Finite Group Databasebeta

← #29834652

Subgroups — #29834652

Order 15616.

546 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#21456330C211yesmaximal, characteristic, complemented
2C4×#14519796C211yesmaximal, characteristic
3#21447982C212yesmaximal, complemented
4#21447974C212yesmaximal, complemented
5#21447972C211yesmaximal, characteristic, complemented
6#21447966C211yesmaximal, characteristic, complemented
7#21447958C211yesmaximal, characteristic, complemented
8#21447600C212yesmaximal, complemented
9C4⋊C16×D61C211yesmaximal, characteristic, complemented
10#21447523C212yesmaximal
11C61×#2224C211yesmaximal, characteristic, complemented
12C2×#14519796C2211yescharacteristic
13#16840317—21no—
14C4×#11758224—21no—
15C2×C16×D61C2212yes—
16#16840167C2211yescharacteristic
17#16840163—21no—
18#16840163C2212yes—
19#16840158—21no—
20C4×Dic244C2211yescharacteristic
21#16839856C2211yescharacteristic
22#16839853—21no—
23C4×#11758200—21no—
24D8×Dic61C2211yescharacteristic
25#16839799—21no—
26#16839799C2212yes—
27#16839799C2211yescharacteristic
28#16839755—21no—
29C4×C8×D61C2211yescharacteristic
30#16839589C2212yes—
31#16839589C2212yes—
32#16839588C2212yes—
33C4⋊#11758185C2211yescharacteristic
34#16839580C2212yes—
35#16839567C2212yes—
36#16839565C2212yes—
37#16839563C2212yes—
38C61×#500C2211yescharacteristic
39C4×D8×C61C2211yescharacteristic
40C61×#366C2212yes—
41C61×C4⋊C16C2211yescharacteristic
42C61×#357C2212yes—
43C2×#11758224—21no—
44#14519796—22no—
45#14519796Q814yescomplemented
46C2×Dic244C2311yescharacteristic
47C2×#11758200—21no—
48C2×C8×D61D411yescharacteristic
49C2×C8×D61C2311yescharacteristic
50#14519777—21no—
51#14519768—22no—
52#14519757—41no—
53#14519753—41no—
54Q8×Dic61—41no—
55C4×Dic122—21no—
56#14519742—21no—
57#14519742—41no—
58D4×Dic61—21no—
59C4×C22⋊D61—41no—
60#14519737—41no—
61#14519735—21no—
62#14519735—22no—
63#14519733—41no—
64C2×C4×Dic61—41no—
65C42×D61D411yescharacteristic
66C2×#11758185C2312yes—
67C16×D61—24no—
68#14519711—21no—
69#14519711C2312yes—
70#14519711C2311yescharacteristic
71#14519708—22no—
72#14519708—21no—
73#14519708—22no—
74#14519702—21no—
75#14519700—21no—
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—
93C22×Dic61—41no—
94C22×Dic61—41no—
95#11758224—24no—
96#11758224—42no—
97C2×C4×D61D811yescharacteristic
98C2×C4×D61D811yescharacteristic
99C2×C4×D61C2×D411yescharacteristic
100C2×Dic122—21no—
101C2×Dic122—41no—
102D8×C61—21no—
103D8×C61C2×Q812yes—
104C2×C8×C61C2×D411yescharacteristic
105C2×C8×C61C2411yescharacteristic
106C4⋊C4×C61—21no—
107C4⋊C4×C61—22no—
108C4⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C42×C61C2×D411yescharacteristic
111C22⋊Dic61—41no—
112#11758200—24no—
113#11758198—41no—
114#11758198—42no—
115C4⋊Dic61—21no—
116C4⋊Dic61—22no—
117C4⋊Dic61—41no—
118C4⋊Dic61—42no—
119#11758196—41no—
120#11758196—41no—
121#11758196—42no—
122C4×Dic61—41no—
123C4×Dic61—41no—
124C4×Dic61—41no—
125C4×Dic61—42no—
126C4×Dic61D811yescharacteristic
127C4×Dic61D811yescharacteristic
128C4×Dic61C2×D411yescharacteristic
129C2×#92418C2×D411yescharacteristic
130C2×#92418C2×D411yescharacteristic
131Dic244—21no—
132Dic244C2×Q812yes—
133C8×D61—22no—
134C8×D61C2×Q812yes—
135C8×D61#4112yes—
136C16×C61—22no—
137#11758185—22no—
138C23×C61—41no—
139C22×D61C2×D811yescharacteristic
140Q8×C61—82no—
141D4×C61—22no—
142D4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—82no—
146C2×C4×C61C2×D811yescharacteristic
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61C22×D411yescharacteristic
149C22⋊D61—44no—
150C2×Dic61—41no—
151C2×Dic61—44no—
152C2×Dic61—41no—
153C2×Dic61—42no—
154C2×Dic61—82no—
155C2×Dic61C2×D811yescharacteristic
156C2×Dic61C2×D811yescharacteristic
157C2×Dic61C2×D811yescharacteristic
158C4×D61—22no—
159C4×D61—41no—
160C4×D61C22⋊Q812yes—
161C4×D61#13712yes—
162Dic122—22no—
163Dic122—41no—
164Dic122—82no—
165C8×C61—21no—
166C8×C61C22×Q811yescharacteristic
167C8×C61C2×#4111yescharacteristic
168#92418—21no—
169#92418C22⋊Q812yes—
170#33626—611nomaximal, Sylow
171C22×C61—42no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61C22×D811yescharacteristic
175C2×D61—21no—
176C2×D61—21no—
177C2×D61#47412yes—
178C4×C61—21no—
179C4×C61—81no—
180C4×C61—82no—
181C4×C61#50812yes—
182C4×C61C2×C22⋊Q811yescharacteristic
183C4×C61C2×#13711yescharacteristic
184Dic61—21no—
185Dic61—21no—
186Dic61—42no—
187Dic61—82no—
188Dic61—81no—
189Dic61#47412yes—
190#3160—611no—
191C4×#135—611no—
192#2229—612no—
193#2228—612no—
194#2227—611no—
195#2226—611no—
196#2225—611no—
197#2224D6111yescharacteristic, complemented
198#2158—612no—
199C2×C4⋊C16—611no—
200#2138—612no—
201C2×C61—82no—
202C2×C61C2×#47411yescharacteristic
203C2×C61C2×#50811yescharacteristic
204C2×C61#341411yescharacteristic
205D61—22no—
206C2×#135—611no—
207#533—1221no—
208C4×#41—1221no—
209C22×C16—612no—
210#500—611no—
211#500C2×D6111yescharacteristic
212#499—612no—
213#499—1221no—
214#498—1221no—
215C4×Q16—611no—
216C4×Q16—611no—
217C4×SD16—1221no—
218C4×SD16—1221no—
219C4×D8—611no—
220C4×D8C2×D6111yescharacteristic
221#427—612no—
222#427—611no—
223#427—1221no—
224#416—1221no—
225C2×C4×C8—611no—
226#367—612no—
227#367—612no—
228#366—612no—
229#366C2×D6112yes—
230C4⋊C16—612no—
231C4⋊C16—611no—
232C4⋊C16C2×D6111yescharacteristic
233#358—612no—
234#358—612no—
235#357—612no—
236#357C2×D6112yes—
237C61#3362611yescharacteristic, complemented, Sylow
238C2×#41—1221no—
239#135—614no—
240#135—1222no—
241C2×Q16—611no—
242C2×SD16—1221no—
243C2×D8C22×D6111yescharacteristic
244C22×C8—611no—
245C22×C8—611no—
246C4⋊Q8—21no—
247C4⋊Q8—1221no—
248#125—1222no—
249C22⋊Q8—2441no—
250C22⋊Q8—2441no—
251C4×Q8—1221no—
252C4×Q8—1221no—
253C4×Q8—2441no—
254C4×Q8—2441no—
255C4×D4—21no—
256C4×D4—1221no—
257C4×D4—2441no—
258C4×D4—2441no—
259#117—1221no—
260#117—1222no—
261#117—2441no—
262C2×C42—611no—
263C2×C42—2441no—
264C2×C16—612no—
265C2×C16—1224no—
266C2×C16C22×D6112yes—
267#107—21no—
268#107—612no—
269#107—611no—
270#107—1221no—
271#107C22×D6112yes—
272#107C22×D6111yescharacteristic
273#106—1221no—
274#106—1222no—
275#106—1222no—
276#103—1221no—
277#103—1221no—
278#102—21no—
279#102—1221no—
280C4×C8—611no—
281C4×C8—611no—
282C4×C8—611no—
283C4×C8C22×D6111yescharacteristic
284#41—1224no—
285#41—2442no—
286C2×Q8—41no—
287C2×Q8—1221no—
288C2×Q8—2441no—
289C2×D4—21no—
290C2×D4—2441no—
291C22×C4—41no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—611no—
295C22×C4—2441no—
296C22×C4—2441no—
297Q16—612no—
298Q16—1221no—
299SD16—1224no—
300D8—21no—
301D8Q8×D6112yes—
302C2×C8—611no—
303C2×C8—612no—
304C2×C8—612no—
305C2×C8—611no—
306C2×C8—1222no—
307C2×C8D4×D6111yescharacteristic
308C2×C8C23×D6111yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—1221no—
313C4⋊C4—1222no—
314C4⋊C4—2441no—
315C4⋊C4—2442no—
316C4⋊C4—2442no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C22⋊C4—41no—
320C22⋊C4—2441no—
321C22⋊C4—2442no—
322C22⋊C4—2441no—
323C42—611no—
324C42—611no—
325C42—611no—
326C42—2441no—
327C42—2441no—
328C42—2442no—
329C42—2441no—
330C42D4×D6111yescharacteristic
331C16—22no—
332C16—1222no—
333C23—41no—
334C23—611no—
335Q8—82no—
336Q8—1222no—
337Q8—4882no—
338Q8—2441no—
339D4—22no—
340D4—41no—
341D4—2444no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—82no—
345C2×C4—611no—
346C2×C4—612no—
347C2×C4—612no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1222no—
351C2×C4—4882no—
352C2×C4—2441no—
353C2×C4—2444no—
354C2×C4—2441no—
355C2×C4—2442no—
356C2×C4—2441no—
357C2×C4D8×D6111yescharacteristic
358C2×C4D8×D6111yescharacteristic
359C2×C4C2×D4×D6111yescharacteristic
360C8—21no—
361C8—612no—
362C8—1221no—
363C8C2×Q8×D6111yescharacteristic
364C8#41×D6111yescharacteristic
365C22—42no—
366C22—81no—
367C22—81no—
368C22—612no—
369C22—1221no—
370C22—1221no—
371C22C2×D8×D6111yescharacteristic
372C4—21no—
373C4—81no—
374C4—82no—
375C4—612no—
376C4—1221no—
377C4—1221no—
378C4—4881no—
379C4—4882no—
380C4—2442no—
381C4#1684019112yes—
382C4C22⋊Q8×D6111yescharacteristic
383C4#137×D6111yescharacteristic
384C2—82no—
385C2—1222no—
386C2#474×D6111yescharacteristic
387C2C2×#1684019111yescharacteristic
388C2#2145895411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2224C2
socleC22×C61C22×D8
prime radicalC2×#14519796C22
hypercenter#2224D61
hypocenterC61#33626
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2224

Complements

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

NH ≅ G/Ntype
1. #21456330C2semidirect
3. #21447982C2semidirect
4. #21447974C2semidirect
5. #21447972C2semidirect
6. #21447966C2semidirect
7. #21447958C2semidirect
8. #21447600C2semidirect
9. C4⋊C16×D61C2semidirect
11. C61×#2224C2semidirect
45. #14519796Q8semidirect
197. #2224D61semidirect
237. C61#33626semidirect

Maximal subgroups

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

subgroupindex
#214563302
C4×#145197962
#214479822
#214479742
#214479722
#214479662
#214479582
#214476002
C4⋊C16×D612
#214475232
C61×#22242
#3362661