Finite Group Databasebeta

← #29583827

Subgroups — #29583827

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×#16839963C211yesmaximal, characteristic
2#21446754C211yesmaximal, characteristic, complemented
3#21446624C211yesmaximal, characteristic
4#21445821C211yesmaximal, characteristic, complemented
5C2×#16839512C211yesmaximal, characteristic, complemented
6C2×#16839505C211yesmaximal, characteristic
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C2×#14519774C2211yescharacteristic
10C2×C4×Dic122C2211yescharacteristic
11#16839963—22no—
12#16839963—22no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519700—21no—
15C2×#14519699—21no—
16C2×#14519697—21no—
17C2×#14519697—21no—
18C2×C4×#92418C2211yescharacteristic
19#16839524—21no—
20#16839516—21no—
21#16839516—21no—
22#16839512—22no—
23#16839505—22no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#384C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244—21no—
29C22×D244—21no—
30C22×D244—21no—
31C2×#11758190—24no—
32C2×#11758190—42no—
33C2×#11758190—42no—
34C22×#92418—21no—
35C22×#92418D411yescharacteristic
36C22×#92418D411yescharacteristic
37#14519774—21no—
38#14519774—21no—
39#14519774—21no—
40#14519774D412yes—
41C4×Dic122—21no—
42C4×Dic122—21no—
43C4×Dic122—21no—
44C4×Dic122—21no—
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758196—21no—
47C2×C4×Dic61—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519700—42no—
51#14519699—24no—
52#14519697—42no—
53#14519697—42no—
54C4×#92418—21no—
55C4×#92418—21no—
56C22×C8×C61—21no—
57C22×C8×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C42×C61C2311yescharacteristic
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61D412yes—
66C23×D61—41no—
67C22×C4×C61—41no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61#4111yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73C2×D244—22no—
74C2×D244—22no—
75C2×D244—22no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—81no—
88C2×D244—81no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×Dic122—21no—
92C2×Dic122—21no—
93C2×Dic122—21no—
94C2×Dic122SD1612yes—
95C2×C8×C61—22no—
96C2×C8×C61—41no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C2×C8×C61—41no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C4⋊C4×C61—41no—
104C4⋊C4×C61—41no—
105C4⋊C4×C61—81no—
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112#11758196—41no—
113#11758196—41no—
114C4×Dic61—41no—
115C4×Dic61—41no—
116C2×#92418—21no—
117C2×#92418—21no—
118C2×#92418—21no—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418SD1612yescomplemented
125#11758190—48no—
126C23×C61#12111yescharacteristic
127C22×D61—42no—
128C22×D61—81no—
129C22×D61—81no—
130C22×D61—81no—
131C22×D61—81no—
132C22×D61—81no—
133C22×D61—81no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—81no—
137C2×C4×C61—81no—
138C2×C4×C61—81no—
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12311yescharacteristic
143C2×C4×C61#12311yescharacteristic
144C2×C4×C61#12411yescharacteristic
145C2×C4×C61C2×SD1611yescharacteristic
146C2×C4×C61C2×SD1611yescharacteristic
147C2×C4×C61#13511yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61#13711yescharacteristic
153C2×Dic61—22no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—41no—
159D244—42no—
160D244—42no—
161D244—42no—
162D244—42no—
163D244—82no—
164D244—82no—
165D244—81no—
166D244—81no—
167D244—81no—
168D244—81no—
169Dic122—22no—
170Dic122—22no—
171Dic122—41no—
172Dic122—41no—
173C8×C61—42no—
174C8×C61—81no—
175#92418—22no—
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—161no—
196C4×C61#44911yescharacteristic
197C4×C61#45011yescharacteristic
198C4×C61#46111yescharacteristic
199C4×C61#46311yescharacteristic
200C4×C61#46511yescharacteristic
201C4×C61#46811yescharacteristic
202C4×C61#48111yescharacteristic
203C4×C61#48211yescharacteristic
204Dic61—42no—
205Dic61—81no—
206C2×#460—611no—
207#1984—611no—
208#1957—611no—
209#1803—611no—
210C2×#334—611no—
211C2×#331—611no—
212#1296D6111yescharacteristic, complemented
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×Q8—611no—
224#460—1222no—
225#460—1222no—
226C2×C4⋊C8—611no—
227C2×C4⋊C8C2×D6111yescharacteristic
228C2×C4⋊C8C2×D6111yescharacteristic
229C2×#103—1221no—
230C2×#102—1221no—
231C2×#102—1221no—
232C2×#102—1221no—
233C2×C4×C8—611no—
234#384C2×D6111yescharacteristic
235#340—1221no—
236#336—1221no—
237#336—1221no—
238#334—1222no—
239#331—1222no—
240C61#1047511yescharacteristic, complemented, Sylow
241C22×Q8—611no—
242C22×D4—1221no—
243C22×D4—1221no—
244C22×D4—1221no—
245C2×SD16—1224no—
246C2×SD16—2442no—
247C2×SD16—2442no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—611no—
251C22×C8—611no—
252C22×C8—1221no—
253#127—612no—
254#127—1221no—
255#127—1221no—
256#127—1221no—
257C4×Q8—1221no—
258C4×Q8—1221no—
259C4×Q8—1221no—
260C4×Q8—1221no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—1221no—
266C2×C42—1221no—
267C2×C42C22×D6111yescharacteristic
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—21no—
271C4⋊C8—1221no—
272C4⋊C8—1221no—
273C4⋊C8D24412yes—
274#103—2442no—
275#102—1224no—
276#102—2442no—
277#102—2442no—
278C4×C8—1221no—
279C4×C8—1221no—
280C24—2441no—
281C2×Q8—612no—
282C2×Q8—1221no—
283C2×Q8—1221no—
284C2×Q8—1221no—
285C2×Q8—1221no—
286C2×Q8—1221no—
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—41no—
304C22×C4—1221no—
305C22×C4—1221no—
306C22×C4#1175822211yescharacteristic
307C22×C4D4×D6111yescharacteristic
308C22×C4D4×D6111yescharacteristic
309SD16—2448no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C2×C8—41no—
316C2×C8—612no—
317C2×C8—1221no—
318C2×C8—1221no—
319C2×C8—1221no—
320C2×C8—1221no—
321C2×C8—1221no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C4⋊C4—41no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—81no—
330C4⋊C4—1221no—
331C4⋊C4—1221no—
332C4⋊C4—2441no—
333C4⋊C4—2441no—
334C42—2441no—
335C42—2441no—
336C42C2×D24411yescharacteristic
337C42#1175822211yescharacteristic
338C42D4×D6111yescharacteristic
339C42#1175822611yescharacteristic
340C23—4881no—
341C23—4881no—
342C23—4881no—
343C23—4881no—
344C23—4881no—
345C23—4881no—
346C23—2442no—
347C23#1451975011yescharacteristic
348Q8—1222no—
349Q8—1222no—
350Q8—2441no—
351Q8—2441no—
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—81no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—1222no—
368C2×C4—2441no—
369C2×C4—2441no—
370C2×C4—2441no—
371C2×C4—2441no—
372C2×C4—2441no—
373C2×C4#1451974711yescharacteristic
374C2×C4#1451975011yescharacteristic
375C2×C4#1451975211yescharacteristic
376C2×C4#1451976211yescharacteristic
377C2×C4#1451976211yescharacteristic
378C2×C4#1451976511yescharacteristic
379C2×C4SD16×D6111yescharacteristic
380C2×C4SD16×D6111yescharacteristic
381C2×C4#1451979811yescharacteristic
382C2×C4#1451980011yescharacteristic
383C2×C4#1451980111yescharacteristic
384C2×C4#1451980111yescharacteristic
385C2×C4#1451980411yescharacteristic
386C2×C4#1451980911yescharacteristic
387C8—42no—
388C8—81no—
389C8—1222no—
390C8—4881no—
391C8—2441no—
392C22—9761no—
393C22—9761no—
394C22—9761no—
395C22—9761no—
396C22—4882no—
397C22—4882no—
398C22—4882no—
399C22#1683968011yescharacteristic
400C22#1683996111yescharacteristic
401C22#1683998711yescharacteristic
402C22#1683999411yescharacteristic
403C22#1684001411yescharacteristic
404C22#1684002811yescharacteristic
405C22#1684003111yescharacteristic
406C4—21no—
407C4—21no—
408C4—161no—
409C4—4881no—
410C4—2442no—
411C4#1683991011yescharacteristic
412C4#1683991411yescharacteristic
413C4#1683996611yescharacteristic
414C4#1683997611yescharacteristic
415C4#1683999211yescharacteristic
416C4#1684000911yescharacteristic
417C4#1684008211yescharacteristic
418C4#1684008911yescharacteristic
419C2—9762no—
420C2#2144517011yescharacteristic
421C2#2144523811yescharacteristic
422C2#2144530211yescharacteristic
423C2#2144539011yescharacteristic
424C2#2144701111yescharacteristic
425C2#2144711411yescharacteristic
426C2#2144713811yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenter#1296D61
hypocenterC61#10475
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #21446754C2semidirect
4. #21445821C2semidirect
5. C2×#16839512C2semidirect
7. C61×#1296C2semidirect
124. C2×#92418SD16semidirect
212. #1296D61semidirect
240. C61#10475semidirect

Maximal subgroups

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

subgroupindex
C2×#168399632
#214467542
#214466242
#214458212
C2×#168395122
C2×#168395052
C61×#12962
#1047561