Finite Group Databasebeta

← #30597070

Subgroups — #30597070

Order 15616.

698 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C211yesmaximal, characteristic
2#21462495C211yesmaximal, characteristic
3#21460707C214yesmaximal, complemented
4C2×#16839607C211yesmaximal, characteristic
5#16840783C412yescomplemented
6#16840783C2212yes—
7#16840782—21no—
8#16840782C412yescomplemented
9#16840779—21no—
10#16840779—21no—
11#16840778—21no—
12#16840778C412yescomplemented
13#16840765—21no—
14#16840765C412yescomplemented
15#16840732—21no—
16#16840732—21no—
17C4×#11758217—21no—
18C4×#11758217C2212yes—
19C22×C4×Dic61—21no—
20C22×C4×Dic61C2211yescharacteristic
21#16839607—21no—
22#16839607—21no—
23#16839607C412yes—
24#16839607C2212yes—
25C2×#14519684—21no—
26C2×#14519684C411yescharacteristic
27C2×#95×C61C411yescharacteristic
28C2×#11758217—22no—
29C2×#11758217—22no—
30#14519844—22no—
31#14519844—22no—
32C4⋊#92420—22no—
33C4⋊#92420C2×C414yescomplemented
34C22⋊#92420—22no—
35C22⋊#92420—22no—
36C22⋊#92420—22no—
37C22⋊#92420—22no—
38#14519832—22no—
39#14519832C2×C414yescomplemented
40C4×#92420—22no—
41C4×#92420—22no—
42C23×Dic61—21no—
43C23×Dic61D411yescharacteristic
44C23×Dic61D411yescharacteristic
45C2×C4×Dic61—28no—
46C2×C4×Dic61—22no—
47C2×C4×Dic61—22no—
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61Q811yescharacteristic
58C2×C4×Dic61Q811yescharacteristic
59C2×C4×Dic61C2311yescharacteristic
60#14519684—21no—
61#14519684—22no—
62#14519684—22no—
63#14519684C2×C412yes—
64C23×C4×C61—21no—
65C23×C4×C61C2×C411yescharacteristic
66#95×C61—21no—
67#95×C61C2×C412yes—
68C24×C61C22⋊C411yescharacteristic
69C22×C4×C61—24no—
70C22×C4×C61—22no—
71C22×C4×C61—42no—
72C22×C4×C61—42no—
73C22×C4×C61—42no—
74C22×C4×C61C4211yescharacteristic
75C22×C4×C61C4211yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C4⋊C411yescharacteristic
78C22×C4×C61C4⋊C411yescharacteristic
79C22×C4×C61C22×C411yescharacteristic
80C22×Dic61—24no—
81C22×Dic61—24no—
82C22×Dic61—22no—
83C22×Dic61—41no—
84C22×Dic61—41no—
85C22×Dic61—42no—
86C22×Dic61—42no—
87C22×Dic61C22⋊C411yescharacteristic
88C22×Dic61C22⋊C411yescharacteristic
89C22×Dic61C22⋊C411yescharacteristic
90C22×Dic61C22⋊C411yescharacteristic
91C22×Dic61C22⋊C411yescharacteristic
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C4⋊C411yescharacteristic
94C22×Dic61C4⋊C411yescharacteristic
95C22×Dic61C4⋊C411yescharacteristic
96C22×Dic61C4⋊C411yescharacteristic
97C22×Dic61C2×D411yescharacteristic
98C22×Dic61C2×D411yescharacteristic
99#11758217—42no—
100#11758217—42no—
101#11758217—44no—
102C2×#92420—24no—
103C2×#92420—24no—
104C4×Dic61—28no—
105C4×Dic61—28no—
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—22no—
123C23×C61—22no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61#9511yescharacteristic
127C23×C61#9511yescharacteristic
128C23×C61C2×C22⋊C411yescharacteristic
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61—24no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—48no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61#9511yescharacteristic
140C2×C4×C61#9511yescharacteristic
141C2×C4×C61C2×C4211yescharacteristic
142C2×C4×C61C2×C4⋊C411yescharacteristic
143C2×Dic61—22no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—22no—
151C2×Dic61—22no—
152C2×Dic61—24no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—48no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61#9511yescharacteristic
161C2×Dic61#9511yescharacteristic
162C2×Dic61#9511yescharacteristic
163C2×Dic61#9511yescharacteristic
164C2×Dic61#10414yes—
165C2×Dic61C2×C22⋊C411yescharacteristic
166C2×Dic61C2×C22⋊C411yescharacteristic
167C2×Dic61C2×C4⋊C411yescharacteristic
168C2×Dic61C2×C4⋊C411yescharacteristic
169#92420—44no—
170#92420—44no—
171#8072—611nomaximal, Sylow
172C22×C61—24no—
173C22×C61—24no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—21no—
179C22×C61—21no—
180C22×C61#33912yes—
181C22×C61#34412yes—
182C22×C61C2×#9511yescharacteristic
183C22×C61#42111yescharacteristic
184C22×C61#42111yescharacteristic
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—44no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61—21no—
194Dic61—21no—
195Dic61—21no—
196Dic61—44no—
197Dic61#33912yes—
198Dic61C2×#10412yes—
199#2920—611no—
200#2920—611no—
201C2×#376—611no—
202#1300—614no—
203C2×C61—21no—
204C2×C61—21no—
205C2×C61—22no—
206C2×C61—22no—
207C2×C61C2×#33911yescharacteristic
208C2×C61#173311yescharacteristic
209C2×C61C2×#34411yescharacteristic
210C22×C42—611no—
211C22×C42—1221no—
212#432—612no—
213#432—612no—
214#432—612no—
215#432—1221no—
216#431—612no—
217#431—1221no—
218#431—1221no—
219#431—1221no—
220#423—612no—
221#423—1221no—
222#407—1221no—
223#407—1221no—
224C4×M16—612no—
225C4×M16—1221no—
226#376—612no—
227#376—612no—
228#376—1221no—
229#376—1221no—
230C2×#95—611no—
231C2×#95—1221no—
232C2×#95#692311yescharacteristic
233C61#807211yescharacteristic, complemented, Sylow
234C23×C4—21no—
235C23×C4—611no—
236C23×C4—611no—
237C23×C4—1221no—
238C23×C4C2×#692311yescharacteristic
239C2×M16—1222no—
240C2×M16—1222no—
241C2×C42—611no—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
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—1222no—
254C2×C42—1222no—
255C2×C42—1228no—
256C4⋊C8—614no—
257C4⋊C8—1222no—
258C4⋊C8—1222no—
259C4⋊C8—1222no—
260C22⋊C8—1222no—
261C22⋊C8—1222no—
262C22⋊C8—1222no—
263C22⋊C8—1222no—
264#97—614no—
265#97—1222no—
266C4×C8—1222no—
267C4×C8—1222no—
268#95—21no—
269#95—612no—
270#95—1222no—
271#95—1222no—
272#95—1221no—
273#95C2×#692312yes—
274C24C22⋊#692311yescharacteristic
275C22×C4—24no—
276C22×C4—22no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—42no—
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—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—1224no—
293C22×C4—1224no—
294C22×C4—1222no—
295C22×C4—2441no—
296C22×C4—2441no—
297C22×C4—2442no—
298C22×C4—2442no—
299C22×C4C4×#692311yescharacteristic
300C22×C4C4×#692311yescharacteristic
301C22×C4C4⋊#692311yescharacteristic
302C22×C4C4⋊#692311yescharacteristic
303C22×C4C22⋊#692311yescharacteristic
304C22×C4C22×#692311yescharacteristic
305M16—2444no—
306M16—2442no—
307M16—2442no—
308C2×C8—1224no—
309C2×C8—1224no—
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—611no—
326C42—1228no—
327C42—1228no—
328C23—21no—
329C23—21no—
330C23—22no—
331C23—22no—
332C23(C2×#6923)⋊C411yescharacteristic
333C23(C2×#6923)⋊C411yescharacteristic
334C23C2×C22⋊#692311yescharacteristic
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—48no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—614no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1222no—
363C2×C4—1224no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2448no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4(C2×#6923)⋊C411yescharacteristic
372C2×C4(C2×#6923)⋊C411yescharacteristic
373C2×C4C2×C4×#692311yescharacteristic
374C2×C4C2×C4⋊#692311yescharacteristic
375C8—2444no—
376C8—2444no—
377C22—24no—
378C22—24no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22#1684063312yes—
386C22#1684064312yes—
387C22C2×(C2×#6923)⋊C411yescharacteristic
388C22#1684076011yescharacteristic
389C22#1684076111yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—44no—
395C4—612no—
396C4—612no—
397C4—1221no—
398C4—1221no—
399C4—1221no—
400C4—1221no—
401C4—1221no—
402C4—1221no—
403C4—2444no—
404C2—21no—
405C2—21no—
406C2—22no—
407C2—22no—
408C2C2×#1684063311yescharacteristic
409C2#2146149811yescharacteristic
410C2C2×#1684064311yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#95×C61C4
socleC22×C61C2×#95
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#95#6923
hypocenterC61#8072
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #21460707C2semidirect
5. #16840783C4semidirect
8. #16840782C4semidirect
12. #16840778C4semidirect
14. #16840765C4semidirect
33. C4⋊#92420C2×C4semidirect
39. #14519832C2×C4semidirect
233. C61#8072semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214607072
C2×#168396072
#807261