Finite Group Databasebeta

← #29593053

Subgroups — #29593053

Order 15616.

388 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 59 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#21452948C211yesmaximal, characteristic
2#21444844C211yesmaximal, characteristic
3#21444776C211yesmaximal, characteristic
4#21443842C211yesmaximal, characteristic
5#21443839C211yesmaximal, characteristic
6#21443767C211yesmaximal, characteristic
7C61×#2062C211yesmaximal, characteristic
8#16840095—21no—
9#16839917—21no—
10#16839701—21no—
11#16839698C2211yescharacteristic
12#16839683—21no—
13#16839674C2211yescharacteristic
14#16839661—21no—
15#16839655—21no—
16#16839645—21no—
17#16839622—21no—
18#16839499—21no—
19#16839499—21no—
20#16839486C2211yescharacteristic
21#16839486C2211yescharacteristic
22C61×#543C2211yescharacteristic
23C61×#385—21no—
24C61×#385C2211yescharacteristic
25C61×#342—21no—
26C61×#342C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C2×#11758202—41no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758196—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C4×Dic61—21no—
37#14519710—41no—
38#14519701—41no—
39#14519700—41no—
40C22⋊#92418—21no—
41C22⋊#92418—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684D411yescharacteristic
48#14519684D411yescharacteristic
49C23×C4×C61D411yescharacteristic
50C22⋊Q8×C61—21no—
51C22⋊Q8×C61—21no—
52C22⋊Q8×C61—41no—
53C22⋊Q8×C61—41no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—41no—
56C2×C22⋊C4×C61—21no—
57C2×C22⋊C4×C61—21no—
58C2×C22⋊C4×C61D411yescharacteristic
59C2×C22⋊C4×C61C2311yescharacteristic
60#95×C61—21no—
61#95×C61—41no—
62C24×C61C2×D411yescharacteristic
63C2×Q8×C61—21no—
64C2×Q8×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—42no—
70C22×C4×C61—41no—
71C22×C4×C61—41no—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C2×Dic122—41no—
79C2×Dic122—81no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—82no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61—22no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61Q1612yescomplemented
93C22⋊Dic61—81no—
94C22⋊Dic61—81no—
95#11758202—82no—
96C4⋊Dic61—42no—
97C4⋊Dic61—41no—
98C4⋊Dic61—81no—
99C4⋊Dic61—81no—
100#11758196—81no—
101C4×Dic61—81no—
102C2×#92418—41no—
103C2×#92418—41no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61#12011yescharacteristic
109C23×C61C2×Q1611yescharacteristic
110C23×C61#13711yescharacteristic
111Q8×C61—81no—
112Q8×C61—81no—
113C2×C4×C61—22no—
114C2×C4×C61—22no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—42no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144Dic122—42no—
145Dic122—81no—
146#92418—81no—
147#92418—81no—
148#12254—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—81no—
158C22×C61#45111yescharacteristic
159C22×C61#45611yescharacteristic
160C22×C61B(4,𝔽2)11yescharacteristic
161C4×C61—42no—
162C4×C61—41no—
163C4×C61—42no—
164C4×C61—41no—
165C4×C61—82no—
166C4×C61—81no—
167C4×C61—81no—
168Dic61—81no—
169Dic61—81no—
170Dic61—81no—
171Dic61—81no—
172#2742—611no—
173#2062D6111yescharacteristic
174#1614—611no—
175#1602—611no—
176#1352—611no—
177#1351—611no—
178#1326—611no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61—41no—
182C2×C61—41no—
183C2×C61#160511yescharacteristic
184C2×C61#219711yescharacteristic
185C2×C61#220011yescharacteristic
186#543C2×D6111yescharacteristic
187#484—1221no—
188#451—1221no—
189#400—1221no—
190#399—611no—
191#395—1221no—
192#393—611no—
193#389—1221no—
194#388—1221no—
195#387—1221no—
196#385—21no—
197#385C2×D6111yescharacteristic
198#380—1221no—
199#342—21no—
200#342C2×D6111yescharacteristic
201#328—1221no—
202#328—1221no—
203#323—611no—
204#323—611no—
205C61#1225411yescharacteristic, complemented, Sylow
206C22×Q8—611no—
207C23×C4C22⋊D6111yescharacteristic
208C2×Q16—2441no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8—41no—
212C22⋊Q8—41no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—1221no—
223C2×C22⋊C4—1221no—
224C2×C22⋊C4C22⋊D6111yescharacteristic
225C2×C22⋊C4C22×D6111yescharacteristic
226C2×C42—1221no—
227#107—2441no—
228#103—2441no—
229#103—2441no—
230C22⋊C8—1221no—
231C22⋊C8—1221no—
232#95—21no—
233#95—41no—
234#95—611no—
235#95—611no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24C2×C22⋊D6111yescharacteristic
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—4881no—
245C2×Q8—2441no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—42no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4D4×D6111yescharacteristic
258C22×C4D4×D6111yescharacteristic
259Q16—4882no—
260C2×C8—2441no—
261C2×C8—2441no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—82no—
268C4⋊C4—4881no—
269C4⋊C4—4881no—
270C4⋊C4—4881no—
271C4⋊C4—2441no—
272C4⋊C4—2442no—
273C22⋊C4—21no—
274C22⋊C4—22no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—4881no—
280C22⋊C4—4881no—
281C22⋊C4#1175820212yescomplemented
282C42—4881no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23#1451974511yescharacteristic
288C23C2×#1175820211yescharacteristic
289C23#1451980711yescharacteristic
290Q8—81no—
291Q8—81no—
292Q8—4881no—
293Q8—2442no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—2441no—
314C2×C4—2441no—
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—
325C8—4881no—
326C8—4881no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—81no—
336C22#1683991711yescharacteristic
337C22#1683994411yescharacteristic
338C22#1683994811yescharacteristic
339C4—42no—
340C4—41no—
341C4—42no—
342C4—41no—
343C4—82no—
344C4—81no—
345C4—81no—
346C4—4881no—
347C4—4881no—
348C4—4881no—
349C4—4881no—
350C2—21no—
351C2—21no—
352C2—41no—
353C2—41no—
354C2#2144479211yescharacteristic
355C2#2144780711yescharacteristic
356C2#2144782311yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2062C2
socleC22×C61B(4,𝔽2)
prime radicalC24×C61C2×D4
hypercenter#2062D61
hypocenterC61#12254
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2062

Complements

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

NH ≅ G/Ntype
92. C22⋊C4×C61Q16semidirect
205. C61#12254semidirect
281. C22⋊C4#11758202semidirect

Maximal subgroups

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

subgroupindex
#214529482
#214448442
#214447762
#214438422
#214438392
#214437672
C61×#20622
#1225461