Finite Group Databasebeta

← #29589515

Subgroups — #29589515

Order 15616.

334 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 79 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#21454524C211yesmaximal, characteristic
2#21447635C211yesmaximal, characteristic, complemented
3#21443756C212yesmaximal, complemented
4#21443754C212yesmaximal, complemented
5C61×#2166C211yesmaximal, characteristic, complemented
6C2×#14519783C411yescharacteristic
7C22×#11758189C411yescharacteristic
8#16840274C411yescharacteristic
9#16839841—21no—
10#16839841—21no—
11#16839835—21no—
12#16839835—21no—
13#16839789C411yescharacteristic
14#16839730C2211yescharacteristic
15#16839725C2211yescharacteristic
16#16839583—21no—
17#16839544C2212yes—
18#16839540—21no—
19C61×#405C2211yescharacteristic
20C61×#364—21no—
21C61×#349C2212yes—
22C61×#347—21no—
23C2×#11758222C2×C411yescharacteristic
24C22×C4×D61C2×C411yescharacteristic
25#14519783—42no—
26C2×#11758194C2×C411yescharacteristic
27C2×#11758189—21no—
28C2×#11758189—21no—
29C2×#11758189—21no—
30C2×#11758189—42no—
31C22×#92418C2×C411yescharacteristic
32C2×C8×D61—21no—
33#14519761—21no—
34#14519757—21no—
35#14519752—21no—
36#14519747—21no—
37C4×D244—21no—
38C4×D244—21no—
39#14519717—22no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42#14519689—21no—
43#14519689—21no—
44#14519689—21no—
45#14519689—21no—
46C2×M16×C61C2311yescharacteristic
47C22×C8×C61C2×C411yescharacteristic
48#117×C61C2×C411yescharacteristic
49M32×C61—22no—
50#97×C61D411yescharacteristic
51#97×C61D411yescharacteristic
52C4×C8×C61D411yescharacteristic
53C4×C8×C61D411yescharacteristic
54C23×D61M1611yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C2×C22⋊D61—21no—
57C22×Dic61M1611yescharacteristic
58#11758222—41no—
59#11758222—41no—
60C2×D244—21no—
61C2×D244—21no—
62C2×D244M1611yescharacteristic
63C2×C4×D61—21no—
64C2×C4×D61—21no—
65C2×C4×D61—21no—
66C2×C4×D61—41no—
67C2×C4×D61—41no—
68C2×Dic122M1611yescharacteristic
69M16×C61—41no—
70C2×C8×C61—22no—
71C2×C8×C61C22⋊C411yescharacteristic
72C2×C8×C61C22⋊C411yescharacteristic
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C4⋊C4×C61—21no—
76C22⋊C4×C61—21no—
77C42×C61C22⋊C411yescharacteristic
78C42×C61C22⋊C411yescharacteristic
79#11758198—21no—
80#11758198—21no—
81#11758198—21no—
82#11758198—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85#11758194—41no—
86C2×#92418—21no—
87C2×#92418—21no—
88C2×#92418—41no—
89#11758189—42no—
90#11758189—42no—
91#11758189—42no—
92C8×D61—42no—
93C16×C61—42no—
94#11758185—42no—
95C23×C61C2×M1611yescharacteristic
96C22×D61—21no—
97C22×D61—21no—
98C22×D61—41no—
99C22×D61—81no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61C2×C22⋊C411yescharacteristic
105C2×C4×C61C2×M1611yescharacteristic
106C22⋊D61—42no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—41no—
110D244—41no—
111D244—81no—
112D244—81no—
113C4×D61—42no—
114C4×D61—41no—
115C4×D61—41no—
116C4×D61—41no—
117C4×D61—41no—
118Dic122—41no—
119C8×C61—21no—
120C8×C61—21no—
121C8×C61—21no—
122C8×C61#10012yes—
123#92418—41no—
124#92418—41no—
125#11538—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—41no—
128C22×C61#40711yescharacteristic
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—82no—
136C4×C61—21no—
137C4×C61—41no—
138C4×C61—41no—
139C4×C61#41011yescharacteristic
140C4×C61C2×#10011yescharacteristic
141Dic61—41no—
142Dic61—41no—
143#2930—611no—
144#2166—611no—
145#2166D6111yescharacteristic, complemented
146#1321—612no—
147#1320—612no—
148C2×C61—21no—
149C2×C61—41no—
150C2×C61#146611yescharacteristic
151D61—81no—
152D61—81no—
153C2×#131—611no—
154C22×M16—611no—
155#525—611no—
156#436—1221no—
157#436—1221no—
158#435—1221no—
159#435—1221no—
160#424—611no—
161#408—611no—
162#407—611no—
163#405C2×D6111yescharacteristic
164#364—21no—
165#364—1221no—
166#349—612no—
167#349C2×D6112yes—
168#347—21no—
169#347—1221no—
170C61#1153811yescharacteristic, complemented, Sylow
171C2×#41—611no—
172C23×C4—611no—
173#131—2442no—
174C2×M16—611no—
175C2×M16—1221no—
176C2×M16—1221no—
177C2×M16—1221no—
178C2×M16—2442no—
179C2×M16C22×D6111yescharacteristic
180C22×C8—611no—
181C22×C8—1221no—
182C22×C8C4×D6111yescharacteristic
183#123—1221no—
184C22⋊Q8—1221no—
185#121—1221no—
186#120—1221no—
187C4×D4—1221no—
188C4×D4—1221no—
189#117C4×D6111yescharacteristic
190M32—22no—
191M32—1222no—
192C4⋊C8—1221no—
193C4⋊C8—1221no—
194C22⋊C8—1221no—
195C22⋊C8—1221no—
196C22⋊C8—1221no—
197C22⋊C8—1221no—
198#97D24411yescharacteristic
199#97C22⋊D6111yescharacteristic
200C4×C8D24411yescharacteristic
201C4×C8C22⋊D6111yescharacteristic
202C24—611no—
203#41—2441no—
204#41—2441no—
205C2×Q8—611no—
206C2×D4—611no—
207C2×D4—1221no—
208C2×D4—1221no—
209C2×D4—1221no—
210C22×C4—611no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—1221no—
214C22×C4—2441no—
215C22×C4—2441no—
216C22×C4C2×C4×D6111yescharacteristic
217M16—41no—
218M16—2442no—
219M16—2442no—
220M16—2442no—
221M16—2441no—
222C2×C8—22no—
223C2×C8—1221no—
224C2×C8—1221no—
225C2×C8—2442no—
226C2×C8—2441no—
227C2×C8#1175819811yescharacteristic
228C2×C8#1175819811yescharacteristic
229C2×C8C2×D24411yescharacteristic
230C2×C8C2×C22⋊D6111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—1221no—
233C4⋊C4—1221no—
234C22⋊C4—21no—
235C22⋊C4—1221no—
236C22⋊C4—1221no—
237C22⋊C4—1221no—
238C22⋊C4—1221no—
239C42#1175819811yescharacteristic
240C42#1175819811yescharacteristic
241C16—42no—
242C16—2442no—
243C23—1221no—
244C23—1221no—
245C23—4881no—
246C23—2441no—
247C23M16×D6111yescharacteristic
248Q8—2441no—
249D4—4881no—
250D4—4881no—
251D4—2441no—
252D4—2442no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—2442no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4C2×#1175819811yescharacteristic
266C2×C4M16×D6111yescharacteristic
267C8—21no—
268C8—21no—
269C8—21no—
270C8—2441no—
271C8—2441no—
272C8#1451969312yes—
273C22—21no—
274C22—41no—
275C22—4882no—
276C22—2441no—
277C22—2441no—
278C22—2441no—
279C22—2441no—
280C22—2441no—
281C22—2441no—
282C22#1683972511yescharacteristic
283C4—21no—
284C4—41no—
285C4—41no—
286C4—2441no—
287C4—2441no—
288C4#1683973511yescharacteristic
289C4C2×#1451969311yescharacteristic
290C2—21no—
291C2—41no—
292C2—4881no—
293C2—4881no—
294C2#2144415911yescharacteristic
subgroupG/H
centerC4#16839735
commutatorC22×C4×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#2166C2
socleC2×C61#1466
prime radical#16840274C4
cosocleC2×M16×C61C23
hypercenter#2166D61
hypocenterC61#11538
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
2. #21447635C2semidirect
3. #21443756C2semidirect
4. #21443754C2semidirect
5. C61×#2166C2semidirect
145. #2166D61semidirect
170. C61#11538semidirect

Maximal subgroups

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

subgroupindex
#214545242
#214476352
#214437562
#214437542
C61×#21662
#1153861