Finite Group Databasebeta

← #30608457

Subgroups — #30608457

Order 15616.

348 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462099C211yesmaximal, characteristic, complemented
2#21462097C211yesmaximal, characteristic, complemented
3#21460959C211yesmaximal, characteristic, complemented
4#21460958C211yesmaximal, characteristic, complemented
5#21460951C211yesmaximal, characteristic, complemented
6#21460951C211yesmaximal, characteristic, complemented
7#21456872C211yesmaximal, characteristic
8#16840743—21no—
9D61⋊#99—21no—
10#16840668—21no—
11#16840667C2211yescharacteristic
12#16840667C2211yescharacteristic
13#16840667C2211yescharacteristic
14#16840667C2211yescharacteristic
15#16840666—21no—
16#16840368C411yescharacteristic, complemented
17#16840330C2211yescharacteristic
18#16840152C411yescharacteristic, complemented
19#16840139C2211yescharacteristic
20#16840128C2211yescharacteristic
21#16839980—21no—
22#16839956—21no—
23#16839910—21no—
24#16839897—21no—
25#16839821C411yescharacteristic, complemented
26C61×#488C411yescharacteristic, complemented
27#14519856—41no—
28C2×C22⋊#6923—41no—
29#14519836—21no—
30#14519836—21no—
31#14519836—21no—
32#14519836—21no—
33#14519836—41no—
34#14519835—41no—
35C2×#11758226D411yescharacteristic
36C2×D4×D61D411yescharacteristic
37C2×#11758201—21no—
38C2×D488—21no—
39C2×D488—21no—
40C2×#11758199—21no—
41#14519774C2×C411yescharacteristic, complemented
42#14519774C2311yescharacteristic
43#14519773D411yescharacteristic
44#14519766D411yescharacteristic
45#14519762—41no—
46#14519752—21no—
47#14519752—41no—
48#14519750—41no—
49#14519747—41no—
50#14519739—21no—
51#14519734C2×C411yescharacteristic
52#14519706—21no—
53#14519697—21no—
54#14519697—21no—
55#14519689—21no—
56#14519688C2×C411yescharacteristic, complemented
57#125×C61C2×C411yescharacteristic, complemented
58#124×C61C2×C411yescharacteristic
59#103×C61—21no—
60#102×C61—21no—
61C4×C8×C61C2×C411yescharacteristic, complemented
62C23×D61—21no—
63C22×#6923—81no—
64C2×Q8×C61C22⋊C411yescharacteristic
65C2×D4×C61C22⋊C411yescharacteristic
66C2×C22⋊D61—21no—
67C2×C22⋊D61—41no—
68#11758226—81no—
69D4×D61—81no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244—41no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244C2×D411yescharacteristic
76C2×D244C2×D411yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—41no—
79C2×C4×D61C22⋊C411yescharacteristic
80C22⋊#6923—41no—
81C22⋊#6923—41no—
82C22⋊#6923—41no—
83C22⋊#6923—41no—
84C22⋊#6923—81no—
85C4⋊#6923—81no—
86C4×#6923—81no—
87C2×C8×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C42×C61C22×C411yescharacteristic
92#11758201—81no—
93#11758199—81no—
94#11758198—21no—
95#11758198—41no—
96#11758198—41no—
97#11758198—41no—
98#11758196—21no—
99C4×Dic61C22⋊C411yescharacteristic
100C2×#92418—21no—
101D488—81no—
102D488—81no—
103C23×C61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—161no—
110C22×D61#9911yescharacteristic
111C2×#6923—81no—
112C2×#6923—81no—
113C2×#6923—81no—
114C2×#6923—81no—
115C2×#6923—162no—
116Q8×C61—41no—
117D4×C61—41no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
121C2×C4×C61C2×C22⋊C411yescharacteristic
122C22⋊D61—81no—
123C22⋊D61—161no—
124C2×Dic61—21no—
125C2×Dic61#9911yescharacteristic
126D244—41no—
127D244—41no—
128D244—41no—
129D244—41no—
130D244—81no—
131D244—161no—
132D244—161no—
133D244—161no—
134C4×D61—41no—
135C4×D61—41no—
136C4×D61—41no—
137C4×D61—161no—
138C8×C61—41no—
139#92418—41no—
140#13609—611nomaximal, Sylow
141C22×C61—41no—
142C22×C61—81no—
143C22×C61C2×#9911yescharacteristic
144C2×D61—21no—
145C2×D61—41no—
146C2×D61—41no—
147C2×D61—41no—
148C2×D61—82no—
149C2×D61—81no—
150C2×D61—81no—
151C2×D61—81no—
152C2×D61—81no—
153C2×D61—81no—
154C2×D61—161no—
155#6923—161no—
156#6923—161no—
157#6923—161no—
158#6923—161no—
159C4×C61—21no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—81no—
163Dic61—21no—
164Dic61—41no—
165#3220—611no—
166#2128—611no—
167#2127—611no—
168#1412—611no—
169#1412—611no—
170#1408—611no—
171#1408—611no—
172C2×C61—21no—
173C2×C61—81no—
174C2×C61#212711yescharacteristic
175D61—41no—
176D61—81no—
177D61—81no—
178D61—161no—
179#540—611no—
180#535—611no—
181#496—611no—
182#493—611no—
183#490—611no—
184#488#692311yescharacteristic, complemented
185#463—1221no—
186#459—1221no—
187#449—1221no—
188#447—1221no—
189#433—611no—
190#410—1221no—
191C2×#99—1221no—
192#354—1221no—
193#353—611no—
194#353—611no—
195#353—611no—
196#353—611no—
197#353—1221no—
198C61#1360911yescharacteristic, complemented, Sylow
199C2×#41—611no—
200C22×D4—611no—
201C2×SD16—1221no—
202C2×D8—1221no—
203C2×D8—1221no—
204C2×D8—1221no—
205#127—611no—
206#127—611no—
207#127—611no—
208#125C2×#692311yescharacteristic, complemented
209#124—611no—
210#124C2×#692311yescharacteristic
211#123—2441no—
212#121—1221no—
213#121—2441no—
214#121—2441no—
215#120—2441no—
216C4×D4—1221no—
217#117—611no—
218#117—2441no—
219C2×C22⋊C4—2441no—
220C4⋊C8—1221no—
221#103—21no—
222#102—21no—
223#102—1221no—
224#102—1221no—
225#99—1221no—
226#99—1221no—
227#99—1221no—
228#99—1221no—
229#99—2441no—
230#99—2441no—
231C22⋊C8—1221no—
232#97—611no—
233C4×C8C2×#692311yescharacteristic, complemented
234C24—1221no—
235#41—4881no—
236C2×Q8C22⋊#692311yescharacteristic
237C2×D4—611no—
238C2×D4—611no—
239C2×D4—1221no—
240C2×D4—1221no—
241C2×D4—1221no—
242C2×D4—4881no—
243C2×D4—2441no—
244C2×D4—2441no—
245C2×D4—2441no—
246C2×D4—2441no—
247C2×D4C22⋊#692311yescharacteristic
248C22×C4—611no—
249C22×C4—1221no—
250C22×C4—4881no—
251C22×C4—2441no—
252SD16—4881no—
253D8—4881no—
254D8—4881no—
255D8—4881no—
256C2×C8—21no—
257C2×C8—1221no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—1221no—
261C4⋊C4—4881no—
262C22⋊C4—41no—
263C22⋊C4—1221no—
264C22⋊C4—4881no—
265C22⋊C4—2441no—
266C22⋊C4—2441no—
267C22⋊C4—2441no—
268C22⋊C4—2441no—
269C22⋊C4—2441no—
270C22⋊C4—2441no—
271C22⋊C4—2441no—
272C42—611no—
273C42—4881no—
274C42C22×#692311yescharacteristic
275C23—21no—
276C23—611no—
277C23—1221no—
278C23—1221no—
279C23—9761no—
280C23—2441no—
281C23—2441no—
282C23—2441no—
283Q8—41no—
284D4—41no—
285D4—9761no—
286D4—9761no—
287D4—9761no—
288D4—9761no—
289D4—4881no—
290D4—4881no—
291D4—2441no—
292D4—2441no—
293D4—2441no—
294D4—2441no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—611no—
299C2×C4—1221no—
300C2×C4—9761no—
301C2×C4—9762no—
302C2×C4—4881no—
303C2×C4—4881no—
304C2×C4—4881no—
305C2×C4—4881no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4C2×C22⋊#692311yescharacteristic
310C8—41no—
311C8—2441no—
312C22—41no—
313C22—81no—
314C22—1221no—
315C22—9761no—
316C22—4881no—
317C22—4881no—
318C22—4881no—
319C22—4881no—
320C22—4882no—
321C22—4881no—
322C22—2441no—
323C22—2441no—
324C22—2441no—
325C22D61⋊#9911yescharacteristic
326C4—21no—
327C4—41no—
328C4—41no—
329C4—81no—
330C4—1221no—
331C4—9761no—
332C4—9761no—
333C4—9761no—
334C4—9761no—
335C4—2441no—
336C2—21no—
337C2—81no—
338C2—9761no—
339C2—4881no—
340C2—4881no—
341C2—2441no—
342C2#2146209711yescharacteristic
subgroupG/H
centerC2#21462097
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#488C4
socleC2×C61#2127
prime radical#21456872C2
cosocle#14519774C23
hypercenter#488#6923
hypocenterC61#13609
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #21462099C2semidirect
2. #21462097C2semidirect
3. #21460959C2semidirect
4. #21460958C2semidirect
5. #21460951C2semidirect
6. #21460951C2semidirect
16. #16840368C4semidirect
18. #16840152C4semidirect
25. #16839821C4semidirect
26. C61×#488C4semidirect
41. #14519774C2×C4semidirect
56. #14519688C2×C4semidirect
57. #125×C61C2×C4semidirect
61. C4×C8×C61C2×C4semidirect
184. #488#6923semidirect
198. C61#13609semidirect
208. #125C2×#6923semidirect
233. C4×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214620992
#214620972
#214609592
#214609582
#214609512
#214568722
#1360961