Finite Group Databasebeta

← #29593308

Subgroups — #29593308

Order 15616.

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

normal subgroups only

This group has 302 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#21457253C211yesmaximal, characteristic
2#21447999C211yesmaximal, characteristic, complemented
3#21447325C211yesmaximal, characteristic, complemented
4#21443835C211yesmaximal, characteristic, complemented
5#21443834C211yesmaximal, characteristic, complemented
6#21443760C211yesmaximal, characteristic, complemented
7C61×#2233C211yesmaximal, characteristic, complemented
8#16840365—21no—
9#16840065—21no—
10#16840060—21no—
11#16840013—21no—
12#16839998C2211yescharacteristic
13#16839956—21no—
14#16839955—21no—
15#16839802—21no—
16#16839788C2211yescharacteristic
17#16839587—21no—
18#16839562—21no—
19C22⋊#11758185C2211yescharacteristic
20#16839531—21no—
21#16839527C2211yescharacteristic
22C61×#466C2211yescharacteristic
23C2×#107×C61C2211yescharacteristic
24C61×#367—21no—
25C61×#357—21no—
26C61×C22⋊C16C2211yescharacteristic
27C2×D488D411yescharacteristic
28C2×#11758199—21no—
29C2×#11758194—21no—
30C2×#11758194D411yescharacteristic
31#14519773—21no—
32#14519768—21no—
33#14519761—41no—
34#14519759—41no—
35#14519751—21no—
36#14519749—41no—
37#14519748—41no—
38D4×Dic61—21no—
39#14519739—21no—
40#14519736D411yescharacteristic
41C2×#11758185—21no—
42#14519711D411yescharacteristic
43#14519710—41no—
44#14519708—21no—
45#14519708—41no—
46#14519706—21no—
47#14519706—21no—
48#14519699—21no—
49#14519698—21no—
50#14519697—21no—
51C2×D8×C61D411yescharacteristic
52C22×C8×C61C2311yescharacteristic
53#121×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C16×C61—21no—
56#107×C61—21no—
57#107×C61—21no—
58#107×C61D411yescharacteristic
59#102×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61C2×D411yescharacteristic
64C2×C22⋊D61—41no—
65C2×C22⋊D61—41no—
66C2×C22⋊D61—41no—
67C22×Dic61—41no—
68C2×D244—21no—
69C2×C4×D61—41no—
70D8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61C2×D411yescharacteristic
73C2×C8×C61C2×D411yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C22⋊C4×C61—41no—
78C22⋊Dic61—21no—
79C22⋊Dic61—41no—
80#11758199—81no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—21no—
84C4⋊Dic61—41no—
85C4⋊Dic61D811yescharacteristic
86C4⋊Dic61D811yescharacteristic
87#11758196—41no—
88C4×Dic61—21no—
89#11758194—22no—
90#11758194—41no—
91#11758194—41no—
92C2×#92418—21no—
93C2×#92418—41no—
94D488—41no—
95C16×C61—41no—
96#11758185—41no—
97C23×C61—41no—
98C23×C61AGL(1,ℤ/8)11yescharacteristic
99C22×D61—41no—
100D4×C61—41no—
101D4×C61—41no—
102D4×C61—161no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—41no—
106C2×C4×C61—81no—
107C2×C4×C61—161no—
108C2×C4×C61#12011yescharacteristic
109C2×C4×C61C2×D811yescharacteristic
110C22⋊D61—161no—
111C22⋊D61—161no—
112C22⋊D61—161no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—41no—
116C2×Dic61—161no—
117D244—41no—
118D244—41no—
119C4×D61—161no—
120C8×C61—21no—
121C8×C61—21no—
122#92418—42no—
123#92418—41no—
124#12294—611nomaximal, Sylow
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—81no—
129C22×C61—81no—
130C22×C61—81no—
131C22×C61#44711yescharacteristic
132C2×D61—81no—
133C2×D61—81no—
134C2×D61—81no—
135C4×C61—21no—
136C4×C61—81no—
137C4×C61—161no—
138C4×C61#45611yescharacteristic
139C4×C61#45811yescharacteristic
140Dic61—41no—
141Dic61—41no—
142Dic61—81no—
143#3259—611no—
144#2233D6111yescharacteristic, complemented
145#2232—611no—
146#2089—611no—
147#1349—611no—
148#1349—611no—
149#1323—611no—
150C2×C61—41no—
151C2×C61—161no—
152C2×C61#161011yescharacteristic
153C2×C61#219211yescharacteristic
154C2×C61#219411yescharacteristic
155D61—161no—
156#540—1221no—
157#478—1221no—
158#478—1221no—
159#469—1221no—
160#466—611no—
161#466C2×D6111yescharacteristic
162#459—1221no—
163#459—1221no—
164#428—1221no—
165C2×#107C2×D6111yescharacteristic
166#424—611no—
167#367—21no—
168#366—1221no—
169#357—21no—
170#357—1221no—
171C22⋊C16—611no—
172C22⋊C16C2×D6111yescharacteristic
173#343—1221no—
174#341—611no—
175C61#1229411yescharacteristic, complemented, Sylow
176C2×D8—611no—
177C2×D8—1221no—
178C2×D8C22⋊D6111yescharacteristic
179C2×M16—611no—
180C2×M16—1221no—
181C22×C8C22×D6111yescharacteristic
182#127—1221no—
183#125—1221no—
184#123—2441no—
185#123—2441no—
186#121—21no—
187#121—1221no—
188#121—2441no—
189#121—2441no—
190C4×D4—1221no—
191C4×D4—1221no—
192#117—611no—
193C2×C4⋊C4—21no—
194C2×C16—21no—
195C2×C16—1221no—
196#107—21no—
197#107—21no—
198#107—611no—
199#107—2441no—
200#107C22⋊D6111yescharacteristic
201#106—1221no—
202#106—2441no—
203C4⋊C8—1221no—
204C4⋊C8—1221no—
205#102—21no—
206#102—1221no—
207#102—1221no—
208#102—1221no—
209C2×D4—21no—
210C2×D4—41no—
211C2×D4—1221no—
212C2×D4—2441no—
213C2×D4—2441no—
214C2×D4—2441no—
215C22×C4—41no—
216C22×C4—2441no—
217C22×C4—2441no—
218C22×C4D4×D6111yescharacteristic
219D8—41no—
220D8—4881no—
221D8—2441no—
222M16—1222no—
223M16—2441no—
224M16—2441no—
225C2×C8—41no—
226C2×C8—1221no—
227C2×C8—2441no—
228C2×C8D4×D6111yescharacteristic
229C2×C8C2×C22⋊D6111yescharacteristic
230C4⋊C4—21no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—611no—
234C4⋊C4—611no—
235C4⋊C4—1221no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C22⋊C4—41no—
239C22⋊C4—1221no—
240C22⋊C4—2441no—
241C22⋊C4—2441no—
242C22⋊C4—2441no—
243C42—1221no—
244C16—41no—
245C16—2441no—
246C23—41no—
247C23—2441no—
248C23#1451980111yescharacteristic
249D4—41no—
250D4—41no—
251D4—161no—
252D4—9761no—
253D4—9761no—
254D4—9761no—
255D4—2441no—
256D4—2441no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—81no—
261C2×C4—161no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—9761no—
265C2×C4—9761no—
266C2×C4—2441no—
267C2×C4#1451974511yescharacteristic
268C2×C4D8×D6111yescharacteristic
269C8—21no—
270C8—21no—
271C8—2442no—
272C8—2441no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—81no—
277C22—81no—
278C22—81no—
279C22—4881no—
280C22—4881no—
281C22—4881no—
282C22#1683989411yescharacteristic
283C4—21no—
284C4—81no—
285C4—161no—
286C4—4881no—
287C4—2441no—
288C4—2441no—
289C4#1683994311yescharacteristic
290C4#1683995111yescharacteristic
291C2—41no—
292C2—161no—
293C2—9761no—
294C2#2144482011yescharacteristic
295C2#2144777311yescharacteristic
296C2#2144778911yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2233C2
socleC22×C61#447
prime radical#21457253C2
hypercenter#2233D61
hypocenterC61#12294
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2233

Complements

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

NH ≅ G/Ntype
2. #21447999C2semidirect
3. #21447325C2semidirect
4. #21443835C2semidirect
5. #21443834C2semidirect
6. #21443760C2semidirect
7. C61×#2233C2semidirect
144. #2233D61semidirect
175. C61#12294semidirect

Maximal subgroups

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

subgroupindex
#214572532
#214479992
#214473252
#214438352
#214438342
#214437602
C61×#22332
#1229461