Finite Group Databasebeta

← #30597076

Subgroups — #30597076

Order 15616.

650 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840783C211yesmaximal, characteristic
2C2×C4×#11758217C211yesmaximal, characteristic
3#21460707C214yesmaximal, complemented
4#21448214C211yesmaximal, characteristic
5C22×#11758217—21no—
6#16840783—21no—
7#16840783—21no—
8#16840783C412yescomplemented
9#16840783C2212yes—
10C2×C4⋊#92420C412yescomplemented
11C2×C22⋊#92420—21no—
12C4×#11758217—21no—
13C4×#11758217—21no—
14C4×#11758217C412yescomplemented
15C4×#11758217C2212yes—
16C2×#14519832—21no—
17C2×#14519832C412yescomplemented
18C2×C4×#92420—21no—
19C22×C4×Dic61C2211yescharacteristic
20#16839629C412yes—
21#16839627—21no—
22#16839623—21no—
23#16839622C411yescharacteristic
24C4⋊C4×Dic61—21no—
25C22⋊C4×Dic61—21no—
26#16839607C2212yes—
27C61×#380C411yescharacteristic
28C2×#11758217—24no—
29C2×#11758217—24no—
30C2×#11758217—22no—
31C2×#11758217—22no—
32C22×#92420—22no—
33C22×#92420—22no—
34C4⋊#92420—22no—
35C4⋊#92420C2×C414yes—
36C22⋊#92420—22no—
37C22⋊#92420—22no—
38#14519832—22no—
39#14519832—22no—
40#14519832—22no—
41#14519832C2×C414yes—
42C4×#92420—22no—
43C4×#92420—22no—
44C23×Dic61D411yescharacteristic
45C23×Dic61D411yescharacteristic
46C2×C4⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C4×Dic61—22no—
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61C2×C411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C2×C4×Dic61Q811yescharacteristic
59C2×C4×Dic61Q811yescharacteristic
60C2×C4×Dic61C2311yescharacteristic
61#14519684—22no—
62#14519684—22no—
63#14519684—22no—
64#14519684C2×C412yes—
65C23×C4×C61C2×C411yescharacteristic
66C2×C4⋊C4×C61—21no—
67C2×C22⋊C4×C61—21no—
68#95×C61C2×C412yes—
69C24×C61C22⋊C411yescharacteristic
70C22×C4×C61—22no—
71C22×C4×C61—42no—
72C22×C4×C61C4211yescharacteristic
73C22×C4×C61C4211yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C4⋊C411yescharacteristic
76C22×C4×C61C4⋊C411yescharacteristic
77C22×C4×C61C22×C411yescharacteristic
78C22×Dic61—22no—
79C22×Dic61—22no—
80C22×Dic61—22no—
81C22×Dic61—42no—
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C22⋊C411yescharacteristic
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C4⋊C411yescharacteristic
89C22×Dic61C4⋊C411yescharacteristic
90C22×Dic61C4⋊C411yescharacteristic
91C22×Dic61C4⋊C411yescharacteristic
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61C2×D411yescharacteristic
94#11758217—28no—
95#11758217—24no—
96#11758217—24no—
97C2×#92420—28no—
98C2×#92420—24no—
99C2×#92420—24no—
100C2×#92420—44no—
101C4⋊C4×C61—42no—
102C22⋊C4×C61—42no—
103C22⋊Dic61—42no—
104C4⋊Dic61—42no—
105C4×Dic61—44no—
106C4×Dic61C4211yescharacteristic
107C4×Dic61C4211yescharacteristic
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C22⋊C411yescharacteristic
112C4×Dic61C4⋊C411yescharacteristic
113C4×Dic61C4⋊C411yescharacteristic
114C4×Dic61C4⋊C411yescharacteristic
115C4×Dic61C4⋊C411yescharacteristic
116C4×Dic61C4⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C22×C411yescharacteristic
119C4×Dic61C22×C411yescharacteristic
120C4×Dic61C2×D411yescharacteristic
121C4×Dic61C2×Q811yescharacteristic
122C23×C61—41no—
123C23×C61—41no—
124C23×C61#9511yescharacteristic
125C23×C61#9511yescharacteristic
126C23×C61#10412yes—
127C23×C61#10412yes—
128C23×C61C2×C22⋊C411yescharacteristic
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61#9511yescharacteristic
139C2×C4×C61#9511yescharacteristic
140C2×C4×C61C2×C4211yescharacteristic
141C2×C4×C61C2×C4⋊C411yescharacteristic
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—22no—
151C2×Dic61—22no—
152C2×Dic61—22no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61#9511yescharacteristic
160C2×Dic61#9511yescharacteristic
161C2×Dic61#9511yescharacteristic
162C2×Dic61#9511yescharacteristic
163C2×Dic61C2×C22⋊C411yescharacteristic
164C2×Dic61C2×C22⋊C411yescharacteristic
165C2×Dic61C2×C4⋊C411yescharacteristic
166C2×Dic61C2×C4⋊C411yescharacteristic
167#92420—28no—
168#92420—44no—
169#8073—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—42no—
177C22×C61—42no—
178C22×C61#33912yes—
179C22×C61#33912yes—
180C22×C61C2×#9511yescharacteristic
181C22×C61C2×#10411yescharacteristic
182C22×C61C2×#10411yescharacteristic
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—82no—
187C4×C61#34412yes—
188Dic61—21no—
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61—21no—
194Dic61—21no—
195Dic61—82no—
196Dic61#42112yes—
197C2×#432—611no—
198C2×C4×M16—611no—
199#2283—611no—
200#1300—614no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—22no—
204C2×C61—22no—
205C2×C61C2×#33911yescharacteristic
206C2×C61#173311yescharacteristic
207C2×C61C2×#34411yescharacteristic
208C22×M16—1221no—
209C22×C42—611no—
210#432—612no—
211#432—612no—
212#432—1221no—
213#432—1221no—
214C2×C4⋊C8—612no—
215C2×C22⋊C8—1221no—
216C4×M16—612no—
217C4×M16—612no—
218C4×M16—1221no—
219C4×M16—1221no—
220C2×#97—612no—
221C2×#97—1221no—
222C2×C4×C8—1221no—
223#383—612no—
224#382—1221no—
225#381—1221no—
226#380—611no—
227#380#692311yescharacteristic
228C4×C4⋊C4—1221no—
229C4×C22⋊C4—1221no—
230#376—612no—
231C61#807311yescharacteristic, complemented, Sylow
232C23×C4—611no—
233C23×C4—611no—
234C23×C4C2×#692311yescharacteristic
235C2×M16—1222no—
236C2×M16—1222no—
237C2×M16—1224no—
238C2×M16—1224no—
239C22×C8—1222no—
240C22×C8—1222no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—1221no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—1221no—
245C2×C42—611no—
246C2×C42—611no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—611no—
256C2×C42—611no—
257C2×C42—1222no—
258C4⋊C8—614no—
259C4⋊C8—1222no—
260C22⋊C8—1222no—
261C22⋊C8—1222no—
262#97—614no—
263#97—1222no—
264#97—1222no—
265#97—1222no—
266C4×C8—1222no—
267C4×C8—1222no—
268#95—612no—
269#95—1222no—
270#95—1222no—
271#95—1222no—
272#95C2×#692312yes—
273C24C22⋊#692311yescharacteristic
274C22×C4—22no—
275C22×C4—42no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—1222no—
289C22×C4—1222no—
290C22×C4—1222no—
291C22×C4—2442no—
292C22×C4C4×#692311yescharacteristic
293C22×C4C4×#692311yescharacteristic
294C22×C4C4⋊#692311yescharacteristic
295C22×C4C4⋊#692311yescharacteristic
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22×#692311yescharacteristic
298M16—1224no—
299M16—1224no—
300M16—1228no—
301C2×C8—1224no—
302C2×C8—1228no—
303C2×C8—1224no—
304C2×C8—2444no—
305C4⋊C4—42no—
306C4⋊C4—2442no—
307C22⋊C4—42no—
308C22⋊C4—2442no—
309C42—611no—
310C42—611no—
311C42—611no—
312C42—611no—
313C42—611no—
314C42—611no—
315C42—611no—
316C42—611no—
317C42—611no—
318C42—611no—
319C42—611no—
320C42—611no—
321C42—611no—
322C42—611no—
323C42—611no—
324C42—611no—
325C42—2444no—
326C23—41no—
327C23—41no—
328C23(C2×#6923)⋊C411yescharacteristic
329C23(C2×#6923)⋊C411yescharacteristic
330C23#1451984112yes—
331C23#1451984212yes—
332C23C2×C22⋊#692311yescharacteristic
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1222no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1222no—
358C2×C4—1222no—
359C2×C4—1222no—
360C2×C4—1222no—
361C2×C4—2441no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2442no—
365C2×C4—2442no—
366C2×C4—2442no—
367C2×C4(C2×#6923)⋊C411yescharacteristic
368C2×C4(C2×#6923)⋊C411yescharacteristic
369C2×C4C2×C4×#692311yescharacteristic
370C2×C4C2×C4⋊#692311yescharacteristic
371C8—1228no—
372C8—2444no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—42no—
380C22—42no—
381C22#1684063212yes—
382C22#1684063212yes—
383C22C2×(C2×#6923)⋊C411yescharacteristic
384C22C2×#1451984111yescharacteristic
385C22C2×#1451984211yescharacteristic
386C4—21no—
387C4—21no—
388C4—21no—
389C4—82no—
390C4—612no—
391C4—1221no—
392C4—1221no—
393C4—1221no—
394C4—1221no—
395C4—1221no—
396C4—1221no—
397C4—1221no—
398C4—4882no—
399C4#1684064312yes—
400C2—21no—
401C2—21no—
402C2—22no—
403C2—22no—
404C2C2×#1684063211yescharacteristic
405C2#2146150011yescharacteristic
406C2C2×#1684064311yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC22×C61C2×#95
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#8073
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460707C2semidirect
8. #16840783C4semidirect
10. C2×C4⋊#92420C4semidirect
14. C4×#11758217C4semidirect
17. C2×#14519832C4semidirect
231. C61#8073semidirect

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
#214607072
#214482142
#807361