Finite Group Databasebeta

← #30604302

Subgroups — #30604302

Order 15616.

748 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 748 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461074C211yesmaximal, characteristic, complemented
2#21461058C211yesmaximal, characteristic, complemented
3#21460743C214yesmaximal, complemented
4#21449169C211yesmaximal, characteristic
5#16840779—21no—
6#16840733—21no—
7#16840608—21no—
8#16840606—21no—
9#16840605C2212yes—
10#16840605C2212yes—
11C2×#14519748—21no—
12C2×#14519746C412yes—
13C2×C4×C22⋊D61C2211yescharacteristic
14#16839676—21no—
15#16839670—21no—
16#16839665—21no—
17#16839622C411yescharacteristic
18#16839618C2212yes—
19C23×D4×C61C411yescharacteristic
20C2×#11758213—41no—
21#14519844—41no—
22#14519834—41no—
23C22⋊#92420—22no—
24C22⋊#92420—22no—
25C4×#92420—41no—
26C22×C22⋊D61—22no—
27C22×C22⋊D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29#14519748—44no—
30#14519746—44no—
31C4×C22⋊D61—41no—
32C4×C22⋊D61—41no—
33C2×C4⋊Dic61—21no—
34C2×#11758196D411yescharacteristic
35C2×C22⋊Dic61—22no—
36C2×C22⋊Dic61—22no—
37C2×C22⋊Dic61—22no—
38C2×C22⋊Dic61C2×C412yes—
39C2×C22⋊Dic61C2311yescharacteristic
40C2×#11758198D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42#14519684—21no—
43C25×C61C2×C412yes—
44C22×D4×C61—21no—
45C22×D4×C61—21no—
46C22×D4×C61—41no—
47C22×D4×C61—41no—
48C22×D4×C61—44no—
49C23×C4×C61C2×C411yescharacteristic
50C24×C61—22no—
51C24×C61—24no—
52C24×C61—42no—
53C24×C61—44no—
54C24×C61—42no—
55C24×C61—82no—
56C24×C61C22×C411yescharacteristic
57C23×D61C22⋊C411yescharacteristic
58C2×D4×C61—24no—
59C2×D4×C61—42no—
60C2×D4×C61—42no—
61C2×D4×C61—44no—
62C2×D4×C61—48no—
63C2×D4×C61—44no—
64C2×D4×C61—44no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—42no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C2×C22⋊D61—22no—
73C2×C22⋊D61—22no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—44no—
76C2×C22⋊D61—44no—
77C2×C22⋊D61—82no—
78C22×Dic61—22no—
79C22×Dic61C22⋊C411yescharacteristic
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⋊Dic61—41no—
89C22⋊Dic61—44no—
90C22⋊Dic61—44no—
91C22⋊Dic61—42no—
92C22⋊Dic61—82no—
93#11758198—41no—
94C4⋊Dic61—42no—
95#11758196—41no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—24no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61—42no—
104C23×C61—42no—
105C23×C61—42no—
106C23×C61—44no—
107C23×C61—42no—
108C23×C61—42no—
109C23×C61—42no—
110C23×C61—44no—
111C23×C61—84no—
112C23×C61—88no—
113C23×C61—88no—
114C23×C61—84no—
115C23×C61C2×C22⋊C411yescharacteristic
116C23×C61#13112yes—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—41no—
121C22×D61—41no—
122D4×C61—44no—
123D4×C61—48no—
124D4×C61—44no—
125C2×C4×C61—22no—
126C2×C4×C61—21no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—41no—
130C2×C4×C61#9911yescharacteristic
131C2×C4×C61#9911yescharacteristic
132C22⋊D61—44no—
133C22⋊D61—88no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—42no—
141C2×Dic61—42no—
142C2×Dic61—42no—
143C2×Dic61#10012yes—
144C4×D61—42no—
145C4×D61—81no—
146#92420—82no—
147#92420—82no—
148#11561—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—22no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61—44no—
155C22×C61—44no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—44no—
159C22×C61—82no—
160C22×C61—82no—
161C22×C61—88no—
162C22×C61—88no—
163C22×C61—82no—
164C22×C61—82no—
165C22×C61#40811yescharacteristic
166C22×C61C2×#9911yescharacteristic
167C22×C61C2×#10011yescharacteristic
168C2×D61—42no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—81no—
173C4×C61—21no—
174C4×C61—41no—
175C4×C61AΣL(1,𝔽16)12yes—
176Dic61—22no—
177Dic61—41no—
178Dic61—41no—
179Dic61—82no—
180#2408—611no—
181#1465—611no—
182#1460—611no—
183#1316—614no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—42no—
187C2×C61—84no—
188C2×C61#147111yescharacteristic
189C2×C61C2×AΣL(1,𝔽16)11yescharacteristic
190C2×C61#212211yescharacteristic
191D61—81no—
192C23×D4#692311yescharacteristic
193C2×#121—1221no—
194C2×#120—612no—
195C2×C4×D4—611no—
196#431—1221no—
197#407—1221no—
198#394—1221no—
199#392—1221no—
200#390—1221no—
201#380—611no—
202#379—612no—
203#324—1221no—
204#323—612no—
205#323—612no—
206#323—1221no—
207C61#1156111yescharacteristic, complemented, Sylow
208C25C2×#692312yes—
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—41no—
212C22×D4—41no—
213C22×D4—44no—
214C22×D4—611no—
215C22×D4—1222no—
216C23×C4—611no—
217C23×C4C2×#692311yescharacteristic
218C2×M16—2441no—
219#121—2444no—
220#120—2444no—
221C4×D4—2441no—
222C4×D4—2441no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—1221no—
225C2×C22⋊C4—611no—
226C2×C22⋊C4—611no—
227C2×C22⋊C4—612no—
228C2×C22⋊C4—1222no—
229C2×C22⋊C4—1222no—
230C2×C22⋊C4—1222no—
231C2×C42—611no—
232C4⋊C8—2441no—
233C22⋊C8—1222no—
234C22⋊C8—1222no—
235C22⋊C8—2441no—
236C4×C8—2441no—
237#95—1221no—
238C24—22no—
239C24—24no—
240C24—42no—
241C24—44no—
242C24—42no—
243C24—82no—
244C24—611no—
245C24C22×#692311yescharacteristic
246C2×D4—24no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—44no—
250C2×D4—48no—
251C2×D4—44no—
252C2×D4—44no—
253C2×D4—41no—
254C2×D4—41no—
255C2×D4—1222no—
256C2×D4—1222no—
257C2×D4—4882no—
258C2×D4—2441no—
259C2×D4—2444no—
260C2×D4—2444no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—42no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1222no—
270C22×C4—2442no—
271C22×C4C22⋊#692311yescharacteristic
272C22×C4C22⋊#692311yescharacteristic
273M16—4882no—
274C2×C8—2442no—
275C2×C8—2442no—
276C4⋊C4—2441no—
277C4⋊C4—2442no—
278C22⋊C4—4882no—
279C22⋊C4—2441no—
280C22⋊C4—2444no—
281C22⋊C4—2441no—
282C22⋊C4—2444no—
283C22⋊C4—2442no—
284C42—1221no—
285C42—1221no—
286C23—21no—
287C23—21no—
288C23—24no—
289C23—41no—
290C23—41no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—44no—
295C23—44no—
296C23—42no—
297C23—42no—
298C23—42no—
299C23—84no—
300C23—88no—
301C23—88no—
302C23—84no—
303C23—1221no—
304C23—1221no—
305C23—1221no—
306C23—2441no—
307C23—2441no—
308C23C2×C22⋊#692311yescharacteristic
309C23#1451986412yes—
310D4—44no—
311D4—48no—
312D4—44no—
313D4—4888no—
314D4—2444no—
315C2×C4—22no—
316C2×C4—21no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—612no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—4881no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4#1451983511yescharacteristic
333C2×C4#1451983511yescharacteristic
334C8—4882no—
335C8—4882no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—42no—
341C22—44no—
342C22—44no—
343C22—41no—
344C22—41no—
345C22—44no—
346C22—82no—
347C22—82no—
348C22—88no—
349C22—88no—
350C22—82no—
351C22—82no—
352C22—4881no—
353C22—2442no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22#1684073611yescharacteristic
358C22C2×#1451983511yescharacteristic
359C22D61⋊#10011yescharacteristic
360C4—21no—
361C4—41no—
362C4—1222no—
363C4—4882no—
364C4—2441no—
365C4—2441no—
366C4#1684066212yes—
367C2—21no—
368C2—21no—
369C2—42no—
370C2—84no—
371C2—4881no—
372C2#2146109411yescharacteristic
373C2C2×#1684066211yescharacteristic
374C2#2146207811yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC24×C61C22×C4
FrattiniC24C22×#6923
FittingC23×D4×C61C4
socleC22×C61C2×#99
prime radical#21449169C2
cosocleC2×C22⋊Dic61C23
hypercenterC23×D4#6923
hypocenterC61#11561
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #21461074C2semidirect
2. #21461058C2semidirect
3. #21460743C2semidirect
207. C61#11561semidirect

Maximal subgroups

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

subgroupindex
#214610742
#214610582
#214607432
#214491692
#1156161