Finite Group Databasebeta

← #29575241

Subgroups — #29575241

Order 15616.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456379C211yesmaximal, characteristic
2#21446738C211yesmaximal, characteristic
3#21444318C211yesmaximal, characteristic, complemented
4#21444217C211yesmaximal, characteristic
5#21443658C211yesmaximal, characteristic, complemented
6#21443657C211yesmaximal, characteristic, complemented
7C61×#2962C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840158C411yescharacteristic, complemented
10#16840136C411yescharacteristic, complemented
11#16840112C411yescharacteristic, complemented
12#16840110C411yescharacteristic, complemented
13#16839993—22no—
14C4×#11758201—22no—
15#16839815C2211yescharacteristic
16C2×#14519703—21no—
17C2×#14519703—21no—
18C2×C4×#92418C2211yescharacteristic
19C4×C4⋊Dic61C2211yescharacteristic
20#16839499—22no—
21#16839489—21no—
22#16839489—21no—
23C61×#533C2211yescharacteristic
24C61×#446—22no—
25C61×#446—21no—
26C8×Q8×C61—21no—
27C61×#424—21no—
28C2×C4⋊C8×C61C2211yescharacteristic
29C61×#405—21no—
30C4×M16×C61C2211yescharacteristic
31C2×#11758222—21no—
32C2×#11758201—22no—
33C22×#92418—21no—
34#14519777C2×C411yescharacteristic
35#14519774C2×C411yescharacteristic
36#14519765—21no—
37#14519751—21no—
38#14519751—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—21no—
42C2×C4×Dic61—21no—
43#14519708—22no—
44C4⋊#92418—21no—
45#14519703—42no—
46#14519703—42no—
47#14519701—22no—
48#14519697—22no—
49C22⋊#92418—21no—
50C4×#92418—21no—
51C4×#92418—21no—
52C4×#92418C2×C411yescharacteristic
53C4×#92418C2×C411yescharacteristic
54#14519684—21no—
55C2×M16×C61D411yescharacteristic
56C2×M16×C61D411yescharacteristic
57C22×C8×C61—21no—
58C4⋊Q8×C61C2×C411yescharacteristic
59C4⋊Q8×C61C2×C411yescharacteristic
60#125×C61—21no—
61C22⋊Q8×C61—21no—
62C22⋊Q8×C61D412yes—
63C4×Q8×C61—21no—
64C4×Q8×C61D412yes—
65#117×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—22no—
68C4⋊C8×C61—22no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61D411yescharacteristic
71C4⋊C8×C61D411yescharacteristic
72#97×C61—22no—
73#97×C61—21no—
74C4×C8×C61—22no—
75C4×C8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61C22⋊C412yes—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C2×C22⋊D61—41no—
82C22×Dic61—41no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—21no—
90C2×C4×D61—41no—
91C2×Dic122—21no—
92M16×C61—21no—
93M16×C61—21no—
94M16×C61—21no—
95M16×C61SD1612yescomplemented
96C2×C8×C61—21no—
97C2×C8×C61—21no—
98C2×C8×C61—21no—
99C2×C8×C61—21no—
100C2×C8×C61—41no—
101C2×C8×C61—41no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—22no—
106C4⋊C4×C61—22no—
107C4⋊C4×C61C22⋊C412yes—
108C22⋊C4×C61—22no—
109C42×C61—22no—
110C42×C61C22×C411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61#4111yescharacteristic
114#11758201—44no—
115#11758198—41no—
116#11758198—41no—
117C4⋊Dic61—22no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120C4⋊Dic61—41no—
121C4×Dic61—41no—
122C4×Dic61—41no—
123C2×#92418—21no—
124C2×#92418—21no—
125C2×#92418—42no—
126C2×#92418—41no—
127C23×C61#12111yescharacteristic
128C22×D61—41no—
129Q8×C61—42no—
130Q8×C61—41no—
131Q8×C61—41no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—41no—
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12311yescharacteristic
143C2×C4×C61C2×SD1611yescharacteristic
144C2×C4×C61#13511yescharacteristic
145C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C61#13711yescharacteristic
147C22⋊D61—81no—
148C22⋊D61—81no—
149C2×Dic61—42no—
150C2×Dic61—41no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153D244—42no—
154D244—41no—
155D244—41no—
156D244—41no—
157D244—41no—
158C4×D61—81no—
159C4×D61—81no—
160Dic122—41no—
161Dic122—41no—
162C8×C61—22no—
163C8×C61—41no—
164C8×C61—41no—
165C8×C61—41no—
166#92418—22no—
167#92418—41no—
168#92418—81no—
169#9054—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61#38611yescharacteristic
173C22×C61#46011yescharacteristic
174C22×C61#46411yescharacteristic
175C2×D61—81no—
176C2×D61—81no—
177C2×D61—81no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—42no—
182C4×C61—42no—
183C4×C61C4×SD1611yescharacteristic
184C4×C61#44011yescharacteristic
185C4×C61#44311yescharacteristic
186C4×C61#44411yescharacteristic
187C4×C61#44811yescharacteristic
188C4×C61#44911yescharacteristic
189Dic61—82no—
190Dic61—81no—
191#3167—611no—
192#2962D6111yescharacteristic, complemented
193#1980—611no—
194#1503—611no—
195#1480—611no—
196#1279—611no—
197#1278—611no—
198C2×C61—21no—
199C2×C61—21no—
200C2×C61#187611yescharacteristic
201C2×C61#188011yescharacteristic
202C2×C61#188411yescharacteristic
203D61—161no—
204#533C2×D6111yescharacteristic
205#532—611no—
206#498—611no—
207#492—611no—
208#487—611no—
209#486—611no—
210#465—1222no—
211#446—22no—
212#446—21no—
213C8×Q8—21no—
214C4×SD16—1222no—
215#431—611no—
216#424—21no—
217C2×C4⋊C8C2×D6111yescharacteristic
218C2×#104—1221no—
219C2×#104—1221no—
220#405—21no—
221C4×M16C2×D6111yescharacteristic
222C2×C4×C8—611no—
223C4×C4⋊C4—611no—
224#328—1222no—
225D4⋊C8—1221no—
226D4⋊C8—1221no—
227C61#905411yescharacteristic, complemented, Sylow
228C2×#41—1221no—
229C2×SD16—1222no—
230C2×M16C22⋊D6111yescharacteristic
231C2×M16C22⋊D6111yescharacteristic
232C22×C8—21no—
233C22×C8—1221no—
234C4⋊Q8—611no—
235C4⋊Q8C4×D6111yescharacteristic
236C4⋊Q8C4×D6111yescharacteristic
237#127—611no—
238#125—21no—
239#124—1221no—
240C22⋊Q8—21no—
241C22⋊Q8D24412yes—
242#121—1221no—
243#121—1221no—
244C4×Q8—21no—
245C4×Q8C22⋊D6112yes—
246C4×D4—1221no—
247C4×D4—1221no—
248#117—21no—
249C2×C4⋊C4—1221no—
250C2×C42—1221no—
251C2×C42C22×D6111yescharacteristic
252#106—1222no—
253C4⋊C8—22no—
254C4⋊C8—22no—
255C4⋊C8—21no—
256C4⋊C8—1221no—
257C4⋊C8C22⋊D6111yescharacteristic
258C4⋊C8C22⋊D6111yescharacteristic
259#104—2442no—
260#104—2442no—
261#103—1222no—
262#102—1222no—
263C22⋊C8—1221no—
264#97—22no—
265#97—21no—
266C4×C8—22no—
267C4×C8—21no—
268C4×C8—611no—
269C4×C8—611no—
270C4×C8—1221no—
271C4×C8—1221no—
272#95—1221no—
273#41—2441no—
274#41—2441no—
275#41—2441no—
276#41—2441no—
277C2×Q8—21no—
278C2×Q8—1221no—
279C2×Q8#1175819812yes—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—1221no—
283C2×D4—2441no—
284C22×C4—2441no—
285C22×C4—2441no—
286C22×C4C2×D24411yescharacteristic
287C22×C4#1175822211yescharacteristic
288C22×C4C2×C22⋊D6111yescharacteristic
289SD16—2444no—
290M16—21no—
291M16—21no—
292M16—21no—
293M16#1175820112yescomplemented
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—1221no—
301C2×C8—1221no—
302C2×C8—2442no—
303C2×C8—2441no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—1222no—
310C4⋊C4—1221no—
311C4⋊C4—1221no—
312C4⋊C4—2441no—
313C4⋊C4#1175819812yes—
314C22⋊C4—22no—
315C22⋊C4—2441no—
316C22⋊C4—2441no—
317C42—22no—
318C42—2441no—
319C42—2441no—
320C42C2×C4×D6111yescharacteristic
321C42#1175822211yescharacteristic
322C42C2×C22⋊D6111yescharacteristic
323C42C2×C22⋊D6111yescharacteristic
324C23—2441no—
325C23#1451975111yescharacteristic
326Q8—42no—
327Q8—41no—
328Q8—41no—
329Q8—2441no—
330Q8—2441no—
331D4—4881no—
332D4—4881no—
333D4—2442no—
334D4—2441no—
335D4—2441no—
336D4—2441no—
337D4—2441no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—4881no—
344C2×C4—4881no—
345C2×C4—4881no—
346C2×C4—4881no—
347C2×C4—2442no—
348C2×C4—2441no—
349C2×C4C2×#1175819811yescharacteristic
350C2×C4C4×C22⋊D6111yescharacteristic
351C2×C4C4×C22⋊D6111yescharacteristic
352C2×C4#1451974611yescharacteristic
353C2×C4#1451975111yescharacteristic
354C2×C4#1451976011yescharacteristic
355C2×C4C2×#1175820111yescharacteristic
356C2×C4#1451979711yescharacteristic
357C2×C4#1451980211yescharacteristic
358C2×C4#1451980811yescharacteristic
359C8—22no—
360C8—41no—
361C8—41no—
362C8—41no—
363C8—1222no—
364C8—4881no—
365C8—2441no—
366C22—21no—
367C22—21no—
368C22—4881no—
369C22—4881no—
370C22—4881no—
371C22#1683964111yescharacteristic
372C22#1683996211yescharacteristic
373C22#1683998411yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—4882no—
380C4—4881no—
381C4C4×#1175820111yescharacteristic
382C4#1683986011yescharacteristic
383C4#1683987711yescharacteristic
384C4#1683988211yescharacteristic
385C4#1683990111yescharacteristic
386C4#1683990711yescharacteristic
387C2—21no—
388C2—21no—
389C2—9761no—
390C2#2144614611yescharacteristic
391C2#2144617411yescharacteristic
392C2#2144620211yescharacteristic
subgroupG/H
centerC2×C4#14519746
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2962C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#2962D61
hypocenterC61#9054
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #21444318C2semidirect
5. #21443658C2semidirect
6. #21443657C2semidirect
7. C61×#2962C2semidirect
9. #16840158C4semidirect
10. #16840136C4semidirect
11. #16840112C4semidirect
12. #16840110C4semidirect
95. M16×C61SD16semidirect
192. #2962D61semidirect
227. C61#9054semidirect
293. M16#11758201semidirect

Maximal subgroups

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

subgroupindex
#214563792
#214467382
#214443182
#214442172
#214436582
#214436572
C61×#29622
#905461