Finite Group Databasebeta

← #29583841

Subgroups — #29583841

Order 15616.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839968C211yesmaximal, characteristic
2#21446779C211yesmaximal, characteristic, complemented
3#21446612C211yesmaximal, characteristic
4#21445816C211yesmaximal, characteristic
5C2×#16839512C211yesmaximal, characteristic, complemented
6C2×#16839507C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×#11758190—21no—
9C2×#14519777C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11#16839968—22no—
12#16839968—22no—
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519702—21no—
15C2×#14519697—21no—
16C2×#14519689—21no—
17C2×#14519689—21no—
18C2×C4×#92418C2211yescharacteristic
19#16839524—21no—
20#16839524—21no—
21#16839524—21no—
22#16839512—22no—
23#16839507—22no—
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C61×#384C2211yescharacteristic
27C22×Dic122—21no—
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C2×#11758190—24no—
31C2×#11758190—42no—
32C2×#11758190—42no—
33C22×#92418—21no—
34C22×#92418D411yescharacteristic
35C22×#92418D411yescharacteristic
36#14519777—21no—
37#14519777—21no—
38#14519777—21no—
39#14519777D412yes—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C4×D244—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758198—21no—
48C4⋊#92418—21no—
49C4⋊#92418—21no—
50#14519702—24no—
51#14519697—42no—
52#14519689—42no—
53#14519689—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—21no—
67C22×C4×C61—41no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61#4111yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—41no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244SD1612yes—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61—41no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×Dic122—22no—
86C2×Dic122—41no—
87C2×Dic122—41no—
88C2×Dic122—41no—
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×C8×C61—22no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—81no—
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105C42×C61#4111yescharacteristic
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—21no—
109C4⋊Dic61—22no—
110C4⋊Dic61—22no—
111C4⋊Dic61—21no—
112C4⋊Dic61—41no—
113C4⋊Dic61—41no—
114C2×#92418—21no—
115C2×#92418—21no—
116C2×#92418—21no—
117C2×#92418—21no—
118C2×#92418—21no—
119C2×#92418—41no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418SD1612yescomplemented
123#11758190—48no—
124C23×C61#12111yescharacteristic
125C22×D61—22no—
126C22×D61—41no—
127C22×D61—41no—
128C22×D61—41no—
129C22×D61—41no—
130C22×D61—41no—
131C22×D61—41no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61—81no—
137C2×C4×C61#12011yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61#12311yescharacteristic
141C2×C4×C61#12311yescharacteristic
142C2×C4×C61#12411yescharacteristic
143C2×C4×C61C2×SD1611yescharacteristic
144C2×C4×C61C2×SD1611yescharacteristic
145C2×C4×C61#13511yescharacteristic
146C2×C4×C61#13511yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
149C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C61#13711yescharacteristic
151C2×Dic61—42no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—81no—
156C2×Dic61—81no—
157D244—22no—
158D244—22no—
159D244—41no—
160D244—41no—
161C4×D61—81no—
162C4×D61—81no—
163C4×D61—81no—
164C4×D61—81no—
165Dic122—42no—
166Dic122—42no—
167Dic122—81no—
168Dic122—81no—
169C8×C61—42no—
170C8×C61—81no—
171#92418—22no—
172#92418—41no—
173#92418—81no—
174#10477—611nomaximal, Sylow
175C22×C61#39411yescharacteristic
176C22×C61#46111yescharacteristic
177C22×C61#46311yescharacteristic
178C22×C61#46511yescharacteristic
179C22×C61#46911yescharacteristic
180C22×C61#47111yescharacteristic
181C22×C61#47311yescharacteristic
182C2×D61—42no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61—81no—
188C2×D61—81no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—161no—
192C4×C61#44911yescharacteristic
193C4×C61#45011yescharacteristic
194C4×C61#46011yescharacteristic
195C4×C61#46411yescharacteristic
196C4×C61#46511yescharacteristic
197C4×C61#46811yescharacteristic
198C4×C61#48111yescharacteristic
199C4×C61#48211yescharacteristic
200Dic61—81no—
201Dic61—82no—
202C2×#461—611no—
203#1990—611no—
204#1954—611no—
205#1802—611no—
206C2×#334—611no—
207C2×#332—611no—
208#1296D6111yescharacteristic, complemented
209C2×C61#167111yescharacteristic
210C2×C61#167911yescharacteristic
211C2×C61#169311yescharacteristic
212C2×C61#170111yescharacteristic
213C2×C61#203411yescharacteristic
214C2×C61#205211yescharacteristic
215C2×C61#205511yescharacteristic
216D61—82no—
217C22×SD16—1221no—
218C2×C4⋊Q8—611no—
219C2×C4×D4—611no—
220#461—1222no—
221#461—1222no—
222C2×C4⋊C8—611no—
223C2×C4⋊C8C2×D6111yescharacteristic
224C2×C4⋊C8C2×D6111yescharacteristic
225C2×#103—1221no—
226C2×#102—1221no—
227C2×C22⋊C8—1221no—
228C2×C22⋊C8—1221no—
229C2×C4×C8—611no—
230#384C2×D6111yescharacteristic
231#340—1221no—
232#340—1221no—
233#340—1221no—
234#334—1222no—
235#332—1222no—
236C61#1047711yescharacteristic, complemented, Sylow
237C22×Q8—1221no—
238C22×D4—611no—
239C23×C4—1221no—
240C2×SD16—1224no—
241C2×SD16—2442no—
242C2×SD16—2442no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—611no—
246C22×C8—611no—
247C22×C8—1221no—
248C4⋊Q8—612no—
249C4⋊Q8—1221no—
250C4⋊Q8—1221no—
251C4⋊Q8—1221no—
252C4×D4—1221no—
253C4×D4—1221no—
254C4×D4—1221no—
255C4×D4—1221no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4—1221no—
261C2×C4⋊C4—1221no—
262C2×C22⋊C4—1221no—
263C2×C42C22×D6111yescharacteristic
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269C4⋊C8D24412yes—
270#103—1224no—
271#102—2442no—
272C22⋊C8—2442no—
273C22⋊C8—2442no—
274C4×C8—1221no—
275C4×C8—1221no—
276C24—1221no—
277C2×Q8—1222no—
278C2×Q8—2441no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C2×Q8—2441no—
282C2×Q8—2441no—
283C2×D4—612no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—1221no—
287C2×D4—1221no—
288C2×D4—1221no—
289C22×C4—41no—
290C22×C4—1221no—
291C22×C4—2441no—
292C22×C4—2441no—
293C22×C4—2441no—
294C22×C4—2441no—
295C22×C4—2441no—
296C22×C4—2441no—
297C22×C4—2441no—
298C22×C4#1175822211yescharacteristic
299C22×C4D4×D6111yescharacteristic
300C22×C4D4×D6111yescharacteristic
301SD16—2448no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C2×C8—612no—
309C2×C8—1221no—
310C2×C8—1221no—
311C2×C8—1221no—
312C2×C8—1221no—
313C2×C8—1221no—
314C2×C8—2441no—
315C2×C8—2441no—
316C2×C8—2441no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—81no—
322C4⋊C4—1221no—
323C4⋊C4—1222no—
324C4⋊C4—1221no—
325C4⋊C4—1222no—
326C4⋊C4—2441no—
327C4⋊C4—2441no—
328C22⋊C4—2441no—
329C22⋊C4—2441no—
330C42C2×D24411yescharacteristic
331C42#1175822211yescharacteristic
332C42D4×D6111yescharacteristic
333C42#1175822611yescharacteristic
334C23—1222no—
335C23—2441no—
336C23—2441no—
337C23—2441no—
338C23—2441no—
339C23—2441no—
340C23—2441no—
341C23#1451975011yescharacteristic
342Q8—4881no—
343Q8—4881no—
344Q8—2442no—
345Q8—2442no—
346D4—1222no—
347D4—1222no—
348D4—2441no—
349D4—2441no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—4881no—
356C2×C4—4881no—
357C2×C4—4881no—
358C2×C4—4881no—
359C2×C4—4881no—
360C2×C4—4881no—
361C2×C4—2441no—
362C2×C4—2442no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4#1451974711yescharacteristic
366C2×C4#1451975011yescharacteristic
367C2×C4#1451975211yescharacteristic
368C2×C4#1451976211yescharacteristic
369C2×C4#1451976211yescharacteristic
370C2×C4#1451976511yescharacteristic
371C2×C4SD16×D6111yescharacteristic
372C2×C4SD16×D6111yescharacteristic
373C2×C4#1451979811yescharacteristic
374C2×C4#1451980011yescharacteristic
375C2×C4#1451980111yescharacteristic
376C2×C4#1451980111yescharacteristic
377C2×C4#1451980411yescharacteristic
378C2×C4#1451980911yescharacteristic
379C8—42no—
380C8—81no—
381C8—1222no—
382C8—4881no—
383C8—2441no—
384C22—4881no—
385C22—4881no—
386C22—4881no—
387C22—4881no—
388C22—2442no—
389C22—2442no—
390C22—2442no—
391C22#1683968011yescharacteristic
392C22#1683996611yescharacteristic
393C22#1683997611yescharacteristic
394C22#1683999411yescharacteristic
395C22#1684001411yescharacteristic
396C22#1684002411yescharacteristic
397C22#1684003611yescharacteristic
398C4—21no—
399C4—21no—
400C4—161no—
401C4—4882no—
402C4—4881no—
403C4#1683991011yescharacteristic
404C4#1683991411yescharacteristic
405C4#1683996111yescharacteristic
406C4#1683998711yescharacteristic
407C4#1683999211yescharacteristic
408C4#1684000911yescharacteristic
409C4#1684008211yescharacteristic
410C4#1684008911yescharacteristic
411C2—4882no—
412C2#2144519711yescharacteristic
413C2#2144524111yescharacteristic
414C2#2144533111yescharacteristic
415C2#2144537911yescharacteristic
416C2#2144701111yescharacteristic
417C2#2144712111yescharacteristic
418C2#2144713811yescharacteristic
subgroupG/H
centerC23#14519750
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#121
prime radicalC22×D244D4
hypercenter#1296D61
hypocenterC61#10477
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. #21446779C2semidirect
5. C2×#16839512C2semidirect
6. C2×#16839507C2semidirect
7. C61×#1296C2semidirect
122. C2×#92418SD16semidirect
208. #1296D61semidirect
236. C61#10477semidirect

Maximal subgroups

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

subgroupindex
C2×#168399682
#214467792
#214466122
#214458162
C2×#168395122
C2×#168395072
C61×#12962
#1047761