Finite Group Databasebeta

← #30599216

Subgroups — #30599216

Order 15616.

642 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461710C212yesmaximal
2#21460657C212yesmaximal
3#21460657C212yesmaximal
4C2×C4×#11758196C211yesmaximal, characteristic
5C2×C22⋊#92420C2214yes—
6#16840628—22no—
7#16840628—22no—
8C22×#11758196C411yescharacteristic
9C22×#11758196C411yescharacteristic
10C22×C4×Dic61C411yescharacteristic
11C22×C4×Dic61C2211yescharacteristic
12C4×#11758196—22no—
13C4×#11758196—22no—
14C2×#14519684C2211yescharacteristic
15C2×#14519684C2211yescharacteristic
16C22×C42×C61C411yescharacteristic
17C22×#92420—24no—
18C22⋊#92420—24no—
19C22⋊#92420—24no—
20C23×Dic61C2×C411yescharacteristic
21C23×Dic61C2×C411yescharacteristic
22C23×Dic61C2×C411yescharacteristic
23C23×Dic61C2311yescharacteristic
24C2×#11758196—22no—
25C2×#11758196—22no—
26C2×#11758196—22no—
27C2×#11758196—22no—
28C2×#11758196—22no—
29C2×#11758196C814yescomplemented
30C2×C4×Dic61—22no—
31C2×C4×Dic61—22no—
32C2×C4×Dic61—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—42no—
35C2×C4×Dic61D412yes—
36C2×C4×Dic61D412yes—
37#14519684—22no—
38#14519684—22no—
39C23×C4×C61C2×C411yescharacteristic
40C23×C4×C61C2×C411yescharacteristic
41C23×C4×C61C2×C411yescharacteristic
42C2×C42×C61—21no—
43C2×C42×C61—21no—
44C2×C42×C61—42no—
45C24×C61C22×C411yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—41no—
55C22×C4×C61—41no—
56C22×C4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C2×C812yes—
61C22×C4×C61M1612yes—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61—41no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—41no—
76C22×Dic61C22⋊C412yes—
77C22×Dic61C2×C812yes—
78C22×Dic61C2×C812yes—
79C22×Dic61M1612yes—
80C22×Dic61M1612yes—
81C22×Dic61C2×D412yes—
82C22×Dic61#4112yes—
83C22×Dic61#4112yes—
84C2×#92420—44no—
85C2×#92420—44no—
86C2×#92420—44no—
87C42×C61—42no—
88C42×C61—42no—
89#11758196—28no—
90#11758196—28no—
91C4×Dic61—24no—
92C4×Dic61—24no—
93C4×Dic61—42no—
94C4×Dic61—42no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61C2×C22⋊C411yescharacteristic
100C23×C61#11711yescharacteristic
101C23×C61#11711yescharacteristic
102C23×C61C22×C811yescharacteristic
103C23×C61C2×M1611yescharacteristic
104C23×C61C2×M1611yescharacteristic
105C23×C61C2×M1611yescharacteristic
106C2×C4×C61—24no—
107C2×C4×C61—24no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—42no—
121C2×C4×C61—42no—
122C2×C4×C61#10012yes—
123C2×C4×C61#10112yes—
124C2×Dic61—22no—
125C2×Dic61—22no—
126C2×Dic61—22no—
127C2×Dic61—22no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61—22no—
131C2×Dic61—22no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—42no—
135C2×Dic61—42no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—42no—
143C2×Dic61—42no—
144C2×Dic61C22⋊C814yes—
145C2×Dic61#12314yes—
146#92420—84no—
147#8701—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
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#38111yescharacteristic
161C22×C61C2×C22⋊C811yescharacteristic
162C22×C61#40711yescharacteristic
163C22×C61#41011yescharacteristic
164C22×C61#41011yescharacteristic
165C22×C61C2×#10011yescharacteristic
166C22×C61C2×#10111yescharacteristic
167C22×C61#43111yescharacteristic
168C22×C61#43111yescharacteristic
169C22×C61#43211yescharacteristic
170C22×C61#43211yescharacteristic
171C4×C61—22no—
172C4×C61—22no—
173C4×C61—42no—
174C4×C61—42no—
175Dic61—24no—
176Dic61—24no—
177Dic61—42no—
178Dic61—42no—
179C2×C4×C4⋊C4—611no—
180#1817—612no—
181#1280—612no—
182#1280—612no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61#146011yescharacteristic
188C2×C61#146111yescharacteristic
189C2×C61#146611yescharacteristic
190C2×C61#146711yescharacteristic
191C2×C61#181711yescharacteristic
192C2×C61#182011yescharacteristic
193C2×C61#182111yescharacteristic
194C22×C4⋊C4—611no—
195C22×C4⋊C4—611no—
196C22×C42—611no—
197C22×C42—611no—
198C22×C42#692311yescharacteristic
199C2×C22⋊C8—614no—
200C4×C4⋊C4—1222no—
201C4×C4⋊C4—1222no—
202C2×#95—611no—
203C2×#95—611no—
204#336—1222no—
205#336—1222no—
206C61#870111yescharacteristic, complemented, Sylow
207C23×C4—611no—
208C23×C4—611no—
209C23×C4—611no—
210C23×C4—611no—
211C23×C4C2×#692311yescharacteristic
212C23×C4C2×#692311yescharacteristic
213C23×C4C2×#692311yescharacteristic
214C22×C8—1224no—
215C2×C4⋊C4—614no—
216C2×C4⋊C4—1222no—
217C2×C4⋊C4—1222no—
218C2×C4⋊C4—1222no—
219C2×C4⋊C4—1222no—
220C2×C4⋊C4—1222no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42—42no—
224C2×C42—612no—
225C2×C42—612no—
226C2×C42—1222no—
227C2×C42—1222no—
228C2×C42—1221no—
229C2×C42—1221no—
230C2×C42—2442no—
231C22⋊C8—1224no—
232C22⋊C8—1224no—
233#95—1222no—
234#95—1222no—
235C24C22×#692311yescharacteristic
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—612no—
249C22×C4—612no—
250C22×C4—612no—
251C22×C4—612no—
252C22×C4—612no—
253C22×C4—612no—
254C22×C4—612no—
255C22×C4—612no—
256C22×C4—1221no—
257C22×C4—1221no—
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×C4D61⋊C812yes—
271C22×C4#1175821312yes—
272C22×C4C22⋊#692311yescharacteristic
273C22×C4C22⋊#692311yescharacteristic
274C2×C8—2444no—
275C2×C8—2444no—
276C2×C8—2444no—
277C4⋊C4—1228no—
278C4⋊C4—1228no—
279C42—42no—
280C42—42no—
281C42—1224no—
282C42—1224no—
283C42—2442no—
284C42—2442no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C2×C22⋊#692311yescharacteristic
290C23#1451985611yescharacteristic
291C23#1451985611yescharacteristic
292C23C2×D61⋊C811yescharacteristic
293C23D61⋊M1611yescharacteristic
294C23D61⋊M1611yescharacteristic
295C23C2×#1175821311yescharacteristic
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—614no—
313C2×C4—614no—
314C2×C4—1222no—
315C2×C4—1222no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4#1451983712yes—
335C2×C4#1451983812yes—
336C8—4884no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22#1684070511yescharacteristic
350C22D61⋊(C22⋊C8)11yescharacteristic
351C22#1684073311yescharacteristic
352C22#1684074111yescharacteristic
353C22#1684074111yescharacteristic
354C22C2×#1451983711yescharacteristic
355C22C2×#1451983811yescharacteristic
356C22#1684078011yescharacteristic
357C22#1684078111yescharacteristic
358C22#1684078411yescharacteristic
359C22#1684078511yescharacteristic
360C4—22no—
361C4—22no—
362C4—42no—
363C4—42no—
364C4—1224no—
365C4—1224no—
366C4—2442no—
367C4—2442no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—21no—
372C2#2146105811yescharacteristic
373C2#2146106111yescharacteristic
374C2#2146107811yescharacteristic
375C2#2146108111yescharacteristic
376C2#2146171111yescharacteristic
377C2#2146171611yescharacteristic
378C2#2146171811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC22×C42×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC22×C42#6923
hypocenterC61#8701
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
29. C2×#11758196C8semidirect
206. C61#8701semidirect

Maximal subgroups

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

subgroupindex
#214617102
#214606572
C2×C4×#117581962
#870161