Finite Group Databasebeta

← #29580769

Subgroups — #29580769

Order 15616.

632 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455823C211yesmaximal, characteristic, complemented
2#21450716C211yesmaximal, characteristic
3#21444383C211yesmaximal, characteristic, complemented
4#21444243C211yesmaximal, characteristic, complemented
5#21444210C211yesmaximal, characteristic, complemented
6#21443679C211yesmaximal, characteristic, complemented
7C61×#3077C211yesmaximal, characteristic, complemented
8C2×#14519748—21no—
9C2×C4×D244C2211yescharacteristic
10#16840090—21no—
11#16840049—21no—
12#16839964—21no—
13#16839912—21no—
14C4×#11758201—22no—
15#16839815C2211yescharacteristic
16#16839815C2211yescharacteristic
17#16839687—21no—
18#16839671—21no—
19#16839641—22no—
20#16839628C2211yescharacteristic
21#16839619—21no—
22#16839499—22no—
23D4⋊#92418—22no—
24#16839489—22no—
25C61×#533C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C61×#478—22no—
28C61×#476—21no—
29C61×#474—21no—
30C61×#428—21no—
31C61×#423C2211yescharacteristic
32C61×#418—21no—
33C22×D244D411yescharacteristic
34C22×C22⋊D61—22no—
35C22×C4×D61—21no—
36C2×#11758201—22no—
37#14519748—42no—
38#14519748—42no—
39C4×D244—21no—
40C4×D244—21no—
41C4×D244—21no—
42C4×D244—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×C22⋊Dic61—22no—
46C2×#11758198—21no—
47C2×#11758198—22no—
48#14519708—22no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51#14519701—22no—
52#14519697—22no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C4×#92418—21no—
56C4×#92418D412yescomplemented
57#14519684—22no—
58#14519684—21no—
59#14519684D412yes—
60C22×D4×C61D411yescharacteristic
61C23×C4×C61—21no—
62C2×M16×C61—21no—
63C4⋊Q8×C61D411yescharacteristic, complemented
64C4⋊Q8×C61D411yescharacteristic, complemented
65#125×C61—21no—
66C22⋊Q8×C61—21no—
67C22⋊Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74#117×C61—21no—
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C22⋊C4×C61—21no—
77C2×C42×C61C2311yescharacteristic
78#107×C61—22no—
79#106×C61—22no—
80C4⋊C8×C61—21no—
81C4⋊C8×C61D412yescomplemented
82#102×C61—22no—
83#102×C61—22no—
84C24×C61—21no—
85C23×D61—21no—
86C2×Q8×C61—21no—
87C2×Q8×C61—21no—
88C2×D4×C61—21no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61SD1612yescomplemented
94C22×C4×C61—21no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61—82no—
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C2×C22⋊D61—44no—
102C2×C22⋊D61—44no—
103C2×C22⋊D61—82no—
104C22×Dic61—21no—
105C22×Dic61—22no—
106C2×D244—21no—
107C2×D244—21no—
108C2×D244—42no—
109C2×C4×D61—41no—
110C2×C4×D61—41no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115M16×C61—41no—
116M16×C61—41no—
117C2×C8×C61—22no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61—21no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—41no—
125C4⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—41no—
129C42×C61—41no—
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61C2×D411yescharacteristic
133C42×C61#4111yescharacteristic
134C22⋊Dic61—44no—
135#11758201—44no—
136#11758198—41no—
137#11758198—41no—
138#11758198—82no—
139C4⋊Dic61—21no—
140C4⋊Dic61—21no—
141C4⋊Dic61—41no—
142C4⋊Dic61—41no—
143C2×#92418—22no—
144C2×#92418—41no—
145C23×C61—22no—
146C23×C61—42no—
147C23×C61—42no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61#12011yescharacteristic
151C22×D61—22no—
152C22×D61—41no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158Q8×C61—42no—
159Q8×C61—81no—
160D4×C61—22no—
161D4×C61—22no—
162D4×C61—41no—
163D4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—42no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—82no—
171C2×C4×C61—82no—
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#12711yescharacteristic
178C2×C4×C61C2×SD1611yescharacteristic
179C2×C4×C61#13511yescharacteristic
180C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C61#13711yescharacteristic
182C22⋊D61—88no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61—41no—
186C2×Dic61—42no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189D244—22no—
190D244—22no—
191D244—41no—
192D244—41no—
193C4×D61—81no—
194C4×D61—81no—
195C4×D61—81no—
196C4×D61—81no—
197C8×C61—42no—
198#92418—42no—
199#92418—81no—
200#10000—611nomaximal, Sylow
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—44no—
204C22×C61—42no—
205C22×C61—82no—
206C22×C61—81no—
207C22×C61—81no—
208C22×C61#39211yescharacteristic
209C22×C61#45011yescharacteristic
210C22×C61#45211yescharacteristic
211C2×D61—42no—
212C2×D61—42no—
213C2×D61—42no—
214C2×D61—81no—
215C2×D61—81no—
216C2×D61—81no—
217C2×D61—81no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61—81no—
225C4×C61#44811yescharacteristic
226C4×C61#44911yescharacteristic
227C4×C61#46511yescharacteristic
228C4×C61#46811yescharacteristic
229Dic61—82no—
230Dic61—81no—
231#3101—611no—
232#3077D6111yescharacteristic, complemented
233#2535—611no—
234#1518—611no—
235#1486—611no—
236#1478—611no—
237#1286—611no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61—82no—
241C2×C61#200011yescharacteristic
242C2×C61#200811yescharacteristic
243C2×C61#201011yescharacteristic
244D61—82no—
245#533C2×D6111yescharacteristic
246C2×#121—1221no—
247C2×C4×D4—611no—
248C2×C4×D4C2×D6111yescharacteristic
249#483—1221no—
250#478—22no—
251#476—21no—
252#476—1221no—
253#474—21no—
254#461—1221no—
255#450—1221no—
256C4×SD16—1222no—
257#431—611no—
258#431—611no—
259#428—21no—
260#423C2×D6111yescharacteristic
261#418—21no—
262#397—1221no—
263#392—1221no—
264#386—1222no—
265#382—611no—
266#380—1221no—
267#328—1222no—
268D4⋊C8—1222no—
269D4⋊C8—1222no—
270C61#1000011yescharacteristic, complemented, Sylow
271C22×D4—611no—
272C22×D4—1222no—
273C22×D4C22⋊D6111yescharacteristic
274C23×C4—21no—
275C23×C4—1221no—
276C2×SD16—1222no—
277C2×M16—21no—
278C4⋊Q8C22⋊D6111yescharacteristic, complemented
279C4⋊Q8C22⋊D6111yescharacteristic, complemented
280#125—21no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283#121—2442no—
284#121—2442no—
285C4×Q8—21no—
286C4×Q8—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—1221no—
292C4×D4—1221no—
293C4×D4—1221no—
294C4×D4—1221no—
295#117—21no—
296C2×C4⋊C4—611no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4C22⋊D6111yescharacteristic
299C2×C22⋊C4—21no—
300C2×C22⋊C4—1222no—
301C2×C22⋊C4—1222no—
302C2×C22⋊C4—1221no—
303C2×C42C22×D6111yescharacteristic
304#107—22no—
305#106—22no—
306#106—1222no—
307C4⋊C8—21no—
308C4⋊C8—1221no—
309C4⋊C8—1221no—
310C4⋊C8C22⋊D6112yescomplemented
311#103—1222no—
312#102—22no—
313#102—22no—
314#102—1222no—
315C22⋊C8—1221no—
316C22⋊C8—1221no—
317C4×C8—612no—
318C4×C8—1221no—
319#95—612no—
320#95—1222no—
321#95—1221no—
322C24—21no—
323C24—1221no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—1221no—
332C2×D4—1221no—
333C2×D4—4882no—
334C2×D4—2442no—
335C2×D4—2444no—
336C2×D4—2444no—
337C2×D4#1175820112yescomplemented
338C22×C4—21no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—82no—
342C22×C4—1222no—
343C22×C4—1221no—
344C22×C4—2441no—
345C22×C4—2441no—
346C22×C4—2441no—
347C22×C4—2441no—
348C22×C4—2441no—
349C22×C4—2441no—
350C22×C4D4×D6111yescharacteristic
351C22×C4D4×D6111yescharacteristic
352C22×C4C2×C22⋊D6111yescharacteristic
353SD16—2444no—
354M16—41no—
355M16—41no—
356C2×C8—22no—
357C2×C8—1222no—
358C2×C8—2441no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—1221no—
368C4⋊C4—1221no—
369C4⋊C4—2441no—
370C4⋊C4—2441no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—4882no—
375C22⋊C4—2444no—
376C22⋊C4—2441no—
377C22⋊C4—2441no—
378C42—41no—
379C42D4×D6111yescharacteristic
380C42#1175822411yescharacteristic
381C42C2×C22⋊D6111yescharacteristic
382C42C2×C22⋊D6111yescharacteristic
383C23—22no—
384C23—42no—
385C23—42no—
386C23—41no—
387C23—41no—
388C23—1222no—
389C23—2441no—
390C23—2441no—
391C23—2441no—
392C23—2441no—
393C23—2441no—
394C23—2441no—
395C23#1451974511yescharacteristic
396Q8—42no—
397Q8—81no—
398D4—22no—
399D4—22no—
400D4—41no—
401D4—41no—
402D4—1222no—
403D4—1222no—
404D4—4888no—
405D4—2441no—
406D4—2441no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—82no—
414C2×C4—82no—
415C2×C4—4881no—
416C2×C4—4881no—
417C2×C4—4881no—
418C2×C4—4881no—
419C2×C4—2442no—
420C2×C4—2442no—
421C2×C4—2441no—
422C2×C4—2442no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4#1451974511yescharacteristic
426C2×C4#1451974611yescharacteristic
427C2×C4#1451974811yescharacteristic
428C2×C4#1451974911yescharacteristic
429C2×C4#1451974911yescharacteristic
430C2×C4#1451977311yescharacteristic
431C2×C4C2×#1175820111yescharacteristic
432C2×C4#1451979711yescharacteristic
433C2×C4#1451980211yescharacteristic
434C2×C4#1451980811yescharacteristic
435C8—42no—
436C8—4881no—
437C8—2442no—
438C22—21no—
439C22—21no—
440C22—44no—
441C22—42no—
442C22—82no—
443C22—81no—
444C22—81no—
445C22—4881no—
446C22—4881no—
447C22—4881no—
448C22—4881no—
449C22—2442no—
450C22—2442no—
451C22—2442no—
452C22#1683967011yescharacteristic
453C22#1683991211yescharacteristic
454C22#1683992211yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—4882no—
463C4—4881no—
464C4#1683990111yescharacteristic
465C4#1683990711yescharacteristic
466C4#1683999311yescharacteristic
467C4#1684001011yescharacteristic
468C2—21no—
469C2—21no—
470C2—82no—
471C2—4882no—
472C2#2144682011yescharacteristic
473C2#2144687011yescharacteristic
474C2#2144688311yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3077C2
socleC22×C61#392
prime radical#21450716C2
hypercenter#3077D61
hypocenterC61#10000
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #21455823C2semidirect
3. #21444383C2semidirect
4. #21444243C2semidirect
5. #21444210C2semidirect
6. #21443679C2semidirect
7. C61×#3077C2semidirect
56. C4×#92418D4semidirect
63. C4⋊Q8×C61D4semidirect
64. C4⋊Q8×C61D4semidirect
81. C4⋊C8×C61D4semidirect
93. C2×D4×C61SD16semidirect
232. #3077D61semidirect
270. C61#10000semidirect
278. C4⋊Q8C22⋊D61semidirect
279. C4⋊Q8C22⋊D61semidirect
310. C4⋊C8C22⋊D61semidirect
337. C2×D4#11758201semidirect

Maximal subgroups

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

subgroupindex
#214558232
#214507162
#214443832
#214442432
#214442102
#214436792
C61×#30772
#1000061