Finite Group Databasebeta

← #29576951

Subgroups — #29576951

Order 15616.

530 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 93 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#21455911C211yesmaximal, characteristic
2#21448463C211yesmaximal, characteristic, complemented
3#21446738C211yesmaximal, characteristic, complemented
4#21444326C211yesmaximal, characteristic, complemented
5#21444263C211yesmaximal, characteristic, complemented
6#21443676C211yesmaximal, characteristic, complemented
7C61×#1300C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9C2×C4×D244C2211yescharacteristic
10#16840081—21no—
11#16840053C412yescomplemented
12#16839958C412yescomplemented
13#16839898—21no—
14#16839875—22no—
15#16839819C2211yescharacteristic
16C2×#14519703—22no—
17#16839664—21no—
18#16839660—21no—
19#16839651—22no—
20#16839624—21no—
21#16839621—21no—
22C4×C4⋊Dic61C2211yescharacteristic
23#16839495—21no—
24#16839495—21no—
25#16839491—22no—
26C61×#432C2211yescharacteristic
27C4×M16×C61C2211yescharacteristic
28C61×#376C2211yescharacteristic
29C2×#11758222—21no—
30C22×D244D411yescharacteristic
31C22×C4×D61—21no—
32C2×D488—22no—
33#14519777C2×C411yescharacteristic
34#14519774C2×C411yescharacteristic
35#14519765—21no—
36#14519751—21no—
37#14519751—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244C2×C412yes—
43C4×D244D412yes—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758196—22no—
47C2×#11758198—21no—
48C2×#11758198—22no—
49C2×#11758198—22no—
50C2×C4×Dic61D412yes—
51#14519709—22no—
52C4⋊#92418—21no—
53#14519703—44no—
54#14519699—22no—
55#14519699—22no—
56C22⋊#92418—21no—
57#14519688—21no—
58#14519684—22no—
59#14519684—21no—
60C2×M16×C61—21no—
61C2×C42×C61—21no—
62C2×C42×C61C2311yescharacteristic
63C4⋊C8×C61C2×C412yes—
64C22⋊C8×C61—21no—
65#97×C61—21no—
66#97×C61—21no—
67C4×C8×C61—21no—
68#95×C61—21no—
69#95×C61D411yescharacteristic
70#95×C61D411yescharacteristic
71C23×D61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C2×C22⋊D61—41no—
78C22×Dic61—21no—
79C22×Dic61—22no—
80#11758222—42no—
81#11758222—42no—
82C2×D244—21no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—21no—
86C2×D244—42no—
87C2×D244C22⋊C412yes—
88C2×C4×D61—22no—
89C2×C4×D61—22no—
90C2×C4×D61—41no—
91C2×C4×D61—82no—
92C2×Dic122—21no—
93M16×C61—22no—
94M16×C61—41no—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C42×C61—42no—
98C42×C61C22×C411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102#11758198—22no—
103#11758198—22no—
104#11758198—41no—
105#11758198—41no—
106#11758198—82no—
107#11758198—82no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—42no—
112C4⋊Dic61C22⋊C412yes—
113#11758196—82no—
114C4×Dic61—42no—
115C2×#92418—41no—
116D488—44no—
117C23×C61#12011yescharacteristic
118C22×D61—22no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61—41no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—22no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61C2×C22⋊C411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12311yescharacteristic
140C22⋊D61—81no—
141C22⋊D61—81no—
142C2×Dic61—22no—
143C2×Dic61—42no—
144C2×Dic61—42no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148D244—22no—
149D244—22no—
150D244—42no—
151D244—42no—
152D244—42no—
153D244—81no—
154C4×D61—82no—
155C4×D61—82no—
156C4×D61—82no—
157Dic122—42no—
158C8×C61—42no—
159C8×C61—42no—
160#92418—81no—
161#9329—611nomaximal, Sylow
162C22×C61—21no—
163C22×C61—21no—
164C22×C61#38611yescharacteristic
165C22×C61#45311yescharacteristic
166C22×C61#45411yescharacteristic
167C2×D61—42no—
168C2×D61—42no—
169C2×D61—42no—
170C2×D61—82no—
171C2×D61—82no—
172C2×D61—81no—
173C2×D61—81no—
174C2×D61—81no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—81no—
181C4×C61—81no—
182C4×C61#42112yes—
183Dic61—42no—
184Dic61—82no—
185Dic61—81no—
186#3109—611no—
187#2319—611no—
188#1980—611no—
189#1505—611no—
190#1490—611no—
191#1300D6111yescharacteristic, complemented
192#1285—611no—
193C2×C61—21no—
194C2×C61—21no—
195C2×C61#188311yescharacteristic
196C2×C61#189711yescharacteristic
197C2×C61#190411yescharacteristic
198D61—82no—
199D61—161no—
200#532—611no—
201C2×C4×D4—611no—
202#481—1221no—
203#476—612no—
204#459—612no—
205#447—1221no—
206#442—1222no—
207#432—611no—
208#432C2×D6111yescharacteristic
209C2×#104—1222no—
210C4×M16C2×D6111yescharacteristic
211#390—1221no—
212#389—1221no—
213#388—1222no—
214#381—1221no—
215#380—1221no—
216C4×C4⋊C4—611no—
217#376C2×D6111yescharacteristic
218#327—1221no—
219#327—1221no—
220D4⋊C8—1222no—
221C61#932911yescharacteristic, complemented, Sylow
222C2×#41—1221no—
223C22×D4—611no—
224C23×C4—1221no—
225C2×D8—1222no—
226C2×M16—21no—
227C4⋊Q8—611no—
228#127—611no—
229#124—1221no—
230#121—1221no—
231#121—1221no—
232C4×D4—612no—
233C4×D4—612no—
234C4×D4—1221no—
235C4×D4—1221no—
236C4×D4—1221no—
237C4×D4—1221no—
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1222no—
240C2×C4⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—1222no—
244C2×C42—21no—
245C2×C42—612no—
246C2×C42C22×D6111yescharacteristic
247#106—1222no—
248C4⋊C8—1221no—
249C4⋊C8C4×D6112yes—
250#104—2444no—
251#102—1222no—
252#102—1222no—
253C22⋊C8—21no—
254C22⋊C8—1221no—
255#97—21no—
256#97—21no—
257#97—1221no—
258C4×C8—21no—
259#95—21no—
260#95—1222no—
261#95—1221no—
262#95D24411yescharacteristic
263#95D24411yescharacteristic
264C24—1221no—
265#41—2442no—
266#41—2442no—
267C2×Q8—1221no—
268C2×D4—612no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—2442no—
274C2×D4—2441no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—1221no—
278C22×C4—1222no—
279C22×C4—1222no—
280C22×C4—1222no—
281C22×C4—4882no—
282C22×C4—2441no—
283C22×C4C2×D24411yescharacteristic
284C22×C4D4×D6111yescharacteristic
285C22×C4D4×D6111yescharacteristic
286D8—2444no—
287M16—22no—
288M16—41no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—2441no—
292C4⋊C4—612no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—4882no—
297C4⋊C4—2442no—
298C22⋊C4—1222no—
299C22⋊C4—1222no—
300C22⋊C4—4882no—
301C22⋊C4—4882no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C42—42no—
305C42—2442no—
306C42C2×C4×D6111yescharacteristic
307C42#1175822211yescharacteristic
308C42D4×D6111yescharacteristic
309C42#1175822611yescharacteristic
310C23—1222no—
311C23—2442no—
312C23—2442no—
313C23—2441no—
314C23—2441no—
315C23—2441no—
316C23#1451974711yescharacteristic
317Q8—2442no—
318D4—1222no—
319D4—1222no—
320D4—4881no—
321D4—4881no—
322D4—4881no—
323D4—2442no—
324D4—2442no—
325D4—2442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—1222no—
337C2×C4—4882no—
338C2×C4—4882no—
339C2×C4—4882no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2441no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4C22⋊C4×D6111yescharacteristic
346C2×C4#1451973911yescharacteristic
347C2×C4C4×D24411yescharacteristic
348C2×C4#1451975011yescharacteristic
349C2×C4#1451975211yescharacteristic
350C2×C4#1451976211yescharacteristic
351C8—42no—
352C8—42no—
353C8—4881no—
354C22—21no—
355C22—21no—
356C22—4882no—
357C22—4882no—
358C22—4881no—
359C22—4881no—
360C22—4881no—
361C22—2442no—
362C22—2442no—
363C22—2442no—
364C22#1683964011yescharacteristic
365C22#1683993111yescharacteristic
366C22#1683993611yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—81no—
373C4—81no—
374C4—4882no—
375C4—4881no—
376C4—2442no—
377C4#1683977712yes—
378C2—21no—
379C2—21no—
380C2—9761no—
381C2—4882no—
382C2#2144619611yescharacteristic
383C2#2144626611yescharacteristic
384C2#2144630511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1300C2
socleC22×C61#386
prime radical#21455911C2
cosocleC2×C42×C61C23
hypercenter#1300D61
hypocenterC61#9329
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
2. #21448463C2semidirect
3. #21446738C2semidirect
4. #21444326C2semidirect
5. #21444263C2semidirect
6. #21443676C2semidirect
7. C61×#1300C2semidirect
11. #16840053C4semidirect
12. #16839958C4semidirect
191. #1300D61semidirect
221. C61#9329semidirect

Maximal subgroups

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

subgroupindex
#214559112
#214484632
#214467382
#214443262
#214442632
#214436762
C61×#13002
#932961