Finite Group Databasebeta

← #29581323

Subgroups — #29581323

Order 15616.

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

normal subgroups only

This group has 526 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×#16840130C211yesmaximal, characteristic, complemented
2C2×#16840124C211yesmaximal, characteristic
3#21453871C211yesmaximal, characteristic
4C2×#16839503C211yesmaximal, characteristic, complemented
5C2×#16839501C211yesmaximal, characteristic
6#21443700C211yesmaximal, characteristic, complemented
7C61×#1993C211yesmaximal, characteristic, complemented
8C2×#14519769C2211yescharacteristic
9C2×#14519765C2211yescharacteristic
10#16840130—22no—
11#16840130—22no—
12#16840124—22no—
13#16840124—22no—
14C2×#14519701—21no—
15C2×#14519701—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×#97×C61C2211yescharacteristic
29C61×#382C2211yescharacteristic
30C61×#340—22no—
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#14519701—24no—
53#14519701—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#97×C61—21no—
72#97×C61—21no—
73#95×C61—21no—
74#95×C61—21no—
75C23×D61—21no—
76C2×Q8×C61—22no—
77C2×Q8×C61—44no—
78C2×Q8×C61—41no—
79C22×C4×C61—22no—
80C22×C4×C61—41no—
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244—42no—
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—42no—
93C2×C8×C61—22no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—42no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105#11758198—41no—
106#11758198—41no—
107#11758198—41no—
108#11758198—41no—
109#11758198—82no—
110#11758198—82no—
111C4⋊Dic61—21no—
112C4⋊Dic61—21no—
113C4⋊Dic61—21no—
114C4⋊Dic61—21no—
115C4⋊Dic61—82no—
116#11758196—41no—
117#11758196—41no—
118#11758196—41no—
119#11758196—41no—
120C2×#92418—22no—
121C2×#92418—22no—
122C2×#92418—42no—
123C2×#92418—42no—
124C23×C61#12011yescharacteristic
125C22×D61—41no—
126C22×D61—42no—
127C22×D61—41no—
128C22×D61—42no—
129C22×D61—41no—
130Q8×C61—44no—
131Q8×C61—82no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—82no—
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61#12011yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#12111yescharacteristic
146C2×C4×C61#12711yescharacteristic
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154D244—42no—
155D244—81no—
156Dic122—42no—
157Dic122—81no—
158C8×C61—42no—
159#92418—42no—
160#92418—42no—
161#10083—611nomaximal, Sylow
162C22×C61#39211yescharacteristic
163C22×C61#45412yes—
164C22×C61#45512yes—
165C22×C61#45511yescharacteristic
166C22×C61#45611yescharacteristic
167C2×D61—82no—
168C2×D61—82no—
169C2×D61—81no—
170C2×D61—81no—
171C2×D61—81no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—82no—
179C4×C61—82no—
180Dic61—81no—
181Dic61—81no—
182Dic61—81no—
183C2×#491—611no—
184C2×#489—611no—
185#2820—611no—
186#1993D6111yescharacteristic, complemented
187C2×#330—611no—
188C2×#329—611no—
189#1295—611no—
190C2×C61#166212yes—
191C2×C61#166412yes—
192C2×C61#200311yescharacteristic
193C2×C61#200411yescharacteristic
194C2×C61#200711yescharacteristic
195D61—161no—
196C2×C4⋊Q8C2×D6111yescharacteristic
197C2×#125—611no—
198C2×#124—611no—
199#491—1222no—
200#491—1222no—
201#489—1222no—
202#489—1222no—
203C2×#103—1221no—
204C2×#103—1221no—
205C2×#103—1221no—
206C2×#102—1221no—
207C2×#97—611no—
208C2×#97—611no—
209C2×#97C2×D6111yescharacteristic
210#399—1221no—
211#397—1221no—
212#396—1222no—
213#395—1221no—
214#394—1221no—
215#382C2×D6111yescharacteristic
216#340—22no—
217#330—1222no—
218#329—1222no—
219C61#1008311yescharacteristic, complemented, Sylow
220C22×Q8—21no—
221C22×Q8—611no—
222C22×D4—611no—
223C22×C8—21no—
224C22×C8—1221no—
225C22×C8—1221no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8D24412yes—
230#125—1221no—
231#125—1221no—
232#125—1221no—
233#125—1221no—
234#124—1221no—
235#124—1221no—
236#124—1221no—
237#124—1221no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—611no—
242C2×C4⋊C4—1222no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C4⋊C4C22⋊D6112yes—
246C2×C22⋊C4—1222no—
247C2×C22⋊C4—1222no—
248C2×C22⋊C4—1221no—
249C2×C22⋊C4—1221no—
250C2×C42C22×D6111yescharacteristic
251#103—1224no—
252#103—1224no—
253#103—1224no—
254#102—1224no—
255#97—21no—
256#97—21no—
257#97—612no—
258#97—612no—
259#97—1221no—
260#97—1221no—
261#95—21no—
262#95—21no—
263#95—1222no—
264C24—1221no—
265C2×Q8—22no—
266C2×Q8—44no—
267C2×Q8—41no—
268C2×Q8—1221no—
269C2×Q8—1221no—
270C2×Q8—2442no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—2442no—
274C22×C4—22no—
275C22×C4—41no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4D4×D6111yescharacteristic
280C22×C4D4×D6111yescharacteristic
281C22×C4C2×C22⋊D6111yescharacteristic
282C2×C8—22no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—1222no—
286C2×C8—1222no—
287C2×C8—2442no—
288C2×C8—2442no—
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—42no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—4882no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C4⋊C4—2441no—
302C4⋊C4—2441no—
303C22⋊C4—4882no—
304C22⋊C4—4882no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C42C2×D24411yescharacteristic
310C42#1175822211yescharacteristic
311C42D4×D6111yescharacteristic
312C42D4×D6111yescharacteristic
313C23—2442no—
314C23—2441no—
315C23—2441no—
316C23—2441no—
317C23—2442no—
318C23#1451974511yescharacteristic
319Q8—44no—
320Q8—82no—
321Q8—4881no—
322Q8—2442no—
323D4—4881no—
324D4—2442no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—82no—
334C2×C4—2442no—
335C2×C4—2442no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4#1451974711yescharacteristic
342C2×C4#1451974711yescharacteristic
343C2×C4#1451975011yescharacteristic
344C2×C4#1451975011yescharacteristic
345C2×C4#1451975111yescharacteristic
346C2×C4#1451977311yescharacteristic
347C8—42no—
348C8—2442no—
349C8—2442no—
350C22—4882no—
351C22—4882no—
352C22—4881no—
353C22—4881no—
354C22—4881no—
355C22#1683967111yescharacteristic
356C22#1683993312yes—
357C22#1683993812yes—
358C22#1683993911yescharacteristic
359C22#1683994411yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—82no—
367C4—82no—
368C4—4881no—
369C4—4881no—
370C4—4881no—
371C2—9761no—
372C2#2144514112yes—
373C2#2144515112yes—
374C2#2144684211yescharacteristic
375C2#2144684911yescharacteristic
376C2#2144686511yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1993C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#1993D61
hypocenterC61#10083
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
1. C2×#16840130C2semidirect
4. C2×#16839503C2semidirect
6. #21443700C2semidirect
7. C61×#1993C2semidirect
186. #1993D61semidirect
219. C61#10083semidirect

Maximal subgroups

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

subgroupindex
C2×#168401302
C2×#168401242
#214538712
C2×#168395032
C2×#168395012
#214437002
C61×#19932
#1008361