Finite Group Databasebeta

← #29590523

Subgroups — #29590523

Order 15616.

446 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 73 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#21450107C211yesmaximal, characteristic
2#343×D61C211yesmaximal, characteristic
3#21444147C211yesmaximal, characteristic
4#21443846C211yesmaximal, characteristic, complemented
5#21443826C211yesmaximal, characteristic, complemented
6#21443824C211yesmaximal, characteristic, complemented
7C61×#1353C211yesmaximal, characteristic, complemented
8C2×M16×D61—21no—
9C2×#14519735C411yescharacteristic
10C2×C4⋊C4×D61C2211yescharacteristic
11#16839724—21no—
12#16839700C411yescharacteristic
13#16839694C411yescharacteristic
14#16839692C2211yescharacteristic
15#16839649—21no—
16#16839645—21no—
17#16839636—21no—
18#16839624—21no—
19#16839624C411yescharacteristic
20#16839531C2211yescharacteristic
21#16839530—21no—
22#16839488C2211yescharacteristic
23#16839487—21no—
24C61×#400C2211yescharacteristic
25C61×#343C2211yescharacteristic
26C61×#324C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28C22×C4×D61D411yescharacteristic
29C22×C4×D61D411yescharacteristic
30C2×#11758194—21no—
31C2×#11758189—41no—
32C2×#11758189—41no—
33M16×D61—24no—
34M16×D61—42no—
35C2×C8×D61—41no—
36#14519735—41no—
37#14519735—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×#11758196—21no—
42C2×#11758196C2×C411yescharacteristic
43C2×#11758196D411yescharacteristic
44C4⋊C4×D61—41no—
45C4⋊C4×D61—41no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×C4×Dic61—21no—
49C22⋊#92418—21no—
50#14519689—41no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684C2×C411yescharacteristic
57C2×M16×C61—21no—
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C4⋊C4×C61C2311yescharacteristic
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61—21no—
63#95×C61C2×C411yescharacteristic
64C23×D61C22⋊C411yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C22⋊C411yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—42no—
85C2×C4×D61—42no—
86M16×C61—22no—
87M16×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92#11758198—42no—
93#11758198—41no—
94#11758198—41no—
95C4⋊Dic61—41no—
96C4⋊Dic61—42no—
97C4⋊Dic61—41no—
98#11758196—41no—
99#11758196—41no—
100#11758196—41no—
101#11758196—41no—
102C4×Dic61—42no—
103#11758194—22no—
104#11758194—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107#11758189—44no—
108#11758189—82no—
109C8×D61—44no—
110C23×C61C2×C22⋊C411yescharacteristic
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—22no—
114C22×D61—41no—
115C22×D61#9911yescharacteristic
116C22×D61#9911yescharacteristic
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—42no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C61#13711yescharacteristic
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61#10412yes—
143C4×D61—22no—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—22no—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61—42no—
150C4×D61—81no—
151C8×C61—42no—
152C8×C61—81no—
153#92418—42no—
154#92418—81no—
155#11764—611nomaximal, Sylow
156C22×C61—21no—
157C22×C61—21no—
158C22×C61C2×#9911yescharacteristic
159C22×C61#41711yescharacteristic
160C22×C61C2×#10411yescharacteristic
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—21no—
166C2×D61—42no—
167C2×D61—42no—
168C2×D61#35212yes—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—81no—
174C4×C61—81no—
175Dic61—22no—
176Dic61—41no—
177Dic61—41no—
178Dic61—81no—
179Dic61—81no—
180#2484—611no—
181C2×#343—611no—
182#1463—611no—
183#1353—611no—
184#1353D6111yescharacteristic, complemented
185#1346—611no—
186#1346—611no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61#150411yescharacteristic
190C2×C61C2×#35211yescharacteristic
191C2×C61#213311yescharacteristic
192D61—22no—
193D61—41no—
194C22×M16—1221no—
195C2×#117—611no—
196C22×C4⋊C4—611no—
197#407—1221no—
198#400—611no—
199#400C2×D6111yescharacteristic
200#398—611no—
201#398—611no—
202#387—1221no—
203#387—1221no—
204#385—1221no—
205#381—611no—
206#381—1221no—
207#343—611no—
208#343—1221no—
209#343C2×D6111yescharacteristic
210#324—611no—
211#324—1221no—
212#324C2×D6111yescharacteristic
213C61#1176411yescharacteristic, complemented, Sylow
214C23×C4—611no—
215C23×C4—611no—
216C23×C4—611no—
217C2×M16—21no—
218C2×M16—1224no—
219C2×M16—1221no—
220C2×M16—2441no—
221C2×M16—2441no—
222C2×M16—2442no—
223C22×C8—2441no—
224#117—2441no—
225#117—2441no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C4⋊C4—611no—
230C2×C4⋊C4—1221no—
231C2×C4⋊C4—1221no—
232C2×C4⋊C4—2441no—
233C2×C4⋊C4—2441no—
234C2×C4⋊C4C4×D6111yescharacteristic
235C2×C4⋊C4C22×D6111yescharacteristic
236C2×C22⋊C4—1221no—
237C2×C22⋊C4—1221no—
238C2×C42—1221no—
239C22⋊C8—21no—
240C22⋊C8—1221no—
241C22⋊C8—2441no—
242#95—21no—
243#95—21no—
244#95—611no—
245#95—1221no—
246#95—1221no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250#95C4×D6111yescharacteristic
251C24—611no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1222no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—2442no—
269C22×C4—2442no—
270C22×C4C2×C4×D6111yescharacteristic
271C22×C4D4×D6111yescharacteristic
272C22×C4D4×D6111yescharacteristic
273M16—22no—
274M16—41no—
275M16—1222no—
276M16—4882no—
277M16—2444no—
278M16—2441no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—2444no—
282C2×C8—2441no—
283C2×C8—2441no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C4⋊C4—2441no—
290C4⋊C4—2442no—
291C4⋊C4—2441no—
292C4⋊C4—2441no—
293C22⋊C4—2441no—
294C22⋊C4—2441no—
295C22⋊C4—2442no—
296C42—2442no—
297C23—611no—
298C23—611no—
299C23—1222no—
300C23—1221no—
301C23—1221no—
302C23—2441no—
303C23C22⋊C4×D6111yescharacteristic
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—612no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—4881no—
325C2×C4—2442no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4#1451980411yescharacteristic
337C2×C4#1451980911yescharacteristic
338C8—42no—
339C8—81no—
340C8—4881no—
341C8—2442no—
342C22—21no—
343C22—21no—
344C22—612no—
345C22—1221no—
346C22—1221no—
347C22—1221no—
348C22—1221no—
349C22—1221no—
350C22—2442no—
351C22—2442no—
352C22#99×D6111yescharacteristic
353C22#1683976211yescharacteristic
354C22#104×D6111yescharacteristic
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—81no—
360C4—81no—
361C4—1222no—
362C4—4881no—
363C4—4881no—
364C4—2441no—
365C4—2441no—
366C2—21no—
367C2—21no—
368C2—1222no—
369C2—2441no—
370C2#2144432211yescharacteristic
371C2#352×D6111yescharacteristic
372C2#2144750511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1353C2
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1353D61
hypocenterC61#11764
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1353

Complements

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

NH ≅ G/Ntype
4. #21443846C2semidirect
5. #21443826C2semidirect
6. #21443824C2semidirect
7. C61×#1353C2semidirect
184. #1353D61semidirect
213. C61#11764semidirect

Maximal subgroups

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

subgroupindex
#214501072
#343×D612
#214441472
#214438462
#214438262
#214438242
C61×#13532
#1176461