Finite Group Databasebeta

← #29578402

Subgroups — #29578402

Order 15616.

454 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#21446746C211yesmaximal, characteristic
2#21446624C211yesmaximal, characteristic
3#21445688C211yesmaximal, characteristic, complemented
4C2×#16839505C211yesmaximal, characteristic
5#21443702C211yesmaximal, characteristic, complemented
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1948C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9C2×C4⋊#92418C2211yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519697—21no—
12C2×#14519697—21no—
13C2×#14519697—21no—
14C2×#14519697—21no—
15C2×#14519688—21no—
16C2×C4×#92418C2211yescharacteristic
17#16839517—21no—
18#16839505C414yescomplemented
19C2×#106×C61—21no—
20C2×C4⋊C8×C61C2211yescharacteristic
21C61×#384C2211yescharacteristic
22C4×C4⋊C4×C61C2211yescharacteristic
23C61×#340—21no—
24C22×D244—21no—
25C22×D244—21no—
26C22×D244—21no—
27C22×#92418—21no—
28C22×#92418—21no—
29C22×#92418D411yescharacteristic
30C22×#92418D411yescharacteristic
31#14519774—21no—
32#14519774—21no—
33#14519774—21no—
34#14519774C2×C412yes—
35C4⋊#92418—21no—
36C4⋊#92418—21no—
37C4⋊#92418—21no—
38C4⋊#92418C2×C412yes—
39#14519697—42no—
40#14519697—42no—
41#14519697—42no—
42#14519697—42no—
43#14519688—42no—
44C4×#92418—21no—
45C4×#92418—21no—
46C22×C8×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C42×C61—21no—
53C2×C42×C61C2311yescharacteristic
54#106×C61—42no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61C2×C412yes—
57#95×C61—21no—
58C23×D61—41no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61#4111yescharacteristic
65C2×D244—22no—
66C2×D244—22no—
67C2×D244—22no—
68C2×D244—41no—
69C2×D244—41no—
70C2×D244—41no—
71C2×D244—41no—
72C2×D244—41no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—81no—
80C2×D244—81no—
81C2×C8×C61—22no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—81no—
93C42×C61—41no—
94C42×C61—41no—
95C42×C61C22×C411yescharacteristic
96C42×C61#4111yescharacteristic
97C42×C61#4111yescharacteristic
98C42×C61#4111yescharacteristic
99C2×#92418—21no—
100C2×#92418—21no—
101C2×#92418—22no—
102C2×#92418—21no—
103C2×#92418—21no—
104C2×#92418—21no—
105C2×#92418—41no—
106C2×#92418—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418SD1612yes—
111C23×C61#12111yescharacteristic
112C22×D61—42no—
113C22×D61—81no—
114C22×D61—81no—
115C22×D61—81no—
116C22×D61—81no—
117C22×D61—81no—
118C22×D61—81no—
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—41no—
126C2×C4×C61—41no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61#11711yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61#12311yescharacteristic
134C2×C4×C61#12411yescharacteristic
135C2×C4×C61#12611yescharacteristic
136C2×C4×C61C2×SD1611yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61#13711yescharacteristic
144D244—42no—
145D244—42no—
146D244—42no—
147D244—42no—
148D244—82no—
149D244—82no—
150D244—81no—
151D244—81no—
152D244—81no—
153D244—81no—
154C8×C61—42no—
155#92418—22no—
156#92418—42no—
157#92418—41no—
158#92418—81no—
159#9572—611nomaximal, Sylow
160C22×C61#38811yescharacteristic
161C22×C61#46011yescharacteristic
162C22×C61#46311yescharacteristic
163C22×C61#46811yescharacteristic
164C22×C61#46911yescharacteristic
165C22×C61#47111yescharacteristic
166C22×C61#47211yescharacteristic
167C2×D61—82no—
168C2×D61—82no—
169C2×D61—82no—
170C2×D61—161no—
171C2×D61—161no—
172C2×D61—161no—
173C2×D61—161no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—81no—
177C4×C61—81no—
178C4×C61—161no—
179C4×C61C4×SD1611yescharacteristic
180C4×C61#44011yescharacteristic
181C4×C61#44211yescharacteristic
182C4×C61#44211yescharacteristic
183C4×C61#48111yescharacteristic
184C4×C61#48211yescharacteristic
185C4×C61#48911yescharacteristic
186C4×C61#49011yescharacteristic
187#1982—611no—
188#1957—611no—
189#1948D6111yescharacteristic, complemented
190#1770—611no—
191C2×#331—611no—
192#1296—611no—
193#1277—611no—
194C2×C61#168611yescharacteristic
195C2×C61#168811yescharacteristic
196C2×C61#169711yescharacteristic
197C2×C61#170111yescharacteristic
198C2×C61#192611yescharacteristic
199C2×C61#193111yescharacteristic
200C2×C61#193611yescharacteristic
201D61—162no—
202C2×#127—611no—
203C2×#106—21no—
204C2×C4⋊C8—611no—
205C2×C4⋊C8—611no—
206C2×C4⋊C8C2×D6111yescharacteristic
207C2×#102—1221no—
208C2×#102—1221no—
209C2×#102—1221no—
210C2×#102—1221no—
211C2×#97—1221no—
212C2×C4×C8—611no—
213#384C2×D6111yescharacteristic
214C4×C4⋊C4C2×D6111yescharacteristic
215#340—21no—
216#336—1221no—
217#331—614no—
218C61#957211yescharacteristic, complemented, Sylow
219C22×D4—1221no—
220C22×D4—1221no—
221C22×D4—1221no—
222C22×C8—21no—
223C22×C8—611no—
224C22×C8—611no—
225C22×C8—1221no—
226C22×C8—1221no—
227#127—612no—
228#127—1221no—
229#127—1221no—
230#127—1221no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4C22⋊D6111yescharacteristic
235C2×C4⋊C4C22⋊D6111yescharacteristic
236C2×C42—21no—
237C2×C42C22×D6111yescharacteristic
238#106—42no—
239C4⋊C8—21no—
240C4⋊C8—612no—
241C4⋊C8—1221no—
242C4⋊C8—1221no—
243C4⋊C8—1221no—
244C4⋊C8C4×D6112yes—
245#102—2442no—
246#102—2442no—
247#102—2442no—
248#102—2442no—
249#97—2442no—
250C4×C8—1221no—
251C4×C8—1221no—
252#95—21no—
253C24—2441no—
254C2×D4—1222no—
255C2×D4—1222no—
256C2×D4—1222no—
257C2×D4—4881no—
258C2×D4—4881no—
259C2×D4—2441no—
260C2×D4—2441no—
261C2×D4—2441no—
262C2×D4—2441no—
263C2×D4—2441no—
264C2×D4—2441no—
265C2×D4—2441no—
266C2×D4—2441no—
267C2×D4—2441no—
268C2×D4—2441no—
269C2×D4—2441no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4D4×D6111yescharacteristic
274C22×C4#1175822411yescharacteristic
275C22×C4C2×C22⋊D6111yescharacteristic
276C2×C8—22no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—612no—
280C2×C8—1221no—
281C2×C8—1221no—
282C2×C8—1222no—
283C2×C8—1221no—
284C2×C8—1221no—
285C2×C8—1221no—
286C2×C8—2441no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8—2441no—
290C2×C8—2441no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—41no—
299C4⋊C4—81no—
300C42—41no—
301C42—41no—
302C42C2×C4×D6111yescharacteristic
303C42#1175822211yescharacteristic
304C42#1175822611yescharacteristic
305C42#1175822611yescharacteristic
306C23—4881no—
307C23—4881no—
308C23—4881no—
309C23—4881no—
310C23—4881no—
311C23—4881no—
312C23—2442no—
313C23#1451974911yescharacteristic
314D4—4882no—
315D4—4882no—
316D4—4881no—
317D4—4881no—
318D4—4881no—
319D4—4881no—
320D4—2442no—
321D4—2442no—
322D4—2442no—
323D4—2442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4#1451973511yescharacteristic
336C2×C4C4×C22⋊D6111yescharacteristic
337C2×C4#1451973911yescharacteristic
338C2×C4#1451976211yescharacteristic
339C2×C4#1451976611yescharacteristic
340C2×C4#1451977211yescharacteristic
341C2×C4SD16×D6111yescharacteristic
342C2×C4#1451979811yescharacteristic
343C2×C4#1451980211yescharacteristic
344C2×C4#1451980211yescharacteristic
345C2×C4#1451980311yescharacteristic
346C2×C4#1451980411yescharacteristic
347C2×C4#1451980411yescharacteristic
348C2×C4#1451980811yescharacteristic
349C8—42no—
350C8—1222no—
351C8—4881no—
352C8—2441no—
353C8—2442no—
354C22—9761no—
355C22—9761no—
356C22—9761no—
357C22—9761no—
358C22—4882no—
359C22—4882no—
360C22—4882no—
361C22#1683965211yescharacteristic
362C22#1683996011yescharacteristic
363C22#1683997911yescharacteristic
364C22#1684001011yescharacteristic
365C22#1684001311yescharacteristic
366C22#1684002711yescharacteristic
367C22#1684003011yescharacteristic
368C4—21no—
369C4—21no—
370C4—81no—
371C4—81no—
372C4—161no—
373C4#1683984911yescharacteristic
374C4#1683986011yescharacteristic
375C4#1683987211yescharacteristic
376C4#1683987311yescharacteristic
377C4#1684008211yescharacteristic
378C4#1684008811yescharacteristic
379C4#1684012411yescharacteristic
380C4#1684012811yescharacteristic
381C2—9762no—
382C2#2144529311yescharacteristic
383C2#2144530111yescharacteristic
384C2#2144535411yescharacteristic
385C2#2144538211yescharacteristic
386C2#2144644511yescharacteristic
387C2#2144648011yescharacteristic
388C2#2144651511yescharacteristic
subgroupG/H
centerC23#14519749
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1948C2
socleC23×C61#121
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1948D61
hypocenterC61#9572
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
3. #21445688C2semidirect
5. #21443702C2semidirect
6. #21443653C2semidirect
7. C61×#1948C2semidirect
18. #16839505C4semidirect
189. #1948D61semidirect
218. C61#9572semidirect

Maximal subgroups

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

subgroupindex
#214467462
#214466242
#214456882
C2×#168395052
#214437022
#214436532
C61×#19482
#957261