Finite Group Databasebeta

← #29573983

Subgroups — #29573983

Order 15616.

532 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 119 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#21454848C211yesmaximal, characteristic
2#21445997C212yesmaximal, complemented
3C4×#14519692C211yesmaximal, characteristic
4#21443665C212yesmaximal, complemented
5C61×#1869C211yesmaximal, characteristic
6#16839834—22no—
7#16839834—22no—
8#16839819—21no—
9C2×#14519706—22no—
10C2×#14519692C412yes—
11#16839726—21no—
12C2×C22⋊#92418C2212yes—
13C4×C22⋊Dic61C2212yes—
14#16839529C411yescharacteristic
15#16839529C411yescharacteristic
16#16839516—22no—
17C23×C8×C61C2211yescharacteristic
18C2×C4×D4×C61C2211yescharacteristic
19C2×C22⋊C8×C61—21no—
20C2×C22⋊C8×C61C2211yescharacteristic
21C61×#336—21no—
22C2×#11758194—21no—
23C2×#11758194—21no—
24C22×#92418D412yes—
25C22×#92418D412yes—
26C2×C22⋊Dic61C2×C412yes—
27C2×C22⋊Dic61C2×C412yes—
28C2×C4×Dic61—22no—
29C4⋊#92418—21no—
30C4⋊#92418—21no—
31#14519706—44no—
32#14519692—24no—
33C22⋊#92418—22no—
34C22⋊#92418—22no—
35C22⋊#92418—22no—
36#14519688—22no—
37#14519684—22no—
38C22×D4×C61C2×C411yescharacteristic
39C23×C4×C61D411yescharacteristic
40C23×C4×C61C2311yescharacteristic
41C22×C8×C61—21no—
42C22×C8×C61—22no—
43C22×C8×C61—21no—
44C22×C8×C61—42no—
45C4×D4×C61—22no—
46C4×D4×C61—22no—
47C2×C4⋊C4×C61Q811yescharacteristic
48C2×C22⋊C4×C61C2×C411yescharacteristic
49C2×C22⋊C4×C61Q811yescharacteristic
50C2×C42×C61D411yescharacteristic
51C22⋊C8×C61—22no—
52C22⋊C8×C61—42no—
53C24×C61C4⋊C411yescharacteristic
54C24×C61C22×C411yescharacteristic
55C2×D4×C61—22no—
56C2×D4×C61—22no—
57C2×D4×C61—21no—
58C2×D4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61—41no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61C4⋊C411yescharacteristic
66C22×C4×C61C4⋊C411yescharacteristic
67C22×C4×C61C4⋊C411yescharacteristic
68C22×C4×C61C2×D412yes—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×Q811yescharacteristic
71C22×C4×C61#4112yes—
72C22×Dic61—22no—
73C22×Dic61—22no—
74C2×C8×C61—22no—
75C2×C8×C61—24no—
76C2×C8×C61—42no—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—22no—
83C22⋊C4×C61—22no—
84C22⋊C4×C61—22no—
85C42×C61—21no—
86C42×C61—21no—
87C22⋊Dic61—22no—
88C22⋊Dic61—22no—
89C22⋊Dic61—22no—
90C22⋊Dic61M1614yescomplemented
91C4×Dic61—42no—
92C4×Dic61—42no—
93#11758194—81no—
94#11758194—81no—
95C2×#92418—22no—
96C2×#92418—22no—
97C2×#92418—42no—
98C2×#92418—42no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61C2×C4⋊C411yescharacteristic
107C23×C61C4×D412yes—
108C23×C61C2×M1612yes—
109C23×C61#13111yescharacteristic
110C23×C61#13111yescharacteristic
111D4×C61—42no—
112D4×C61—42no—
113C2×C4×C61—22no—
114C2×C4×C61—21no—
115C2×C4×C61—22no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—41no—
123C2×C4×C61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—81no—
129C2×C4×C61#12011yescharacteristic
130C2×C4×C61C22⋊Q812yes—
131C2×C4×C61#12311yescharacteristic
132C2×Dic61—24no—
133C2×Dic61—42no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C8×C61—42no—
139C8×C61—81no—
140#92418—42no—
141#92418—42no—
142#8852—611nomaximal, Sylow
143C22×C61—22no—
144C22×C61—21no—
145C22×C61—22no—
146C22×C61—21no—
147C22×C61—42no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—42no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—81no—
155C22×C61#38511yescharacteristic
156C22×C61#42311yescharacteristic
157C22×C61#42411yescharacteristic
158C22×C61#43512yes—
159C22×C61#43612yes—
160C4×C61—21no—
161C4×C61—22no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61B(4,𝔽2)11yescharacteristic
166C4×C61#45811yescharacteristic
167Dic61—44no—
168Dic61—82no—
169#2973—611no—
170#1869D6111yescharacteristic
171#1850—612no—
172C4×#99—611no—
173#1282—612no—
174C2×C61—22no—
175C2×C61—22no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61—81no—
179C2×C61#185111yescharacteristic
180C2×C61#186711yescharacteristic
181C2×C61#186811yescharacteristic
182C23×C8C2×D6111yescharacteristic
183C2×C4×D4C2×D6111yescharacteristic
184#435—1222no—
185#435—1222no—
186#432—1221no—
187C2×C4⋊C8—1222no—
188C2×#99—612no—
189#407—1221no—
190C2×C22⋊C8—21no—
191C2×C22⋊C8—612no—
192C2×C22⋊C8C2×D6111yescharacteristic
193C4×C22⋊C4—612no—
194#342—611no—
195#342—611no—
196#336—21no—
197#336—1222no—
198C61#885211yescharacteristic, complemented, Sylow
199C22×D4C4×D6111yescharacteristic
200C23×C4C22⋊D6111yescharacteristic
201C23×C4C22×D6111yescharacteristic
202C2×M16—1221no—
203C2×M16—1221no—
204C22×C8—22no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—42no—
208C22×C8—612no—
209C22×C8—612no—
210C4×D4—22no—
211C4×D4—22no—
212C2×C4⋊C4Dic12211yescharacteristic
213C2×C22⋊C4—612no—
214C2×C22⋊C4—612no—
215C2×C22⋊C4Dic12211yescharacteristic
216C2×C22⋊C4C4×D6111yescharacteristic
217C2×C42—1222no—
218C2×C42C22⋊D6111yescharacteristic
219C4⋊C8—1221no—
220C4⋊C8—1221no—
221C4⋊C8—2444no—
222#99—1224no—
223C22⋊C8—22no—
224C22⋊C8—42no—
225C22⋊C8—1222no—
226C22⋊C8—1222no—
227C22⋊C8—1222no—
228#97—1222no—
229#95—1222no—
230C24#1175819611yescharacteristic
231C24C2×C4×D6111yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—21no—
235C2×D4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—1222no—
243C22×C4—1222no—
244C22×C4#1175819611yescharacteristic
245C22×C4#1175819611yescharacteristic
246C22×C4#1175819611yescharacteristic
247C22×C4C2×Dic12211yescharacteristic
248C22×C4D4×D6112yes—
249C22×C4#1175822412yes—
250C22×C4C2×C22⋊D6111yescharacteristic
251M16—4881no—
252M16—4881no—
253C2×C8—22no—
254C2×C8—24no—
255C2×C8—42no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—1222no—
262C2×C8—1222no—
263C2×C8—2442no—
264C2×C8—2442no—
265C4⋊C4—22no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—614no—
269C22⋊C4—1222no—
270C22⋊C4—1222no—
271C22⋊C4—1222no—
272C42—21no—
273C42—21no—
274C42—2442no—
275C42—2442no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23C2×#1175819611yescharacteristic
284C23#1451973712yes—
285C23M16×D6112yes—
286C23#1451978311yescharacteristic
287C23#1451978311yescharacteristic
288D4—42no—
289D4—42no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—1224no—
307C2×C4—2442no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4#1451974511yescharacteristic
313C2×C4#1451975412yes—
314C2×C4#1451975811yescharacteristic
315C8—42no—
316C8—81no—
317C8—2442no—
318C8—2442no—
319C22—21no—
320C22—22no—
321C22—21no—
322C22—22no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#1683963411yescharacteristic
332C22#1683978511yescharacteristic
333C22#1683978811yescharacteristic
334C22#1683983612yes—
335C22#1683983712yes—
336C4—21no—
337C4—22no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—4882no—
342C4—2444no—
343C4#1683994811yescharacteristic
344C4#1683995111yescharacteristic
345C2—22no—
346C2—22no—
347C2—21no—
348C2—21no—
349C2—81no—
350C2#2144600111yescharacteristic
351C2#2144609911yescharacteristic
352C2#2144610411yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1869C2
socleC22×C61#385
prime radicalC22×D4×C61C2×C4
cosocleC23×C4×C61C23
hypercenter#1869D61
hypocenterC61#8852
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #21445997C2semidirect
4. #21443665C2semidirect
90. C22⋊Dic61M16semidirect
198. C61#8852semidirect

Maximal subgroups

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

subgroupindex
#214548482
#214459972
C4×#145196922
#214436652
C61×#18692
#885261