no—
284C8—4881no—
285C8—2441no—
286C8#1451979611yescharacteristic
287C8#1451980111yescharacteristic
288C22—81no—
289C22—81no—
290C22—81no—
291C22—4881no—
292C22—4881no—
293C22—4881no—
294C22#1683989411yescharacteristic
295C4—21no—
296C4—21no—
297C4—81no—
298C4—161no—
299C4—4881no—
300C4—2441no—
301C4—2441no—
302C4#1683990411yescharacteristic
303C4#1683992911yescharacteristic
304C2—161no—
305C2—9761no—
306C2#2144488111yescharacteristic
307C2#2144776811yescharacteristic
308C2#2144778711yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2251C2
socleC22×C61#447
prime radical#21458910C2
hypercenter#2251D61
hypocenterC61#12338
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2251

Complements

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

NH ≅ G/Ntype
2. #21447861C2semidirect
3. #21445310C2semidirect
4. #21443862C2semidirect
5. #21443802C2semidirect
6. #21443787C2semidirect
7. C61×#2251C2semidirect
151. #2251D61semidirect
181. C61#12338semidirect

Maximal subgroups

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

subgroupindex
#214589102
#214478612
#214453102
#214438622
#214438022
#214437872
C61×#22512
#1233861