Finite Group Databasebeta

← #29576780

Subgroups — #29576780

Order 15616.

542 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455283C211yesmaximal, characteristic
2#21454843C211yesmaximal, characteristic, complemented
3#21444378C211yesmaximal, characteristic, complemented
4#21444217C211yesmaximal, characteristic, complemented
5#21443716C211yesmaximal, characteristic, complemented
6#21443677C211yesmaximal, characteristic, complemented
7C61×#1804C211yesmaximal, characteristic, complemented
8C2×#14519803—21no—
9#16840312C2211yescharacteristic
10#16839977—22no—
11#16839967C412yescomplemented
12#16839957C412yescomplemented
13D4×#92418—22no—
14D4×#92418—22no—
15#16839815C2211yescharacteristic
16#16839815C2211yescharacteristic
17#16839786C2211yescharacteristic
18#16839761—21no—
19C2×C22⋊#92418—22no—
20#16839495—22no—
21#16839489—22no—
22C2×C4×D4×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×#102×C61—21no—
25C61×#382C2211yescharacteristic
26C61×#340—21no—
27C2×#11758222—21no—
28#14519803—42no—
29#14519803—42no—
30C2×#11758200—22no—
31C2×#11758199—22no—
32C2×#11758194—21no—
33C22×#92418—24no—
34#14519777C2×C411yescharacteristic
35#14519774C2×C411yescharacteristic
36#14519765—21no—
37#14519751—21no—
38#14519751—21no—
39C4×D244—21no—
40C4×D244—21no—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418C2×C412yes—
45#14519700—22no—
46#14519697—22no—
47C22⋊#92418—24no—
48C22⋊#92418—21no—
49C22⋊#92418D412yes—
50C4×#92418—21no—
51C4×#92418D412yes—
52C22×D4×C61D411yescharacteristic
53C23×C4×C61—21no—
54C22×C8×C61—21no—
55C4×D4×C61—21no—
56C4×D4×C61—21no—
57C4×D4×C61C2×C412yes—
58C4×D4×C61D412yes—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61D411yescharacteristic
61C2×C22⋊C4×C61—21no—
62C2×C42×C61C2311yescharacteristic
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65#102×C61—42no—
66#95×C61—21no—
67#95×C61—21no—
68C24×C61—21no—
69C2×D4×C61—21no—
70C2×D4×C61—21no—
71C2×D4×C61—21no—
72C2×D4×C61C22⋊C412yes—
73C2×D4×C61D812yes—
74C2×D4×C61SD1612yes—
75C22×C4×C61—21no—
76C22×C4×C61—22no—
77C22×C4×C61—22no—
78C22×C4×C61—41no—
79C22×C4×C61—82no—
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C2×C22⋊D61—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87#11758222—41no—
88C2×D244—21no—
89C2×D244—21no—
90C2×D244—21no—
91C2×C4×D61—41no—
92C2×Dic122—21no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C4⋊C4×C61—21no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61C22⋊C412yes—
100C22⋊C4×C61—22no—
101C22⋊C4×C61—22no—
102C42×C61C22×C411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61C2×D411yescharacteristic
105C42×C61#4111yescharacteristic
106#11758200—44no—
107#11758199—44no—
108#11758198—41no—
109#11758198—41no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112#11758194—41no—
113#11758194—41no—
114C2×#92418—22no—
115C2×#92418—22no—
116C2×#92418—22no—
117C2×#92418—84no—
118C23×C61—22no—
119C23×C61—22no—
120C23×C61—22no—
121C23×C61—81no—
122C23×C61—81no—
123C23×C61#12111yescharacteristic
124C22×D61—41no—
125D4×C61—22no—
126D4×C61—22no—
127D4×C61—22no—
128D4×C61#10214yes—
129C2×C4×C61—22no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—44no—
133C2×C4×C61—82no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12311yescharacteristic
144C2×C4×C61C2×D811yescharacteristic
145C2×C4×C61C2×SD1611yescharacteristic
146C2×C4×C61#13511yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C22⋊D61—81no—
149C22⋊D61—81no—
150C2×Dic61—41no—
151D244—42no—
152D244—41no—
153D244—41no—
154D244—81no—
155C4×D61—81no—
156C4×D61—81no—
157Dic122—41no—
158Dic122—41no—
159C8×C61—81no—
160#92418—42no—
161#92418—42no—
162#92418—42no—
163#9305—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—24no—
167C22×C61—42no—
168C22×C61—42no—
169C22×C61—82no—
170C22×C61—82no—
171C22×C61#38611yescharacteristic
172C22×C61#46511yescharacteristic
173C22×C61#46611yescharacteristic
174C2×D61—81no—
175C2×D61—81no—
176C2×D61—81no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—21no—
181C4×C61—42no—
182C4×C61—161no—
183C4×C61C2×#10211yescharacteristic
184C4×C61#41611yescharacteristic
185C4×C61#46511yescharacteristic
186C4×C61#46611yescharacteristic
187Dic61—81no—
188#3036—611no—
189#2972—611no—
190#1804D6111yescharacteristic, complemented
191#1517—611no—
192#1480—611no—
193#1301—611no—
194#1286—611no—
195C2×C61—21no—
196C2×C61—21no—
197C2×C61—44no—
198C2×C61#188111yescharacteristic
199C2×C61#189311yescharacteristic
200C2×C61#190411yescharacteristic
201D61—161no—
202C2×AGL(1,ℤ/8)—1221no—
203#532—611no—
204C2×C4×D4C2×D6111yescharacteristic
205#463—1222no—
206#461—612no—
207#459—612no—
208C8×D4—1222no—
209C8×D4—1222no—
210#431—611no—
211#431—611no—
212#423—611no—
213C2×C4⋊C8C2×D6111yescharacteristic
214#417—1221no—
215C2×#102—21no—
216C2×C22⋊C8—1222no—
217#382C2×D6111yescharacteristic
218#340—21no—
219#327—1222no—
220D4⋊C8—1222no—
221C61#930511yescharacteristic, complemented, Sylow
222C2×#41—1221no—
223C22×D4C22⋊D6111yescharacteristic
224C23×C4—21no—
225AGL(1,ℤ/8)—2442no—
226AGL(1,ℤ/8)—2442no—
227C2×SD16—1222no—
228C2×D8—1222no—
229C2×M16—1221no—
230C22×C8—21no—
231C22×C8—1224no—
232C4⋊Q8—611no—
233#127—611no—
234#124—1221no—
235#121—1221no—
236#121—1221no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—1221no—
240C4×D4—1221no—
241C4×D4C4×D6112yes—
242C4×D4D24412yes—
243C2×C4⋊C4—21no—
244C2×C4⋊C4C22⋊D6111yescharacteristic
245C2×C22⋊C4—21no—
246C2×C42C22×D6111yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—612no—
250C4⋊C8—1221no—
251C4⋊C8—1221no—
252C4⋊C8—1221no—
253#103—1222no—
254#102—42no—
255#102—1222no—
256C22⋊C8—612no—
257C22⋊C8—1224no—
258C22⋊C8—1221no—
259C4×C8—612no—
260C4×C8—1221no—
261#95—21no—
262#95—21no—
263C24—21no—
264#41—2441no—
265#41—2441no—
266#41—2441no—
267#41—2441no—
268C2×Q8—1221no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—2441no—
276C2×D4#1175819812yes—
277C2×D4#1175819912yes—
278C2×D4#1175820112yes—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—82no—
284C22×C4—2441no—
285C22×C4D4×D6111yescharacteristic
286C22×C4#1175822411yescharacteristic
287C22×C4C2×C22⋊D6111yescharacteristic
288SD16—2444no—
289D8—2444no—
290M16—2441no—
291M16—2441no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—1222no—
296C2×C8—1222no—
297C2×C8—1222no—
298C2×C8—4884no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C4⋊C4#1175819812yes—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C42C2×C4×D6111yescharacteristic
310C42C2×D24411yescharacteristic
311C42D4×D6111yescharacteristic
312C42#1175822411yescharacteristic
313C23—22no—
314C23—22no—
315C23—22no—
316C23—81no—
317C23—81no—
318C23—2441no—
319C23#1451974911yescharacteristic
320Q8—2441no—
321Q8—2441no—
322D4—22no—
323D4—22no—
324D4—22no—
325D4—4881no—
326D4—4881no—
327D4—4881no—
328D4—2442no—
329D4—2441no—
330D4—2441no—
331D4#1451969714yes—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—44no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—4881no—
342C2×C4—4881no—
343C2×C4—2441no—
344C2×C4C2×#1175819811yescharacteristic
345C2×C4#1451973711yescharacteristic
346C2×C4#1451973711yescharacteristic
347C2×C4#1451974711yescharacteristic
348C2×C4#1451974911yescharacteristic
349C2×C4#1451976111yescharacteristic
350C2×C4C2×#1175819911yescharacteristic
351C2×C4C2×#1175820111yescharacteristic
352C2×C4#1451979711yescharacteristic
353C2×C4#1451979711yescharacteristic
354C8—81no—
355C8—2442no—
356C8—2442no—
357C8—2442no—
358C22—21no—
359C22—21no—
360C22—24no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22—82no—
365C22—4881no—
366C22—4881no—
367C22—4881no—
368C22#1683963911yescharacteristic
369C22#1683999311yescharacteristic
370C22#1683999611yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—161no—
377C4—4881no—
378C4C2×#1451969711yescharacteristic
379C4#1683975611yescharacteristic
380C4#1683999311yescharacteristic
381C4#1683999611yescharacteristic
382C2—21no—
383C2—21no—
384C2—44no—
385C2—9761no—
386C2#2144617911yescharacteristic
387C2#2144624511yescharacteristic
388C2#2144630411yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1804C2
socleC22×C61#386
prime radical#21455283C2
cosocleC2×C42×C61C23
hypercenter#1804D61
hypocenterC61#9305
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. #21454843C2semidirect
3. #21444378C2semidirect
4. #21444217C2semidirect
5. #21443716C2semidirect
6. #21443677C2semidirect
7. C61×#1804C2semidirect
11. #16839967C4semidirect
12. #16839957C4semidirect
190. #1804D61semidirect
221. C61#9305semidirect

Maximal subgroups

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

subgroupindex
#214552832
#214548432
#214443782
#214442172
#214437162
#214436772
C61×#18042
#930561