Finite Group Databasebeta

← #29835389

Subgroups — #29835389

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840163C211yesmaximal, characteristic, complemented
2#21456243C211yesmaximal, characteristic
3#21448063C212yesmaximal, complemented
4#21448059C212yesmaximal, complemented
5#21448052C212yesmaximal, complemented
6#21448049C212yesmaximal, complemented
7#21447532C211yesmaximal, characteristic, complemented
8#21447531C211yesmaximal, characteristic, complemented
9#21447529C211yesmaximal, characteristic, complemented
10M32×Dic61C211yesmaximal, characteristic, complemented
11C61×#2139C211yesmaximal, characteristic, complemented
12C2×#14519799C2211yescharacteristic
13C2×#14519797—21no—
14#16840308—21no—
15C2×#14519768—21no—
16C2×#14519717C2211yescharacteristic
17#16840163—21no—
18#16840163—21no—
19#16840163C2212yes—
20#16840163C2212yes—
21#16840147C2211yescharacteristic
22#16840145C2211yescharacteristic
23#16840143—21no—
24#16840140C2211yescharacteristic
25#16840137C2211yescharacteristic
26#16840133—21no—
27C2×#14519711C2211yescharacteristic
28C2×#14519708—21no—
29C2×C8×Dic61C2211yescharacteristic
30#16839567C2212yes—
31#16839566C2212yes—
32#16839565C2212yes—
33#16839564C2212yes—
34#16839563C2212yes—
35#16839562C2212yes—
36#16839537C2212yes—
37C16×Dic61C2212yes—
38C2×#135×C61C2211yescharacteristic
39C2×M32×C61C2211yescharacteristic
40C2×#107×C61C2211yescharacteristic
41C61×#358C2212yes—
42C61×#357C2212yes—
43C2×#11758222—21no—
44#14519799—22no—
45#14519799—22no—
46#14519797—44no—
47C2×Dic244C2311yescharacteristic
48C2×#11758202—21no—
49C2×#11758190—21no—
50C2×#11758200—21no—
51C2×#11758201—21no—
52C2×D488C2311yescharacteristic
53C2×#11758199—21no—
54C22×#92418D411yescharacteristic
55#14519775—21no—
56#14519773—21no—
57#14519768—22no—
58#14519768—22no—
59#14519768—41no—
60#14519768—41no—
61#14519766—21no—
62#14519764—21no—
63#14519749—41no—
64#14519749—41no—
65C4×C22⋊D61—41no—
66C4×C22⋊D61—41no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—41no—
69C2×#11758196—41no—
70C2×C4×Dic61D411yescharacteristic
71#14519717—22no—
72C2×#11758185C2312yes—
73#14519711—21no—
74#14519711C2312yes—
75#14519708—22no—
76#14519708—22no—
77C8×Dic61D411yescharacteristic
78C8×Dic61D411yescharacteristic
79C8×Dic61C2311yescharacteristic
80C8×Dic61C2311yescharacteristic
81C2×#41×C61—21no—
82#135×C61—22no—
83#135×C61—22no—
84C2×Q16×C61C2311yescharacteristic
85C2×SD16×C61—21no—
86C2×D8×C61C2311yescharacteristic
87C22×C8×C61C2311yescharacteristic
88C2×C4⋊C4×C61—21no—
89M32×C61—22no—
90C2×C16×C61C2312yes—
91#107×C61—21no—
92#107×C61C2312yes—
93#41×C61—42no—
94#41×C61—42no—
95C2×Q8×C61—21no—
96C2×D4×C61—21no—
97C2×D4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61C2×D411yescharacteristic
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—41no—
104C22×Dic61—41no—
105C22×Dic61D811yescharacteristic
106C22×Dic61D811yescharacteristic
107#11758222—42no—
108#11758222—42no—
109C2×D244—21no—
110C2×C4×D61—41no—
111C2×Dic122—21no—
112Q16×C61—21no—
113Q16×C61—21no—
114SD16×C61—42no—
115D8×C61—21no—
116D8×C61—21no—
117C2×C8×C61C2×D411yescharacteristic
118C2×C8×C61#4112yes—
119C2×C8×C61#4112yes—
120C2×C8×C61C2411yescharacteristic
121C4⋊C4×C61—22no—
122C4⋊C4×C61—41no—
123C22⋊Dic61—41no—
124C22⋊Dic61—41no—
125#11758202—42no—
126#11758201—42no—
127#11758200—42no—
128#11758199—42no—
129#11758198—41no—
130#11758198—41no—
131C4⋊Dic61—22no—
132C4⋊Dic61—41no—
133C4⋊Dic61—42no—
134C4⋊Dic61—42no—
135#11758196—42no—
136#11758196—42no—
137#11758196—41no—
138#11758196—41no—
139C4×Dic61D811yescharacteristic
140C4×Dic61D811yescharacteristic
141C4×Dic61C2×D411yescharacteristic
142C4×Dic61C2×D411yescharacteristic
143C2×#92418SD1614yes—
144C2×#92418C2×D411yescharacteristic
145C2×#92418C2×D411yescharacteristic
146Dic244—21no—
147Dic244—21no—
148D488—21no—
149D488—21no—
150#11758190—42no—
151C16×C61—22no—
152#11758185—22no—
153C23×C61—41no—
154C23×C61C2×D811yescharacteristic
155C22×D61—41no—
156Q8×C61—41no—
157Q8×C61—41no—
158D4×C61—41no—
159D4×C61—41no—
160D4×C61—82no—
161C2×C4×C61—42no—
162C2×C4×C61—41no—
163C2×C4×C61—82no—
164C2×C4×C61—82no—
165C2×C4×C61#12412yes—
166C2×C4×C61C2×D811yescharacteristic
167C2×C4×C61C2×SD1612yes—
168C2×C4×C61C22×D411yescharacteristic
169C22⋊D61—82no—
170C22⋊D61—82no—
171C22⋊D61—82no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—42no—
175C2×Dic61—41no—
176C2×Dic61—82no—
177C2×Dic61C2×D811yescharacteristic
178C2×Dic61C2×D811yescharacteristic
179C2×Dic61C2×D811yescharacteristic
180C2×Dic61C2×D811yescharacteristic
181D244—41no—
182D244—41no—
183C4×D61—82no—
184Dic122—41no—
185Dic122—41no—
186C8×C61#12412yes—
187C8×C61C2×#4111yescharacteristic
188C8×C61C2×#4111yescharacteristic
189#92418C2×SD1612yes—
190#92418C2×SD1612yes—
191#33708—611nomaximal, Sylow
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—81no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61#48612yes—
198C22×C61C22×D811yescharacteristic
199C2×D61—81no—
200C2×D61—81no—
201C2×D61—81no—
202C4×C61—81no—
203C4×C61—82no—
204C4×C61#48612yes—
205C4×C61C2×#12411yescharacteristic
206C4×C61C22×SD1611yescharacteristic
207Dic61—21no—
208Dic61—21no—
209Dic61—21no—
210Dic61—21no—
211Dic61—81no—
212Dic61—82no—
213C2×#499—611no—
214#3147—611no—
215#2245—612no—
216#2244—612no—
217#2242—612no—
218#2242—612no—
219#2139—611no—
220#2139—611no—
221#2139—611no—
222#2139D6111yescharacteristic, complemented
223C4×M32—611no—
224C2×C61—22no—
225C2×C61—161no—
226C2×C61C2×#48611yescharacteristic
227C2×C61#341411yescharacteristic
228C2×C61#341411yescharacteristic
229D61—161no—
230C2×#135—611no—
231C2×#135—1221no—
232C2×#135C2×D6111yescharacteristic
233#532—1221no—
234C2×#125—1221no—
235C2×M32—611no—
236C2×M32C2×D6111yescharacteristic
237#499—612no—
238#499—612no—
239#499—1221no—
240#499—1221no—
241#495—611no—
242#495—611no—
243#495—1221no—
244#494—611no—
245#493—611no—
246#492—1221no—
247C2×#107—611no—
248C2×#107C2×D6111yescharacteristic
249C2×#106—1221no—
250C2×C4×C8—611no—
251#358—612no—
252#358—612no—
253#358—612no—
254#358C2×D6112yes—
255#357—612no—
256#357—612no—
257#357—612no—
258#357C2×D6112yes—
259#346—612no—
260C4×C16—612no—
261C61#3370811yescharacteristic, complemented, Sylow
262C2×#41—21no—
263C2×#41—1221no—
264#135—22no—
265#135—22no—
266#135—1222no—
267#135—1222no—
268#135—2444no—
269C2×Q16—611no—
270C2×Q16—1221no—
271C2×Q16C22×D6111yescharacteristic
272C2×SD16—21no—
273C2×SD16—1221no—
274C2×SD16—1221no—
275C2×SD16—1221no—
276C2×D8—611no—
277C2×D8—1221no—
278C2×D8C22×D6111yescharacteristic
279C22×C8—611no—
280C22×C8C22×D6111yescharacteristic
281C4⋊Q8—1221no—
282#127—1221no—
283#125—1222no—
284#125—1222no—
285#125—2441no—
286#125—2441no—
287#124—1221no—
288#124—1221no—
289#121—2441no—
290#121—2441no—
291C4×D4—2441no—
292C4×D4—2441no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—1221no—
295C2×C4⋊C4—2441no—
296C2×C4⋊C4—2441no—
297C2×C42—611no—
298M32—22no—
299M32—1222no—
300C2×C16—612no—
301C2×C16C22×D6112yes—
302#107—21no—
303#107—612no—
304#107—1221no—
305#107C22×D6112yes—
306#106—1222no—
307#106—1222no—
308C4×C8—611no—
309C4×C8—611no—
310C4×C8—611no—
311C4×C8—611no—
312#41—42no—
313#41—42no—
314#41—2442no—
315#41—2442no—
316C2×Q8—21no—
317C2×Q8—1221no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4—1221no—
321C2×D4—2441no—
322C2×D4—2441no—
323C2×D4—2441no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—611no—
327C22×C4—611no—
328C22×C4—2441no—
329C22×C4—2441no—
330C22×C4D4×D6111yescharacteristic
331Q16—21no—
332Q16—21no—
333Q16—1221no—
334Q16—1221no—
335Q16—2442no—
336SD16—42no—
337SD16—2442no—
338SD16—2442no—
339SD16—2442no—
340D8—21no—
341D8—21no—
342D8—1221no—
343D8—1221no—
344D8—2442no—
345C2×C8—611no—
346C2×C8—611no—
347C2×C8—614no—
348C2×C8#1175822212yes—
349C2×C8D4×D6111yescharacteristic
350C2×C8#1175822412yes—
351C2×C8C23×D6111yescharacteristic
352C4⋊C4—22no—
353C4⋊C4—41no—
354C4⋊C4—1222no—
355C4⋊C4—2442no—
356C4⋊C4—2442no—
357C4⋊C4—2442no—
358C4⋊C4—2442no—
359C4⋊C4—2441no—
360C4⋊C4—2441no—
361C4⋊C4—2441no—
362C22⋊C4—2441no—
363C22⋊C4—2441no—
364C22⋊C4—2441no—
365C22⋊C4—2441no—
366C42—611no—
367C42—611no—
368C42—611no—
369C42—611no—
370C16—22no—
371C16—1222no—
372C23—41no—
373C23—2441no—
374C23D8×D6111yescharacteristic
375Q8—41no—
376Q8—41no—
377Q8—2441no—
378Q8—2441no—
379D4—41no—
380D4—41no—
381D4—82no—
382D4—4882no—
383D4—4882no—
384D4—4882no—
385D4—2441no—
386D4—2441no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—82no—
390C2×C4—82no—
391C2×C4—611no—
392C2×C4—611no—
393C2×C4—611no—
394C2×C4—611no—
395C2×C4—4882no—
396C2×C4—4882no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2441no—
400C2×C4—2442no—
401C2×C4#1451976312yes—
402C2×C4D8×D6111yescharacteristic
403C2×C4SD16×D6112yes—
404C2×C4C2×D4×D6111yescharacteristic
405C8—612no—
406C8—612no—
407C8#1451976312yes—
408C8C2×#1175822411yescharacteristic
409C8C2×#1175822211yescharacteristic
410C22—21no—
411C22—21no—
412C22—81no—
413C22—81no—
414C22—81no—
415C22—4881no—
416C22—4881no—
417C22—4881no—
418C22#1684010712yes—
419C22C2×D8×D6111yescharacteristic
420C4—82no—
421C4—81no—
422C4—1221no—
423C4—1221no—
424C4—1221no—
425C4—1221no—
426C4—4882no—
427C4—4881no—
428C4#1684010712yes—
429C4C2×#1451976311yescharacteristic
430C4C2×SD16×D6111yescharacteristic
431C2—22no—
432C2—161no—
433C2—9761no—
434C2C2×#1684010711yescharacteristic
435C2#2145895111yescharacteristic
436C2#2145895411yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2139C2
socleC22×C61C22×D8
prime radical#21456243C2
hypercenter#2139D61
hypocenterC61#33708
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2139

Complements

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

NH ≅ G/Ntype
1. C2×#16840163C2semidirect
3. #21448063C2semidirect
4. #21448059C2semidirect
5. #21448052C2semidirect
6. #21448049C2semidirect
7. #21447532C2semidirect
8. #21447531C2semidirect
9. #21447529C2semidirect
10. M32×Dic61C2semidirect
11. C61×#2139C2semidirect
222. #2139D61semidirect
261. C61#33708semidirect

Maximal subgroups

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

subgroupindex
C2×#168401632
#214562432
#214480632
#214480592
#214480522
#214480492
#214475322
#214475312
#214475292
M32×Dic612
C61×#21392
#3370861