Finite Group Databasebeta

← #29834662

Subgroups — #29834662

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×#14519800C211yesmaximal, characteristic
3#21447985C212yesmaximal, complemented
4#21447979C212yesmaximal, complemented
5#21447963C211yesmaximal, characteristic, complemented
6#21447961C211yesmaximal, characteristic, complemented
7#21447957C211yesmaximal, characteristic, complemented
8#21447600C212yesmaximal, complemented
9C4⋊C16×D61C211yesmaximal, characteristic, complemented
10#21447525C212yesmaximal
11C61×#2227C211yesmaximal, characteristic, complemented
12C2×#14519800C2211yescharacteristic
13#16840317—21no—
14C4×#11758226—21no—
15C2×C16×D61C2212yes—
16#16840167C2211yescharacteristic
17#16840163—21no—
18#16840163C2212yes—
19#16840158—21no—
20Q16×Dic61C2211yescharacteristic
21C4×#11758201—21no—
22#16839847—21no—
23C4×D488C2211yescharacteristic
24#16839844C2211yescharacteristic
25#16839799—21no—
26#16839799C2212yes—
27#16839799C2211yescharacteristic
28#16839757—21no—
29C4×C8×D61C2211yescharacteristic
30#16839589C2212yes—
31#16839589C2212yes—
32#16839588C2212yes—
33C4⋊#11758185C2211yescharacteristic
34#16839580C2212yes—
35#16839566C2212yes—
36#16839564C2212yes—
37#16839562C2212yes—
38C61×#500C2211yescharacteristic
39C4×Q16×C61C2211yescharacteristic
40C61×#366C2212yes—
41C61×C4⋊C16C2211yescharacteristic
42C61×#358C2212yes—
43C2×#11758226—21no—
44#14519800—22no—
45#14519800Q814yescomplemented
46C2×#11758201—21no—
47C2×D488C2311yescharacteristic
48C2×C8×D61D411yescharacteristic
49C2×C8×D61C2311yescharacteristic
50#14519777—21no—
51#14519768—22no—
52#14519757—41no—
53#14519753—41no—
54Q8×Dic61—21no—
55Q8×Dic61—41no—
56#14519742—41no—
57C4×D244—21no—
58C4×D244—41no—
59#14519739—21no—
60#14519739—41no—
61#14519735—21no—
62#14519735—22no—
63#14519735—41no—
64C42×D61—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#14519701—21no—
75#14519699—21no—
76#14519697—21no—
77C4×#92418D411yescharacteristic
78C8×Dic61D411yescharacteristic
79C8×Dic61C2311yescharacteristic
80C2×Q16×C61C2311yescharacteristic
81C4⋊Q8×C61—21no—
82C4×Q8×C61—21no—
83C2×C16×C61C2312yes—
84#107×C61—21no—
85#107×C61C2312yes—
86#107×C61C2311yescharacteristic
87#103×C61—21no—
88C4×C8×C61C2311yescharacteristic
89C2×Q8×C61—21no—
90C2×Q8×C61—41no—
91#11758226—24no—
92#11758226—42no—
93C2×D244—21no—
94C2×D244—41no—
95C2×C4×D61—41no—
96C2×C4×D61—41no—
97C2×C4×D61—41no—
98C2×C4×D61D811yescharacteristic
99C2×C4×D61D811yescharacteristic
100C2×C4×D61C2×D411yescharacteristic
101C2×Dic122—41no—
102Q16×C61—21no—
103Q16×C61C2×Q812yes—
104C2×C8×C61C2×D411yescharacteristic
105C2×C8×C61C2411yescharacteristic
106C4⋊C4×C61—21no—
107C4⋊C4×C61—22no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C42×C61—41no—
111C42×C61C2×D411yescharacteristic
112#11758201—24no—
113#11758198—41no—
114#11758198—42no—
115#11758198—41no—
116#11758198—41no—
117C4⋊Dic61—21no—
118C4⋊Dic61—22no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4⋊Dic61—42no—
122#11758196—42no—
123C4×Dic61—41no—
124C4×Dic61—41no—
125C4×Dic61—42no—
126C4×Dic61D811yescharacteristic
127C4×Dic61D811yescharacteristic
128C4×Dic61C2×D411yescharacteristic
129C2×#92418C2×D411yescharacteristic
130C2×#92418C2×D411yescharacteristic
131D488—21no—
132D488C2×Q812yes—
133C8×D61—22no—
134C8×D61C2×Q812yes—
135C8×D61#4112yes—
136C16×C61—22no—
137#11758185—22no—
138C22×D61—41no—
139C22×D61C2×D811yescharacteristic
140Q8×C61—22no—
141Q8×C61—41no—
142Q8×C61—82no—
143C2×C4×C61—41no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61C2×D811yescharacteristic
147C2×C4×C61C2×D811yescharacteristic
148C2×C4×C61C22×D411yescharacteristic
149C2×Dic61—41no—
150C2×Dic61—42no—
151C2×Dic61C2×D811yescharacteristic
152C2×Dic61C2×D811yescharacteristic
153C2×Dic61C2×D811yescharacteristic
154D244—22no—
155D244—44no—
156D244—41no—
157C4×D61—22no—
158C4×D61—41no—
159C4×D61—44no—
160C4×D61—82no—
161C4×D61—82no—
162C4×D61C22⋊Q812yes—
163C4×D61#13712yes—
164Dic122—82no—
165C8×C61—21no—
166C8×C61C22×Q811yescharacteristic
167C8×C61C2×#4111yescharacteristic
168#92418—21no—
169#92418C22⋊Q812yes—
170#33626—611nomaximal, Sylow
171C22×C61C22×D811yescharacteristic
172C2×D61—21no—
173C2×D61—21no—
174C2×D61—42no—
175C2×D61—81no—
176C2×D61—81no—
177C2×D61#47412yes—
178C4×C61—21no—
179C4×C61—42no—
180C4×C61—81no—
181C4×C61—82no—
182C4×C61#50812yes—
183C4×C61C2×C22⋊Q811yescharacteristic
184C4×C61C2×#13711yescharacteristic
185Dic61—21no—
186Dic61—21no—
187Dic61—82no—
188Dic61—81no—
189Dic61#47412yes—
190#3160—611no—
191C4×#135—611no—
192#2229—612no—
193#2228—612no—
194#2227D6111yescharacteristic, complemented
195#2226—611no—
196#2225—611no—
197#2224—611no—
198#2158—612no—
199C2×C4⋊C16—611no—
200#2138—612no—
201C2×C61C2×#47411yescharacteristic
202C2×C61C2×#50811yescharacteristic
203C2×C61#341411yescharacteristic
204D61—22no—
205D61—82no—
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×Q16C2×D6111yescharacteristic
217C4×SD16—1221no—
218C4×SD16—1221no—
219C4×D8—611no—
220C4×D8—611no—
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#358C2×D6112yes—
235#357—612no—
236#357—612no—
237C61#3362611yescharacteristic, complemented, Sylow
238C2×#41—1221no—
239#135—614no—
240#135—1222no—
241C2×Q16C22×D6111yescharacteristic
242C2×SD16—1221no—
243C2×D8—611no—
244C22×C8—611no—
245C22×C8—611no—
246C4⋊Q8—21no—
247C4⋊Q8—1221no—
248#125—1222no—
249C22⋊Q8—2441no—
250C22⋊Q8—2441no—
251C4×Q8—21no—
252C4×Q8—1221no—
253C4×Q8—2441no—
254C4×Q8—2441no—
255C4×D4—1221no—
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—21no—
277#103—1221no—
278#102—1221no—
279#102—1221no—
280C4×C8—611no—
281C4×C8—611no—
282C4×C8—611no—
283C4×C8C22×D6111yescharacteristic
284#41—1224no—
285#41—2442no—
286C2×Q8—21no—
287C2×Q8—41no—
288C2×Q8—2441no—
289C2×D4—1221no—
290C2×D4—2441no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—611no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4—2441no—
297Q16—21no—
298Q16Q8×D6112yes—
299SD16—1224no—
300D8—612no—
301D8—1221no—
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—41no—
313C4⋊C4—1221no—
314C4⋊C4—1222no—
315C4⋊C4—2442no—
316C4⋊C4—2441no—
317C4⋊C4—2442no—
318C4⋊C4—2441no—
319C22⋊C4—2441no—
320C22⋊C4—2441no—
321C22⋊C4—2442no—
322C22⋊C4—2441no—
323C42—41no—
324C42—611no—
325C42—611no—
326C42—611no—
327C42—2441no—
328C42—2441no—
329C42—2442no—
330C42D4×D6111yescharacteristic
331C16—22no—
332C16—1222no—
333C23—611no—
334C23—2441no—
335Q8—22no—
336Q8—41no—
337Q8—82no—
338Q8—4882no—
339D4—1222no—
340D4—2444no—
341D4—2441no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—611no—
346C2×C4—612no—
347C2×C4—612no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1222no—
351C2×C4—4882no—
352C2×C4—4882no—
353C2×C4—2441no—
354C2×C4—2444no—
355C2×C4—2441no—
356C2×C4—2442no—
357C2×C4D8×D6111yescharacteristic
358C2×C4D8×D6111yescharacteristic
359C2×C4C2×D4×D6111yescharacteristic
360C8—21no—
361C8—612no—
362C8—1221no—
363C8C2×Q8×D6111yescharacteristic
364C8#41×D6111yescharacteristic
365C22—612no—
366C22—1221no—
367C22—1221no—
368C22—4881no—
369C22—4881no—
370C22—2442no—
371C22C2×D8×D6111yescharacteristic
372C4—21no—
373C4—42no—
374C4—81no—
375C4—82no—
376C4—612no—
377C4—1221no—
378C4—1221no—
379C4—4881no—
380C4—4882no—
381C4#1684019512yes—
382C4C22⋊Q8×D6111yescharacteristic
383C4#137×D6111yescharacteristic
384C2—1222no—
385C2—4882no—
386C2#474×D6111yescharacteristic
387C2C2×#1684019511yescharacteristic
388C2#2145895111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2227C2
socleC22×C61C22×D8
prime radicalC2×#14519800C22
hypercenter#2227D61
hypocenterC61#33626
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2227

Complements

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

NH ≅ G/Ntype
1. #21456330C2semidirect
3. #21447985C2semidirect
4. #21447979C2semidirect
5. #21447963C2semidirect
6. #21447961C2semidirect
7. #21447957C2semidirect
8. #21447600C2semidirect
9. C4⋊C16×D61C2semidirect
11. C61×#2227C2semidirect
45. #14519800Q8semidirect
194. #2227D61semidirect
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×#145198002
#214479852
#214479792
#214479632
#214479612
#214479572
#214476002
C4⋊C16×D612
#214475252
C61×#22272
#3362661