Finite Group Databasebeta

← #30596882

Subgroups — #30596882

Order 15616.

722 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840783C211yesmaximal, characteristic
2C2×C4×#11758217C211yesmaximal, characteristic
3#21460695C214yesmaximal, complemented
4C2×#16839627C211yesmaximal, characteristic
5C22×#11758217—21no—
6#16840783—22no—
7#16840783C414yescomplemented
8C2×C4⋊#92420—21no—
9C2×C22⋊#92420—21no—
10C4×#11758217—22no—
11C4×#11758217C414yescomplemented
12C2×#14519832C2212yes—
13C2×#14519832C2212yes—
14C2×C4×#92420—21no—
15C22×C4⋊Dic61C411yescharacteristic
16C22×C4×Dic61C2211yescharacteristic
17#16839627—21no—
18#16839627—21no—
19#16839627C412yes—
20#16839627C2212yes—
21C2×#14519684—21no—
22C2×#14519684—21no—
23C22×C4⋊C4×C61C411yescharacteristic
24C2×#11758217—24no—
25C2×#11758217—24no—
26C2×#11758217—24no—
27C22×#92420—22no—
28C22×#92420—22no—
29C4⋊#92420—24no—
30C22⋊#92420—24no—
31#14519832—22no—
32#14519832—22no—
33#14519832C2×C414yescomplemented
34#14519832C2×C414yescomplemented
35C4×#92420—24no—
36C23×Dic61—21no—
37C23×Dic61D411yescharacteristic
38C23×Dic61D411yescharacteristic
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—42no—
41C2×C4⋊Dic61C2×C412yes—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61C2×C412yes—
44C2×C4×Dic61C2×C412yes—
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D412yes—
48C2×C4×Dic61Q812yes—
49C2×C4×Dic61C2311yescharacteristic
50#14519684—22no—
51#14519684—22no—
52#14519684—22no—
53#14519684—22no—
54C23×C4×C61—21no—
55C23×C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—42no—
58C2×C4⋊C4×C61C2×C412yes—
59C24×C61C22⋊C411yescharacteristic
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—42no—
64C22×C4×C61—42no—
65C22×C4×C61—42no—
66C22×C4×C61C4212yes—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C4⋊C412yes—
69C22×C4×C61C22×C411yescharacteristic
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61—41no—
74C22×Dic61—41no—
75C22×Dic61—42no—
76C22×Dic61—42no—
77C22×Dic61—42no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C412yes—
81C22×Dic61C22⋊C412yes—
82C22×Dic61C4⋊C412yes—
83C22×Dic61C4⋊C412yes—
84C22×Dic61C2×D411yescharacteristic
85C22×Dic61C2×D411yescharacteristic
86#11758217—216no—
87C2×#92420—24no—
88C2×#92420—24no—
89C2×#92420—24no—
90C2×#92420—24no—
91C2×#92420—42no—
92C2×#92420—42no—
93C4⋊C4×C61—42no—
94C4⋊C4×C61—42no—
95C4⋊Dic61—42no—
96C4⋊Dic61—42no—
97C4×Dic61C4212yes—
98C4×Dic61C22⋊C412yes—
99C4×Dic61C22⋊C412yes—
100C4×Dic61C4⋊C412yes—
101C4×Dic61C4⋊C412yes—
102C4×Dic61C4⋊C412yes—
103C4×Dic61C22×C411yescharacteristic
104C4×Dic61C22×C411yescharacteristic
105C4×Dic61C2×D411yescharacteristic
106C4×Dic61C2×Q811yescharacteristic
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61#9512yes—
112C23×C61#10412yes—
113C23×C61#10412yes—
114C23×C61C2×C22⋊C411yescharacteristic
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—24no—
118C2×C4×C61—24no—
119C2×C4×C61—42no—
120C2×C4×C61—42no—
121C2×C4×C61—42no—
122C2×C4×C61—84no—
123C2×C4×C61#9512yes—
124C2×C4×C61#10012yes—
125C2×C4×C61#10112yes—
126C2×C4×C61C2×C4211yescharacteristic
127C2×C4×C61C2×C4⋊C411yescharacteristic
128C2×Dic61—24no—
129C2×Dic61—24no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61—84no—
144C2×Dic61#9512yes—
145C2×Dic61#9512yes—
146C2×Dic61C2×C22⋊C411yescharacteristic
147C2×Dic61C2×C22⋊C411yescharacteristic
148C2×Dic61C2×C4⋊C411yescharacteristic
149C2×Dic61C2×C4⋊C411yescharacteristic
150#92420—28no—
151#92420—44no—
152#8033—611nomaximal, Sylow
153C22×C61—22no—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61#33914yes—
160C22×C61C2×#9511yescharacteristic
161C22×C61C2×#10011yescharacteristic
162C22×C61C2×#10111yescharacteristic
163C22×C61C2×#10411yescharacteristic
164C22×C61C2×#10411yescharacteristic
165C22×C61#42111yescharacteristic
166C22×C61#42111yescharacteristic
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—82no—
170C4×C61#34314yes—
171Dic61—21no—
172Dic61—22no—
173Dic61—21no—
174Dic61—21no—
175Dic61—22no—
176Dic61—21no—
177Dic61—82no—
178C2×#432—611no—
179C2×C4×M16—611no—
180C2×#382—611no—
181#1295—614no—
182C2×C61—24no—
183C2×C61#152711yescharacteristic
184C2×C61#152711yescharacteristic
185C2×C61#152811yescharacteristic
186C2×C61#152811yescharacteristic
187C2×C61C2×#33911yescharacteristic
188C2×C61#173311yescharacteristic
189C2×C61C2×#34311yescharacteristic
190C22×M16—1221no—
191C22×C4⋊C4—611no—
192C22×C4⋊C4#692311yescharacteristic
193C22×C42—611no—
194#432—614no—
195#432—1222no—
196C2×C4⋊C8—1221no—
197C2×C22⋊C8—1221no—
198C4×M16—614no—
199C4×M16—1222no—
200C2×#97—612no—
201C2×#97—612no—
202C2×C4×C8—1221no—
203#382—612no—
204#382—612no—
205#382—1221no—
206#382—1221no—
207C2×#95—1221no—
208C2×#95—1221no—
209C61#803311yescharacteristic, complemented, Sylow
210C23×C4—21no—
211C23×C4—611no—
212C23×C4—611no—
213C23×C4—1221no—
214C23×C4C2×#692311yescharacteristic
215C2×M16—1224no—
216C2×M16—1224no—
217C2×M16—1224no—
218C22×C8—1222no—
219C22×C8—1222no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—42no—
222C2×C4⋊C4—612no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—2442no—
225C2×C4⋊C4C2×#692312yes—
226C2×C42—612no—
227C2×C42—612no—
228C2×C42—612no—
229C2×C42—612no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—611no—
234C4⋊C8—1224no—
235C22⋊C8—1224no—
236#97—614no—
237#97—614no—
238#97—1222no—
239#97—1222no—
240C4×C8—1224no—
241#95—1222no—
242#95—1222no—
243#95—1222no—
244#95—1222no—
245C24C22⋊#692311yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4—612no—
253C22×C4—612no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—612no—
259C22×C4—612no—
260C22×C4—1222no—
261C22×C4—1222no—
262C22×C4—1222no—
263C22×C4—2441no—
264C22×C4—2441no—
265C22×C4—2442no—
266C22×C4—2442no—
267C22×C4—2442no—
268C22×C4C4×#692312yes—
269C22×C4C4⋊#692312yes—
270C22×C4C22⋊#692311yescharacteristic
271C22×C4C22×#692311yescharacteristic
272M16—12216no—
273C2×C8—1224no—
274C2×C8—1224no—
275C2×C8—1224no—
276C2×C8—1224no—
277C2×C8—2442no—
278C2×C8—2442no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—2442no—
282C4⋊C4—2442no—
283C42—612no—
284C42—612no—
285C42—612no—
286C42—612no—
287C42—611no—
288C42—611no—
289C42—612no—
290C42—611no—
291C42—612no—
292C42—611no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23(C2×#6923)⋊C412yes—
298C23#1451984112yes—
299C23#1451984212yes—
300C23C2×C22⋊#692311yescharacteristic
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—84no—
309C2×C4—612no—
310C2×C4—612no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1224no—
324C2×C4—1224no—
325C2×C4—4884no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2442no—
331C2×C4(C2×#6923)⋊C412yes—
332C2×C4#1451983712yes—
333C2×C4#1451983812yes—
334C2×C4C2×C4×#692311yescharacteristic
335C2×C4C2×C4⋊#692311yescharacteristic
336C8—1228no—
337C8—2444no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22#1684063214yes—
345C22C2×(C2×#6923)⋊C411yescharacteristic
346C22C2×#1451983711yescharacteristic
347C22C2×#1451983811yescharacteristic
348C22C2×#1451984111yescharacteristic
349C22C2×#1451984211yescharacteristic
350C22#1684076011yescharacteristic
351C22#1684076111yescharacteristic
352C4—21no—
353C4—21no—
354C4—82no—
355C4—1221no—
356C4—1222no—
357C4—1221no—
358C4—1221no—
359C4—1222no—
360C4—1221no—
361C4—4882no—
362C4#1684064214yes—
363C2—24no—
364C2#2146127811yescharacteristic
365C2#2146128011yescharacteristic
366C2#2146128111yescharacteristic
367C2#2146128311yescharacteristic
368C2C2×#1684063211yescharacteristic
369C2#2146149811yescharacteristic
370C2C2×#1684064211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#8033
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460695C2semidirect
7. #16840783C4semidirect
11. C4×#11758217C4semidirect
33. #14519832C2×C4semidirect
34. #14519832C2×C4semidirect
209. C61#8033semidirect

Maximal subgroups

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

subgroupindex
C2×#168407832
C2×C4×#117582172
#214606952
C2×#168396272
#803361