Finite Group Databasebeta

← #30620824

Subgroups — #30620824

Order 15616.

724 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461920C211yesmaximal, characteristic, complemented
2#21461919C211yesmaximal, characteristic, complemented
3#21461879C211yesmaximal, characteristic, complemented
4#21461876C211yesmaximal, characteristic, complemented
5#21461875C211yesmaximal, characteristic, complemented
6#21461872C211yesmaximal, characteristic, complemented
7#21461677C211yesmaximal, characteristic
8#21461677C211yesmaximal, characteristic
9#21461673C211yesmaximal, characteristic
10#21461618C211yesmaximal, characteristic, complemented
11#21461618C211yesmaximal, characteristic, complemented
12#21461549C211yesmaximal, characteristic
13#21461549C211yesmaximal, characteristic
14#21461545C211yesmaximal, characteristic
15#21448221C211yesmaximal, characteristic
16C2×#14519844C2211yescharacteristic
17C2×#14519844C2211yescharacteristic
18C2×C4⋊#92420C2211yescharacteristic
19C2×C4⋊#92420C2211yescharacteristic
20C2×C4⋊#92420C2211yescharacteristic
21C2×C4⋊#92420C2211yescharacteristic
22C2×C22⋊#92420C2211yescharacteristic
23C2×C22⋊#92420C2211yescharacteristic
24C2×C22⋊#92420C2211yescharacteristic
25C2×C22⋊#92420C2211yescharacteristic
26C2×#14519832C2211yescharacteristic
27C2×#14519832C2211yescharacteristic
28C2×#14519832C2211yescharacteristic
29C2×#14519832C2211yescharacteristic
30C2×C4×#92420C2211yescharacteristic
31C2×C4×#92420C2211yescharacteristic
32#16840628C2211yescharacteristic
33#16840628C2211yescharacteristic
34#16840628C2211yescharacteristic
35#16840628C2211yescharacteristic
36#16840628C2211yescharacteristic
37#16840628C2211yescharacteristic
38#16840628C2211yescharacteristic
39#16840628C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44C2×#14519733C2211yescharacteristic
45C2×#14519733C2211yescharacteristic
46C22×C4×Dic61C2211yescharacteristic
47#16839631C411yescharacteristic
48#16839631C411yescharacteristic
49#16839626C411yescharacteristic
50#16839626C411yescharacteristic
51#16839622C411yescharacteristic
52#16839620C411yescharacteristic
53#16839620C411yescharacteristic
54C4⋊C4×Dic61C2211yescharacteristic
55C4⋊C4×Dic61C2211yescharacteristic
56#16839613C2211yescharacteristic
57#16839613C2211yescharacteristic
58C61×#380C411yescharacteristic
59C22×#92420C2311yescharacteristic
60C22×#92420C2311yescharacteristic
61C22×#92420C2311yescharacteristic
62C22×#92420C2311yescharacteristic
63C22×#92420C2311yescharacteristic
64C22×#92420C2311yescharacteristic
65C22×#92420C2311yescharacteristic
66C22×#92420C2311yescharacteristic
67#14519844—41no—
68#14519844—41no—
69C4⋊#92420—22no—
70C4⋊#92420—22no—
71C4⋊#92420—41no—
72C4⋊#92420—41no—
73C22⋊#92420—22no—
74C22⋊#92420—22no—
75C22⋊#92420—22no—
76C22⋊#92420Q814yes—
77#14519832—22no—
78#14519832—22no—
79#14519832—41no—
80#14519832—41no—
81C4×#92420—41no—
82C4×#92420—41no—
83C23×Dic61C2×C411yescharacteristic
84C23×Dic61C2311yescharacteristic
85#14519733—41no—
86#14519733—41no—
87#14519733—41no—
88#14519733—41no—
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×#11758196C2×C411yescharacteristic
92C2×#11758196C2×C411yescharacteristic
93C2×#11758196C2×C411yescharacteristic
94C2×#11758196C2×C411yescharacteristic
95C2×#11758196C2×C411yescharacteristic
96C2×#11758196C2×C411yescharacteristic
97C2×#11758196C2×C411yescharacteristic
98C2×#11758196C2×C411yescharacteristic
99C2×C22⋊Dic61C2×C411yescharacteristic
100C2×C22⋊Dic61C2×C411yescharacteristic
101C2×C4×Dic61—22no—
102C2×C4×Dic61—22no—
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111#14519684C2×C411yescharacteristic
112#14519684C2×C411yescharacteristic
113#14519684C2×C411yescharacteristic
114#14519684C2×C411yescharacteristic
115#14519684C2×C411yescharacteristic
116#14519684C2×C411yescharacteristic
117C23×C4×C61C2×C411yescharacteristic
118C2×C4⋊C4×C61C2×C411yescharacteristic
119C2×C4⋊C4×C61C2×C411yescharacteristic
120C2×C22⋊C4×C61C2×C411yescharacteristic
121C2×C22⋊C4×C61C2×C411yescharacteristic
122#95×C61C2×C411yescharacteristic
123#95×C61C2×C411yescharacteristic
124C24×C61C22×C411yescharacteristic
125C22×C4×C61—22no—
126C22×C4×C61—22no—
127C22×C4×C61—41no—
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C22×C411yescharacteristic
130C22×C4×C61C22×C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—22no—
139C22×Dic61—41no—
140C22×Dic61—41no—
141C22×Dic61C22×C411yescharacteristic
142C22×Dic61C22×C411yescharacteristic
143C22×Dic61C22×C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C2×Q812yes—
149C22×Dic61#4112yes—
150C22×Dic61C2411yescharacteristic
151C2×#92420—21no—
152C2×#92420—21no—
153C2×#92420—21no—
154C2×#92420—21no—
155C2×#92420—21no—
156C2×#92420—21no—
157C2×#92420—21no—
158C2×#92420—21no—
159C2×#92420—21no—
160C2×#92420—21no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—21no—
171C2×#92420—21no—
172C2×#92420—21no—
173C2×#92420C2×Q812yes—
174C2×#92420C2×Q812yes—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—41no—
177C22⋊C4×C61—41no—
178C22⋊C4×C61—41no—
179C22⋊Dic61—41no—
180C22⋊Dic61—41no—
181C4⋊Dic61—22no—
182C4⋊Dic61—41no—
183#11758196—41no—
184#11758196—41no—
185#11758196—41no—
186#11758196—41no—
187#11758196—41no—
188#11758196—41no—
189#11758196—41no—
190#11758196—41no—
191C4×Dic61—22no—
192C4×Dic61—22no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61#4112yes—
204C4×Dic61#4112yes—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61C4×Q812yes—
212C23×C61C23×C411yescharacteristic
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—44no—
230C2×C4×C61#11712yes—
231C2×C4×C61#13112yes—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—44no—
256C2×Dic61#11712yes—
257C2×Dic61C4×Q812yes—
258C2×Dic61C22×Q811yescharacteristic
259C2×Dic61C2×#4111yescharacteristic
260C2×Dic61C2×#4111yescharacteristic
261C2×Dic61C2×#4111yescharacteristic
262C2×Dic61H(5,𝔽2)11yescharacteristic
263C2×Dic61H(5,𝔽2)11yescharacteristic
264#92420—22no—
265#92420—22no—
266#92420—41no—
267#92420—41no—
268#92420—41no—
269#92420—41no—
270#92420—41no—
271#92420—41no—
272#22628—611nomaximal, Sylow
273C22×C61—22no—
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61—41no—
280C22×C61C2×#11711yescharacteristic
281C22×C61C2×C4×Q811yescharacteristic
282C22×C61#51811yescharacteristic
283C22×C61C2×#13111yescharacteristic
284C22×C61#56811yescharacteristic
285C22×C61#56811yescharacteristic
286C22×C61#56811yescharacteristic
287C4×C61—22no—
288C4×C61—22no—
289C4×C61—41no—
290C4×C61—41no—
291C4×C61—41no—
292C4×C61—41no—
293Dic61—22no—
294Dic61—22no—
295Dic61—41no—
296Dic61—41no—
297Dic61—41no—
298Dic61—41no—
299Dic61—41no—
300Dic61#55311yescharacteristic
301Dic61#55311yescharacteristic
302Dic61#55411yescharacteristic
303Dic61#55411yescharacteristic
304#2285—611no—
305#1940—611no—
306#1940—611no—
307#1917—611no—
308#1917—611no—
309#1916—611no—
310#1916—611no—
311#1798—611no—
312#1798—611no—
313#1797—611no—
314#1771—611no—
315#1771—611no—
316#1750—611no—
317#1750—611no—
318#1749—611no—
319C2×C61—42no—
320C2×C61#234511yescharacteristic
321C2×C61#292111yescharacteristic
322C2×C61#292411yescharacteristic
323C2×C61#296111yescharacteristic
324C2×C61#296211yescharacteristic
325C2×C61#298011yescharacteristic
326C2×C61#298111yescharacteristic
327C2×#117—611no—
328C2×#117—611no—
329C22×C42—611no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8—611no—
334C2×C4⋊C8—611no—
335C2×C4⋊C8—611no—
336C2×C22⋊C8—611no—
337C2×C22⋊C8—611no—
338C2×C22⋊C8—611no—
339C2×C22⋊C8—611no—
340C2×#97—611no—
341C2×#97—611no—
342C2×#97—611no—
343C2×#97—611no—
344C2×C4×C8—611no—
345C2×C4×C8—611no—
346#384—611no—
347#384—611no—
348#382—611no—
349#382—611no—
350#380—611no—
351#380—611no—
352#380—611no—
353#380#692311yescharacteristic
354C4×C4⋊C4—611no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—611no—
357C4×C4⋊C4—611no—
358#336—611no—
359#336—611no—
360#336—611no—
361#336—611no—
362#336—611no—
363#336—611no—
364#336—611no—
365#336—611no—
366#336—611no—
367#336—611no—
368#336—611no—
369#336—611no—
370C61#2262811yescharacteristic, complemented, Sylow
371C23×C4—611no—
372C23×C4—611no—
373C23×C4C2×#692311yescharacteristic
374C22×C8—611no—
375C22×C8—611no—
376C22×C8—611no—
377C22×C8—611no—
378C22×C8—611no—
379C22×C8—611no—
380C22×C8—611no—
381C22×C8—611no—
382#117—2441no—
383#117—2441no—
384#117—2441no—
385#117—2441no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—611no—
393C2×C4⋊C4—611no—
394C2×C4⋊C4—611no—
395C2×C4⋊C4—611no—
396C2×C4⋊C4C2×#692311yescharacteristic
397C2×C4⋊C4C2×#692311yescharacteristic
398C2×C22⋊C4—611no—
399C2×C22⋊C4—611no—
400C2×C22⋊C4C2×#692311yescharacteristic
401C2×C22⋊C4C2×#692311yescharacteristic
402C2×C42—611no—
403C2×C42—611no—
404C2×C42—611no—
405C2×C42—611no—
406C2×C42—611no—
407C2×C42—611no—
408C2×C42—611no—
409C2×C42—611no—
410C2×C42—1222no—
411C2×C42—1222no—
412C4⋊C8—1222no—
413C4⋊C8—1222no—
414C4⋊C8—2441no—
415C4⋊C8—2441no—
416C4⋊C8—2441no—
417C4⋊C8—2441no—
418C22⋊C8—614no—
419C22⋊C8—1222no—
420C22⋊C8—1222no—
421C22⋊C8—1222no—
422#97—1222no—
423#97—1222no—
424#97—2441no—
425#97—2441no—
426C4×C8—2441no—
427C4×C8—2441no—
428#95—611no—
429#95—611no—
430#95—611no—
431#95—611no—
432#95—611no—
433#95—611no—
434#95C2×#692311yescharacteristic
435#95C2×#692311yescharacteristic
436C24C22×#692311yescharacteristic
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—41no—
440C22×C4—611no—
441C22×C4—612no—
442C22×C4—612no—
443C22×C4—611no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—611no—
448C22×C4—611no—
449C22×C4—611no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1222no—
455C22×C4—2441no—
456C22×C4—2441no—
457C22×C4C22×#692311yescharacteristic
458C22×C4C22×#692311yescharacteristic
459C22×C4C22×#692311yescharacteristic
460C22×C4C22×#692311yescharacteristic
461C22×C4C22×#692311yescharacteristic
462C22×C4C22×#692311yescharacteristic
463C2×C8—612no—
464C2×C8—612no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1221no—
480C2×C8—1221no—
481C2×C8—1221no—
482C2×C8—1221no—
483C2×C8—1221no—
484C2×C8—1221no—
485C2×C8—1221no—
486C2×C8—1221no—
487C4⋊C4—22no—
488C4⋊C4—41no—
489C4⋊C4—1222no—
490C4⋊C4—2441no—
491C4⋊C4—2441no—
492C4⋊C4—2441no—
493C4⋊C4—2441no—
494C4⋊C4—2441no—
495C4⋊C4—2441no—
496C4⋊C4—2441no—
497C4⋊C4—2441no—
498C4⋊C4—2441no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—2441no—
502C22⋊C4—2441no—
503C42—612no—
504C42—612no—
505C42—1221no—
506C42—1221no—
507C42—1221no—
508C42—1221no—
509C42—1221no—
510C42—1221no—
511C42—1221no—
512C42—1221no—
513C42—1221no—
514C42—1221no—
515C42—1222no—
516C42—1222no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23Q8×#692312yes—
524C23C23×#692311yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—44no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—611no—
546C2×C4—611no—
547C2×C4—611no—
548C2×C4—612no—
549C2×C4—612no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—2444no—
574C2×C4#1451985612yes—
575C2×C4#1451986412yes—
576C8—1222no—
577C8—1222no—
578C8—2441no—
579C8—2441no—
580C8—2441no—
581C8—2441no—
582C8—2441no—
583C8—2441no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22C2×#1451985611yescharacteristic
592C22C2×Q8×#692311yescharacteristic
593C22#1684082911yescharacteristic
594C22C2×#1451986411yescharacteristic
595C22#1684084011yescharacteristic
596C22#1684084111yescharacteristic
597C22#1684084111yescharacteristic
598C4—22no—
599C4—22no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—611no—
605C4—611no—
606C4—611no—
607C4—611no—
608C4—1222no—
609C4—1222no—
610C4—2441no—
611C4—2441no—
612C4—2441no—
613C4—2441no—
614C4—2441no—
615C2—42no—
616C2#2146232811yescharacteristic
617C2#2146250011yescharacteristic
618C2#2146250811yescharacteristic
619C2#2146261011yescharacteristic
620C2#2146261411yescharacteristic
621C2#2146270311yescharacteristic
622C2#2146270911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#380C4
prime radicalC24×C61C22×C4
cosocleC22×Dic61C24
hypercenter#380#6923
hypocenterC61#22628
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. #21461920C2semidirect
2. #21461919C2semidirect
3. #21461879C2semidirect
4. #21461876C2semidirect
5. #21461875C2semidirect
6. #21461872C2semidirect
10. #21461618C2semidirect
11. #21461618C2semidirect
370. C61#22628semidirect

Maximal subgroups

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

subgroupindex
#214619202
#214619192
#214618792
#214618762
#214618752
#214618722
#214616772
#214616732
#214616182
#214615492
#214615452
#214482212
#2262861