Finite Group Databasebeta

← #29568902

Subgroups — #29568902

Order 15616.

392 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 81 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#21453769C211yesmaximal, characteristic
2#21447062C211yesmaximal, characteristic
3#21446957C211yesmaximal, characteristic
4#21443644C211yesmaximal, characteristic
5#21443643C211yesmaximal, characteristic
6#21443642C211yesmaximal, characteristic
7C61×#2058C211yesmaximal, characteristic
8C2×#14519701—21no—
9C2×#14519701—21no—
10C2×#14519700—21no—
11#16839704—21no—
12#16839700—21no—
13#16839682—21no—
14#16839668C2211yescharacteristic
15#16839660C2211yescharacteristic
16#16839657—21no—
17#16839648—21no—
18#16839647—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×#106×C61—21no—
24C61×#389C2211yescharacteristic
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×#92418—21no—
29C22×#92418—21no—
30C2×C4⋊Dic61D411yescharacteristic
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C4×Dic61—21no—
37#14519701—42no—
38#14519701—42no—
39#14519700—42no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C22×Q8×C61—21no—
49C22×C8×C61—21no—
50C4⋊Q8×C61—42no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57#106×C61—42no—
58#95×C61—21no—
59C2×Q8×C61—22no—
60C2×Q8×C61—41no—
61C2×Q8×C61—41no—
62C2×Q8×C61—41no—
63C2×Q8×C61—41no—
64C2×Q8×C61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—41no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C2×Dic122—21no—
76C2×Dic122—21no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×C8×C61—22no—
80C2×C8×C61—41no—
81C2×C8×C61—41no—
82C4⋊C4×C61—22no—
83C4⋊C4×C61—22no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C42×C61—41no—
92C4⋊Dic61—21no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61SD1612yes—
96#11758196—41no—
97#11758196—41no—
98#11758196—81no—
99#11758196—81no—
100C4×Dic61—81no—
101C2×#92418—41no—
102C2×#92418—41no—
103C2×#92418—41no—
104C2×#92418—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107C23×C61#12011yescharacteristic
108Q8×C61—42no—
109Q8×C61—42no—
110Q8×C61—81no—
111Q8×C61—81no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61C2×SD1611yescharacteristic
128C2×C4×C61#13511yescharacteristic
129C2×C4×C61#13511yescharacteristic
130C2×C4×C61#13711yescharacteristic
131C2×C4×C61#13711yescharacteristic
132C2×C4×C61#13711yescharacteristic
133C2×Dic61—22no—
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—
144C2×Dic61—41no—
145Dic122—42no—
146Dic122—81no—
147C8×C61—42no—
148#92418—81no—
149#92418—81no—
150#7767—611nomaximal, Sylow
151C22×C61#44811yescharacteristic
152C22×C61#45211yescharacteristic
153C22×C61#45211yescharacteristic
154C22×C61#45411yescharacteristic
155C22×C61#45511yescharacteristic
156C22×C61#45611yescharacteristic
157C22×C61B(4,𝔽2)11yescharacteristic
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—82no—
165C4×C61—81no—
166C4×C61—81no—
167Dic61—42no—
168Dic61—81no—
169Dic61—81no—
170Dic61—81no—
171#2805—611no—
172#2058D6111yescharacteristic
173#2043—611no—
174#2024—611no—
175#1272—611no—
176#1271—611no—
177#1271—611no—
178C2×C61#159911yescharacteristic
179C2×C61#160311yescharacteristic
180C2×C61#160611yescharacteristic
181C2×C61#163811yescharacteristic
182C2×C61#164311yescharacteristic
183C2×C61#165311yescharacteristic
184C2×C61#166411yescharacteristic
185C2×C4⋊Q8C2×D6111yescharacteristic
186C2×#106—21no—
187C2×#103—1221no—
188C2×#103—1221no—
189C2×#103—1221no—
190#400—1221no—
191#400—1221no—
192#395—1221no—
193#391—611no—
194#389—611no—
195#389—1221no—
196#389C2×D6111yescharacteristic
197#387—1221no—
198#387—1221no—
199#340—21no—
200#340—1221no—
201#336—611no—
202#336—611no—
203#336C2×D6111yescharacteristic
204C61#776711yescharacteristic, complemented, Sylow
205C22×Q8—21no—
206C22×Q8—611no—
207C22×C8—21no—
208C22×C8—1221no—
209C22×C8—1221no—
210C4⋊Q8—42no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4C22⋊D6111yescharacteristic
221C2×C4⋊C4C22⋊D6111yescharacteristic
222C2×C42—1221no—
223C2×C42C22×D6111yescharacteristic
224#106—42no—
225#103—2442no—
226#103—2442no—
227#103—2442no—
228#95—21no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—1221no—
244C2×Q8—1221no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4D4×D6111yescharacteristic
255C22×C4D4×D6111yescharacteristic
256C22×C4C2×C22⋊D6111yescharacteristic
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—2441no—
261C2×C8—2441no—
262C2×C8—2441no—
263C2×C8—2441no—
264C2×C8—2441no—
265C2×C8—2441no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—612no—
276C4⋊C4—1221no—
277C4⋊C4—4881no—
278C4⋊C4—4881no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C42—41no—
284C42—4881no—
285C23#1451974511yescharacteristic
286Q8—42no—
287Q8—42no—
288Q8—81no—
289Q8—81no—
290Q8—4881no—
291Q8—2442no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—1222no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4SD16×D6111yescharacteristic
320C2×C4#1451979711yescharacteristic
321C2×C4#1451979811yescharacteristic
322C2×C4#1451980611yescharacteristic
323C2×C4#1451980611yescharacteristic
324C2×C4#1451980811yescharacteristic
325C8—42no—
326C8—4881no—
327C8—4881no—
328C22#1683989911yescharacteristic
329C22#1683992111yescharacteristic
330C22#1683992211yescharacteristic
331C22#1683993311yescharacteristic
332C22#1683993811yescharacteristic
333C22#1683994411yescharacteristic
334C22#1683994811yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—81no—
342C4—82no—
343C4—81no—
344C4—4881no—
345C4—4881no—
346C4—4881no—
347C4—2442no—
348C2#2144475711yescharacteristic
349C2#2144478011yescharacteristic
350C2#2144479611yescharacteristic
351C2#2144498911yescharacteristic
352C2#2144502511yescharacteristic
353C2#2144509311yescharacteristic
354C2#2144515111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2058C2
socle, prime radicalC23×C61#120
hypercenter#2058D61
hypocenterC61#7767
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2058

Complements

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

NH ≅ G/Ntype
204. C61#7767semidirect

Maximal subgroups

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

subgroupindex
#214537692
#214470622
#214469572
#214436442
#214436432
#214436422
C61×#20582
#776761