Finite Group Databasebeta

← #29593599

Subgroups — #29593599

Order 15616.

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

normal subgroups only

This group has 308 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
2#21448091C211yesmaximal, characteristic
3#21447870C211yesmaximal, characteristic, complemented
4#21445314C211yesmaximal, characteristic, complemented
5#21443800C211yesmaximal, characteristic, complemented
6#21443788C211yesmaximal, characteristic, complemented
7C61×#1360C211yesmaximal, characteristic
8#16840481—21no—
9C2×Dic488—21no—
10C2×#14519723—21no—
11C2×#14519721—21no—
12#16840153—21no—
13#16840142C2211yescharacteristic
14#16840048—21no—
15#16839981—21no—
16#16839975—21no—
17#16839970—21no—
18#16839892C2211yescharacteristic
19#16839863—21no—
20C4×Dic244C2211yescharacteristic
21#16839567—21no—
22#16839538C2211yescharacteristic
23#16839507—21no—
24C61×#495C2211yescharacteristic
25C61×C4⋊C16C2211yescharacteristic
26C61×#334C2211yescharacteristic
27C2×Dic244—21no—
28C2×Dic244—21no—
29C2×Dic244D411yescharacteristic
30C2×#11758202—21no—
31C2×#11758200—21no—
32#14519777—21no—
33#14519775—21no—
34#14519770—41no—
35#14519770—41no—
36#14519764—21no—
37#14519754—41no—
38Q8×Dic61—21no—
39C4×Dic122—21no—
40C4×Dic122D411yescharacteristic
41D4×Dic61—21no—
42#14519733—41no—
43Dic488—42no—
44#14519723—42no—
45#14519721—42no—
46C2×#11758185—21no—
47#14519711D411yescharacteristic
48#14519709—41no—
49C4⋊#92418D411yescharacteristic
50#14519706—21no—
51#14519702—21no—
52#14519702—41no—
53#14519701—21no—
54#14519698—21no—
55#14519687—21no—
56C2×Q16×C61D411yescharacteristic
57C2×SD16×C61—21no—
58C2×D8×C61D411yescharacteristic
59#124×C61—21no—
60C2×C16×C61—21no—
61C4⋊C8×C61—21no—
62C4×C8×C61C2311yescharacteristic
63C2×Q8×C61—21no—
64C2×D4×C61—21no—
65C22×Dic61—41no—
66C2×Dic122—21no—
67C2×Dic122—41no—
68C2×Dic122D811yescharacteristic
69Q16×C61—41no—
70SD16×C61—41no—
71SD16×C61—41no—
72D8×C61—41no—
73C2×C8×C61—41no—
74C2×C8×C61C2×D411yescharacteristic
75C2×C8×C61C2×D411yescharacteristic
76C22⋊C4×C61—41no—
77C22⋊C4×C61—41no—
78C42×C61C2×D411yescharacteristic
79C22⋊Dic61—41no—
80C22⋊Dic61—41no—
81C22⋊Dic61—41no—
82#11758202—81no—
83#11758200—81no—
84C4⋊Dic61—21no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61D811yescharacteristic
89#11758196—21no—
90#11758196—41no—
91#11758196—41no—
92#11758196—41no—
93C4×Dic61—21no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96C2×#92418—21no—
97Dic244—21no—
98Dic244—21no—
99Dic244—41no—
100Dic244—41no—
101Dic244—41no—
102Dic244—41no—
103C16×C61—41no—
104#11758185—22no—
105C23×C61—41no—
106Q8×C61—41no—
107Q8×C61—41no—
108D4×C61—41no—
109D4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61#12011yescharacteristic
112C2×C4×C61C2×D811yescharacteristic
113C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—82no—
119C2×Dic61—81no—
120Dic122—41no—
121Dic122—41no—
122Dic122—41no—
123Dic122—81no—
124Dic122—81no—
125C8×C61—21no—
126C8×C61—81no—
127C8×C61#13511yescharacteristic
128C8×C61AGL(1,ℤ/8)11yescharacteristic
129#92418—41no—
130#12339—611nomaximal, Sylow
131C22×C61—81no—
132C22×C61—81no—
133C22×C61—81no—
134C22×C61#44711yescharacteristic
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—81no—
138C4×C61#44911yescharacteristic
139C4×C61#45311yescharacteristic
140Dic61—41no—
141Dic61—41no—
142Dic61—81no—
143Dic61—81no—
144Dic61—161no—
145#3402—611no—
146#2251—611no—
147#2209—611no—
148#1690—611no—
149#1360D6111yescharacteristic
150#1338—611no—
151#1334—611no—
152C2×C61—161no—
153C2×C61#162111yescharacteristic
154C2×C61#219111yescharacteristic
155C2×C61#219511yescharacteristic
156#556—1221no—
157C2×Q32—1221no—
158C2×Q32—1221no—
159C2×SD32—1221no—
160#497—1221no—
161#495C2×D6111yescharacteristic
162#494—611no—
163#475—1221no—
164#464—1221no—
165#463—1221no—
166#462—1221no—
167#446—611no—
168#440—1221no—
169C4×Q16—611no—
170C4⋊C16C2×D6111yescharacteristic
171#358—1221no—
172#346—611no—
173#334C2×D6111yescharacteristic
174#332—1221no—
175C61#1233911yescharacteristic, complemented, Sylow
176C2×Q16—611no—
177C2×Q16—1221no—
178C2×Q16—1221no—
179C2×Q16—1221no—
180C2×Q16D24411yescharacteristic
181C2×SD16—21no—
182C2×SD16—1221no—
183C2×D8D24411yescharacteristic
184C4⋊Q8—1221no—
185C4⋊Q8—1221no—
186#126—2441no—
187#126—2441no—
188#124—21no—
189#124—1221no—
190C22⋊Q8—2441no—
191C4×Q8—611no—
192C4×Q8—1221no—
193C4×Q8—1221no—
194C4×D4—1221no—
195#117—2441no—
196Q32—2442no—
197Q32—2442no—
198SD32—2442no—
199C2×C16—21no—
200C2×C16—1221no—
201#107—611no—
202#106—2441no—
203C4⋊C8—21no—
204C4⋊C8—611no—
205C4⋊C8—1221no—
206#103—1221no—
207#103—1221no—
208#103—2441no—
209#102—1221no—
210#97—1221no—
211C4×C8C22×D6111yescharacteristic
212C2×Q8—21no—
213C2×Q8—611no—
214C2×Q8—1221no—
215C2×Q8—2441no—
216C2×D4—21no—
217C22×C4—2441no—
218Q16—41no—
219Q16—1221no—
220Q16—1221no—
221Q16—4881no—
222Q16—2441no—
223Q16—2441no—
224Q16—2441no—
225Q16—2441no—
226SD16—41no—
227SD16—41no—
228SD16—4881no—
229D8—41no—
230C2×C8—41no—
231C2×C8—1221no—
232C2×C8C2×D24411yescharacteristic
233C2×C8D4×D6111yescharacteristic
234C4⋊C4—611no—
235C4⋊C4—1221no—
236C4⋊C4—1221no—
237C4⋊C4—2441no—
238C4⋊C4—2441no—
239C4⋊C4—2441no—
240C4⋊C4—2441no—
241C4⋊C4—2441no—
242C4⋊C4—2441no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—2441no—
246C22⋊C4—2441no—
247C22⋊C4—2441no—
248C42—1221no—
249C42—2441no—
250C42—2441no—
251C42D4×D6111yescharacteristic
252C16—41no—
253C16—1222no—
254C23—41no—
255Q8—41no—
256Q8—41no—
257Q8—4881no—
258Q8—4881no—
259Q8—2441no—
260Q8—2441no—
261Q8—2441no—
262D4—41no—
263D4—41no—
264C2×C4—41no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—4881no—
268C2×C4—4882no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4#1451974711yescharacteristic
272C2×C4D8×D6111yescharacteristic
273C2×C4#1451980411yescharacteristic
274C8—21no—
275C8—81no—
276C8—2441no—
277C8#1451979811yescharacteristic
278C8#1451980111yescharacteristic
279C22—81no—
280C22—81no—
281C22—81no—
282C22#1683989711yescharacteristic
283C4—21no—
284C4—21no—
285C4—81no—
286C4—9761no—
287C4—4881no—
288C4—4881no—
289C4—2441no—
290C4—2441no—
291C4#1683990811yescharacteristic
292C4#1683993211yescharacteristic
293C2—161no—
294C2#2144488511yescharacteristic
295C2#2144777111yescharacteristic
296C2#2144779811yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1360C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#1360D61
hypocenterC61#12339
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1360

Complements

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

NH ≅ G/Ntype
3. #21447870C2semidirect
4. #21445314C2semidirect
5. #21443800C2semidirect
6. #21443788C2semidirect
175. C61#12339semidirect

Maximal subgroups

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

subgroupindex
#214589012
#214480912
#214478702
#214453142
#214438002
#214437882
C61×#13602
#1233961