Finite Group Databasebeta

← #29736935

Subgroups — #29736935

Order 15616.

1028 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840490C211yesmaximal, characteristic, complemented
2C2×#16840116C211yesmaximal, characteristic
3C2×#16839981C211yesmaximal, characteristic
4#21446970C211yesmaximal, characteristic, complemented
5#21446965C211yesmaximal, characteristic
6#21446960C211yesmaximal, characteristic, complemented
7#21446955C211yesmaximal, characteristic
8#21446776C211yesmaximal, characteristic, complemented
9#21446756C211yesmaximal, characteristic, complemented
10#21446177C211yesmaximal, characteristic
11#21446177C211yesmaximal, characteristic
12#21446163C211yesmaximal, characteristic, complemented
13#21446163C211yesmaximal, characteristic, complemented
14C4×#14519700C211yesmaximal, characteristic, complemented
15C61×#2592C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18#16840490—24no—
19#16840490—24no—
20C2×#14519777C2211yescharacteristic
21C2×#14519775—21no—
22C2×#14519769C2211yescharacteristic
23C2×#14519769C2211yescharacteristic
24C2×#14519767—21no—
25C2×#14519767—21no—
26C2×C4×Dic122C2211yescharacteristic
27C2×C4×Dic122C2211yescharacteristic
28C2×C4×Dic122C2211yescharacteristic
29C2×#14519742—21no—
30#16840116—24no—
31#16839981—24no—
32C2×C4⋊#92418C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519698C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C2×#124×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C61×#397—21no—
55C61×#393—21no—
56C61×#391C2211yescharacteristic
57C61×#391C2211yescharacteristic
58C61×#390C2211yescharacteristic
59C61×#390C2211yescharacteristic
60C61×#388—21no—
61C61×#388—21no—
62C4×C4⋊C4×C61C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C2×#11758202—22no—
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758200—22no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75#14519777—22no—
76#14519777—22no—
77#14519775—28no—
78#14519769—22no—
79#14519769—22no—
80#14519769—22no—
81#14519769D414yes—
82#14519767—28no—
83#14519767—28no—
84C4×Dic122—22no—
85C4×Dic122—22no—
86C4×Dic122—22no—
87C4×Dic122—22no—
88C4×Dic122—22no—
89C4×Dic122D414yes—
90#14519742—28no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×#11758196—21no—
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C4⋊#92418—22no—
106#14519701—22no—
107#14519701—22no—
108#14519701—22no—
109#14519700—22no—
110#14519700—22no—
111#14519698—22no—
112#14519698—22no—
113#14519698—22no—
114C4×#92418—22no—
115C22×Q8×C61D411yescharacteristic
116C22×Q8×C61C2311yescharacteristic
117C22×D4×C61C2311yescharacteristic
118#124×C61—22no—
119#124×C61—22no—
120C4×Q8×C61—22no—
121C4×Q8×C61—22no—
122C2×C4⋊C4×C61D411yescharacteristic
123C2×C4⋊C4×C61D411yescharacteristic
124C2×C4⋊C4×C61D411yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130C2×C22⋊C4×C61—21no—
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C42×C61—21no—
134C2×C42×C61C2311yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137#95×C61—21no—
138#95×C61—21no—
139#95×C61—21no—
140#95×C61—21no—
141#95×C61—21no—
142C24×C61—21no—
143C2×Q8×C61—22no—
144C2×Q8×C61—22no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—41no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C2×Dic122—21no—
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—24no—
176C2×Dic122—42no—
177C2×Dic122—42no—
178C2×Dic122C2×D412yes—
179C2×Dic122#4112yes—
180C2×Dic122#4112yes—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61—21no—
188C22⋊C4×C61—42no—
189C22⋊C4×C61—42no—
190C22⋊C4×C61—42no—
191C22⋊C4×C61—42no—
192C22⋊C4×C61—81no—
193C22⋊C4×C61—81no—
194C42×C61—21no—
195C42×C61—21no—
196C42×C61—21no—
197C42×C61—21no—
198C42×C61—81no—
199C42×C61C2×D412yes—
200C42×C61C2×D412yes—
201#11758202—44no—
202#11758200—44no—
203C4⋊Dic61—24no—
204C4⋊Dic61—21no—
205C4⋊Dic61—21no—
206C4⋊Dic61—21no—
207C4⋊Dic61C2×D412yes—
208C4⋊Dic61C2×D412yes—
209C4⋊Dic61C2×D412yes—
210#11758196—24no—
211#11758196—24no—
212#11758196—24no—
213#11758196—24no—
214#11758196—24no—
215#11758196—24no—
216#11758196—24no—
217C4×Dic61—24no—
218C4×Dic61—24no—
219C4×Dic61—24no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C23×C61—41no—
233C23×C61—41no—
234C23×C61—41no—
235C23×C61—41no—
236C23×C61—41no—
237C23×C61—41no—
238C23×C61—41no—
239C23×C61C22×D411yescharacteristic
240Q8×C61—44no—
241Q8×C61—41no—
242Q8×C61—41no—
243Q8×C61—41no—
244Q8×C61—41no—
245D4×C61—41no—
246D4×C61—41no—
247D4×C61—41no—
248D4×C61—41no—
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—21no—
263C2×C4×C61—21no—
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—41no—
272C2×C4×C61—41no—
273C2×C4×C61#12012yes—
274C2×C4×C61#12012yes—
275C2×C4×C61#13512yes—
276C2×C4×C61C22×D411yescharacteristic
277C2×C4×C61C22×D411yescharacteristic
278C2×C4×C61C2×#4111yescharacteristic
279C2×C4×C61C2×#4111yescharacteristic
280C2×C4×C612−1+411yescharacteristic
281C2×C4×C612−1+411yescharacteristic
282C2×Dic61—22no—
283C2×Dic61—22no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—41no—
289C2×Dic61—41no—
290C2×Dic61—41no—
291C2×Dic61—41no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294Dic122—22no—
295Dic122—22no—
296Dic122—22no—
297Dic122—48no—
298Dic122#12414yes—
299#92418—41no—
300#92418—41no—
301#92418—41no—
302#92418—41no—
303#25937—611nomaximal, Sylow
304C22×C61—81no—
305C22×C61—81no—
306C22×C61—81no—
307C22×C61—81no—
308C22×C61—81no—
309C22×C61—81no—
310C22×C61—81no—
311C22×C61C2×#12011yescharacteristic
312C22×C61#54811yescharacteristic
313C22×C61#54811yescharacteristic
314C22×C61C2×#13511yescharacteristic
315C22×C61#57511yescharacteristic
316C22×C61#57711yescharacteristic
317C22×C61#57811yescharacteristic
318C4×C61—22no—
319C4×C61—22no—
320C4×C61—22no—
321C4×C61—41no—
322C4×C61—41no—
323C4×C61—41no—
324C4×C61—81no—
325C4×C61—81no—
326C4×C61—81no—
327C4×C61C2×#12411yescharacteristic
328C4×C61#53611yescharacteristic
329C4×C61#54811yescharacteristic
330C4×C61#54811yescharacteristic
331Dic61—24no—
332Dic61—42no—
333Dic61—42no—
334Dic61—42no—
335C2×#557—611no—
336C2×#488—611no—
337C2×#464—611no—
338#2592D6111yescharacteristic
339#2026—611no—
340#2025—611no—
341#2024—611no—
342#2023—611no—
343#1989—611no—
344#1984—611no—
345#1880—611no—
346#1880—611no—
347#1878—611no—
348#1878—611no—
349C4×#103—611no—
350C2×C61—161no—
351C2×C61#243611yescharacteristic
352C2×C61#300211yescharacteristic
353C2×C61#301311yescharacteristic
354C2×C61#336411yescharacteristic
355C2×C61#336511yescharacteristic
356C2×C61#337111yescharacteristic
357C2×C61#337711yescharacteristic
358C22×Q16—611no—
359C22×SD16—611no—
360#557—1224no—
361#557—1224no—
362C2×C4⋊Q8—611no—
363C2×C4⋊Q8—1221no—
364C2×#125—611no—
365C2×#125—611no—
366C2×#125—1221no—
367C2×#125—1221no—
368C2×#124C2×D6111yescharacteristic
369C2×C4×Q8—611no—
370C2×C4×Q8—611no—
371C2×C4×Q8—611no—
372C2×C4×Q8—1221no—
373C2×C4×Q8C2×D6111yescharacteristic
374#488—1224no—
375#464—1224no—
376C2×C4⋊C8—611no—
377C2×#103—611no—
378C2×#103—611no—
379C2×#103—611no—
380C2×#103—611no—
381C2×#103—611no—
382C2×#102—611no—
383C2×#102—611no—
384C2×#102—611no—
385C2×C4×C8—611no—
386#397—21no—
387#393—21no—
388#391C2×D6111yescharacteristic
389#391C2×D6111yescharacteristic
390#390C2×D6111yescharacteristic
391#390C2×D6111yescharacteristic
392#388—21no—
393#388—21no—
394C4×C4⋊C4C2×D6111yescharacteristic
395#340—611no—
396#340—611no—
397#340—611no—
398#340—611no—
399#340—611no—
400#340—611no—
401#336—611no—
402#336—611no—
403#336—611no—
404#336—611no—
405C61#2593711yescharacteristic, complemented, Sylow
406C22×Q8—611no—
407C22×Q8—1221no—
408C22×Q8C22⋊D6111yescharacteristic
409C22×Q8C22×D6111yescharacteristic
410C22×D4C22×D6111yescharacteristic
411C2×Q16—1222no—
412C2×Q16—1222no—
413C2×Q16—1222no—
414C2×SD16—1222no—
415C2×SD16—1222no—
416C2×SD16—1222no—
417C22×C8—611no—
418C22×C8—611no—
419C22×C8—611no—
420C22×C8—611no—
421C4⋊Q8—1222no—
422C4⋊Q8—1222no—
423C4⋊Q8—1228no—
424#125—614no—
425#125—1222no—
426#125—1222no—
427#125—1228no—
428#125—1228no—
429#125—1222no—
430#124—22no—
431#124—22no—
432C4×Q8—22no—
433C4×Q8—22no—
434C4×Q8—614no—
435C4×Q8—1222no—
436C4×Q8—1222no—
437C4×Q8—1222no—
438C4×Q8—1222no—
439C4×Q8—1228no—
440C4×Q8—1222no—
441C2×C4⋊C4—611no—
442C2×C4⋊C4—611no—
443C2×C4⋊C4—611no—
444C2×C4⋊C4—1221no—
445C2×C4⋊C4—1221no—
446C2×C4⋊C4—1221no—
447C2×C4⋊C4—1221no—
448C2×C4⋊C4—1221no—
449C2×C4⋊C4—1221no—
450C2×C4⋊C4—1221no—
451C2×C4⋊C4—1221no—
452C2×C4⋊C4C22⋊D6111yescharacteristic
453C2×C4⋊C4C22⋊D6111yescharacteristic
454C2×C4⋊C4C22⋊D6111yescharacteristic
455C2×C4⋊C4C22×D6111yescharacteristic
456C2×C4⋊C4C22×D6111yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C42—21no—
464C2×C42—1221no—
465C2×C42—1221no—
466C2×C42—1221no—
467C2×C42C22×D6111yescharacteristic
468C2×C42C22×D6111yescharacteristic
469C2×C42C22×D6111yescharacteristic
470C4⋊C8—1222no—
471#103—1222no—
472#103—1222no—
473#103—1222no—
474#103—1222no—
475#103—1222no—
476#102—1222no—
477#102—1222no—
478#102—1222no—
479C4×C8—1222no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485C24—21no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—41no—
495C2×Q8—612no—
496C2×Q8—612no—
497C2×Q8—612no—
498C2×Q8—1224no—
499C2×Q8—1221no—
500C2×Q8—1221no—
501C2×Q8—1221no—
502C2×Q8—2442no—
503C2×Q8—2442no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4C2×C22⋊D6111yescharacteristic
518C22×C4C2×C22⋊D6111yescharacteristic
519C22×C4C2×C22⋊D6111yescharacteristic
520C22×C4C2×C22⋊D6111yescharacteristic
521C22×C4C2×C22⋊D6111yescharacteristic
522C22×C4C2×C22⋊D6111yescharacteristic
523C22×C4C23×D6111yescharacteristic
524Q16—2444no—
525SD16—2444no—
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—
535C2×C8—1221no—
536C2×C8—1221no—
537C2×C8—1221no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—612no—
546C4⋊C4—612no—
547C4⋊C4—612no—
548C4⋊C4—1224no—
549C4⋊C4—1224no—
550C4⋊C4—1224no—
551C4⋊C4—1224no—
552C4⋊C4—1224no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C4⋊C4—1224no—
557C4⋊C4—1224no—
558C4⋊C4—1224no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—81no—
564C22⋊C4—81no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—81no—
570C42—1224no—
571C42—1224no—
572C42—1224no—
573C42D4×D6112yes—
574C42D4×D6112yes—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23C22×C22⋊D6111yescharacteristic
583Q8—44no—
584Q8—41no—
585Q8—41no—
586Q8—41no—
587Q8—41no—
588Q8—614no—
589Q8—1222no—
590Q8—1222no—
591Q8—1222no—
592Q8—2448no—
593D4—41no—
594D4—41no—
595D4—41no—
596D4—41no—
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—41no—
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—1222no—
622C2×C4—1222no—
623C2×C4—1222no—
624C2×C4—1222no—
625C2×C4—1222no—
626C2×C4—1222no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4—2441no—
630C2×C4—2441no—
631C2×C4—2441no—
632C2×C4—2441no—
633C2×C4#1451974512yes—
634C2×C4#1451974512yes—
635C2×C4#1451979712yes—
636C2×C4C2×D4×D6111yescharacteristic
637C2×C4C2×D4×D6111yescharacteristic
638C2×C4#41×D6111yescharacteristic
639C2×C4#41×D6111yescharacteristic
640C2×C4#1451982411yescharacteristic
641C2×C4#1451982411yescharacteristic
642C8—2441no—
643C8—2441no—
644C8—2441no—
645C8—2441no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22C2×#1451974511yescharacteristic
654C22#1684041911yescharacteristic
655C22#1684041911yescharacteristic
656C22C2×#1451979711yescharacteristic
657C22#1684056011yescharacteristic
658C22#1684057311yescharacteristic
659C22#1684057711yescharacteristic
660C4—22no—
661C4—22no—
662C4—22no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—81no—
667C4—81no—
668C4—81no—
669C4—1224no—
670C4—2442no—
671C4—2442no—
672C4—2442no—
673C4#124×D6111yescharacteristic
674C4#1684033211yescharacteristic
675C4#1684042011yescharacteristic
676C4#1684042011yescharacteristic
677C2—161no—
678C2#2144947411yescharacteristic
679C2#2145503511yescharacteristic
680C2#2145513111yescharacteristic
681C2#2145850011yescharacteristic
682C2#2145851111yescharacteristic
683C2#2145858111yescharacteristic
684C2#2145865511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2592C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
hypercenter#2592D61
hypocenterC61#25937
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2592

Complements

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

NH ≅ G/Ntype
1. C2×#16840490C2semidirect
4. #21446970C2semidirect
6. #21446960C2semidirect
8. #21446776C2semidirect
9. #21446756C2semidirect
12. #21446163C2semidirect
13. #21446163C2semidirect
14. C4×#14519700C2semidirect
405. C61#25937semidirect

Maximal subgroups

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

subgroupindex
C2×#168404902
C2×#168401162
C2×#168399812
#214469702
#214469652
#214469602
#214469552
#214467762
#214467562
#214461772
#214461632
C4×#145197002
C61×#25922
#2593761