Finite Group Databasebeta

← #30597458

Subgroups — #30597458

Order 15616.

698 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461545C212yesmaximal
2C2×#16840607C212yesmaximal
3#21460657C212yesmaximal
4C2×C4×C4⋊Dic61C211yesmaximal, characteristic
5C2×C22⋊#92420C2214yes—
6C2×#14519832—22no—
7#16840628—22no—
8#16840607C418yescomplemented
9C22×C4⋊Dic61C411yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C22×C4×Dic61C411yescharacteristic
12C22×C4×Dic61C2211yescharacteristic
13C4×C4⋊Dic61—22no—
14C4×C4⋊Dic61—22no—
15C2×#14519684C411yescharacteristic
16C2×#14519684C2211yescharacteristic
17C22×C42×C61C411yescharacteristic
18C22×#92420—24no—
19C22⋊#92420—24no—
20C22⋊#92420C2×C418yes—
21#14519832—44no—
22C23×Dic61C2×C411yescharacteristic
23C23×Dic61C2×C411yescharacteristic
24C23×Dic61C2×C411yescharacteristic
25C23×Dic61C2311yescharacteristic
26C2×C4⋊Dic61—22no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61—22no—
30C2×C4⋊Dic61—22no—
31C2×C4⋊Dic61C2×C414yes—
32C2×C4×Dic61—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—42no—
35C2×C4×Dic61—42no—
36C2×C4×Dic61D412yes—
37C2×C4×Dic61D412yes—
38#14519684—22no—
39#14519684—22no—
40C23×C4×C61C2×C411yescharacteristic
41C23×C4×C61C2×C411yescharacteristic
42C23×C4×C61C2×C411yescharacteristic
43C2×C42×C61—21no—
44C2×C42×C61—21no—
45C2×C42×C61—22no—
46C2×C42×C61—22no—
47C24×C61C22×C411yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61C4212yes—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61M1612yes—
64C22×C4×C61M1612yes—
65C22×C4×C61M1612yes—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—41no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61—41no—
79C22×Dic61—41no—
80C22×Dic61C4212yes—
81C22×Dic61C22⋊C412yes—
82C22×Dic61M1612yes—
83C22×Dic61C22×C412yes—
84C22×Dic61C2×D412yes—
85C22×Dic61#4112yes—
86C2×#92420—28no—
87C2×#92420—44no—
88C2×#92420—44no—
89C42×C61—24no—
90C42×C61—24no—
91C4⋊Dic61—28no—
92C4⋊Dic61—28no—
93C4×Dic61—24no—
94C4×Dic61—42no—
95C4×Dic61—42no—
96C4×Dic61—42no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61C2×C4211yescharacteristic
102C23×C61C2×C22⋊C411yescharacteristic
103C23×C61#11711yescharacteristic
104C23×C61C2×M1611yescharacteristic
105C23×C61C2×M1611yescharacteristic
106C23×C61C2×M1611yescharacteristic
107C23×C61C2×M1611yescharacteristic
108C2×C4×C61—24no—
109C2×C4×C61—24no—
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61—22no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—22no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—42no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61#9714yescomplemented
126C2×C4×C61#9912yes—
127C2×C4×C61#10112yes—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—22no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—22no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61C4×D414yes—
148#92420—48no—
149#8153—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61C4×C22⋊C411yescharacteristic
163C22×C61C2×#9711yescharacteristic
164C22×C61C4×M1611yescharacteristic
165C22×C61#40711yescharacteristic
166C22×C61#40711yescharacteristic
167C22×C61C2×#9911yescharacteristic
168C22×C61#41011yescharacteristic
169C22×C61C2×#10111yescharacteristic
170C22×C61#41311yescharacteristic
171C22×C61#43211yescharacteristic
172C22×C61#43211yescharacteristic
173C4×C61—22no—
174C4×C61—22no—
175C4×C61—24no—
176C4×C61—42no—
177Dic61—24no—
178Dic61—42no—
179Dic61—42no—
180Dic61—42no—
181C2×C4×C4⋊C4—611no—
182#1749—612no—
183C2×#324—612no—
184#1280—612no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61#146311yescharacteristic
190C2×C61#146411yescharacteristic
191C2×C61#146511yescharacteristic
192C2×C61#146711yescharacteristic
193C2×C61#174911yescharacteristic
194C2×C61C4×#9911yescharacteristic
195C2×C61C4×#10111yescharacteristic
196C22×C4⋊C4—611no—
197C22×C4⋊C4—611no—
198C22×C42—611no—
199C22×C42—611no—
200C22×C42#692311yescharacteristic
201C2×C22⋊C8—614no—
202C2×#97—1222no—
203C4×C4⋊C4—1222no—
204C4×C4⋊C4—1222no—
205C2×#95—611no—
206C2×#95—611no—
207#336—1222no—
208#324—618no—
209C61#815311yescharacteristic, complemented, Sylow
210C23×C4—611no—
211C23×C4—611no—
212C23×C4—611no—
213C23×C4—611no—
214C23×C4C2×#692311yescharacteristic
215C23×C4C2×#692311yescharacteristic
216C23×C4C2×#692311yescharacteristic
217C22×C8—1224no—
218C2×C4⋊C4—614no—
219C2×C4⋊C4—1222no—
220C2×C4⋊C4—1222no—
221C2×C4⋊C4—1222no—
222C2×C4⋊C4—1222no—
223C2×C4⋊C4—1222no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42—21no—
227C2×C42—21no—
228C2×C42—612no—
229C2×C42—612no—
230C2×C42—1221no—
231C2×C42—1221no—
232C2×C42—2442no—
233C2×C42—2442no—
234C22⋊C8—618no—
235C22⋊C8—1224no—
236#97—2444no—
237#95—1222no—
238#95—1222no—
239C24C22×#692311yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—612no—
253C22×C4—612no—
254C22×C4—612no—
255C22×C4—612no—
256C22×C4—612no—
257C22×C4—612no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—2441no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4#1175821312yes—
273C22×C4C4×#692312yes—
274C22×C4#1175821712yes—
275C22×C4#1175821712yes—
276C22×C4C22⋊#692311yescharacteristic
277C22×C4C22⋊#692311yescharacteristic
278C2×C8—1228no—
279C2×C8—2444no—
280C2×C8—2444no—
281C4⋊C4—1228no—
282C4⋊C4—1228no—
283C42—24no—
284C42—24no—
285C42—1224no—
286C42—2442no—
287C42—2442no—
288C42—2442no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23C2×C4×#692311yescharacteristic
294C23C2×C22⋊#692311yescharacteristic
295C23#1451985611yescharacteristic
296C23C2×#1175821711yescharacteristic
297C23C2×#1175821711yescharacteristic
298C23D61⋊M1611yescharacteristic
299C23C2×#1175821311yescharacteristic
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—614no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4#1451983214yescomplemented
338C2×C4#1451983612yes—
339C2×C4#1451983812yes—
340C8—2448no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22C4×C22⋊#692311yescharacteristic
354C22C2×#1451983211yescharacteristic
355C22C4×#1175821711yescharacteristic
356C22#1684073211yescharacteristic
357C22#1684073311yescharacteristic
358C22C2×#1451983611yescharacteristic
359C22#1684074111yescharacteristic
360C22C2×#1451983811yescharacteristic
361C22#1684074811yescharacteristic
362C22#1684078211yescharacteristic
363C22#1684078311yescharacteristic
364C4—24no—
365C4—22no—
366C4—22no—
367C4—42no—
368C4—1224no—
369C4—2442no—
370C4—2442no—
371C4—2442no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2#2146106711yescharacteristic
377C2#2146107011yescharacteristic
378C2#2146107611yescharacteristic
379C2#2146108111yescharacteristic
380C2#2146154511yescharacteristic
381C2C4×#1451983611yescharacteristic
382C2C4×#1451983811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC22×C42×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC22×C42#6923
hypocenterC61#8153
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
8. #16840607C4semidirect
125. C2×C4×C61#97semidirect
209. C61#8153semidirect
337. C2×C4#14519832semidirect

Maximal subgroups

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

subgroupindex
#214615452
C2×#168406072
#214606572
C2×C4×C4⋊Dic612
#815361