Finite Group Databasebeta

← #29599486

Subgroups — #29599486

Order 15616.

444 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 75 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#21452851C211yesmaximal, characteristic
2C2×#16839560C212yesmaximal
3#21446212C212yesmaximal
4#21443946C211yesmaximal, characteristic
5C61×#1857C211yesmaximal, characteristic
6C2×#14519775C2212yes—
7#16839770—22no—
8C2×#14519696C2212yes—
9#16839692—21no—
10#16839683—22no—
11#16839660—21no—
12#16839647—22no—
13#16839560—24no—
14#16839521—22no—
15C61×#519C2211yescharacteristic
16C61×#428—21no—
17C2×#101×C61C2211yescharacteristic
18C61×#391C2211yescharacteristic
19C61×#339—21no—
20C22×Dic122D412yes—
21C2×#11758194—22no—
22#14519775—22no—
23#14519775—22no—
24#14519775—22no—
25#14519775—22no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61—21no—
29C2×#11758196—22no—
30C2×#11758196—22no—
31C2×C4×Dic61D412yes—
32#14519700—42no—
33#14519700—42no—
34#14519696—22no—
35#14519696—22no—
36#14519684—22no—
37#14519684—22no—
38#14519684—21no—
39C22×Q8×C61C2311yescharacteristic
40C2×M16×C61—21no—
41C4×Q8×C61—41no—
42C4×Q8×C61—41no—
43#117×C61—21no—
44#117×C61—22no—
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C42×C61D411yescharacteristic
47#107×C61—41no—
48#106×C61—41no—
49#101×C61—21no—
50#101×C61D412yes—
51#95×C61—22no—
52C2×Q8×C61—41no—
53C2×Q8×C61—41no—
54C2×Q8×C61C2×D411yescharacteristic
55C2×Q8×C61#4111yescharacteristic
56C2×Q8×C61#4112yes—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C2×D412yes—
60C22×C4×C61C2×D411yescharacteristic
61C22×Dic61—22no—
62C22×Dic61—22no—
63C2×Dic122—22no—
64C2×Dic122—22no—
65C2×Dic122—42no—
66C2×Dic122—42no—
67M16×C61—22no—
68M16×C61—41no—
69C2×C8×C61—41no—
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—22no—
73C4⋊C4×C61—22no—
74C4⋊C4×C61—41no—
75C22⋊C4×C61—41no—
76C42×C61—42no—
77C42×C61—41no—
78C42×C61—41no—
79C4⋊Dic61—24no—
80C4⋊Dic61—81no—
81C4⋊Dic61—81no—
82#11758196—42no—
83#11758196—42no—
84#11758196—42no—
85#11758196—42no—
86C4×Dic61—22no—
87C4×Dic61—22no—
88#11758194—42no—
89#11758194—42no—
90C2×#92418—42no—
91C23×C61#12011yescharacteristic
92Q8×C61—41no—
93Q8×C61—42no—
94Q8×C61—41no—
95C2×C4×C61—22no—
96C2×C4×C61—21no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—42no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61#12111yescharacteristic
107C2×C4×C61#12112yes—
108C2×C4×C61#12312yes—
109C2×C4×C61#12411yescharacteristic
110C2×Dic61—24no—
111C2×Dic61—42no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115C2×Dic61—42no—
116Dic122—44no—
117Dic122—82no—
118C8×C61—42no—
119#92418—82no—
120#13428—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#39411yescharacteristic
124C22×C61B(4,𝔽2)11yescharacteristic
125C22×C61#45811yescharacteristic
126C4×C61—22no—
127C4×C61—21no—
128C4×C61—22no—
129C4×C61—21no—
130C4×C61—42no—
131C4×C61—81no—
132C4×C61—81no—
133C4×C61—81no—
134Dic61—44no—
135Dic61—82no—
136#2734—611no—
137C2×#356—612no—
138#1886—612no—
139#1857D6111yescharacteristic
140#1394—611no—
141C2×C61—21no—
142C2×C61—21no—
143C2×C61#204411yescharacteristic
144C2×C61#220311yescharacteristic
145C2×C61#220511yescharacteristic
146C2×C4⋊Q8—612no—
147#519C2×D6111yescharacteristic
148#428—21no—
149#419—1222no—
150C2×#101—612no—
151C2×#101C2×D6111yescharacteristic
152#398—1221no—
153#395—1222no—
154#391C2×D6111yescharacteristic
155#389—1221no—
156#387—1222no—
157#356—1224no—
158#339—21no—
159#339—1222no—
160C61#1342811yescharacteristic, complemented, Sylow
161C22×Q8—612no—
162C22×Q8C22×D6111yescharacteristic
163C2×M16—21no—
164C2×M16—1222no—
165C4⋊Q8—1222no—
166C4⋊Q8—1222no—
167C4⋊Q8—1222no—
168C4⋊Q8—1222no—
169C4×Q8—41no—
170C4×Q8—41no—
171#117—22no—
172#117—21no—
173C2×C4⋊C4—1221no—
174C2×C4⋊C4—1221no—
175C2×C4⋊C4—1221no—
176C2×C4⋊C4—1222no—
177C2×C4⋊C4—1222no—
178C2×C4⋊C4C22⋊D6111yescharacteristic
179C2×C42—612no—
180C2×C42C22⋊D6111yescharacteristic
181#107—41no—
182#106—41no—
183#103—2442no—
184#103—2442no—
185#101—21no—
186#101—1222no—
187#101—1222no—
188#101D24412yes—
189#95—22no—
190#95—1221no—
191#95—1222no—
192#95—1222no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—1222no—
196C2×Q8—1222no—
197C2×Q8—2442no—
198C2×Q8—2442no—
199C2×Q8C2×D24411yescharacteristic
200C2×Q8#1175822211yescharacteristic
201C2×Q8#1175822612yes—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—1222no—
205C22×C4—1222no—
206C22×C4D4×D6112yes—
207C22×C4C2×C22⋊D6111yescharacteristic
208M16—22no—
209M16—41no—
210M16—2442no—
211M16—2442no—
212C2×C8—41no—
213C2×C8—2442no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—1224no—
220C4⋊C4—4881no—
221C4⋊C4—4881no—
222C4⋊C4—2442no—
223C4⋊C4—2442no—
224C4⋊C4—2442no—
225C4⋊C4—2442no—
226C22⋊C4—41no—
227C42—41no—
228C42—41no—
229C42—42no—
230C42—1222no—
231C42—1222no—
232C23#1451974511yescharacteristic
233Q8—41no—
234Q8—41no—
235Q8—42no—
236Q8—4882no—
237Q8—2444no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—1224no—
250C2×C4—2442no—
251C2×C4—2442no—
252C2×C4—2442no—
253C2×C4—2442no—
254C2×C4—2442no—
255C2×C4#1451975111yescharacteristic
256C2×C4#1451975212yes—
257C2×C4#1451976212yes—
258C2×C4#1451976611yescharacteristic
259C8—42no—
260C8—4882no—
261C22—21no—
262C22—21no—
263C22#1683967911yescharacteristic
264C22#1683994811yescharacteristic
265C22#1683995111yescharacteristic
266C4—21no—
267C4—22no—
268C4—22no—
269C4—21no—
270C4—42no—
271C4—81no—
272C4—81no—
273C4—81no—
274C4—4882no—
275C4—2444no—
276C2—21no—
277C2—21no—
278C2#2144707011yescharacteristic
279C2#2144783911yescharacteristic
280C2#2144784811yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC22×Q8×C61C23
FrattiniC22×Q8C22×D61
FittingC61×#1857C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1857D61
hypocenterC61#13428
LCSG ▷ C22×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

Complements

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

NH ≅ G/Ntype
160. C61#13428semidirect

Maximal subgroups

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

subgroupindex
#214528512
C2×#168395602
#214462122
#214439462
C61×#18572
#1342861