Finite Group Databasebeta

← #30604134

Subgroups — #30604134

Order 15616.

750 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 84 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#21461064C211yesmaximal, characteristic
2#21461064C211yesmaximal, characteristic
3#21460764C214yesmaximal, complemented
4C2×#16839635C211yesmaximal, characteristic
5#16840732—21no—
6#16840732—21no—
7#16840605—21no—
8#16840605—21no—
9#16840605C2212yes—
10#16840605C2212yes—
11C22×#11758196—21no—
12C22×C22⋊Dic61C411yescharacteristic
13C22×C22⋊Dic61C2211yescharacteristic
14#16839635—21no—
15#16839635—21no—
16#16839635C412yes—
17#16839635C2212yes—
18C2×#14519684—21no—
19C24×C4×C61C411yescharacteristic
20C2×#11758217—41no—
21C2×#11758217—41no—
22C22⋊#92420—22no—
23C22⋊#92420—22no—
24C22⋊#92420—41no—
25C22⋊#92420—41no—
26C23×Dic61—21no—
27C23×Dic61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C2×#11758196—22no—
30C2×#11758196—22no—
31C2×#11758196—44no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—24no—
34C2×C22⋊Dic61—41no—
35C2×C22⋊Dic61—41no—
36C2×C22⋊Dic61C2×C412yes—
37C2×C22⋊Dic61C2×C411yescharacteristic
38C2×C22⋊Dic61D411yescharacteristic
39C2×C22⋊Dic61D411yescharacteristic
40C2×C22⋊Dic61C2311yescharacteristic
41#14519684—22no—
42#14519684—22no—
43C25×C61C2×C411yescharacteristic
44C23×C4×C61—21no—
45C23×C4×C61—21no—
46C23×C4×C61—44no—
47C23×C4×C61—41no—
48C23×C4×C61—41no—
49C23×C4×C61C2×C412yes—
50C24×C61—21no—
51C24×C61—21no—
52C24×C61—22no—
53C24×C61—22no—
54C24×C61—42no—
55C24×C61—42no—
56C24×C61C22⋊C411yescharacteristic
57C24×C61C22⋊C411yescharacteristic
58C24×C61C22×C411yescharacteristic
59C22×C4×C61—24no—
60C22×C4×C61—22no—
61C22×C4×C61—44no—
62C22×C4×C61—44no—
63C22×C4×C61—42no—
64C22×C4×C61—42no—
65C22×C4×C61—48no—
66C22×C4×C61—44no—
67C22×C4×C61—41no—
68C22×C4×C61—41no—
69C22×C4×C61—42no—
70C22×C4×C61—44no—
71C22×Dic61—24no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—22no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—42no—
78C22×Dic61—42no—
79C22×Dic61—42no—
80C22×Dic61—42no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C22×Dic61C2×D411yescharacteristic
85#11758217—82no—
86#11758217—82no—
87C2×#92420—42no—
88C2×#92420—42no—
89C22⋊Dic61—24no—
90C22⋊Dic61—22no—
91C22⋊Dic61—41no—
92C22⋊Dic61—41no—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61M1614yescomplemented
96#11758196—44no—
97#11758196—44no—
98C23×C61—22no—
99C23×C61—22no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—24no—
103C23×C61—24no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—42no—
109C23×C61—48no—
110C23×C61—48no—
111C23×C61—42no—
112C23×C61—41no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—42no—
117C23×C61—42no—
118C23×C61#9911yescharacteristic
119C23×C61#9911yescharacteristic
120C23×C61#10112yes—
121C23×C61C2×C22⋊C411yescharacteristic
122C23×C61C2×M1612yes—
123C2×C4×C61—24no—
124C2×C4×C61—42no—
125C2×C4×C61—44no—
126C2×C4×C61—48no—
127C2×C4×C61—44no—
128C2×C4×C61—44no—
129C2×C4×C61—42no—
130C2×C4×C61—44no—
131C2×Dic61—24no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—42no—
137C2×Dic61—48no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147#92420—82no—
148#92420—82no—
149#11517—611nomaximal, Sylow
150C22×C61—24no—
151C22×C61—24no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—22no—
159C22×C61—22no—
160C22×C61—42no—
161C22×C61—42no—
162C22×C61—42no—
163C22×C61—48no—
164C22×C61—48no—
165C22×C61—42no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61AΣL(1,𝔽16)12yes—
171C22×C61#35212yes—
172C22×C61#40711yescharacteristic
173C22×C61C2×#9911yescharacteristic
174C22×C61C2×#10111yescharacteristic
175C4×C61—44no—
176Dic61—44no—
177Dic61—41no—
178Dic61—41no—
179Dic61—41no—
180Dic61—41no—
181C2×#385—611no—
182#1462—611no—
183#1462—611no—
184#1326—614no—
185C2×C61—21no—
186C2×C61—22no—
187C2×C61—22no—
188C2×C61—21no—
189C2×C61—42no—
190C2×C61—42no—
191C2×C61#146311yescharacteristic
192C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
193C2×C61C2×#35211yescharacteristic
194C24×C4#692311yescharacteristic
195C22×C4⋊C4—1221no—
196C22×C22⋊C4—611no—
197C22×C22⋊C4—611no—
198#407—1221no—
199#407—1221no—
200#385—612no—
201#385—612no—
202#385—1221no—
203#385—1221no—
204C2×#95—1221no—
205#323—612no—
206#323—612no—
207#323—1221no—
208#323—1221no—
209C61#1151711yescharacteristic, complemented, Sylow
210C25C2×#692311yescharacteristic
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—44no—
214C23×C4—41no—
215C23×C4—41no—
216C23×C4—611no—
217C23×C4—611no—
218C23×C4—1221no—
219C23×C4C2×#692312yes—
220C2×M16—2441no—
221C2×M16—2441no—
222C2×C4⋊C4—1222no—
223C2×C4⋊C4—1222no—
224C2×C4⋊C4—2444no—
225C2×C22⋊C4—612no—
226C2×C22⋊C4—611no—
227C2×C22⋊C4—611no—
228C2×C22⋊C4—611no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—1224no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4—2441no—
233C2×C22⋊C4—2441no—
234C22⋊C8—1222no—
235C22⋊C8—1222no—
236C22⋊C8—2441no—
237C22⋊C8—2441no—
238#95—1222no—
239#95—1222no—
240C24—21no—
241C24—21no—
242C24—22no—
243C24—22no—
244C24—42no—
245C24—42no—
246C24C22⋊#692311yescharacteristic
247C24C22⋊#692311yescharacteristic
248C24C22×#692311yescharacteristic
249C22×C4—24no—
250C22×C4—22no—
251C22×C4—44no—
252C22×C4—44no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—48no—
256C22×C4—44no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—42no—
260C22×C4—44no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1224no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1222no—
271C22×C4—2442no—
272C22×C4—2442no—
273C22×C4—2442no—
274C22×C4—2442no—
275M16—4882no—
276M16—4882no—
277C2×C8—2442no—
278C2×C8—2442no—
279C4⋊C4—2444no—
280C4⋊C4—2444no—
281C22⋊C4—614no—
282C22⋊C4—1224no—
283C22⋊C4—1222no—
284C22⋊C4—2441no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C22⋊C4—2441no—
288C23—21no—
289C23—21no—
290C23—22no—
291C23—22no—
292C23—24no—
293C23—24no—
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—42no—
303C23—48no—
304C23—48no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23#1451983511yescharacteristic
309C23#1451983511yescharacteristic
310C23#1451983812yes—
311C23C2×C22⋊#692311yescharacteristic
312C23D61⋊M1612yes—
313C2×C4—24no—
314C2×C4—42no—
315C2×C4—44no—
316C2×C4—48no—
317C2×C4—44no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—1224no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—2442no—
329C2×C4—2448no—
330C2×C4—2442no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C8—4882no—
338C8—4882no—
339C22—24no—
340C22—24no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—22no—
349C22—42no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—48no—
354C22—48no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22#1684066212yes—
360C22#1684066412yes—
361C22#1684073411yescharacteristic
362C22C2×#1451983511yescharacteristic
363C22C2×#1451983811yescharacteristic
364C4—44no—
365C4—2444no—
366C4—2441no—
367C4—2441no—
368C4—2441no—
369C4—2441no—
370C2—21no—
371C2—21no—
372C2—22no—
373C2—22no—
374C2—42no—
375C2—42no—
376C2#2146106911yescharacteristic
377C2C2×#1684066211yescharacteristic
378C2C2×#1684066411yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC24×C4×C61C4
socleC22×C61C2×#99
prime radicalC25×C61C2×C4
cosocleC2×C22⋊Dic61C23
hypercenterC24×C4#6923
hypocenterC61#11517
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C25 ◁ C24×C4

Complements

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

NH ≅ G/Ntype
3. #21460764C2semidirect
95. C22⋊Dic61M16semidirect
209. C61#11517semidirect

Maximal subgroups

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

subgroupindex
#214610642
#214607642
C2×#168396352
#1151761