Finite Group Databasebeta

← #29593313

Subgroups — #29593313

Order 15616.

302 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 59 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#21457258C211yesmaximal, characteristic
2#21448005C211yesmaximal, characteristic, complemented
3#21448000C211yesmaximal, characteristic, complemented
4#21447324C211yesmaximal, characteristic, complemented
5#21443835C211yesmaximal, characteristic, complemented
6#21443835C211yesmaximal, characteristic, complemented
7C61×#1323C211yesmaximal, characteristic, complemented
8#16840367—21no—
9#16840063—21no—
10#16840063—21no—
11#16840015—21no—
12#16839998C2211yescharacteristic
13#16839998C2211yescharacteristic
14#16839958—21no—
15#16839958—21no—
16#16839805—21no—
17C2×#14519711C2211yescharacteristic
18#16839590—21no—
19#16839588—21no—
20#16839564—21no—
21#16839564—21no—
22#16839530—21no—
23#16839527C2211yescharacteristic
24C61×#424C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×C22⋊C16C2211yescharacteristic
27C2×D488—21no—
28C2×D488D411yescharacteristic
29C2×D488D411yescharacteristic
30C2×#11758194—21no—
31#14519774—21no—
32#14519769—21no—
33#14519762—41no—
34#14519762—41no—
35#14519751—21no—
36#14519751—21no—
37#14519750—41no—
38#14519750—41no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—21no—
42#14519711—21no—
43#14519711—21no—
44#14519711D411yescharacteristic
45#14519711D411yescharacteristic
46#14519710—41no—
47#14519709—21no—
48#14519708—41no—
49#14519699—21no—
50#14519699—21no—
51#14519699—21no—
52#14519699—21no—
53C2×M16×C61D411yescharacteristic
54C22×C8×C61C2311yescharacteristic
55#117×C61D411yescharacteristic
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C22×C4×C61C2×D411yescharacteristic
61C2×C22⋊D61—41no—
62C2×C22⋊D61—41no—
63C22×Dic61—41no—
64C2×D244—21no—
65C2×D244—21no—
66C2×D244—41no—
67C2×D244—41no—
68C2×C4×D61—41no—
69C2×C4×D61—41no—
70M16×C61—41no—
71C2×C8×C61—21no—
72C2×C8×C61—41no—
73C2×C8×C61C2×D411yescharacteristic
74C2×C8×C61C2×D411yescharacteristic
75C4⋊C4×C61D811yescharacteristic
76C4⋊C4×C61D811yescharacteristic
77C22⋊C4×C61—21no—
78C42×C61—21no—
79#11758198—41no—
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—21no—
84C4⋊Dic61—21no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87#11758196—41no—
88#11758196—41no—
89#11758194—22no—
90#11758194—41no—
91C2×#92418—41no—
92D488—41no—
93D488—41no—
94D488—81no—
95C16×C61—41no—
96C16×C61—41no—
97C23×C61AGL(1,ℤ/8)11yescharacteristic
98C22×D61—41no—
99C22×D61—41no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61#12011yescharacteristic
105C2×C4×C61C2×D811yescharacteristic
106C22⋊D61—161no—
107C22⋊D61—161no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—81no—
111C2×Dic61—161no—
112D244—41no—
113D244—41no—
114D244—41no—
115D244—41no—
116D244—161no—
117D244—161no—
118C4×D61—161no—
119C4×D61—161no—
120C8×C61—21no—
121C8×C61—21no—
122C8×C61—41no—
123#92418—42no—
124#12294—611nomaximal, Sylow
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—21no—
128C22×C61#44711yescharacteristic
129C2×D61—81no—
130C2×D61—81no—
131C2×D61—81no—
132C2×D61—81no—
133C2×D61—81no—
134C2×D61—81no—
135C4×C61—21no—
136C4×C61—41no—
137C4×C61—41no—
138C4×C61#45611yescharacteristic
139C4×C61#45811yescharacteristic
140Dic61—81no—
141Dic61—81no—
142Dic61—161no—
143#3259—611no—
144#2233—611no—
145#2232—611no—
146#2089—611no—
147#1349—611no—
148#1349—611no—
149#1323D6111yescharacteristic, complemented
150C2×C61—41no—
151C2×C61#161011yescharacteristic
152C2×C61#219211yescharacteristic
153C2×C61#219411yescharacteristic
154D61—161no—
155D61—161no—
156#540—1221no—
157#478—1221no—
158#478—1221no—
159#469—1221no—
160#466—611no—
161#466—611no—
162#459—1221no—
163#459—1221no—
164#428—1221no—
165C2×#107—611no—
166#424C2×D6111yescharacteristic
167#367—1221no—
168#366—1221no—
169#357—1221no—
170#357—1221no—
171C22⋊C16C2×D6111yescharacteristic
172C22⋊C16C2×D6111yescharacteristic
173#343—1221no—
174#341—611no—
175C61#1229411yescharacteristic, complemented, Sylow
176C2×D8—611no—
177C2×D8—611no—
178C2×D8—1221no—
179C2×M16—1221no—
180C2×M16D24411yescharacteristic
181C22×C8C22×D6111yescharacteristic
182#127—1221no—
183#125—1221no—
184#123—2441no—
185#123—2441no—
186#121—1221no—
187#121—1221no—
188#121—2441no—
189#121—2441no—
190C4×D4—1221no—
191C4×D4—1221no—
192#117D24411yescharacteristic
193C2×C4⋊C4—1221no—
194C2×C16—21no—
195C2×C16—21no—
196#107—611no—
197#107—611no—
198#107—1221no—
199#107—1221no—
200#107—2441no—
201#106—1221no—
202#106—2441no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205#102—1221no—
206#102—1221no—
207#102—1221no—
208#102—1221no—
209C2×D4—1221no—
210C2×D4—1221no—
211C2×D4—2441no—
212C2×D4—2441no—
213C2×D4—2441no—
214C2×D4—2441no—
215C22×C4—2441no—
216C22×C4—2441no—
217C22×C4—2441no—
218C22×C4C2×D24411yescharacteristic
219D8—4881no—
220D8—2441no—
221D8—2441no—
222M16—41no—
223M16—1222no—
224M16—2441no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8—2441no—
228C2×C8D4×D6111yescharacteristic
229C2×C8D4×D6111yescharacteristic
230C4⋊C4—1221no—
231C4⋊C4—1221no—
232C4⋊C4—2441no—
233C4⋊C4—2441no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4D48811yescharacteristic
237C4⋊C4D48811yescharacteristic
238C22⋊C4—21no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C22⋊C4—2441no—
242C22⋊C4—2441no—
243C42—21no—
244C16—41no—
245C16—41no—
246C23—2441no—
247C23—2441no—
248C23#1451980511yescharacteristic
249D4—9761no—
250D4—9761no—
251D4—9761no—
252D4—9761no—
253D4—2441no—
254D4—2441no—
255D4—2441no—
256D4—2441no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—9761no—
262C2×C4—9761no—
263C2×C4—9761no—
264C2×C4—4881no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4#1451974711yescharacteristic
268C2×C4C2×D48811yescharacteristic
269C8—21no—
270C8—21no—
271C8—41no—
272C8—2442no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—4881no—
277C22—4881no—
278C22—4881no—
279C22—4881no—
280C22—4881no—
281C22—4881no—
282C22#1683989811yescharacteristic
283C4—21no—
284C4—41no—
285C4—41no—
286C4—9761no—
287C4—4881no—
288C4—4881no—
289C4#1683994711yescharacteristic
290C4#1683995311yescharacteristic
291C2—41no—
292C2—9761no—
293C2—9761no—
294C2#2144482411yescharacteristic
295C2#2144777811yescharacteristic
296C2#2144779211yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1323C2
socleC22×C61#447
prime radical#21457258C2
hypercenter#1323D61
hypocenterC61#12294
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #21448005C2semidirect
3. #21448000C2semidirect
4. #21447324C2semidirect
5. #21443835C2semidirect
6. #21443835C2semidirect
7. C61×#1323C2semidirect
149. #1323D61semidirect
175. C61#12294semidirect

Maximal subgroups

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

subgroupindex
#214572582
#214480052
#214480002
#214473242
#214438352
C61×#13232
#1229461