Finite Group Databasebeta

← #30596632

Subgroups — #30596632

Order 15616.

564 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#21462495C211yesmaximal, characteristic
2C2×#16840783C211yesmaximal, characteristic
3#21460678C214yesmaximal, complemented
4#21448213C211yesmaximal, characteristic
5#16840783—21no—
6#16840783—21no—
7#16840783—21no—
8#16840783C412yescomplemented
9#16840783C2212yes—
10#16840782—21no—
11#16840779C412yescomplemented
12#16840778C412yescomplemented
13#16840765—21no—
14C2×C4⋊#92420—21no—
15#16840732—21no—
16C2×C22⋊#92420—21no—
17C4×#11758217C2212yes—
18C2×#14519832C412yescomplemented
19C22×C4×Dic61C2211yescharacteristic
20#16839629C2212yes—
21#16839626C412yes—
22#16839623—21no—
23#16839620—21no—
24C4×#11758196—21no—
25C4×C22⋊Dic61C411yescharacteristic
26#16839608—21no—
27C4×C22⋊C4×C61C411yescharacteristic
28C2×#11758217—22no—
29C22×#92420—22no—
30#14519844—22no—
31C4⋊#92420—22no—
32C4⋊#92420—22no—
33C4⋊#92420—22no—
34C22⋊#92420—22no—
35C22⋊#92420—22no—
36C22⋊#92420—22no—
37C22⋊#92420—22no—
38#14519832—22no—
39#14519832—22no—
40#14519832C2×C414yes—
41C4×#92420C2×C414yes—
42C23×Dic61D411yescharacteristic
43C23×Dic61D411yescharacteristic
44C2×#11758196—22no—
45C2×C22⋊Dic61—21no—
46C2×C4×Dic61—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61Q811yescharacteristic
57C2×C4×Dic61Q811yescharacteristic
58C2×C4×Dic61C2311yescharacteristic
59#14519684—22no—
60#14519684—22no—
61#14519684—22no—
62#14519684C2×C412yes—
63C23×C4×C61C2×C411yescharacteristic
64C2×C22⋊C4×C61—21no—
65C2×C42×C61—21no—
66#95×C61C2×C412yes—
67C24×C61C22⋊C411yescharacteristic
68C22×C4×C61—22no—
69C22×C4×C61—42no—
70C22×C4×C61C4211yescharacteristic
71C22×C4×C61C4211yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C4⋊C411yescharacteristic
74C22×C4×C61C4⋊C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C22×Dic61—22no—
77C22×Dic61—42no—
78C22×Dic61—42no—
79C22×Dic61C22⋊C411yescharacteristic
80C22×Dic61C22⋊C411yescharacteristic
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C4⋊C411yescharacteristic
86C22×Dic61C4⋊C411yescharacteristic
87C22×Dic61C4⋊C411yescharacteristic
88C22×Dic61C4⋊C411yescharacteristic
89C22×Dic61C2×D411yescharacteristic
90C22×Dic61C2×D411yescharacteristic
91#11758217—44no—
92C2×#92420—24no—
93C2×#92420—24no—
94C2×#92420—44no—
95C22⋊C4×C61—42no—
96C42×C61—42no—
97C22⋊Dic61—42no—
98#11758196—44no—
99C4×Dic61—42no—
100C4×Dic61C4211yescharacteristic
101C4×Dic61C4211yescharacteristic
102C4×Dic61C22⋊C411yescharacteristic
103C4×Dic61C22⋊C411yescharacteristic
104C4×Dic61C22⋊C411yescharacteristic
105C4×Dic61C22⋊C411yescharacteristic
106C4×Dic61C4⋊C411yescharacteristic
107C4×Dic61C4⋊C411yescharacteristic
108C4×Dic61C4⋊C411yescharacteristic
109C4×Dic61C4⋊C411yescharacteristic
110C4×Dic61C4⋊C411yescharacteristic
111C4×Dic61C4⋊C411yescharacteristic
112C4×Dic61C22×C411yescharacteristic
113C4×Dic61C22×C411yescharacteristic
114C4×Dic61C2×D411yescharacteristic
115C4×Dic61C2×Q811yescharacteristic
116C23×C61—22no—
117C23×C61—22no—
118C23×C61—41no—
119C23×C61#9511yescharacteristic
120C23×C61#9511yescharacteristic
121C23×C61C2×C22⋊C411yescharacteristic
122C2×C4×C61—22no—
123C2×C4×C61—22no—
124C2×C4×C61—22no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—42no—
129C2×C4×C61—42no—
130C2×C4×C61—42no—
131C2×C4×C61#9511yescharacteristic
132C2×C4×C61#9511yescharacteristic
133C2×C4×C61C2×C4211yescharacteristic
134C2×C4×C61C2×C4⋊C411yescharacteristic
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61#9511yescharacteristic
151C2×Dic61#9511yescharacteristic
152C2×Dic61#9511yescharacteristic
153C2×Dic61#9511yescharacteristic
154C2×Dic61C2×C22⋊C411yescharacteristic
155C2×Dic61C2×C22⋊C411yescharacteristic
156C2×Dic61C2×C4⋊C411yescharacteristic
157C2×Dic61C2×C4⋊C411yescharacteristic
158#92420—44no—
159#92420—44no—
160#7978—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—44no—
169C22×C61H(3,ℤ/4)12yes—
170C22×C61C2×#9511yescharacteristic
171C22×C61#42112yes—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—82no—
176C4×C61#34412yes—
177Dic61—21no—
178Dic61—21no—
179Dic61—21no—
180Dic61—21no—
181Dic61—21no—
182Dic61—21no—
183Dic61—21no—
184Dic61—21no—
185Dic61—82no—
186#2920—611no—
187C2×#432—611no—
188#2283—611no—
189#1288—614no—
190C2×C61—22no—
191C2×C61—22no—
192C2×C61—41no—
193C2×C61C2×H(3,ℤ/4)11yescharacteristic
194C2×C61#173311yescharacteristic
195C2×C61C2×#34411yescharacteristic
196C22×C42—611no—
197#432—612no—
198#432—612no—
199#432—1221no—
200#432—1221no—
201#432—1221no—
202#432—1221no—
203#431—612no—
204#431—612no—
205#423—1221no—
206C2×C4⋊C8—1221no—
207#407—1221no—
208C2×C22⋊C8—1221no—
209C4×M16—612no—
210C2×#97—612no—
211#383—612no—
212#382—612no—
213#381—1221no—
214#380—1221no—
215C4×C4⋊C4—1221no—
216C4×C22⋊C4—611no—
217C4×C22⋊C4#692311yescharacteristic
218#376—1221no—
219C61#797811yescharacteristic, complemented, Sylow
220C23×C4—611no—
221C23×C4—611no—
222C23×C4C2×#692311yescharacteristic
223C2×M16—1222no—
224C22×C8—1222no—
225C2×C4⋊C4—1222no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—1221no—
228C2×C42—21no—
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—611no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—611no—
235C2×C42—611no—
236C2×C42—611no—
237C2×C42—611no—
238C2×C42—611no—
239C2×C42—611no—
240C2×C42—611no—
241C2×C42—1221no—
242C4⋊C8—1222no—
243C4⋊C8—1222no—
244C4⋊C8—1222no—
245C4⋊C8—1222no—
246C22⋊C8—1222no—
247C22⋊C8—1222no—
248C22⋊C8—1222no—
249C22⋊C8—1222no—
250#97—614no—
251#97—1222no—
252#97—1222no—
253C4×C8—614no—
254#95—612no—
255#95—1222no—
256#95—1222no—
257#95—1222no—
258#95C2×#692312yes—
259C24C22⋊#692311yescharacteristic
260C22×C4—22no—
261C22×C4—42no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—611no—
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—1222no—
275C22×C4—2442no—
276C22×C4—2442no—
277C22×C4C4×#692311yescharacteristic
278C22×C4C4×#692311yescharacteristic
279C22×C4C4⋊#692311yescharacteristic
280C22×C4C4⋊#692311yescharacteristic
281C22×C4C22⋊#692311yescharacteristic
282C22×C4C22×#692311yescharacteristic
283M16—2444no—
284C2×C8—1224no—
285C2×C8—1224no—
286C2×C8—2444no—
287C4⋊C4—2444no—
288C22⋊C4—42no—
289C22⋊C4—2442no—
290C42—42no—
291C42—611no—
292C42—611no—
293C42—611no—
294C42—611no—
295C42—611no—
296C42—611no—
297C42—611no—
298C42—611no—
299C42—611no—
300C42—611no—
301C42—611no—
302C42—611no—
303C42—611no—
304C42—611no—
305C42—611no—
306C42—611no—
307C42—2442no—
308C23—22no—
309C23—22no—
310C23—41no—
311C23(C2×#6923)⋊C411yescharacteristic
312C23(C2×#6923)⋊C411yescharacteristic
313C23C2×C22⋊#692311yescharacteristic
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—611no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—611no—
329C2×C4—611no—
330C2×C4—611no—
331C2×C4—1222no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2441no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4(C2×#6923)⋊C411yescharacteristic
347C2×C4(C2×#6923)⋊C411yescharacteristic
348C2×C4C2×C4×#692311yescharacteristic
349C2×C4C2×C4⋊#692311yescharacteristic
350C8—2444no—
351C8—2444no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—44no—
360C22#1684062912yes—
361C22C2×(C2×#6923)⋊C411yescharacteristic
362C22#1684075912yes—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—1221no—
368C4—1221no—
369C4—1221no—
370C4—1221no—
371C4—1221no—
372C4—1221no—
373C4—1221no—
374C4—1221no—
375C4—4882no—
376C4#1684064312yes—
377C2—22no—
378C2—22no—
379C2—41no—
380C2C2×#1684062911yescharacteristic
381C2#2146149911yescharacteristic
382C2C2×#1684064311yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#7978
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460678C2semidirect
8. #16840783C4semidirect
11. #16840779C4semidirect
12. #16840778C4semidirect
18. C2×#14519832C4semidirect
219. C61#7978semidirect

Maximal subgroups

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

subgroupindex
#214624952
C2×#168407832
#214606782
#214482132
#797861