Finite Group Databasebeta

← #29580935

Subgroups — #29580935

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#21456372C211yesmaximal, characteristic
2#21451695C211yesmaximal, characteristic
3#21444445C211yesmaximal, characteristic
4#21444370C211yesmaximal, characteristic
5#21444266C211yesmaximal, characteristic
6#21443685C211yesmaximal, characteristic
7C61×#3113C211yesmaximal, characteristic
8C2×#14519769C2211yescharacteristic
9#16840168—21no—
10#16840168—21no—
11#16840161—22no—
12#16839819C2211yescharacteristic
13#16839805—21no—
14#16839805—21no—
15C4×#11758194C2211yescharacteristic
16#16839701—21no—
17#16839700—21no—
18#16839692—21no—
19#16839681—21no—
20#16839646—22no—
21#16839630C2211yescharacteristic
22#16839503—22no—
23#16839499—22no—
24Q8⋊#92418—22no—
25C61×#533C2211yescharacteristic
26C2×C4×Q8×C61C2211yescharacteristic
27C61×#483—21no—
28C61×#475—21no—
29C61×#462—21no—
30C61×#451—21no—
31C61×#441—22no—
32C61×#432C2211yescharacteristic
33C2×#11758194—21no—
34#14519769—21no—
35#14519769—21no—
36#14519769—21no—
37#14519769—21no—
38C2×C4⋊Dic61D411yescharacteristic
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—22no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43#14519710—22no—
44#14519710—22no—
45#14519708—22no—
46#14519708—22no—
47C4⋊#92418—21no—
48C22⋊#92418—21no—
49#14519688—21no—
50#14519688—21no—
51C4×#92418D412yes—
52#14519684—22no—
53#14519684—22no—
54#14519684—22no—
55#14519684—21no—
56#14519684—21no—
57#14519684D412yes—
58C22×Q8×C61D411yescharacteristic
59C2×Q16×C61—22no—
60C4⋊Q8×C61D411yescharacteristic
61C4⋊Q8×C61D411yescharacteristic
62#125×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71#117×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C42×C61—21no—
75C2×C42×C61C2311yescharacteristic
76#106×C61—22no—
77C4⋊C8×C61—21no—
78#103×C61—22no—
79#103×C61—22no—
80C22⋊C8×C61—21no—
81#97×C61D412yes—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—21no—
85C2×Q8×C61—21no—
86C2×Q8×C61—42no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×Dic61—22no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95Q16×C61—44no—
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—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C22⋊C4×C61—41no—
108C42×C61—41no—
109C42×C61—41no—
110C42×C61—41no—
111C42×C61C2×D411yescharacteristic
112C42×C61C2×D411yescharacteristic
113C42×C61C2×D411yescharacteristic
114C42×C61#4111yescharacteristic
115C4⋊Dic61—21no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119#11758196—44no—
120#11758196—41no—
121#11758196—41no—
122#11758196—41no—
123#11758196—41no—
124#11758194—24no—
125C2×#92418—22no—
126C2×#92418—41no—
127C23×C61#12011yescharacteristic
128Q8×C61—22no—
129Q8×C61—22no—
130Q8×C61—41no—
131Q8×C61—41no—
132Q8×C61—42no—
133Q8×C61—81no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—42no—
144C2×C4×C61#12011yescharacteristic
145C2×C4×C61#12011yescharacteristic
146C2×C4×C61#12111yescharacteristic
147C2×C4×C61#12111yescharacteristic
148C2×C4×C61#12111yescharacteristic
149C2×C4×C61#12711yescharacteristic
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C8×C61—42no—
158#92418—24no—
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—42no—
172C4×C61—81no—
173C4×C61—81no—
174C4×C61—81no—
175Dic61—82no—
176Dic61—81no—
177Dic61—81no—
178#3166—611no—
179#3113D6111yescharacteristic
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×#125—611no—
191C2×C4×Q8C2×D6111yescharacteristic
192#501—1221no—
193#501—1221no—
194#499—1222no—
195#483—21no—
196#475—21no—
197#462—21no—
198#451—21no—
199#441—22no—
200#432—611no—
201#432C2×D6111yescharacteristic
202#428—1221no—
203#428—1221no—
204C4×M16—611no—
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×Q8C22⋊D6111yescharacteristic
216C2×Q16—22no—
217C2×M16—1221no—
218C4⋊Q8C22⋊D6111yescharacteristic
219C4⋊Q8C22⋊D6111yescharacteristic
220#125—21no—
221#125—1221no—
222#125—1221no—
223#125—1221no—
224#125—1221no—
225C22⋊Q8—21no—
226C22⋊Q8—21no—
227C4×Q8—21no—
228C4×Q8—21no—
229C4×Q8—21no—
230C4×Q8—21no—
231C4×Q8—21no—
232C4×Q8—21no—
233#117—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4—1221no—
239C2×C4⋊C4—1221no—
240C2×C4⋊C4C22⋊D6111yescharacteristic
241C2×C42—21no—
242C2×C42C22×D6111yescharacteristic
243#107—1222no—
244#107—1222no—
245#106—22no—
246#106—1222no—
247#106—1222no—
248C4⋊C8—21no—
249C4⋊C8—1221no—
250#103—22no—
251#103—22no—
252C22⋊C8—21no—
253C22⋊C8—1221no—
254#97—1221no—
255#97—1221no—
256#97C22⋊D6112yes—
257C4×C8—612no—
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—21no—
267C2×Q8—21no—
268C2×Q8—42no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—1222no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4D4×D6111yescharacteristic
275C22×C4D4×D6111yescharacteristic
276C22×C4C2×C22⋊D6111yescharacteristic
277Q16—44no—
278M16—1224no—
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—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—2444no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C22⋊C4—41no—
302C42—41no—
303C42—41no—
304C42—41no—
305C42D4×D6111yescharacteristic
306C42#1175822411yescharacteristic
307C42C2×C22⋊D6111yescharacteristic
308C42C2×C22⋊D6111yescharacteristic
309C23#1451974511yescharacteristic
310Q8—22no—
311Q8—22no—
312Q8—41no—
313Q8—41no—
314Q8—42no—
315Q8—81no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2442no—
329C2×C4—2442no—
330C2×C4—2442no—
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—42no—
340C8—1224no—
341C8—4881no—
342C22—21no—
343C22—21no—
344C22#1683967011yescharacteristic
345C22#1683994312yes—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—81no—
354C4—81no—
355C4—81no—
356C4—4882no—
357C4—4881no—
358C4—4881no—
359C2—22no—
360C2#2144685211yescharacteristic
361C2#2144687711yescharacteristic
362C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3113C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#3113D61
hypocenterC61#10025
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3113

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
#214563722
#214516952
#214444452
#214443702
#214442662
#214436852
C61×#31132
#1002561