Finite Group Databasebeta

← #29593581

Subgroups — #29593581

Order 15616.

324 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 61 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#21458901C211yesmaximal, characteristic, complemented
2#21447856C211yesmaximal, characteristic, complemented
3#21445300C211yesmaximal, characteristic, complemented
4#21443862C211yesmaximal, characteristic, complemented
5#21443802C211yesmaximal, characteristic, complemented
6#21443790C211yesmaximal, characteristic, complemented
7C61×#2250C211yesmaximal, characteristic
8#16840481—21no—
9C2×#14519721—21no—
10#16840153—21no—
11#16839981—21no—
12#16839975—21no—
13#16839970—21no—
14#16839959—21no—
15#16839892C2211yescharacteristic
16#16839863—21no—
17C4×Dic244C2211yescharacteristic
18C4⋊#11758185C2211yescharacteristic
19#16839563—21no—
20#16839513C2211yescharacteristic
21#16839506—21no—
22C2×SD32×C61—21no—
23C2×D16×C61—21no—
24C61×#495C2211yescharacteristic
25C61×#493C2211yescharacteristic
26C61×#346C2211yescharacteristic
27C2×Dic244D411yescharacteristic
28C2×#11758202—21no—
29C2×#11758200—21no—
30C2×#11758200—41no—
31#14519775—21no—
32#14519770—41no—
33#14519770—41no—
34#14519764—21no—
35#14519754—41no—
36Q8×Dic61—21no—
37C4×Dic122—21no—
38C4×Dic122D411yescharacteristic
39D4×Dic61—21no—
40#14519733—41no—
41#14519721—42no—
42C2×#11758185—21no—
43#14519711D411yescharacteristic
44C4⋊#92418—21no—
45C4⋊#92418D411yescharacteristic
46#14519706—21no—
47#14519702—21no—
48#14519701—21no—
49#14519698—21no—
50#14519698—41no—
51#14519687—21no—
52C2×Q16×C61D411yescharacteristic
53C2×SD16×C61—21no—
54C2×D8×C61—21no—
55C2×D8×C61—21no—
56C2×D8×C61D411yescharacteristic
57#127×C61—21no—
58#124×C61—21no—
59SD32×C61—42no—
60D16×C61—42no—
61C2×C16×C61—21no—
62C4×C8×C61C2311yescharacteristic
63C2×Q8×C61—21no—
64C2×D4×C61—21no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C2×D4×C61—41no—
68C22×Dic61—41no—
69C2×Dic122—21no—
70C2×Dic122D811yescharacteristic
71Q16×C61—41no—
72SD16×C61—41no—
73SD16×C61—41no—
74D8×C61—41no—
75D8×C61—41no—
76D8×C61—41no—
77D8×C61—41no—
78D8×C61—41no—
79C2×C8×C61C2×D411yescharacteristic
80C2×C8×C61C2×D411yescharacteristic
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C42×C61C2×D411yescharacteristic
84C22⋊Dic61—41no—
85C22⋊Dic61—41no—
86C22⋊Dic61—41no—
87#11758202—81no—
88#11758200—81no—
89#11758200—82no—
90C4⋊Dic61—21no—
91C4⋊Dic61—41no—
92C4⋊Dic61D811yescharacteristic
93#11758196—21no—
94#11758196—41no—
95#11758196—41no—
96#11758196—41no—
97C4×Dic61—21no—
98C4×Dic61—41no—
99C4×Dic61—41no—
100C2×#92418—21no—
101C2×#92418—41no—
102Dic244—21no—
103Dic244—21no—
104C16×C61—22no—
105#11758185—41no—
106C23×C61—41no—
107C23×C61—81no—
108Q8×C61—41no—
109Q8×C61—41no—
110D4×C61—41no—
111D4×C61—41no—
112D4×C61—81no—
113D4×C61—81no—
114D4×C61—81no—
115D4×C61—81no—
116D4×C61—161no—
117C2×C4×C61—41no—
118C2×C4×C61#12011yescharacteristic
119C2×C4×C61C2×D811yescharacteristic
120C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—82no—
126Dic122—41no—
127Dic122—41no—
128Dic122—41no—
129C8×C61—21no—
130C8×C61#13511yescharacteristic
131C8×C61AGL(1,ℤ/8)11yescharacteristic
132#92418—41no—
133#92418—81no—
134#12337—611nomaximal, Sylow
135C22×C61—81no—
136C22×C61—81no—
137C22×C61—81no—
138C22×C61—161no—
139C22×C61—161no—
140C22×C61—161no—
141C22×C61#44711yescharacteristic
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—81no—
145C4×C61#44911yescharacteristic
146C4×C61#45311yescharacteristic
147Dic61—41no—
148Dic61—41no—
149Dic61—81no—
150Dic61—81no—
151#3402—611no—
152#2250D6111yescharacteristic
153#2207—611no—
154#1688—611no—
155#1360—611no—
156#1338—611no—
157#1334—611no—
158C2×C61—161no—
159C2×C61—321no—
160C2×C61#162111yescharacteristic
161C2×C61#219011yescharacteristic
162C2×C61#219311yescharacteristic
163#556—1221no—
164C2×SD32—21no—
165C2×SD32—1221no—
166C2×D16—21no—
167#497—1221no—
168#495C2×D6111yescharacteristic
169#493C2×D6111yescharacteristic
170#464—1221no—
171#463—1221no—
172#462—1221no—
173#460—1221no—
174#446—611no—
175#440—1221no—
176C4×Q16—611no—
177C4⋊C16—611no—
178#357—1221no—
179#346C2×D6111yescharacteristic
180#334—611no—
181#331—1221no—
182C61#1233711yescharacteristic, complemented, Sylow
183C2×Q16—611no—
184C2×Q16—1221no—
185C2×Q16C22⋊D6111yescharacteristic
186C2×SD16—21no—
187C2×SD16—1221no—
188C2×SD16—2441no—
189C2×D8—21no—
190C2×D8—21no—
191C2×D8C22⋊D6111yescharacteristic
192C4⋊Q8—1221no—
193#127—21no—
194#126—2441no—
195#126—2441no—
196#124—21no—
197#124—1221no—
198C22⋊Q8—2441no—
199C4×Q8—611no—
200C4×Q8—1221no—
201C4×Q8—1221no—
202C4×D4—1221no—
203#117—2441no—
204SD32—42no—
205SD32—2442no—
206D16—42no—
207C2×C16—21no—
208C2×C16—1221no—
209#107—611no—
210C4⋊C8—611no—
211C4⋊C8—1221no—
212C4⋊C8—1221no—
213#103—1221no—
214#103—1221no—
215#102—1221no—
216#102—2441no—
217#97—1221no—
218C4×C8C22×D6111yescharacteristic
219C2×Q8—21no—
220C2×Q8—611no—
221C2×Q8—1221no—
222C2×D4—21no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4—41no—
226C22×C4—2441no—
227Q16—41no—
228Q16—1221no—
229Q16—1221no—
230Q16—4881no—
231SD16—41no—
232SD16—41no—
233SD16—4882no—
234SD16—4881no—
235D8—41no—
236D8—41no—
237D8—41no—
238D8—41no—
239D8—41no—
240C2×C8—1221no—
241C2×C8—2441no—
242C2×C8D4×D6111yescharacteristic
243C2×C8C2×C22⋊D6111yescharacteristic
244C4⋊C4—611no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—2441no—
248C4⋊C4—2441no—
249C4⋊C4—2441no—
250C4⋊C4—2441no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—2441no—
254C22⋊C4—2441no—
255C22⋊C4—2441no—
256C42—1221no—
257C42—2441no—
258C42—2441no—
259C42D4×D6111yescharacteristic
260C16—22no—
261C16—2441no—
262C23—41no—
263C23—81no—
264Q8—41no—
265Q8—41no—
266Q8—2441no—
267Q8—2441no—
268Q8—2441no—
269D4—41no—
270D4—41no—
271D4—81no—
272D4—81no—
273D4—81no—
274D4—81no—
275D4—161no—
276C2×C4—41no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—4882no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4#1451974511yescharacteristic
283C2×C4D8×D6111yescharacteristic
284C2×C4#1451980111yescharacteristic
285C8—21no—
286C8—4881no—
287C8—2441no—
288C8#1451979611yescharacteristic
289C8#1451980111yescharacteristic
290C22—81no—
291C22—81no—
292C22—81no—
293C22—161no—
294C22—161no—
295C22—161no—
296C22#1683989411yescharacteristic
297C4—21no—
298C4—21no—
299C4—81no—
300C4—4881no—
301C4—4881no—
302C4—2441no—
303C4—2441no—
304C4#1683990411yescharacteristic
305C4#1683992911yescharacteristic
306C2—161no—
307C2—321no—
308C2#2144488111yescharacteristic
309C2#2144776311yescharacteristic
310C2#2144778011yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
Fitting, prime radicalC61×#2250C2
socleC22×C61#447
hypercenter#2250D61
hypocenterC61#12337
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2250

Complements

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

NH ≅ G/Ntype
1. #21458901C2semidirect
2. #21447856C2semidirect
3. #21445300C2semidirect
4. #21443862C2semidirect
5. #21443802C2semidirect
6. #21443790C2semidirect
182. C61#12337semidirect

Maximal subgroups

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

subgroupindex
#214589012
#214478562
#214453002
#214438622
#214438022
#214437902
C61×#22502
#1233761