Finite Group Databasebeta

← #29578014

Subgroups — #29578014

Order 15616.

626 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 91 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#21454858C211yesmaximal, characteristic, complemented
2#21450709C211yesmaximal, characteristic
3#21444155C211yesmaximal, characteristic, complemented
4#21444146C211yesmaximal, characteristic, complemented
5#21443726C211yesmaximal, characteristic, complemented
6#21443724C211yesmaximal, characteristic, complemented
7C61×#1462C211yesmaximal, characteristic, complemented
8C2×#14519760C411yescharacteristic
9C2×#14519746C411yescharacteristic
10C2×C4×C22⋊D61C2211yescharacteristic
11#16839838—22no—
12#16839837—22no—
13#16839812—21no—
14#16839726C2211yescharacteristic
15#16839726C2211yescharacteristic
16#16839724—21no—
17#16839685—21no—
18#16839678—21no—
19#16839650—21no—
20#16839638—21no—
21#16839625C411yescharacteristic
22#16839622C2211yescharacteristic
23#16839618C411yescharacteristic
24#16839487—21no—
25#16839486—22no—
26#16839485—21no—
27C22×C22⋊C4×C61C2211yescharacteristic
28C61×#407C2211yescharacteristic
29C61×#407C2211yescharacteristic
30C61×#323—22no—
31C22×C22⋊D61—21no—
32C22×C22⋊D61C2×C411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C2×#11758194—21no—
35C2×#11758194—21no—
36C2×#11758189—22no—
37#14519760—42no—
38#14519746—42no—
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41C4×C22⋊D61—21no—
42C4×C22⋊D61—21no—
43C2×C4⋊Dic61—21no—
44C2×#11758196—21no—
45C2×#11758196D411yescharacteristic
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61C2×C411yescharacteristic
50C2×C22⋊Dic61C2×C411yescharacteristic
51C2×C22⋊Dic61C2×C411yescharacteristic
52C2×#11758198—21no—
53C2×#11758198D411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55#14519706—22no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59C22⋊#92418D412yescomplemented
60#14519689—22no—
61C8×Dic61—22no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65C25×C61C2×C411yescharacteristic
66C23×C4×C61C2×C411yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C2×M16×C61—21no—
69C2×M16×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61—21no—
79C22⋊C8×C61D412yescomplemented
80C24×C61—21no—
81C24×C61—21no—
82C24×C61—21no—
83C24×C61—42no—
84C24×C61—41no—
85C24×C61—41no—
86C24×C61—81no—
87C24×C61C22×C411yescharacteristic
88C23×D61C22⋊C411yescharacteristic
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—81no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61#4111yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C2×C22⋊D61—21no—
102C2×C22⋊D61—21no—
103C2×C22⋊D61—22no—
104C2×C22⋊D61—41no—
105C2×C22⋊D61—42no—
106C2×C22⋊D61—42no—
107C2×C22⋊D61—81no—
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C22⋊C411yescharacteristic
112C22×Dic61C22⋊C411yescharacteristic
113C2×C4×D61—21no—
114C2×C4×D61—21no—
115C2×C4×D61—81no—
116M16×C61—81no—
117M16×C61—81no—
118C2×C8×C61—22no—
119C2×C8×C61—41no—
120C22⋊C4×C61—41no—
121C22⋊C4×C61—41no—
122C22⋊C4×C61—41no—
123C22⋊C4×C61—41no—
124C22⋊Dic61—21no—
125C22⋊Dic61—21no—
126C22⋊Dic61—42no—
127C22⋊Dic61—42no—
128C22⋊Dic61—41no—
129C22⋊Dic61—41no—
130C22⋊Dic61—81no—
131#11758198—21no—
132#11758198—21no—
133#11758198—42no—
134C4⋊Dic61—81no—
135#11758196—21no—
136#11758196—21no—
137#11758196—42no—
138C4×Dic61—21no—
139C4×Dic61—21no—
140#11758194—81no—
141#11758194—81no—
142C2×#92418—22no—
143C2×#92418—41no—
144#11758189—82no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—22no—
148C23×C61—22no—
149C23×C61—22no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61—81no—
161C23×C61—81no—
162C23×C61—81no—
163C23×C61—81no—
164C23×C61—84no—
165C23×C61—84no—
166C23×C61C2×C22⋊C411yescharacteristic
167C23×C61C4×D411yescharacteristic
168C23×C61C4×D411yescharacteristic
169C22×D61—21no—
170C22×D61—21no—
171C22×D61—21no—
172C22×D61—41no—
173C22×D61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—81no—
184C2×C4×C61—81no—
185C2×C4×C61#12011yescharacteristic
186C2×C4×C61#12111yescharacteristic
187C2×C4×C61#12111yescharacteristic
188C2×C4×C61#12311yescharacteristic
189C22⋊D61—42no—
190C22⋊D61—42no—
191C22⋊D61—84no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61#10012yes—
205C4×D61—42no—
206C4×D61—81no—
207C8×C61—42no—
208C8×C61—81no—
209#92418—42no—
210#92418—81no—
211#9516—611nomaximal, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—42no—
221C22×C61—42no—
222C22×C61—42no—
223C22×C61—42no—
224C22×C61—42no—
225C22×C61—81no—
226C22×C61—81no—
227C22×C61—82no—
228C22×C61—82no—
229C22×C61—82no—
230C22×C61—82no—
231C22×C61—81no—
232C22×C61—81no—
233C22×C61#38611yescharacteristic
234C22×C61C2×#10011yescharacteristic
235C22×C61#41311yescharacteristic
236C2×D61—42no—
237C2×D61—41no—
238C2×D61—41no—
239C2×D61—41no—
240C2×D61—81no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—81no—
246Dic61—22no—
247Dic61—41no—
248Dic61—41no—
249Dic61—81no—
250Dic61—81no—
251#2975—611no—
252#2534—611no—
253#1465—611no—
254#1462—611no—
255#1462D6111yescharacteristic, complemented
256#1305—611no—
257#1305—611no—
258C2×C61—21no—
259C2×C61—21no—
260C2×C61—41no—
261C2×C61—41no—
262C2×C61—82no—
263C2×C61#189111yescharacteristic
264C2×C61#190011yescharacteristic
265C2×C61#191311yescharacteristic
266D61—81no—
267C2×#123—611no—
268C2×#120—611no—
269C2×C4×D4—611no—
270C22×C22⋊C4C2×D6111yescharacteristic
271#436—1222no—
272#436—1222no—
273#431—1221no—
274#407—611no—
275#407—611no—
276#407—1221no—
277#407C2×D6111yescharacteristic
278#407C2×D6111yescharacteristic
279#396—1221no—
280#394—1221no—
281#388—1221no—
282#386—1221no—
283#381—611no—
284#380—611no—
285#379—611no—
286#324—1221no—
287#323—22no—
288#323—1221no—
289#323—1222no—
290C61#951611yescharacteristic, complemented, Sylow
291C25C4×D6111yescharacteristic
292C22×D4—611no—
293C22×D4—1221no—
294C23×C4—611no—
295C23×C4C4×D6111yescharacteristic
296C23×C4C22×D6111yescharacteristic
297C2×M16—21no—
298C2×M16—21no—
299C2×M16—1222no—
300C2×M16—1221no—
301C2×M16—1221no—
302#123—2442no—
303#120—2442no—
304C4×D4—1221no—
305C4×D4—1221no—
306C4×D4—1221no—
307C4×D4—1221no—
308C2×C4⋊C4—611no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1221no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—611no—
318C2×C22⋊C4—611no—
319C2×C22⋊C4—611no—
320C2×C22⋊C4—611no—
321C2×C22⋊C4—1221no—
322C2×C22⋊C4—1221no—
323C2×C22⋊C4—1221no—
324C2×C22⋊C4—1221no—
325C2×C42—611no—
326C4⋊C8—1222no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C22⋊C8—612no—
331C22⋊C8—1222no—
332C22⋊C8—1221no—
333C22⋊C8—1221no—
334C22⋊C8—1221no—
335C22⋊C8C22⋊D6112yescomplemented
336C4×C8—1222no—
337#95—1221no—
338#95—1221no—
339#95—1221no—
340C24—21no—
341C24—21no—
342C24—21no—
343C24—42no—
344C24—41no—
345C24—41no—
346C24—81no—
347C24—611no—
348C24C2×C4×D6111yescharacteristic
349C2×D4—1222no—
350C2×D4—1221no—
351C2×D4—1221no—
352C2×D4—4881no—
353C2×D4—2441no—
354C2×D4—2442no—
355C2×D4—2442no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—81no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—1221no—
366C22×C4—1221no—
367C22×C4—1221no—
368C22×C4—1221no—
369C22×C4—4881no—
370C22×C4#1175822211yescharacteristic
371C22×C4D4×D6111yescharacteristic
372C22×C4D4×D6111yescharacteristic
373C22×C4D4×D6111yescharacteristic
374C22×C4#1175822411yescharacteristic
375C22×C4C2×C22⋊D6111yescharacteristic
376M16—81no—
377M16—81no—
378M16—4882no—
379M16—4881no—
380M16—4881no—
381C2×C8—22no—
382C2×C8—41no—
383C2×C8—1222no—
384C2×C8—2441no—
385C4⋊C4—1221no—
386C4⋊C4—1221no—
387C4⋊C4—4881no—
388C4⋊C4—2442no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—1221no—
394C22⋊C4—1221no—
395C22⋊C4—1221no—
396C22⋊C4—1221no—
397C22⋊C4—4881no—
398C22⋊C4—2442no—
399C22⋊C4—2442no—
400C22⋊C4—2442no—
401C22⋊C4—2441no—
402C22⋊C4—2441no—
403C42—1221no—
404C42—1221no—
405C23—21no—
406C23—21no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—41no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—81no—
421C23—81no—
422C23—81no—
423C23—81no—
424C23—84no—
425C23—84no—
426C23—1221no—
427C23—1221no—
428C23—1221no—
429C23—2441no—
430C23—2441no—
431C23C22⋊C4×D6111yescharacteristic
432C23#1451973711yescharacteristic
433C23C4×C22⋊D6111yescharacteristic
434D4—4884no—
435D4—2442no—
436D4—2442no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—612no—
449C2×C4—1221no—
450C2×C4—1221no—
451C2×C4—1221no—
452C2×C4—1221no—
453C2×C4—4881no—
454C2×C4—2442no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4—2441no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4#1451974511yescharacteristic
464C2×C4#1451974811yescharacteristic
465C2×C4#1451975011yescharacteristic
466C2×C4#1451975911yescharacteristic
467C8—42no—
468C8—81no—
469C8—4881no—
470C8—2442no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—81no—
485C22—81no—
486C22—82no—
487C22—82no—
488C22—82no—
489C22—82no—
490C22—81no—
491C22—81no—
492C22—4881no—
493C22—2442no—
494C22—2441no—
495C22—2441no—
496C22—2441no—
497C22#1683963811yescharacteristic
498C22#100×D6111yescharacteristic
499C22#1683974311yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—81no—
505C4—1222no—
506C4—4881no—
507C4—4881no—
508C4—2441no—
509C4—2441no—
510C2—21no—
511C2—21no—
512C2—41no—
513C2—41no—
514C2—82no—
515C2—4881no—
516C2#2144623411yescharacteristic
517C2#2144627911yescharacteristic
518C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1462C2
socleC22×C61#386
prime radicalC2×#14519746C4
cosocleC23×C4×C61C23
hypercenter#1462D61
hypocenterC61#9516
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
1. #21454858C2semidirect
3. #21444155C2semidirect
4. #21444146C2semidirect
5. #21443726C2semidirect
6. #21443724C2semidirect
7. C61×#1462C2semidirect
59. C22⋊#92418D4semidirect
79. C22⋊C8×C61D4semidirect
255. #1462D61semidirect
290. C61#9516semidirect
335. C22⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214548582
#214507092
#214441552
#214441462
#214437262
#214437242
C61×#14622
#951661