Finite Group Databasebeta

← #30595915

Subgroups — #30595915

Order 15616.

634 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461711C211yesmaximal, characteristic, complemented
2#21461676C211yesmaximal, characteristic, complemented
3#21460636C214yesmaximal, complemented
4#21454165C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×#14519834—21no—
7C2×#14519834—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
20C22×#92420—22no—
21C22×#92420—22no—
22#14519844—42no—
23#14519834—42no—
24#14519834—42no—
25C22×D244—22no—
26C22×D244—21no—
27C22×D244—21no—
28C22×D244C2×C412yes—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32#14519774—42no—
33#14519752—44no—
34#14519752—42no—
35#14519752—42no—
36#14519752—44no—
37C2×#11758198—22no—
38C2×#11758198—22no—
39C2×#11758198—22no—
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61C2311yescharacteristic
43C42×D61—42no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61C2×C412yes—
47C2×C42×C61C2×C411yescharacteristic
48C23×D61—22no—
49C23×D61C22⋊C411yescharacteristic
50C22×C4×C61—22no—
51C22×C4×C61C22⋊C411yescharacteristic
52C22×C4×C61C22⋊C411yescharacteristic
53C22×C4×C61C22×C411yescharacteristic
54C22×Dic61C22⋊C411yescharacteristic
55C22×Dic61C2×D411yescharacteristic
56C22×Dic61C2×D411yescharacteristic
57C2×D244—24no—
58C2×D244—42no—
59C2×D244—42no—
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×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—22no—
72C2×C4×D61—22no—
73C2×C4×D61—41no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61D812yes—
78C2×C4×D61SD1612yes—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C2×#92420—42no—
83C2×#92420—42no—
84C2×#92420—42no—
85C4⋊C4×C61—42no—
86C4⋊C4×C61—42no—
87C4⋊C4×C61—42no—
88C42×C61—22no—
89#11758198—44no—
90#11758198—42no—
91#11758198—42no—
92#11758198—44no—
93C4×Dic61—22no—
94C4×Dic61—41no—
95C4×Dic61—41no—
96C23×C61C2×C22⋊C411yescharacteristic
97C22×D61—21no—
98C22×D61—21no—
99C22×D61—21no—
100C22×D61—21no—
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—42no—
104C22×D61—42no—
105C22×D61—42no—
106C22×D61—42no—
107C22×D61—42no—
108C22×D61—42no—
109C22×D61—42no—
110C22×D61#10212yes—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—42no—
118C2×C4×C61—42no—
119C2×C4×C61—42no—
120C2×C4×C61#9912yes—
121C2×C4×C61#10212yes—
122C2×C4×C61#13112yes—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61#10012yes—
130C2×Dic61C2×D811yescharacteristic
131C2×Dic61C2×SD1611yescharacteristic
132C2×Dic61AGL(1,ℤ/8)12yes—
133D244—84no—
134D244—84no—
135D244—84no—
136D244—88no—
137C4×D61—42no—
138C4×D61—42no—
139C4×D61—44no—
140C4×D61—44no—
141#92420—82no—
142#92420—82no—
143#7724—611nomaximal, Sylow
144C22×C61#40811yescharacteristic
145C22×C61C2×#9911yescharacteristic
146C22×C61C2×#10011yescharacteristic
147C22×C61C2×#10211yescharacteristic
148C22×C61#41811yescharacteristic
149C22×C61#42111yescharacteristic
150C22×C61#42111yescharacteristic
151C2×D61—22no—
152C2×D61—22no—
153C2×D61—22no—
154C2×D61—41no—
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
158C2×D61—82no—
159C2×D61—82no—
160C2×D61—82no—
161C2×D61—82no—
162C2×D61—82no—
163C2×D61—82no—
164C2×D61—82no—
165C4×C61—22no—
166C4×C61—22no—
167C4×C61—22no—
168C4×C61—82no—
169Dic61—22no—
170Dic61—22no—
171Dic61—21no—
172Dic61—21no—
173#2856—611no—
174#1817—611no—
175#1797—611no—
176#1270—614no—
177C2×C61#147111yescharacteristic
178C2×C61#148011yescharacteristic
179C2×C61#149611yescharacteristic
180C2×C61#151011yescharacteristic
181C2×C61#151911yescharacteristic
182C2×C61#153611yescharacteristic
183C2×C61#154511yescharacteristic
184D61—42no—
185D61—162no—
186C2×#127—611no—
187C2×#121—612no—
188C2×#121—1221no—
189C2×#121—1221no—
190C22×C42—611no—
191C2×C4⋊C8—1221no—
192C2×C22⋊C8—1221no—
193C2×C22⋊C8—1221no—
194#390—612no—
195#390—1221no—
196#390—1221no—
197#384#692311yescharacteristic
198#336—612no—
199#336—612no—
200#336—1221no—
201C61#772411yescharacteristic, complemented, Sylow
202C22×D4—612no—
203C22×D4—1222no—
204C22×D4—1221no—
205C22×D4—1221no—
206C23×C4—611no—
207C23×C4—611no—
208C23×C4—611no—
209C22×C8—1222no—
210C22×C8—1222no—
211#127—2442no—
212#121—2442no—
213#121—2442no—
214#121—2444no—
215#121—2444no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×#692312yes—
219C2×C22⋊C4—1222no—
220C2×C22⋊C4—1222no—
221C2×C22⋊C4—1222no—
222C2×C42—611no—
223C2×C42—611no—
224C2×C42—611no—
225C2×C42—2442no—
226C2×C42C2×#692311yescharacteristic
227C4⋊C8—2442no—
228C22⋊C8—2442no—
229C22⋊C8—2442no—
230C24—611no—
231C24—1222no—
232C2×D4—1224no—
233C2×D4—2442no—
234C2×D4—2442no—
235C2×D4—2442no—
236C2×D4—2442no—
237C2×D4—2442no—
238C2×D4—2442no—
239C2×D4—2444no—
240C2×D4—2444no—
241C2×D4—2444no—
242C2×D4—2442no—
243C2×D4—2442no—
244C22×C4—22no—
245C22×C4—611no—
246C22×C4—611no—
247C22×C4—611no—
248C22×C4—612no—
249C22×C4—612no—
250C22×C4—1222no—
251C22×C4—1222no—
252C22×C4—1222no—
253C22×C4—1222no—
254C22×C4—2441no—
255C22×C4—2441no—
256C22×C4—2441no—
257C22×C4—2441no—
258C22×C4C22⋊#692311yescharacteristic
259C22×C4C22⋊#692311yescharacteristic
260C22×C4C22×#692311yescharacteristic
261C2×C8—2442no—
262C2×C8—2442no—
263C2×C8—2442no—
264C2×C8—2442no—
265C2×C8—2442no—
266C2×C8—2442no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C22⋊C4—2444no—
271C22⋊C4—2442no—
272C22⋊C4—2442no—
273C22⋊C4—2444no—
274C42—22no—
275C42—1222no—
276C42—2441no—
277C42—2441no—
278C23—612no—
279C23—1221no—
280C23—1221no—
281C23—1221no—
282C23—1221no—
283C23—1221no—
284C23—1221no—
285C23—2442no—
286C23—2442no—
287C23—2442no—
288C23—2442no—
289C23—2442no—
290C23—2442no—
291C23—2442no—
292C23C2×C22⋊#692311yescharacteristic
293D4—4884no—
294D4—4884no—
295D4—4884no—
296D4—4888no—
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—612no—
307C2×C4—611no—
308C2×C4—611no—
309C2×C4—612no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1221no—
315C2×C4—1221no—
316C2×C4—2442no—
317C2×C4—2442no—
318C2×C4—2444no—
319C2×C4—2444no—
320C2×C4#1451983612yes—
321C2×C4#1451983912yes—
322C2×C4#1451986512yes—
323C8—4882no—
324C8—4882no—
325C22—1222no—
326C22—1222no—
327C22—1222no—
328C22—4882no—
329C22—4882no—
330C22—4882no—
331C22—4882no—
332C22—4882no—
333C22—4882no—
334C22—4882no—
335C22—2441no—
336C22—2441no—
337C22—2441no—
338C22—2441no—
339C22#1684073711yescharacteristic
340C22C2×#1451983611yescharacteristic
341C22D61⋊#10011yescharacteristic
342C22C2×#1451983911yescharacteristic
343C22#1684075411yescharacteristic
344C22#1684076111yescharacteristic
345C22#1684076111yescharacteristic
346C4—22no—
347C4—22no—
348C4—22no—
349C4—82no—
350C4—1221no—
351C4—1221no—
352C4—1222no—
353C4—1222no—
354C2—9762no—
355C2—2442no—
356C2#2146109611yescharacteristic
357C2#2146112611yescharacteristic
358C2#2146118011yescharacteristic
359C2#2146122611yescharacteristic
360C2#2146125611yescharacteristic
361C2#2146130911yescharacteristic
362C2#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#7724
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. #21461711C2semidirect
2. #21461676C2semidirect
3. #21460636C2semidirect
201. C61#7724semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214616762
#214606362
#214541652
#772461