Finite Group Databasebeta

← #30593982

Subgroups — #30593982

Order 15616.

490 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461675C211yesmaximal, characteristic
2#21461675C211yesmaximal, characteristic
3#21444047C211yesmaximal, characteristic
4C2×#14519844—21no—
5C2×#14519844C412yescomplemented
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8#16840628—21no—
9#16840628C412yescomplemented
10C22×#11758196—21no—
11C22×C4×Dic61C2211yescharacteristic
12C2×#14519684—21no—
13C2×#14519684C411yescharacteristic
14C2×#95×C61C411yescharacteristic
15C22×#92420—22no—
16C22×#92420—22no—
17#14519844—42no—
18#14519844—42no—
19C22⋊#92420—41no—
20C22⋊#92420—41no—
21C22⋊#92420—41no—
22C22⋊#92420—41no—
23C23×Dic61—21no—
24C23×Dic61D411yescharacteristic
25C23×Dic61D411yescharacteristic
26C2×#11758196—24no—
27C2×#11758196—42no—
28C2×#11758196—41no—
29C2×#11758196—41no—
30C2×C4×Dic61—42no—
31C2×C4×Dic61C2×C411yescharacteristic
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C2×C4×Dic61Q811yescharacteristic
35#14519684—41no—
36#14519684—41no—
37#14519684—41no—
38C23×C4×C61—21no—
39C23×C4×C61C2×C411yescharacteristic
40#95×C61—41no—
41C24×C61C22⋊C411yescharacteristic
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61—22no—
45C22×C4×C61—41no—
46C22×C4×C61—41no—
47C22×C4×C61—41no—
48C22×C4×C61—41no—
49C22×C4×C61—41no—
50C22×C4×C61—41no—
51C22×C4×C61—41no—
52C22×C4×C61—41no—
53C22×C4×C61C4211yescharacteristic
54C22×C4×C61C4⋊C411yescharacteristic
55C22×Dic61—22no—
56C22×Dic61—22no—
57C22×Dic61—22no—
58C22×Dic61—41no—
59C22×Dic61—41no—
60C22×Dic61—41no—
61C22×Dic61—41no—
62C22×Dic61—41no—
63C22×Dic61—41no—
64C22×Dic61—41no—
65C22×Dic61—41no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C4⋊C411yescharacteristic
69C22×Dic61C4⋊C411yescharacteristic
70C22×Dic61D811yescharacteristic
71C22×Dic61D811yescharacteristic
72C22×Dic61SD1611yescharacteristic
73C22×Dic61SD1611yescharacteristic
74C22×Dic61SD1611yescharacteristic
75C22×Dic61SD1611yescharacteristic
76C22×Dic61Q1611yescharacteristic
77C22×Dic61Q1611yescharacteristic
78C2×#92420—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84#11758196—44no—
85#11758196—44no—
86C4×Dic61—22no—
87C4×Dic61—22no—
88C4×Dic61—41no—
89C4×Dic61—41no—
90C23×C61—21no—
91C23×C61—21no—
92C23×C61—21no—
93C23×C61—21no—
94C23×C61#9511yescharacteristic
95C23×C61#10011yescharacteristic
96C23×C61#10111yescharacteristic
97C23×C61#10211yescharacteristic
98C23×C61#10211yescharacteristic
99C23×C61#10311yescharacteristic
100C23×C61#10311yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—42no—
108C2×C4×C61—42no—
109C2×C4×C61—42no—
110C2×C4×C61—42no—
111C2×C4×C61—42no—
112C2×C4×C61—81no—
113C2×C4×C61—81no—
114C2×C4×C61—81no—
115C2×C4×C61—81no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—22no—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—22no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—42no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—81no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137C2×Dic61#9912yes—
138C2×Dic61#10211yescharacteristic
139C2×Dic61#10211yescharacteristic
140C2×Dic61#10311yescharacteristic
141C2×Dic61#10311yescharacteristic
142C2×Dic61#10412yes—
143C2×Dic61#10611yescharacteristic
144C2×Dic61#10611yescharacteristic
145C2×Dic61#10711yescharacteristic
146C2×Dic61#10711yescharacteristic
147#92420—82no—
148#92420—82no—
149#7039—611nomaximal, Sylow
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—21no—
161C22×C61—21no—
162C22×C61#33111yescharacteristic
163C22×C61#33211yescharacteristic
164C22×C61#33211yescharacteristic
165C22×C61#33311yescharacteristic
166C22×C61H(3,ℤ/4)11yescharacteristic
167C22×C61#33911yescharacteristic
168C22×C61#34011yescharacteristic
169C22×C61#34011yescharacteristic
170C22×C61#34211yescharacteristic
171C22×C61#34311yescharacteristic
172C22×C61#34411yescharacteristic
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—82no—
176Dic61—21no—
177Dic61—21no—
178Dic61—21no—
179Dic61—21no—
180Dic61—21no—
181Dic61—21no—
182Dic61—82no—
183Dic61#32712yes—
184Dic61#32812yes—
185#1797—611no—
186#1797—611no—
187C4⋊#95—611no—
188C2×C61—21no—
189C2×C61—21no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#128511yescharacteristic
193C2×C61#128611yescharacteristic
194C2×C61#128911yescharacteristic
195C2×C61#129411yescharacteristic
196C2×C61#129611yescharacteristic
197C2×C61#130311yescharacteristic
198C2×C61#130511yescharacteristic
199C22×C4⋊C4—1221no—
200C22×C42—611no—
201C2×C4⋊C8—612no—
202C2×C4⋊C8—1221no—
203C2×C22⋊C8—1221no—
204C2×C22⋊C8—1221no—
205C2×#95—611no—
206C2×#95—1221no—
207C2×#95#692311yescharacteristic
208#336—612no—
209#336—1221no—
210C61#703911yescharacteristic, complemented, Sylow
211C23×C4—21no—
212C23×C4—611no—
213C23×C4—611no—
214C23×C4—1221no—
215C23×C4C2×#692311yescharacteristic
216C22×C8—1222no—
217C22×C8—1222no—
218C2×C4⋊C4—1224no—
219C2×C4⋊C4—2441no—
220C2×C4⋊C4—2441no—
221C2×C4⋊C4—2442no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—611no—
226C2×C42—2442no—
227C4⋊C8—2442no—
228C4⋊C8—2442no—
229C22⋊C8—2441no—
230C22⋊C8—2441no—
231C22⋊C8—2441no—
232C22⋊C8—2441no—
233#95—41no—
234#95—2441no—
235#95—2441no—
236#95—2441no—
237C24C22⋊#692311yescharacteristic
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—1222no—
262C22×C4—1222no—
263C22×C4—1222no—
264C22×C4—2441no—
265C22×C4—2441no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4C4×#692311yescharacteristic
273C22×C4C4⋊#692311yescharacteristic
274C2×C8—2442no—
275C2×C8—2442no—
276C2×C8—2442no—
277C2×C8—2442no—
278C2×C8—2442no—
279C2×C8—2442no—
280C4⋊C4—2444no—
281C4⋊C4—2444no—
282C42—1222no—
283C42—1222no—
284C42—2441no—
285C42—2441no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23(C2×#6923)⋊C411yescharacteristic
291C23#1451983711yescharacteristic
292C23#1451983811yescharacteristic
293C23#1451983911yescharacteristic
294C23#1451983911yescharacteristic
295C23#1451984011yescharacteristic
296C23#1451984011yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—612no—
313C2×C4—611no—
314C2×C4—611no—
315C2×C4—612no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—611no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—1222no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—4881no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C8—4882no—
344C8—4882no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22#1684062011yescharacteristic
358C22#1684062111yescharacteristic
359C22#1684062111yescharacteristic
360C22#1684062211yescharacteristic
361C22#1684062911yescharacteristic
362C22#1684063311yescharacteristic
363C22#1684063511yescharacteristic
364C22#1684063511yescharacteristic
365C22#1684063911yescharacteristic
366C22#1684064211yescharacteristic
367C22#1684064311yescharacteristic
368C4—41no—
369C4—41no—
370C4—82no—
371C4—612no—
372C4—612no—
373C4—1221no—
374C4—1221no—
375C4—1221no—
376C4—1221no—
377C4—1221no—
378C4—1221no—
379C4—4882no—
380C2—21no—
381C2—21no—
382C2—21no—
383C2—21no—
384C2#2146067011yescharacteristic
385C2#2146067211yescharacteristic
386C2#2146068111yescharacteristic
387C2#2146069311yescharacteristic
388C2#2146069711yescharacteristic
389C2#2146071711yescharacteristic
390C2#2146072011yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC2×#95×C61C4
socleC23×C61#95
prime radicalC24×C61C22⋊C4
cosocleC22×C4×Dic61C22
hypercenterC2×#95#6923
hypocenterC61#7039
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
5. C2×#14519844C4semidirect
9. #16840628C4semidirect
210. C61#7039semidirect

Maximal subgroups

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

subgroupindex
#214616752
#214440472
#703961