Finite Group Databasebeta

← #29593255

Subgroups — #29593255

Order 15616.

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

normal subgroups only

This group has 318 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#21456722C211yesmaximal, characteristic
2#21448004C211yesmaximal, characteristic, complemented
3#21447260C211yesmaximal, characteristic, complemented
4#21443837C211yesmaximal, characteristic, complemented
5#21443835C211yesmaximal, characteristic, complemented
6#21443744C211yesmaximal, characteristic, complemented
7C61×#2235C211yesmaximal, characteristic, complemented
8#16840342—21no—
9#16840096—21no—
10#16840077—21no—
11#16840010—21no—
12#16839998C2211yescharacteristic
13#16839923—21no—
14#16839910—21no—
15#16839761—21no—
16#16839728C2211yescharacteristic
17#16839589—21no—
18#16839562—21no—
19C22⋊#11758185C2211yescharacteristic
20#16839531—21no—
21#16839527C2211yescharacteristic
22C61×#467C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#367—21no—
25C61×#358—21no—
26C61×C22⋊C16C2211yescharacteristic
27C2×#11758226—21no—
28C2×#11758222D411yescharacteristic
29C2×#11758201—21no—
30C2×D488D411yescharacteristic
31C2×#11758194—21no—
32C2×#11758194D411yescharacteristic
33#14519755—41no—
34#14519753—21no—
35#14519752—21no—
36#14519752—41no—
37#14519751—21no—
38#14519750—41no—
39#14519750—41no—
40C4⋊C4×D61—21no—
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519710—21no—
44#14519701—21no—
45#14519700—41no—
46#14519699—21no—
47#14519697—21no—
48#14519697—41no—
49#14519689—21no—
50#14519689—21no—
51C2×Q16×C61D411yescharacteristic
52C22×C8×C61C2311yescharacteristic
53C22⋊Q8×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C16×C61—21no—
56#107×C61—21no—
57#107×C61—21no—
58#107×C61D411yescharacteristic
59#103×C61—21no—
60C2×Q8×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61C2×D411yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—41no—
65#11758226—81no—
66#11758226—81no—
67#11758222—41no—
68#11758222—41no—
69C2×D244—21no—
70C2×D244—41no—
71C2×D244—41no—
72C2×D244D811yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×Dic122D811yescharacteristic
77Q16×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61C2×D411yescharacteristic
80C2×C8×C61C2×D411yescharacteristic
81C4⋊C4×C61—21no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C22⋊C4×C61—41no—
86#11758201—81no—
87#11758198—41no—
88#11758198—41no—
89#11758198—41no—
90C4⋊Dic61—21no—
91#11758196—41no—
92#11758196—41no—
93#11758194—41no—
94#11758194—41no—
95#11758194—41no—
96C2×#92418—21no—
97C2×#92418—41no—
98D488—41no—
99C16×C61—41no—
100#11758185—41no—
101C23×C61AGL(1,ℤ/8)11yescharacteristic
102C22×D61—21no—
103C22×D61—41no—
104Q8×C61—41no—
105Q8×C61—41no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—81no—
111C2×C4×C61—161no—
112C2×C4×C61#12011yescharacteristic
113C2×C4×C61C2×D811yescharacteristic
114C22⋊D61—81no—
115C22⋊D61—161no—
116C2×Dic61—21no—
117C2×Dic61—41no—
118D244—41no—
119D244—41no—
120D244—41no—
121D244—82no—
122D244—161no—
123C4×D61—41no—
124C4×D61—41no—
125C4×D61—82no—
126C4×D61—161no—
127Dic122—41no—
128C8×C61—21no—
129C8×C61—21no—
130#92418—41no—
131#92418—81no—
132#12285—611nomaximal, Sylow
133C22×C61—21no—
134C22×C61—21no—
135C22×C61—21no—
136C22×C61#44711yescharacteristic
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—41no—
140C2×D61—81no—
141C2×D61—81no—
142C2×D61—81no—
143C4×C61—21no—
144C4×C61—81no—
145C4×C61—81no—
146C4×C61—161no—
147C4×C61#45511yescharacteristic
148C4×C61#45811yescharacteristic
149Dic61—41no—
150Dic61—81no—
151#3203—611no—
152#2235D6111yescharacteristic, complemented
153#2233—611no—
154#2078—611no—
155#1350—611no—
156#1349—611no—
157#1315—611no—
158C2×C61—41no—
159C2×C61#160711yescharacteristic
160C2×C61#219311yescharacteristic
161C2×C61#219411yescharacteristic
162D61—81no—
163D61—161no—
164#537—1221no—
165#484—1221no—
166#480—1221no—
167#468—1221no—
168#467C2×D6111yescharacteristic
169#466—611no—
170#452—1221no—
171#449—1221no—
172C2×#107C2×D6111yescharacteristic
173#417—1221no—
174#408—611no—
175#367—21no—
176#367—1221no—
177#358—21no—
178#357—1221no—
179C22⋊C16—611no—
180C22⋊C16C2×D6111yescharacteristic
181#343—1221no—
182#341—611no—
183C61#1228511yescharacteristic, complemented, Sylow
184C2×#41—611no—
185C2×#41—1221no—
186C2×Q16C22⋊D6111yescharacteristic
187C2×SD16—1221no—
188C2×D8—611no—
189C2×M16—611no—
190C2×M16—1221no—
191C22×C8C22×D6111yescharacteristic
192C22⋊Q8—21no—
193C22⋊Q8—1221no—
194C22⋊Q8—2441no—
195#121—1221no—
196#121—1221no—
197#121—2441no—
198#121—2441no—
199#121—2441no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—1221no—
202C2×C16—21no—
203C2×C16—1221no—
204#107—21no—
205#107—21no—
206#107—611no—
207#107—1221no—
208#107C22⋊D6111yescharacteristic
209#103—21no—
210#103—1221no—
211#103—2441no—
212#102—1221no—
213#102—1221no—
214#102—2441no—
215C22⋊C8—1221no—
216C22⋊C8—1221no—
217#41—4881no—
218#41—4881no—
219#41—2441no—
220#41—2441no—
221C2×Q8—21no—
222C2×Q8—611no—
223C2×D4—611no—
224C2×D4—1221no—
225C2×D4—1221no—
226C2×D4—2441no—
227C2×D4—2441no—
228C2×D4—2441no—
229C22×C4—41no—
230C22×C4—1221no—
231C22×C4—2441no—
232C22×C4—2441no—
233C22×C4D4×D6111yescharacteristic
234Q16—41no—
235SD16—4881no—
236D8—2441no—
237M16—2441no—
238M16—2441no—
239M16—2441no—
240C2×C8—41no—
241C2×C8—1221no—
242C2×C8—2441no—
243C2×C8D4×D6111yescharacteristic
244C2×C8C2×C22⋊D6111yescharacteristic
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—1221no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C22⋊C4—41no—
253C22⋊C4—2441no—
254C22⋊C4—2441no—
255C22⋊C4—2441no—
256C16—41no—
257C16—2441no—
258C23—1221no—
259C23—2441no—
260C23#1451980111yescharacteristic
261Q8—41no—
262Q8—41no—
263Q8—2441no—
264D4—9761no—
265D4—9761no—
266D4—4882no—
267D4—4881no—
268D4—2441no—
269D4—2441no—
270D4—2441no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—161no—
277C2×C4—1221no—
278C2×C4—9761no—
279C2×C4—4882no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4#1451974511yescharacteristic
284C2×C4D8×D6111yescharacteristic
285C8—21no—
286C8—21no—
287C8—4881no—
288C8—2441no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—4881no—
293C22—4881no—
294C22—4881no—
295C22—2441no—
296C22—2441no—
297C22—2441no—
298C22#1683989411yescharacteristic
299C4—21no—
300C4—81no—
301C4—81no—
302C4—161no—
303C4—4881no—
304C4—2441no—
305C4#1683993811yescharacteristic
306C4#1683995111yescharacteristic
307C2—41no—
308C2—9761no—
309C2—4881no—
310C2#2144480311yescharacteristic
311C2#2144778211yescharacteristic
312C2#2144778711yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2235C2
socleC22×C61#447
prime radical#21456722C2
hypercenter#2235D61
hypocenterC61#12285
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2235

Complements

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

NH ≅ G/Ntype
2. #21448004C2semidirect
3. #21447260C2semidirect
4. #21443837C2semidirect
5. #21443835C2semidirect
6. #21443744C2semidirect
7. C61×#2235C2semidirect
152. #2235D61semidirect
183. C61#12285semidirect

Maximal subgroups

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

subgroupindex
#214567222
#214480042
#214472602
#214438372
#214438352
#214437442
C61×#22352
#1228561