Finite Group Databasebeta

← #29600398

Subgroups — #29600398

Order 15616.

344 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 57 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#21456872C211yesmaximal, characteristic
2#21447509C211yesmaximal, characteristic, complemented
3#21447487C211yesmaximal, characteristic, complemented
4#21443994C211yesmaximal, characteristic, complemented
5#21443977C211yesmaximal, characteristic, complemented
6#21443975C211yesmaximal, characteristic, complemented
7C61×#1414C211yesmaximal, characteristic, complemented
8#16840368C411yescharacteristic, complemented
9#16840330C2211yescharacteristic
10#16840152C2211yescharacteristic
11#16840139C411yescharacteristic, complemented
12#16840128C411yescharacteristic, complemented
13#16839980—21no—
14#16839956—21no—
15#16839910—21no—
16#16839897—21no—
17#16839821C411yescharacteristic, complemented
18#16839745—21no—
19#99×D61—21no—
20#16839559C2211yescharacteristic
21#16839558—21no—
22#16839557C2211yescharacteristic
23#16839554—21no—
24C61×#488C2211yescharacteristic
25C61×#355C2211yescharacteristic
26C61×#354C2211yescharacteristic
27C2×#11758226D411yescharacteristic
28C2×D4×D61D411yescharacteristic
29C2×#11758201—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×#11758199—21no—
33M16×D61—41no—
34#14519774C2×C411yescharacteristic
35#14519774C2×C411yescharacteristic, complemented
36#14519773D411yescharacteristic
37#14519766D411yescharacteristic
38#14519762—41no—
39#14519752—21no—
40#14519752—41no—
41#14519750—41no—
42#14519747—41no—
43#14519739—21no—
44#14519734C2×C411yescharacteristic
45C22⋊C4×D61—41no—
46#14519706—21no—
47#14519697—21no—
48#14519697—21no—
49#14519696—21no—
50#14519693—41no—
51#14519692—21no—
52#14519691—41no—
53#14519689—21no—
54#14519688C2×C411yescharacteristic, complemented
55#125×C61C2×C411yescharacteristic, complemented
56#124×C61C2311yescharacteristic
57#103×C61—21no—
58#102×C61—21no—
59#101×C61—21no—
60#99×C61—21no—
61C4×C8×C61C2×C411yescharacteristic, complemented
62C23×D61—21no—
63C2×Q8×C61C2×D411yescharacteristic
64C2×D4×C61C2×D411yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—41no—
67#11758226—81no—
68D4×D61—81no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—41no—
72C2×D244—41no—
73C2×D244—41no—
74C2×D244C22⋊C411yescharacteristic
75C2×D244C22⋊C411yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—41no—
78C2×C4×D61—81no—
79C2×C4×D61C22⋊C411yescharacteristic
80M16×C61—41no—
81C2×C8×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86C42×C61C22×C411yescharacteristic
87C22⋊Dic61—41no—
88#11758201—81no—
89#11758199—81no—
90#11758198—21no—
91#11758198—41no—
92#11758198—41no—
93#11758198—41no—
94#11758198—81no—
95#11758196—21no—
96C4×Dic61C22⋊C411yescharacteristic
97#11758194—41no—
98C2×#92418—21no—
99D488—81no—
100D488—81no—
101#11758189—81no—
102C8×D61—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
111Q8×C61—41no—
112D4×C61—41no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—41no—
116C2×C4×C61—81no—
117C2×C4×C61C2×C22⋊C411yescharacteristic
118C22⋊D61—81no—
119C22⋊D61—161no—
120C2×Dic61—21no—
121C2×Dic61—81no—
122C2×Dic61#9911yescharacteristic
123D244—41no—
124D244—41no—
125D244—41no—
126D244—41no—
127D244—81no—
128D244—161no—
129D244—161no—
130D244—161no—
131C4×D61—41no—
132C4×D61—41no—
133C4×D61—41no—
134C4×D61—161no—
135C4×D61—162no—
136C8×C61—41no—
137C8×C61—81no—
138#92418—41no—
139#92418—81no—
140#13605—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—
155C4×C61—21no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—81no—
159C4×C61—161no—
160Dic61—21no—
161Dic61—41no—
162Dic61—161no—
163#3220—611no—
164#2134—611no—
165#2127—611no—
166#1414—611no—
167#1414D6111yescharacteristic, complemented
168#1406—611no—
169#1406—611no—
170C2×C61—21no—
171C2×C61—81no—
172C2×C61#212711yescharacteristic
173D61—41no—
174D61—81no—
175D61—81no—
176D61—161no—
177#540—611no—
178#535—611no—
179#496—611no—
180#493—611no—
181#490—611no—
182#488C2×D6111yescharacteristic
183#463—1221no—
184#459—1221no—
185#449—1221no—
186#447—1221no—
187#433—611no—
188#413—1221no—
189C2×#99—1221no—
190#355—611no—
191#355—1221no—
192#355C2×D6111yescharacteristic
193#354—611no—
194#354C2×D6111yescharacteristic
195#353—1221no—
196C61#1360511yescharacteristic, complemented, Sylow
197C2×#41—611no—
198C22×D4—611no—
199C2×SD16—1221no—
200C2×D8—1221no—
201C2×D8—1221no—
202C2×D8—1221no—
203C2×M16—2441no—
204#127—611no—
205#127—611no—
206#127—611no—
207#125C4×D6111yescharacteristic, complemented
208#124—611no—
209#124C22×D6111yescharacteristic
210#123—2441no—
211#121—1221no—
212#121—2441no—
213#121—2441no—
214#120—2441no—
215C4×D4—1221no—
216#117—611no—
217C2×C22⋊C4—2441no—
218C4⋊C8—1221no—
219#103—21no—
220#102—21no—
221#102—1221no—
222#102—1221no—
223#101—21no—
224#101—1221no—
225#100—2441no—
226#99—21no—
227#99—1221no—
228#99—2441no—
229C22⋊C8—1221no—
230#97—611no—
231C4×C8C4×D6111yescharacteristic, complemented
232C24—1221no—
233#41—4881no—
234C2×Q8D4×D6111yescharacteristic
235C2×D4—611no—
236C2×D4—611no—
237C2×D4—1221no—
238C2×D4—1221no—
239C2×D4—1221no—
240C2×D4—4881no—
241C2×D4—2441no—
242C2×D4—2441no—
243C2×D4—2441no—
244C2×D4—2441no—
245C2×D4D4×D6111yescharacteristic
246C22×C4—611no—
247C22×C4—1221no—
248C22×C4—4881no—
249C22×C4—2441no—
250SD16—4881no—
251D8—4881no—
252D8—4881no—
253D8—4881no—
254M16—41no—
255M16—4881no—
256M16—2441no—
257C2×C8—21no—
258C2×C8—1221no—
259C2×C8—4881no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—1221no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—1221no—
266C22⋊C4—4881no—
267C22⋊C4—2441no—
268C22⋊C4—2441no—
269C22⋊C4—2441no—
270C22⋊C4—2441no—
271C42—611no—
272C42C2×C4×D6111yescharacteristic
273C23—21no—
274C23—611no—
275C23—1221no—
276C23—1221no—
277C23—9761no—
278C23—2441no—
279C23—2441no—
280C23—2441no—
281Q8—41no—
282D4—41no—
283D4—9761no—
284D4—9761no—
285D4—9761no—
286D4—9761no—
287D4—4881no—
288D4—4881no—
289D4—2441no—
290D4—2441no—
291D4—2441no—
292D4—2441no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—81no—
297C2×C4—611no—
298C2×C4—1221no—
299C2×C4—9761no—
300C2×C4—9762no—
301C2×C4—4881no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4C22⋊C4×D6111yescharacteristic
306C8—41no—
307C8—81no—
308C8—4881no—
309C8—2441no—
310C22—41no—
311C22—81no—
312C22—1221no—
313C22—9761no—
314C22—4881no—
315C22—4881no—
316C22—4881no—
317C22—4881no—
318C22—4882no—
319C22—4881no—
320C22—2441no—
321C22—2441no—
322C22—2441no—
323C22#99×D6111yescharacteristic
324C4—21no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—161no—
329C4—1221no—
330C4—9761no—
331C4—2441no—
332C2—21no—
333C2—81no—
334C2—9761no—
335C2—4881no—
336C2—4881no—
337C2—2441no—
338C2#2144748711yescharacteristic
subgroupG/H
centerC2#21447487
commutatorC42×C61C22×C4
Frattini#124C22×D61
FittingC61×#1414C2
socleC2×C61#2127
prime radical#21456872C2
cosocle#124×C61C23
hypercenter#1414D61
hypocenterC61#13605
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #1414

Complements

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

NH ≅ G/Ntype
2. #21447509C2semidirect
3. #21447487C2semidirect
4. #21443994C2semidirect
5. #21443977C2semidirect
6. #21443975C2semidirect
7. C61×#1414C2semidirect
8. #16840368C4semidirect
11. #16840139C4semidirect
12. #16840128C4semidirect
17. #16839821C4semidirect
35. #14519774C2×C4semidirect
54. #14519688C2×C4semidirect
55. #125×C61C2×C4semidirect
61. C4×C8×C61C2×C4semidirect
167. #1414D61semidirect
196. C61#13605semidirect
207. #125C4×D61semidirect
231. C4×C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214568722
#214475092
#214474872
#214439942
#214439772
#214439752
C61×#14142
#1360561