Finite Group Databasebeta

← #29593441

Subgroups — #29593441

Order 15616.

400 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 67 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#21457577C211yesmaximal, characteristic, complemented
2#21447856C211yesmaximal, characteristic, complemented
3#21445171C211yesmaximal, characteristic, complemented
4#21443865C211yesmaximal, characteristic, complemented
5#21443784C211yesmaximal, characteristic, complemented
6#21443775C211yesmaximal, characteristic, complemented
7C61×#2246C211yesmaximal, characteristic, complemented
8C2×#14519796—21no—
9#16840432—21no—
10C2×#14519721—21no—
11#16839995—21no—
12#16839959—21no—
13#16839954—21no—
14#16839904—22no—
15C4×Dic244C2211yescharacteristic
16C8×D244C2211yescharacteristic
17C4⋊#11758185C2211yescharacteristic
18#16839563—21no—
19#16839515C2211yescharacteristic
20#16839506—21no—
21C2×D16×C61—22no—
22C61×#493C2211yescharacteristic
23C61×#493C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×#11758224—22no—
26#14519796—42no—
27#14519796—42no—
28C2×Dic244D411yescharacteristic
29C2×#11758200—22no—
30C2×#11758199—41no—
31C2×C8×D61—21no—
32#14519773—41no—
33#14519749—42no—
34#14519748—22no—
35C4×Dic122—21no—
36C4×D244D411yescharacteristic
37D4×Dic61—41no—
38#14519721—42no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41C4⋊#92418—21no—
42C4⋊#92418D411yescharacteristic
43#14519702—21no—
44#14519698—22no—
45#14519698—41no—
46#14519689—21no—
47C2×D8×C61—21no—
48C2×D8×C61—21no—
49C2×D8×C61—21no—
50C2×D8×C61D412yes—
51#127×C61—21no—
52#127×C61—21no—
53D16×C61—44no—
54C2×C16×C61—21no—
55C4×C8×C61C2311yescharacteristic
56C2×D4×C61—22no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C2×D4×C61—41no—
60C2×D4×C61—41no—
61C2×D4×C61—41no—
62C2×C22⋊D61—42no—
63C2×C22⋊D61—42no—
64C22×Dic61—42no—
65#11758224—44no—
66#11758224—82no—
67C2×D244D811yescharacteristic
68C2×C4×D61—21no—
69C2×Dic122—21no—
70D8×C61—42no—
71D8×C61—42no—
72D8×C61—41no—
73D8×C61—41no—
74D8×C61—41no—
75D8×C61—41no—
76C2×C8×C61C2×D411yescharacteristic
77C2×C8×C61C2×D411yescharacteristic
78C42×C61C2×D411yescharacteristic
79C22⋊Dic61—42no—
80#11758200—44no—
81#11758199—82no—
82#11758198—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61D811yescharacteristic
85#11758196—41no—
86C4×Dic61—41no—
87C2×#92418—21no—
88C2×#92418—41no—
89Dic244—21no—
90Dic244D812yescomplemented
91C8×D61—41no—
92C8×D61—41no—
93C16×C61—22no—
94#11758185—41no—
95C23×C61—42no—
96C23×C61—81no—
97C22×D61—21no—
98D4×C61—42no—
99D4×C61—42no—
100D4×C61—81no—
101D4×C61—81no—
102D4×C61—81no—
103D4×C61—81no—
104D4×C61—81no—
105D4×C61—81no—
106D4×C61—161no—
107D4×C61—161no—
108C2×C4×C61#12011yescharacteristic
109C2×C4×C61C2×D811yescharacteristic
110C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
111C22⋊D61—84no—
112C22⋊D61—162no—
113C2×Dic61—21no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—84no—
117D244—21no—
118D244—21no—
119C4×D61—41no—
120C4×D61—41no—
121Dic122—22no—
122Dic122—41no—
123C8×C61—21no—
124C8×C61C2×D811yescharacteristic
125C8×C61AGL(1,ℤ/8)11yescharacteristic
126#92418—41no—
127#92418—81no—
128#12317—611nomaximal, Sylow
129C22×C61—82no—
130C22×C61—82no—
131C22×C61—82no—
132C22×C61—161no—
133C22×C61—161no—
134C22×C61—161no—
135C22×C61#44711yescharacteristic
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—41no—
139C4×C61—21no—
140C4×C61#44711yescharacteristic
141C4×C61#45311yescharacteristic
142C4×C61#50811yescharacteristic
143C4×C61#50911yescharacteristic
144Dic61—42no—
145Dic61—41no—
146Dic61—81no—
147#3287—611no—
148#2246D6111yescharacteristic, complemented
149#2207—611no—
150#1667—611no—
151#1361—611no—
152#1332—611no—
153D4⋊C16—611no—
154C2×C61—162no—
155C2×C61—321no—
156C2×C61#161911yescharacteristic
157C2×C61#218611yescharacteristic
158C2×C61#219211yescharacteristic
159D61—81no—
160C2×#135—1221no—
161#550—1221no—
162C2×SD32—1221no—
163C2×D16—22no—
164#493C2×D6111yescharacteristic
165#493C2×D6111yescharacteristic
166#466—1221no—
167#460—1221no—
168#459—1221no—
169#449—1222no—
170C4×Q16—611no—
171C8×D4—611no—
172C4⋊C16—611no—
173#357—1221no—
174C4×C16C2×D6111yescharacteristic
175#335—611no—
176#331—1221no—
177C61#1231711yescharacteristic, complemented, Sylow
178C2×#41—1222no—
179#135—2442no—
180#135—2442no—
181C2×Q16—611no—
182C2×SD16—1222no—
183C2×D8—21no—
184C2×D8—21no—
185C2×D8—21no—
186C2×D8—2441no—
187C2×D8C22⋊D6112yes—
188C22×C8—1221no—
189#127—21no—
190#127—21no—
191#127—2441no—
192#121—1222no—
193#121—2442no—
194C4×Q8—1221no—
195C4×D4—611no—
196C4×D4—2441no—
197SD32—2442no—
198D16—44no—
199C2×C16—21no—
200C2×C16—1221no—
201#107—611no—
202C4⋊C8—611no—
203C4⋊C8—1221no—
204#103—1221no—
205#102—1222no—
206#102—2441no—
207C22⋊C8—1221no—
208C4×C8C22×D6111yescharacteristic
209#41—4882no—
210#41—2444no—
211C2×Q8—1221no—
212C2×D4—22no—
213C2×D4—41no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—611no—
219C2×D4—2442no—
220C2×D4—2442no—
221C22×C4—1221no—
222C22×C4—2442no—
223Q16—612no—
224Q16—1221no—
225SD16—2444no—
226D8—42no—
227D8—42no—
228D8—41no—
229D8—41no—
230D8—41no—
231D8—41no—
232D8—4882no—
233C2×C8—1221no—
234C2×C8—2441no—
235C2×C8—2441no—
236C2×C8—2441no—
237C2×C8D4×D6111yescharacteristic
238C2×C8C2×C22⋊D6111yescharacteristic
239C4⋊C4—611no—
240C4⋊C4—1221no—
241C4⋊C4—2441no—
242C22⋊C4—1221no—
243C22⋊C4—2442no—
244C42—2441no—
245C42D4×D6111yescharacteristic
246C16—22no—
247C16—2441no—
248C23—42no—
249C23—81no—
250C23—1221no—
251Q8—1222no—
252Q8—2441no—
253D4—42no—
254D4—42no—
255D4—81no—
256D4—81no—
257D4—81no—
258D4—81no—
259D4—81no—
260D4—81no—
261D4—161no—
262D4—161no—
263D4—1221no—
264D4—1221no—
265D4—9762no—
266D4—4884no—
267C2×C4—1221no—
268C2×C4—4884no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4#1451974511yescharacteristic
274C2×C4D8×D6111yescharacteristic
275C2×C4#1451980111yescharacteristic
276C8—21no—
277C8—4881no—
278C8—2441no—
279C8D8×D6111yescharacteristic
280C8#1451980111yescharacteristic
281C22—82no—
282C22—82no—
283C22—82no—
284C22—161no—
285C22—161no—
286C22—161no—
287C22—2441no—
288C22—2441no—
289C22—2441no—
290C22#1683989411yescharacteristic
291C4—21no—
292C4—4881no—
293C4—2441no—
294C4—2442no—
295C4#1683989411yescharacteristic
296C4#1683992911yescharacteristic
297C4#1684019111yescharacteristic
298C4#1684019611yescharacteristic
299C2—162no—
300C2—321no—
301C2—4881no—
302C2#2144487111yescharacteristic
303C2#2144773911yescharacteristic
304C2#2144777511yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2246C2
socleC22×C61#447
hypercenter#2246D61
hypocenterC61#12317
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. #21457577C2semidirect
2. #21447856C2semidirect
3. #21445171C2semidirect
4. #21443865C2semidirect
5. #21443784C2semidirect
6. #21443775C2semidirect
7. C61×#2246C2semidirect
90. Dic244D8semidirect
148. #2246D61semidirect
177. C61#12317semidirect

Maximal subgroups

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

subgroupindex
#214575772
#214478562
#214451712
#214438652
#214437842
#214437752
C61×#22462
#1231761