Finite Group Databasebeta

← #30597232

Subgroups — #30597232

Order 15616.

994 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 156 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#21462263C212yesmaximal
2#21460718C214yesmaximal
3#21448198C211yesmaximal, characteristic
4C2×#14519856—22no—
5#16840705—22no—
6#16840704—22no—
7#16840704C414yescomplemented
8#16840703C2214yes—
9C4×C22⋊#6923—22no—
10C4×C22⋊#6923C414yescomplemented
11C23×C4×D61C2211yescharacteristic
12C2×#14519736C411yescharacteristic, complemented
13#16839623C412yescomplemented
14#16839619—22no—
15#16839617C2212yes—
16C4×#11758198—22no—
17C2×#117×C61C411yescharacteristic, complemented
18#14519856—44no—
19#14519856—44no—
20C2×C4⋊#6923—24no—
21C2×C22⋊#6923—24no—
22C2×C22⋊#6923—24no—
23C2×C22⋊#6923C2×C418yes—
24C2×C4×#6923—24no—
25(C2×#6923)⋊C4—24no—
26(C2×#6923)⋊C4—24no—
27C24×D61C2311yescharacteristic
28C23×Dic61C2×C411yescharacteristic
29C22×C4×D61—42no—
30C22×C4×D61—42no—
31C22×C4×D61C2×C412yes—
32C22×C4×D61C2×C412yes—
33C22×C4×D61D412yes—
34C22×C4×D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C22×C4×D61D412yes—
37C22×C4×D61Q811yescharacteristic
38C22×C4×D61Q811yescharacteristic
39#14519736—42no—
40C2×C4⋊Dic61—21no—
41C2×C22⋊Dic61C2×C412yes—
42C2×#11758198—24no—
43C2×C4×Dic61—21no—
44#14519684—24no—
45C23×C4×C61C2×C411yescharacteristic
46#117×C61—42no—
47C2×C4⋊C4×C61—21no—
48C2×C22⋊C4×C61C2×C412yes—
49C2×C42×C61—21no—
50C24×C61C22×C411yescharacteristic
51C23×D61—44no—
52C23×D61—41no—
53C23×D61—41no—
54C23×D61C22×C412yes—
55C23×D61C2×D411yescharacteristic
56C23×D61C2×D412yes—
57C23×D61C2×Q811yescharacteristic
58C22×#6923—28no—
59C22×C4×C61—22no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61C4211yescharacteristic
63C22×C4×C61C4211yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C4⋊C411yescharacteristic
67C22×C4×C61C4⋊C411yescharacteristic
68C22×Dic61—22no—
69C22×Dic61—41no—
70C22×Dic61—41no—
71C22×Dic61C4212yes—
72C22×Dic61C22⋊C412yes—
73C22×Dic61C4⋊C411yescharacteristic
74C22×Dic61C4⋊C411yescharacteristic
75C2×C4×D61—24no—
76C2×C4×D61—24no—
77C2×C4×D61—44no—
78C2×C4×D61—44no—
79C2×C4×D61—42no—
80C2×C4×D61—42no—
81C2×C4×D61—42no—
82C2×C4×D61—42no—
83C2×C4×D61—42no—
84C2×C4×D61—42no—
85C2×C4×D61C22⋊C412yes—
86C2×C4×D61C22⋊C412yes—
87C2×C4×D61C22⋊C412yes—
88C2×C4×D61C22⋊C412yes—
89C2×C4×D61C4⋊C412yes—
90C2×C4×D61C4⋊C412yes—
91C2×C4×D61C4⋊C412yes—
92C2×C4×D61C4⋊C412yes—
93C22⋊#6923—48no—
94C22⋊#6923—44no—
95C22⋊#6923—44no—
96C22⋊#6923—48no—
97C4⋊#6923—48no—
98C4×#6923—48no—
99C4⋊C4×C61—42no—
100C22⋊C4×C61—42no—
101C42×C61—42no—
102C22⋊Dic61—42no—
103#11758198—48no—
104C4⋊Dic61—42no—
105C4×Dic61—42no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—42no—
109C23×C61C2×C4211yescharacteristic
110C23×C61C2×C22⋊C411yescharacteristic
111C23×C61C2×C4⋊C411yescharacteristic
112C22×D61—22no—
113C22×D61—22no—
114C22×D61—24no—
115C22×D61—24no—
116C22×D61—24no—
117C22×D61—42no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61—48no—
124C22×D61—48no—
125C22×D61C2×C22⋊C412yes—
126C22×D61C2×C4⋊C412yes—
127C2×#6923—48no—
128C2×#6923—48no—
129C2×#6923—48no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—44no—
137C2×C4×C61—42no—
138C2×C4×C61#9511yescharacteristic
139C2×C4×C61#9511yescharacteristic
140C2×C4×C61#9511yescharacteristic
141C2×C4×C61#9511yescharacteristic
142C2×C4×C61#9912yes—
143C2×C4×C61#9912yes—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—42no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—44no—
150C2×Dic61—42no—
151C2×Dic61#9512yes—
152C2×Dic61#9512yes—
153C4×D61—24no—
154C4×D61—24no—
155C4×D61—24no—
156C4×D61—24no—
157C4×D61—42no—
158C4×D61—42no—
159C4×D61—42no—
160C4×D61—42no—
161#8100—611nomaximal, Sylow
162C22×C61—22no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—42no—
168C22×C61—42no—
169C22×C61C2×#9511yescharacteristic
170C22×C61C2×#9911yescharacteristic
171C22×C61C2×#9911yescharacteristic
172C2×D61—22no—
173C2×D61—22no—
174C2×D61—22no—
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—44no—
178C2×D61—44no—
179C2×D61—44no—
180C2×D61—48no—
181C2×D61—44no—
182C2×D61#41014yes—
183#6923—88no—
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—82no—
187C4×C61#34212yes—
188C4×C61#34212yes—
189Dic61—22no—
190Dic61—22no—
191Dic61—82no—
192#2280—611no—
193#2280—612no—
194#1304—614no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—41no—
198C2×C61—41no—
199C2×C61C2×#34211yescharacteristic
200C2×C61#174012yes—
201D61—24no—
202D61—42no—
203C24×C4—611no—
204C2×#117—611no—
205C2×#117—1222no—
206C2×#117#692311yescharacteristic, complemented
207#381—612no—
208#381—1222no—
209#380—614no—
210#380—1222no—
211#380—1222no—
212#379—614no—
213#379—612no—
214C4×C22⋊C4—614no—
215C4×C22⋊C4—1222no—
216C4×C22⋊C4—1222no—
217C61#810011yescharacteristic, complemented, Sylow
218C25—611no—
219C23×C4—611no—
220C23×C4—612no—
221C23×C4—612no—
222C23×C4—612no—
223C23×C4—611no—
224C23×C4—611no—
225C23×C4—611no—
226C23×C4—611no—
227C23×C4—612no—
228C23×C4—2442no—
229C23×C4—2442no—
230C23×C4C2×#692311yescharacteristic
231#117—42no—
232#117—2444no—
233#117—2444no—
234#117—2442no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—1224no—
237C2×C4⋊C4—1221no—
238C2×C22⋊C4—618no—
239C2×C22⋊C4—612no—
240C2×C22⋊C4—1224no—
241C2×C22⋊C4—1224no—
242C2×C22⋊C4—1224no—
243C2×C22⋊C4C2×#692312yes—
244C2×C42—21no—
245C2×C42—1224no—
246C2×C42—1221no—
247#95—1224no—
248#95—1224no—
249#95—1224no—
250C24—612no—
251C24—611no—
252C24—612no—
253C24—611no—
254C24—2441no—
255C24—2441no—
256C24—2444no—
257C24C22×#692311yescharacteristic
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—612no—
262C22×C4—612no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—612no—
266C22×C4—612no—
267C22×C4—612no—
268C22×C4—612no—
269C22×C4—612no—
270C22×C4—612no—
271C22×C4—612no—
272C22×C4—612no—
273C22×C4—1224no—
274C22×C4—1224no—
275C22×C4—1228no—
276C22×C4—1222no—
277C22×C4—2444no—
278C22×C4—2444no—
279C22×C4—2442no—
280C22×C4—2442no—
281C22×C4—2442no—
282C22×C4—2442no—
283C22×C4—2442no—
284C22×C4—2442no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4C4×#692311yescharacteristic
288C22×C4C4×#692311yescharacteristic
289C22×C4C4⋊#692311yescharacteristic
290C22×C4C4⋊#692311yescharacteristic
291C22×C4C22⋊#692311yescharacteristic
292C22×C4C22⋊#692311yescharacteristic
293C4⋊C4—42no—
294C4⋊C4—2442no—
295C4⋊C4—2448no—
296C22⋊C4—42no—
297C22⋊C4—2448no—
298C22⋊C4—2444no—
299C22⋊C4—2444no—
300C22⋊C4—2448no—
301C22⋊C4—2442no—
302C22⋊C4—2448no—
303C42—42no—
304C42—2448no—
305C42—2442no—
306C23—21no—
307C23—21no—
308C23—42no—
309C23—612no—
310C23—612no—
311C23—1224no—
312C23—1224no—
313C23—1224no—
314C23—1222no—
315C23—1222no—
316C23—2442no—
317C23—2441no—
318C23—2441no—
319C23—2442no—
320C23—2442no—
321C23—2442no—
322C23—2448no—
323C23—2448no—
324C23C2×C4×#692311yescharacteristic
325C23C2×C22⋊#692311yescharacteristic
326C23C2×C4⋊#692311yescharacteristic
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—612no—
336C2×C4—612no—
337C2×C4—1222no—
338C2×C4—1222no—
339C2×C4—1224no—
340C2×C4—1224no—
341C2×C4—1224no—
342C2×C4—1224no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4—2442no—
348C2×C4—2441no—
349C2×C4—2441no—
350C2×C4—2444no—
351C2×C4—2448no—
352C2×C4—2448no—
353C2×C4—2448no—
354C2×C4—2442no—
355C2×C4(C2×#6923)⋊C411yescharacteristic
356C2×C4(C2×#6923)⋊C411yescharacteristic
357C2×C4(C2×#6923)⋊C411yescharacteristic
358C2×C4(C2×#6923)⋊C411yescharacteristic
359C2×C4#1451983512yes—
360C2×C4#1451983612yes—
361C22—22no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22—42no—
367C22—42no—
368C22—614no—
369C22—1222no—
370C22—1222no—
371C22—1222no—
372C22—1222no—
373C22—1222no—
374C22—2444no—
375C22—2444no—
376C22—2444no—
377C22—2448no—
378C22—2444no—
379C22C2×(C2×#6923)⋊C411yescharacteristic
380C22C2×#1451983511yescharacteristic
381C22C2×#1451983611yescharacteristic
382C4—21no—
383C4—21no—
384C4—82no—
385C4—1222no—
386C4—1222no—
387C4—4882no—
388C4—4888no—
389C4#1684064012yes—
390C4#1684064012yes—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—1224no—
396C2—2442no—
397C2C2×#1684064011yescharacteristic
398C2#2146151712yes—
subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#95
prime radical, cosocleC24×D61C23
hypercenterC2×#117#6923
hypocenterC61#8100
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
7. #16840704C4semidirect
10. C4×C22⋊#6923C4semidirect
12. C2×#14519736C4semidirect
13. #16839623C4semidirect
17. C2×#117×C61C4semidirect
206. C2×#117#6923semidirect
217. C61#8100semidirect

Maximal subgroups

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

subgroupindex
#214622632
#214607182
#214481982
#810061