Finite Group Databasebeta

← #30595771

Subgroups — #30595771

Order 15616.

702 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C4×#14519834C211yesmaximal, characteristic, complemented
2#21461483C211yesmaximal, characteristic, complemented
3#21460636C214yesmaximal, complemented
4#21454165C211yesmaximal, characteristic
5C22×#11758213—21no—
6C2×#14519834—21no—
7C2×C4×#92420—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519774C411yescharacteristic
12C2×#14519752—21no—
13C2×#14519752—21no—
14C2×#14519752C412yes—
15C2×C42×D61C2211yescharacteristic
16#16839663—21no—
17#16839663—21no—
18#16839663C2212yes—
19C61×#384C411yescharacteristic
20C2×#11758213—24no—
21C2×#11758213—42no—
22C2×#11758213—42no—
23C22×#92420—22no—
24C22×#92420—22no—
25#14519834—24no—
26C4×#92420—42no—
27C22×D244—22no—
28C22×D244—21no—
29C22×D244—21no—
30C22×D244C2×C412yes—
31C22×C4×D61C2×C411yescharacteristic
32C22×C4×D61D411yescharacteristic
33C22×C4×D61D411yescharacteristic
34#14519774—42no—
35#14519752—44no—
36#14519752—42no—
37#14519752—42no—
38#14519752—44no—
39C2×#11758198—22no—
40C2×#11758198—22no—
41C2×#11758198—22no—
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61C2311yescharacteristic
45C42×D61—42no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61C2×C412yes—
49C2×C42×C61C2×C411yescharacteristic
50C23×D61—22no—
51C23×D61C22⋊C411yescharacteristic
52C22×C4×C61—22no—
53C22×C4×C61C22⋊C411yescharacteristic
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C2×D411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C2×D244—24no—
60C2×D244—42no—
61C2×D244—42no—
62C2×D244—42no—
63C2×D244—42no—
64C2×D244—44no—
65C2×D244—44no—
66C2×D244—44no—
67C2×D244—42no—
68C2×D244—42no—
69C2×D244—42no—
70C2×D244—42no—
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—22no—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61D812yes—
80C2×C4×D61SD1612yes—
81C2×#92420—24no—
82C2×#92420—24no—
83C2×#92420—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86C2×#92420—42no—
87#11758213—48no—
88C4⋊C4×C61—42no—
89C4⋊C4×C61—42no—
90C4⋊C4×C61—42no—
91C42×C61—22no—
92#11758198—44no—
93#11758198—42no—
94#11758198—42no—
95#11758198—44no—
96C4×Dic61—22no—
97C4×Dic61—41no—
98C4×Dic61—41no—
99C23×C61C2×C22⋊C411yescharacteristic
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—42no—
107C22×D61—42no—
108C22×D61—42no—
109C22×D61—42no—
110C22×D61—42no—
111C22×D61—42no—
112C22×D61—42no—
113C22×D61#10212yes—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—42no—
119C2×C4×C61—42no—
120C2×C4×C61—42no—
121C2×C4×C61#9912yes—
122C2×C4×C61#10212yes—
123C2×C4×C61#10412yes—
124C2×C4×C61#10412yes—
125C2×C4×C61#13112yes—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61#10012yes—
133C2×Dic61C2×D811yescharacteristic
134C2×Dic61C2×SD1611yescharacteristic
135C2×Dic61AGL(1,ℤ/8)12yes—
136D244—84no—
137D244—84no—
138D244—88no—
139D244—84no—
140C4×D61—24no—
141C4×D61—24no—
142C4×D61—44no—
143C4×D61—44no—
144#92420—44no—
145#92420—44no—
146#7684—611nomaximal, Sylow
147C22×C61#40811yescharacteristic
148C22×C61C2×#9911yescharacteristic
149C22×C61C2×#10011yescharacteristic
150C22×C61C2×#10211yescharacteristic
151C22×C61#41811yescharacteristic
152C22×C61C2×#10411yescharacteristic
153C22×C61C2×#10411yescharacteristic
154C2×D61—22no—
155C2×D61—22no—
156C2×D61—22no—
157C2×D61—41no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—82no—
162C2×D61—82no—
163C2×D61—82no—
164C2×D61—82no—
165C2×D61—82no—
166C2×D61—82no—
167C2×D61—82no—
168C4×C61—22no—
169C4×C61—22no—
170C4×C61—82no—
171C4×C61#32714yes—
172Dic61—22no—
173Dic61—21no—
174Dic61—21no—
175Dic61—22no—
176#2856—611no—
177C4×C22⋊C8—611no—
178#1728—611no—
179#1270—614no—
180C2×C61#147111yescharacteristic
181C2×C61#148411yescharacteristic
182C2×C61#149211yescharacteristic
183C2×C61C2×#32711yescharacteristic
184C2×C61#150711yescharacteristic
185C2×C61#152511yescharacteristic
186C2×C61#154511yescharacteristic
187D61—42no—
188D61—162no—
189C22×M16—1221no—
190C2×#127—611no—
191C2×#121—612no—
192C2×#121—1221no—
193C2×#121—1221no—
194C22×C42—611no—
195C2×C22⋊C8—1221no—
196C2×C4×C8—1221no—
197#390—612no—
198#390—1221no—
199#390—1221no—
200#384#692311yescharacteristic
201#336—612no—
202#336—612no—
203#336—1221no—
204C61#768411yescharacteristic, complemented, Sylow
205C22×D4—612no—
206C22×D4—1222no—
207C22×D4—1221no—
208C22×D4—1221no—
209C23×C4—611no—
210C23×C4—611no—
211C23×C4—611no—
212C2×M16—1224no—
213C2×M16—2442no—
214C2×M16—2442no—
215C22×C8—1222no—
216C22×C8—1222no—
217#127—2442no—
218#121—2442no—
219#121—2442no—
220#121—2444no—
221#121—2444no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C2×#692312yes—
225C2×C22⋊C4—1222no—
226C2×C22⋊C4—1222no—
227C2×C22⋊C4—1222no—
228C2×C42—611no—
229C2×C42—611no—
230C2×C42—611no—
231C2×C42—2442no—
232C2×C42C2×#692311yescharacteristic
233C22⋊C8—1224no—
234C4×C8—2442no—
235C24—611no—
236C24—1222no—
237C2×D4—1224no—
238C2×D4—2442no—
239C2×D4—2442no—
240C2×D4—2442no—
241C2×D4—2442no—
242C2×D4—2444no—
243C2×D4—2444no—
244C2×D4—2444no—
245C2×D4—2442no—
246C2×D4—2442no—
247C2×D4—2442no—
248C2×D4—2442no—
249C22×C4—22no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—612no—
254C22×C4—612no—
255C22×C4—1222no—
256C22×C4—1222no—
257C22×C4—1222no—
258C22×C4—1222no—
259C22×C4—1222no—
260C22×C4—1222no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4C22⋊#692311yescharacteristic
264C22×C4C22⋊#692311yescharacteristic
265C22×C4C22×#692311yescharacteristic
266M16—2448no—
267C2×C8—1224no—
268C2×C8—1224no—
269C2×C8—2442no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8—2442no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C22⋊C4—2444no—
277C22⋊C4—2442no—
278C22⋊C4—2442no—
279C22⋊C4—2444no—
280C42—22no—
281C42—1222no—
282C42—2441no—
283C42—2441no—
284C23—612no—
285C23—1221no—
286C23—1221no—
287C23—1221no—
288C23—1221no—
289C23—1221no—
290C23—1221no—
291C23—2442no—
292C23—2442no—
293C23—2442no—
294C23—2442no—
295C23—2442no—
296C23—2442no—
297C23—2442no—
298C23C2×C22⋊#692311yescharacteristic
299D4—4884no—
300D4—4884no—
301D4—4888no—
302D4—4884no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—612no—
311C2×C4—611no—
312C2×C4—611no—
313C2×C4—612no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—1221no—
317C2×C4—1221no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1224no—
321C2×C4—1224no—
322C2×C4—2444no—
323C2×C4—2444no—
324C2×C4#1451983612yes—
325C2×C4#1451983912yes—
326C2×C4#1451984212yes—
327C2×C4#1451984212yes—
328C2×C4#1451986512yes—
329C8—2444no—
330C8—2444no—
331C22—1222no—
332C22—1222no—
333C22—1222no—
334C22—4882no—
335C22—4882no—
336C22—4882no—
337C22—4882no—
338C22—4882no—
339C22—4882no—
340C22—4882no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22#1684073711yescharacteristic
346C22C2×#1451983611yescharacteristic
347C22D61⋊#10011yescharacteristic
348C22C2×#1451983911yescharacteristic
349C22#1684075411yescharacteristic
350C22C2×#1451984211yescharacteristic
351C22C2×#1451984211yescharacteristic
352C4—22no—
353C4—22no—
354C4—82no—
355C4—1222no—
356C4—1221no—
357C4—1221no—
358C4—1222no—
359C4#1684061414yes—
360C2—9762no—
361C2—2442no—
362C2#2146109611yescharacteristic
363C2#2146114011yescharacteristic
364C2#2146116611yescharacteristic
365C2C2×#1684061411yescharacteristic
366C2#2146121611yescharacteristic
367C2#2146127511yescharacteristic
368C2#2146132711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC23×C61C2×C22⋊C4
prime radical#21454165C2
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#7684
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C4×#14519834C2semidirect
2. #21461483C2semidirect
3. #21460636C2semidirect
204. C61#7684semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
#214614832
#214606362
#214541652
#768461