Finite Group Databasebeta

← #29680558

Subgroups — #29680558

Order 15616.

894 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C8×D61C211yesmaximal, characteristic
2#21448215C212yesmaximal
3#21445982C212yesmaximal, complemented
4#21445948C212yesmaximal, complemented
5#21445845C212yesmaximal
6#21445843C212yesmaximal
7C4×#14519711C211yesmaximal, characteristic, complemented
8C4×#14519708C212yesmaximal, complemented
9C4×#107×C61C211yesmaximal, characteristic, complemented
10C22×C8×D61C2211yescharacteristic
11C22×C8×D61C2211yescharacteristic
12C2×C42×D61C2211yescharacteristic
13C2×#14519711C2212yes—
14C2×#14519708C2214yes—
15C2×C4×#92418C2211yescharacteristic
16C2×C8×Dic61C2211yescharacteristic
17C2×C8×Dic61C2211yescharacteristic
18C4×C8×D61C418yescomplemented
19#16839629—22no—
20#16839627C2214yes—
21#16839624—22no—
22#16839619C2214yes—
23C4×C4⋊Dic61C2212yes—
24C4×#11758198—22no—
25#16839608—22no—
26#16839525C2212yes—
27#16839524C2214yes—
28C2×#107×C61C2212yes—
29C2×C4×C8×C61C2211yescharacteristic
30C4×C4⋊C4×C61C2212yes—
31C61×#340C2212yes—
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×C4×D61C2311yescharacteristic
35C22×#92418C2311yescharacteristic
36C22×#92418C2311yescharacteristic
37C2×C8×D61—24no—
38C2×C8×D61—24no—
39C2×C8×D61C2×C414yes—
40C2×C8×D61C2×C414yes—
41C2×C4⋊Dic61C2314yes—
42C2×#11758198—24no—
43C2×C4×Dic61—22no—
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47C42×D61C2×C414yes—
48C42×D61Q814yes—
49#14519711—24no—
50#14519708—28no—
51C4×#92418C2×C414yes—
52C8×Dic61C2×C414yes—
53C8×Dic61C2×C414yes—
54#14519684—22no—
55#14519684—24no—
56#14519684—24no—
57#14519684—24no—
58C22×C8×C61C2311yescharacteristic
59C22×C8×C61C2311yescharacteristic
60C2×C4⋊C4×C61C2314yes—
61C2×C42×C61—22no—
62C2×C42×C61C2311yescharacteristic
63#107×C61—24no—
64C4×C8×C61C2×C414yes—
65#95×C61—22no—
66C23×D61C2×D411yescharacteristic
67C22×C4×C61—24no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2411yescharacteristic
71C22×Dic61—24no—
72C22×Dic61C2×D411yescharacteristic
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C2×C4×D61—24no—
76C2×C4×D61—22no—
77C2×C4×D61—22no—
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61C4⋊C414yes—
81C2×C4×D61C4⋊C414yes—
82C2×C4×D61C22×C412yes—
83C2×C4×D61C2×Q812yes—
84C2×C8×C61—22no—
85C2×C8×C61C22×C412yes—
86C2×C8×C61C22×C412yes—
87C2×C8×C61#4114yes—
88C4⋊C4×C61—24no—
89C4⋊C4×C61—24no—
90C42×C61—44no—
91C42×C61C22×C412yes—
92C42×C61C2×Q812yes—
93#11758198—48no—
94C4⋊Dic61—24no—
95C4⋊Dic61—24no—
96C4×Dic61—44no—
97C4×Dic61C4⋊C414yes—
98C4×Dic61C4⋊C414yes—
99C4×Dic61C22×C412yes—
100C4×Dic61C2×Q812yes—
101C2×#92418—22no—
102C2×#92418C22×C412yes—
103C2×#92418C22×C412yes—
104C2×#92418#4114yes—
105C8×D61—28no—
106C8×D61—28no—
107C23×C61C22×D411yescharacteristic
108C22×D61—22no—
109C22×D61—21no—
110C22×D61—21no—
111C22×D61C2×C4⋊C412yes—
112C22×D61#13514yes—
113C2×C4×C61—22no—
114C2×C4×C61—44no—
115C2×C4×C61—44no—
116C2×C4×C61—44no—
117C2×C4×C61C2×C4⋊C412yes—
118C2×C4×C61C2×C4⋊C412yes—
119C2×C4×C61#13512yes—
120C2×C4×C61#13512yes—
121C2×C4×C61C23×C411yescharacteristic
122C2×C4×C61C22×Q811yescharacteristic
123C2×C4×C61C2×#4112yes—
124C2×C4×C61C2×#4112yes—
125C2×Dic61—22no—
126C2×Dic61—22no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—44no—
130C2×Dic61—44no—
131C2×Dic61—44no—
132C2×Dic61C2×C4⋊C412yes—
133C2×Dic61C2×C4⋊C412yes—
134C2×Dic61C2×C4⋊C412yes—
135C4×D61—28no—
136C4×D61—22no—
137C4×D61—22no—
138C4×D61—24no—
139C4×D61—28no—
140C8×C61—22no—
141C8×C61#11714yes—
142#92418—22no—
143#92418#11714yes—
144#20818—611nomaximal, Sylow
145C22×C61C22×C4⋊C411yescharacteristic
146C22×C61#53212yes—
147C22×C61C2×#13512yes—
148C22×C61C2×#13511yescharacteristic
149C22×C61C2×#13511yescharacteristic
150C2×D61—22no—
151C2×D61—24no—
152C2×D61—24no—
153C2×D61—22no—
154C2×D61#42714yes—
155C4×C61—22no—
156C4×C61—84no—
157C4×C61#42714yes—
158C4×C61C2×#11711yescharacteristic
159C4×C61C2×#11711yescharacteristic
160C4×C61#53312yes—
161Dic61—22no—
162Dic61—22no—
163Dic61—22no—
164Dic61—84no—
165C22×C4×C8—611no—
166#2283—612no—
167#1846—612no—
168#1835—612no—
169#1808—612no—
170#1807—612no—
171C4×#107—611no—
172C4×#107D6111yescharacteristic, complemented
173C4×#106—612no—
174C2×C61#228511yescharacteristic
175C2×C61C2×#42711yescharacteristic
176C2×C61C2×#42711yescharacteristic
177C2×C61#316812yes—
178C2×C61#316812yes—
179D61—24no—
180C23×C8—611no—
181C23×C8—611no—
182C22×C42—611no—
183C2×#107—612no—
184C2×#107C2×D6112yes—
185C2×#106—614no—
186C2×C4×C8—611no—
187C2×C4×C8—611no—
188C2×C4×C8—611no—
189C2×C4×C8—618no—
190C2×C4×C8C2×D6111yescharacteristic
191#383—1222no—
192#382—614no—
193#381—1222no—
194#380—614no—
195C4×C4⋊C4—612no—
196C4×C4⋊C4C2×D6112yes—
197C4×C22⋊C4—1222no—
198#376—1222no—
199#340—612no—
200#340—614no—
201#340C2×D6112yes—
202C61#2081811yescharacteristic, complemented, Sylow
203C23×C4—611no—
204C23×C4—611no—
205C23×C4—611no—
206C22×C8—611no—
207C22×C8—611no—
208C22×C8—614no—
209C22×C8—614no—
210C22×C8—1224no—
211C22×C8—1224no—
212C22×C8C22×D6111yescharacteristic
213C22×C8C22×D6111yescharacteristic
214C2×C4⋊C4—614no—
215C2×C4⋊C4C22×D6114yes—
216C2×C22⋊C4—1224no—
217C2×C42—22no—
218C2×C42—611no—
219C2×C42—611no—
220C2×C42—611no—
221C2×C42—614no—
222C2×C42—614no—
223C2×C42—1222no—
224C2×C42C22×D6111yescharacteristic
225#107—24no—
226#107—1224no—
227#106—1228no—
228C4×C8—614no—
229C4×C8—614no—
230C4×C8—614no—
231C4×C8C4×D6114yes—
232#95—22no—
233#95—1224no—
234#95—1224no—
235#95—1224no—
236#95—1222no—
237C24—611no—
238C22×C4—24no—
239C22×C4—611no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—612no—
243C22×C4—612no—
244C22×C4—614no—
245C22×C4—614no—
246C22×C4—1224no—
247C22×C4—1222no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4—1222no—
251C22×C4—1224no—
252C22×C4D4×D6111yescharacteristic
253C22×C4D4×D6111yescharacteristic
254C22×C4C23×D6111yescharacteristic
255C2×C8—22no—
256C2×C8—612no—
257C2×C8—614no—
258C2×C8—612no—
259C2×C8—1228no—
260C2×C8—1222no—
261C2×C8—1228no—
262C2×C8C2×C4×D6112yes—
263C2×C8C2×C4×D6112yes—
264C2×C8#1175822214yes—
265C4⋊C4—24no—
266C4⋊C4—24no—
267C4⋊C4—1224no—
268C4⋊C4—1224no—
269C22⋊C4—2448no—
270C42—44no—
271C42—612no—
272C42—612no—
273C42—614no—
274C42—614no—
275C42—2444no—
276C42C2×C4×D6112yes—
277C42Q8×D6112yes—
278C23—612no—
279C23—614no—
280C23—1221no—
281C23—1221no—
282C23—1222no—
283C23C2×D4×D6111yescharacteristic
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—612no—
289C2×C4—612no—
290C2×C4—612no—
291C2×C4—1228no—
292C2×C4—1222no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1222no—
296C2×C4—1222no—
297C2×C4—1222no—
298C2×C4—1228no—
299C2×C4—1224no—
300C2×C4—2444no—
301C2×C4—2444no—
302C2×C4—2444no—
303C2×C4C4⋊C4×D6112yes—
304C2×C4C4⋊C4×D6112yes—
305C2×C4#1451979612yes—
306C2×C4#1451980012yes—
307C2×C4C22×C4×D6111yescharacteristic
308C2×C4C2×Q8×D6111yescharacteristic
309C2×C4#41×D6112yes—
310C2×C4C2×#1175822212yes—
311C8—22no—
312C8—614no—
313C8—1222no—
314C8#1451973414yes—
315C22—614no—
316C22—1224no—
317C22—1224no—
318C22—1222no—
319C22—1222no—
320C22C2×C4⋊C4×D6111yescharacteristic
321C22#1684030912yes—
322C22#135×D6112yes—
323C22C2×#1451979611yescharacteristic
324C22C2×#1451980011yescharacteristic
325C4—22no—
326C4—84no—
327C4—1222no—
328C4—1222no—
329C4—1222no—
330C4—4884no—
331C4#1683979914yes—
332C4#117×D6111yescharacteristic
333C4C2×#1451973411yescharacteristic
334C4#1684031612yes—
335C2—1224no—
336C2#2144822311yescharacteristic
337C2#427×D6111yescharacteristic
338C2C2×#1683979911yescharacteristic
339C2#2145638712yes—
340C2#2145639212yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#107×C61C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenterC4×#107D61
hypocenterC61#20818
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#107

Complements

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

NH ≅ G/Ntype
3. #21445982C2semidirect
4. #21445948C2semidirect
7. C4×#14519711C2semidirect
8. C4×#14519708C2semidirect
9. C4×#107×C61C2semidirect
18. C4×C8×D61C4semidirect
172. C4×#107D61semidirect
202. C61#20818semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C8×D612
#214482152
#214459822
#214459482
#214458452
#214458432
C4×#145197112
C4×#145197082
C4×#107×C612
#2081861