Finite Group Databasebeta

← #29593577

Subgroups — #29593577

Order 15616.

336 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 67 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#21448086C211yesmaximal, characteristic, complemented
2#21447854C211yesmaximal, characteristic, complemented
3#21445303C211yesmaximal, characteristic, complemented
4#21443862C211yesmaximal, characteristic, complemented
5#21443801C211yesmaximal, characteristic, complemented
6#21443786C211yesmaximal, characteristic, complemented
7C61×#3403C211yesmaximal, characteristic, complemented
8C2×#14519720—21no—
9C2×#14519718—21no—
10C2×#14519718—21no—
11#16840139C2211yescharacteristic
12#16839962—21no—
13C4⋊#11758185C2211yescharacteristic
14#16839562—21no—
15#16839538C2211yescharacteristic
16#16839513C2211yescharacteristic
17#16839505—21no—
18C61×#559—21no—
19C61×#496—21no—
20C61×#495C2211yescharacteristic
21C61×#464—21no—
22C61×#463—21no—
23C61×#459—21no—
24C61×#446C2211yescharacteristic
25C61×#440—21no—
26C4×D8×C61C2211yescharacteristic
27C2×#11758201—41no—
28C2×D488—21no—
29C2×D488—21no—
30#14519774—21no—
31#14519720—42no—
32#14519718—42no—
33#14519718—42no—
34C2×#11758185—21no—
35C2×#11758185—21no—
36C4⋊#92418—21no—
37#14519697—41no—
38C2×Q16×C61D411yescharacteristic
39C2×SD16×C61—21no—
40C2×SD16×C61—21no—
41C2×D8×C61—21no—
42C2×D8×C61D411yescharacteristic
43C2×D8×C61D411yescharacteristic
44#127×C61—21no—
45#124×C61—21no—
46#124×C61—21no—
47#124×C61—41no—
48#123×C61—41no—
49#123×C61—41no—
50C4×Q8×C61—21no—
51C4×Q8×C61D411yescharacteristic
52C4×D4×C61—21no—
53C4×D4×C61—21no—
54C4×D4×C61—41no—
55#107×C61D411yescharacteristic
56C4⋊C8×C61—21no—
57C4⋊C8×C61D411yescharacteristic
58#103×C61—21no—
59#102×C61—21no—
60#102×C61—21no—
61#97×C61—21no—
62C4×C8×C61C2311yescharacteristic
63C2×Q8×C61—21no—
64C2×Q8×C61D811yescharacteristic
65C2×D4×C61—21no—
66C2×D4×C61—21no—
67C2×D4×C61—41no—
68C2×D4×C61—41no—
69C22×C4×C61—41no—
70C22×C4×C61—41no—
71C2×D244—41no—
72C2×D244—41no—
73C2×D244—41no—
74Q16×C61—41no—
75SD16×C61—41no—
76SD16×C61—41no—
77SD16×C61—81no—
78D8×C61—21no—
79D8×C61—21no—
80D8×C61—41no—
81D8×C61—81no—
82C2×C8×C61—21no—
83C2×C8×C61C2×D411yescharacteristic
84C2×C8×C61C2×D411yescharacteristic
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61D811yescharacteristic
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C42×C61—21no—
96C42×C61—41no—
97C42×C61C2×D411yescharacteristic
98#11758201—82no—
99C2×#92418—41no—
100D488—41no—
101D488—41no—
102D488—41no—
103D488—41no—
104#11758185—22no—
105#11758185—41no—
106C23×C61—41no—
107C23×C61—41no—
108C22×D61—81no—
109Q8×C61—41no—
110Q8×C61—41no—
111Q8×C61—41no—
112D4×C61—41no—
113D4×C61—41no—
114D4×C61—41no—
115D4×C61—41no—
116D4×C61—82no—
117D4×C61—161no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—161no—
123C2×C4×C61—161no—
124C2×C4×C61#12011yescharacteristic
125C2×C4×C61C2×D811yescharacteristic
126C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
127D244—81no—
128D244—81no—
129D244—81no—
130D244—81no—
131D244—161no—
132C8×C61—21no—
133C8×C61—41no—
134C8×C61#13511yescharacteristic
135C8×C61AGL(1,ℤ/8)11yescharacteristic
136#92418—81no—
137#12336—611nomaximal, Sylow
138C22×C61—81no—
139C22×C61—81no—
140C22×C61—81no—
141C22×C61—81no—
142C22×C61—81no—
143C22×C61—81no—
144C22×C61#44711yescharacteristic
145C2×D61—161no—
146C2×D61—161no—
147C2×D61—161no—
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—81no—
153C4×C61—81no—
154C4×C61#44911yescharacteristic
155C4×C61#45311yescharacteristic
156#3403D6111yescharacteristic, complemented
157#2250—611no—
158#2206—611no—
159#1688—611no—
160#1360—611no—
161#1338—611no—
162#1333—611no—
163C2×C61—161no—
164C2×C61—161no—
165C2×C61#162111yescharacteristic
166C2×C61#219011yescharacteristic
167C2×C61#219211yescharacteristic
168D61—321no—
169#559—21no—
170C2×SD32—1221no—
171C2×D16—1221no—
172C2×D16—1221no—
173#496—21no—
174#495C2×D6111yescharacteristic
175#493—611no—
176#464—21no—
177#463—21no—
178#460—1221no—
179#459—21no—
180#446C2×D6111yescharacteristic
181#440—21no—
182C4×D8C2×D6111yescharacteristic
183C4⋊C16—611no—
184#357—1221no—
185#346—611no—
186#334—611no—
187#331—1221no—
188C61#1233611yescharacteristic, complemented, Sylow
189C2×Q16C22⋊D6111yescharacteristic
190C2×SD16—21no—
191C2×SD16—21no—
192C2×SD16—2441no—
193C2×D8—21no—
194C2×D8—1221no—
195C2×D8—1221no—
196C2×D8C22⋊D6111yescharacteristic
197C2×D8C22⋊D6111yescharacteristic
198#127—21no—
199#127—1221no—
200#124—21no—
201#124—21no—
202#124—41no—
203#123—41no—
204#123—41no—
205C4×Q8—21no—
206C4×Q8C22⋊D6111yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—41no—
210SD32—2442no—
211D16—2442no—
212D16—2442no—
213C2×C16—1221no—
214C2×C16—1221no—
215#107C22⋊D6111yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—1221no—
218C4⋊C8C22⋊D6111yescharacteristic
219#103—21no—
220#102—21no—
221#102—21no—
222#102—2441no—
223#97—21no—
224C4×C8C22×D6111yescharacteristic
225C2×Q8—21no—
226C2×Q8#1175819911yescharacteristic
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—2441no—
232C2×D4—2441no—
233C2×D4—2441no—
234C22×C4—41no—
235C22×C4—41no—
236Q16—41no—
237SD16—41no—
238SD16—41no—
239SD16—81no—
240SD16—4882no—
241D8—21no—
242D8—21no—
243D8—41no—
244D8—81no—
245D8—2441no—
246D8—2441no—
247D8—2441no—
248D8—2441no—
249C2×C8—21no—
250C2×C8—2441no—
251C2×C8C2×C22⋊D6111yescharacteristic
252C2×C8C2×C22⋊D6111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4#1175819911yescharacteristic
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C42—21no—
264C42—41no—
265C42C2×C22⋊D6111yescharacteristic
266C16—1222no—
267C16—2441no—
268C23—41no—
269C23—41no—
270C23—4881no—
271Q8—41no—
272Q8—41no—
273Q8—41no—
274D4—41no—
275D4—41no—
276D4—41no—
277D4—41no—
278D4—82no—
279D4—161no—
280D4—9761no—
281D4—4881no—
282D4—4881no—
283D4—4881no—
284D4—4881no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—161no—
290C2×C4—161no—
291C2×C4#1451974611yescharacteristic
292C2×C4C2×#1175819911yescharacteristic
293C2×C4#1451980311yescharacteristic
294C8—21no—
295C8—41no—
296C8—4881no—
297C8#1451979711yescharacteristic
298C8#1451980211yescharacteristic
299C22—81no—
300C22—81no—
301C22—81no—
302C22—81no—
303C22—81no—
304C22—81no—
305C22—9761no—
306C22—9761no—
307C22—9761no—
308C22#1683989611yescharacteristic
309C4—21no—
310C4—21no—
311C4—41no—
312C4—41no—
313C4—81no—
314C4—81no—
315C4#1683990711yescharacteristic
316C4#1683993011yescharacteristic
317C2—161no—
318C2—161no—
319C2—19521no—
320C2#2144488411yescharacteristic
321C2#2144776511yescharacteristic
322C2#2144777611yescharacteristic
subgroupG/H
centerC22#16839896
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#3403C2
socleC22×C61#447
hypercenter#3403D61
hypocenterC61#12336
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #3403

Complements

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

NH ≅ G/Ntype
1. #21448086C2semidirect
2. #21447854C2semidirect
3. #21445303C2semidirect
4. #21443862C2semidirect
5. #21443801C2semidirect
6. #21443786C2semidirect
7. C61×#3403C2semidirect
156. #3403D61semidirect
188. C61#12336semidirect

Maximal subgroups

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

subgroupindex
#214480862
#214478542
#214453032
#214438622
#214438012
#214437862
C61×#34032
#1233661