Finite Group Databasebeta

← #29573978

Subgroups — #29573978

Order 15616.

558 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454843C211yesmaximal, characteristic
2#21445997C212yesmaximal, complemented
3C4×#14519692C211yesmaximal, characteristic
4#21443665C212yesmaximal, complemented
5C61×#1869C211yesmaximal, characteristic
6D4×#92418—22no—
7D4×#92418—22no—
8#16839815—21no—
9C2×#14519706—22no—
10C2×#14519692C411yescharacteristic
11C2×#14519692C411yescharacteristic
12C2×C22⋊#92418—21no—
13C2×C22⋊#92418C2212yes—
14C4×C22⋊Dic61C2212yes—
15#16839529C412yes—
16#16839516—22no—
17C23×C8×C61C2211yescharacteristic
18C2×C4×D4×C61C2211yescharacteristic
19C2×C22⋊C8×C61—21no—
20C2×C22⋊C8×C61C2211yescharacteristic
21C61×#336—21no—
22C22×#92418—21no—
23C22×#92418—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—22no—
33#14519692C814yescomplemented
34C22⋊#92418—22no—
35C22⋊#92418—22no—
36C22⋊#92418—22no—
37C4×#92418—22no—
38#14519684—22no—
39C22×D4×C61C2×C411yescharacteristic
40C23×C4×C61D411yescharacteristic
41C23×C4×C61C2311yescharacteristic
42C22×C8×C61—21no—
43C22×C8×C61—22no—
44C22×C8×C61—21no—
45C22×C8×C61—42no—
46C4×D4×C61—22no—
47C4×D4×C61—22no—
48C2×C4⋊C4×C61Q811yescharacteristic
49C2×C22⋊C4×C61C2×C411yescharacteristic
50C2×C22⋊C4×C61Q811yescharacteristic
51C2×C42×C61D411yescharacteristic
52C22⋊C8×C61—22no—
53C22⋊C8×C61—42no—
54C24×C61C4⋊C411yescharacteristic
55C24×C61C22×C411yescharacteristic
56C2×D4×C61—22no—
57C2×D4×C61—22no—
58C2×D4×C61C2×C812yes—
59C2×D4×C61M1612yes—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—41no—
63C22×C4×C61—41no—
64C22×C4×C61—41no—
65C22×C4×C61—41no—
66C22×C4×C61C4⋊C411yescharacteristic
67C22×C4×C61C4⋊C411yescharacteristic
68C22×C4×C61C4⋊C411yescharacteristic
69C22×C4×C61C2×D412yes—
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×Q811yescharacteristic
72C22×C4×C61#4112yes—
73C22×Dic61—22no—
74C22×Dic61—22no—
75C2×C8×C61—22no—
76C2×C8×C61—24no—
77C2×C8×C61—42no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C2×C8×C61—41no—
83C4⋊C4×C61—22no—
84C22⋊C4×C61—22no—
85C22⋊C4×C61—22no—
86C42×C61—21no—
87C42×C61—21no—
88C22⋊Dic61—22no—
89C22⋊Dic61—22no—
90C22⋊Dic61—22no—
91C22⋊Dic61C2×C814yescomplemented
92C4×Dic61—42no—
93C4×Dic61—42no—
94C2×#92418—22no—
95C2×#92418—22no—
96C2×#92418—42no—
97C2×#92418—42no—
98C2×#92418—81no—
99C2×#92418—81no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61C4⋊C812yescomplemented
107C23×C61C2×C4⋊C411yescharacteristic
108C23×C61C4×D412yes—
109C23×C61C22×C811yescharacteristic
110C23×C61C2×M1611yescharacteristic
111C23×C61#13112yes—
112D4×C61—24no—
113D4×C61—24no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—22no—
117C2×C4×C61—21no—
118C2×C4×C61—22no—
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×C61C4⋊C812yescomplemented
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61C22⋊Q812yes—
132C2×C4×C61#12311yescharacteristic
133C2×Dic61—24no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C8×C61—42no—
140C8×C61—81no—
141#92418—42no—
142#92418—42no—
143#8851—611nomaximal, Sylow
144C22×C61—22no—
145C22×C61—21no—
146C22×C61—22no—
147C22×C61—21no—
148C22×C61—22no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—81no—
156C22×C61#38511yescharacteristic
157C22×C61C2×C4⋊C811yescharacteristic
158C22×C61#42411yescharacteristic
159C22×C61C8×D412yes—
160C22×C61#43512yes—
161C4×C61—22no—
162C4×C61—21no—
163C4×C61—22no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61B(4,𝔽2)11yescharacteristic
167C4×C61#45811yescharacteristic
168Dic61—44no—
169Dic61—82no—
170#2972—611no—
171#1869D6111yescharacteristic
172#1850—612no—
173C4×#99—611no—
174#1282—612no—
175C2×C61—22no—
176C2×C61—22no—
177C2×C61—21no—
178C2×C61—21no—
179C2×C61—42no—
180C2×C61#185011yescharacteristic
181C2×C61#186711yescharacteristic
182C2×C61#186811yescharacteristic
183C23×C8C2×D6111yescharacteristic
184C2×C4×D4C2×D6111yescharacteristic
185C8×D4—1222no—
186C8×D4—1222no—
187#431—1221no—
188C2×C4⋊C8—1222no—
189C2×#99—611no—
190C2×#99—611no—
191C2×C22⋊C8—21no—
192C2×C22⋊C8—612no—
193C2×C22⋊C8—1221no—
194C2×C22⋊C8C2×D6111yescharacteristic
195C4×C22⋊C4—612no—
196#342—612no—
197#336—21no—
198#336—1222no—
199C61#885111yescharacteristic, complemented, Sylow
200C22×D4C4×D6111yescharacteristic
201C23×C4C22⋊D6111yescharacteristic
202C23×C4C22×D6111yescharacteristic
203C22×C8—22no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—42no—
207C22×C8—612no—
208C22×C8—612no—
209C22×C8—1221no—
210C22×C8—1221no—
211C4×D4—22no—
212C4×D4—22no—
213C2×C4⋊C4Dic12211yescharacteristic
214C2×C22⋊C4—612no—
215C2×C22⋊C4—612no—
216C2×C22⋊C4Dic12211yescharacteristic
217C2×C22⋊C4C4×D6111yescharacteristic
218C2×C42—1222no—
219C2×C42C22⋊D6111yescharacteristic
220C4⋊C8—1221no—
221C4⋊C8—1221no—
222C4⋊C8—2444no—
223#99—614no—
224#99—1222no—
225C22⋊C8—22no—
226C22⋊C8—42no—
227C22⋊C8—1222no—
228C22⋊C8—1222no—
229C22⋊C8—1222no—
230C4×C8—1222no—
231#95—1222no—
232C24#1175819611yescharacteristic
233C24C2×C4×D6111yescharacteristic
234C2×D4—22no—
235C2×D4—22no—
236C2×D4C8×D6112yes—
237C2×D4#1175818912yes—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—1222no—
245C22×C4—1222no—
246C22×C4#1175819611yescharacteristic
247C22×C4#1175819611yescharacteristic
248C22×C4#1175819611yescharacteristic
249C22×C4C2×Dic12211yescharacteristic
250C22×C4D4×D6112yes—
251C22×C4#1175822412yes—
252C22×C4C2×C22⋊D6111yescharacteristic
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—4881no—
264C2×C8—4881no—
265C2×C8—2442no—
266C2×C8—2442no—
267C4⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C22⋊C4—614no—
271C22⋊C4—1222no—
272C22⋊C4—1222no—
273C22⋊C4—1222no—
274C42—21no—
275C42—21no—
276C42—2442no—
277C42—2442no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23#1451970612yescomplemented
285C23C2×#1175819611yescharacteristic
286C23#1451973712yes—
287C23C2×C8×D6111yescharacteristic
288C23C2×#1175818911yescharacteristic
289C23#1451978512yes—
290D4—24no—
291D4—24no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—81no—
307C2×C4—1224no—
308C2×C4—2442no—
309C2×C4—2442no—
310C2×C4—2442no—
311C2×C4—2442no—
312C2×C4—2442no—
313C2×C4#1451970612yescomplemented
314C2×C4#1451974511yescharacteristic
315C2×C4#1451975412yes—
316C2×C4#1451975811yescharacteristic
317C8—42no—
318C8—81no—
319C8—2442no—
320C8—2442no—
321C22—21no—
322C22—22no—
323C22—21no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—42no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22#1683963411yescharacteristic
334C22C2×#1451970611yescharacteristic
335C22#1683979011yescharacteristic
336C22#1683982512yes—
337C22#1683983012yes—
338C4—22no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—4882no—
344C4—2444no—
345C4#1683994811yescharacteristic
346C4#1683995111yescharacteristic
347C2—22no—
348C2—22no—
349C2—21no—
350C2—21no—
351C2—42no—
352C2#2144599611yescharacteristic
353C2#2144609911yescharacteristic
354C2#2144610411yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC23×C61C22×C8
FrattiniC23×C4C22×D61
FittingC61×#1869C2
socleC22×C61#385
prime radicalC22×D4×C61C2×C4
cosocleC23×C4×C61C23
hypercenter#1869D61
hypocenterC61#8851
LCSG ▷ C23×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
33. #14519692C8semidirect
91. C22⋊Dic61C2×C8semidirect
106. C23×C61C4⋊C8semidirect
129. C2×C4×C61C4⋊C8semidirect
199. C61#8851semidirect
284. C23#14519706semidirect
313. C2×C4#14519706semidirect

Maximal subgroups

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

subgroupindex
#214548432
#214459972
C4×#145196922
#214436652
C61×#18692
#885161