Finite Group Databasebeta

← #29582321

Subgroups — #29582321

Order 15616.

676 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#16839959C212yesmaximal
2#21451192C211yesmaximal, characteristic, complemented
3C2×#16839494C212yesmaximal, complemented
4#21443702C211yesmaximal, characteristic, complemented
5C61×#1957C211yesmaximal, characteristic
6C22×#11758200—22no—
7C2×C4×Dic122C2212yes—
8#16839959—24no—
9#16839959—24no—
10C2×C4⋊#92418C2212yes—
11C2×#14519698—22no—
12#16839692—22no—
13#16839667—22no—
14#16839661—22no—
15#16839494—24no—
16C2×#127×C61C2211yescharacteristic
17C2×#102×C61—22no—
18C2×C4×C8×C61C2211yescharacteristic
19C61×#384C2211yescharacteristic
20C22×Dic122D412yes—
21C2×#11758200—28no—
22C2×#11758200—44no—
23C2×#11758200—44no—
24C22×#92418—22no—
25C4×Dic122—22no—
26C4×Dic122—22no—
27C4×Dic122—22no—
28C4×Dic122—22no—
29C2×C4⋊Dic61—22no—
30C2×C4⋊Dic61D412yes—
31C2×#11758196—22no—
32C2×C4×Dic61—22no—
33C4⋊#92418—22no—
34C4⋊#92418D414yes—
35#14519698—28no—
36#14519684—24no—
37#14519684—22no—
38C22×D4×C61—22no—
39C22×D4×C61—21no—
40C22×C8×C61—21no—
41#127×C61—22no—
42#127×C61—21no—
43#127×C61D412yes—
44C2×C4⋊C4×C61—22no—
45C2×C4⋊C4×C61D412yes—
46C2×C42×C61C2311yescharacteristic
47#102×C61—44no—
48C4×C8×C61—22no—
49C24×C61—41no—
50C2×D4×C61—24no—
51C2×D4×C61—22no—
52C2×D4×C61—42no—
53C2×D4×C61—42no—
54C2×D4×C61—42no—
55C2×D4×C61—41no—
56C2×D4×C61—42no—
57C2×D4×C61—42no—
58C2×D4×C61—42no—
59C2×D4×C61—42no—
60C22×C4×C61—22no—
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D412yes—
63C22×Dic61—22no—
64C22×Dic61—22no—
65C2×Dic122—22no—
66C2×Dic122—22no—
67C2×Dic122—22no—
68C2×Dic122—22no—
69C2×Dic122—22no—
70C2×Dic122SD1614yescomplemented
71C2×C8×C61—22no—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C4⋊C4×C61—42no—
75C4⋊C4×C61—42no—
76C4⋊C4×C61—42no—
77C42×C61C2×D411yescharacteristic
78C42×C61C2×D412yes—
79C42×C61#4111yescharacteristic
80#11758200—416no—
81C4⋊Dic61—22no—
82C4⋊Dic61—22no—
83C4⋊Dic61—82no—
84#11758196—42no—
85#11758196—42no—
86C4×Dic61—42no—
87C4×Dic61—42no—
88C2×#92418—24no—
89C2×#92418—42no—
90C2×#92418—42no—
91C23×C61—42no—
92C23×C61—82no—
93C23×C61—82no—
94C23×C61—81no—
95C23×C61—81no—
96C23×C61#12011yescharacteristic
97D4×C61—44no—
98D4×C61—44no—
99D4×C61—44no—
100D4×C61—82no—
101D4×C61—82no—
102D4×C61—82no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—44no—
106C2×C4×C61—42no—
107C2×C4×C61#12012yes—
108C2×C4×C61#12111yescharacteristic
109C2×C4×C61#12112yes—
110C2×C4×C61#12711yescharacteristic
111C2×C4×C61C2×SD1612yes—
112C2×C4×C61#13512yes—
113C2×C4×C61AGL(1,ℤ/8)12yes—
114C2×C4×C61#13712yes—
115C2×Dic61—24no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—42no—
121Dic122—24no—
122Dic122—24no—
123Dic122—42no—
124Dic122—42no—
125C8×C61—42no—
126#92418—44no—
127#10230—611nomaximal, Sylow
128C22×C61—84no—
129C22×C61—82no—
130C22×C61—161no—
131C22×C61—161no—
132C22×C61—162no—
133C22×C61#39211yescharacteristic
134C22×C61#44812yes—
135C22×C61#44912yes—
136C22×C61#45311yescharacteristic
137C22×C61#45411yescharacteristic
138C4×C61—21no—
139C4×C61—21no—
140C4×C61—82no—
141C4×C61#45012yes—
142C4×C61#45212yes—
143C4×C61#46512yes—
144C4×C61#46812yes—
145Dic61—44no—
146Dic61—82no—
147C2×#460—612no—
148#2582—611no—
149#1957D6111yescharacteristic
150C2×Q8⋊C8—612no—
151#1296—611no—
152C2×C61—162no—
153C2×C61#162011yescharacteristic
154C2×C61#162311yescharacteristic
155C2×C61#162612yes—
156C2×C61#200012yes—
157C2×C61#200611yescharacteristic
158C22×SD16—1222no—
159C2×#127C2×D6111yescharacteristic
160C2×C4×Q8—612no—
161#460—1224no—
162#460—1224no—
163C2×C4⋊C8—612no—
164C2×#102—22no—
165C2×#102—1222no—
166C2×C4×C8C2×D6111yescharacteristic
167#398—1222no—
168#391—1222no—
169#389—1222no—
170#384C2×D6111yescharacteristic
171Q8⋊C8—1224no—
172C61#1023011yescharacteristic, complemented, Sylow
173C22×Q8—612no—
174C22×D4—22no—
175C22×D4—21no—
176C2×SD16—1228no—
177C2×SD16—2444no—
178C2×SD16—2444no—
179C22×C8—21no—
180C22×C8—1222no—
181#127—21no—
182#127—22no—
183#127D24412yes—
184C4×Q8—1222no—
185C4×Q8—1222no—
186C4×Q8—1222no—
187C4×Q8—1222no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—612no—
190C2×C4⋊C4—1222no—
191C2×C4⋊C4—1222no—
192C2×C4⋊C4C22⋊D6112yes—
193C2×C42—1222no—
194C2×C42C22×D6111yescharacteristic
195C4⋊C8—614no—
196C4⋊C8—1222no—
197#102—44no—
198#102—1228no—
199C4×C8—22no—
200#95—1224no—
201#95—1222no—
202C24—41no—
203C2×Q8—614no—
204C2×Q8—1222no—
205C2×Q8—1222no—
206C2×Q8—1222no—
207C2×Q8—1222no—
208C2×Q8—1222no—
209C2×D4—24no—
210C2×D4—22no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—41no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C22×C4—22no—
220C22×C4—1222no—
221C22×C4—1222no—
222C22×C4D4×D6112yes—
223C22×C4C2×C22⋊D6111yescharacteristic
224SD16—24416no—
225C2×C8—22no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—1224no—
229C2×C8—2442no—
230C2×C8—2442no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—1222no—
235C4⋊C4—1222no—
236C4⋊C4—4882no—
237C4⋊C4—2442no—
238C4⋊C4—2442no—
239C42—2442no—
240C42—2442no—
241C42C2×D24411yescharacteristic
242C42#1175822211yescharacteristic
243C42D4×D6112yes—
244C23—42no—
245C23—82no—
246C23—82no—
247C23—81no—
248C23—81no—
249C23#1451974511yescharacteristic
250Q8—1224no—
251Q8—1224no—
252Q8—2442no—
253Q8—2442no—
254D4—44no—
255D4—44no—
256D4—44no—
257D4—82no—
258D4—82no—
259D4—82no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—44no—
263C2×C4—42no—
264C2×C4—1224no—
265C2×C4—2442no—
266C2×C4—2442no—
267C2×C4—2442no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4#1451974712yes—
271C2×C4#1451975012yes—
272C2×C4#1451975111yescharacteristic
273C2×C4#1451977311yescharacteristic
274C2×C4SD16×D6112yes—
275C2×C4#1451979612yes—
276C2×C4#1451980112yes—
277C2×C4#1451980612yes—
278C8—42no—
279C8—2444no—
280C22—84no—
281C22—82no—
282C22—161no—
283C22—161no—
284C22—162no—
285C22#1683967111yescharacteristic
286C22#1683989912yes—
287C22#1683990412yes—
288C22#1683992911yescharacteristic
289C22#1683993411yescharacteristic
290C4—21no—
291C4—21no—
292C4—82no—
293C4—4882no—
294C4—2444no—
295C4#1683991412yes—
296C4#1683992512yes—
297C4#1683999012yes—
298C4#1684000712yes—
299C2—162no—
300C2#2144487611yescharacteristic
301C2#2144489511yescharacteristic
302C2#2144491212yes—
303C2#2144682312yes—
304C2#2144686011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1957C2
socleC23×C61#120
prime radicalC2×#127×C61C22
hypercenter#1957D61
hypocenterC61#10230
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #21451192C2semidirect
3. C2×#16839494C2semidirect
4. #21443702C2semidirect
70. C2×Dic122SD16semidirect
172. C61#10230semidirect

Maximal subgroups

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

subgroupindex
C2×#168399592
#214511922
C2×#168394942
#214437022
C61×#19572
#1023061