Finite Group Databasebeta

← #29836366

Subgroups — #29836366

Order 15616.

490 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456406C211yesmaximal, characteristic, complemented
2#21456387C211yesmaximal, characteristic
3#21447986C212yesmaximal, complemented
4#21447968C211yesmaximal, characteristic, complemented
5#21447931C212yesmaximal
6#21447928C212yesmaximal, complemented
7#21447880C212yesmaximal, complemented
8#21447870C211yesmaximal, characteristic, complemented
9#21447864C211yesmaximal, characteristic, complemented
10#21447573C211yesmaximal, characteristic, complemented
11C61×#2226C211yesmaximal, characteristic, complemented
12#16840317—21no—
13#16840294—21no—
14C2×Dic488C2212yes—
15C2×#14519721C2212yes—
16C2×#14519716C2212yes—
17#16840163C2211yescharacteristic
18#16840145C2211yescharacteristic
19#16840142C2211yescharacteristic
20#16840115—21no—
21#16840114—21no—
22#16840004—21no—
23#16840004C2211yescharacteristic
24#16840004C2212yes—
25#16839995C2211yescharacteristic
26#16839990—21no—
27C4×Dic244C2211yescharacteristic
28#16839856—21no—
29#16839856C2212yes—
30C4×#11758200—21no—
31C4×C8×D61C2211yescharacteristic
32#16839587C2212yes—
33C4⋊#11758185C2211yescharacteristic
34#16839580C2212yes—
35#16839567C2212yes—
36#16839565C2212yes—
37#16839565C2212yes—
38C61×#500C2211yescharacteristic
39C4×D8×C61C2211yescharacteristic
40C61×#367C2212yes—
41C61×C4⋊C16C2211yescharacteristic
42C61×#357C2212yes—
43C2×Dic244—21no—
44C2×Dic244C2311yescharacteristic
45C2×Dic244C2312yes—
46C2×#11758200—21no—
47C2×C8×D61D411yescharacteristic
48C2×C8×D61C2311yescharacteristic
49#14519777—21no—
50#14519770—41no—
51#14519768—21no—
52#14519768—41no—
53#14519764—21no—
54#14519759—41no—
55#14519757—21no—
56#14519757—22no—
57#14519753—41no—
58#14519748—21no—
59Q8×Dic61—41no—
60C4×Dic122—21no—
61#14519742—22no—
62C4×C22⋊D61—41no—
63#14519736—41no—
64#14519735—41no—
65C42×D61D411yescharacteristic
66Dic488—42no—
67#14519721—42no—
68#14519716—42no—
69C2×#11758185C2312yes—
70#14519711C2311yescharacteristic
71#14519708—21no—
72#14519702—21no—
73#14519700—22no—
74#14519700—21no—
75#14519700—22no—
76#14519698—21no—
77C4×#92418D411yescharacteristic
78C8×Dic61D411yescharacteristic
79C8×Dic61C2311yescharacteristic
80C2×D8×C61C2311yescharacteristic
81C4⋊Q8×C61—21no—
82C4×D4×C61—21no—
83C2×C16×C61C2312yes—
84#107×C61—21no—
85#107×C61C2312yes—
86#107×C61C2311yescharacteristic
87#102×C61—21no—
88C4×C8×C61C2311yescharacteristic
89C2×Q8×C61—41no—
90C2×D4×C61—21no—
91C22×C4×C61—41no—
92C2×C22⋊D61—41no—
93C2×C4×D61D811yescharacteristic
94C2×C4×D61D811yescharacteristic
95C2×C4×D61C2×D411yescharacteristic
96C2×Dic122—22no—
97C2×Dic122—21no—
98D8×C61—21no—
99D8×C61—21no—
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61C2411yescharacteristic
102C4⋊C4×C61—21no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—41no—
105C22⋊C4×C61—41no—
106C42×C61C2×D411yescharacteristic
107C22⋊Dic61—41no—
108C22⋊Dic61—41no—
109C22⋊Dic61—41no—
110#11758200—42no—
111#11758198—42no—
112#11758198—41no—
113C4⋊Dic61—21no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116C4⋊Dic61—41no—
117C4⋊Dic61—41no—
118C4⋊Dic61—42no—
119#11758196—41no—
120#11758196—41no—
121#11758196—42no—
122C4×Dic61—41no—
123C4×Dic61—42no—
124C4×Dic61D811yescharacteristic
125C4×Dic61D811yescharacteristic
126C4×Dic61C2×D411yescharacteristic
127C2×#92418C2×D411yescharacteristic
128C2×#92418C2×D411yescharacteristic
129Dic244—22no—
130Dic244—21no—
131Dic244—21no—
132Dic244—22no—
133Dic244—42no—
134C8×D61—21no—
135C8×D61—21no—
136C8×D61—41no—
137C16×C61—22no—
138#11758185—22no—
139C23×C61—41no—
140C22×D61C2×D811yescharacteristic
141Q8×C61—82no—
142D4×C61—41no—
143D4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—82no—
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61C2×D811yescharacteristic
149C2×C4×C61C22×D411yescharacteristic
150C22⋊D61—82no—
151C2×Dic61—41no—
152C2×Dic61—42no—
153C2×Dic61—41no—
154C2×Dic61C2×D811yescharacteristic
155C2×Dic61C2×D811yescharacteristic
156C2×Dic61C2×D811yescharacteristic
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—22no—
160C4×D61—41no—
161Dic122—42no—
162Dic122—41no—
163Dic122—42no—
164Dic122—41no—
165C8×C61—21no—
166C8×C61H(5,𝔽2)11yescharacteristic
167C8×C612−1+411yescharacteristic
168#92418—21no—
169#92418—21no—
170#33818—611nomaximal, Sylow
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61C22×D811yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61—21no—
178C4×C61—21no—
179C4×C61—81no—
180C4×C61—82no—
181C4×C61#51012yes—
182C4×C61#53711yescharacteristic
183C4×C61#57511yescharacteristic
184Dic61—21no—
185Dic61—21no—
186Dic61—21no—
187Dic61—81no—
188Dic61—82no—
189Dic61—81no—
190#3170—611no—
191#3168—611no—
192#2229—612no—
193#2227—611no—
194#2226D6111yescharacteristic, complemented
195#2220—612no—
196#2219—612no—
197#2211—612no—
198#2209—611no—
199#2208—611no—
200#2150—611no—
201C2×C61—161no—
202C2×C61#324511yescharacteristic
203C2×C61C2×#51011yescharacteristic
204C2×C61#341411yescharacteristic
205D61—41no—
206#533—1221no—
207#529—1221no—
208C2×Q32—612no—
209C2×SD32—612no—
210C2×M32—612no—
211#500C2×D6111yescharacteristic
212#499—611no—
213#495—611no—
214#494—611no—
215#488—1221no—
216#487—1221no—
217#467—611no—
218#467—612no—
219#467—1221no—
220#466—611no—
221#465—1221no—
222C4×Q16—612no—
223C4×Q16—611no—
224C4×Q16—1221no—
225C4×SD16—1221no—
226C4×D8C2×D6111yescharacteristic
227C2×C4×C8—611no—
228#367C2×D6112yes—
229#366—612no—
230C4⋊C16—612no—
231C4⋊C16—611no—
232C4⋊C16C2×D6111yescharacteristic
233#358—612no—
234#358—612no—
235#358—612no—
236#357C2×D6112yes—
237C61#3381811yescharacteristic, complemented, Sylow
238C2×Q16—612no—
239C2×Q16—611no—
240C2×Q16—1221no—
241C2×SD16—1221no—
242C2×D8C22×D6111yescharacteristic
243C22×C8—611no—
244C22×C8—611no—
245C4⋊Q8—21no—
246C4⋊Q8—1221no—
247#126—2441no—
248#125—1221no—
249#125—2441no—
250#124—1221no—
251#123—2441no—
252C22⋊Q8—1221no—
253C22⋊Q8—1222no—
254C22⋊Q8—2441no—
255#121—1221no—
256C4×Q8—1222no—
257C4×Q8—1221no—
258C4×Q8—2441no—
259C4×D4—21no—
260C4×D4—2441no—
261#117—2441no—
262#117—2441no—
263C2×C42—611no—
264Q32—2442no—
265SD32—2442no—
266M32—2442no—
267C2×C16—612no—
268C2×C16C22×D6112yes—
269#107—21no—
270#107—611no—
271#107C22×D6112yes—
272#107C22×D6111yescharacteristic
273#106—1221no—
274#103—1221no—
275#103—1222no—
276#103—1222no—
277#103—1221no—
278#102—21no—
279#102—1221no—
280C4×C8—611no—
281C4×C8—611no—
282C4×C8—611no—
283C4×C8C22×D6111yescharacteristic
284C2×Q8—41no—
285C2×Q8—1221no—
286C2×Q8—1222no—
287C2×D4—21no—
288C2×D4—2441no—
289C22×C4—41no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293Q16—1222no—
294Q16—1221no—
295Q16—1222no—
296Q16—1221no—
297Q16—2442no—
298SD16—2442no—
299D8—21no—
300D8—21no—
301C2×C8—611no—
302C2×C8—611no—
303C2×C8—1221no—
304C2×C8—1221no—
305C2×C8—2441no—
306C2×C8D4×D6111yescharacteristic
307C2×C8C23×D6111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—1221no—
312C4⋊C4—2441no—
313C4⋊C4—2442no—
314C4⋊C4—2441no—
315C4⋊C4—2441no—
316C4⋊C4—2442no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C4⋊C4—2441no—
320C22⋊C4—41no—
321C22⋊C4—2442no—
322C22⋊C4—2441no—
323C22⋊C4—2441no—
324C22⋊C4—2441no—
325C22⋊C4—2441no—
326C42—611no—
327C42—611no—
328C42—611no—
329C42—2442no—
330C42—2441no—
331C42D4×D6111yescharacteristic
332C16—22no—
333C16—1222no—
334C23—41no—
335C23—611no—
336Q8—82no—
337Q8—2441no—
338Q8—2442no—
339Q8—2442no—
340Q8—2441no—
341D4—41no—
342D4—41no—
343D4—4882no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—82no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1222no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—2441no—
354C2×C4—2441no—
355C2×C4—2441no—
356C2×C4—2442no—
357C2×C4D8×D6111yescharacteristic
358C2×C4D8×D6111yescharacteristic
359C2×C4C2×D4×D6111yescharacteristic
360C8—21no—
361C8—1221no—
362C8—1221no—
363C8#1451982311yescharacteristic
364C8#1451982511yescharacteristic
365C22—81no—
366C22—81no—
367C22—81no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22C2×D8×D6111yescharacteristic
372C4—21no—
373C4—81no—
374C4—82no—
375C4—1221no—
376C4—1221no—
377C4—1221no—
378C4—4881no—
379C4—4881no—
380C4—4882no—
381C4#1684020112yes—
382C4#1684034211yescharacteristic
383C4#1684056111yescharacteristic
384C2—161no—
385C2—2441no—
386C2#2145712811yescharacteristic
387C2C2×#1684020111yescharacteristic
388C2#2145895111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2226C2
socleC22×C61C22×D8
prime radical#16839995C22
hypercenter#2226D61
hypocenterC61#33818
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. #21456406C2semidirect
3. #21447986C2semidirect
4. #21447968C2semidirect
6. #21447928C2semidirect
7. #21447880C2semidirect
8. #21447870C2semidirect
9. #21447864C2semidirect
10. #21447573C2semidirect
11. C61×#2226C2semidirect
194. #2226D61semidirect
237. C61#33818semidirect

Maximal subgroups

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

subgroupindex
#214564062
#214563872
#214479862
#214479682
#214479312
#214479282
#214478802
#214478702
#214478642
#214475732
C61×#22262
#3381861