Finite Group Databasebeta

← #29583313

Subgroups — #29583313

Order 15616.

694 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446127C211yesmaximal, characteristic, complemented
2#21446006C211yesmaximal, characteristic, complemented
3C2×#16839499C211yesmaximal, characteristic, complemented
4C2×#16839486C211yesmaximal, characteristic
5#21444064C211yesmaximal, characteristic
6#21443697C211yesmaximal, characteristic, complemented
7C61×#2626C211yesmaximal, characteristic
8C22×C4⋊Dic61C2211yescharacteristic
9C22×C22⋊Dic61—21no—
10C2×#14519710—21no—
11C2×#14519701—21no—
12C2×C22⋊#92418C2211yescharacteristic
13C2×C22⋊#92418C2211yescharacteristic
14C2×#14519684—21no—
15C2×#14519684C2211yescharacteristic
16#16839524—21no—
17#16839524—21no—
18#16839499—22no—
19#16839486—22no—
20C2×C22⋊Q8×C61C2211yescharacteristic
21C22×C22⋊C4×C61C2211yescharacteristic
22C61×#399—21no—
23C61×#396—21no—
24C61×#396—21no—
25C61×#393—21no—
26C61×#385—21no—
27C61×#380C2211yescharacteristic
28C61×#379—21no—
29C23×Dic61—21no—
30C23×Dic61—21no—
31C22×#92418—21no—
32C22×#92418—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—42no—
36C2×C22⋊Dic61—42no—
37C2×C22⋊Dic61—42no—
38C2×C22⋊Dic61—42no—
39#14519710—42no—
40#14519701—42no—
41C22⋊#92418—21no—
42C22⋊#92418—21no—
43C22⋊#92418—21no—
44C22⋊#92418D412yes—
45#14519684—21no—
46#14519684—21no—
47#14519684—42no—
48C25×C61D411yescharacteristic
49C22×Q8×C61D411yescharacteristic
50C23×C4×C61D411yescharacteristic
51C23×C4×C61C2311yescharacteristic
52C22⋊Q8×C61—21no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61—21no—
55C22⋊Q8×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61D411yescharacteristic
60C2×C4⋊C4×C61D411yescharacteristic
61C2×C4⋊C4×C61D411yescharacteristic
62C2×C22⋊C4×C61—21no—
63C2×C22⋊C4×C61—21no—
64C2×C22⋊C4×C61—21no—
65C2×C22⋊C4×C61—21no—
66C2×C22⋊C4×C61—21no—
67C2×C22⋊C4×C61—21no—
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74#95×C61—21no—
75#95×C61—21no—
76#95×C61—21no—
77C24×C61—21no—
78C24×C61—21no—
79C24×C61—21no—
80C24×C61—21no—
81C24×C61—21no—
82C24×C61—21no—
83C24×C61—41no—
84C24×C61—41no—
85C24×C61—41no—
86C24×C61—41no—
87C24×C61Q1612yes—
88C24×C61C2×D411yescharacteristic
89C2×Q8×C61—21no—
90C2×Q8×C61—21no—
91C2×Q8×C61—41no—
92C2×Q8×C61—41no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61—41no—
103C22×C4×C61—41no—
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61#4111yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C22×Dic61—22no—
111C22×Dic61—22no—
112C22×Dic61—41no—
113C22×Dic61—41no—
114C22×Dic61—41no—
115C22×Dic61—41no—
116C22×Dic61—41no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C22×Dic61—41no—
121C22×Dic61—41no—
122C22×Dic61—41no—
123C22×Dic61—41no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61—21no—
126C4⋊C4×C61—41no—
127C4⋊C4×C61—41no—
128C4⋊C4×C61—41no—
129C4⋊C4×C61—41no—
130C4⋊C4×C61—81no—
131C4⋊C4×C61—81no—
132C22⋊C4×C61—41no—
133C22⋊C4×C61—41no—
134C22⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C22⋊C4×C61—81no—
141C22⋊C4×C61—81no—
142C22⋊C4×C61—81no—
143C22⋊C4×C61—81no—
144C22⋊Dic61—48no—
145C4⋊Dic61—22no—
146C4⋊Dic61—22no—
147C4⋊Dic61—41no—
148C4⋊Dic61—41no—
149C2×#92418—22no—
150C2×#92418—41no—
151C2×#92418—41no—
152C2×#92418—41no—
153C2×#92418—41no—
154C2×#92418—41no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—21no—
159C23×C61—22no—
160C23×C61—22no—
161C23×C61—22no—
162C23×C61—42no—
163C23×C61—42no—
164C23×C61—42no—
165C23×C61—42no—
166C23×C61—42no—
167C23×C61—42no—
168C23×C61—41no—
169C23×C61—41no—
170C23×C61—41no—
171C23×C61—41no—
172C23×C61—41no—
173C23×C61—41no—
174C23×C61—41no—
175C23×C61—41no—
176C23×C61—81no—
177C23×C61—81no—
178C23×C61—81no—
179C23×C61—81no—
180C23×C61—81no—
181C23×C61—81no—
182C23×C61#12011yescharacteristic
183C23×C61#12111yescharacteristic
184C23×C61#12311yescharacteristic
185C23×C61C2×Q1611yescharacteristic
186C23×C61#13511yescharacteristic
187C23×C61AGL(1,ℤ/8)11yescharacteristic
188C23×C61#13711yescharacteristic
189Q8×C61—42no—
190Q8×C61—81no—
191C2×C4×C61—21no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—42no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—81no—
216C2×C4×C61#12111yescharacteristic
217C2×C4×C61#12111yescharacteristic
218C2×C4×C61#12311yescharacteristic
219C2×C4×C61#12411yescharacteristic
220C2×Dic61—42no—
221C2×Dic61—42no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61—42no—
225C2×Dic61—42no—
226C2×Dic61—81no—
227C2×Dic61—81no—
228C2×Dic61—81no—
229C2×Dic61—81no—
230C2×Dic61—81no—
231C2×Dic61—81no—
232C2×Dic61—81no—
233C2×Dic61—81no—
234#92418—42no—
235#92418—81no—
236#10399—611nomaximal, Sylow
237C22×C61—21no—
238C22×C61—21no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—21no—
249C22×C61—44no—
250C22×C61—42no—
251C22×C61—42no—
252C22×C61—42no—
253C22×C61—82no—
254C22×C61—82no—
255C22×C61—82no—
256C22×C61—81no—
257C22×C61—81no—
258C22×C61—81no—
259C22×C61—81no—
260C22×C61#39411yescharacteristic
261C22×C61#44911yescharacteristic
262C22×C61#45111yescharacteristic
263C22×C61#45311yescharacteristic
264C22×C61#45511yescharacteristic
265C22×C61B(4,𝔽2)11yescharacteristic
266C22×C61#45811yescharacteristic
267C22×C61#46711yescharacteristic
268C22×C61#46811yescharacteristic
269C22×C61#48411yescharacteristic
270C22×C61#48511yescharacteristic
271C4×C61—21no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61—81no—
279C4×C61—81no—
280Dic61—82no—
281Dic61—82no—
282#2626D6111yescharacteristic
283#1872—611no—
284#1852—611no—
285C2×#328—611no—
286C2×#323—611no—
287#1439—611no—
288#1294—611no—
289C2×C61—21no—
290C2×C61—21no—
291C2×C61—21no—
292C2×C61—21no—
293C2×C61—82no—
294C2×C61#160011yescharacteristic
295C2×C61#160211yescharacteristic
296C2×C61#161211yescharacteristic
297C2×C61#161411yescharacteristic
298C2×C61#203611yescharacteristic
299C2×C61#203711yescharacteristic
300C2×C61#204411yescharacteristic
301C2×C22⋊Q8C2×D6111yescharacteristic
302C22×C4⋊C4—611no—
303C22×C22⋊C4—1221no—
304C22×C22⋊C4C2×D6111yescharacteristic
305C2×#107—1221no—
306C2×#103—1221no—
307C2×C22⋊C8—611no—
308C2×C22⋊C8—611no—
309#399—21no—
310#396—21no—
311#396—21no—
312#393—21no—
313#385—21no—
314#380C2×D6111yescharacteristic
315#379—21no—
316C2×#95—611no—
317C2×#95—1221no—
318#340—1221no—
319#340—1221no—
320#328—1222no—
321#323—1222no—
322C61#1039911yescharacteristic, complemented, Sylow
323C25C22⋊D6111yescharacteristic
324C22×Q8C22⋊D6111yescharacteristic
325C23×C4—1221no—
326C23×C4—1221no—
327C23×C4C22⋊D6111yescharacteristic
328C23×C4C22×D6111yescharacteristic
329C22×C8—1221no—
330C22×C8—1221no—
331C22⋊Q8—21no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—1221no—
339C2×C4⋊C4—1221no—
340C2×C4⋊C4—2442no—
341C2×C4⋊C4C22⋊D6111yescharacteristic
342C2×C4⋊C4C22⋊D6111yescharacteristic
343C2×C4⋊C4C22⋊D6111yescharacteristic
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—2442no—
357C2×C22⋊C4—2442no—
358C2×C22⋊C4—2442no—
359#107—2442no—
360#103—2442no—
361C22⋊C8—612no—
362C22⋊C8—1221no—
363C22⋊C8—1221no—
364C22⋊C8—1221no—
365#95—21no—
366#95—21no—
367#95—21no—
368#95—1221no—
369#95—1221no—
370#95—2442no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24#1175820212yes—
382C24C2×C22⋊D6111yescharacteristic
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—41no—
386C2×Q8—41no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—1222no—
399C22×C4—1222no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4—2441no—
403C22×C4—2441no—
404C22×C4—2441no—
405C22×C4—2441no—
406C22×C4—2441no—
407C22×C4—2441no—
408C22×C4—2441no—
409C22×C4—2441no—
410C22×C4—2441no—
411C22×C4—2441no—
412C22×C4D4×D6111yescharacteristic
413C22×C4#1175822411yescharacteristic
414C22×C4#1175822411yescharacteristic
415C22×C4#1175822411yescharacteristic
416C22×C4C2×C22⋊D6111yescharacteristic
417C22×C4C2×C22⋊D6111yescharacteristic
418C2×C8—1222no—
419C2×C8—2441no—
420C2×C8—2441no—
421C2×C8—2441no—
422C2×C8—2441no—
423C2×C8—2441no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—81no—
431C4⋊C4—81no—
432C4⋊C4—1222no—
433C4⋊C4—1222no—
434C4⋊C4—2441no—
435C4⋊C4—2441no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—81no—
445C22⋊C4—81no—
446C22⋊C4—81no—
447C22⋊C4—81no—
448C22⋊C4—2448no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—81no—
471C23—81no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—81no—
476C23#1451974611yescharacteristic
477C23#1451974911yescharacteristic
478C23#1451975811yescharacteristic
479C23C2×#1175820211yescharacteristic
480C23#1451979711yescharacteristic
481C23#1451980211yescharacteristic
482C23#1451980811yescharacteristic
483Q8—42no—
484Q8—81no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—81no—
510C2×C4—4881no—
511C2×C4—4881no—
512C2×C4—4881no—
513C2×C4—4881no—
514C2×C4—4881no—
515C2×C4—4881no—
516C2×C4—4881no—
517C2×C4—4881no—
518C2×C4—2442no—
519C2×C4—2442no—
520C2×C4—2442no—
521C2×C4—2442no—
522C2×C4—2442no—
523C2×C4—2442no—
524C2×C4#1451974811yescharacteristic
525C2×C4#1451974911yescharacteristic
526C2×C4#1451975811yescharacteristic
527C2×C4#1451976411yescharacteristic
528C8—4881no—
529C8—2442no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22#1683967611yescharacteristic
554C22#1683990711yescharacteristic
555C22#1683991811yescharacteristic
556C22#1683993011yescharacteristic
557C22#1683994011yescharacteristic
558C22#1683994911yescharacteristic
559C22#1683995211yescharacteristic
560C22#1684000111yescharacteristic
561C22#1684001011yescharacteristic
562C22#1684009511yescharacteristic
563C22#1684010011yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—4882no—
574C4—4882no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—82no—
580C2#2144476511yescharacteristic
581C2#2144477611yescharacteristic
582C2#2144483311yescharacteristic
583C2#2144484411yescharacteristic
584C2#2144701911yescharacteristic
585C2#2144702611yescharacteristic
586C2#2144706711yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2626C2
socleC23×C61#120
prime radicalC25×C61D4
hypercenter#2626D61
hypocenterC61#10399
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2626

Complements

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

NH ≅ G/Ntype
1. #21446127C2semidirect
2. #21446006C2semidirect
3. C2×#16839499C2semidirect
6. #21443697C2semidirect
322. C61#10399semidirect

Maximal subgroups

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

subgroupindex
#214461272
#214460062
C2×#168394992
C2×#168394862
#214440642
#214436972
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