Finite Group Databasebeta

← #29590925

Subgroups — #29590925

Order 15616.

396 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 71 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#21445898C211yesmaximal, characteristic
3#324×D61C211yesmaximal, characteristic
4#21443846C211yesmaximal, characteristic, complemented
5#21443826C211yesmaximal, characteristic, complemented
6#21443824C211yesmaximal, characteristic, complemented
7C61×#1353C211yesmaximal, characteristic, complemented
8C2×#14519735C411yescharacteristic
9C2×C4⋊C4×D61C2211yescharacteristic
10#16839725—21no—
11C22⋊C8×D61—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×C8×D61—41no—
32#14519735—41no—
33#14519735—41no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61C2×C411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196C2×C411yescharacteristic
39C2×#11758196D411yescharacteristic
40C4⋊C4×D61—41no—
41C4⋊C4×D61—41no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×C4×Dic61—21no—
45C22⋊#92418—21no—
46#14519689—41no—
47#14519689—41no—
48#14519689—41no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684C2×C411yescharacteristic
55C2×M16×C61—21no—
56C2×C4⋊C4×C61C2×C411yescharacteristic
57C2×C4⋊C4×C61C2311yescharacteristic
58C22⋊C8×C61—21no—
59#95×C61—21no—
60#95×C61—21no—
61#95×C61C2×C411yescharacteristic
62C23×D61C22⋊C411yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61C22⋊C411yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—41no—
82C2×C4×D61—42no—
83C2×C4×D61—42no—
84M16×C61—41no—
85M16×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90#11758198—42no—
91#11758198—41no—
92#11758198—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—42no—
95C4⋊Dic61—41no—
96#11758196—41no—
97#11758196—41no—
98#11758196—41no—
99#11758196—41no—
100C4×Dic61—42no—
101#11758194—41no—
102#11758194—41no—
103C2×#92418—41no—
104C2×#92418—41no—
105C8×D61—82no—
106C23×C61C2×C22⋊C411yescharacteristic
107C22×D61—21no—
108C22×D61—21no—
109C22×D61—22no—
110C22×D61—41no—
111C22×D61#9911yescharacteristic
112C22×D61#9911yescharacteristic
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—42no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61#13511yescharacteristic
125C2×C4×C61#13511yescharacteristic
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C4×D61—41no—
140C4×D61—41no—
141C4×D61—41no—
142C4×D61—41no—
143C4×D61—42no—
144C4×D61—42no—
145C4×D61—42no—
146C4×D61—81no—
147C8×C61—81no—
148C8×C61—81no—
149#92418—81no—
150#92418—81no—
151#11850—611nomaximal, Sylow
152C22×C61—21no—
153C22×C61—21no—
154C22×C61C2×#9911yescharacteristic
155C22×C61#41611yescharacteristic
156C22×C61#42111yescharacteristic
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—21no—
161C2×D61—21no—
162C2×D61—42no—
163C2×D61—42no—
164C2×D61#35212yes—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—81no—
170C4×C61—81no—
171Dic61—41no—
172Dic61—41no—
173Dic61—41no—
174Dic61—81no—
175Dic61—81no—
176#2484—611no—
177#1821—611no—
178C2×#324—611no—
179#1353—611no—
180#1353D6111yescharacteristic, complemented
181#1346—611no—
182#1346—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61#151611yescharacteristic
186C2×C61C2×#35211yescharacteristic
187C2×C61#213311yescharacteristic
188D61—22no—
189D61—41no—
190C2×#117—611no—
191C22×C4⋊C4—611no—
192#407—1221no—
193C2×C22⋊C8—1221no—
194#400—611no—
195#400C2×D6111yescharacteristic
196#398—611no—
197#398—611no—
198#387—1221no—
199#387—1221no—
200#385—1221no—
201#381—611no—
202#381—1221no—
203#343—611no—
204#343—1221no—
205#343C2×D6111yescharacteristic
206#324—611no—
207#324—1221no—
208#324C2×D6111yescharacteristic
209C61#1185011yescharacteristic, complemented, Sylow
210C23×C4—611no—
211C23×C4—611no—
212C23×C4—611no—
213C2×M16—21no—
214C2×M16—1221no—
215C22×C8—2441no—
216#117—2441no—
217#117—2441no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—2441no—
225C2×C4⋊C4—2441no—
226C2×C4⋊C4C4×D6111yescharacteristic
227C2×C4⋊C4C22×D6111yescharacteristic
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C42—1221no—
231C22⋊C8—21no—
232C22⋊C8—1221no—
233C22⋊C8—2441no—
234C22⋊C8—2441no—
235C22⋊C8—2441no—
236#95—21no—
237#95—21no—
238#95—611no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95C4×D6111yescharacteristic
245C24—611no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—2441no—
262C22×C4—2442no—
263C22×C4—2442no—
264C22×C4C2×C4×D6111yescharacteristic
265C22×C4D4×D6111yescharacteristic
266C22×C4D4×D6111yescharacteristic
267M16—41no—
268M16—41no—
269M16—2441no—
270M16—2441no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—4882no—
274C2×C8—2441no—
275C2×C8—2441no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2442no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C22⋊C4—2442no—
288C42—2442no—
289C23—611no—
290C23—611no—
291C23—1222no—
292C23—1221no—
293C23—1221no—
294C23—2441no—
295C23C22⋊C4×D6111yescharacteristic
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—4881no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2442no—
318C2×C4—2442no—
319C2×C4—2442no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4#1451979811yescharacteristic
329C2×C4#1451980011yescharacteristic
330C8—81no—
331C8—81no—
332C8—4881no—
333C8—4881no—
334C22—21no—
335C22—21no—
336C22—612no—
337C22—1221no—
338C22—1221no—
339C22—1221no—
340C22—1221no—
341C22—1221no—
342C22—2442no—
343C22—2442no—
344C22#99×D6111yescharacteristic
345C22#1683975711yescharacteristic
346C22#1683977711yescharacteristic
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—4881no—
354C4—4881no—
355C4—2441no—
356C4—2441no—
357C4—2441no—
358C2—21no—
359C2—21no—
360C2—1222no—
361C2—2441no—
362C2#2144437411yescharacteristic
363C2#352×D6111yescharacteristic
364C2#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#11850
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
180. #1353D61semidirect
209. C61#11850semidirect

Maximal subgroups

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

subgroupindex
#214501072
#214458982
#324×D612
#214438462
#214438262
#214438242
C61×#13532
#1185061