Finite Group Databasebeta

← #30604166

Subgroups — #30604166

Order 15616.

470 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461078C211yesmaximal, characteristic
2#21461074C211yesmaximal, characteristic
3#21460763C212yesmaximal, complemented
4#21460746C212yesmaximal, complemented
5C4×#14519761C211yesmaximal, characteristic
6#16840783—21no—
7#16840733—21no—
8#16840608—21no—
9#16840606—21no—
10#16840605C2212yes—
11#16840605C2212yes—
12C2×#14519761C411yescharacteristic
13C2×C4×C22⋊D61C2211yescharacteristic
14C22×C4×Dic61C411yescharacteristic
15#16839654—21no—
16#16839647—21no—
17#16839639C411yescharacteristic
18#16839637C2211yescharacteristic
19#16839623C2211yescharacteristic
20C4×C4⋊Dic61—21no—
21C4×#11758198—21no—
22C4×C22⋊C4×C61C411yescharacteristic
23C2×#11758213—41no—
24C4⋊#92420—41no—
25#14519834—41no—
26C22⋊#92420—22no—
27C22⋊#92420—22no—
28#14519832—41no—
29C22×C22⋊D61C2×C411yescharacteristic
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33#14519761—22no—
34#14519761—22no—
35C4×C22⋊D61—41no—
36C4×C22⋊D61—41no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×#11758196D411yescharacteristic
40C2×C22⋊Dic61C2311yescharacteristic
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198D411yescharacteristic
44C2×C4×Dic61—21no—
45C2×C4×Dic61—21no—
46C2×C4×Dic61—41no—
47C2×C4×Dic61—41no—
48C2×C4×Dic61D411yescharacteristic
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C23×C4×C61C2×C411yescharacteristic
54C2×C22⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61C2×C411yescharacteristic
56C2×C42×C61—21no—
57#95×C61—21no—
58C24×C61C22×C411yescharacteristic
59C23×D61C22⋊C411yescharacteristic
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—42no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—41no—
70C2×C22⋊D61—41no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—42no—
75C22×Dic61—41no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61C22⋊C411yescharacteristic
79C22×Dic61M1612yescomplemented
80C22×Dic61C2×D411yescharacteristic
81C22×Dic61C2×D411yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87#11758213—82no—
88C22⋊C4×C61—21no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61M1612yescomplemented
91C42×C61—42no—
92C22⋊Dic61—41no—
93#11758198—24no—
94#11758198—41no—
95#11758198—42no—
96C4⋊Dic61—24no—
97C4⋊Dic61—42no—
98#11758196—41no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—42no—
102C4×Dic61—41no—
103C4×Dic61—41no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61C2×C22⋊C411yescharacteristic
109C23×C61C2×M1611yescharacteristic
110C23×C61C2×M1611yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—41no—
115C22×D61—41no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—21no—
119C2×C4×C61—42no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—42no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61#9911yescharacteristic
128C2×C4×C61#9911yescharacteristic
129C22⋊D61—42no—
130C22⋊D61—42no—
131C2×Dic61—22no—
132C2×Dic61—21no—
133C2×Dic61—22no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—41no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C4×D61—42no—
149C4×D61—81no—
150#92420—82no—
151#92420—82no—
152#11526—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—42no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61#40711yescharacteristic
163C22×C61C2×#9911yescharacteristic
164C22×C61#41311yescharacteristic
165C2×D61—42no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—81no—
170C4×C61—21no—
171C4×C61—42no—
172C4×C61—41no—
173C4×C61—81no—
174C4×C61#35212yes—
175Dic61—41no—
176Dic61—41no—
177Dic61—42no—
178Dic61—41no—
179Dic61—42no—
180C4×#123—611no—
181#1466—611no—
182#1465—611no—
183#1326—612no—
184#1317—612no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—41no—
188C2×C61—41no—
189C2×C61#146511yescharacteristic
190C2×C61C2×#35211yescharacteristic
191C2×C61#212011yescharacteristic
192D61—81no—
193C2×#123—611no—
194C2×C4×D4—611no—
195C22×C42—611no—
196#432—1221no—
197#407—1221no—
198#388—1221no—
199#387—1221no—
200#386—611no—
201#385—611no—
202#381—611no—
203C4×C4⋊C4—1221no—
204C4×C22⋊C4—1221no—
205C4×C22⋊C4#692311yescharacteristic
206#324—1221no—
207#323—612no—
208#323—612no—
209#323—1221no—
210C61#1152611yescharacteristic, complemented, Sylow
211C22×D4—611no—
212C23×C4—611no—
213C23×C4—611no—
214C23×C4—611no—
215C23×C4C2×#692311yescharacteristic
216C2×M16—2441no—
217#123—1222no—
218#123—1222no—
219C4×D4—2441no—
220C4×D4—2441no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C22⋊C4—611no—
225C2×C22⋊C4—611no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4C2×#692311yescharacteristic
229C2×C22⋊C4C2×#692311yescharacteristic
230C2×C42—21no—
231C2×C42—611no—
232C2×C42—1221no—
233C2×C42—1221no—
234C2×C42—2441no—
235C2×C42—2441no—
236C4⋊C8—2441no—
237C22⋊C8—1222no—
238C22⋊C8—1222no—
239C22⋊C8—2441no—
240#97—2441no—
241#95—21no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246C24—611no—
247C24C22×#692311yescharacteristic
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—2441no—
251C2×D4—2441no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—42no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—612no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—2442no—
267C22×C4—2442no—
268C22×C4—2441no—
269C22×C4—2441no—
270C22×C4—2441no—
271C22×C4C22⋊#692311yescharacteristic
272C22×C4C22⋊#692311yescharacteristic
273M16—4882no—
274C2×C8—2442no—
275C2×C8—2442no—
276C4⋊C4—1224no—
277C4⋊C4—2441no—
278C4⋊C4—2442no—
279C22⋊C4—21no—
280C22⋊C4—41no—
281C22⋊C4—1224no—
282C22⋊C4—2441no—
283C22⋊C4—2442no—
284C22⋊C4—2441no—
285C22⋊C4#1175821312yescomplemented
286C42—42no—
287C42—1221no—
288C42—1221no—
289C42—2442no—
290C42—2441no—
291C42—2441no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—1221no—
297C23—1221no—
298C23—1221no—
299C23—2441no—
300C23—2441no—
301C23C2×C22⋊#692311yescharacteristic
302C23D61⋊M1611yescharacteristic
303C23C2×#1175821311yescharacteristic
304D4—2442no—
305D4—2442no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—4881no—
325C2×C4—2441no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2442no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4#1451983611yescharacteristic
337C2×C4#1451983611yescharacteristic
338C8—4882no—
339C8—4882no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—4881no—
350C22—2442no—
351C22—2441no—
352C22—2441no—
353C22—2441no—
354C22#1684073311yescharacteristic
355C22C2×#1451983611yescharacteristic
356C22#1684074811yescharacteristic
357C4—21no—
358C4—42no—
359C4—41no—
360C4—81no—
361C4—2441no—
362C4—2441no—
363C4—2442no—
364C4—2441no—
365C4—2442no—
366C4#1684066512yes—
367C2—21no—
368C2—21no—
369C2—41no—
370C2—41no—
371C2—4881no—
372C2#2146107611yescharacteristic
373C2C2×#1684066511yescharacteristic
374C2#2146207211yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#11526
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460763C2semidirect
4. #21460746C2semidirect
79. C22×Dic61M16semidirect
90. C22⋊C4×C61M16semidirect
210. C61#11526semidirect
285. C22⋊C4#11758213semidirect

Maximal subgroups

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

subgroupindex
#214610782
#214610742
#214607632
#214607462
C4×#145197612
#1152661