Finite Group Databasebeta

← #29721359

Subgroups — #29721359

Order 15616.

794 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840063C211yesmaximal, characteristic, complemented
2#21451649C211yesmaximal, characteristic, complemented
3#21448512C211yesmaximal, characteristic
4#21447252C211yesmaximal, characteristic, complemented
5#21447247C211yesmaximal, characteristic, complemented
6#21447002C211yesmaximal, characteristic
7#21447002C211yesmaximal, characteristic
8#21446774C211yesmaximal, characteristic, complemented
9#21446578C211yesmaximal, characteristic, complemented
10#21446557C211yesmaximal, characteristic, complemented
11#21446552C211yesmaximal, characteristic, complemented
12#21446516C211yesmaximal, characteristic, complemented
13#21446502C211yesmaximal, characteristic, complemented
14#21445820C211yesmaximal, characteristic, complemented
15C2×C61×#433C211yesmaximal, characteristic, complemented
16C2×#14519769C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19#16840063—24no—
20C2×#14519711C2211yescharacteristic
21C2×#14519711C2211yescharacteristic
22C2×#14519711C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519699C2211yescharacteristic
28#16839695—21no—
29#16839695—21no—
30#16839685—21no—
31#16839685—21no—
32#16839664C2211yescharacteristic
33#16839662—21no—
34#16839660C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839652—21no—
38#16839638—21no—
39#16839633—21no—
40#16839632C2211yescharacteristic
41#16839622C2211yescharacteristic
42#16839622C2211yescharacteristic
43#16839622C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53C2×#117×C61C2211yescharacteristic
54C61×#433—24no—
55C2×C4⋊C8×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×C22⋊C8×C61C2211yescharacteristic
58C2×C22⋊C8×C61C2211yescharacteristic
59C2×#97×C61C2211yescharacteristic
60C2×C4×C8×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64#14519769—22no—
65#14519769—22no—
66#14519751—22no—
67#14519751—22no—
68C4×D244—22no—
69C4×D244—22no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×C4×Dic61—21no—
92#14519711—22no—
93#14519711—22no—
94#14519711—22no—
95#14519709—22no—
96#14519699—22no—
97#14519699—22no—
98#14519699—22no—
99#14519699—22no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107C23×C4×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112#117×C61—22no—
113#117×C61—22no—
114C2×C4⋊C4×C61D411yescharacteristic
115C2×C4⋊C4×C61D411yescharacteristic
116C2×C22⋊C4×C61D411yescharacteristic
117C2×C22⋊C4×C61D411yescharacteristic
118C2×C42×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120C4⋊C8×C61—22no—
121C4⋊C8×C61D414yescomplemented
122C22⋊C8×C61—22no—
123C22⋊C8×C61—22no—
124#97×C61—22no—
125C4×C8×C61—22no—
126C24×C61C2×D411yescharacteristic
127C23×D61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—21no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2411yescharacteristic
140C2×C22⋊D61—24no—
141C2×C22⋊D61—81no—
142C2×C22⋊D61—81no—
143C22×Dic61—21no—
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244#4112yes—
156C2×C4×D61—42no—
157C2×C4×D61—81no—
158C2×C4×D61—81no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61C2×D412yes—
170C2×C8×C61C2×D412yes—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—22no—
173C22⋊C4×C61—22no—
174C22⋊C4×C61—22no—
175C42×C61—21no—
176C42×C61—21no—
177C42×C61C2×D412yes—
178C42×C61#4112yes—
179C22⋊Dic61—81no—
180C22⋊Dic61—81no—
181C22⋊Dic61—81no—
182#11758198—24no—
183#11758198—42no—
184#11758198—81no—
185#11758198—81no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—81no—
200C4⋊Dic61—81no—
201C4⋊Dic61#4112yes—
202#11758196—42no—
203#11758196—42no—
204#11758196—81no—
205#11758196—81no—
206#11758196—81no—
207C4×Dic61—81no—
208C23×C61—21no—
209C23×C61—21no—
210C23×C61—21no—
211C23×C61—21no—
212C23×C61—21no—
213C23×C61—21no—
214C23×C61—21no—
215C23×C61C22×D411yescharacteristic
216C22×D61—22no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220C22×D61—41no—
221C22×D61—41no—
222C22×D61—41no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61#12112yes—
241C2×C4×C61#12112yes—
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C61C2×#4111yescharacteristic
246C2×C4×C612−1+411yescharacteristic
247C2×C4×C612−1+411yescharacteristic
248C22⋊D61—84no—
249C2×Dic61—22no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264C2×Dic61—41no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270D244—22no—
271D244—22no—
272D244—41no—
273D244—41no—
274C4×D61—84no—
275C8×C61—22no—
276C8×C61—22no—
277C8×C61—41no—
278C8×C61—41no—
279#24713—611nomaximal, Sylow
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61—41no—
285C22×C61—41no—
286C22×C61—41no—
287C22×C61C2×#12111yescharacteristic
288C22×C61#52511yescharacteristic
289C22×C61#53611yescharacteristic
290C22×C61#57611yescharacteristic
291C22×C61#57611yescharacteristic
292C22×C61#57711yescharacteristic
293C22×C61#57811yescharacteristic
294C2×D61—42no—
295C2×D61—42no—
296C2×D61—42no—
297C2×D61—81no—
298C2×D61—81no—
299C2×D61—81no—
300C2×D61—81no—
301C4×C61—22no—
302C4×C61—22no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61#54711yescharacteristic
307C4×C61#54811yescharacteristic
308C4×C61#55211yescharacteristic
309C4×C61#55611yescharacteristic
310Dic61—42no—
311Dic61—81no—
312Dic61—81no—
313Dic61—81no—
314Dic61—81no—
315Dic61—81no—
316Dic61—81no—
317C2×#478—611no—
318C2×#433D6111yescharacteristic, complemented
319#2629—611no—
320#2324—611no—
321#2077—611no—
322#2076—611no—
323#2033—611no—
324#2033—611no—
325#1989—611no—
326#1947—611no—
327#1943—611no—
328#1942—611no—
329#1936—611no—
330#1934—611no—
331#1802—611no—
332C2×C61—81no—
333C2×C61#241511yescharacteristic
334C2×C61#306111yescharacteristic
335C2×C61#306211yescharacteristic
336C2×C61#312011yescharacteristic
337C2×C61#312211yescharacteristic
338C2×C61#324111yescharacteristic
339C2×C61#324311yescharacteristic
340D61—82no—
341C2×#125—611no—
342C2×#121—611no—
343C2×C4×D4—611no—
344C2×#117C2×D6111yescharacteristic
345#478—1224no—
346#433—24no—
347C2×#107—611no—
348C2×#107—611no—
349C2×#107—611no—
350C2×#106—611no—
351C2×C4⋊C8C2×D6111yescharacteristic
352C2×C4⋊C8C2×D6111yescharacteristic
353C2×#102—611no—
354C2×#102—611no—
355C2×#102—611no—
356C2×#102—611no—
357C2×C22⋊C8C2×D6111yescharacteristic
358C2×C22⋊C8C2×D6111yescharacteristic
359C2×#97C2×D6111yescharacteristic
360C2×C4×C8C2×D6111yescharacteristic
361#398—1221no—
362#398—1221no—
363#396—1221no—
364#396—1221no—
365#390—611no—
366#390—1221no—
367#389—611no—
368#389—611no—
369#389—611no—
370#388—1221no—
371#386—1221no—
372#385—1221no—
373#384—611no—
374#380—611no—
375#380—611no—
376#380—611no—
377C4×C4⋊C4—611no—
378#340—611no—
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#340—611no—
385#340—611no—
386C61#2471311yescharacteristic, complemented, Sylow
387C22×D4—611no—
388C22×D4—1221no—
389C23×C4—1221no—
390C23×C4C22×D6111yescharacteristic
391C22×C8C22×D6111yescharacteristic
392C22×C8C22×D6111yescharacteristic
393C22×C8C22×D6111yescharacteristic
394C22×C8C22×D6111yescharacteristic
395#125—1222no—
396#125—1222no—
397#121—1222no—
398#121—1222no—
399C4×D4—1222no—
400C4×D4—1222no—
401#117—22no—
402#117—22no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—611no—
409C2×C4⋊C4—611no—
410C2×C4⋊C4—1221no—
411C2×C4⋊C4—1221no—
412C2×C4⋊C4—1221no—
413C2×C4⋊C4—1221no—
414C2×C4⋊C4—1221no—
415C2×C4⋊C4—1221no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4D24411yescharacteristic
418C2×C4⋊C4D24411yescharacteristic
419C2×C22⋊C4—1221no—
420C2×C22⋊C4—1221no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C22⋊C4—1221no—
424C2×C22⋊C4—1221no—
425C2×C22⋊C4—1221no—
426C2×C22⋊C4D24411yescharacteristic
427C2×C22⋊C4D24411yescharacteristic
428C2×C42—1221no—
429C2×C42C22×D6111yescharacteristic
430C2×C42C22×D6111yescharacteristic
431#107—1222no—
432#107—1222no—
433#107—1222no—
434#106—1222no—
435C4⋊C8—22no—
436C4⋊C8C22⋊D6114yescomplemented
437#102—1222no—
438#102—1222no—
439#102—1222no—
440#102—1222no—
441C22⋊C8—22no—
442C22⋊C8—22no—
443#97—22no—
444C4×C8—22no—
445#95—1221no—
446#95—1221no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452C24—1221no—
453C24C2×D24411yescharacteristic
454C2×D4—612no—
455C2×D4—1224no—
456C2×D4—1221no—
457C2×D4—1221no—
458C2×D4—1221no—
459C2×D4—1221no—
460C2×D4—1221no—
461C2×D4—4881no—
462C2×D4—4881no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—4881no—
477C22×C4—4881no—
478C22×C4—2442no—
479C22×C4C2×D24411yescharacteristic
480C22×C4C2×D24411yescharacteristic
481C22×C4C2×D24411yescharacteristic
482C22×C4C2×D24411yescharacteristic
483C22×C4C2×D24411yescharacteristic
484C22×C4C23×D6111yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8C2×C22⋊D6112yes—
496C2×C8C2×C22⋊D6112yes—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—612no—
500C4⋊C4—1221no—
501C4⋊C4—1221no—
502C4⋊C4—1221no—
503C4⋊C4—1221no—
504C4⋊C4—1221no—
505C4⋊C4—1221no—
506C4⋊C4—1221no—
507C4⋊C4—1221no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—4881no—
514C4⋊C4—4881no—
515C4⋊C4—4881no—
516C4⋊C4—4881no—
517C4⋊C4—4881no—
518C4⋊C4—2442no—
519C4⋊C4—2442no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—1224no—
523C22⋊C4—4881no—
524C22⋊C4—4881no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—4881no—
528C22⋊C4—2442no—
529C42—21no—
530C42—21no—
531C42—4881no—
532C42#1175822212yes—
533C42C2×C22⋊D6112yes—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—1222no—
542C23—2441no—
543C23—2441no—
544C23—2441no—
545C23—2441no—
546C23—2441no—
547C23—2441no—
548C23C22×D24411yescharacteristic
549D4—1222no—
550D4—1222no—
551D4—4884no—
552D4—2441no—
553D4—2441no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—1222no—
572C2×C4—4884no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4#1451975112yes—
594C2×C4#1451975112yes—
595C2×C4C22×C22⋊D6111yescharacteristic
596C2×C4#41×D6111yescharacteristic
597C2×C4#41×D6111yescharacteristic
598C2×C4C2×#1175822211yescharacteristic
599C2×C4#1451982411yescharacteristic
600C2×C4#1451982411yescharacteristic
601C8—22no—
602C8—22no—
603C8—41no—
604C8—41no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—4881no—
613C22—4881no—
614C22—4881no—
615C22—4881no—
616C22—2442no—
617C22—2442no—
618C22—2442no—
619C22C2×#1451975111yescharacteristic
620C22#1684027411yescharacteristic
621C22#1684033811yescharacteristic
622C22#1684056711yescharacteristic
623C22#1684056711yescharacteristic
624C22#1684057411yescharacteristic
625C22#1684057911yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—4881no—
632C4—4881no—
633C4—4881no—
634C4—4881no—
635C4—4881no—
636C4—4881no—
637C4—2442no—
638C4#1684041111yescharacteristic
639C4#1684041911yescharacteristic
640C4#1684045111yescharacteristic
641C4#1684048011yescharacteristic
642C2—81no—
643C2—4882no—
644C2#2144924211yescharacteristic
645C2#2145548911yescharacteristic
646C2#2145549911yescharacteristic
647C2#2145603511yescharacteristic
648C2#2145606311yescharacteristic
649C2#2145707411yescharacteristic
650C2#2145710411yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#433C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenterC2×#433D61
hypocenterC61#24713
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16840063C2semidirect
2. #21451649C2semidirect
4. #21447252C2semidirect
5. #21447247C2semidirect
8. #21446774C2semidirect
9. #21446578C2semidirect
10. #21446557C2semidirect
11. #21446552C2semidirect
12. #21446516C2semidirect
13. #21446502C2semidirect
14. #21445820C2semidirect
15. C2×C61×#433C2semidirect
121. C4⋊C8×C61D4semidirect
318. C2×#433D61semidirect
386. C61#24713semidirect
436. C4⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400632
#214516492
#214485122
#214472522
#214472472
#214470022
#214467742
#214465782
#214465572
#214465522
#214465162
#214465022
#214458202
C2×C61×#4332
#2471361