Finite Group Databasebeta

← #29663364

Subgroups — #29663364

Order 15616.

630 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456791C212yesmaximal, complemented
2#21456398C211yesmaximal, characteristic, complemented
3#21445387C212yesmaximal, complemented
4#21445380C212yesmaximal, complemented
5#21445213C211yesmaximal, characteristic, complemented
6#21445208C211yesmaximal, characteristic, complemented
7#21445179C211yesmaximal, characteristic, complemented
8#21445174C211yesmaximal, characteristic, 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#16839515C2211yescharacteristic
30#16839515C2211yescharacteristic
31#16839513C2212yes—
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—21no—
159Q8×C61—21no—
160D4×C61—21no—
161D4×C61—21no—
162D4×C61—42no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61C22×D411yescharacteristic
177C2×C4×C61C22×D411yescharacteristic
178C2×C4×C61C2×#4111yescharacteristic
179C22⋊D61—84no—
180C2×Dic61—42no—
181D244—42no—
182D244—42no—
183D244—42no—
184D244—42no—
185D244—82no—
186C4×D61—84no—
187Dic122—42no—
188Dic122—42no—
189C8×C61—21no—
190C8×C61—21no—
191C8×C61—21no—
192C8×C61—41no—
193C8×C61—41no—
194C8×C61#13512yes—
195#92418—42no—
196#92418—42no—
197#19219—611nomaximal, Sylow
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—41no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61C2×#12111yescharacteristic
205C2×D61—82no—
206C2×D61—82no—
207C2×D61—82no—
208C4×C61—21no—
209C4×C61—21no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—41no—
213C4×C61—41no—
214C4×C61—41no—
215C4×C61C2×#13511yescharacteristic
216C4×C61#57511yescharacteristic
217C4×C61#57611yescharacteristic
218C4×C61#57611yescharacteristic
219Dic61—82no—
220#3212—612no—
221#3169—611no—
222#2966D6111yescharacteristic, complemented
223#1702—612no—
224#1701—612no—
225#1674—611no—
226#1673—611no—
227#1668—611no—
228#1667—611no—
229#1564—611no—
230#1553—612no—
231C2×C61—41no—
232C2×C61—81no—
233C2×C61#303511yescharacteristic
234C2×C61#305811yescharacteristic
235C2×C61#306711yescharacteristic
236D61—162no—
237#532—612no—
238#529C2×D6111yescharacteristic
239#500—611no—
240#495—1222no—
241#493—611no—
242#488—1222no—
243#486—612no—
244#466—1221no—
245#466—1221no—
246#462—612no—
247#461—612no—
248#460—612no—
249#459—612no—
250#452—1222no—
251#449—1222no—
252#446C2×D6111yescharacteristic
253C8×Q8C2×D6111yescharacteristic
254C4×D8—1221no—
255C4×D8—1221no—
256#436C2×D6111yescharacteristic
257#435—21no—
258C8×D4—21no—
259C8×D4C2×D6111yescharacteristic
260#433—21no—
261#432C2×D6111yescharacteristic
262#431—612no—
263#405—21no—
264C2×C4×C8C2×D6111yescharacteristic
265#335—611no—
266#335—611no—
267#334—612no—
268#332—612no—
269#332—612no—
270#331—612no—
271#331—612no—
272C61#1921911yescharacteristic, complemented, Sylow
273C2×#41—1222no—
274C2×Q16—1222no—
275C2×SD16—1222no—
276C2×SD16—1222no—
277C2×D8—1222no—
278C2×D8—1221no—
279C2×D8—1221no—
280C2×M16—21no—
281C22×C8—21no—
282C22×C8C22⋊D6111yescharacteristic
283C22×C8C22⋊D6111yescharacteristic
284C4⋊Q8—612no—
285#127—612no—
286#126—21no—
287#125D24411yescharacteristic
288#124—1222no—
289#124D24411yescharacteristic
290#123—21no—
291C22⋊Q8D24411yescharacteristic
292#121—1222no—
293#121—1222no—
294#121D24411yescharacteristic
295C4×Q8C22×D6111yescharacteristic
296C4×D4—21no—
297C4×D4—1222no—
298C4×D4—1222no—
299C4×D4C22×D6111yescharacteristic
300#117—21no—
301C2×C42C22×D6111yescharacteristic
302#107—1221no—
303#107—1221no—
304C4⋊C8—21no—
305C4⋊C8—21no—
306C4⋊C8—612no—
307C4⋊C8—612no—
308C4⋊C8C22×D6111yescharacteristic
309C4⋊C8C22×D6111yescharacteristic
310#103—1222no—
311#103—1222no—
312#102—1222no—
313#102—1222no—
314#102—1222no—
315#102—1222no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—1222no—
320#97—21no—
321#97—21no—
322C4×C8—21no—
323C4×C8—1222no—
324C4×C8C22⋊D6111yescharacteristic
325C4×C8C22⋊D6111yescharacteristic
326C4×C8C22×D6111yescharacteristic
327C4×C8C22×D6111yescharacteristic
328#41—4882no—
329#41—4882no—
330C2×Q8—1222no—
331C2×Q8C2×D24411yescharacteristic
332C2×D4—21no—
333C2×D4—1222no—
334C2×D4—1222no—
335C2×D4—1222no—
336C2×D4—2442no—
337C2×D4C2×D24411yescharacteristic
338C22×C4—21no—
339C22×C4—2442no—
340C22×C4C2×D24411yescharacteristic
341C22×C4#1175822211yescharacteristic
342C22×C4C2×C22⋊D6111yescharacteristic
343Q16—4882no—
344SD16—4882no—
345SD16—4882no—
346D8—4882no—
347D8—2442no—
348D8—2442no—
349M16—42no—
350C2×C8—22no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—41no—
354C2×C8—42no—
355C2×C8—1222no—
356C2×C8—1222no—
357C2×C8C2×C22⋊D6111yescharacteristic
358C2×C8C2×C22⋊D6111yescharacteristic
359C2×C8C2×C22⋊D6111yescharacteristic
360C2×C8C2×C22⋊D6111yescharacteristic
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—1222no—
366C4⋊C4—1222no—
367C4⋊C4C2×D24411yescharacteristic
368C4⋊C4C2×D24411yescharacteristic
369C22⋊C4—21no—
370C22⋊C4—21no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—21no—
374C22⋊C4—2442no—
375C22⋊C4—2442no—
376C42—21no—
377C42C2×D24411yescharacteristic
378C42#1175822211yescharacteristic
379C42C2×C22⋊D6111yescharacteristic
380C42C23×D6111yescharacteristic
381C23—21no—
382C23—2442no—
383C23#1451975111yescharacteristic
384Q8—21no—
385Q8—21no—
386Q8—2442no—
387Q8—2442no—
388D4—21no—
389D4—21no—
390D4—42no—
391D4—4882no—
392D4—4884no—
393D4—2442no—
394D4—2442no—
395D4—2442no—
396D4—2442no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—4884no—
408C2×C4—2442no—
409C2×C4#1451975111yescharacteristic
410C2×C4#1451975111yescharacteristic
411C2×C4#1451975111yescharacteristic
412C2×C4C22×C22⋊D6111yescharacteristic
413C2×C4C22×D24411yescharacteristic
414C2×C4C2×#1175822211yescharacteristic
415C8—21no—
416C8—21no—
417C8—21no—
418C8—41no—
419C8—41no—
420C8—2442no—
421C8—2442no—
422C8#1451979712yes—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—4882no—
430C22—4882no—
431C22—4882no—
432C22C2×#1451975111yescharacteristic
433C4—21no—
434C4—21no—
435C4—21no—
436C4—21no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—4882no—
441C4C2×#1451979711yescharacteristic
442C4#1684056011yescharacteristic
443C4#1684056711yescharacteristic
444C4#1684056711yescharacteristic
445C2—41no—
446C2—81no—
447C2—9762no—
448C2#2145527411yescharacteristic
449C2#2145546711yescharacteristic
450C2#2145553911yescharacteristic
subgroupG/H
centerC22C2×#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2966C2
socleC22×C61C2×#121
hypercenter#2966D61
hypocenterC61#19219
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. #21445387C2semidirect
4. #21445380C2semidirect
5. #21445213C2semidirect
6. #21445208C2semidirect
7. #21445179C2semidirect
8. #21445174C2semidirect
9. #21444567C2semidirect
10. #21444525C2semidirect
11. C61×#2966C2semidirect
222. #2966D61semidirect
272. C61#19219semidirect

Maximal subgroups

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

subgroupindex
#214567912
#214563982
#214453872
#214453802
#214452132
#214452082
#214451792
#214451742
#214445672
#214445252
C61×#29662
#1921961