Finite Group Databasebeta

← #29600679

Subgroups — #29600679

Order 15616.

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

normal subgroups only

This group has 288 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
1C2×#16840195C211yesmaximal, characteristic
2C2×#16839599C211yesmaximal, characteristic, complemented
3#21447907C211yesmaximal, characteristic, complemented
4#21444000C211yesmaximal, characteristic, complemented
5#21443998C211yesmaximal, characteristic, complemented
6#21443956C211yesmaximal, characteristic, complemented
7C2×C61×Q64C211yesmaximal, characteristic, complemented
8C2×#14519800—21no—
9#16840195—22no—
10#16840195—22no—
11C2×#14519720—21no—
12C2×D976C2211yescharacteristic
13C2×C16×D61C2211yescharacteristic
14#16840000—21no—
15#16839599—22no—
16C2×#14519683C2211yescharacteristic
17#16839588C2211yescharacteristic
18#16839566—21no—
19C2×Q32×C61C2211yescharacteristic
20C2×Q32×C61C2211yescharacteristic
21C61×Q64—22no—
22C2×C32×C61C2211yescharacteristic
23C2×#11758226—41no—
24#14519800—24no—
25#14519800—42no—
26C2×#11758201—41no—
27C2×D488—21no—
28C2×C8×D61D411yescharacteristic
29#14519753—41no—
30#14519720—24no—
31D976—21no—
32D976D412yes—
33C2×#11758185D411yescharacteristic
34C16×D61—21no—
35C16×D61—21no—
36#14519711—21no—
37#14519701—41no—
38#14519683—21no—
39C2×Q16×C61—21no—
40C2×Q16×C61—21no—
41Q32×C61—21no—
42Q32×C61—21no—
43Q32×C61—21no—
44Q32×C61D412yes—
45C2×C16×C61C2311yescharacteristic
46C32×C61—21no—
47C2×Q8×C61—41no—
48C2×Q8×C61—41no—
49#11758226—44no—
50#11758226—82no—
51C2×D244—41no—
52C2×D244—81no—
53C2×C4×D61—81no—
54C2×C4×D61D811yescharacteristic
55Q16×C61—22no—
56Q16×C61—41no—
57Q16×C61—41no—
58Q16×C61—41no—
59C2×C8×C61C2×D411yescharacteristic
60#11758201—44no—
61#11758198—81no—
62C4⋊Dic61—41no—
63#11758196—81no—
64C2×#92418D811yescharacteristic
65D488—22no—
66D488—41no—
67C8×D61—21no—
68C8×D61—21no—
69C16×C61C2×D411yescharacteristic
70C16×C61C2×D411yescharacteristic
71#11758185—21no—
72C22×D61—81no—
73C22×D61D1611yescharacteristic
74Q8×C61—42no—
75Q8×C61—81no—
76Q8×C61—81no—
77Q8×C61—81no—
78C2×C4×C61—81no—
79C2×C4×C61—81no—
80C2×C4×C61C2×D811yescharacteristic
81C2×Dic61—81no—
82C2×Dic61D1611yescharacteristic
83D244—42no—
84D244—84no—
85D244—81no—
86C4×D61—21no—
87C4×D61—21no—
88C4×D61—84no—
89C8×C61#12011yescharacteristic
90C8×C61AGL(1,ℤ/8)11yescharacteristic
91#92418—21no—
92#13666—611nomaximal, Sylow
93C22×C61C2×D1611yescharacteristic
94C2×D61—21no—
95C2×D61—21no—
96C2×D61—21no—
97C2×D61—82no—
98C2×D61—161no—
99C2×D61—161no—
100C4×C61—82no—
101C4×C61—161no—
102C4×C61#44711yescharacteristic
103C4×C61#50911yescharacteristic
104Dic61—21no—
105Dic61—161no—
106C2×#508—611no—
107C2×Q64D6111yescharacteristic, complemented
108C2×SD64—611no—
109#2216—611no—
110#1416—611no—
111#1415—611no—
112C22⋊C32—611no—
113C2×C61#218411yescharacteristic
114C2×C61#226211yescharacteristic
115C2×C61#226411yescharacteristic
116D61—41no—
117D61—162no—
118C2×#135—1221no—
119#508—1222no—
120#508—1222no—
121C2×Q32C2×D6111yescharacteristic
122C2×Q32C2×D6111yescharacteristic
123C2×SD32—1221no—
124C2×D16—611no—
125C22×C16—611no—
126#467—1221no—
127Q64—22no—
128SD64—1222no—
129C2×C32—611no—
130C2×C32C2×D6111yescharacteristic
131#366—611no—
132#358—1221no—
133C61#1366611yescharacteristic, complemented, Sylow
134C2×#41—2441no—
135#135—1224no—
136#135—2442no—
137C2×Q16—21no—
138C2×Q16—21no—
139C2×SD16—2441no—
140C2×D8—1221no—
141C22×C8—611no—
142C22⋊Q8—2441no—
143Q32—21no—
144Q32—21no—
145Q32—21no—
146Q32C22⋊D6112yes—
147SD32—1224no—
148D16—612no—
149D16—1221no—
150C2×C16—611no—
151C2×C16—1221no—
152C2×C16—1221no—
153C2×C16C22×D6111yescharacteristic
154#107—1221no—
155#103—2441no—
156C32—21no—
157C32—1221no—
158#41—4882no—
159#41—2444no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×D4—4881no—
163C2×D4—2441no—
164C22×C4—611no—
165C22×C4—4881no—
166Q16—22no—
167Q16—41no—
168Q16—41no—
169Q16—41no—
170SD16—2444no—
171D8—1222no—
172D8—2441no—
173C2×C8—611no—
174C2×C8—1221no—
175C2×C8—1221no—
176C2×C8D4×D6111yescharacteristic
177C4⋊C4—4881no—
178C4⋊C4—2441no—
179C22⋊C4—4881no—
180C16—1221no—
181C16D4×D6111yescharacteristic
182C16C2×C22⋊D6111yescharacteristic
183C23—611no—
184C23—4881no—
185Q8—42no—
186Q8—81no—
187Q8—81no—
188Q8—81no—
189D4—4884no—
190D4—4881no—
191D4—2442no—
192C2×C4—81no—
193C2×C4—81no—
194C2×C4—611no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—4884no—
198C2×C4—4881no—
199C2×C4D8×D6111yescharacteristic
200C8—1221no—
201C8#1451974511yescharacteristic
202C8#1451980111yescharacteristic
203C22—1221no—
204C22—1221no—
205C22—1221no—
206C22—9761no—
207C22—9761no—
208C22—4882no—
209C22D16×D6111yescharacteristic
210C4—82no—
211C4—161no—
212C4—1221no—
213C4—9761no—
214C4#1683989411yescharacteristic
215C4#1684019611yescharacteristic
216C2—9762no—
217C2—2441no—
218C2#2144772911yescharacteristic
219C2#2144812911yescharacteristic
220C2#2144813811yescharacteristic
subgroupG/H
centerC22D16×D61
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC2×C61×Q64C2
socleC22×C61C2×D16
prime radicalC2×#16840195C2
hypercenterC2×Q64D61
hypocenterC61#13666
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q64

Complements

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

NH ≅ G/Ntype
2. C2×#16839599C2semidirect
3. #21447907C2semidirect
4. #21444000C2semidirect
5. #21443998C2semidirect
6. #21443956C2semidirect
7. C2×C61×Q64C2semidirect
107. C2×Q64D61semidirect
133. C61#13666semidirect

Maximal subgroups

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

subgroupindex
C2×#168401952
C2×#168395992
#214479072
#214440002
#214439982
#214439562
C2×C61×Q642
#1366661