Finite Group Databasebeta

← #29577636

Subgroups — #29577636

Order 15616.

434 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 89 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#21456371C211yesmaximal, characteristic
2#21448924C211yesmaximal, characteristic
3#21444445C211yesmaximal, characteristic
4#21444332C211yesmaximal, characteristic
5#21444330C211yesmaximal, characteristic
6#21443713C211yesmaximal, characteristic
7C61×#1300C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×#14519769C2211yescharacteristic
10#16840171C412yescomplemented
11#16840171C412yescomplemented
12#16840164—22no—
13#16839819C2211yescharacteristic
14#16839804—21no—
15#16839804—21no—
16#16839647—21no—
17#16839646—21no—
18#16839645—21no—
19#16839644—21no—
20C4×#11758196—21no—
21#16839613—21no—
22#16839608C2211yescharacteristic
23#16839503—22no—
24#16839500—21no—
25#16839500—21no—
26#16839498—21no—
27#16839498—21no—
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#376C2211yescharacteristic
31#14519777C2×C411yescharacteristic
32#14519777C2×C411yescharacteristic
33#14519769—21no—
34#14519769—21no—
35#14519769—21no—
36#14519769C2×C412yes—
37#14519769D412yes—
38#14519756—21no—
39#14519756—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42#14519736—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—21no—
51C2×C4×Dic61—21no—
52#14519711—22no—
53#14519711—22no—
54#14519709—22no—
55#14519709—22no—
56C4⋊#92418—21no—
57C22⋊#92418—21no—
58#14519688—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684D411yescharacteristic
65#14519684D411yescharacteristic
66C2×M16×C61—21no—
67C2×C42×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71#97×C61—21no—
72#97×C61C2×C412yes—
73C4×C8×C61—21no—
74#95×C61—21no—
75#95×C61D411yescharacteristic
76#95×C61D411yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C2×Dic122—21no—
87C2×Dic122—21no—
88M16×C61—22no—
89M16×C61—22no—
90C2×C8×C61—22no—
91C2×C8×C61—41no—
92C42×C61—42no—
93C42×C61C22×C411yescharacteristic
94C42×C61C2×D411yescharacteristic
95C42×C61#4111yescharacteristic
96C42×C61#4111yescharacteristic
97C22⋊Dic61—41no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61C22⋊C412yes—
105C4⋊Dic61C22⋊C412yes—
106#11758196—22no—
107#11758196—22no—
108#11758196—22no—
109#11758196—22no—
110#11758196—42no—
111#11758196—42no—
112#11758196—41no—
113#11758196—41no—
114C4×Dic61—42no—
115C4×Dic61—42no—
116C4×Dic61—42no—
117C4×Dic61—41no—
118C2×#92418—41no—
119C23×C61#12011yescharacteristic
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—22no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61C2×C22⋊C411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12311yescharacteristic
136C2×Dic61—22no—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—41no—
150Dic122—81no—
151Dic122—81no—
152C8×C61—24no—
153C8×C61—81no—
154#92418—81no—
155#9440—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61#38611yescharacteristic
159C22×C61#45611yescharacteristic
160C22×C61#45611yescharacteristic
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—42no—
168C4×C61—81no—
169Dic61—42no—
170Dic61—42no—
171Dic61—42no—
172Dic61—81no—
173Dic61—81no—
174Dic61—81no—
175#3166—611no—
176#2371—611no—
177#1534—611no—
178#1506—611no—
179#1506—611no—
180#1300—611no—
181#1300D6111yescharacteristic
182C2×C61—21no—
183C2×C61—21no—
184C2×C61#188611yescharacteristic
185C2×C61#190611yescharacteristic
186C2×C61#190611yescharacteristic
187#533—611no—
188C2×#125—611no—
189#501—612no—
190#501—612no—
191#499—1222no—
192#432—611no—
193#432C2×D6111yescharacteristic
194#428—1221no—
195#428—1221no—
196C4×M16C2×D6111yescharacteristic
197#387—1221no—
198#387—1221no—
199#387—1221no—
200#387—1221no—
201C4×C4⋊C4—1221no—
202C4×C4⋊C4—1221no—
203#376—611no—
204#376C2×D6111yescharacteristic
205#330—1222no—
206#328—1221no—
207#328—1221no—
208#328—1221no—
209#328—1221no—
210C61#944011yescharacteristic, complemented, Sylow
211C2×M16—21no—
212C4⋊Q8—611no—
213C4⋊Q8—611no—
214#125—612no—
215#125—612no—
216#125—1221no—
217#125—1221no—
218#125—1221no—
219C22⋊Q8—1221no—
220C22⋊Q8—1221no—
221C4×Q8—1221no—
222C4×Q8—1221no—
223#117—1221no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C42—21no—
231C2×C42—1221no—
232C2×C42—1221no—
233C2×C42—1221no—
234C2×C42C22×D6111yescharacteristic
235#107—1222no—
236#107—1222no—
237#106—1222no—
238#106—1222no—
239C4⋊C8—21no—
240C4⋊C8—1221no—
241C22⋊C8—21no—
242C22⋊C8—1221no—
243#97—21no—
244#97—1221no—
245#97C4×D6112yes—
246C4×C8—21no—
247#95—21no—
248#95—611no—
249#95—611no—
250#95—1221no—
251#95—1221no—
252#95—1221no—
253#95—1221no—
254#95—1221no—
255#95D24411yescharacteristic
256#95D24411yescharacteristic
257C2×Q8—1221no—
258C2×Q8—1221no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4C2×D24411yescharacteristic
266C22×C4D4×D6111yescharacteristic
267C22×C4D4×D6111yescharacteristic
268M16—22no—
269M16—22no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—2441no—
273C4⋊C4—612no—
274C4⋊C4—612no—
275C4⋊C4—1222no—
276C4⋊C4—1222no—
277C4⋊C4—1222no—
278C4⋊C4—1222no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—2442no—
286C4⋊C4—2442no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C22⋊C4—2441no—
290C42—42no—
291C42—2442no—
292C42—2442no—
293C42—2442no—
294C42—2441no—
295C42C2×C4×D6111yescharacteristic
296C42#1175822211yescharacteristic
297C42D4×D6111yescharacteristic
298C42#1175822611yescharacteristic
299C23#1451974711yescharacteristic
300Q8—4881no—
301Q8—4881no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—1222no—
313C2×C4—1222no—
314C2×C4—1222no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4C22⋊C4×D6111yescharacteristic
327C2×C4#1451973911yescharacteristic
328C2×C4C4×D24411yescharacteristic
329C2×C4#1451975011yescharacteristic
330C2×C4#1451975211yescharacteristic
331C2×C4#1451976211yescharacteristic
332C8—24no—
333C8—81no—
334C8—4881no—
335C22—21no—
336C22—21no—
337C22#1683964011yescharacteristic
338C22#1683994611yescharacteristic
339C22#1683994611yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—42no—
347C4—81no—
348C4—4881no—
349C4—4881no—
350C4—4881no—
351C4—2442no—
352C4—2442no—
353C4—2442no—
354C2—21no—
355C2—21no—
356C2#2144621111yescharacteristic
357C2#2144631911yescharacteristic
358C2#2144632111yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1300C2
socleC22×C61#386
prime radicalC23×C61#120
cosocleC2×C42×C61C23
hypercenter#1300D61
hypocenterC61#9440
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
10. #16840171C4semidirect
11. #16840171C4semidirect
210. C61#9440semidirect

Maximal subgroups

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

subgroupindex
#214563712
#214489242
#214444452
#214443322
#214443302
#214437132
C61×#13002
#944061