Finite Group Databasebeta

← #29583824

Subgroups — #29583824

Order 15616.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839962C211yesmaximal, characteristic
2#21446756C211yesmaximal, characteristic, complemented
3#21446624C211yesmaximal, characteristic
4C2×#16839512C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443702C211yesmaximal, characteristic, complemented
7C61×#1803C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C2×#14519774C2211yescharacteristic
10#16839962—22no—
11#16839962—22no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519697—21no—
15C2×#14519697—21no—
16C2×#14519697—21no—
17C2×C4×#92418C2211yescharacteristic
18#16839517—21no—
19#16839517—21no—
20#16839512—22no—
21#16839505—22no—
22C2×C4×Q8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×#103×C61—21no—
25C61×#384C2211yescharacteristic
26C61×#340—21no—
27C22×D244—21no—
28C22×D244—21no—
29C22×D244—21no—
30C2×#11758201—24no—
31C2×#11758201—42no—
32C2×#11758201—42no—
33C22×#92418—21no—
34C22×#92418—21no—
35C22×#92418D411yescharacteristic
36C22×#92418D411yescharacteristic
37#14519774—21no—
38#14519774—21no—
39#14519774—21no—
40#14519774D412yes—
41C4⋊#92418—21no—
42C4⋊#92418—21no—
43C4⋊#92418—21no—
44C4⋊#92418D412yes—
45#14519697—24no—
46#14519697—42no—
47#14519697—42no—
48C4×#92418—21no—
49C4×#92418—21no—
50C22×Q8×C61D411yescharacteristic
51C22×C8×C61—21no—
52C4×Q8×C61—21no—
53C4×Q8×C61—21no—
54C4×Q8×C61—21no—
55C4×Q8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61D411yescharacteristic
61C2×C42×C61—21no—
62C2×C42×C61C2311yescharacteristic
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65#103×C61—42no—
66C23×D61—41no—
67C2×Q8×C61—21no—
68C2×Q8×C61—21no—
69C2×Q8×C61—21no—
70C2×Q8×C61—21no—
71C2×Q8×C61—21no—
72C2×Q8×C61SD1612yes—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—41no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C2×D244—22no—
80C2×D244—22no—
81C2×D244—22no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—81no—
94C2×D244—81no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—41no—
106C4⋊C4×C61—81no—
107C42×C61—41no—
108C42×C61—41no—
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61#4111yescharacteristic
112C42×C61#4111yescharacteristic
113#11758201—48no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—22no—
117C2×#92418—21no—
118C2×#92418—21no—
119C2×#92418—21no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—41no—
125C2×#92418SD1612yescomplemented
126C23×C61#12111yescharacteristic
127C22×D61—42no—
128C22×D61—81no—
129C22×D61—81no—
130C22×D61—81no—
131C22×D61—81no—
132C22×D61—81no—
133C22×D61—81no—
134Q8×C61—22no—
135Q8×C61—22no—
136Q8×C61—41no—
137Q8×C61—41no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—22no—
141C2×C4×C61—41no—
142C2×C4×C61—41no—
143C2×C4×C61—41no—
144C2×C4×C61—41no—
145C2×C4×C61—41no—
146C2×C4×C61—81no—
147C2×C4×C61—81no—
148C2×C4×C61—81no—
149C2×C4×C61#12011yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12111yescharacteristic
152C2×C4×C61#12311yescharacteristic
153C2×C4×C61#12311yescharacteristic
154C2×C4×C61#12411yescharacteristic
155C2×C4×C61C2×SD1611yescharacteristic
156C2×C4×C61C2×SD1611yescharacteristic
157C2×C4×C61#13511yescharacteristic
158C2×C4×C61#13511yescharacteristic
159C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C61#13711yescharacteristic
163D244—42no—
164D244—42no—
165D244—42no—
166D244—42no—
167D244—82no—
168D244—82no—
169D244—81no—
170D244—81no—
171D244—81no—
172D244—81no—
173C8×C61—81no—
174#92418—22no—
175#92418—42no—
176#92418—41no—
177#92418—81no—
178#10475—611nomaximal, Sylow
179C22×C61#39411yescharacteristic
180C22×C61#46011yescharacteristic
181C22×C61#46411yescharacteristic
182C22×C61#46511yescharacteristic
183C22×C61#46911yescharacteristic
184C22×C61#47111yescharacteristic
185C22×C61#47211yescharacteristic
186C2×D61—82no—
187C2×D61—82no—
188C2×D61—82no—
189C2×D61—161no—
190C2×D61—161no—
191C2×D61—161no—
192C2×D61—161no—
193C4×C61—21no—
194C4×C61—21no—
195C4×C61—42no—
196C4×C61—81no—
197C4×C61—161no—
198C4×C61#44911yescharacteristic
199C4×C61#45011yescharacteristic
200C4×C61#46111yescharacteristic
201C4×C61#46311yescharacteristic
202C4×C61#46511yescharacteristic
203C4×C61#46811yescharacteristic
204C4×C61#48111yescharacteristic
205C4×C61#48211yescharacteristic
206C2×#460—611no—
207#1984—611no—
208#1957—611no—
209#1803D6111yescharacteristic, complemented
210C2×#334—611no—
211C2×#331—611no—
212#1296—611no—
213C2×C61#166611yescharacteristic
214C2×C61#167811yescharacteristic
215C2×C61#168811yescharacteristic
216C2×C61#170211yescharacteristic
217C2×C61#203411yescharacteristic
218C2×C61#205111yescharacteristic
219C2×C61#205511yescharacteristic
220D61—162no—
221C22×SD16—1221no—
222C2×#127—611no—
223C2×C4×Q8C2×D6111yescharacteristic
224#460—1222no—
225#460—1222no—
226C2×C4⋊C8—611no—
227C2×C4⋊C8—611no—
228C2×C4⋊C8C2×D6111yescharacteristic
229C2×#103—21no—
230C2×#102—1221no—
231C2×#102—1221no—
232C2×#102—1221no—
233C2×C4×C8—611no—
234#384C2×D6111yescharacteristic
235#340—21no—
236#336—1221no—
237#336—1221no—
238#334—1222no—
239#331—1222no—
240C61#1047511yescharacteristic, complemented, Sylow
241C22×Q8C22⋊D6111yescharacteristic
242C22×D4—1221no—
243C22×D4—1221no—
244C22×D4—1221no—
245C2×SD16—1224no—
246C2×SD16—2442no—
247C2×SD16—2442no—
248C22×C8—21no—
249C22×C8—611no—
250C22×C8—611no—
251C22×C8—1221no—
252C22×C8—1221no—
253#127—612no—
254#127—1221no—
255#127—1221no—
256#127—1221no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C22⋊D6111yescharacteristic
266C2×C42—21no—
267C2×C42C22×D6111yescharacteristic
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—612no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8—1221no—
274#103—42no—
275#102—1224no—
276#102—2442no—
277#102—2442no—
278C4×C8—1221no—
279C4×C8—1221no—
280C24—2441no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8#1175820112yes—
287C2×D4—1222no—
288C2×D4—1222no—
289C2×D4—1222no—
290C2×D4—4881no—
291C2×D4—4881no—
292C2×D4—2441no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C2×D4—2441no—
302C2×D4—2441no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4D4×D6111yescharacteristic
307C22×C4#1175822411yescharacteristic
308C22×C4C2×C22⋊D6111yescharacteristic
309SD16—2448no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—612no—
314C2×C8—1221no—
315C2×C8—1221no—
316C2×C8—1221no—
317C2×C8—1222no—
318C2×C8—1221no—
319C2×C8—1221no—
320C2×C8—2441no—
321C2×C8—2441no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—81no—
334C42—41no—
335C42—41no—
336C42#1175822211yescharacteristic
337C42#1175822211yescharacteristic
338C42D4×D6111yescharacteristic
339C42D4×D6111yescharacteristic
340C23—4881no—
341C23—4881no—
342C23—4881no—
343C23—4881no—
344C23—4881no—
345C23—4881no—
346C23—2442no—
347C23#1451974911yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—41no—
351Q8—41no—
352D4—4882no—
353D4—4882no—
354D4—4881no—
355D4—4881no—
356D4—4881no—
357D4—4881no—
358D4—2442no—
359D4—2442no—
360D4—2442no—
361D4—2442no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4#1451974511yescharacteristic
374C2×C4#1451975011yescharacteristic
375C2×C4#1451975011yescharacteristic
376C2×C4#1451975911yescharacteristic
377C2×C4#1451976011yescharacteristic
378C2×C4#1451976311yescharacteristic
379C2×C4SD16×D6111yescharacteristic
380C2×C4C2×#1175820111yescharacteristic
381C2×C4#1451979711yescharacteristic
382C2×C4#1451980011yescharacteristic
383C2×C4#1451980211yescharacteristic
384C2×C4#1451980311yescharacteristic
385C2×C4#1451980411yescharacteristic
386C2×C4#1451980911yescharacteristic
387C8—81no—
388C8—1222no—
389C8—4881no—
390C8—2441no—
391C8—2442no—
392C22—9761no—
393C22—9761no—
394C22—9761no—
395C22—9761no—
396C22—4882no—
397C22—4882no—
398C22—4882no—
399C22#1683967711yescharacteristic
400C22#1683996011yescharacteristic
401C22#1683998611yescharacteristic
402C22#1683999311yescharacteristic
403C22#1684001311yescharacteristic
404C22#1684002711yescharacteristic
405C22#1684003011yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—161no—
411C4#1683990511yescharacteristic
412C4#1683991211yescharacteristic
413C4#1683996611yescharacteristic
414C4#1683998011yescharacteristic
415C4#1683999411yescharacteristic
416C4#1684001111yescharacteristic
417C4#1684008011yescharacteristic
418C4#1684008611yescharacteristic
419C2—9762no—
420C2#2144516911yescharacteristic
421C2#2144523711yescharacteristic
422C2#2144530111yescharacteristic
423C2#2144538911yescharacteristic
424C2#2144700811yescharacteristic
425C2#2144710911yescharacteristic
426C2#2144713311yescharacteristic
subgroupG/H
centerC23#14519749
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1803C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenter#1803D61
hypocenterC61#10475
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. #21446756C2semidirect
4. C2×#16839512C2semidirect
6. #21443702C2semidirect
7. C61×#1803C2semidirect
125. C2×#92418SD16semidirect
209. #1803D61semidirect
240. C61#10475semidirect

Maximal subgroups

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

subgroupindex
C2×#168399622
#214467562
#214466242
C2×#168395122
C2×#168395052
#214437022
C61×#18032
#1047561