Finite Group Databasebeta

← #29593349

Subgroups — #29593349

Order 15616.

328 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 59 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#21448036C211yesmaximal, characteristic, complemented
2#21448031C211yesmaximal, characteristic, complemented
3#21447335C211yesmaximal, characteristic, complemented
4#21443813C211yesmaximal, characteristic, complemented
5#21443810C211yesmaximal, characteristic, complemented
6#21443755C211yesmaximal, characteristic, complemented
7C61×#3197C211yesmaximal, characteristic
8#16839811C2211yescharacteristic
9#16839810—21no—
10#16839726—21no—
11#16839584—21no—
12#16839584—21no—
13#16839578—21no—
14#16839575—21no—
15#16839544C2211yescharacteristic
16#16839544C2211yescharacteristic
17#16839520C2211yescharacteristic
18C61×#525—21no—
19C61×#485—21no—
20C61×#482—21no—
21C61×#470C2211yescharacteristic
22C61×#469C2211yescharacteristic
23C61×#468—21no—
24C61×#452—21no—
25C61×#449—21no—
26C61×#407C2211yescharacteristic
27C2×#11758194—21no—
28C2×#11758194—21no—
29#14519717—21no—
30#14519717—21no—
31#14519713—21no—
32#14519713—21no—
33#14519712—42no—
34C22⋊#92418—42no—
35C2×#41×C61—21no—
36C23×C4×C61D411yescharacteristic
37C2×Q16×C61D411yescharacteristic
38C2×SD16×C61—21no—
39C2×D8×C61D411yescharacteristic
40C2×M16×C61D411yescharacteristic
41C2×M16×C61C2311yescharacteristic
42#123×C61—41no—
43C22⋊Q8×C61—21no—
44C22⋊Q8×C61—21no—
45#121×C61—21no—
46#121×C61—21no—
47#120×C61—41no—
48C4×D4×C61—41no—
49C4×D4×C61—41no—
50#117×C61—21no—
51#107×C61—21no—
52#106×C61D411yescharacteristic
53#106×C61D411yescharacteristic
54#103×C61—21no—
55#103×C61—21no—
56#102×C61—21no—
57#102×C61—21no—
58C22⋊C8×C61—21no—
59C22⋊C8×C61—21no—
60C24×C61SD1611yescharacteristic
61#41×C61—81no—
62#41×C61—81no—
63C2×Q8×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61—41no—
73C22×C4×C61SD1611yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75Q16×C61—41no—
76SD16×C61—81no—
77D8×C61—41no—
78M16×C61—41no—
79M16×C61—41no—
80C2×C8×C61—21no—
81C2×C8×C61C2×D411yescharacteristic
82C2×C8×C61C2×D411yescharacteristic
83C4⋊C4×C61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C42×C61—41no—
93#11758194—41no—
94#11758194—41no—
95#11758194—41no—
96#11758194—41no—
97C2×#92418—22no—
98C2×#92418—41no—
99#11758185—41no—
100#11758185—41no—
101C23×C61—21no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—81no—
105C23×C61C2×SD1611yescharacteristic
106Q8×C61—41no—
107Q8×C61—41no—
108D4×C61—41no—
109D4×C61—41no—
110D4×C61—82no—
111D4×C61—82no—
112D4×C61—82no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—81no—
123C2×C4×C61—82no—
124C2×C4×C61#12011yescharacteristic
125C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
126C8×C61—21no—
127C8×C61—21no—
128C8×C61—41no—
129#92418—42no—
130#92418—81no—
131#12300—611nomaximal, Sylow
132C22×C61—21no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61—42no—
137C22×C61—41no—
138C22×C61—81no—
139C22×C61—81no—
140C22×C61—81no—
141C22×C61—81no—
142C22×C61#45011yescharacteristic
143C4×C61—21no—
144C4×C61—41no—
145C4×C61—81no—
146C4×C61—81no—
147C4×C61—81no—
148C4×C61#45311yescharacteristic
149C4×C61#45811yescharacteristic
150#3197D6111yescharacteristic
151#2239—611no—
152#2238—611no—
153#2091—611no—
154#1342—611no—
155#1341—611no—
156#1320—611no—
157C2×C61—21no—
158C2×C61—41no—
159C2×C61—81no—
160C2×C61—161no—
161C2×C61#161311yescharacteristic
162#525—21no—
163#485—21no—
164#482—21no—
165#470C2×D6111yescharacteristic
166#469C2×D6111yescharacteristic
167#468—21no—
168#452—21no—
169#449—21no—
170#430—611no—
171#430—1221no—
172#407—1221no—
173#407C2×D6111yescharacteristic
174#365—1221no—
175#365—1221no—
176#362—1221no—
177#361—1221no—
178#349—611no—
179#349—611no—
180#338—611no—
181C61#1230011yescharacteristic, complemented, Sylow
182C2×#41—21no—
183C23×C4C22⋊D6111yescharacteristic
184C2×Q16C22⋊D6111yescharacteristic
185C2×SD16—21no—
186C2×D8C22⋊D6111yescharacteristic
187C2×M16—1221no—
188C2×M16—1221no—
189C2×M16C22⋊D6111yescharacteristic
190C2×M16C22×D6111yescharacteristic
191#123—41no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194#121—21no—
195#121—21no—
196#120—41no—
197C4×D4—41no—
198C4×D4—41no—
199#117—21no—
200M32—1221no—
201M32—1221no—
202#108—1221no—
203#108—1221no—
204#108—2442no—
205#107—21no—
206#106C22⋊D6111yescharacteristic
207#106C22⋊D6111yescharacteristic
208#103—21no—
209#103—21no—
210#102—21no—
211#102—21no—
212C22⋊C8—21no—
213C22⋊C8—21no—
214C22⋊C8—2442no—
215C24#1175820011yescharacteristic
216#41—81no—
217#41—81no—
218C2×Q8—21no—
219C2×D4—21no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—41no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4#1175820011yescharacteristic
229C22×C4C2×C22⋊D6111yescharacteristic
230Q16—41no—
231SD16—81no—
232D8—41no—
233M16—41no—
234M16—41no—
235M16—2441no—
236M16—2441no—
237M16—2441no—
238M16—2441no—
239C2×C8—21no—
240C2×C8—1222no—
241C2×C8—2441no—
242C2×C8C2×C22⋊D6111yescharacteristic
243C2×C8C2×C22⋊D6111yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C42—41no—
254C16—2441no—
255C16—2441no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—81no—
260C23C2×#1175820011yescharacteristic
261Q8—41no—
262Q8—41no—
263D4—41no—
264D4—41no—
265D4—82no—
266D4—82no—
267D4—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—82no—
279C2×C4#1451974611yescharacteristic
280C2×C4#1451980311yescharacteristic
281C8—21no—
282C8—21no—
283C8—41no—
284C8—4881no—
285C8—2442no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—42no—
291C22—41no—
292C22—81no—
293C22—81no—
294C22—81no—
295C22—81no—
296C22#1683991311yescharacteristic
297C4—21no—
298C4—41no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4#1683993011yescharacteristic
303C4#1683995211yescharacteristic
304C2—21no—
305C2—41no—
306C2—81no—
307C2—161no—
308C2#2144483911yescharacteristic
subgroupG/H
centerC2#21444839
commutator, cosocleC2×M16×C61C23
FrattiniC2×M16C22×D61
Fitting, prime radicalC61×#3197C2
socleC2×C61#1613
hypercenter#3197D61
hypocenterC61#12300
LCSG ▷ C2×M16×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3197

Complements

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

NH ≅ G/Ntype
1. #21448036C2semidirect
2. #21448031C2semidirect
3. #21447335C2semidirect
4. #21443813C2semidirect
5. #21443810C2semidirect
6. #21443755C2semidirect
181. C61#12300semidirect

Maximal subgroups

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

subgroupindex
#214480362
#214480312
#214473352
#214438132
#214438102
#214437552
C61×#31972
#1230061