Finite Group Databasebeta

← #29593823

Subgroups — #29593823

Order 15616.

418 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 73 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
1D4×D488C211yesmaximal, characteristic
2#21448043C211yesmaximal, characteristic, complemented
3#21447967C211yesmaximal, characteristic, complemented
4#21445218C211yesmaximal, characteristic, complemented
5#21443866C211yesmaximal, characteristic, complemented
6#21443781C211yesmaximal, characteristic, complemented
7C61×D4⋊C16C211yesmaximal, characteristic, complemented
8C22×D488—21no—
9D4×D244—21no—
10#16840167C2211yescharacteristic, complemented
11#16840139C2211yescharacteristic
12#16840052—21no—
13#16839998—21no—
14#16839958—21no—
15#16839898—22no—
16C4×D488C2211yescharacteristic
17#16839590—21no—
18#16839564—21no—
19#16839564—22no—
20#16839515C2211yescharacteristic, complemented
21#16839510—21no—
22C8×D4×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic, complemented
24C4×C16×C61C2211yescharacteristic, complemented
25C22×D244—22no—
26C2×D4×D61—41no—
27C2×D488—22no—
28C2×D488—21no—
29C2×D488—42no—
30C2×D488—42no—
31C2×D488D411yescharacteristic
32C2×D488D412yes—
33#14519777—21no—
34#14519774—21no—
35#14519752—41no—
36#14519751—22no—
37#14519747—42no—
38C4×D244—21no—
39#14519711—21no—
40#14519711—21no—
41#14519711D411yescharacteristic
42#14519708—41no—
43C4⋊#92418—21no—
44#14519699—22no—
45#14519699—21no—
46#14519698—41no—
47C22×C8×C61—21no—
48C4×D4×C61D411yescharacteristic
49C2×C16×C61—21no—
50C2×C16×C61—21no—
51C4⋊C8×C61D411yescharacteristic
52C22⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C23×D61—42no—
55C2×D4×C61D811yescharacteristic
56C22×C4×C61—21no—
57C2×C22⋊D61—42no—
58D4×D61—82no—
59D4×D61—82no—
60C2×D244—21no—
61C2×D244—22no—
62C2×D244—44no—
63C2×D244—42no—
64C2×D244—41no—
65C2×D244—41no—
66C2×D244—82no—
67C2×C4×D61—41no—
68C2×Dic122—41no—
69C2×C8×C61—21no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61C2×D411yescharacteristic
73C2×C8×C61C2×D411yescharacteristic
74C4⋊C4×C61D811yescharacteristic
75C22⋊C4×C61—21no—
76C42×C61C2×D411yescharacteristic
77#11758198—42no—
78#11758198—41no—
79C4⋊Dic61—21no—
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C2×#92418—41no—
83D488—21no—
84D488—42no—
85D488—44no—
86D488—41no—
87D488—41no—
88D488SD1612yes—
89C16×C61—41no—
90C16×C61—41no—
91C23×C61—21no—
92C22×D61—41no—
93C22×D61—42no—
94C22×D61—84no—
95C22×D61—84no—
96C22×D61—162no—
97D4×C61—21no—
98D4×C61SD3212yes—
99C2×C4×C61—21no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61#12011yescharacteristic
103C2×C4×C61C2×D811yescharacteristic
104C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
105C22⋊D61—84no—
106C2×Dic61—41no—
107C2×Dic61—81no—
108D244—22no—
109D244—42no—
110D244—41no—
111D244—42no—
112D244—84no—
113D244—81no—
114D244—81no—
115D244—161no—
116C4×D61—81no—
117C4×D61—81no—
118Dic122—161no—
119C8×C61—21no—
120C8×C61—41no—
121C8×C61C2×SD1611yescharacteristic
122C8×C61AGL(1,ℤ/8)11yescharacteristic
123#92418—81no—
124#12372—611nomaximal, Sylow
125C22×C61—22no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61#44711yescharacteristic
129C2×D61—42no—
130C2×D61—81no—
131C2×D61—81no—
132C2×D61—82no—
133C2×D61—82no—
134C2×D61—82no—
135C2×D61—168no—
136C4×C61—21no—
137C4×C61—41no—
138C4×C61#45011yescharacteristic
139C4×C61#45511yescharacteristic
140C4×C61C2×SD3211yescharacteristic
141C4×C61#50911yescharacteristic
142Dic61—81no—
143Dic61—161no—
144D4×D8—611no—
145#2240—611no—
146#2226—611no—
147#1675—611no—
148#1361—611no—
149#1331—611no—
150D4⋊C16D6111yescharacteristic, complemented
151C2×C61—42no—
152C2×C61#163911yescharacteristic
153C2×C61#218711yescharacteristic
154C2×C61#219211yescharacteristic
155D61—82no—
156D61—162no—
157C22×D8—1221no—
158D42—1221no—
159#500—611no—
160#493—611no—
161#476—1221no—
162#466—1221no—
163#459—1221no—
164#447—1222no—
165C4×D8—611no—
166C8×D4C2×D6111yescharacteristic
167#367—1221no—
168C4⋊C16C2×D6111yescharacteristic, complemented
169#357—1221no—
170#357—1222no—
171C4×C16C2×D6111yescharacteristic, complemented
172#335—611no—
173#333—1221no—
174C61#1237211yescharacteristic, complemented, Sylow
175C22×D4—1222no—
176C22×D4—2441no—
177C2×D8—611no—
178C2×D8—612no—
179C2×D8—1222no—
180C2×D8—1221no—
181C2×D8—2442no—
182C2×D8—2442no—
183C22×C8—21no—
184C4⋊Q8—1221no—
185#127—1221no—
186#121—1222no—
187#121—2441no—
188#120—2442no—
189C4×D4—1221no—
190C4×D4D24411yescharacteristic
191C2×C16—21no—
192C2×C16—21no—
193#107—611no—
194#107—1221no—
195#107—1221no—
196#106—2441no—
197C4⋊C8—1221no—
198C4⋊C8D24411yescharacteristic
199#102—1222no—
200#102—1221no—
201#102—2441no—
202C22⋊C8—21no—
203C4×C8C22×D6111yescharacteristic
204C24—2442no—
205C2×Q8—2441no—
206C2×D4—1221no—
207C2×D4—1222no—
208C2×D4—4882no—
209C2×D4—4882no—
210C2×D4—4882no—
211C2×D4—2442no—
212C2×D4—2444no—
213C2×D4—2442no—
214C2×D4—2441no—
215C2×D4—2441no—
216C2×D4D48811yescharacteristic
217C22×C4—21no—
218C22×C4—2441no—
219D8—612no—
220D8—1221no—
221D8—2442no—
222D8—2444no—
223D8—2441no—
224D8—2441no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—2441no—
229C2×C8D4×D6111yescharacteristic
230C2×C8D4×D6111yescharacteristic
231C4⋊C4—1221no—
232C4⋊C4—2441no—
233C4⋊C4—2441no—
234C4⋊C4D48811yescharacteristic
235C22⋊C4—21no—
236C22⋊C4—2442no—
237C22⋊C4—2441no—
238C42C2×D24411yescharacteristic
239C16—41no—
240C16—41no—
241C23—21no—
242C23—9762no—
243C23—4884no—
244C23—4884no—
245C23—2442no—
246C23—2441no—
247Q8—9761no—
248D4—21no—
249D4—1222no—
250D4—9761no—
251D4—4884no—
252D4—4884no—
253D4—4881no—
254D4—4881no—
255D4—2442no—
256D4—2441no—
257D4—2442no—
258D4#1451972212yes—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—4881no—
263C2×C4—4881no—
264C2×C4—4881no—
265C2×C4—2441no—
266C2×C4#1451974711yescharacteristic
267C2×C4C2×D48811yescharacteristic
268C2×C4#1451980511yescharacteristic
269C8—21no—
270C8—41no—
271C8—4881no—
272C8SD16×D6111yescharacteristic
273C8#1451980111yescharacteristic
274C22—22no—
275C22—41no—
276C22—41no—
277C22—9768no—
278C22—4882no—
279C22—4882no—
280C22—4882no—
281C22—4881no—
282C22—4881no—
283C22—2442no—
284C22#1683989811yescharacteristic
285C4—21no—
286C4—41no—
287C4—9761no—
288C4—4881no—
289C4#1683991411yescharacteristic
290C4#1683994111yescharacteristic
291C4C2×#1451972211yescharacteristic
292C4#1684020011yescharacteristic
293C2—42no—
294C2—9762no—
295C2—4882no—
296C2#2144500011yescharacteristic
297C2#2144775011yescharacteristic
298C2#2144777811yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×D4⋊C16C2
socleC22×C61#447
prime radicalD4×D488C2
hypercenterD4⋊C16D61
hypocenterC61#12372
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4⋊C16

Complements

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

NH ≅ G/Ntype
2. #21448043C2semidirect
3. #21447967C2semidirect
4. #21445218C2semidirect
5. #21443866C2semidirect
6. #21443781C2semidirect
7. C61×D4⋊C16C2semidirect
10. #16840167C22semidirect
20. #16839515C22semidirect
23. C61×C4⋊C16C22semidirect
24. C4×C16×C61C22semidirect
150. D4⋊C16D61semidirect
168. C4⋊C16C2×D61semidirect
171. C4×C16C2×D61semidirect
174. C61#12372semidirect

Maximal subgroups

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

subgroupindex
D4×D4882
#214480432
#214479672
#214452182
#214438662
#214437812
C61×D4⋊C162
#1237261