Finite Group Databasebeta

← #29580845

Subgroups — #29580845

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#21457021C211yesmaximal, characteristic
2#21451207C211yesmaximal, characteristic
3#21446764C211yesmaximal, characteristic
4#21444422C211yesmaximal, characteristic
5#21444266C211yesmaximal, characteristic
6#21443674C211yesmaximal, characteristic
7C61×#3113C211yesmaximal, characteristic
8C2×#14519769C2211yescharacteristic
9#16840168—21no—
10#16840130—21no—
11#16840095—21no—
12#16840090—21no—
13#16840069—22no—
14#16839819C2211yescharacteristic
15C4×#11758194C2211yescharacteristic
16#16839693—21no—
17#16839681—21no—
18#16839660—21no—
19#16839660—21no—
20#16839657—22no—
21C4×C4⋊Dic61C2211yescharacteristic
22#16839521—22no—
23#16839503—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⋊Dic61—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—22no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—22no—
45C2×C4×Dic61D412yes—
46#14519710—22no—
47#14519708—22no—
48C4⋊#92418D412yes—
49#14519701—22no—
50#14519701—22no—
51C22⋊#92418—21no—
52#14519688—21no—
53#14519688—21no—
54C4×#92418—21no—
55#14519684—22no—
56#14519684—22no—
57#14519684—21no—
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—24no—
116C4⋊Dic61—21no—
117C4⋊Dic61—21no—
118C4⋊Dic61—21no—
119C4⋊Dic61—21no—
120#11758196—44no—
121#11758196—41no—
122#11758196—41no—
123#11758196—41no—
124#11758196—41no—
125#11758196—82no—
126C4×Dic61—42no—
127#11758194—22no—
128#11758194—41no—
129C2×#92418—22no—
130C2×#92418—41no—
131C23×C61#12011yescharacteristic
132Q8×C61—22no—
133Q8×C61—22no—
134Q8×C61—41no—
135Q8×C61—41no—
136Q8×C61—42no—
137Q8×C61—42no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—22no—
141C2×C4×C61—22no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—41no—
149C2×C4×C61—41no—
150C2×C4×C61#12011yescharacteristic
151C2×C4×C61#12011yescharacteristic
152C2×C4×C61#12111yescharacteristic
153C2×C4×C61#12111yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12711yescharacteristic
156C2×Dic61—24no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61—41no—
161C2×Dic61—41no—
162C2×Dic61—41no—
163C2×Dic61—41no—
164C8×C61—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—42no—
179C4×C61—81no—
180C4×C61—81no—
181C4×C61—81no—
182C4×C61#45612yes—
183Dic61—44no—
184Dic61—81no—
185Dic61—81no—
186#3236—611no—
187#3113D6111yescharacteristic
188#2584—611no—
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#533C2×D6111yescharacteristic
199C2×#125—611no—
200C2×C4×Q8C2×D6111yescharacteristic
201#501—1221no—
202#491—1221no—
203#484—1221no—
204#483—21no—
205#483—1221no—
206#479—1222no—
207#475—21no—
208#462—21no—
209#451—21no—
210#441—22no—
211#432—611no—
212#432C2×D6111yescharacteristic
213C4×M16—611no—
214#398—1221no—
215#395—1221no—
216#389—1221no—
217#389—1221no—
218#389—1222no—
219C4×C4⋊C4—611no—
220#339—1222no—
221#330—1222no—
222Q8⋊C8—1222no—
223C61#1001111yescharacteristic, complemented, Sylow
224C22×Q8C22⋊D6111yescharacteristic
225C2×Q16—22no—
226C2×M16—1221no—
227C4⋊Q8C22⋊D6111yescharacteristic
228C4⋊Q8C22⋊D6111yescharacteristic
229#125—21no—
230#125—1221no—
231#125—1221no—
232#125—1221no—
233#125—1221no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C4×Q8—21no—
237C4×Q8—21no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8—21no—
242#117—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—611no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4—1221no—
247C2×C4⋊C4—1222no—
248C2×C4⋊C4—1222no—
249C2×C4⋊C4—1221no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4C22⋊D6111yescharacteristic
252C2×C42—21no—
253C2×C42—612no—
254C2×C42C22×D6111yescharacteristic
255#107—1222no—
256#106—22no—
257#106—1222no—
258C4⋊C8—21no—
259C4⋊C8—612no—
260#103—22no—
261#103—22no—
262#103—1222no—
263#103—1222no—
264C22⋊C8—21no—
265C22⋊C8—1221no—
266#97—1221no—
267#97—1221no—
268#97C22⋊D6112yes—
269C4×C8—1221no—
270#95—1222no—
271#95—1222no—
272#95—1221no—
273C2×Q8—21no—
274C2×Q8—21no—
275C2×Q8—21no—
276C2×Q8—21no—
277C2×Q8—42no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—1222no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4D4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285C22×C4C2×C22⋊D6111yescharacteristic
286Q16—44no—
287M16—1222no—
288M16—2441no—
289C2×C8—22no—
290C2×C8—1222no—
291C2×C8—2441no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—41no—
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—1224no—
303C4⋊C4—1221no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4—1221no—
307C4⋊C4—4882no—
308C4⋊C4—2444no—
309C4⋊C4—2441no—
310C4⋊C4—2441no—
311C4⋊C4—2441no—
312C4⋊C4—2441no—
313C22⋊C4—41no—
314C42—41no—
315C42—41no—
316C42—41no—
317C42—2442no—
318C42D4×D6111yescharacteristic
319C42#1175822411yescharacteristic
320C42C2×C22⋊D6111yescharacteristic
321C42C2×C22⋊D6111yescharacteristic
322C23#1451974511yescharacteristic
323Q8—22no—
324Q8—22no—
325Q8—41no—
326Q8—41no—
327Q8—42no—
328Q8—42no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—1224no—
342C2×C4—2442no—
343C2×C4—2441no—
344C2×C4—2441no—
345C2×C4—2441no—
346C2×C4—2441no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4#1451974511yescharacteristic
350C2×C4#1451974611yescharacteristic
351C2×C4#1451974811yescharacteristic
352C2×C4#1451974911yescharacteristic
353C2×C4#1451974911yescharacteristic
354C2×C4#1451977311yescharacteristic
355C8—42no—
356C8—2442no—
357C8—2442no—
358C22—21no—
359C22—21no—
360C22#1683967011yescharacteristic
361C22#1683993811yescharacteristic
362C22#1683994311yescharacteristic
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—42no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—4881no—
373C4—4881no—
374C4—2444no—
375C4#1683994312yes—
376C2—21no—
377C2—21no—
378C2#2144685211yescharacteristic
379C2#2144686411yescharacteristic
380C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3113C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#3113D61
hypocenterC61#10011
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
223. C61#10011semidirect

Maximal subgroups

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

subgroupindex
#214570212
#214512072
#214467642
#214444222
#214442662
#214436742
C61×#31132
#1001161