Finite Group Databasebeta

← #29740020

Subgroups — #29740020

Order 15616.

908 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839977C211yesmaximal, characteristic
2C2×C4×#11758199C211yesmaximal, characteristic
3#21449606C211yesmaximal, characteristic, complemented
4#21447370C211yesmaximal, characteristic, complemented
5#21447310C211yesmaximal, characteristic, complemented
6#21447233C211yesmaximal, characteristic, complemented
7#21447060C211yesmaximal, characteristic, complemented
8#21446494C211yesmaximal, characteristic, complemented
9#21446378C211yesmaximal, characteristic, complemented
10#21446167C211yesmaximal, characteristic
11#21446153C211yesmaximal, characteristic, complemented
12#21446153C211yesmaximal, characteristic, complemented
13#21446080C211yesmaximal, characteristic, complemented
14#21446079C211yesmaximal, characteristic, complemented
15C61×#2349C211yesmaximal, characteristic, complemented
16C22×#11758200C2211yescharacteristic
17C22×#11758199C2211yescharacteristic
18C2×#14519765C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20#16839977—24no—
21C4×#11758199—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519700C2211yescharacteristic
26C2×#14519700C2211yescharacteristic
27C2×#14519700C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×#14519697C2211yescharacteristic
33C2×C4×#92418C2211yescharacteristic
34#16839691—21no—
35#16839688—21no—
36#16839668C2211yescharacteristic
37#16839668C2211yescharacteristic
38#16839664C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839633—21no—
41#16839624—21no—
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C2×C4×D4×C61C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C61×#385—21no—
56C61×#385—21no—
57C61×#382C2211yescharacteristic
58C61×#380—21no—
59C4×C4⋊C4×C61C2211yescharacteristic
60C2×#95×C61—21no—
61C22×Dic122C2311yescharacteristic
62C22×D244C2311yescharacteristic
63C22×C4×D61—21no—
64C2×#11758200—22no—
65C2×#11758200—22no—
66C2×#11758200—22no—
67C2×#11758199—22no—
68C2×#11758199—22no—
69C2×#11758199D414yes—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74#14519765—22no—
75#14519765—41no—
76C4×D244—22no—
77C4×D244—41no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758196—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86#14519710—22no—
87#14519708—41no—
88C4⋊#92418—22no—
89#14519700—22no—
90#14519700—22no—
91#14519700—41no—
92#14519698—22no—
93#14519698—22no—
94#14519697—22no—
95#14519697—22no—
96#14519697—22no—
97C4×#92418—22no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103C22×D4×C61C2311yescharacteristic
104C23×C4×C61—21no—
105C23×C4×C61—21no—
106C23×C4×C61—21no—
107C4×D4×C61—22no—
108C4×D4×C61—22no—
109C4×D4×C61—22no—
110C4×D4×C61—22no—
111C4×D4×C61—41no—
112C4×D4×C61—41no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61D411yescharacteristic
116C2×C4⋊C4×C61D411yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
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×C61D411yescharacteristic
131#95×C61D411yescharacteristic
132C24×C61—21no—
133C23×D61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61C2×D412yes—
138C2×D4×C61#4112yes—
139C2×D4×C61#4112yes—
140C22×C4×C61—21no—
141C22×C4×C61—24no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—42no—
145C22×C4×C61—42no—
146C22×C4×C61—42no—
147C22×C4×C61—42no—
148C22×C4×C61—81no—
149C22×C4×C61—81no—
150C22×C4×C61—81no—
151C22×C4×C61—81no—
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244C2×D412yes—
168C2×C4×D61—42no—
169C2×C4×D61—42no—
170C2×C4×D61—81no—
171C2×Dic122—21no—
172C2×Dic122—21no—
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—41no—
184C4⋊C4×C61—81no—
185C4⋊C4×C61—81no—
186C4⋊C4×C61#4112yes—
187C22⋊C4×C61—24no—
188C22⋊C4×C61—42no—
189C22⋊C4×C61—42no—
190C42×C61—21no—
191C42×C61—21no—
192C42×C61—21no—
193C42×C61—21no—
194C42×C61—21no—
195C42×C61—21no—
196#11758200—44no—
197#11758199—28no—
198#11758198—42no—
199#11758198—42no—
200#11758198—42no—
201#11758198—42no—
202#11758198—81no—
203C4⋊Dic61—21no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207#11758196—81no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
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×#92418C2×D412yes—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61C22×D411yescharacteristic
228C22×D61—22no—
229C22×D61—41no—
230C22×D61—41no—
231C22×D61—41no—
232C22×D61—41no—
233C22×D61—41no—
234C22×D61—41no—
235D4×C61—22no—
236D4×C61—22no—
237D4×C61—22no—
238D4×C61#12314yes—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—22no—
244C2×C4×C61—21no—
245C2×C4×C61—21no—
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—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—84no—
266C2×C4×C61—84no—
267C2×C4×C61—84no—
268C2×C4×C61#13512yes—
269C2×C4×C61C22×D411yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61C2×#4111yescharacteristic
273C2×C4×C61H(5,𝔽2)11yescharacteristic
274C2×C4×C612−1+411yescharacteristic
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284D244—22no—
285D244—22no—
286D244—41no—
287D244—41no—
288C4×D61—84no—
289Dic122—41no—
290Dic122—41no—
291Dic122—41no—
292Dic122—41no—
293#92418—22no—
294#92418—41no—
295#92418—41no—
296#92418—41no—
297#26160—611nomaximal, Sylow
298C22×C61—24no—
299C22×C61—42no—
300C22×C61—42no—
301C22×C61—42no—
302C22×C61—42no—
303C22×C61—42no—
304C22×C61—42no—
305C22×C61#52511yescharacteristic
306C22×C61D4211yescharacteristic
307C22×C61#54811yescharacteristic
308C22×C61C2×#13511yescharacteristic
309C22×C61#57511yescharacteristic
310C22×C61#57611yescharacteristic
311C22×C61#57711yescharacteristic
312C2×D61—42no—
313C2×D61—42no—
314C2×D61—42no—
315C2×D61—81no—
316C2×D61—81no—
317C2×D61—81no—
318C2×D61—81no—
319C4×C61—22no—
320C4×C61—41no—
321C4×C61—41no—
322C4×C61—42no—
323C4×C61—41no—
324C4×C61—41no—
325C4×C61—41no—
326C4×C61—81no—
327C4×C61—81no—
328C4×C61C2×#12311yescharacteristic
329C4×C61#53911yescharacteristic
330C4×C61#54711yescharacteristic
331C4×C61#55311yescharacteristic
332Dic61—81no—
333Dic61—81no—
334Dic61—81no—
335C2×#463—611no—
336C2×C4×D8—611no—
337#2447—611no—
338#2349D6111yescharacteristic, complemented
339#2097—611no—
340#2086—611no—
341#2073—611no—
342#2042—611no—
343#1933—611no—
344#1916—611no—
345#1879—611no—
346#1877—611no—
347#1877—611no—
348#1864—611no—
349#1864—611no—
350C2×C61—44no—
351C2×C61#244311yescharacteristic
352C2×C61#310211yescharacteristic
353C2×C61#311811yescharacteristic
354C2×C61#326711yescharacteristic
355C2×C61#328011yescharacteristic
356C2×C61#336011yescharacteristic
357C2×C61#337011yescharacteristic
358D61—82no—
359C22×SD16—611no—
360C22×D8—611no—
361C2×#124—611no—
362C2×C4×D4—611no—
363C2×C4×D4C2×D6111yescharacteristic
364C2×C4×D4C2×D6111yescharacteristic
365C2×C4×D4C2×D6111yescharacteristic
366#463—1224no—
367C4×D8—1224no—
368C2×#107—611no—
369C2×#106—611no—
370C2×C4⋊C8—611no—
371C2×#103—611no—
372C2×#103—611no—
373C2×#103—611no—
374C2×#102—611no—
375C2×#102—611no—
376C2×#102—611no—
377C2×#102—611no—
378C2×#102—611no—
379C2×C4×C8—611no—
380#397—1221no—
381#397—1221no—
382#391—611no—
383#391—611no—
384#390—611no—
385#389—611no—
386#389C2×D6111yescharacteristic
387#389C2×D6111yescharacteristic
388#385—21no—
389#385—21no—
390#385—1221no—
391#382C2×D6111yescharacteristic
392#381—1221no—
393#380—21no—
394C4×C4⋊C4C2×D6111yescharacteristic
395C2×#95—21no—
396#340—611no—
397#340—611no—
398#340—611no—
399#340—611no—
400#336—611no—
401#336—611no—
402#336—611no—
403#336—611no—
404C61#2616011yescharacteristic, complemented, Sylow
405C22×Q8—611no—
406C22×D4—611no—
407C22×D4C22×D6111yescharacteristic
408C23×C4—21no—
409C23×C4—21no—
410C23×C4—21no—
411C23×C4—1221no—
412C2×SD16—1222no—
413C2×SD16—1222no—
414C2×SD16—1222no—
415C2×D8—614no—
416C2×D8—1222no—
417C2×D8—1222no—
418C22×C8—611no—
419C22×C8—611no—
420C22×C8—611no—
421C22×C8—611no—
422#124—1222no—
423#124—2441no—
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—22no—
428C4×D4—41no—
429C4×D4—41no—
430C4×D4—1222no—
431C4×D4—2441no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4C22⋊D6111yescharacteristic
438C2×C4⋊C4C22⋊D6111yescharacteristic
439C2×C4⋊C4C22×D6111yescharacteristic
440C2×C4⋊C4C22×D6111yescharacteristic
441C2×C4⋊C4C22×D6111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—1221no—
446C2×C22⋊C4—1221no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C42C22×D6111yescharacteristic
451C2×C42C22×D6111yescharacteristic
452C2×C42C22×D6111yescharacteristic
453#107—1222no—
454#106—2441no—
455C4⋊C8—1222no—
456#103—1222no—
457#103—1222no—
458#103—2441no—
459#102—1222no—
460#102—1222no—
461#102—1222no—
462#102—1222no—
463#102—1222no—
464C4×C8—1222no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—1221no—
470#95—1221no—
471#95—1221no—
472#95—1221no—
473#95—1221no—
474#95C22⋊D6111yescharacteristic
475#95C22⋊D6111yescharacteristic
476C24—21no—
477C24—1221no—
478C2×Q8—1221no—
479C2×Q8—1221no—
480C2×Q8—1221no—
481C2×Q8—1221no—
482C2×Q8—1221no—
483C2×Q8—1221no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—612no—
488C2×D4—1221no—
489C2×D4—1221no—
490C2×D4—1221no—
491C2×D4—1221no—
492C2×D4—1221no—
493C2×D4#1175822212yes—
494C2×D4D4×D6112yes—
495C2×D4#1175822612yes—
496C22×C4—21no—
497C22×C4—24no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—81no—
507C22×C4—81no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—4881no—
512C22×C4—2442no—
513C22×C4—2442no—
514C22×C4C2×C22⋊D6111yescharacteristic
515C22×C4C2×C22⋊D6111yescharacteristic
516C22×C4C2×C22⋊D6111yescharacteristic
517C22×C4C2×C22⋊D6111yescharacteristic
518C22×C4C2×C22⋊D6111yescharacteristic
519C22×C4C2×C22⋊D6111yescharacteristic
520C22×C4C23×D6111yescharacteristic
521SD16—2444no—
522D8—1228no—
523C2×C8—612no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—1221no—
527C2×C8—1221no—
528C2×C8—1221no—
529C2×C8—1221no—
530C2×C8—1221no—
531C2×C8—1221no—
532C2×C8—1221no—
533C2×C8—1221no—
534C2×C8—1221no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—41no—
542C4⋊C4—81no—
543C4⋊C4—81no—
544C4⋊C4—1221no—
545C4⋊C4—1221no—
546C4⋊C4—1221no—
547C4⋊C4—1221no—
548C4⋊C4—4881no—
549C4⋊C4#1175822212yes—
550C22⋊C4—24no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—4881no—
554C22⋊C4—2442no—
555C22⋊C4—2442no—
556C22⋊C4—2442no—
557C22⋊C4—2442no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C23—22no—
565C23—22no—
566C23—22no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—1222no—
572C23—2441no—
573C23—2441no—
574C23—2441no—
575C23—2441no—
576C23—2441no—
577C23—2441no—
578C23C22×C22⋊D6111yescharacteristic
579Q8—2441no—
580Q8—2441no—
581Q8—2441no—
582Q8—2441no—
583D4—22no—
584D4—22no—
585D4—22no—
586D4—1222no—
587D4—1222no—
588D4—2441no—
589D4—2441no—
590D4#1451976214yes—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
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—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—84no—
618C2×C4—84no—
619C2×C4—84no—
620C2×C4—4884no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4#1451979712yes—
631C2×C4C2×D4×D6111yescharacteristic
632C2×C4C2×#1175822211yescharacteristic
633C2×C4C2×#1175822211yescharacteristic
634C2×C4C2×#1175822611yescharacteristic
635C2×C4#1451982211yescharacteristic
636C2×C4#1451982511yescharacteristic
637C8—1222no—
638C8—2441no—
639C8—2441no—
640C8—2441no—
641C22—24no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—4881no—
649C22—4881no—
650C22—4881no—
651C22—4881no—
652C22—2442no—
653C22—2442no—
654C22—2442no—
655C22#1684027311yescharacteristic
656C22D4×C22⋊D6111yescharacteristic
657C22#1684042311yescharacteristic
658C22C2×#1451979711yescharacteristic
659C22#1684056011yescharacteristic
660C22#1684056511yescharacteristic
661C22#1684057311yescharacteristic
662C4—22no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—81no—
670C4—81no—
671C4—4881no—
672C4—4881no—
673C4—4881no—
674C4C2×#1451976211yescharacteristic
675C4#1684035911yescharacteristic
676C4#1684041311yescharacteristic
677C4#1684046011yescharacteristic
678C2—44no—
679C2—4882no—
680C2#2144955411yescharacteristic
681C2#2145583711yescharacteristic
682C2#2145600311yescharacteristic
683C2#2145734011yescharacteristic
684C2#2145750011yescharacteristic
685C2#2145846811yescharacteristic
686C2#2145857211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2349C2
socleC23×C61C22×D4
prime radicalC22×#11758199C22
hypercenter#2349D61
hypocenterC61#26160
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #21449606C2semidirect
4. #21447370C2semidirect
5. #21447310C2semidirect
6. #21447233C2semidirect
7. #21447060C2semidirect
8. #21446494C2semidirect
9. #21446378C2semidirect
11. #21446153C2semidirect
12. #21446153C2semidirect
13. #21446080C2semidirect
14. #21446079C2semidirect
15. C61×#2349C2semidirect
338. #2349D61semidirect
404. C61#26160semidirect

Maximal subgroups

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

subgroupindex
C2×#168399772
C2×C4×#117581992
#214496062
#214473702
#214473102
#214472332
#214470602
#214464942
#214463782
#214461672
#214461532
#214460802
#214460792
C61×#23492
#2616061