Finite Group Databasebeta

← #29740077

Subgroups — #29740077

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839974C211yesmaximal, characteristic
2C2×C4×#11758199C211yesmaximal, characteristic
3C4⋊C4×D244C211yesmaximal, characteristic, complemented
4#21447357C211yesmaximal, characteristic, complemented
5#21447315C211yesmaximal, characteristic, complemented
6#21447222C211yesmaximal, characteristic, complemented
7#21447055C211yesmaximal, characteristic, complemented
8#21446498C211yesmaximal, characteristic, complemented
9#21446378C211yesmaximal, characteristic, complemented
10#21446170C211yesmaximal, characteristic
11#21446156C211yesmaximal, characteristic, complemented
12#21446156C211yesmaximal, characteristic, complemented
13#21446066C211yesmaximal, characteristic, complemented
14#21446065C211yesmaximal, characteristic, complemented
15C61×#2447C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×C4⋊C4×D61—21no—
22#16839974—24no—
23C4×#11758199—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519697C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839636—21no—
39#16839636—21no—
40#16839632C2211yescharacteristic
41#16839619—21no—
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C2×#124×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C61×#397—21no—
53C61×#397—21no—
54C61×#391C2211yescharacteristic
55C61×#391C2211yescharacteristic
56C61×#390C2211yescharacteristic
57C61×#389C2211yescharacteristic
58C61×#385—21no—
59C61×#381—21no—
60C4×C4⋊C4×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C4×D61—21no—
63C22×C4×D61—21no—
64C22×C4×D61—21no—
65C2×#11758201—22no—
66C2×#11758201—22no—
67C2×#11758201—22no—
68C2×#11758199—22no—
69C2×#11758199—22no—
70C2×#11758199D414yes—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C4×D244—22no—
76C4×D244—22no—
77C4×D244—22no—
78C4×D244—22no—
79C4×D244—41no—
80C4×D244—41no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C4⋊C4×D61—44no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92#14519710—22no—
93#14519710—41no—
94C4⋊#92418—22no—
95#14519701—22no—
96#14519701—22no—
97#14519701—41no—
98#14519698—22no—
99#14519698—22no—
100#14519698—22no—
101#14519697—22no—
102#14519697—22no—
103C4×#92418—22no—
104#14519684—21no—
105#14519684—21no—
106C22×Q8×C61C2311yescharacteristic
107C22×D4×C61C2311yescharacteristic
108C23×C4×C61—21no—
109#124×C61—22no—
110#124×C61—41no—
111C4×D4×C61—22no—
112C4×D4×C61—41no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61D411yescharacteristic
115C2×C4⋊C4×C61D411yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—21no—
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61—21no—
122C2×C22⋊C4×C61—21no—
123C2×C42×C61C2311yescharacteristic
124C2×C42×C61C2311yescharacteristic
125C2×C42×C61C2311yescharacteristic
126#95×C61—21no—
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61D411yescharacteristic
132#95×C61D411yescharacteristic
133C24×C61—21no—
134C23×D61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×D4×C61—21no—
142C2×D4×C61—21no—
143C2×D4×C61—21no—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61C2×D412yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—42no—
151C22×C4×C61—42no—
152C22×C4×C61—81no—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2411yescharacteristic
160C22×Dic61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244C2×D412yes—
167C2×D244#4112yes—
168C2×D244#4112yes—
169C2×C4×D61—24no—
170C2×C4×D61—42no—
171C2×C4×D61—42no—
172C2×C4×D61—42no—
173C2×C4×D61—42no—
174C2×C4×D61—42no—
175C2×C4×D61—42no—
176C2×C4×D61—81no—
177C2×C4×D61—81no—
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—81no—
185C22⋊C4×C61—42no—
186C22⋊C4×C61—42no—
187C22⋊C4×C61—42no—
188C22⋊C4×C61—42no—
189C22⋊C4×C61—81no—
190C42×C61—21no—
191C42×C61—21no—
192C42×C61—21no—
193C42×C61—21no—
194C42×C61—21no—
195C42×C61—21no—
196#11758201—44no—
197#11758199—28no—
198#11758198—24no—
199#11758198—42no—
200#11758198—42no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—42no—
207C4⋊Dic61—81no—
208C4⋊Dic61#4112yes—
209#11758196—42no—
210#11758196—42no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418C2×D412yes—
223C23×C61—22no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61—41no—
229C23×C61—41no—
230C23×C61C22×D411yescharacteristic
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—22no—
234C22×D61—41no—
235C22×D61—41no—
236C22×D61—41no—
237C22×D61—41no—
238Q8×C61—41no—
239Q8×C61—41no—
240Q8×C61—41no—
241Q8×C61—41no—
242D4×C61—22no—
243D4×C61—22no—
244D4×C61—41no—
245D4×C61—41no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61—41no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—84no—
272C2×C4×C61#13512yes—
273C2×C4×C61AGL(1,ℤ/8)12yes—
274C2×C4×C61C22×D411yescharacteristic
275C2×C4×C61C2×#4111yescharacteristic
276C2×C4×C61C2×#4111yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61H(5,𝔽2)11yescharacteristic
279C2×C4×C612−1+411yescharacteristic
280C2×Dic61—22no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61—41no—
289D244—22no—
290D244—22no—
291D244—22no—
292D244#12314yes—
293C4×D61—48no—
294C4×D61—84no—
295C4×D61—84no—
296#92418—22no—
297#92418—41no—
298#92418—41no—
299#92418—41no—
300#26164—611nomaximal, Sylow
301C22×C61—42no—
302C22×C61—42no—
303C22×C61—42no—
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61#52511yescharacteristic
309C22×C61D4211yescharacteristic
310C22×C61#54811yescharacteristic
311C22×C61C2×#13511yescharacteristic
312C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
313C22×C61#57611yescharacteristic
314C22×C61#57811yescharacteristic
315C2×D61—24no—
316C2×D61—42no—
317C2×D61—42no—
318C2×D61—42no—
319C2×D61—42no—
320C2×D61—42no—
321C2×D61—42no—
322C4×C61—22no—
323C4×C61—22no—
324C4×C61—41no—
325C4×C61—41no—
326C4×C61—41no—
327C4×C61—41no—
328C4×C61—81no—
329C4×C61—81no—
330C4×C61—81no—
331C4×C61C2×#12311yescharacteristic
332C4×C61#53911yescharacteristic
333C4×C61#54711yescharacteristic
334C4×C61#55311yescharacteristic
335Dic61—42no—
336Dic61—81no—
337Dic61—81no—
338C2×#463—611no—
339C2×C4×D8—611no—
340#2447D6111yescharacteristic, complemented
341D4×C4⋊C4—611no—
342#2095—611no—
343#2087—611no—
344#2071—611no—
345#2042—611no—
346#1933—611no—
347#1916—611no—
348#1879—611no—
349#1877—611no—
350#1877—611no—
351#1862—611no—
352#1862—611no—
353C2×C61—82no—
354C2×C61#244311yescharacteristic
355C2×C61#310511yescharacteristic
356C2×C61#312411yescharacteristic
357C2×C61#326411yescharacteristic
358C2×C61#328311yescharacteristic
359C2×C61#336111yescharacteristic
360C2×C61#336711yescharacteristic
361D61—44no—
362C22×SD16—611no—
363C22×D8—611no—
364C2×#124C2×D6111yescharacteristic
365C2×C4×D4—611no—
366C2×C4×D4—611no—
367C2×C4×D4—611no—
368C2×C4×D4C2×D6111yescharacteristic
369C22×C4⋊C4—1221no—
370#463—1224no—
371C4×D8—1224no—
372C2×#107—611no—
373C2×#107—611no—
374C2×C4⋊C8—611no—
375C2×#103—611no—
376C2×#103—611no—
377C2×#103—611no—
378C2×#102—611no—
379C2×#102—611no—
380C2×#102—611no—
381C2×#102—611no—
382C2×#102—611no—
383C2×C4×C8—611no—
384#397—21no—
385#397—21no—
386#391C2×D6111yescharacteristic
387#391C2×D6111yescharacteristic
388#390C2×D6111yescharacteristic
389#389—611no—
390#389—611no—
391#389C2×D6111yescharacteristic
392#385—21no—
393#385—1221no—
394#385—1221no—
395#384—611no—
396#381—21no—
397#380—1221no—
398C4×C4⋊C4C2×D6111yescharacteristic
399#340—611no—
400#340—611no—
401#340—611no—
402#340—611no—
403#336—611no—
404#336—611no—
405#336—611no—
406#336—611no—
407C61#2616411yescharacteristic, complemented, Sylow
408C22×Q8C22×D6111yescharacteristic
409C22×D4—611no—
410C22×D4C22×D6111yescharacteristic
411C23×C4—21no—
412C23×C4—1221no—
413C23×C4—1221no—
414C23×C4—1221no—
415C2×SD16—1222no—
416C2×SD16—1222no—
417C2×SD16—1222no—
418C2×D8—614no—
419C2×D8—1222no—
420C2×D8—1222no—
421C22×C8—611no—
422C22×C8—611no—
423C22×C8—611no—
424C22×C8—611no—
425#124—22no—
426#124—41no—
427C4×D4—22no—
428C4×D4—41no—
429C4×D4—1222no—
430C4×D4—1222no—
431C4×D4—1222no—
432C4×D4—1222no—
433C4×D4—2441no—
434C4×D4—2441no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—611no—
437C2×C4⋊C4—611no—
438C2×C4⋊C4—611no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4—1221no—
442C2×C4⋊C4—1221no—
443C2×C4⋊C4—2444no—
444C2×C4⋊C4C22⋊D6111yescharacteristic
445C2×C4⋊C4C22⋊D6111yescharacteristic
446C2×C4⋊C4C22×D6111yescharacteristic
447C2×C4⋊C4C22×D6111yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—1221no—
454C2×C22⋊C4—1221no—
455C2×C22⋊C4—1221no—
456C2×C42C22×D6111yescharacteristic
457C2×C42C22×D6111yescharacteristic
458C2×C42C22×D6111yescharacteristic
459#107—1222no—
460#107—2441no—
461C4⋊C8—1222no—
462#103—1222no—
463#103—1222no—
464#103—2441no—
465#102—1222no—
466#102—1222no—
467#102—1222no—
468#102—1222no—
469#102—1222no—
470C4×C8—1222no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—1221no—
477#95—1221no—
478#95C22⋊D6111yescharacteristic
479#95C22⋊D6111yescharacteristic
480C24—21no—
481C24—1221no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—612no—
494C2×D4—612no—
495C2×D4—612no—
496C2×D4—1221no—
497C2×D4—1221no—
498C2×D4—1221no—
499C2×D4D4×D6112yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—81no—
506C22×C4—1224no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—4881no—
511C22×C4—4881no—
512C22×C4—2442no—
513C22×C4—2442no—
514C22×C4—2442no—
515C22×C4—2442no—
516C22×C4—2442no—
517C22×C4—2442no—
518C22×C4C2×C22⋊D6111yescharacteristic
519C22×C4C2×C22⋊D6111yescharacteristic
520C22×C4C2×C22⋊D6111yescharacteristic
521C22×C4C2×C22⋊D6111yescharacteristic
522C22×C4C2×C22⋊D6111yescharacteristic
523C22×C4C2×C22⋊D6111yescharacteristic
524C22×C4C23×D6111yescharacteristic
525SD16—2444no—
526D8—1228no—
527C2×C8—612no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C2×C8—1221no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—81no—
546C4⋊C4—612no—
547C4⋊C4—1221no—
548C4⋊C4—1221no—
549C4⋊C4—1221no—
550C4⋊C4—1221no—
551C4⋊C4—1221no—
552C4⋊C4—4881no—
553C4⋊C4—2442no—
554C4⋊C4—2442no—
555C4⋊C4—2442no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—81no—
561C22⋊C4—1224no—
562C22⋊C4—2442no—
563C22⋊C4—2442no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—1222no—
578C23—1222no—
579C23—1222no—
580C23—2441no—
581C23—2441no—
582C23—2441no—
583C23—2441no—
584C23C22×C22⋊D6111yescharacteristic
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589D4—22no—
590D4—22no—
591D4—41no—
592D4—41no—
593D4—614no—
594D4—1222no—
595D4—1222no—
596D4—1222no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—84no—
623C2×C4—1222no—
624C2×C4—4884no—
625C2×C4—4884no—
626C2×C4—2448no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4—2441no—
634C2×C4—2441no—
635C2×C4#1451979712yes—
636C2×C4#1451980212yes—
637C2×C4C2×D4×D6111yescharacteristic
638C2×C4#41×D6111yescharacteristic
639C2×C4#41×D6111yescharacteristic
640C2×C4#41×D6111yescharacteristic
641C2×C4#1451982211yescharacteristic
642C2×C4#1451982411yescharacteristic
643C8—1222no—
644C8—2441no—
645C8—2441no—
646C8—2441no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—1224no—
655C22—2442no—
656C22—2442no—
657C22—2442no—
658C22—2442no—
659C22—2442no—
660C22—2442no—
661C22#1684026911yescharacteristic
662C22D4×C22⋊D6111yescharacteristic
663C22#1684041911yescharacteristic
664C22C2×#1451979711yescharacteristic
665C22C2×#1451980211yescharacteristic
666C22#1684056511yescharacteristic
667C22#1684057711yescharacteristic
668C4—22no—
669C4—22no—
670C4—41no—
671C4—41no—
672C4—41no—
673C4—41no—
674C4—81no—
675C4—81no—
676C4—81no—
677C4—4881no—
678C4—4881no—
679C4—2442no—
680C4#123×D6111yescharacteristic
681C4#1684035511yescharacteristic
682C4#1684041011yescharacteristic
683C4#1684045711yescharacteristic
684C2—82no—
685C2—2444no—
686C2#2144955111yescharacteristic
687C2#2145586211yescharacteristic
688C2#2145607511yescharacteristic
689C2#2145730011yescharacteristic
690C2#2145753711yescharacteristic
691C2#2145847511yescharacteristic
692C2#2145853311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2447C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenter#2447D61
hypocenterC61#26164
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2447

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×D244C2semidirect
4. #21447357C2semidirect
5. #21447315C2semidirect
6. #21447222C2semidirect
7. #21447055C2semidirect
8. #21446498C2semidirect
9. #21446378C2semidirect
11. #21446156C2semidirect
12. #21446156C2semidirect
13. #21446066C2semidirect
14. #21446065C2semidirect
15. C61×#2447C2semidirect
340. #2447D61semidirect
407. C61#26164semidirect

Maximal subgroups

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

subgroupindex
C2×#168399742
C2×C4×#117581992
C4⋊C4×D2442
#214473572
#214473152
#214472222
#214470552
#214464982
#214463782
#214461702
#214461562
#214460662
#214460652
C61×#24472
#2616461