Finite Group Databasebeta

← #29663438

Subgroups — #29663438

Order 15616.

630 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456791C212yesmaximal, complemented
2#21456398C211yesmaximal, characteristic, complemented
3#21445337C211yesmaximal, characteristic, complemented
4#21445332C211yesmaximal, characteristic, complemented
5#21445303C211yesmaximal, characteristic, complemented
6#21445298C211yesmaximal, characteristic, complemented
7#21445263C212yesmaximal, complemented
8#21445256C212yesmaximal, complemented
9#21444567C211yesmaximal, characteristic, complemented
10#21444525C212yesmaximal, complemented
11C61×#2966C211yesmaximal, characteristic, complemented
12#16840312C2212yes—
13#16840167C2211yescharacteristic
14#16840144—22no—
15#16840139C2211yescharacteristic
16#16840119—22no—
17#16840109C2212yes—
18#16839998—21no—
19#16839998—21no—
20#16839972C2212yes—
21#16839967C2212yes—
22#16839962C2212yes—
23#16839957C2212yes—
24#16839922—22no—
25#16839905—22no—
26C4×D488—21no—
27C4×D488—21no—
28#16839815C2212yes—
29#16839515C2212yes—
30#16839513C2211yescharacteristic
31#16839513C2211yescharacteristic
32#16839507C2212yes—
33#16839507C2212yes—
34#16839505C2212yes—
35#16839505C2212yes—
36C61×#529C2211yescharacteristic
37C61×#446C2211yescharacteristic
38C8×Q8×C61C2211yescharacteristic
39C61×#436C2211yescharacteristic
40C61×#435—21no—
41C8×D4×C61—21no—
42C8×D4×C61C2211yescharacteristic
43C61×#433—21no—
44C61×#432C2211yescharacteristic
45C61×#405—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×#11758222—22no—
48C2×#11758202—22no—
49C2×#11758200—22no—
50C2×#11758201—22no—
51C2×D488—21no—
52C2×D488—21no—
53C2×#11758199—22no—
54#14519777C2312yes—
55#14519774C2312yes—
56#14519765—22no—
57#14519751—22no—
58#14519751—22no—
59C4×D244—22no—
60C4×D244—22no—
61#14519711—21no—
62#14519711—21no—
63C4⋊#92418C2312yes—
64C4⋊#92418C2312yes—
65#14519700—22no—
66#14519700—22no—
67#14519699—22no—
68#14519699—22no—
69#14519697—22no—
70#14519697—22no—
71C22⋊#92418—22no—
72C4×#92418—22no—
73C2×M16×C61—21no—
74C22×C8×C61—21no—
75C22×C8×C61D411yescharacteristic
76C22×C8×C61D411yescharacteristic
77#126×C61—21no—
78#125×C61D411yescharacteristic
79#124×C61D411yescharacteristic
80#123×C61—21no—
81C22⋊Q8×C61D411yescharacteristic
82#121×C61D411yescharacteristic
83C4×Q8×C61C2311yescharacteristic
84C4×D4×C61—21no—
85C4×D4×C61C2311yescharacteristic
86#117×C61—21no—
87C2×C42×C61C2311yescharacteristic
88C4⋊C8×C61—21no—
89C4⋊C8×C61—21no—
90C4⋊C8×C61C2311yescharacteristic
91C4⋊C8×C61C2311yescharacteristic
92C22⋊C8×C61—21no—
93C22⋊C8×C61—21no—
94C22⋊C8×C61—21no—
95#97×C61—21no—
96#97×C61—21no—
97C4×C8×C61—21no—
98C4×C8×C61D411yescharacteristic
99C4×C8×C61D411yescharacteristic
100C4×C8×C61C2311yescharacteristic
101C4×C8×C61C2311yescharacteristic
102C2×Q8×C61C2×D411yescharacteristic
103C2×D4×C61—21no—
104C2×D4×C61C2×D411yescharacteristic
105C22×C4×C61—21no—
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C2×C22⋊D61—42no—
110#11758222—82no—
111#11758222—82no—
112C2×D244—22no—
113C2×D244—22no—
114C2×D244—22no—
115C2×C4×D61—42no—
116C2×Dic122—22no—
117M16×C61—42no—
118C2×C8×C61—22no—
119C2×C8×C61—21no—
120C2×C8×C61—21no—
121C2×C8×C61—41no—
122C2×C8×C61—42no—
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2×D411yescharacteristic
125C2×C8×C61C2×D411yescharacteristic
126C2×C8×C61C2×D411yescharacteristic
127C4⋊C4×C61—21no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—21no—
131C4⋊C4×C61C2×D411yescharacteristic
132C4⋊C4×C61C2×D411yescharacteristic
133C22⋊C4×C61—21no—
134C22⋊C4×C61—21no—
135C22⋊C4×C61—21no—
136C22⋊C4×C61—21no—
137C22⋊C4×C61—21no—
138C42×C61—21no—
139C42×C61C2×D411yescharacteristic
140C42×C61C2×D411yescharacteristic
141C42×C61#4111yescharacteristic
142C42×C61C2411yescharacteristic
143#11758202—82no—
144#11758201—82no—
145#11758200—82no—
146#11758199—82no—
147#11758198—42no—
148#11758198—42no—
149C4⋊Dic61—22no—
150C4⋊Dic61—22no—
151C2×#92418—22no—
152C2×#92418—22no—
153D488—42no—
154D488—42no—
155C23×C61—21no—
156C23×C61#12111yescharacteristic
157C22×D61—42no—
158Q8×C61—22no—
159D4×C61—22no—
160D4×C61—42no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—22no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61#12111yescharacteristic
171C2×C4×C61#12111yescharacteristic
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61C22×D411yescharacteristic
174C2×C4×C61C22×D411yescharacteristic
175C2×C4×C61C2×#4111yescharacteristic
176C22⋊D61—84no—
177C2×Dic61—42no—
178D244—42no—
179D244—42no—
180D244—42no—
181D244—42no—
182D244—82no—
183C4×D61—84no—
184Dic122—42no—
185Dic122—42no—
186C8×C61—21no—
187C8×C61—21no—
188C8×C61—21no—
189C8×C61—41no—
190C8×C61—41no—
191C8×C61#13512yes—
192#92418—42no—
193#92418—42no—
194#19225—611nomaximal, Sylow
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61C2×#12111yescharacteristic
202C2×D61—82no—
203C2×D61—82no—
204C2×D61—82no—
205C4×C61—21no—
206C4×C61—21no—
207C4×C61—21no—
208C4×C61—21no—
209C4×C61—41no—
210C4×C61—41no—
211C4×C61—41no—
212C4×C61C2×#13511yescharacteristic
213C4×C61#57511yescharacteristic
214C4×C61#57612yes—
215Dic61—82no—
216#3212—612no—
217#3169—611no—
218#2966D6111yescharacteristic, complemented
219#1694—611no—
220#1693—611no—
221#1688—611no—
222#1687—611no—
223#1682—612no—
224#1681—612no—
225#1564—611no—
226#1553—612no—
227C2×C61—41no—
228C2×C61—81no—
229C2×C61#303511yescharacteristic
230C2×C61#305811yescharacteristic
231C2×C61#306711yescharacteristic
232D61—162no—
233#532—612no—
234#529C2×D6111yescharacteristic
235#500—611no—
236#495—1222no—
237#493—611no—
238#488—1222no—
239#486—612no—
240#466—1221no—
241#466—1221no—
242#462—612no—
243#461—612no—
244#460—612no—
245#459—612no—
246#452—1222no—
247#449—1222no—
248#446C2×D6111yescharacteristic
249C8×Q8C2×D6111yescharacteristic
250C4×D8—1221no—
251C4×D8—1221no—
252#436C2×D6111yescharacteristic
253#435—21no—
254C8×D4—21no—
255C8×D4C2×D6111yescharacteristic
256#433—21no—
257#432C2×D6111yescharacteristic
258#431—612no—
259#405—21no—
260C2×C4×C8C2×D6111yescharacteristic
261#335—612no—
262#334—611no—
263#334—611no—
264#332—612no—
265#332—612no—
266#331—612no—
267#331—612no—
268C61#1922511yescharacteristic, complemented, Sylow
269C2×#41—1222no—
270C2×Q16—1222no—
271C2×SD16—1222no—
272C2×SD16—1222no—
273C2×D8—1222no—
274C2×D8—1221no—
275C2×D8—1221no—
276C2×M16—21no—
277C22×C8—21no—
278C22×C8C22⋊D6111yescharacteristic
279C22×C8C22⋊D6111yescharacteristic
280C4⋊Q8—612no—
281#127—612no—
282#126—21no—
283#125D24411yescharacteristic
284#124—1222no—
285#124D24411yescharacteristic
286#123—21no—
287C22⋊Q8D24411yescharacteristic
288#121—1222no—
289#121—1222no—
290#121D24411yescharacteristic
291C4×Q8C22×D6111yescharacteristic
292C4×D4—21no—
293C4×D4—1222no—
294C4×D4—1222no—
295C4×D4C22×D6111yescharacteristic
296#117—21no—
297C2×C42C22×D6111yescharacteristic
298#107—1221no—
299#107—1221no—
300C4⋊C8—21no—
301C4⋊C8—21no—
302C4⋊C8—612no—
303C4⋊C8—612no—
304C4⋊C8C22×D6111yescharacteristic
305C4⋊C8C22×D6111yescharacteristic
306#103—1222no—
307#103—1222no—
308#102—1222no—
309#102—1222no—
310#102—1222no—
311#102—1222no—
312C22⋊C8—21no—
313C22⋊C8—21no—
314C22⋊C8—21no—
315C22⋊C8—1222no—
316#97—21no—
317#97—21no—
318C4×C8—21no—
319C4×C8—1222no—
320C4×C8C22⋊D6111yescharacteristic
321C4×C8C22⋊D6111yescharacteristic
322C4×C8C22×D6111yescharacteristic
323C4×C8C22×D6111yescharacteristic
324#41—4882no—
325#41—4882no—
326C2×Q8—1222no—
327C2×Q8C2×D24411yescharacteristic
328C2×D4—21no—
329C2×D4—1222no—
330C2×D4—1222no—
331C2×D4—1222no—
332C2×D4—2442no—
333C2×D4C2×D24411yescharacteristic
334C22×C4—21no—
335C22×C4—2442no—
336C22×C4C2×D24411yescharacteristic
337C22×C4#1175822211yescharacteristic
338C22×C4C2×C22⋊D6111yescharacteristic
339Q16—4882no—
340SD16—4882no—
341SD16—4882no—
342D8—4882no—
343D8—2442no—
344D8—2442no—
345M16—42no—
346C2×C8—22no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—41no—
350C2×C8—42no—
351C2×C8—1222no—
352C2×C8—1222no—
353C2×C8C2×C22⋊D6111yescharacteristic
354C2×C8C2×C22⋊D6111yescharacteristic
355C2×C8C2×C22⋊D6111yescharacteristic
356C2×C8C2×C22⋊D6111yescharacteristic
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—1222no—
362C4⋊C4—1222no—
363C4⋊C4C2×D24411yescharacteristic
364C4⋊C4C2×D24411yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—2442no—
371C22⋊C4—2442no—
372C42—21no—
373C42C2×D24411yescharacteristic
374C42#1175822211yescharacteristic
375C42C2×C22⋊D6111yescharacteristic
376C42C23×D6111yescharacteristic
377C23—21no—
378C23—2442no—
379C23#1451975111yescharacteristic
380Q8—22no—
381Q8—2442no—
382Q8—2442no—
383D4—22no—
384D4—42no—
385D4—4882no—
386D4—4884no—
387D4—2442no—
388D4—2442no—
389D4—2442no—
390D4—2442no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—22no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—4884no—
401C2×C4—2442no—
402C2×C4#1451975111yescharacteristic
403C2×C4#1451975111yescharacteristic
404C2×C4#1451975111yescharacteristic
405C2×C4C22×C22⋊D6111yescharacteristic
406C2×C4C22×D24411yescharacteristic
407C2×C4C2×#1175822211yescharacteristic
408C8—21no—
409C8—21no—
410C8—21no—
411C8—41no—
412C8—41no—
413C8—2442no—
414C8—2442no—
415C8#1451979712yes—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—4882no—
423C22—4882no—
424C22—4882no—
425C22C2×#1451975111yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—21no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—4882no—
434C4C2×#1451979711yescharacteristic
435C4#1684056011yescharacteristic
436C4#1684056712yes—
437C2—41no—
438C2—81no—
439C2—9762no—
440C2#2145527411yescharacteristic
441C2#2145546711yescharacteristic
442C2#2145553911yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2966C2
socleC22×C61C2×#121
hypercenter#2966D61
hypocenterC61#19225
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2966

Complements

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

NH ≅ G/Ntype
1. #21456791C2semidirect
2. #21456398C2semidirect
3. #21445337C2semidirect
4. #21445332C2semidirect
5. #21445303C2semidirect
6. #21445298C2semidirect
7. #21445263C2semidirect
8. #21445256C2semidirect
9. #21444567C2semidirect
10. #21444525C2semidirect
11. C61×#2966C2semidirect
218. #2966D61semidirect
268. C61#19225semidirect

Maximal subgroups

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

subgroupindex
#214567912
#214563982
#214453372
#214453322
#214453032
#214452982
#214452632
#214452562
#214445672
#214445252
C61×#29662
#1922561