Finite Group Databasebeta

← #29575088

Subgroups — #29575088

Order 15616.

484 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 111 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#21454904C211yesmaximal, characteristic
2C4×#14519696C211yesmaximal, characteristic
3#21444266C212yesmaximal
4#21443712C212yesmaximal
5C61×#2399C211yesmaximal, characteristic
6#16839893—24no—
7#16839819—21no—
8#16839819C2212yes—
9#16839815—21no—
10C2×#14519696—21no—
11C4×#11758194C2212yes—
12#16839531—21no—
13Q8⋊#92418—24no—
14C2×C4×Q8×C61C2211yescharacteristic
15C2×C4×Q8×C61C2211yescharacteristic
16C61×#398—21no—
17C61×#398C411yescharacteristic
18C61×#398C411yescharacteristic
19C61×#395—21no—
20C61×#395C411yescharacteristic
21C61×#395C411yescharacteristic
22C4×C4⋊C4×C61—21no—
23C4×C4⋊C4×C61—21no—
24C61×#376C2211yescharacteristic
25C2×#11758194—22no—
26C4⋊#92418—22no—
27C4⋊#92418—22no—
28C4⋊#92418D414yes—
29#14519696—24no—
30C22⋊#92418—22no—
31#14519688—22no—
32#14519688—22no—
33#14519688—22no—
34C4×#92418—22no—
35C4×#92418—22no—
36C22×Q8×C61C2×C411yescharacteristic
37C22×Q8×C61D411yescharacteristic
38C4×Q8×C61—22no—
39C4×Q8×C61—22no—
40C4×Q8×C61—22no—
41C4×Q8×C61—22no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C42×C61—21no—
52C2×C42×C61—21no—
53C2×C42×C61D411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62#95×C61C2×C411yescharacteristic
63C2×Q8×C61—22no—
64C2×Q8×C61—22no—
65C2×Q8×C61—22no—
66C2×Q8×C61—41no—
67C2×Q8×C61—42no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C4⋊C4×C61—22no—
80C4⋊C4×C61—22no—
81C4⋊C4×C61—22no—
82C4⋊C4×C61—22no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—42no—
85C4⋊C4×C61—42no—
86C4⋊C4×C61—42no—
87C4⋊C4×C61—42no—
88C42×C61—24no—
89C42×C61—21no—
90C42×C61—21no—
91C42×C61—21no—
92C42×C61—21no—
93C42×C61—41no—
94C42×C61—41no—
95C42×C61C2×D412yes—
96C42×C61#4112yes—
97#11758194—24no—
98#11758194—42no—
99C2×#92418—24no—
100C2×#92418—42no—
101C23×C61C2×C22⋊C411yescharacteristic
102Q8×C61—24no—
103Q8×C61—44no—
104Q8×C61—42no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61—22no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61#10412yes—
131C2×C4×C61C4×D412yes—
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61#12112yes—
134C2×C4×C61#12311yescharacteristic
135#92418—44no—
136#92418—44no—
137#9030—611nomaximal, Sylow
138C22×C61—21no—
139C22×C61—21no—
140C22×C61#38611yescharacteristic
141C22×C61C2×#10411yescharacteristic
142C22×C61#42111yescharacteristic
143C4×C61—22no—
144C4×C61—22no—
145C4×C61—21no—
146C4×C61—22no—
147C4×C61—42no—
148C4×C61—42no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—41no—
152C4×C61—42no—
153C4×C61—81no—
154C4×C61#45612yes—
155#2983—611no—
156#2399D6111yescharacteristic
157C4×#101—611no—
158#1491—612no—
159#1300—612no—
160C2×C61—21no—
161C2×C61—21no—
162C2×C61#187111yescharacteristic
163C2×C61#188611yescharacteristic
164C2×C61#189111yescharacteristic
165C2×C4×Q8C2×D6111yescharacteristic
166C2×C4×Q8C2×D6111yescharacteristic
167#446—1224no—
168#432—612no—
169#432—1221no—
170#431—1221no—
171C2×#101—1221no—
172C4×M16—612no—
173#398—21no—
174#398Dic6111yescharacteristic
175#398Dic6111yescharacteristic
176#395—21no—
177#395Dic6111yescharacteristic
178#395Dic6111yescharacteristic
179C4×C4⋊C4—21no—
180C4×C4⋊C4—21no—
181#376C2×D6111yescharacteristic
182#343—1221no—
183Q8⋊C8—1224no—
184C61#903011yescharacteristic, complemented, Sylow
185C22×Q8C2×Dic6111yescharacteristic
186C22×Q8C22⋊D6111yescharacteristic
187C2×M16—1222no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—22no—
191C4×Q8—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C2×Dic6111yescharacteristic
198C2×C4⋊C4C2×Dic6111yescharacteristic
199C2×C4⋊C4C2×Dic6111yescharacteristic
200C2×C4⋊C4C22⋊D6111yescharacteristic
201C2×C42—21no—
202C2×C42—21no—
203C2×C42C22⋊D6111yescharacteristic
204C2×C42C22⋊D6111yescharacteristic
205C2×C42C22×D6111yescharacteristic
206C4⋊C8—614no—
207C4⋊C8—1222no—
208C4⋊C8—1222no—
209#101—1224no—
210C22⋊C8—1222no—
211#97—1222no—
212#97—1222no—
213#97—1222no—
214C4×C8—1222no—
215C4×C8—1222no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95C2×Dic6111yescharacteristic
222#95C2×Dic6111yescharacteristic
223C2×Q8—22no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—42no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4C22⋊Dic6111yescharacteristic
233C22×C4C22⋊Dic6111yescharacteristic
234C22×C4C22⋊Dic6111yescharacteristic
235C22×C4C22⋊Dic6111yescharacteristic
236C22×C4C22×Dic6111yescharacteristic
237C22×C4C2×C22⋊D6111yescharacteristic
238C22×C4C2×C22⋊D6111yescharacteristic
239M16—1224no—
240M16—2442no—
241C2×C8—1224no—
242C2×C8—2442no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C42—24no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—41no—
258C42—41no—
259C42D4×D6112yes—
260C42#1175822412yes—
261C23C2×C22⋊Dic6111yescharacteristic
262Q8—24no—
263Q8—44no—
264Q8—42no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4#1451970412yes—
291C2×C4D4×Dic6112yes—
292C2×C4#1451974511yescharacteristic
293C2×C4#1451974912yes—
294C2×C4#1451975811yescharacteristic
295C8—2444no—
296C8—2444no—
297C22—21no—
298C22—21no—
299C22#1683964211yescharacteristic
300C22C2×#1451970411yescharacteristic
301C22#1683977911yescharacteristic
302C4—21no—
303C4—22no—
304C4—22no—
305C4—22no—
306C4—42no—
307C4—42no—
308C4—41no—
309C4—41no—
310C4—42no—
311C4—41no—
312C4—81no—
313C4#1683994412yes—
314C2—21no—
315C2—21no—
316C2#2144612211yescharacteristic
317C2#2144621311yescharacteristic
318C2#2144623811yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2399C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2399D61
hypocenterC61#9030
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
184. C61#9030semidirect

Maximal subgroups

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

subgroupindex
#214549042
C4×#145196962
#214442662
#214437122
C61×#23992
#903061