Finite Group Databasebeta

← #29835583

Subgroups — #29835583

Order 15616.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456396C211yesmaximal, characteristic, complemented
2#21456386C211yesmaximal, characteristic, complemented
3#21448105C211yesmaximal, characteristic, complemented
4#21448060C211yesmaximal, characteristic, complemented
5#21448055C211yesmaximal, characteristic, complemented
6#21447929C212yesmaximal, complemented
7#21447919C212yesmaximal, complemented
8SD32×Dic61C212yesmaximal, complemented
9D16×Dic61C212yesmaximal, complemented
10#21447412C211yesmaximal, characteristic, complemented
11C61×#2250C211yesmaximal, characteristic, complemented
12#16840310—21no—
13#16840291—21no—
14C2×#14519716C2212yes—
15#16840167C2211yescharacteristic
16#16840164C2211yescharacteristic
17#16840116—21no—
18#16840108—21no—
19#16840000C2211yescharacteristic
20#16839995—21no—
21#16839995C2211yescharacteristic
22#16839995C2212yes—
23#16839988—21no—
24Q16×Dic61C2211yescharacteristic
25SD16×Dic61—21no—
26D8×Dic61—21no—
27D8×Dic61C2211yescharacteristic
28D8×Dic61C2212yes—
29C4×C8×D61C2211yescharacteristic
30#16839590C2212yes—
31#16839588C2212yes—
32#16839566C2212yes—
33#16839563C2212yes—
34#16839563C2212yes—
35#16839563C2212yes—
36#16839538C2211yescharacteristic
37C16×Dic61C2212yes—
38C2×SD32×C61C2212yes—
39C2×D16×C61C2212yes—
40C61×#495C2211yescharacteristic
41C61×#493C2211yescharacteristic
42C61×#346C2211yescharacteristic
43C2×#11758224—41no—
44C2×C8×D61D411yescharacteristic
45C2×C8×D61C2311yescharacteristic
46#14519777—21no—
47#14519770—41no—
48#14519769—21no—
49#14519764—41no—
50#14519759—41no—
51#14519753—21no—
52#14519748—21no—
53#14519748—22no—
54#14519748—41no—
55Q8×Dic61—21no—
56D4×Dic61—21no—
57D4×Dic61—22no—
58D4×Dic61—41no—
59#14519737—41no—
60#14519733—41no—
61C42×D61D411yescharacteristic
62#14519716—24no—
63C2×#11758185C2312yes—
64#14519711—21no—
65#14519711C2311yescharacteristic
66#14519711C2312yes—
67#14519711C2311yescharacteristic
68#14519709—21no—
69#14519701—21no—
70#14519701—21no—
71#14519698—21no—
72#14519698—22no—
73#14519698—22no—
74#14519698—21no—
75C4×#92418D411yescharacteristic
76C8×Dic61D411yescharacteristic
77C8×Dic61C2311yescharacteristic
78C2×Q16×C61C2311yescharacteristic
79C2×SD16×C61—21no—
80C2×D8×C61—21no—
81C2×D8×C61C2312yes—
82C2×D8×C61C2311yescharacteristic
83#127×C61—21no—
84#124×C61—21no—
85SD32×C61—24no—
86D16×C61—24no—
87C2×C16×C61C2312yes—
88C4×C8×C61C2311yescharacteristic
89C2×Q8×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—22no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×C22⋊D61—42no—
95C2×C22⋊D61—41no—
96C22×Dic61—42no—
97C22×Dic61—41no—
98#11758224—84no—
99C2×C4×D61D811yescharacteristic
100C2×C4×D61D811yescharacteristic
101C2×C4×D61C2×D411yescharacteristic
102C2×Dic122—41no—
103Q16×C61—22no—
104SD16×C61—42no—
105D8×C61—22no—
106D8×C61—22no—
107D8×C61—22no—
108D8×C61—42no—
109C2×C8×C61C2×D411yescharacteristic
110C2×C8×C61C2411yescharacteristic
111C22⋊C4×C61—41no—
112C22⋊C4×C61—41no—
113C42×C61C2×D411yescharacteristic
114C22⋊Dic61—41no—
115C22⋊Dic61—42no—
116C22⋊Dic61—41no—
117C22⋊Dic61—42no—
118#11758198—41no—
119C4⋊Dic61—22no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—41no—
123C4⋊Dic61—41no—
124#11758196—41no—
125#11758196—41no—
126#11758196—41no—
127C4×Dic61—41no—
128C4×Dic61D811yescharacteristic
129C4×Dic61D811yescharacteristic
130C4×Dic61C2×D411yescharacteristic
131C2×#92418C2×D411yescharacteristic
132C2×#92418C2×D411yescharacteristic
133C8×D61—22no—
134C8×D61—22no—
135C16×C61#4114yescomplemented
136#11758185—22no—
137C23×C61—41no—
138C23×C61—42no—
139C22×D61C2×D811yescharacteristic
140Q8×C61—41no—
141Q8×C61—41no—
142D4×C61—41no—
143D4×C61—42no—
144D4×C61—42no—
145D4×C61—41no—
146D4×C61—82no—
147D4×C61—82no—
148C2×C4×C61—41no—
149C2×C4×C61C2×D811yescharacteristic
150C2×C4×C61C2×D811yescharacteristic
151C2×C4×C61C22×D411yescharacteristic
152C22⋊D61—84no—
153C22⋊D61—82no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—84no—
158C2×Dic61—82no—
159C2×Dic61C2×D811yescharacteristic
160C2×Dic61C2×D811yescharacteristic
161C2×Dic61C2×D811yescharacteristic
162C4×D61—21no—
163C4×D61—21no—
164C4×D61—22no—
165C4×D61—41no—
166Dic122—82no—
167C8×C61#13512yes—
168C8×C61C2×#4112yes—
169#92418—21no—
170#92418—21no—
171#33737—611nomaximal, Sylow
172C22×C61—82no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61—82no—
176C22×C61—82no—
177C22×C61—81no—
178C22×C61C22×D811yescharacteristic
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—81no—
185C4×C61#53211yescharacteristic
186C4×C61C2×#13511yescharacteristic
187Dic61—21no—
188Dic61—21no—
189Dic61—82no—
190Dic61—81no—
191Dic61—81no—
192Dic61#50912yes—
193#3169—611no—
194#3168—611no—
195#2255—611no—
196#2250D6111yescharacteristic, complemented
197#2244—611no—
198#2243—611no—
199#2220—612no—
200#2218—612no—
201C4×SD32—612no—
202C4×D16—612no—
203C4×M32—611no—
204C2×C61—162no—
205C2×C61—161no—
206C2×C61#316911yescharacteristic
207C2×C61C2×#50911yescharacteristic
208C2×C61#341411yescharacteristic
209D61—41no—
210#532—1221no—
211#529—1221no—
212C2×SD32C2×D6112yes—
213C2×D16C2×D6112yes—
214C2×M32—612no—
215#500—611no—
216#499—611no—
217#495C2×D6111yescharacteristic
218#493C2×D6111yescharacteristic
219#488—1221no—
220#486—1221no—
221#467—611no—
222#466—611no—
223#466—612no—
224#466—1221no—
225#465—1221no—
226C4×Q16—611no—
227C4×SD16—1221no—
228C4×D8—611no—
229C4×D8—612no—
230C4×D8—1221no—
231C2×C4×C8—611no—
232#367—612no—
233#366—612no—
234#358—612no—
235#357—612no—
236#357—612no—
237#357—612no—
238#346—611no—
239#346C2×D6111yescharacteristic
240C4×C16—612no—
241C61#3373711yescharacteristic, complemented, Sylow
242C2×#41—2441no—
243C2×Q16C22×D6111yescharacteristic
244C2×SD16—21no—
245C2×D8—21no—
246C2×D8C22×D6112yes—
247C2×D8C22×D6111yescharacteristic
248C22×C8—611no—
249C22×C8—611no—
250C4⋊Q8—1221no—
251#127—21no—
252#126—2441no—
253#125—1221no—
254#124—21no—
255#124—2441no—
256#123—2441no—
257C22⋊Q8—1221no—
258#121—1221no—
259#121—1222no—
260#121—2441no—
261C4×Q8—1221no—
262C4×D4—1221no—
263C4×D4—1222no—
264C4×D4—2441no—
265C4×D4—2441no—
266#117—2441no—
267C2×C42—611no—
268SD32—24no—
269D16—24no—
270M32—1224no—
271C2×C16—612no—
272C2×C16C22×D6112yes—
273#107—611no—
274#107—611no—
275#107—612no—
276#107—1221no—
277#106—1221no—
278#103—1221no—
279#103—1221no—
280#102—1221no—
281#102—1222no—
282#102—1222no—
283#102—1221no—
284C4×C8—611no—
285C4×C8—611no—
286C4×C8—611no—
287C4×C8C22×D6111yescharacteristic
288#41—4884no—
289C2×Q8—21no—
290C2×Q8—2441no—
291C2×D4—21no—
292C2×D4—22no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—2441no—
296C2×D4—2442no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—2441no—
301C22×C4—2442no—
302Q16—22no—
303SD16—42no—
304D8—22no—
305D8—22no—
306D8—22no—
307D8—42no—
308C2×C8—611no—
309C2×C8—611no—
310C2×C8—1222no—
311C2×C8—1222no—
312C2×C8D4×D6111yescharacteristic
313C2×C8C23×D6111yescharacteristic
314C4⋊C4—1222no—
315C4⋊C4—1221no—
316C4⋊C4—1221no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—2441no—
325C22⋊C4—2441no—
326C22⋊C4—2442no—
327C22⋊C4—2441no—
328C22⋊C4—2442no—
329C42—611no—
330C42—611no—
331C42—611no—
332C42—2441no—
333C42D4×D6111yescharacteristic
334C16—1222no—
335C16#1175822414yescomplemented
336C23—41no—
337C23—42no—
338C23—611no—
339Q8—41no—
340Q8—41no—
341Q8—4882no—
342D4—42no—
343D4—41no—
344D4—41no—
345D4—42no—
346D4—82no—
347D4—82no—
348D4—4882no—
349D4—4884no—
350C2×C4—41no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—1222no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—4882no—
358C2×C4—4884no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2442no—
363C2×C4D8×D6111yescharacteristic
364C2×C4D8×D6111yescharacteristic
365C2×C4C2×D4×D6111yescharacteristic
366C8—1221no—
367C8—1221no—
368C8#1451979612yes—
369C8C2×#1175822412yes—
370C22—82no—
371C22—81no—
372C22—82no—
373C22—81no—
374C22—82no—
375C22—81no—
376C22—1221no—
377C22—1221no—
378C22—1221no—
379C22C2×D8×D6111yescharacteristic
380C4—21no—
381C4—21no—
382C4—81no—
383C4—612no—
384C4—1221no—
385C4—1221no—
386C4—4881no—
387C4—4881no—
388C4—4882no—
389C4#1684031011yescharacteristic
390C4C2×#1451979611yescharacteristic
391C2—162no—
392C2—161no—
393C2—2441no—
394C2#2145639611yescharacteristic
395C2#509×D6111yescharacteristic
396C2#2145895111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2250C2
socleC22×C61C22×D8
hypercenter#2250D61
hypocenterC61#33737
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2250

Complements

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

NH ≅ G/Ntype
1. #21456396C2semidirect
2. #21456386C2semidirect
3. #21448105C2semidirect
4. #21448060C2semidirect
5. #21448055C2semidirect
6. #21447929C2semidirect
7. #21447919C2semidirect
8. SD32×Dic61C2semidirect
9. D16×Dic61C2semidirect
10. #21447412C2semidirect
11. C61×#2250C2semidirect
135. C16×C61#41semidirect
196. #2250D61semidirect
241. C61#33737semidirect
335. C16#11758224semidirect

Maximal subgroups

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

subgroupindex
#214563962
#214563862
#214481052
#214480602
#214480552
#214479292
#214479192
SD32×Dic612
D16×Dic612
#214474122
C61×#22502
#3373761