Finite Group Databasebeta

← #29737198

Subgroups — #29737198

Order 15616.

966 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840054C211yesmaximal, characteristic, complemented
2C2×#16839755C211yesmaximal, characteristic
3#21449506C211yesmaximal, characteristic, complemented
4#21448658C211yesmaximal, characteristic
5#21447342C211yesmaximal, characteristic, complemented
6#21447207C211yesmaximal, characteristic, complemented
7#21447203C211yesmaximal, characteristic, complemented
8#21446090C211yesmaximal, characteristic, complemented
9#21446074C211yesmaximal, characteristic, complemented
10#21446019C211yesmaximal, characteristic, complemented
11#21445998C211yesmaximal, characteristic, complemented
12#21445847C211yesmaximal, characteristic, complemented
13#21445833C211yesmaximal, characteristic, complemented
14#21445756C211yesmaximal, characteristic
15C61×#2023C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C2×#14519742C2211yescharacteristic
20C2×#14519735C2211yescharacteristic
21#16840054—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28#16839755—24no—
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519689C2211yescharacteristic
36#16839684—21no—
37#16839673—21no—
38#16839669—21no—
39#16839665C2211yescharacteristic
40#16839662—21no—
41#16839662—21no—
42#16839661C2211yescharacteristic
43#16839660C2211yescharacteristic
44#16839643—21no—
45#16839627C2211yescharacteristic
46#16839620—21no—
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49C22⋊C4×Dic61—21no—
50C4×#11758198C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839516C2211yescharacteristic
54C2×C4⋊Q8×C61C2211yescharacteristic
55C2×#102×C61C2211yescharacteristic
56C2×#102×C61C2211yescharacteristic
57C61×#390C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#336C2211yescharacteristic
61C2×#11758224—22no—
62C2×#11758224—22no—
63C2×#11758224—22no—
64C2×#11758224—41no—
65C2×#11758224—41no—
66C2×#11758224Q814yescomplemented
67C22×Dic122C2311yescharacteristic
68C22×C22⋊D61—21no—
69C23×Dic61—21no—
70C22×C4×D61C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C2×C8×D61—22no—
74C2×C8×D61—22no—
75C2×C8×D61—41no—
76C4×Dic122—22no—
77C4×Dic122—41no—
78#14519742—22no—
79#14519742—41no—
80#14519735—22no—
81#14519735—41no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198D411yescharacteristic
95C2×#11758198D411yescharacteristic
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2311yescharacteristic
100#14519710—22no—
101#14519710—22no—
102#14519710—41no—
103#14519709—41no—
104C4⋊#92418—22no—
105#14519706—41no—
106#14519702—22no—
107#14519702—22no—
108#14519700—22no—
109#14519700D414yes—
110#14519698—22no—
111#14519698—41no—
112#14519689—22no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684D411yescharacteristic
120#14519684D411yescharacteristic
121C22×Q8×C61—21no—
122C22×D4×C61C2311yescharacteristic
123C22×C8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C4⋊Q8×C61—22no—
126C4⋊Q8×C61—41no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C42×C61C2311yescharacteristic
134#102×C61—22no—
135#102×C61—41no—
136C24×C61—21no—
137C23×D61C2×D411yescharacteristic
138C2×Q8×C61—42no—
139C2×Q8×C61—42no—
140C2×Q8×C61—81no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61C2×Q812yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C2×C22⋊D61—24no—
154C2×C22⋊D61—42no—
155C2×C22⋊D61—42no—
156C22×Dic61—21no—
157C22×Dic61—24no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—42no—
162C22×Dic61—42no—
163C22×Dic61C2×D411yescharacteristic
164C22×Dic61C2×D411yescharacteristic
165C22×Dic61C2×D411yescharacteristic
166#11758224—28no—
167#11758224—44no—
168#11758224—44no—
169#11758224—44no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61C2×Q812yes—
175C2×C4×D61#4112yes—
176C2×Dic122—21no—
177C2×Dic122—21no—
178C2×Dic122—21no—
179C2×Dic122C2×D412yes—
180C2×Dic122C2×Q812yes—
181C2×Dic122#4112yes—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61—21no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—42no—
194C4⋊C4×C61C2×D412yes—
195C22⋊C4×C61—42no—
196C22⋊C4×C61—81no—
197C42×C61—21no—
198C42×C61—21no—
199C22⋊Dic61—42no—
200C22⋊Dic61—81no—
201#11758198—22no—
202#11758198—41no—
203#11758198—42no—
204#11758198—81no—
205#11758198—81no—
206C4⋊Dic61—21no—
207C4⋊Dic61—21no—
208C4⋊Dic61—21no—
209C4⋊Dic61—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61—81no—
213#11758196—42no—
214#11758196—42no—
215#11758196—42no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—42no—
219C4×Dic61—42no—
220C4×Dic61—42no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418C2×D412yes—
227C8×D61—44no—
228C23×C61—22no—
229C23×C61—41no—
230C23×C61—41no—
231C23×C61—41no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61C22×D411yescharacteristic
236C22×D61—21no—
237C22×D61—21no—
238C22×D61—21no—
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—21no—
242C22×D61C22⋊Q812yes—
243Q8×C61—84no—
244D4×C61—22no—
245D4×C61—22no—
246D4×C61—41no—
247D4×C61—41no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—22no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61#13512yes—
263C2×C4×C61C22×D411yescharacteristic
264C2×C4×C61C22×Q811yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61H(5,𝔽2)11yescharacteristic
268C2×C4×C61H(5,𝔽2)11yescharacteristic
269C22⋊D61—48no—
270C2×Dic61—22no—
271C2×Dic61—21no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
277C2×Dic61—21no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—48no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61C22⋊Q812yes—
292C4×D61—22no—
293C4×D61—22no—
294C4×D61—22no—
295C4×D61—22no—
296Dic122—22no—
297Dic122—22no—
298Dic122—22no—
299Dic122C22⋊Q814yes—
300C8×C61—41no—
301C8×C61—41no—
302#92418—22no—
303#92418—41no—
304#25959—611nomaximal, Sylow
305C22×C61—42no—
306C22×C61—42no—
307C22×C61—42no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61C2×C22⋊Q811yescharacteristic
313C22×C61D4211yescharacteristic
314C22×C61#54611yescharacteristic
315C22×C61C2×#13511yescharacteristic
316C22×C61#57511yescharacteristic
317C22×C61#57611yescharacteristic
318C22×C61#57811yescharacteristic
319C2×D61—22no—
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—41no—
323C2×D61—41no—
324C2×D61—41no—
325C2×D61—41no—
326C4×C61—22no—
327C4×C61—41no—
328C4×C61—42no—
329C4×C61—81no—
330C4×C61—81no—
331C4×C61C2×C22⋊Q811yescharacteristic
332C4×C61#54311yescharacteristic
333C4×C61#54611yescharacteristic
334C4×C61#55111yescharacteristic
335Dic61—24no—
336Dic61—22no—
337Dic61—41no—
338Dic61—41no—
339Dic61—81no—
340Dic61—81no—
341Dic61—81no—
342C2×#477—611no—
343C2×#416—611no—
344#2439—611no—
345#2341—611no—
346#2092—611no—
347#2067—611no—
348#2067—611no—
349#2023D6111yescharacteristic, complemented
350#1865—611no—
351#1863—611no—
352#1854—611no—
353#1850—611no—
354#1808—611no—
355#1805—611no—
356#1788—611no—
357C2×C61—82no—
358C2×C61#243711yescharacteristic
359C2×C61#307611yescharacteristic
360C2×C61#308311yescharacteristic
361C2×C61#326811yescharacteristic
362C2×C61#328511yescharacteristic
363C2×C61#330511yescharacteristic
364C2×C61#331311yescharacteristic
365D61—42no—
366C22×#41—611no—
367C23×C8—611no—
368C2×C4⋊Q8C2×D6111yescharacteristic
369C2×C4×Q8—611no—
370C2×C4×Q8—611no—
371C2×#117—611no—
372#477—1224no—
373C2×#107—611no—
374C2×#107—611no—
375C2×#107—611no—
376C2×#106—611no—
377C2×C4⋊C8—611no—
378C2×C4⋊C8—611no—
379#416—1224no—
380C2×#103—611no—
381C2×#103—611no—
382C2×#103—611no—
383C2×#103—611no—
384C2×#102—611no—
385C2×#102—611no—
386C2×#102C2×D6111yescharacteristic
387C2×#102C2×D6111yescharacteristic
388C2×C22⋊C8—611no—
389#396—1221no—
390#393—1221no—
391#391—1221no—
392#390—611no—
393#390—1221no—
394#390—1221no—
395#390C2×D6111yescharacteristic
396#389—611no—
397#389—611no—
398#387—1221no—
399#382—611no—
400#380—611no—
401#380—611no—
402#380—1221no—
403C4×C22⋊C4—611no—
404C4×C22⋊C4—1221no—
405#340—611no—
406#340—611no—
407#340C2×D6111yescharacteristic
408#340C2×D6111yescharacteristic
409#336—611no—
410#336C2×D6111yescharacteristic
411C61#2595911yescharacteristic, complemented, Sylow
412C2×#41—614no—
413C2×#41—1222no—
414C2×#41—1222no—
415C2×#41—1222no—
416C2×#41—2441no—
417C2×#41—2441no—
418C22×Q8—21no—
419C22×Q8—611no—
420C22×D4—1221no—
421C22×D4C22×D6111yescharacteristic
422C23×C4—611no—
423C23×C4—1221no—
424C22×C8—611no—
425C22×C8—611no—
426C22×C8—1222no—
427C22×C8—1222no—
428C22×C8—2441no—
429C22×C8C22×D6111yescharacteristic
430C22×C8C22×D6111yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8—41no—
433C4×Q8—1222no—
434C4×Q8—1222no—
435C4×Q8—2441no—
436C4×Q8—2441no—
437#117—1222no—
438#117—2441no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—611no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—1221no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4C22×D6111yescharacteristic
448C2×C4⋊C4C22×D6111yescharacteristic
449C2×C4⋊C4C22×D6111yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—611no—
453C2×C22⋊C4—611no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C22⋊C4—1221no—
457C2×C22⋊C4—1221no—
458C2×C22⋊C4—1221no—
459C2×C42—611no—
460C2×C42—1221no—
461C2×C42—1221no—
462C2×C42—1221no—
463C2×C42C22×D6111yescharacteristic
464#107—1222no—
465#107—1222no—
466#107—2441no—
467#106—2441no—
468C4⋊C8—1222no—
469C4⋊C8—2441no—
470#103—614no—
471#103—1222no—
472#103—1222no—
473#103—1222no—
474#102—22no—
475#102—41no—
476#102—1222no—
477#102—2441no—
478C22⋊C8—1222no—
479#95—611no—
480#95—611no—
481#95—1221no—
482#95—1221no—
483#95—1221no—
484#95—1221no—
485#95—1221no—
486#95—1221no—
487C24—21no—
488C24—611no—
489#41—1228no—
490#41—2444no—
491#41—2444no—
492#41—2444no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—81no—
496C2×Q8—612no—
497C2×Q8—612no—
498C2×Q8—612no—
499C2×Q8—1221no—
500C2×Q8—1221no—
501C2×Q8—1221no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—1224no—
508C2×D4—2442no—
509C2×D4—2442no—
510C2×D4Q8×D6112yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—611no—
515C22×C4—612no—
516C22×C4—612no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—1224no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1221no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4—1221no—
526C22×C4—1221no—
527C22×C4—1221no—
528C22×C4—2442no—
529C22×C4—2442no—
530C22×C4D4×D6111yescharacteristic
531C22×C4D4×D6111yescharacteristic
532C22×C4C23×D6111yescharacteristic
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—612no—
540C2×C8—1221no—
541C2×C8—1221no—
542C2×C8—1221no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—2444no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C4⋊C4—1221no—
557C4⋊C4—1221no—
558C4⋊C4—4881no—
559C4⋊C4—2442no—
560C4⋊C4—2442no—
561C4⋊C4—2442no—
562C4⋊C4D4×D6112yes—
563C22⋊C4—42no—
564C22⋊C4—81no—
565C22⋊C4—1222no—
566C22⋊C4—4881no—
567C22⋊C4—4881no—
568C22⋊C4—4881no—
569C22⋊C4—2441no—
570C22⋊C4—2442no—
571C22⋊C4—2442no—
572C42—21no—
573C42—21no—
574C42—1221no—
575C42—1221no—
576C42—2442no—
577C42—2442no—
578C42—2442no—
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—612no—
587C23—1221no—
588C23—1221no—
589C23—1221no—
590C23—1221no—
591C23—1221no—
592C23—1221no—
593C23C2×D4×D6111yescharacteristic
594Q8—84no—
595Q8—614no—
596Q8—1222no—
597Q8—1222no—
598Q8—1222no—
599D4—22no—
600D4—22no—
601D4—41no—
602D4—41no—
603D4—2448no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—612no—
619C2×C4—1222no—
620C2×C4—1221no—
621C2×C4—1222no—
622C2×C4—1222no—
623C2×C4—1221no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—1222no—
628C2×C4—1221no—
629C2×C4—1221no—
630C2×C4—1221no—
631C2×C4—1221no—
632C2×C4—1221no—
633C2×C4—1221no—
634C2×C4—2448no—
635C2×C4—2441no—
636C2×C4—2441no—
637C2×C4—2441no—
638C2×C4—2441no—
639C2×C4—2441no—
640C2×C4—2441no—
641C2×C4—2441no—
642C2×C4—2441no—
643C2×C4—2441no—
644C2×C4#1451979812yes—
645C2×C4C2×D4×D6111yescharacteristic
646C2×C4C2×Q8×D6111yescharacteristic
647C2×C4#41×D6111yescharacteristic
648C2×C4#41×D6111yescharacteristic
649C2×C4#1451982211yescharacteristic
650C2×C4#1451982311yescharacteristic
651C8—41no—
652C8—41no—
653C8—1222no—
654C8—2441no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—1222no—
663C22—1222no—
664C22—1222no—
665C22—2441no—
666C22—2441no—
667C22—2441no—
668C22—2441no—
669C22C22⋊Q8×D6111yescharacteristic
670C22#1684039411yescharacteristic
671C22#1684040511yescharacteristic
672C22C2×#1451979811yescharacteristic
673C22#1684055811yescharacteristic
674C22#1684056311yescharacteristic
675C22#1684057811yescharacteristic
676C4—22no—
677C4—41no—
678C4—42no—
679C4—81no—
680C4—81no—
681C4—1222no—
682C4—1224no—
683C4—4881no—
684C4—4881no—
685C4—4881no—
686C4—2441no—
687C4—2441no—
688C4C22⋊Q8×D6111yescharacteristic
689C4#1684038711yescharacteristic
690C4#1684040511yescharacteristic
691C4#1684044211yescharacteristic
692C2—82no—
693C2—2442no—
694C2#2144947911yescharacteristic
695C2#2145560811yescharacteristic
696C2#2145566511yescharacteristic
697C2#2145735711yescharacteristic
698C2#2145755311yescharacteristic
699C2#2145776811yescharacteristic
700C2#2145788411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2023C2
socleC23×C61C22×D4
prime radicalC22×#11758224C22
hypercenter#2023D61
hypocenterC61#25959
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. C2×#16840054C2semidirect
3. #21449506C2semidirect
5. #21447342C2semidirect
6. #21447207C2semidirect
7. #21447203C2semidirect
8. #21446090C2semidirect
9. #21446074C2semidirect
10. #21446019C2semidirect
11. #21445998C2semidirect
12. #21445847C2semidirect
13. #21445833C2semidirect
15. C61×#2023C2semidirect
66. C2×#11758224Q8semidirect
349. #2023D61semidirect
411. C61#25959semidirect

Maximal subgroups

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

subgroupindex
C2×#168400542
C2×#168397552
#214495062
#214486582
#214473422
#214472072
#214472032
#214460902
#214460742
#214460192
#214459982
#214458472
#214458332
#214457562
C61×#20232
#2595961