Finite Group Databasebeta

← #29652873

Subgroups — #29652873

Order 15616.

902 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 902 conjugacy classes of subgroups — too many to draw. Only its 167 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#21459629C211yesmaximal, characteristic
2#21455949C212yesmaximal
3#21444826C214yesmaximal
4#21444792C214yesmaximal
5#21444330C212yesmaximal
6#21444163C211yesmaximal, characteristic
7C61×#2399C211yesmaximal, characteristic
8Q8×Dic122—22no—
9#16840491—22no—
10#16840488—24no—
11#16840393—21no—
12#16840393C2214yes—
13#16840319—22no—
14#16840319C2212yes—
15#16840240—21no—
16#16840092C2214yes—
17#16840047—22no—
18#16839972—22no—
19#16839918C2214yes—
20#16839867—24no—
21#16839819C2212yes—
22#16839498C2218yes—
23#16839488C2214yes—
24C2×C4×Q8×C61C2211yescharacteristic
25C2×C4×Q8×C61C2211yescharacteristic
26C61×#398—21no—
27C61×#398C2212yes—
28C61×#395—21no—
29C61×#395C2212yes—
30C4×C4⋊C4×C61—22no—
31C61×#376C2211yescharacteristic
32C2×#11758202—24no—
33#14519777—22no—
34#14519777—22no—
35#14519777D412yes—
36#14519777D412yes—
37#14519776—24no—
38#14519776—28no—
39#14519769—24no—
40#14519769—22no—
41#14519768—24no—
42#14519768—28no—
43#14519756—22no—
44#14519756—24no—
45#14519756C2314yes—
46Q8×Dic61—24no—
47Q8×Dic61—24no—
48C4×Dic122—24no—
49C4×Dic122—24no—
50C4×Dic122—22no—
51C4×Dic122D414yes—
52#14519736—24no—
53#14519736—22no—
54#14519708—24no—
55C4⋊#92418—22no—
56#14519701—24no—
57#14519700—24no—
58C22⋊#92418C2314yes—
59#14519688—22no—
60C22×Q8×C61D411yescharacteristic
61C22×Q8×C61C2311yescharacteristic
62C4×Q8×C61—22no—
63C4×Q8×C61—22no—
64C4×Q8×C61—22no—
65C4×Q8×C61—22no—
66C2×C4⋊C4×C61—22no—
67C2×C4⋊C4×C61—22no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C4⋊C4×C61C2311yescharacteristic
71C2×C4⋊C4×C61C2312yes—
72C2×C42×C61—21no—
73C2×C42×C61—21no—
74C2×C42×C61D412yes—
75C2×C42×C61C2311yescharacteristic
76#95×C61—21no—
77#95×C61—22no—
78#95×C61—22no—
79#95×C61C2312yes—
80C2×Q8×C61—22no—
81C2×Q8×C61—24no—
82C2×Q8×C61—22no—
83C2×Q8×C61—42no—
84C22×C4×C61—22no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D412yes—
90C22×C4×C61C2×D412yes—
91C22×C4×C61C2411yescharacteristic
92C2×Dic122—22no—
93C2×Dic122—24no—
94C2×Dic122C2×D414yes—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—24no—
97C4⋊C4×C61—22no—
98C4⋊C4×C61—44no—
99C4⋊C4×C61—42no—
100C4⋊C4×C61—44no—
101C42×C61—24no—
102C42×C61—22no—
103C42×C61—22no—
104C42×C61—41no—
105C42×C61—41no—
106C42×C61C2×D412yes—
107C42×C61C2×D412yes—
108C22⋊Dic61—24no—
109#11758202—48no—
110C4⋊Dic61—24no—
111C4⋊Dic61—24no—
112C4⋊Dic61—24no—
113C4⋊Dic61—22no—
114C4⋊Dic61—22no—
115C4⋊Dic61—22no—
116C4⋊Dic61C2×D414yes—
117#11758196—28no—
118#11758196—24no—
119#11758196—24no—
120C4×Dic61—28no—
121C4×Dic61—24no—
122C2×#92418—24no—
123C23×C61C22×D411yescharacteristic
124Q8×C61—28no—
125Q8×C61—24no—
126Q8×C61—42no—
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—22no—
131C2×C4×C61—24no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61#12012yes—
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12011yescharacteristic
145C2×C4×C61#13714yes—
146C2×C4×C61C22×D412yes—
147C2×Dic61—24no—
148C2×Dic61—24no—
149Dic122—44no—
150Dic122—44no—
151Dic122—84no—
152#92418—44no—
153#18189—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61C2×#12011yescharacteristic
157C22×C61C2×#13712yes—
158C4×C61—22no—
159C4×C61—24no—
160C4×C61—21no—
161C4×C61—22no—
162C4×C61—44no—
163C4×C61—42no—
164C4×C61—42no—
165C4×C61—81no—
166C4×C61#45612yes—
167Dic61—44no—
168Dic61—44no—
169#3502—611no—
170#3113—612no—
171#2399D6111yescharacteristic
172#1611—614no—
173#1605—614no—
174#1506—612no—
175#1467—611no—
176C2×C61—22no—
177C2×C61#300411yescharacteristic
178C2×C61C2×#45611yescharacteristic
179C2×C61#302511yescharacteristic
180Q82—1222no—
181#557—1224no—
182#557—1222no—
183#544—614no—
184#544—1221no—
185#533—612no—
186#533—1222no—
187#519—1221no—
188C2×C4×Q8C2×D6111yescharacteristic
189C2×C4×Q8C2×D6111yescharacteristic
190#483—614no—
191#475—1222no—
192#462—1222no—
193#451—614no—
194#441—1224no—
195#432—612no—
196#398—21no—
197#398C2×D6112yes—
198#395—21no—
199#395C2×D6112yes—
200C4×C4⋊C4—22no—
201#376C2×D6111yescharacteristic
202#328—618no—
203#324—614no—
204C61#1818911yescharacteristic, complemented, Sylow
205C22×Q8C22⋊D6111yescharacteristic
206C22×Q8C22×D6111yescharacteristic
207C2×Q16—1224no—
208C4⋊Q8—612no—
209C4⋊Q8—612no—
210C4⋊Q8—1222no—
211C4⋊Q8—1222no—
212C4⋊Q8—1228no—
213C4⋊Q8—1224no—
214#125—1224no—
215#125—1228no—
216#125—1224no—
217#125—1222no—
218C22⋊Q8—614no—
219C22⋊Q8—1222no—
220C22⋊Q8—1224no—
221C4×Q8—22no—
222C4×Q8—22no—
223C4×Q8—22no—
224C4×Q8—22no—
225C4×Q8—614no—
226C4×Q8—1224no—
227C4×Q8—1224no—
228C4×Q8—1224no—
229C4×Q8—1224no—
230C4×Q8—1222no—
231#117—1222no—
232#117—1224no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4C22⋊D6111yescharacteristic
237C2×C4⋊C4C22×D6111yescharacteristic
238C2×C4⋊C4C22×D6112yes—
239C2×C42—21no—
240C2×C42—21no—
241C2×C42C22⋊D6112yes—
242C2×C42C22×D6111yescharacteristic
243#106—1224no—
244C4⋊C8—1222no—
245#103—1224no—
246#103—1224no—
247C22⋊C8—614no—
248#97—1222no—
249#95—21no—
250#95—22no—
251#95—22no—
252#95C22×D6112yes—
253C2×Q8—22no—
254C2×Q8—24no—
255C2×Q8—22no—
256C2×Q8—42no—
257C2×Q8—614no—
258C2×Q8—1224no—
259C2×Q8—1222no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4C2×C22⋊D6111yescharacteristic
264C22×C4C2×C22⋊D6111yescharacteristic
265C22×C4C2×C22⋊D6112yes—
266C22×C4C2×C22⋊D6112yes—
267C22×C4C23×D6111yescharacteristic
268Q16—2448no—
269C2×C8—1224no—
270C4⋊C4—24no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—44no—
274C4⋊C4—42no—
275C4⋊C4—44no—
276C4⋊C4—614no—
277C4⋊C4—1228no—
278C4⋊C4—1224no—
279C4⋊C4—1224no—
280C4⋊C4—1224no—
281C4⋊C4—1224no—
282C4⋊C4—1224no—
283C4⋊C4—1222no—
284C4⋊C4—1222no—
285C4⋊C4—1222no—
286C22⋊C4—1224no—
287C42—24no—
288C42—22no—
289C42—22no—
290C42—41no—
291C42—41no—
292C42—1228no—
293C42—1224no—
294C42D4×D6112yes—
295C42D4×D6112yes—
296C23C22×C22⋊D6111yescharacteristic
297Q8—28no—
298Q8—24no—
299Q8—42no—
300Q8—4884no—
301Q8—2444no—
302Q8—2444no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—1224no—
319C2×C4—1224no—
320C2×C4#1451974511yescharacteristic
321C2×C4#1451974512yes—
322C2×C4#1451974511yescharacteristic
323C2×C4#1451980714yes—
324C2×C4C2×D4×D6112yes—
325C8—2444no—
326C22—21no—
327C22—21no—
328C22C2×#1451974511yescharacteristic
329C22C2×#1451980712yes—
330C4—21no—
331C4—22no—
332C4—22no—
333C4—24no—
334C4—44no—
335C4—42no—
336C4—42no—
337C4—81no—
338C4—2444no—
339C4—2444no—
340C4#1683994412yes—
341C2—22no—
342C2#2145505211yescharacteristic
343C2C2×#1683994411yescharacteristic
344C2#2145521011yescharacteristic
subgroupG/H
centerC22C2×#14519745
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2399C2
socleC22×C61C2×#120
prime radicalC23×C61C22×D4
hypercenter#2399D61
hypocenterC61#18189
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
204. C61#18189semidirect

Maximal subgroups

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

subgroupindex
#214596292
#214559492
#214448262
#214447922
#214443302
#214441632
C61×#23992
#1818961