Finite Group Databasebeta

← #29589324

Subgroups — #29589324

Order 15616.

364 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 83 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#21454534C211yesmaximal, characteristic
2#21447438C212yesmaximal, complemented
3#21443769C212yesmaximal, complemented
4#21443757C211yesmaximal, characteristic, complemented
5C61×#1321C211yesmaximal, characteristic, complemented
6C2×#14519785C2211yescharacteristic
7C2×#14519784C411yescharacteristic
8#16840308C411yescharacteristic
9M32×D61—22no—
10#16839836—22no—
11#16839830—22no—
12#16839785C2211yescharacteristic
13#16839728C411yescharacteristic
14C2×#14519687C411yescharacteristic
15#16839544C2212yes—
16#16839543—22no—
17C61×#408C2211yescharacteristic
18C61×#349C2212yes—
19C2×#11758222C2×C411yescharacteristic
20#14519785—42no—
21#14519784—42no—
22C2×#11758194—21no—
23C2×#11758194C2×C411yescharacteristic
24C2×#11758189D412yes—
25C22×#92418—21no—
26C22×#92418C2×C411yescharacteristic
27C2×C8×D61D412yes—
28#14519775C811yescharacteristic
29#14519773C811yescharacteristic
30#14519766C811yescharacteristic
31#14519764C811yescharacteristic
32#14519749—22no—
33C4×C22⋊D61—22no—
34C2×C4×Dic61C2×C411yescharacteristic
35#14519717—22no—
36#14519716—42no—
37C16×D61—42no—
38#14519706—22no—
39#14519689—22no—
40#14519687—21no—
41#14519687—21no—
42C2×#41×C61C2×C411yescharacteristic
43C2×M16×C61C2311yescharacteristic
44C22×C8×C61C2×C411yescharacteristic
45M32×C61—22no—
46C22⋊C8×C61—22no—
47#41×C61—41no—
48#41×C61—41no—
49C2×Q8×C61C2×C811yescharacteristic
50C2×D4×C61—21no—
51C2×D4×C61C2×C811yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61C22×C411yescharacteristic
54C2×C22⋊D61—22no—
55C2×C22⋊D61M1612yes—
56C22×Dic61—21no—
57#11758222—41no—
58#11758222—41no—
59C2×D244C2×C811yescharacteristic
60C2×C4×D61C22⋊C412yes—
61C2×Dic122C2×C811yescharacteristic
62M16×C61—41no—
63C2×C8×C61—21no—
64C2×C8×C61—41no—
65C2×C8×C61C2×D412yes—
66C22⋊Dic61—22no—
67#11758198—22no—
68#11758196—22no—
69C4×Dic61—21no—
70C4×Dic61C2×C811yescharacteristic
71C4×Dic61C2×C811yescharacteristic
72#11758194—42no—
73#11758194—41no—
74C2×#92418—22no—
75C2×#92418—21no—
76C2×#92418—42no—
77C2×#92418C22⋊C411yescharacteristic
78C2×#92418C22⋊C411yescharacteristic
79#11758189—42no—
80C8×D61—22no—
81C8×D61—22no—
82C16×C61—42no—
83#11758185—42no—
84C23×C61—21no—
85C23×C61C2×M1611yescharacteristic
86C22×D61C22⋊C812yes—
87Q8×C61—41no—
88D4×C61—41no—
89D4×C61—42no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61C2×C22⋊C411yescharacteristic
96C2×C4×C61C22×C811yescharacteristic
97C22⋊D61—42no—
98C22⋊D61—82no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—81no—
102C2×Dic61C22⋊C812yes—
103D244—41no—
104C4×D61—22no—
105C4×D61—22no—
106Dic122—41no—
107C8×C61—22no—
108C8×C61—41no—
109#92418—21no—
110#92418—41no—
111#92418#9912yes—
112#11486—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—41no—
115C22×C61—42no—
116C22×C61—41no—
117C22×C61C2×C22⋊C811yescharacteristic
118C2×D61—22no—
119C2×D61—42no—
120C4×C61—21no—
121C4×C61—41no—
122C4×C61C2×#9911yescharacteristic
123C4×C61#41311yescharacteristic
124Dic61—22no—
125Dic61—41no—
126Dic61—41no—
127#2932—611no—
128#2115—612no—
129#1327—612no—
130#1321—611no—
131#1321D6111yescharacteristic, complemented
132C2×C61—21no—
133C2×C61—41no—
134C2×C61—81no—
135C2×C61#145911yescharacteristic
136D61—42no—
137C2×#131—611no—
138C2×#131—611no—
139#532—611no—
140C2×M32—1222no—
141#435—1222no—
142#435—1222no—
143#423—611no—
144#408—611no—
145#408C2×D6111yescharacteristic
146C2×#97—611no—
147#349—612no—
148#349—1222no—
149#349C2×D6112yes—
150C61#1148611yescharacteristic, complemented, Sylow
151C2×#41—611no—
152C2×#41C4×D6111yescharacteristic
153#131—2442no—
154#131—2442no—
155C2×M16—612no—
156C2×M16—611no—
157C2×M16—1221no—
158C2×M16C22×D6111yescharacteristic
159C22×C8—611no—
160C22×C8—612no—
161C22×C8—1221no—
162C22×C8C4×D6111yescharacteristic
163C4⋊Q8—611no—
164#127—611no—
165#124—611no—
166#124—611no—
167#121—1222no—
168C4×D4—1222no—
169C2×C42—611no—
170M32—22no—
171M32—1222no—
172M32—2442no—
173C2×C16—2442no—
174C4⋊C8—1222no—
175C22⋊C8—22no—
176C22⋊C8—1222no—
177#97—1221no—
178#97—1221no—
179#41—41no—
180#41—41no—
181#41—2441no—
182#41—2441no—
183C2×Q8—611no—
184C2×Q8C8×D6111yescharacteristic
185C2×D4—21no—
186C2×D4—612no—
187C2×D4—611no—
188C2×D4—1222no—
189C2×D4C8×D6111yescharacteristic
190C22×C4—21no—
191C22×C4—612no—
192C22×C4—1221no—
193C22×C4C2×C4×D6111yescharacteristic
194M16—41no—
195M16—2442no—
196M16—2442no—
197M16—2441no—
198C2×C8—21no—
199C2×C8—41no—
200C2×C8—611no—
201C2×C8—611no—
202C2×C8—1222no—
203C2×C8—1222no—
204C2×C8—1222no—
205C2×C8—1221no—
206C2×C8—2442no—
207C2×C8D4×D6112yes—
208C4⋊C4—1222no—
209C22⋊C4—1222no—
210C22⋊C4—1222no—
211C42—611no—
212C42—611no—
213C42—1221no—
214C16—42no—
215C16—2442no—
216C23—21no—
217C23—612no—
218C23M16×D6111yescharacteristic
219Q8—41no—
220Q8—2441no—
221D4—41no—
222D4—42no—
223D4—4882no—
224D4—2441no—
225D4—2442no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—612no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—4881no—
237C2×C4C22⋊C4×D6111yescharacteristic
238C2×C4C2×C8×D6111yescharacteristic
239C8—22no—
240C8—41no—
241C8—612no—
242C8—1221no—
243C8—2441no—
244C22—21no—
245C22—41no—
246C22—42no—
247C22—41no—
248C22—1222no—
249C22—2442no—
250C22C22⋊C8×D6111yescharacteristic
251C4—21no—
252C4—41no—
253C4—1222no—
254C4—2441no—
255C4—2441no—
256C4#99×D6111yescharacteristic
257C4#1683974311yescharacteristic
258C2—21no—
259C2—41no—
260C2—81no—
261C2—2442no—
262C2#2144413411yescharacteristic
subgroupG/H
centerC4#99×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×M16C22×D61
FittingC61×#1321C2
socleC2×C61#1459
prime radical#16840308C4
cosocleC2×M16×C61C23
hypercenter#1321D61
hypocenterC61#11486
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #21447438C2semidirect
3. #21443769C2semidirect
4. #21443757C2semidirect
5. C61×#1321C2semidirect
131. #1321D61semidirect
150. C61#11486semidirect

Maximal subgroups

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

subgroupindex
#214545342
#214474382
#214437692
#214437572
C61×#13212
#1148661