Finite Group Databasebeta

← #29580848

Subgroups — #29580848

Order 15616.

496 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 85 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#21457025C211yesmaximal, characteristic
2#21455949C211yesmaximal, characteristic
3#21446762C211yesmaximal, characteristic
4#21444421C211yesmaximal, characteristic
5#21444266C211yesmaximal, characteristic
6#21443675C211yesmaximal, characteristic
7C61×#2584C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840172—21no—
10#16840132—21no—
11#16840097—21no—
12#16840092—21no—
13#16840092—21no—
14#16840066—22no—
15#16840047—21no—
16#16839972—21no—
17#16839918—21no—
18#16839867—22no—
19#16839819C2211yescharacteristic
20#16839819C2211yescharacteristic
21C4×#11758194C2211yescharacteristic
22#16839522—22no—
23#16839504—22no—
24Q8⋊#92418—22no—
25C2×#125×C61C2211yescharacteristic
26C2×C4×Q8×C61C2211yescharacteristic
27C61×#398—21no—
28C61×#395—21no—
29C61×#389—21no—
30C61×#389—21no—
31C61×#389—22no—
32C4×C4⋊C4×C61C2211yescharacteristic
33C2×#11758202—22no—
34C2×#11758194—21no—
35#14519777D411yescharacteristic
36#14519777D411yescharacteristic
37#14519769—21no—
38#14519756—21no—
39#14519756—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42#14519736—21no—
43#14519710—22no—
44#14519708—22no—
45#14519708—22no—
46C4⋊#92418—21no—
47C4⋊#92418D412yes—
48#14519701—22no—
49#14519700—22no—
50#14519700—22no—
51#14519700—22no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519688—21no—
55#14519688—21no—
56#14519688D412yes—
57C4×#92418—21no—
58C22×Q8×C61D411yescharacteristic
59#125×C61—21no—
60#125×C61—21no—
61#125×C61—21no—
62#125×C61—21no—
63C4×Q8×C61—21no—
64C4×Q8×C61—21no—
65C4×Q8×C61—21no—
66C4×Q8×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—22no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—22no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C42×C61—21no—
77C2×C42×C61D412yes—
78C2×C42×C61C2311yescharacteristic
79#95×C61—22no—
80#95×C61—22no—
81#95×C61—21no—
82C2×Q8×C61—21no—
83C2×Q8×C61—21no—
84C2×Q8×C61—42no—
85C22×C4×C61—22no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—21no—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C2×Dic122—21no—
94C2×Dic122—21no—
95C4⋊C4×C61—24no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—44no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—41no—
107C4⋊C4×C61—41no—
108C4⋊C4×C61—41no—
109C4⋊C4×C61—82no—
110C42×C61—42no—
111C42×C61—41no—
112C42×C61—41no—
113C42×C61C2×D411yescharacteristic
114C42×C61C2×D411yescharacteristic
115C42×C61C2×D411yescharacteristic
116C42×C61#4111yescharacteristic
117C22⋊Dic61—41no—
118#11758202—44no—
119C4⋊Dic61—21no—
120C4⋊Dic61—21no—
121C4⋊Dic61—21no—
122C4⋊Dic61—21no—
123#11758196—41no—
124#11758196—41no—
125C4×Dic61—41no—
126#11758194—22no—
127#11758194—41no—
128C2×#92418—22no—
129C2×#92418—22no—
130C2×#92418—41no—
131C23×C61#12011yescharacteristic
132Q8×C61—22no—
133Q8×C61—22no—
134Q8×C61—41no—
135Q8×C61—41no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—22no—
139C2×C4×C61—24no—
140C2×C4×C61—22no—
141C2×C4×C61—41no—
142C2×C4×C61—42no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—42no—
146C2×C4×C61—42no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—41no—
154C2×C4×C61#12011yescharacteristic
155C2×C4×C61#12011yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12111yescharacteristic
158C2×C4×C61#12111yescharacteristic
159C2×C4×C61#12711yescharacteristic
160C2×Dic61—41no—
161C2×Dic61—41no—
162Dic122—42no—
163Dic122—42no—
164#92418—42no—
165#92418—42no—
166#92418—42no—
167#10011—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61#39211yescharacteristic
171C22×C61#45511yescharacteristic
172C22×C61#45611yescharacteristic
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—44no—
179C4×C61—42no—
180C4×C61—81no—
181C4×C61—81no—
182C4×C61—81no—
183C4×C61#45612yes—
184Dic61—81no—
185Dic61—81no—
186#3236—611no—
187#3113—611no—
188#2584D6111yescharacteristic
189#1986—611no—
190#1528—611no—
191#1491—611no—
192#1285—611no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61#200511yescharacteristic
196C2×C61#200711yescharacteristic
197C2×C61#201011yescharacteristic
198#533—611no—
199C2×#125C2×D6111yescharacteristic
200C2×C4×Q8C2×D6111yescharacteristic
201#501—1221no—
202#491—1221no—
203#484—1221no—
204#483—1221no—
205#483—1221no—
206#479—1222no—
207#475—1221no—
208#462—1221no—
209#451—1221no—
210#441—1222no—
211#432—611no—
212#432—611no—
213C4×M16—611no—
214#398—21no—
215#395—21no—
216#389—21no—
217#389—21no—
218#389—22no—
219C4×C4⋊C4C2×D6111yescharacteristic
220#339—1222no—
221#330—1222no—
222Q8⋊C8—1222no—
223C61#1001111yescharacteristic, complemented, Sylow
224C22×Q8C22⋊D6111yescharacteristic
225C2×Q16—1222no—
226C2×M16—1221no—
227C4⋊Q8—611no—
228C4⋊Q8—611no—
229#125—21no—
230#125—21no—
231#125—21no—
232#125—21no—
233#125—1221no—
234C22⋊Q8—1221no—
235C22⋊Q8—1221no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—1221no—
241C4×Q8—1221no—
242#117—1221no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4C22⋊D6111yescharacteristic
250C2×C4⋊C4C22⋊D6111yescharacteristic
251C2×C4⋊C4C22⋊D6111yescharacteristic
252C2×C42—21no—
253C2×C42C22⋊D6112yes—
254C2×C42C22×D6111yescharacteristic
255#107—1222no—
256#106—1222no—
257#106—1222no—
258C4⋊C8—612no—
259C4⋊C8—1221no—
260#103—1222no—
261#103—1222no—
262#103—1222no—
263#103—1222no—
264C22⋊C8—1221no—
265C22⋊C8—1221no—
266#97—612no—
267#97—1221no—
268#97—1221no—
269C4×C8—1221no—
270#95—22no—
271#95—22no—
272#95—21no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—42no—
276C2×Q8—1221no—
277C2×Q8—1221no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4C2×C22⋊D6111yescharacteristic
284C22×C4C2×C22⋊D6111yescharacteristic
285C22×C4C2×C22⋊D6111yescharacteristic
286Q16—2444no—
287M16—1222no—
288M16—2441no—
289C2×C8—1222no—
290C2×C8—1222no—
291C2×C8—2441no—
292C4⋊C4—24no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—44no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—82no—
307C4⋊C4—1221no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C4⋊C4—1221no—
311C4⋊C4—2441no—
312C4⋊C4—2441no—
313C22⋊C4—2441no—
314C42—42no—
315C42—41no—
316C42—41no—
317C42—2441no—
318C42D4×D6111yescharacteristic
319C42D4×D6111yescharacteristic
320C42D4×D6111yescharacteristic
321C42#1175822411yescharacteristic
322C23#1451974611yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—2442no—
328Q8—2442no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—2441no—
348C2×C4—2441no—
349C2×C4#1451974511yescharacteristic
350C2×C4#1451974511yescharacteristic
351C2×C4#1451974811yescharacteristic
352C2×C4#1451974911yescharacteristic
353C2×C4#1451974911yescharacteristic
354C2×C4#1451977311yescharacteristic
355C8—2442no—
356C8—2442no—
357C8—2442no—
358C22—21no—
359C22—21no—
360C22#1683967011yescharacteristic
361C22#1683994011yescharacteristic
362C22#1683994511yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—44no—
369C4—42no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—4881no—
374C4—4881no—
375C4#1683994412yes—
376C2—21no—
377C2—21no—
378C2#2144685511yescharacteristic
379C2#2144686611yescharacteristic
380C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2584C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#2584D61
hypocenterC61#10011
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2584

Complements

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

NH ≅ G/Ntype
223. C61#10011semidirect

Maximal subgroups

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

subgroupindex
#214570252
#214559492
#214467622
#214444212
#214442662
#214436752
C61×#25842
#1001161