Finite Group Databasebeta

← #30595637

Subgroups — #30595637

Order 15616.

584 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 104 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#21461674C211yesmaximal, characteristic, complemented
3#21460638C212yesmaximal, complemented
4#21460635C212yesmaximal, complemented
5C4×#14519748C211yesmaximal, characteristic
6C2×C4⋊#92420—21no—
7C2×#14519834—21no—
8C2×#14519834—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×#14519748C411yescharacteristic
13C2×C4×C22⋊D61—21no—
14C2×C42×D61C2211yescharacteristic
15#16839665C2211yescharacteristic
16#16839658C2211yescharacteristic
17#16839650—21no—
18#16839638—21no—
19#16839619C411yescharacteristic
20C4×C4⋊Dic61C411yescharacteristic
21C4×C22⋊Dic61—21no—
22C2×C4×D4×C61C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4⋊#92420—42no—
26#14519834—42no—
27#14519834—42no—
28C22×C22⋊D61—21no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32#14519748—22no—
33#14519748—22no—
34C4×C22⋊D61—42no—
35C4×C22⋊D61—42no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×#11758198—21no—
43C2×C4×Dic61—21no—
44C2×C4×Dic61D411yescharacteristic
45C2×C4×Dic61D411yescharacteristic
46C2×C4×Dic61C2311yescharacteristic
47C42×D61—42no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×D4×C61C2×C411yescharacteristic
52C23×C4×C61—21no—
53C4×D4×C61—42no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C42×C61C2×C411yescharacteristic
57C24×C61—21no—
58C23×D61C22⋊C411yescharacteristic
59C2×D4×C61—21no—
60C2×D4×C61—41no—
61C2×D4×C61—41no—
62C2×D4×C61M1612yes—
63C22×C4×C61—21no—
64C22×C4×C61—42no—
65C22×C4×C61—42no—
66C22×C4×C61—42no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C2×C22⋊D61—24no—
71C2×C22⋊D61—42no—
72C2×C22⋊D61—42no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×C4×D61—22no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—22no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×C4×D61—41no—
87C2×C4×D61D812yes—
88C2×C4×D61SD1612yes—
89C2×#92420—42no—
90C2×#92420—42no—
91C2×#92420—42no—
92C2×#92420—42no—
93C2×#92420—42no—
94C2×#92420—42no—
95C4⋊C4×C61—41no—
96C22⋊C4×C61—42no—
97C42×C61—22no—
98C22⋊Dic61—24no—
99C22⋊Dic61—41no—
100C22⋊Dic61—41no—
101C22⋊Dic61—42no—
102#11758198—42no—
103C4⋊Dic61—21no—
104C4⋊Dic61—41no—
105C4⋊Dic61M1612yes—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—22no—
109C4×Dic61—41no—
110C4×Dic61—41no—
111C4×Dic61—42no—
112C23×C61—22no—
113C23×C61—41no—
114C23×C61—41no—
115C23×C61—41no—
116C23×C61—41no—
117C23×C61—41no—
118C23×C61—41no—
119C23×C61C2×C22⋊C411yescharacteristic
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61#10212yes—
127D4×C61—42no—
128D4×C61—42no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—84no—
139C2×C4×C61#9912yes—
140C2×C4×C61#10212yes—
141C2×C4×C61C2×M1611yescharacteristic
142C2×C4×C61C2×M1611yescharacteristic
143C22⋊D61—48no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—22no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—21no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61C2×D811yescharacteristic
158C2×Dic61C2×SD1611yescharacteristic
159C2×Dic61#13512yes—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61—44no—
163C4×D61—42no—
164C4×D61—42no—
165#92420—82no—
166#92420—82no—
167#7647—611nomaximal, Sylow
168C22×C61—42no—
169C22×C61—42no—
170C22×C61—42no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61—81no—
174C22×C61—81no—
175C22×C61#40711yescharacteristic
176C22×C61C2×#9911yescharacteristic
177C22×C61#41311yescharacteristic
178C22×C61C2×#10211yescharacteristic
179C22×C61#41611yescharacteristic
180C22×C61#42111yescharacteristic
181C22×C61#42111yescharacteristic
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—41no—
186C2×D61—41no—
187C2×D61—41no—
188C2×D61—41no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—22no—
192C4×C61—22no—
193C4×C61—81no—
194Dic61—22no—
195Dic61—21no—
196Dic61—21no—
197Dic61—41no—
198Dic61—42no—
199Dic61—81no—
200C4×#121—611no—
201#1817—611no—
202#1797—611no—
203#1271—612no—
204#1270—612no—
205C2×C61—82no—
206C2×C61#146511yescharacteristic
207C2×C61#148611yescharacteristic
208C2×C61#148811yescharacteristic
209C2×C61#151611yescharacteristic
210C2×C61#151911yescharacteristic
211C2×C61#153511yescharacteristic
212C2×C61#154011yescharacteristic
213D61—42no—
214C2×#121—611no—
215C2×C4×D4—1221no—
216C2×C4×D4#692311yescharacteristic
217C22×C42—611no—
218C2×C4⋊C8—1221no—
219C2×C22⋊C8—1221no—
220C2×C22⋊C8—1221no—
221#390—611no—
222#389—611no—
223#388—1221no—
224#386—1221no—
225#380—611no—
226C4×C4⋊C4—611no—
227C4×C22⋊C4—1221no—
228#336—612no—
229#336—612no—
230#336—1221no—
231C61#764711yescharacteristic, complemented, Sylow
232C22×D4—1221no—
233C22×D4C2×#692311yescharacteristic
234C23×C4—21no—
235C23×C4—611no—
236C23×C4—611no—
237C23×C4—611no—
238C22×C8—1222no—
239C22×C8—1222no—
240#121—1222no—
241#121—1222no—
242C4×D4—42no—
243C4×D4—2442no—
244C4×D4—2442no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—611no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4C2×#692311yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—1221no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C22⋊C4—1221no—
254C2×C42—611no—
255C2×C42—611no—
256C2×C42—611no—
257C2×C42—1221no—
258C2×C42—2442no—
259C2×C42C2×#692311yescharacteristic
260C4⋊C8—2442no—
261C22⋊C8—2442no—
262C22⋊C8—2442no—
263#95—1221no—
264#95—1221no—
265#95—1221no—
266C24—21no—
267C24—611no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—1224no—
272C2×D4—2442no—
273C2×D4—2442no—
274C2×D4#1175821312yes—
275C22×C4—21no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—42no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—612no—
282C22×C4—612no—
283C22×C4—611no—
284C22×C4—1222no—
285C22×C4—1221no—
286C22×C4—1222no—
287C22×C4—1221no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—2441no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4C22⋊#692311yescharacteristic
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22×#692311yescharacteristic
298C2×C8—2442no—
299C2×C8—2442no—
300C2×C8—2442no—
301C2×C8—2442no—
302C2×C8—2442no—
303C2×C8—2442no—
304C4⋊C4—41no—
305C4⋊C4—612no—
306C4⋊C4—1221no—
307C4⋊C4—2441no—
308C4⋊C4—2441no—
309C4⋊C4—2441no—
310C22⋊C4—42no—
311C22⋊C4—1224no—
312C22⋊C4—2442no—
313C22⋊C4—2441no—
314C22⋊C4—2441no—
315C22⋊C4—2442no—
316C42—22no—
317C42—1222no—
318C42—2441no—
319C42—2441no—
320C42—2442no—
321C23—22no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—612no—
329C23—1221no—
330C23—1221no—
331C23—1221no—
332C23—1221no—
333C23—1221no—
334C23—1221no—
335C23C2×C22⋊#692311yescharacteristic
336D4—42no—
337D4—42no—
338D4—2448no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—84no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—612no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1222no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2444no—
363C2×C4—2442no—
364C2×C4—2442no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4#1451983512yes—
371C2×C4#1451983912yes—
372C2×C4D61⋊M1611yescharacteristic
373C2×C4C2×#1175821311yescharacteristic
374C8—4882no—
375C8—4882no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—1222no—
384C22—1222no—
385C22—1222no—
386C22—2441no—
387C22—2441no—
388C22—2441no—
389C22—2441no—
390C22#1684073311yescharacteristic
391C22C2×#1451983511yescharacteristic
392C22#1684074811yescharacteristic
393C22C2×#1451983911yescharacteristic
394C22#1684075211yescharacteristic
395C22#1684075911yescharacteristic
396C22#1684076011yescharacteristic
397C4—22no—
398C4—21no—
399C4—21no—
400C4—22no—
401C4—81no—
402C4—1221no—
403C4—1221no—
404C4—1222no—
405C4—4881no—
406C4—2441no—
407C4—2442no—
408C2—82no—
409C2—2442no—
410C2#2146107411yescharacteristic
411C2#2146114511yescharacteristic
412C2#2146115111yescharacteristic
413C2#2146124511yescharacteristic
414C2#2146125511yescharacteristic
415C2#2146130311yescharacteristic
416C2#2146131611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519748C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61#7647
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21461711C2semidirect
2. #21461674C2semidirect
3. #21460638C2semidirect
4. #21460635C2semidirect
231. C61#7647semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214616742
#214606382
#214606352
C4×#145197482
#764761