Finite Group Databasebeta

← #29580799

Subgroups — #29580799

Order 15616.

692 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 85 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#21456806C211yesmaximal, characteristic, complemented
2#21455910C211yesmaximal, characteristic, complemented
3#21446737C211yesmaximal, characteristic, complemented
4#21444417C211yesmaximal, characteristic, complemented
5#21444262C211yesmaximal, characteristic, complemented
6#21443675C211yesmaximal, characteristic, complemented
7C61×#2540C211yesmaximal, characteristic, complemented
8#16840312C2211yescharacteristic
9#16840152—21no—
10#16840121—21no—
11#16840080—21no—
12#16840052—21no—
13#16839974—22no—
14#16839957—21no—
15#16839901—21no—
16#16839896—21no—
17#16839896—21no—
18#16839872—22no—
19#16839819C2211yescharacteristic
20#16839819C2211yescharacteristic
21C2×#14519705—22no—
22C4×#11758194C2211yescharacteristic
23#16839502—22no—
24D4⋊#92418—22no—
25C2×#124×C61C2211yescharacteristic
26C2×C22⋊Q8×C61—21no—
27C2×#121×C61—21no—
28C2×C4×D4×C61C2211yescharacteristic
29C61×#399—21no—
30C61×#392—21no—
31C61×#390—22no—
32C4×C4⋊C4×C61C2211yescharacteristic
33C2×#11758222—21no—
34C2×#11758201—22no—
35C2×#11758199—22no—
36C2×#11758199—22no—
37C2×#11758194—21no—
38#14519777D411yescharacteristic, complemented
39#14519774D411yescharacteristic, complemented
40#14519765—21no—
41#14519751—21no—
42#14519751—21no—
43C4×D244—21no—
44C4×D244—21no—
45#14519708—22no—
46C4⋊#92418—21no—
47C4⋊#92418D412yescomplemented
48#14519705—44no—
49#14519701—22no—
50#14519698—22no—
51#14519698—22no—
52#14519697—22no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55#14519688—21no—
56#14519688—21no—
57#14519688D412yescomplemented
58C4×#92418—21no—
59C22×Q8×C61D411yescharacteristic
60C22×D4×C61—22no—
61C22×D4×C61D411yescharacteristic
62C22×D4×C61D411yescharacteristic
63C23×C4×C61—21no—
64#124×C61—21no—
65#124×C61—21no—
66#124×C61—21no—
67#124×C61—21no—
68C22⋊Q8×C61—44no—
69#121×C61—44no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C4×D4×C61—21no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61—22no—
76C2×C4⋊C4×C61D411yescharacteristic
77C2×C22⋊C4×C61—22no—
78C2×C22⋊C4×C61—22no—
79C2×C22⋊C4×C61—21no—
80C2×C22⋊C4×C61—21no—
81C2×C22⋊C4×C61—21no—
82C2×C42×C61D412yes—
83C2×C42×C61C2311yescharacteristic
84#95×C61—21no—
85C24×C61—21no—
86C24×C61—21no—
87C2×Q8×C61—21no—
88C2×Q8×C61—21no—
89C2×Q8×C61—42no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—42no—
95C2×D4×C61—44no—
96C2×D4×C61—42no—
97C2×D4×C61—44no—
98C2×D4×C61—82no—
99C22×C4×C61—22no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—42no—
103C22×C4×C61—42no—
104C22×C4×C61—41no—
105C22×C4×C61—41no—
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C2×C22⋊D61—41no—
110#11758222—42no—
111#11758222—42no—
112C2×D244—21no—
113C2×D244—21no—
114C2×D244—21no—
115C2×C4×D61—41no—
116C2×Dic122—21no—
117C4⋊C4×C61—24no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—44no—
121C22⋊C4×C61—44no—
122C22⋊C4×C61—44no—
123C22⋊C4×C61—41no—
124C22⋊C4×C61—41no—
125C22⋊C4×C61—41no—
126C22⋊C4×C61—41no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—41no—
129C42×C61—42no—
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61C2×D411yescharacteristic
133C42×C61#4111yescharacteristic
134#11758201—82no—
135#11758199—44no—
136#11758199—82no—
137#11758198—41no—
138#11758198—41no—
139C4⋊Dic61—21no—
140C4⋊Dic61—21no—
141#11758194—22no—
142#11758194—41no—
143C2×#92418—22no—
144C2×#92418—22no—
145C2×#92418—41no—
146C23×C61—22no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61—42no—
151C23×C61—42no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61#12011yescharacteristic
159C22×D61—41no—
160Q8×C61—42no—
161Q8×C61—81no—
162D4×C61—22no—
163D4×C61—22no—
164D4×C61—41no—
165D4×C61—41no—
166D4×C61—42no—
167D4×C61—81no—
168D4×C61—88no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—22no—
172C2×C4×C61—24no—
173C2×C4×C61—41no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—41no—
177C2×C4×C61—42no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—82no—
182C2×C4×C61—82no—
183C2×C4×C61#12011yescharacteristic
184C2×C4×C61#12011yescharacteristic
185C2×C4×C61#12111yescharacteristic
186C2×C4×C61#12111yescharacteristic
187C2×C4×C61#12111yescharacteristic
188C2×C4×C61#12711yescharacteristic
189C22⋊D61—81no—
190C22⋊D61—81no—
191C2×Dic61—41no—
192D244—42no—
193D244—42no—
194D244—42no—
195C4×D61—82no—
196Dic122—42no—
197#92418—42no—
198#92418—42no—
199#92418—42no—
200#10004—611nomaximal, Sylow
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—42no—
204C22×C61—42no—
205C22×C61—42no—
206C22×C61—81no—
207C22×C61—81no—
208C22×C61—82no—
209C22×C61—82no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61—81no—
213C22×C61—81no—
214C22×C61—81no—
215C22×C61#39211yescharacteristic
216C22×C61#45311yescharacteristic
217C22×C61#45411yescharacteristic
218C2×D61—81no—
219C2×D61—81no—
220C2×D61—81no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—44no—
227C4×C61—81no—
228C4×C61—81no—
229C4×C61#45312yes—
230Dic61—81no—
231#3213—611no—
232#3109—611no—
233#2540D6111yescharacteristic, complemented
234#1980—611no—
235#1527—611no—
236#1490—611no—
237#1285—611no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61—82no—
241C2×C61—161no—
242C2×C61#200211yescharacteristic
243C2×C61#200611yescharacteristic
244C2×C61#201011yescharacteristic
245D61—161no—
246#532—611no—
247C2×#124C2×D6111yescharacteristic
248C2×C22⋊Q8—21no—
249C2×#121—21no—
250C2×C4×D4C2×D6111yescharacteristic
251#496—1221no—
252#489—1221no—
253#481—1221no—
254#476—1221no—
255#463—1222no—
256#459—1221no—
257#448—1221no—
258#447—1221no—
259#447—1221no—
260#442—1222no—
261#432—611no—
262#432—611no—
263C2×#104—1222no—
264C4×M16—611no—
265#399—21no—
266#392—21no—
267#390—22no—
268C4×C4⋊C4C2×D6111yescharacteristic
269#329—1222no—
270D4⋊C8—1222no—
271C61#1000411yescharacteristic, complemented, Sylow
272C2×#41—1221no—
273C22×Q8C22⋊D6111yescharacteristic
274C22×D4—22no—
275C22×D4C22⋊D6111yescharacteristic
276C22×D4C22⋊D6111yescharacteristic
277C23×C4—21no—
278C2×SD16—1222no—
279C2×D8—1222no—
280C2×D8—1222no—
281C2×M16—1221no—
282C4⋊Q8—611no—
283#127—611no—
284#124—21no—
285#124—21no—
286#124—21no—
287#124—21no—
288#124—1221no—
289C22⋊Q8—44no—
290#121—44no—
291#121—1221no—
292#121—1221no—
293C4×D4—21no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4—21no—
297C4×D4—1221no—
298C4×D4—1221no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4C22⋊D6111yescharacteristic
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C42C22⋊D6112yes—
308C2×C42C22×D6111yescharacteristic
309#106—1222no—
310C4⋊C8—612no—
311C4⋊C8—1221no—
312#104—2444no—
313#103—1222no—
314#102—1222no—
315#102—1222no—
316#102—1222no—
317C22⋊C8—1221no—
318C22⋊C8—1221no—
319#97—612no—
320#97—1221no—
321#97—1221no—
322C4×C8—1221no—
323#95—21no—
324C24—21no—
325C24—21no—
326#41—2442no—
327#41—2442no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—42no—
331C2×Q8—1221no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—21no—
336C2×D4—42no—
337C2×D4—44no—
338C2×D4—42no—
339C2×D4—44no—
340C2×D4—82no—
341C2×D4—1221no—
342C2×D4—1221no—
343C2×D4—1221no—
344C2×D4—2441no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—2441no—
353C22×C4C2×C22⋊D6111yescharacteristic
354C22×C4C2×C22⋊D6111yescharacteristic
355C22×C4C2×C22⋊D6111yescharacteristic
356SD16—4882no—
357D8—4882no—
358D8—2444no—
359M16—1222no—
360M16—2441no—
361C2×C8—1222no—
362C2×C8—1222no—
363C2×C8—2441no—
364C4⋊C4—24no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—44no—
368C4⋊C4—1221no—
369C4⋊C4—1221no—
370C22⋊C4—44no—
371C22⋊C4—44no—
372C22⋊C4—41no—
373C22⋊C4—41no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—2441no—
379C22⋊C4—2441no—
380C42—42no—
381C42D4×D6111yescharacteristic
382C42D4×D6111yescharacteristic
383C42D4×D6111yescharacteristic
384C42#1175822411yescharacteristic
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—42no—
390C23—42no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—2441no—
398C23#1451974611yescharacteristic
399Q8—42no—
400Q8—81no—
401Q8—2442no—
402D4—22no—
403D4—22no—
404D4—41no—
405D4—41no—
406D4—42no—
407D4—81no—
408D4—88no—
409D4—4881no—
410D4—4881no—
411D4—2442no—
412D4—2442no—
413D4—2442no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—4882no—
429C2×C4—2441no—
430C2×C4#1451974511yescharacteristic
431C2×C4#1451974511yescharacteristic
432C2×C4#1451974811yescharacteristic
433C2×C4#1451974911yescharacteristic
434C2×C4#1451974911yescharacteristic
435C2×C4#1451977311yescharacteristic
436C8—2442no—
437C8—2442no—
438C8—2442no—
439C22—21no—
440C22—21no—
441C22—42no—
442C22—42no—
443C22—42no—
444C22—81no—
445C22—81no—
446C22—82no—
447C22—82no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—4881no—
454C22—4881no—
455C22—4881no—
456C22#1683967011yescharacteristic
457C22#1683993011yescharacteristic
458C22#1683993511yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—44no—
465C4—81no—
466C4—81no—
467C4—4881no—
468C4#1683992912yes—
469C2—21no—
470C2—21no—
471C2—82no—
472C2—161no—
473C2—9761no—
474C2#2144683411yescharacteristic
475C2#2144686111yescharacteristic
476C2#2144688411yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2540C2
socleC22×C61#392
hypercenter#2540D61
hypocenterC61#10004
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. #21456806C2semidirect
2. #21455910C2semidirect
3. #21446737C2semidirect
4. #21444417C2semidirect
5. #21444262C2semidirect
6. #21443675C2semidirect
7. C61×#2540C2semidirect
38. #14519777D4semidirect
39. #14519774D4semidirect
47. C4⋊#92418D4semidirect
57. #14519688D4semidirect
233. #2540D61semidirect
271. C61#10004semidirect

Maximal subgroups

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

subgroupindex
#214568062
#214559102
#214467372
#214444172
#214442622
#214436752
C61×#25402
#1000461