Finite Group Databasebeta

← #29581342

Subgroups — #29581342

Order 15616.

542 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#16840168C211yesmaximal, characteristic, complemented
2C2×#16840124C211yesmaximal, characteristic
3#21453871C211yesmaximal, characteristic
4C2×#16839503C211yesmaximal, characteristic, complemented
5C2×#16839501C211yesmaximal, characteristic
6#21443700C211yesmaximal, characteristic, complemented
7C61×#1960C211yesmaximal, characteristic, complemented
8C2×#14519769C2211yescharacteristic
9C2×#14519765C2211yescharacteristic
10#16840168—22no—
11#16840168—22no—
12#16840124—22no—
13#16840124—22no—
14C2×#14519710—21no—
15C2×#14519708—21no—
16C2×#14519700—21no—
17C2×#14519697—21no—
18C2×#14519688C2211yescharacteristic
19C2×#14519688C2211yescharacteristic
20#16839699—21no—
21#16839689—21no—
22#16839684—22no—
23#16839683—21no—
24#16839680—21no—
25#16839503—22no—
26#16839501—22no—
27C2×C4⋊Q8×C61C2211yescharacteristic
28C2×#103×C61—22no—
29C2×#97×C61C2211yescharacteristic
30C61×#382C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C22×D244D411yescharacteristic
33C22×#92418—21no—
34C22×#92418—21no—
35#14519769—21no—
36#14519769—21no—
37#14519769—21no—
38#14519769—21no—
39#14519765—21no—
40#14519765—21no—
41#14519765—21no—
42#14519765—21no—
43C2×C4⋊Dic61—22no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—22no—
51C2×#11758198—22no—
52#14519710—24no—
53#14519708—24no—
54#14519700—24no—
55#14519697—24no—
56#14519688—21no—
57#14519688—21no—
58#14519688D412yes—
59#14519688D412yes—
60#14519684—22no—
61C22×Q8×C61—21no—
62C22×C8×C61—21no—
63C4⋊Q8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61D412yes—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61D412yes—
70C2×C42×C61C2311yescharacteristic
71#103×C61—44no—
72#97×C61—21no—
73#97×C61—21no—
74#95×C61—21no—
75#95×C61—21no—
76C23×D61—21no—
77C2×Q8×C61—22no—
78C2×Q8×C61—42no—
79C2×Q8×C61—42no—
80C2×Q8×C61—41no—
81C22×C4×C61—22no—
82C22×C4×C61—41no—
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×Dic61—21no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×D244—42no—
92C2×Dic122—21no—
93C2×Dic122—21no—
94C2×Dic122—42no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—22no—
99C4⋊C4×C61—22no—
100C4⋊C4×C61—42no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107#11758198—41no—
108#11758198—41no—
109#11758198—41no—
110#11758198—41no—
111#11758198—82no—
112#11758198—82no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—82no—
118#11758196—41no—
119#11758196—41no—
120#11758196—41no—
121#11758196—41no—
122C2×#92418—24no—
123C2×#92418—22no—
124C2×#92418—22no—
125C2×#92418—42no—
126C23×C61#12011yescharacteristic
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—42no—
131C22×D61—42no—
132Q8×C61—44no—
133Q8×C61—82no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61—42no—
142C2×C4×C61—81no—
143C2×C4×C61—81no—
144C2×C4×C61#12011yescharacteristic
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12711yescharacteristic
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157D244—42no—
158D244—81no—
159Dic122—42no—
160Dic122—81no—
161C8×C61—42no—
162#92418—24no—
163#92418—42no—
164#10086—611nomaximal, Sylow
165C22×C61#39211yescharacteristic
166C22×C61#45311yescharacteristic
167C22×C61#45411yescharacteristic
168C22×C61#45512yes—
169C22×C61#45612yes—
170C2×D61—82no—
171C2×D61—82no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—82no—
182C4×C61—82no—
183Dic61—81no—
184Dic61—81no—
185Dic61—81no—
186C2×#501—611no—
187C2×#489—611no—
188#2820—611no—
189#1960D6111yescharacteristic, complemented
190C2×#330—611no—
191C2×#329—611no—
192#1295—611no—
193C2×C61#166112yes—
194C2×C61#166412yes—
195C2×C61#200411yescharacteristic
196C2×C61#200511yescharacteristic
197C2×C61#200611yescharacteristic
198D61—161no—
199C2×C4⋊Q8C2×D6111yescharacteristic
200C2×#125—611no—
201C2×#124—611no—
202#501—1222no—
203#501—1222no—
204#489—1222no—
205#489—1222no—
206C2×#107—1221no—
207C2×#106—1221no—
208C2×#103—22no—
209C2×#103—1221no—
210C2×#102—1221no—
211C2×#97—611no—
212C2×#97—611no—
213C2×#97C2×D6111yescharacteristic
214#399—1221no—
215#397—1221no—
216#396—1222no—
217#395—1221no—
218#394—1221no—
219#382C2×D6111yescharacteristic
220#330—1222no—
221#329—1222no—
222C61#1008611yescharacteristic, complemented, Sylow
223C22×Q8—21no—
224C22×Q8—611no—
225C22×D4—611no—
226C22×C8—21no—
227C22×C8—1221no—
228C22×C8—1221no—
229C4⋊Q8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8D24412yes—
233#125—1221no—
234#125—1221no—
235#125—1221no—
236#125—1221no—
237#124—1221no—
238#124—1221no—
239#124—1221no—
240#124—1221no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—611no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—1222no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1221no—
248C2×C4⋊C4C22⋊D6112yes—
249C2×C22⋊C4—1222no—
250C2×C22⋊C4—1222no—
251C2×C22⋊C4—1221no—
252C2×C22⋊C4—1221no—
253C2×C42C22×D6111yescharacteristic
254#107—1224no—
255#106—1224no—
256#103—44no—
257#103—1224no—
258#102—1224no—
259#97—21no—
260#97—21no—
261#97—612no—
262#97—612no—
263#97—1221no—
264#97—1221no—
265#95—21no—
266#95—21no—
267#95—1222no—
268C24—1221no—
269C2×Q8—22no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—41no—
273C2×Q8—1221no—
274C2×Q8—1221no—
275C2×Q8—2442no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—2442no—
279C22×C4—22no—
280C22×C4—41no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1221no—
284C22×C4D4×D6111yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C22×C4C2×C22⋊D6111yescharacteristic
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—1224no—
291C2×C8—1222no—
292C2×C8—1222no—
293C2×C8—2442no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—42no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—1221no—
300C4⋊C4—1221no—
301C4⋊C4—1221no—
302C4⋊C4—1221no—
303C4⋊C4—4882no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C4⋊C4—2441no—
307C4⋊C4—2441no—
308C22⋊C4—4882no—
309C22⋊C4—4882no—
310C22⋊C4—2441no—
311C22⋊C4—2441no—
312C22⋊C4—2441no—
313C22⋊C4—2441no—
314C42C2×D24411yescharacteristic
315C42#1175822211yescharacteristic
316C42D4×D6111yescharacteristic
317C42D4×D6111yescharacteristic
318C23—2442no—
319C23—2442no—
320C23—2441no—
321C23—2441no—
322C23—2441no—
323C23#1451974511yescharacteristic
324Q8—44no—
325Q8—82no—
326Q8—4881no—
327Q8—2442no—
328D4—4881no—
329D4—2442no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2441no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4#1451974711yescharacteristic
348C2×C4#1451974711yescharacteristic
349C2×C4#1451975011yescharacteristic
350C2×C4#1451975011yescharacteristic
351C2×C4#1451975111yescharacteristic
352C2×C4#1451977311yescharacteristic
353C8—42no—
354C8—1224no—
355C8—2442no—
356C22—4882no—
357C22—4882no—
358C22—4881no—
359C22—4881no—
360C22—4881no—
361C22#1683967111yescharacteristic
362C22#1683992911yescharacteristic
363C22#1683993411yescharacteristic
364C22#1683993812yes—
365C22#1683994312yes—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—82no—
374C4—4881no—
375C4—4881no—
376C4—4881no—
377C2—9761no—
378C2#2144513312yes—
379C2#2144515012yes—
380C2#2144684911yescharacteristic
381C2#2144685611yescharacteristic
382C2#2144686011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1960C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1960D61
hypocenterC61#10086
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
1. C2×#16840168C2semidirect
4. C2×#16839503C2semidirect
6. #21443700C2semidirect
7. C61×#1960C2semidirect
189. #1960D61semidirect
222. C61#10086semidirect

Maximal subgroups

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

subgroupindex
C2×#168401682
C2×#168401242
#214538712
C2×#168395032
C2×#168395012
#214437002
C61×#19602
#1008661