Finite Group Databasebeta

← #29835580

Subgroups — #29835580

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#21456389C211yesmaximal, characteristic, complemented
2#21448102C211yesmaximal, characteristic, complemented
3#21448083C211yesmaximal, characteristic, complemented
4#21448060C211yesmaximal, characteristic, complemented
5#21448058C211yesmaximal, characteristic, complemented
6#21447930C212yesmaximal, complemented
7#21447920C212yesmaximal, complemented
8C4×#14519721C212yesmaximal, complemented
9C4×#14519718C212yesmaximal, complemented
10C4×#14519717C211yesmaximal, characteristic, complemented
11C61×#3169C211yesmaximal, characteristic, complemented
12#16840296—21no—
13C2×#14519721C2212yes—
14C2×#14519718C2212yes—
15C2×#14519717C2212yes—
16#16840164C2211yescharacteristic
17#16840146C2211yescharacteristic
18#16840117—21no—
19#16840003C2211yescharacteristic
20#16839998C2211yescharacteristic
21#16839991—21no—
22C4×Dic244C2211yescharacteristic
23C4×#11758190—21no—
24C4×D488C2211yescharacteristic
25#16839589C2212yes—
26#16839587C2212yes—
27#16839565C2212yes—
28#16839563C2212yes—
29#16839563C2212yes—
30#16839562C2212yes—
31#16839538C2211yescharacteristic
32#16839538C2211yescharacteristic
33C4×#11758185C2212yes—
34C61×#532—21no—
35C61×#500C2211yescharacteristic
36C61×#493C2211yescharacteristic
37C61×#486—21no—
38C61×#466—21no—
39C61×#466C2212yes—
40C4×D8×C61—21no—
41C4×D8×C61C2212yes—
42C2×C4×C8×C61C2211yescharacteristic
43C2×Dic244C2311yescharacteristic
44C2×#11758190—21no—
45C2×D488C2311yescharacteristic
46#14519771—41no—
47#14519769—21no—
48#14519765—21no—
49#14519760—41no—
50#14519756—21no—
51#14519751—21no—
52C4×Dic122—21no—
53C4×D244—21no—
54C4×C22⋊D61—41no—
55#14519734—41no—
56#14519721—24no—
57#14519718—24no—
58#14519717—24no—
59C2×#11758185C2312yes—
60C2×#11758185C2312yes—
61#14519711C2311yescharacteristic
62#14519711C2311yescharacteristic
63#14519709—21no—
64#14519702—21no—
65#14519702—21no—
66#14519699—21no—
67#14519699—21no—
68C2×#41×C61—41no—
69C2×D8×C61—21no—
70C2×D8×C61C2312yes—
71C22×C8×C61D411yescharacteristic
72C22×C8×C61C2311yescharacteristic
73C4⋊Q8×C61—21no—
74#127×C61—21no—
75#124×C61—41no—
76#121×C61—22no—
77#121×C61—41no—
78C4×D4×C61—22no—
79C4×D4×C61—41no—
80C2×C42×C61D411yescharacteristic
81#107×C61—21no—
82#107×C61C2312yes—
83#102×C61—22no—
84#102×C61—22no—
85C4×C8×C61D411yescharacteristic
86C4×C8×C61D411yescharacteristic
87C4×C8×C61C2311yescharacteristic
88C4×C8×C61C2311yescharacteristic
89#41×C61—84no—
90C2×Q8×C61—41no—
91C2×D4×C61—22no—
92C2×D4×C61—42no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C22×C4×C61—42no—
96C22×C4×C61D811yescharacteristic
97C22×C4×C61D811yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C2×C22⋊D61—41no—
100C2×D244—21no—
101C2×C4×D61—41no—
102C2×Dic122—21no—
103D8×C61—22no—
104D8×C61—22no—
105D8×C61—42no—
106C2×C8×C61—22no—
107C2×C8×C61—22no—
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2×D411yescharacteristic
110C2×C8×C61C2×D411yescharacteristic
111C2×C8×C61C2411yescharacteristic
112C4⋊C4×C61—22no—
113C4⋊C4×C61—41no—
114C22⋊C4×C61—42no—
115C22⋊C4×C61—42no—
116C42×C61D811yescharacteristic
117C42×C61D811yescharacteristic
118C42×C61C2×D411yescharacteristic
119C42×C61C2×D411yescharacteristic
120C22⋊Dic61—41no—
121#11758198—41no—
122#11758198—41no—
123#11758198—41no—
124#11758198—41no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127#11758196—41no—
128#11758196—41no—
129#11758196—41no—
130#11758196—41no—
131C4×Dic61—41no—
132Dic244—22no—
133D488—22no—
134#11758190—42no—
135#11758185—22no—
136#11758185#4114yescomplemented
137C23×C61—42no—
138C23×C61C2×D811yescharacteristic
139C22×D61—41no—
140Q8×C61—82no—
141D4×C61—42no—
142D4×C61—42no—
143D4×C61—82no—
144D4×C61—82no—
145D4×C61—84no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—22no—
149C2×C4×C61—41no—
150C2×C4×C61—42no—
151C2×C4×C61—84no—
152C2×C4×C61C2×D811yescharacteristic
153C2×C4×C61C2×D811yescharacteristic
154C2×C4×C61C2×D811yescharacteristic
155C2×C4×C61C2×D811yescharacteristic
156C2×C4×C61C2×D811yescharacteristic
157C2×C4×C61C22×D411yescharacteristic
158C22⋊D61—82no—
159C2×Dic61—41no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162D244—41no—
163D244—41no—
164C4×D61—82no—
165Dic122—41no—
166Dic122—41no—
167C8×C61—21no—
168C8×C61—21no—
169C8×C61#13512yes—
170C8×C61C2×#4112yes—
171#33737—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—82no—
176C22×C61—82no—
177C22×C61—82no—
178C22×C61C22×D811yescharacteristic
179C2×D61—81no—
180C2×D61—81no—
181C2×D61—81no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—82no—
187C4×C61#50912yes—
188C4×C61#53211yescharacteristic
189C4×C61C2×#13511yescharacteristic
190Dic61—81no—
191Dic61—81no—
192Dic61—81no—
193#3169D6111yescharacteristic, complemented
194#3168—611no—
195#2255—611no—
196#2250—611no—
197#2244—611no—
198#2243—611no—
199#2220—612no—
200#2218—612no—
201C4×SD32—612no—
202C4×D16—612no—
203C4×M32—611no—
204C2×C61—41no—
205C2×C61—162no—
206C2×C61#316911yescharacteristic
207C2×C61C2×#50911yescharacteristic
208C2×C61#341411yescharacteristic
209D61—161no—
210#532—21no—
211#529—1221no—
212C2×SD32—612no—
213C2×D16—612no—
214C2×M32—612no—
215#500C2×D6111yescharacteristic
216#499—611no—
217#495—611no—
218#493C2×D6111yescharacteristic
219#488—1221no—
220#486—21no—
221#467—611no—
222#466—21no—
223#466—611no—
224#466C2×D6112yes—
225#465—1221no—
226C4×Q16—611no—
227C4×SD16—1221no—
228C4×D8—21no—
229C4×D8—611no—
230C4×D8C2×D6112yes—
231C2×C4×C8C2×D6111yescharacteristic
232#367—612no—
233#366—612no—
234#358—612no—
235#357—612no—
236#357—612no—
237#357—612no—
238#346—611no—
239#346—611no—
240C4×C16—612no—
241C61#3373711yescharacteristic, complemented, Sylow
242C2×#41—41no—
243C2×Q16—611no—
244C2×SD16—1221no—
245C2×D8—21no—
246C2×D8—611no—
247C2×D8C22×D6112yes—
248C22×C8C22⋊D6111yescharacteristic
249C22×C8C22×D6111yescharacteristic
250C4⋊Q8—21no—
251#127—21no—
252#126—2441no—
253#125—1221no—
254#124—41no—
255#124—1221no—
256#123—2441no—
257C22⋊Q8—1221no—
258#121—22no—
259#121—41no—
260#121—1221no—
261C4×Q8—1221no—
262C4×D4—22no—
263C4×D4—41no—
264C4×D4—1221no—
265C4×D4—2441no—
266#117—2441no—
267C2×C42C22⋊D6111yescharacteristic
268SD32—1224no—
269D16—1224no—
270M32—1224no—
271C2×C16—612no—
272C2×C16—612no—
273#107—21no—
274#107—611no—
275#107—611no—
276#107C22×D6112yes—
277#106—1221no—
278#103—1221no—
279#103—1221no—
280#102—22no—
281#102—22no—
282#102—1221no—
283#102—1221no—
284C4×C8C22⋊D6111yescharacteristic
285C4×C8C22⋊D6111yescharacteristic
286C4×C8C22×D6111yescharacteristic
287C4×C8C22×D6111yescharacteristic
288#41—84no—
289C2×Q8—41no—
290C2×Q8—1221no—
291C2×D4—22no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—1221no—
296C2×D4—2441no—
297C22×C4—42no—
298C22×C4—2441no—
299C22×C4#1175819911yescharacteristic
300C22×C4#1175819911yescharacteristic
301C22×C4C2×C22⋊D6111yescharacteristic
302Q16—1222no—
303SD16—2442no—
304D8—22no—
305D8—22no—
306D8—42no—
307D8—1222no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8C2×C22⋊D6111yescharacteristic
311C2×C8C2×C22⋊D6111yescharacteristic
312C2×C8C2×C22⋊D6111yescharacteristic
313C2×C8C23×D6111yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2441no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C22⋊C4—2441no—
325C22⋊C4—2441no—
326C22⋊C4—2441no—
327C22⋊C4—2441no—
328C22⋊C4—2441no—
329C42—2441no—
330C42#1175819911yescharacteristic
331C42#1175819911yescharacteristic
332C42C2×C22⋊D6111yescharacteristic
333C42C2×C22⋊D6111yescharacteristic
334C16—614no—
335C16—1222no—
336C23—42no—
337C23—2441no—
338C23C2×#1175819911yescharacteristic
339Q8—82no—
340Q8—2441no—
341Q8—2441no—
342D4—42no—
343D4—42no—
344D4—82no—
345D4—82no—
346D4—84no—
347D4—4882no—
348D4—2441no—
349D4—2441no—
350C2×C4—22no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—84no—
356C2×C4—4882no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4C2×#1175819911yescharacteristic
361C2×C4C2×#1175819911yescharacteristic
362C2×C4C2×#1175819911yescharacteristic
363C2×C4C2×#1175819911yescharacteristic
364C2×C4C2×#1175819911yescharacteristic
365C2×C4C22×C22⋊D6111yescharacteristic
366C8—21no—
367C8—21no—
368C8#1451979712yes—
369C8#41×D6112yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—4881no—
377C22—4881no—
378C22—4881no—
379C22C22×#1175819911yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—4881no—
386C4—4881no—
387C4—4881no—
388C4#1684019812yes—
389C4#1684030811yescharacteristic
390C4C2×#1451979711yescharacteristic
391C2—41no—
392C2—162no—
393C2—9761no—
394C2#2145639411yescharacteristic
395C2C2×#1684019811yescharacteristic
396C2#2145895311yescharacteristic
subgroupG/H
centerC2×C4C2×#11758199
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#3169C2
socleC22×C61C22×D8
hypercenter#3169D61
hypocenterC61#33737
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #21456389C2semidirect
2. #21448102C2semidirect
3. #21448083C2semidirect
4. #21448060C2semidirect
5. #21448058C2semidirect
6. #21447930C2semidirect
7. #21447920C2semidirect
8. C4×#14519721C2semidirect
9. C4×#14519718C2semidirect
10. C4×#14519717C2semidirect
11. C61×#3169C2semidirect
136. #11758185#41semidirect
193. #3169D61semidirect
241. C61#33737semidirect

Maximal subgroups

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

subgroupindex
#214563892
#214481022
#214480832
#214480602
#214480582
#214479302
#214479202
C4×#145197212
C4×#145197182
C4×#145197172
C61×#31692
#3373761