Finite Group Databasebeta

← #29583204

Subgroups — #29583204

Order 15616.

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

normal subgroups only

This group has 390 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#21451471C211yesmaximal, characteristic, complemented
2#21446737C211yesmaximal, characteristic
3#21444367C211yesmaximal, characteristic
4#21444328C211yesmaximal, characteristic
5#21443711C211yesmaximal, characteristic, complemented
6#21443685C211yesmaximal, characteristic, complemented
7C61×#1285C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9C2×#14519705—21no—
10C2×#14519705—21no—
11C4×#11758194C2211yescharacteristic
12#16839695—21no—
13#16839695—21no—
14#16839660—21no—
15#16839659—21no—
16#16839649—21no—
17#16839646—21no—
18#16839630C2211yescharacteristic
19#16839608C2211yescharacteristic
20#16839497—21no—
21#16839497—21no—
22#16839497—21no—
23#16839497—21no—
24C61×#432C2211yescharacteristic
25C61×#432C2211yescharacteristic
26C4×C4⋊C4×C61C2211yescharacteristic
27C2×#11758222—21no—
28C2×#11758194—21no—
29#14519777Q811yescharacteristic
30#14519774Q811yescharacteristic
31#14519765—21no—
32#14519751—21no—
33#14519751—21no—
34C4×D244—21no—
35C4×D244—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×C4×Dic61—21no—
43#14519705—42no—
44#14519705—42no—
45#14519688—21no—
46C4×#92418—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684D411yescharacteristic
53#14519684D411yescharacteristic
54#14519684D411yescharacteristic
55#14519684D411yescharacteristic
56C2×C4⋊C4×C61—21no—
57C2×C42×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#97×C61—21no—
65#97×C61—21no—
66#95×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C2×C22⋊D61—41no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77#11758222—41no—
78#11758222—41no—
79#11758222—41no—
80#11758222—41no—
81C2×D244—21no—
82C2×D244—21no—
83C2×D244—21no—
84C2×C4×D61—41no—
85C2×Dic122—21no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C4⋊C4×C61—42no—
89C42×C61—41no—
90C42×C61—41no—
91C42×C61C2×Q811yescharacteristic
92C42×C61#4111yescharacteristic
93C42×C61#4111yescharacteristic
94C42×C61#4111yescharacteristic
95#11758198—41no—
96#11758198—41no—
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61—42no—
100C4⋊Dic61—81no—
101#11758196—42no—
102#11758196—42no—
103#11758196—42no—
104#11758196—81no—
105C4×Dic61—42no—
106#11758194—22no—
107#11758194—41no—
108C2×#92418—41no—
109C23×C61#12011yescharacteristic
110C22×D61—41no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—22no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61C22⋊Q811yescharacteristic
122C2×C4×C61C22⋊Q811yescharacteristic
123C2×C4×C61C22⋊Q811yescharacteristic
124C2×C4×C61#12411yescharacteristic
125C2×C4×C61#12411yescharacteristic
126C2×C4×C61#12411yescharacteristic
127C22⋊D61—81no—
128C22⋊D61—81no—
129C2×Dic61—22no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142D244—41no—
143D244—41no—
144D244—81no—
145D244—81no—
146C4×D61—81no—
147C4×D61—81no—
148Dic122—41no—
149Dic122—41no—
150C8×C61—81no—
151C8×C61—81no—
152#92418—42no—
153#10380—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—21no—
156C22×C61#39311yescharacteristic
157C22×C61#45311yescharacteristic
158C22×C61#45411yescharacteristic
159C2×D61—81no—
160C2×D61—81no—
161C2×D61—81no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—42no—
169C4×C61—81no—
170Dic61—42no—
171Dic61—81no—
172Dic61—81no—
173Dic61—81no—
174Dic61—81no—
175#2606—611no—
176#1980—611no—
177#1514—611no—
178#1505—611no—
179#1300—611no—
180#1288—611no—
181#1285D6111yescharacteristic, complemented
182C2×C61—21no—
183C2×C61—21no—
184C2×C61#202711yescharacteristic
185C2×C61#203111yescharacteristic
186C2×C61#203111yescharacteristic
187D61—161no—
188#532—611no—
189#432C2×D6111yescharacteristic
190#432C2×D6111yescharacteristic
191C2×#104—1221no—
192C2×#104—1221no—
193C4×M16—611no—
194#398—1221no—
195#398—1221no—
196#389—1221no—
197#389—1221no—
198#387—1221no—
199#387—1221no—
200#383—611no—
201C4×C4⋊C4C2×D6111yescharacteristic
202#376—611no—
203#327—1221no—
204#327—1221no—
205#327—1221no—
206#327—1221no—
207C61#1038011yescharacteristic, complemented, Sylow
208C2×#41—1221no—
209C2×M16—1221no—
210C4⋊Q8—611no—
211#127—611no—
212#124—1221no—
213#121—1221no—
214#121—1221no—
215C4×D4—1221no—
216C4×D4—1221no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C42—1221no—
225C2×C42D24411yescharacteristic
226C2×C42D24411yescharacteristic
227C2×C42C22×D6111yescharacteristic
228C4⋊C8—21no—
229C4⋊C8—21no—
230#104—2442no—
231#104—2442no—
232C22⋊C8—21no—
233C22⋊C8—21no—
234#97—21no—
235#97—21no—
236#97—1221no—
237C4×C8—1221no—
238#95—21no—
239#95—611no—
240#95—611no—
241#95—611no—
242#95—611no—
243#95—1221no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247#95—1221no—
248#41—2441no—
249#41—2441no—
250#41—2441no—
251#41—2441no—
252C2×Q8—1221no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—2441no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—2441no—
264C22×C4C2×D24411yescharacteristic
265C22×C4D4×D6111yescharacteristic
266C22×C4D4×D6111yescharacteristic
267M16—1222no—
268M16—2441no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—2441no—
272C4⋊C4—42no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—4881no—
276C4⋊C4—4881no—
277C4⋊C4—2442no—
278C4⋊C4—2442no—
279C4⋊C4—2442no—
280C4⋊C4—2442no—
281C22⋊C4—2441no—
282C22⋊C4—2441no—
283C42—41no—
284C42—41no—
285C42—2442no—
286C42#1175822211yescharacteristic
287C42#1175822211yescharacteristic
288C42#1175822411yescharacteristic
289C42Q8×D6111yescharacteristic
290C23—2441no—
291C23#1451974711yescharacteristic
292Q8—2441no—
293Q8—2441no—
294D4—4881no—
295D4—4881no—
296D4—4881no—
297D4—4881no—
298D4—2441no—
299D4—2441no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—1222no—
311C2×C4—4881no—
312C2×C4—4881no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4#1451975511yescharacteristic
326C2×C4#1451975511yescharacteristic
327C2×C4#1451975711yescharacteristic
328C2×C4#1451976311yescharacteristic
329C2×C4#1451976311yescharacteristic
330C2×C4#1451976511yescharacteristic
331C8—81no—
332C8—81no—
333C8—2442no—
334C22—21no—
335C22—21no—
336C22—4881no—
337C22—4881no—
338C22—4881no—
339C22#1683967511yescharacteristic
340C22#1683993211yescharacteristic
341C22#1683993711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—81no—
350C4—4881no—
351C4—4881no—
352C4—4881no—
353C4—4881no—
354C4—2442no—
355C2—21no—
356C2—21no—
357C2—9761no—
358C2#2144697611yescharacteristic
359C2#2144699011yescharacteristic
360C2#2144699211yescharacteristic
subgroupG/H
centerC22#16839675
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1285C2
socleC22×C61#393
prime radical#16840312C22
hypercenter#1285D61
hypocenterC61#10380
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
1. #21451471C2semidirect
5. #21443711C2semidirect
6. #21443685C2semidirect
7. C61×#1285C2semidirect
181. #1285D61semidirect
207. C61#10380semidirect

Maximal subgroups

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

subgroupindex
#214514712
#214467372
#214443672
#214443282
#214437112
#214436852
C61×#12852
#1038061