Finite Group Databasebeta

← #29686556

Subgroups — #29686556

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840002C211yesmaximal, characteristic
2C2×#16839854C211yesmaximal, characteristic, complemented
3C2×#16839719C211yesmaximal, characteristic
4#21448504C211yesmaximal, characteristic
5#21448499C211yesmaximal, characteristic
6#21446679C211yesmaximal, characteristic, complemented
7#21446549C211yesmaximal, characteristic, complemented
8#21446509C211yesmaximal, characteristic, complemented
9#21446251C211yesmaximal, characteristic
10#21446249C211yesmaximal, characteristic
11#21445847C211yesmaximal, characteristic
12#21445711C211yesmaximal, characteristic, complemented
13#21445651C211yesmaximal, characteristic, complemented
14#21445648C211yesmaximal, characteristic, complemented
15C61×#1935C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C2×#14519757C2211yescharacteristic
20C2×#14519753C2211yescharacteristic
21C2×Q8×Dic61C2211yescharacteristic
22C2×#14519742C2211yescharacteristic
23C2×#14519734C2211yescharacteristic
24#16840002C418yescomplemented
25#16839854—24no—
26C2×#14519710C2211yescharacteristic
27C2×#14519710C2211yescharacteristic
28C2×#14519710C2211yescharacteristic
29C2×#14519702C2211yescharacteristic
30C2×#14519702C2211yescharacteristic
31C2×#14519701C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33#16839719—24no—
34C2×#14519687C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic
36C2×C8×Dic61C2211yescharacteristic
37#16839668C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839659—21no—
40#16839658—21no—
41#16839654—21no—
42#16839652—21no—
43#16839651—21no—
44#16839651—21no—
45#16839645—21no—
46#16839644—21no—
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49C4⋊C4×Dic61C2211yescharacteristic
50C4⋊C4×Dic61C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×#97×C61C2211yescharacteristic
58C61×#391C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C22×Dic122C2311yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C2×#11758202—22no—
65C2×#11758202—22no—
66C2×#11758202C2×C414yes—
67C2×#11758189—22no—
68C2×#11758189—22no—
69C2×#11758189—22no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C2×C8×D61—22no—
73C2×C8×D61—22no—
74C2×C8×D61C2×C414yes—
75#14519757—22no—
76#14519757C2×C414yes—
77#14519753—22no—
78#14519753C2×C414yes—
79Q8×Dic61—22no—
80Q8×Dic61—22no—
81#14519742—22no—
82#14519742—22no—
83#14519734—22no—
84#14519734—22no—
85C2×C4⋊Dic61—21no—
86C2×C4⋊Dic61—21no—
87C2×C4⋊Dic61C2311yescharacteristic
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196D411yescharacteristic
94C2×#11758196D411yescharacteristic
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198D411yescharacteristic
100C2×#11758198D411yescharacteristic
101C2×C4×Dic61—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61C2311yescharacteristic
106#14519710—22no—
107#14519710—22no—
108#14519710C2×C414yes—
109#14519702—22no—
110#14519702C2×C414yes—
111#14519701—22no—
112#14519700—22no—
113#14519687—22no—
114C4×#92418—22no—
115C8×Dic61D414yes—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119#14519684—21no—
120#14519684—21no—
121#14519684—21no—
122#14519684—21no—
123C22×Q8×C61C2311yescharacteristic
124C22×C8×C61C2311yescharacteristic
125C22×C8×C61C2311yescharacteristic
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C42×C61C2311yescharacteristic
131#103×C61—22no—
132#103×C61C2×C414yes—
133#97×C61—22no—
134#95×C61—21no—
135#95×C61—21no—
136#95×C61—21no—
137C23×D61C2×D411yescharacteristic
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61C22×C412yes—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2411yescharacteristic
151C22×Dic61—21no—
152C22×Dic61—21no—
153C22×Dic61—21no—
154C22×Dic61—21no—
155C22×Dic61C2×D411yescharacteristic
156C22×Dic61C2×D411yescharacteristic
157C22×Dic61C2×D411yescharacteristic
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61C22×C412yes—
163C2×C4×D61#4112yes—
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122C22×C412yes—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61C22×C412yes—
175C2×C8×C61C2×D412yes—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—81no—
182C4⋊C4×C61C22×C412yes—
183C42×C61—21no—
184C42×C61—21no—
185#11758202—28no—
186#11758198—24no—
187#11758198—24no—
188#11758198—22no—
189#11758198—22no—
190#11758198—81no—
191#11758198—81no—
192C4⋊Dic61—21no—
193C4⋊Dic61—24no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—42no—
199C4⋊Dic61C22×C412yes—
200#11758196—24no—
201#11758196—22no—
202#11758196—22no—
203#11758196—42no—
204#11758196—81no—
205C4×Dic61—42no—
206C4×Dic61—42no—
207C4×Dic61—81no—
208C4×Dic61—81no—
209C4×Dic61C2×D412yes—
210C4×Dic61#4112yes—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418C22×C412yes—
214C2×#92418C2×D412yes—
215C2×#92418#4112yes—
216C2×#92418#4112yes—
217#11758189—28no—
218C8×D61—28no—
219C23×C61C22×D411yescharacteristic
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61C4×D412yes—
227Q8×C61—22no—
228Q8×C61—22no—
229Q8×C61—41no—
230Q8×C61—41no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61C23×C411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—22no—
262C2×Dic61—22no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61C4×D412yes—
274C2×Dic61#12112yes—
275C2×Dic61#12112yes—
276C4×D61—22no—
277C4×D61—22no—
278C4×D61—22no—
279C4×D61—22no—
280Dic122—22no—
281Dic122—22no—
282Dic122—41no—
283Dic122—41no—
284C8×C61—22no—
285C8×C61—22no—
286#92418—22no—
287#92418C4×D414yes—
288#21525—611nomaximal, Sylow
289C22×C61C2×C4×D411yescharacteristic
290C22×C61C2×#12111yescharacteristic
291C22×C61#53211yescharacteristic
292C22×C61#57611yescharacteristic
293C22×C61#57811yescharacteristic
294C22×C61#57811yescharacteristic
295C22×C61#57811yescharacteristic
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—41no—
300C2×D61—41no—
301C2×D61—41no—
302C2×D61—41no—
303C4×C61—42no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—42no—
307C4×C61—81no—
308C4×C61—81no—
309C4×C61C2×C4×D411yescharacteristic
310C4×C61C4×#4111yescharacteristic
311C4×C61#52511yescharacteristic
312C4×C61#52911yescharacteristic
313Dic61—22no—
314Dic61—22no—
315Dic61—22no—
316Dic61—42no—
317Dic61—42no—
318Dic61—81no—
319Dic61—81no—
320C2×#467—611no—
321C2×C4×Q16—611no—
322C2×#405—611no—
323#2323—611no—
324#2323—611no—
325#1969—611no—
326#1942—611no—
327#1935—611no—
328#1935D6111yescharacteristic, complemented
329#1894—611no—
330#1894—611no—
331#1808—611no—
332C4×#107—611no—
333#1763—611no—
334#1763—611no—
335C2×C61C4×#12111yescharacteristic
336C2×C61#295011yescharacteristic
337C2×C61#295111yescharacteristic
338C2×C61#305911yescharacteristic
339C2×C61#306111yescharacteristic
340C2×C61#317511yescharacteristic
341C2×C61#317711yescharacteristic
342D61—42no—
343C22×Q16—611no—
344C22×M16—611no—
345C23×C8—611no—
346C2×C22⋊Q8—611no—
347C2×C22⋊Q8—611no—
348C2×C4×Q8—611no—
349C2×C4×Q8—611no—
350C2×#117—611no—
351#467—618no—
352C4×Q16—1224no—
353C2×#107—611no—
354C2×#107—611no—
355C2×#107—611no—
356C2×#103—611no—
357C2×#103—611no—
358C2×#103—611no—
359C2×#103—611no—
360C2×#103C2×D6111yescharacteristic
361C2×#103C2×D6111yescharacteristic
362#405—1224no—
363C2×#97—611no—
364C2×#97C2×D6111yescharacteristic
365C2×C4×C8—611no—
366C2×C4×C8—611no—
367#391—611no—
368#391C2×D6111yescharacteristic
369#389—611no—
370#389—1221no—
371#389—1221no—
372#389C2×D6111yescharacteristic
373#388—1221no—
374#388—1221no—
375#388—1221no—
376#388—1221no—
377#387—1221no—
378#387—1221no—
379#380—611no—
380#380—611no—
381C4×C4⋊C4—611no—
382C4×C4⋊C4—611no—
383#340—611no—
384#340—611no—
385#340—611no—
386#340—611no—
387#340C2×D6111yescharacteristic
388#340C2×D6111yescharacteristic
389C61#2152511yescharacteristic, complemented, Sylow
390C22×Q8—611no—
391C22×Q8C22×D6111yescharacteristic
392C23×C4—611no—
393C2×Q16—614no—
394C2×Q16—1222no—
395C2×Q16—1222no—
396C2×M16—1222no—
397C2×M16—1222no—
398C2×M16—1222no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—614no—
402C22×C8—1222no—
403C22×C8—1222no—
404C22×C8C22×D6111yescharacteristic
405C22×C8C22×D6111yescharacteristic
406C22⋊Q8—614no—
407C22⋊Q8—614no—
408C22⋊Q8—1222no—
409C22⋊Q8—1222no—
410C4×Q8—1222no—
411C4×Q8—1222no—
412C4×Q8—1222no—
413C4×Q8—1222no—
414#117—1222no—
415#117—1222no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4C22×D6111yescharacteristic
428C2×C4⋊C4C22×D6111yescharacteristic
429C2×C4⋊C4C22×D6111yescharacteristic
430C2×C22⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C22⋊C4—1221no—
433C2×C22⋊C4—1221no—
434C2×C22⋊C4—1221no—
435C2×C22⋊C4—1221no—
436C2×C42—611no—
437C2×C42—1221no—
438C2×C42—1221no—
439C2×C42—1221no—
440C2×C42—1221no—
441C2×C42C22×D6111yescharacteristic
442#107—614no—
443#107—1222no—
444#107—1222no—
445#103—22no—
446#103—614no—
447#103—1222no—
448#103—1222no—
449#103—1222no—
450#103C4×D6114yes—
451#97—22no—
452#97—1222no—
453C4×C8—614no—
454C4×C8—1222no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—1221no—
459#95—1221no—
460#95—1221no—
461#95—1221no—
462#95—1221no—
463#95—1221no—
464#95—1221no—
465C24—611no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—612no—
472C2×Q8—1221no—
473C2×Q8—1221no—
474C2×Q8—1221no—
475C2×Q8—1221no—
476C2×Q8—1221no—
477C2×Q8C2×C4×D6112yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—612no—
486C22×C4—612no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4D4×D6111yescharacteristic
496C22×C4D4×D6111yescharacteristic
497C22×C4C23×D6111yescharacteristic
498Q16—1228no—
499M16—1228no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—612no—
505C2×C8—612no—
506C2×C8—612no—
507C2×C8—612no—
508C2×C8—1228no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8C2×C4×D6112yes—
512C2×C8D4×D6112yes—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—81no—
519C4⋊C4—612no—
520C4⋊C4—1222no—
521C4⋊C4—1222no—
522C4⋊C4—1224no—
523C4⋊C4—1224no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—4881no—
530C4⋊C4—2442no—
531C4⋊C4—2442no—
532C4⋊C4C2×C4×D6112yes—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C22⋊C4—1224no—
536C22⋊C4—1224no—
537C22⋊C4—4881no—
538C22⋊C4—4881no—
539C42—21no—
540C42—21no—
541C42—612no—
542C42—612no—
543C42—4881no—
544C42—4881no—
545C42—2442no—
546C42—2442no—
547C23—612no—
548C23—1221no—
549C23—1221no—
550C23—1221no—
551C23—1221no—
552C23—1221no—
553C23—1221no—
554C23C2×D4×D6111yescharacteristic
555Q8—22no—
556Q8—22no—
557Q8—41no—
558Q8—41no—
559Q8—1222no—
560Q8—1222no—
561Q8—2441no—
562Q8—2441no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—612no—
582C2×C4—612no—
583C2×C4—612no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—1221no—
590C2×C4—1222no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—1222no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4C22×C4×D6111yescharacteristic
607C2×C4C2×D4×D6111yescharacteristic
608C2×C4#41×D6111yescharacteristic
609C2×C4#41×D6111yescharacteristic
610C2×C4#41×D6111yescharacteristic
611C2×C4#41×D6111yescharacteristic
612C8—22no—
613C8—22no—
614C8—614no—
615C8—1222no—
616C22—1222no—
617C22—1222no—
618C22—1222no—
619C22—2441no—
620C22—2441no—
621C22—2441no—
622C22—2441no—
623C22C4×D4×D6111yescharacteristic
624C22#121×D6111yescharacteristic
625C22#1684031111yescharacteristic
626C22#1684056611yescharacteristic
627C22#1684057811yescharacteristic
628C22#1684057811yescharacteristic
629C22#1684057811yescharacteristic
630C4—42no—
631C4—41no—
632C4—41no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—1222no—
637C4—1222no—
638C4—1222no—
639C4—4881no—
640C4—4881no—
641C4—2442no—
642C4—2442no—
643C4C4×D4×D6111yescharacteristic
644C4#1684023011yescharacteristic
645C4#1684027011yescharacteristic
646C4#1684029511yescharacteristic
647C2—2442no—
648C2#2144833111yescharacteristic
649C2#2145468411yescharacteristic
650C2#2145469111yescharacteristic
651C2#2145547211yescharacteristic
652C2#2145548711yescharacteristic
653C2#2145645711yescharacteristic
654C2#2145647711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1935C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1935D61
hypocenterC61#21525
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
2. C2×#16839854C2semidirect
6. #21446679C2semidirect
7. #21446549C2semidirect
8. #21446509C2semidirect
12. #21445711C2semidirect
13. #21445651C2semidirect
14. #21445648C2semidirect
15. C61×#1935C2semidirect
24. #16840002C4semidirect
328. #1935D61semidirect
389. C61#21525semidirect

Maximal subgroups

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

subgroupindex
C2×#168400022
C2×#168398542
C2×#168397192
#214485042
#214484992
#214466792
#214465492
#214465092
#214462512
#214462492
#214458472
#214457112
#214456512
#214456482
C61×#19352
#2152561