Finite Group Databasebeta

← #29567810

Subgroups — #29567810

Order 15616.

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

normal subgroups only

This group has 266 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#21447504C211yesmaximal, characteristic
2#21446652C211yesmaximal, characteristic
3C61×#2132C211yesmaximal, characteristic
4#16839786C411yescharacteristic
5C2×#14519704—21no—
6C2×#14519704—21no—
7#16839746—21no—
8#16839608C411yescharacteristic
9#16839561—21no—
10#16839559C412yescomplemented
11C61×#532C2211yescharacteristic
12C61×#413—21no—
13C61×#356—21no—
14C61×#355C412yescomplemented
15C2×#11758194—21no—
16C2×#11758194—41no—
17C2×C4×Dic61—21no—
18C4⋊#92418—41no—
19#14519704—42no—
20#14519704—42no—
21#14519696—22no—
22#14519694—41no—
23#14519684—41no—
24C2×#41×C61D411yescharacteristic
25C2×#41×C61D411yescharacteristic
26C2×M16×C61—41no—
27C4⋊Q8×C61D411yescharacteristic
28#127×C61Q811yescharacteristic
29#124×C61C2×C411yescharacteristic
30#124×C61C2×C411yescharacteristic
31#121×C61—41no—
32C4×D4×C61—41no—
33C2×C42×C61C2×C411yescharacteristic
34#101×C61—22no—
35#100×C61—41no—
36#41×C61—41no—
37#41×C61—41no—
38#41×C61—41no—
39#41×C61—41no—
40C2×Q8×C61C22⋊C411yescharacteristic
41C2×Q8×C61C22⋊C411yescharacteristic
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61—41no—
45C2×D4×C61C4⋊C411yescharacteristic
46C2×D4×C61C4⋊C411yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×Dic61—41no—
52M16×C61—42no—
53M16×C61—81no—
54C2×C8×C61—81no—
55C4⋊C4×C61—41no—
56C22⋊C4×C61—41no—
57C22⋊C4×C61—41no—
58C42×C61—21no—
59C42×C61C4211yescharacteristic
60C42×C61C4⋊C411yescharacteristic
61C4×Dic61—22no—
62C4×Dic61—41no—
63#11758194—42no—
64#11758194—41no—
65#11758194—41no—
66#11758194—81no—
67C2×#92418—41no—
68C2×#92418—81no—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61#9911yescharacteristic
72Q8×C61—41no—
73Q8×C61—41no—
74D4×C61—41no—
75D4×C61—41no—
76D4×C61—81no—
77D4×C61—81no—
78D4×C61—82no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—81no—
90C2×C4×C61#9511yescharacteristic
91C2×C4×C61#9911yescharacteristic
92C2×Dic61—42no—
93C2×Dic61—82no—
94C8×C61—82no—
95#92418—82no—
96#92418—81no—
97#7507—611nomaximal, Sylow
98C22×C61—21no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—81no—
103C22×C61—81no—
104C22×C61#34211yescharacteristic
105C4×C61—21no—
106C4×C61—41no—
107C4×C61—41no—
108C4×C61—41no—
109C4×C61—41no—
110C4×C61#35311yescharacteristic
111C4×C61#35411yescharacteristic
112Dic61—82no—
113#2132—611no—
114#2132D6111yescharacteristic
115#1963—611no—
116C2×C61—21no—
117C2×C61—41no—
118C2×C61—81no—
119C2×C61—81no—
120C2×C61#139311yescharacteristic
121#532C2×D6111yescharacteristic
122#423—611no—
123C2×#104—1221no—
124C2×#104—1221no—
125#413—21no—
126#413—1221no—
127#376—611no—
128#356—21no—
129#356—1221no—
130#355—612no—
131#355Dic6112yescomplemented
132C61#750711yescharacteristic, complemented, Sylow
133C2×#41D24411yescharacteristic
134C2×#41C22⋊D6111yescharacteristic
135C2×M16—41no—
136C2×M16—1221no—
137C2×M16—2441no—
138C4⋊Q8C22⋊D6111yescharacteristic
139#127Dic12211yescharacteristic
140#124C4×D6111yescharacteristic
141#124C2×Dic6111yescharacteristic
142#121—41no—
143C4×D4—41no—
144C2×C42—1221no—
145C2×C42C4×D6111yescharacteristic
146C4⋊C8—2441no—
147#104—2442no—
148#104—2442no—
149#101—22no—
150#101—1222no—
151#100—41no—
152#100—2441no—
153#95—2441no—
154#41—41no—
155#41—41no—
156#41—41no—
157#41—41no—
158C2×Q8#1175819811yescharacteristic
159C2×Q8C22⋊Dic6111yescharacteristic
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4#1175819611yescharacteristic
164C2×D4C4⋊Dic6111yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—2441no—
169C22×C4#1175819811yescharacteristic
170M16—42no—
171M16—81no—
172M16—4881no—
173M16—2442no—
174M16—2441no—
175M16—2441no—
176C2×C8—81no—
177C2×C8—4881no—
178C2×C8—2441no—
179C4⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C42—21no—
183C42—1222no—
184C42—2441no—
185C42C4×Dic6111yescharacteristic
186C42#1175819611yescharacteristic
187C23—21no—
188C23—21no—
189C23#1451969111yescharacteristic
190Q8—41no—
191Q8—41no—
192D4—41no—
193D4—41no—
194D4—81no—
195D4—81no—
196D4—82no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4—4882no—
209C2×C4—2442no—
210C2×C4#1451968411yescharacteristic
211C2×C4#1451969111yescharacteristic
212C8—82no—
213C8—4882no—
214C8—4881no—
215C22—21no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—81no—
221C22#1683952811yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—41no—
227C4—4882no—
228C4#1683955411yescharacteristic
229C4#1683955611yescharacteristic
230C2—21no—
231C2—41no—
232C2—81no—
233C2—81no—
234C2#2144394311yescharacteristic
subgroupG/H
centerC4#16839554
commutatorC42×C61C42
Frattini#532C2×D61
FittingC61×#2132C2
socleC2×C61#1393
prime radical, cosocleC61×#532C22
hypercenter#2132D61
hypocenterC61#7507
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #2132

Complements

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

NH ≅ G/Ntype
10. #16839559C4semidirect
14. C61×#355C4semidirect
131. #355Dic61semidirect
132. C61#7507semidirect

Maximal subgroups

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

subgroupindex
#214475042
#214466522
C61×#21322
#750761