Finite Group Databasebeta

← #29578070

Subgroups — #29578070

Order 15616.

686 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 89 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#21455079C211yesmaximal, characteristic
2#21448572C211yesmaximal, characteristic, complemented
3#21445763C211yesmaximal, characteristic
4#21444351C211yesmaximal, characteristic, complemented
5#21443727C211yesmaximal, characteristic, complemented
6#21443671C211yesmaximal, characteristic, complemented
7C61×#1782C211yesmaximal, characteristic
8C2×#14519807—21no—
9C2×#14519756C2211yescharacteristic
10#16839924—22no—
11#16839918C412yescomplemented
12#16839913C412yescomplemented
13C2×#14519704—21no—
14C2×#14519704—21no—
15#16839763—21no—
16#16839726C2211yescharacteristic
17#16839726C2211yescharacteristic
18#16839666—21no—
19#16839656—21no—
20#16839650—21no—
21#16839645—21no—
22#16839644—21no—
23#16839613—21no—
24C4×C22⋊Dic61C2211yescharacteristic
25#16839498—22no—
26C22×#41×C61C2211yescharacteristic
27C2×#99×C61—21no—
28C2×#99×C61—21no—
29C61×#381C2211yescharacteristic
30C61×#381C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32#14519807—42no—
33#14519807—42no—
34C2×#11758202—22no—
35C2×#11758200—22no—
36C2×#11758194—21no—
37C2×#11758194—21no—
38#14519756—21no—
39#14519756—21no—
40#14519756C2×C412yes—
41#14519756D412yes—
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C4×Dic61—21no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52#14519704—42no—
53#14519704—42no—
54#14519701—22no—
55#14519698—22no—
56C22⋊#92418—21no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59C22⋊#92418C2×C412yes—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65C2×#41×C61—21no—
66C2×#41×C61—21no—
67C2×#41×C61—21no—
68C2×#41×C61—21no—
69C2×#41×C61—42no—
70C2×#41×C61—42no—
71C22×Q8×C61C2×C411yescharacteristic
72C22×D4×C61—21no—
73C22×D4×C61C2×C411yescharacteristic
74C23×C4×C61—21no—
75C23×C4×C61C2311yescharacteristic
76C2×C22⋊C4×C61—21no—
77C2×C22⋊C4×C61D411yescharacteristic
78C2×C22⋊C4×C61D411yescharacteristic
79#99×C61—42no—
80#99×C61—42no—
81#95×C61—21no—
82#95×C61—21no—
83#95×C61—21no—
84#95×C61—21no—
85C24×C61—21no—
86C24×C61C2×D411yescharacteristic
87#41×C61—22no—
88#41×C61—22no—
89#41×C61—22no—
90#41×C61—22no—
91#41×C61—41no—
92#41×C61—41no—
93#41×C61—41no—
94#41×C61—41no—
95#41×C61—42no—
96#41×C61—42no—
97#41×C61—42no—
98#41×C61—42no—
99C2×Q8×C61—21no—
100C2×Q8×C61—21no—
101C2×Q8×C61—42no—
102C2×D4×C61—22no—
103C2×D4×C61—22no—
104C2×D4×C61—21no—
105C2×D4×C61—21no—
106C2×D4×C61—42no—
107C2×D4×C61—41no—
108C2×D4×C61—41no—
109C2×D4×C61—41no—
110C2×D4×C61—41no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61—42no—
117C22×C4×C61—42no—
118C22×C4×C61—41no—
119C22×C4×C61—41no—
120C22×C4×C61—41no—
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61#4111yescharacteristic
126C22×C4×C61#4111yescharacteristic
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C2×Dic122—21no—
132C2×Dic122—41no—
133C2×Dic122—41no—
134C2×Dic122C22⋊C412yes—
135C22⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C22⋊Dic61—22no—
140C22⋊Dic61—22no—
141C22⋊Dic61—42no—
142#11758202—44no—
143#11758200—44no—
144C4⋊Dic61—21no—
145C4⋊Dic61C22⋊C412yes—
146#11758196—22no—
147#11758196—22no—
148#11758196—42no—
149#11758196—81no—
150C4×Dic61—42no—
151C4×Dic61—41no—
152C4×Dic61—41no—
153C4×Dic61—81no—
154#11758194—41no—
155#11758194—41no—
156#11758194—41no—
157#11758194—41no—
158C2×#92418—22no—
159C2×#92418—41no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—22no—
163C23×C61—41no—
164C23×C61—41no—
165C23×C61—41no—
166C23×C61—41no—
167C23×C61—81no—
168C23×C61—81no—
169C23×C61C4×D411yescharacteristic
170C23×C61#12011yescharacteristic
171C23×C61#12111yescharacteristic
172Q8×C61—22no—
173Q8×C61—22no—
174Q8×C61—41no—
175Q8×C61—41no—
176D4×C61—22no—
177D4×C61—22no—
178D4×C61—41no—
179D4×C61—41no—
180D4×C61—42no—
181D4×C61—42no—
182D4×C61—42no—
183D4×C61—42no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—22no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—42no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—42no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—81no—
206C2×C4×C61—81no—
207C2×C4×C61—81no—
208C2×C4×C61C2×C22⋊C411yescharacteristic
209C2×C4×C61C4×D411yescharacteristic
210C2×C4×C61#12111yescharacteristic
211C2×C4×C61#12311yescharacteristic
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—22no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61—41no—
219C2×Dic61—41no—
220C2×Dic61—41no—
221C2×Dic61—41no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224Dic122—42no—
225Dic122—81no—
226#92418—42no—
227#92418—81no—
228#9524—611nomaximal, Sylow
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—42no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61—82no—
241C22×C61—82no—
242C22×C61—81no—
243C22×C61—81no—
244C22×C61#38611yescharacteristic
245C22×C61B(4,𝔽2)11yescharacteristic
246C22×C61B(4,𝔽2)11yescharacteristic
247C4×C61—21no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—42no—
252C4×C61—81no—
253C4×C61—81no—
254C4×C61—161no—
255Dic61—42no—
256Dic61—42no—
257Dic61—42no—
258Dic61—81no—
259#3007—611no—
260#2332—611no—
261#1789—611no—
262#1782D6111yescharacteristic
263#1511—611no—
264#1306—611no—
265#1284—611no—
266C2×C61—21no—
267C2×C61—21no—
268C2×C61—41no—
269C2×C61—41no—
270C2×C61—82no—
271C2×C61#188911yescharacteristic
272C2×C61#190511yescharacteristic
273C2×C61#190611yescharacteristic
274C22×#41C2×D6111yescharacteristic
275C2×#137—1221no—
276C2×C22⋊Q8—611no—
277#452—1222no—
278#451—612no—
279#450—612no—
280C2×#104—1221no—
281C2×#104—1221no—
282#417—1221no—
283C2×#99—21no—
284C2×#99—21no—
285#407—611no—
286#407—611no—
287#391—1221no—
288#388—1221no—
289#388—1221no—
290#387—1221no—
291#387—1221no—
292#381C2×D6111yescharacteristic
293#381C2×D6111yescharacteristic
294C4×C4⋊C4—1221no—
295C4×C22⋊C4—611no—
296#328—1222no—
297C61#952411yescharacteristic, complemented, Sylow
298C2×#41—21no—
299C2×#41—21no—
300C2×#41—21no—
301C2×#41—21no—
302C2×#41—42no—
303C2×#41—42no—
304C22×Q8—611no—
305C22×Q8C4×D6111yescharacteristic
306C22×D4—21no—
307C22×D4C4×D6111yescharacteristic
308C23×C4—21no—
309C23×C4C22×D6111yescharacteristic
310#137—2442no—
311#137—2442no—
312C2×Q16—1222no—
313C2×SD16—1222no—
314C2×M16—1221no—
315C2×M16—1221no—
316C22⋊Q8—612no—
317C22⋊Q8—612no—
318C22⋊Q8—1221no—
319C22⋊Q8—1221no—
320C2×C4⋊C4—611no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4—1221no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—1221no—
326C2×C22⋊C4—1221no—
327C2×C22⋊C4C22⋊D6111yescharacteristic
328C2×C22⋊C4C22⋊D6111yescharacteristic
329C2×C42—611no—
330C2×C42—611no—
331C2×C42—1221no—
332C2×C42—1221no—
333#104—2442no—
334#104—2442no—
335#103—1222no—
336#102—1222no—
337#99—42no—
338#99—42no—
339C22⋊C8—612no—
340C22⋊C8—1221no—
341C22⋊C8—1221no—
342C22⋊C8—1221no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—1221no—
348#95—1221no—
349#95—1221no—
350#95—1221no—
351#95—1221no—
352C24—21no—
353C24C2×C22⋊D6111yescharacteristic
354#41—22no—
355#41—22no—
356#41—22no—
357#41—22no—
358#41—41no—
359#41—41no—
360#41—41no—
361#41—41no—
362#41—42no—
363#41—42no—
364#41—42no—
365#41—42no—
366C2×Q8—21no—
367C2×Q8—21no—
368C2×Q8—42no—
369C2×Q8—612no—
370C2×Q8—1221no—
371C2×Q8—2441no—
372C2×Q8—2441no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—42no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—1221no—
395C22×C4—1221no—
396C22×C4C2×C4×D6111yescharacteristic
397C22×C4#1175822211yescharacteristic
398C22×C4D4×D6111yescharacteristic
399C22×C4D4×D6111yescharacteristic
400C22×C4D4×D6111yescharacteristic
401C22×C4#1175822411yescharacteristic
402Q16—2444no—
403SD16—2444no—
404M16—2441no—
405M16—2441no—
406M16—2441no—
407M16—2441no—
408C2×C8—1222no—
409C2×C8—2441no—
410C4⋊C4—612no—
411C4⋊C4—1222no—
412C4⋊C4—1222no—
413C4⋊C4—1221no—
414C4⋊C4—4881no—
415C4⋊C4—2442no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—1222no—
421C22⋊C4—1222no—
422C22⋊C4—2442no—
423C42—4881no—
424C42—2441no—
425C42—2441no—
426C42—2442no—
427C23—21no—
428C23—21no—
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—81no—
435C23—81no—
436C23C4×C22⋊D6111yescharacteristic
437C23#1451974511yescharacteristic
438C23#1451974811yescharacteristic
439Q8—22no—
440Q8—22no—
441Q8—41no—
442Q8—41no—
443Q8—4881no—
444Q8—2442no—
445D4—22no—
446D4—22no—
447D4—41no—
448D4—41no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4C22⋊C4×D6111yescharacteristic
490C2×C4#1451973711yescharacteristic
491C2×C4#1451975011yescharacteristic
492C2×C4#1451975911yescharacteristic
493C8—4881no—
494C8—2442no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—42no—
504C22—81no—
505C22—81no—
506C22—82no—
507C22—82no—
508C22—81no—
509C22—81no—
510C22#1683963811yescharacteristic
511C22#1683994811yescharacteristic
512C22#1683994811yescharacteristic
513C4—21no—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—42no—
518C4—81no—
519C4—81no—
520C4—161no—
521C4—4881no—
522C4—2442no—
523C4—2442no—
524C4—2442no—
525C2—21no—
526C2—21no—
527C2—41no—
528C2—41no—
529C2—82no—
530C2#2144622411yescharacteristic
531C2#2144631611yescharacteristic
532C2#2144631711yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1782C2
socleC22×C61#386
prime radicalC22×#41×C61C22
cosocleC23×C4×C61C23
hypercenter#1782D61
hypocenterC61#9524
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1782

Complements

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

NH ≅ G/Ntype
2. #21448572C2semidirect
4. #21444351C2semidirect
5. #21443727C2semidirect
6. #21443671C2semidirect
11. #16839918C4semidirect
12. #16839913C4semidirect
297. C61#9524semidirect

Maximal subgroups

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

subgroupindex
#214550792
#214485722
#214457632
#214443512
#214437272
#214436712
C61×#17822
#952461