Finite Group Databasebeta

← #29835284

Subgroups — #29835284

Order 15616.

536 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 131 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#21456469C211yesmaximal, characteristic, complemented
2#21454723C211yesmaximal, characteristic, complemented
3#21448034C212yesmaximal, complemented
4#21447996C212yesmaximal, complemented
5#21447896C212yesmaximal, complemented
6#21447767C212yesmaximal, complemented
7#21447719C214yesmaximal, complemented
8C61×#2166C211yesmaximal, characteristic, complemented
9#16840562C2211yescharacteristic
10C2×#14519783—21no—
11#16840367—21no—
12#16840200C2214yes—
13#16840164C2211yescharacteristic, complemented
14#16840139C2211yescharacteristic, complemented
15#16840127—21no—
16#16840015C2212yes—
17#16839998—21no—
18#16839885—21no—
19#16839885C2212yes—
20#16839880—21no—
21#16839880C2212yes—
22#16839875C2212yescomplemented
23C4×D488—21no—
24#16839811C2211yescharacteristic
25#16839780—21no—
26#16839585C2214yescomplemented
27#16839576C2214yescomplemented
28#16839573C2214yes—
29C61×#405C2211yescharacteristic
30C61×#364C2212yescomplemented
31C61×#349C2212yes—
32C61×#347C2212yescomplemented
33C2×#11758222—21no—
34#14519810—22no—
35#14519805—22no—
36#14519799—21no—
37#14519799C2312yes—
38C2×D488—21no—
39C2×D488C2312yes—
40#14519783—22no—
41#14519783—22no—
42#14519783—41no—
43#14519783—41no—
44C2×#11758194—21no—
45C2×#11758189—41no—
46C2×C8×D61—41no—
47#14519774—21no—
48#14519769—21no—
49#14519762—42no—
50#14519751—22no—
51#14519750—42no—
52C4×D244—22no—
53#14519722—24no—
54D976—24no—
55#14519713—21no—
56#14519713C2312yes—
57#14519711—21no—
58#14519709C2312yes—
59#14519705—22no—
60#14519705—22no—
61#14519699—22no—
62#14519699—22no—
63C2×M16×C61C2311yescharacteristic
64C22×C8×C61D411yescharacteristic
65#117×C61D411yescharacteristic
66M32×C61C2314yes—
67#97×C61D411yescharacteristic
68#97×C61C2311yescharacteristic
69C4×C8×C61D411yescharacteristic
70C4×C8×C61C2311yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—41no—
73C2×C22⋊D61—42no—
74#11758222—22no—
75#11758222—22no—
76#11758222—41no—
77#11758222—41no—
78C2×D244—21no—
79C2×D244—22no—
80C2×D244—42no—
81C2×C4×D61—41no—
82C2×C4×D61—42no—
83C2×Dic122—21no—
84M16×C61—22no—
85C2×C8×C61—21no—
86C2×C8×C61—21no—
87C2×C8×C61C2×D411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61C2×D411yescharacteristic
90C2×C8×C61C2411yescharacteristic
91C4⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C42×C61C2×D411yescharacteristic
94C42×C61C2×D411yescharacteristic
95#11758198—42no—
96#11758198—42no—
97C4⋊Dic61—22no—
98#11758196—42no—
99#11758194—22no—
100#11758194—41no—
101C2×#92418—41no—
102Dic244—21no—
103Dic244#4112yes—
104D488—21no—
105D488—24no—
106D488—41no—
107D488—41no—
108D488#4112yes—
109#11758190—22no—
110#11758190—22no—
111#11758189—42no—
112#11758189—42no—
113C8×D61—42no—
114C8×D61—42no—
115C16×C61—24no—
116C23×C61AGL(1,ℤ/8)11yescharacteristic
117C22×D61—41no—
118C22×D61—42no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C61C22×D411yescharacteristic
125C22⋊D61—42no—
126C22⋊D61—42no—
127C22⋊D61—162no—
128C2×Dic61—41no—
129C2×Dic61—42no—
130D244—22no—
131D244—41no—
132D244—42no—
133D244—42no—
134D244—162no—
135C4×D61—42no—
136C4×D61—42no—
137C4×D61—162no—
138Dic122—22no—
139Dic122—41no—
140C8×C61—21no—
141C8×C61—21no—
142C8×C61AGL(1,ℤ/8)11yescharacteristic
143C8×C61AGL(1,ℤ/8)11yescharacteristic
144C8×C61C2×#4112yes—
145#92418—42no—
146#33692—611nomaximal, Sylow
147C22×C61—21no—
148C22×C61—41no—
149C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
150C2×D61—42no—
151C2×D61—82no—
152C2×D61—82no—
153C2×D61—82no—
154C2×D61—82no—
155C4×C61—21no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61#52511yescharacteristic
159C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
160Dic61—42no—
161Dic61—82no—
162#3176—611no—
163#2955—611no—
164#2238—612no—
165#2231—612no—
166#2213—612no—
167#2190—612no—
168AGL(1,ℤ/16)—614no—
169#2166D6111yescharacteristic, complemented
170C2×C61—21no—
171C2×C61—41no—
172C2×C61#310911yescharacteristic
173D61—82no—
174D61—162no—
175#575—611no—
176C2×#131—1221no—
177#540—1221no—
178#509—614no—
179#499—611no—
180#493—611no—
181#490—1221no—
182#469—612no—
183#466—1221no—
184#444—612no—
185#444—1221no—
186#443—612no—
187#443—1221no—
188#442—612no—
189C4×D8—1221no—
190#430—611no—
191#421—1221no—
192#405C2×D6111yescharacteristic
193#365—614no—
194#364C2×D6112yescomplemented
195#361—614no—
196#360—614no—
197#349C2×D6112yes—
198#347C2×D6112yescomplemented
199C61#3369211yescharacteristic, complemented, Sylow
200C2×#41—1221no—
201#137—1222no—
202AGL(1,ℤ/8)—1222no—
203#135—612no—
204#135—1221no—
205C2×D8—612no—
206C2×D8—1221no—
207#131—1222no—
208#131—1222no—
209#131—2441no—
210#131—2441no—
211C2×M16—1221no—
212C2×M16—2441no—
213C2×M16C22×D6111yescharacteristic
214C22×C8—2441no—
215C22×C8D24411yescharacteristic
216#127—1221no—
217#125—1221no—
218#123—2442no—
219#121—1222no—
220#121—2442no—
221C4×D4—1222no—
222#117D24411yescharacteristic
223SD32—1224no—
224D16—1224no—
225M32C22×D6114yes—
226#108—612no—
227#108—1221no—
228#107—1221no—
229#106—612no—
230#104—1222no—
231#104—1222no—
232#102—1222no—
233#102—1222no—
234#97D24411yescharacteristic
235#97C22×D6111yescharacteristic
236C4×C8D24411yescharacteristic
237C4×C8C22×D6111yescharacteristic
238#41—1222no—
239#41—1222no—
240#41—2441no—
241#41—2441no—
242C2×Q8—1221no—
243C2×D4—1221no—
244C2×D4—1222no—
245C2×D4—2442no—
246C2×D4—2442no—
247C2×D4—2441no—
248C22×C4—2442no—
249C22×C4—2441no—
250C22×C4C2×D24411yescharacteristic
251Q16—612no—
252Q16—1221no—
253SD16—1222no—
254SD16—1222no—
255D8—612no—
256D8—1221no—
257D8—1224no—
258D8—2441no—
259D8—2441no—
260M16—22no—
261M16—1222no—
262M16—2442no—
263M16—2441no—
264M16—2442no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—2442no—
268C2×C8—2441no—
269C2×C8—2442no—
270C2×C8C2×D24411yescharacteristic
271C2×C8C2×D24411yescharacteristic
272C2×C8C2×D24411yescharacteristic
273C2×C8C23×D6111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—1222no—
276C4⋊C4—2442no—
277C22⋊C4—21no—
278C22⋊C4—2442no—
279C22⋊C4—2442no—
280C42C2×D24411yescharacteristic
281C42C2×D24411yescharacteristic
282C16—24no—
283C23—2441no—
284C23—2442no—
285C23#1451980511yescharacteristic
286Q8—1222no—
287Q8—2441no—
288D4—1222no—
289D4—9762no—
290D4—9762no—
291D4—2441no—
292D4—2442no—
293D4—2442no—
294D4—2442no—
295D4—2442no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—9762no—
301C2×C4—2442no—
302C2×C4—2442no—
303C2×C4—2441no—
304C2×C4—2442no—
305C2×C4#1451980511yescharacteristic
306C2×C4C22×D24411yescharacteristic
307C8—21no—
308C8—21no—
309C8—2442no—
310C8#1451980511yescharacteristic
311C8#1451980511yescharacteristic
312C8#41×D6112yes—
313C22—21no—
314C22—41no—
315C22—4882no—
316C22—4882no—
317C22—4882no—
318C22—4882no—
319C22—2442no—
320C22C2×#1451980511yescharacteristic
321C4—21no—
322C4—41no—
323C4—41no—
324C4—4882no—
325C4—2442no—
326C4#1684027411yescharacteristic
327C4C2×#1451980511yescharacteristic
328C2—21no—
329C2—41no—
330C2—9762no—
331C2—4882no—
332C2#2145591111yescharacteristic
subgroupG/H
centerC2#21455911
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2166C2
socleC2×C61#3109
hypercenter#2166D61
hypocenterC61#33692
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
1. #21456469C2semidirect
2. #21454723C2semidirect
3. #21448034C2semidirect
4. #21447996C2semidirect
5. #21447896C2semidirect
6. #21447767C2semidirect
7. #21447719C2semidirect
8. C61×#2166C2semidirect
13. #16840164C22semidirect
14. #16840139C22semidirect
22. #16839875C22semidirect
26. #16839585C22semidirect
27. #16839576C22semidirect
30. C61×#364C22semidirect
32. C61×#347C22semidirect
169. #2166D61semidirect
194. #364C2×D61semidirect
198. #347C2×D61semidirect
199. C61#33692semidirect

Maximal subgroups

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

subgroupindex
#214564692
#214547232
#214480342
#214479962
#214478962
#214477672
#214477192
C61×#21662
#3369261