Finite Group Databasebeta

← #29580936

Subgroups — #29580936

Order 15616.

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

normal subgroups only

This group has 470 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#21455945C211yesmaximal, characteristic
2#21451696C211yesmaximal, characteristic
3#21444446C211yesmaximal, characteristic
4#21444370C211yesmaximal, characteristic
5#21444267C211yesmaximal, characteristic
6#21443684C211yesmaximal, characteristic
7C61×#3166C211yesmaximal, characteristic
8C2×C4×Dic122C2211yescharacteristic
9#16840090—21no—
10#16840044—21no—
11#16839969—21no—
12#16839917—21no—
13#16839867—22no—
14#16839819C2211yescharacteristic
15#16839819C2211yescharacteristic
16#16839701—21no—
17#16839700—21no—
18#16839693—21no—
19#16839682—21no—
20#16839643—22no—
21#16839630C2211yescharacteristic
22#16839504—22no—
23#16839499—22no—
24#16839494—22no—
25C61×#533C2211yescharacteristic
26C2×#125×C61C2211yescharacteristic
27C61×#501—21no—
28C61×#501—21no—
29C61×#499—22no—
30C61×#428—21no—
31C61×#428—21no—
32C4×M16×C61C2211yescharacteristic
33C22×Dic122D411yescharacteristic
34C2×#11758202—22no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—22no—
41C2×#11758196—21no—
42C2×C4×Dic61—21no—
43#14519708—22no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46#14519701—22no—
47#14519700—22no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50#14519688—21no—
51#14519688D412yes—
52#14519684—22no—
53#14519684—22no—
54#14519684—22no—
55#14519684—21no—
56#14519684—21no—
57#14519684D412yes—
58C2×M16×C61—21no—
59C4⋊Q8×C61D411yescharacteristic
60C4⋊Q8×C61D411yescharacteristic
61#125×C61—21no—
62#125×C61—21no—
63#125×C61—21no—
64#125×C61—21no—
65#125×C61—21no—
66C22⋊Q8×C61—21no—
67C22⋊Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70#117×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C42×C61C2311yescharacteristic
76#107×C61—22no—
77#107×C61—22no—
78#106×C61—22no—
79#106×C61—22no—
80#97×C61—21no—
81C4×C8×C61D412yes—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×Dic61—21no—
90C22×Dic61—22no—
91C22×Dic61—21no—
92C2×Dic122—21no—
93C2×Dic122—21no—
94C2×Dic122—42no—
95M16×C61—24no—
96C2×C8×C61—22no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—21no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—41no—
110C4⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C42×C61—41no—
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117#11758202—44no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120#11758196—44no—
121#11758196—41no—
122#11758196—41no—
123C4×Dic61—41no—
124C4×Dic61—41no—
125C2×#92418—22no—
126C2×#92418—41no—
127C23×C61#12011yescharacteristic
128Q8×C61—42no—
129Q8×C61—81no—
130C2×C4×C61—22no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12011yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12711yescharacteristic
145C2×Dic61—22no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—41no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153Dic122—22no—
154Dic122—22no—
155Dic122—41no—
156Dic122—41no—
157C8×C61—24no—
158#92418—42no—
159#92418—81no—
160#10025—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61#39211yescharacteristic
164C22×C61#45612yes—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—81no—
172C4×C61—81no—
173C4×C61—81no—
174C4×C61—81no—
175Dic61—42no—
176Dic61—82no—
177Dic61—81no—
178#3166D6111yescharacteristic
179#3113—611no—
180#2634—611no—
181#1534—611no—
182#1515—611no—
183#1491—611no—
184#1288—611no—
185C2×C61—22no—
186C2×C61#200511yescharacteristic
187C2×C61#200911yescharacteristic
188C2×C61#201011yescharacteristic
189#533C2×D6111yescharacteristic
190C2×#125C2×D6111yescharacteristic
191C2×C4×Q8—611no—
192#501—21no—
193#501—21no—
194#499—22no—
195#483—1221no—
196#475—1221no—
197#462—1221no—
198#451—1221no—
199#441—1222no—
200#432—611no—
201#432—611no—
202#428—21no—
203#428—21no—
204C4×M16C2×D6111yescharacteristic
205#400—1221no—
206#400—1221no—
207#398—1221no—
208#395—1221no—
209#387—1222no—
210#383—611no—
211#330—1222no—
212#328—1222no—
213Q8⋊C8—1222no—
214C61#1002511yescharacteristic, complemented, Sylow
215C22×Q8—611no—
216C2×Q16—1222no—
217C2×M16—21no—
218C4⋊Q8C22⋊D6111yescharacteristic
219C4⋊Q8C22⋊D6111yescharacteristic
220#125—21no—
221#125—21no—
222#125—21no—
223#125—21no—
224#125—21no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—1221no—
230C4×Q8—1221no—
231C4×Q8—1221no—
232C4×Q8—1221no—
233#117—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4C22⋊D6111yescharacteristic
240C2×C4⋊C4C22⋊D6111yescharacteristic
241C2×C42—1221no—
242C2×C42C22×D6111yescharacteristic
243#107—22no—
244#107—22no—
245#106—22no—
246#106—22no—
247#106—1222no—
248C4⋊C8—1221no—
249C4⋊C8—1221no—
250#103—1222no—
251#103—1222no—
252C22⋊C8—1221no—
253C22⋊C8—1221no—
254#97—21no—
255#97—612no—
256#97—1221no—
257C4×C8C22⋊D6112yes—
258#95—612no—
259#95—1222no—
260#95—1222no—
261#95—1222no—
262#95—1221no—
263#95—1221no—
264C2×Q8—21no—
265C2×Q8—21no—
266C2×Q8—1221no—
267C2×Q8—1221no—
268C2×Q8—2442no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—1221no—
272C22×C4—1222no—
273C22×C4—1221no—
274C22×C4D4×D6111yescharacteristic
275C22×C4D4×D6111yescharacteristic
276C22×C4C2×C22⋊D6111yescharacteristic
277Q16—2444no—
278M16—24no—
279C2×C8—22no—
280C2×C8—1222no—
281C2×C8—2441no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—2444no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C22⋊C4—41no—
302C42—41no—
303C42—2441no—
304C42—2441no—
305C42D4×D6111yescharacteristic
306C42#1175822411yescharacteristic
307C42C2×C22⋊D6111yescharacteristic
308C42C2×C22⋊D6111yescharacteristic
309C23#1451974511yescharacteristic
310Q8—42no—
311Q8—81no—
312Q8—1222no—
313Q8—1222no—
314Q8—2441no—
315Q8—2441no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—1222no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4#1451974511yescharacteristic
334C2×C4#1451974611yescharacteristic
335C2×C4#1451974811yescharacteristic
336C2×C4#1451974911yescharacteristic
337C2×C4#1451974911yescharacteristic
338C2×C4#1451977311yescharacteristic
339C8—24no—
340C8—4881no—
341C8—2442no—
342C22—21no—
343C22—21no—
344C22#1683967011yescharacteristic
345C22#1683994412yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—81no—
353C4—81no—
354C4—81no—
355C4—81no—
356C4—4882no—
357C4—4881no—
358C4—2442no—
359C2—22no—
360C2#2144685511yescharacteristic
361C2#2144687611yescharacteristic
362C2#2144688311yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3166C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#3166D61
hypocenterC61#10025
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3166

Complements

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

NH ≅ G/Ntype
214. C61#10025semidirect

Maximal subgroups

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

subgroupindex
#214559452
#214516962
#214444462
#214443702
#214442672
#214436842
C61×#31662
#1002561