Finite Group Databasebeta

← #29721395

Subgroups — #29721395

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840069C211yesmaximal, characteristic, complemented
2C2×#16839823C211yesmaximal, characteristic
3#21451649C211yesmaximal, characteristic
4#21447256C211yesmaximal, characteristic
5#21447245C211yesmaximal, characteristic
6#21447019C211yesmaximal, characteristic
7#21447019C211yesmaximal, characteristic
8#21446776C211yesmaximal, characteristic, complemented
9#21446577C211yesmaximal, characteristic, complemented
10#21446554C211yesmaximal, characteristic, complemented
11#21446549C211yesmaximal, characteristic, complemented
12#21446512C211yesmaximal, characteristic, complemented
13#21446498C211yesmaximal, characteristic, complemented
14#21445824C211yesmaximal, characteristic, complemented
15C61×#2323C211yesmaximal, characteristic
16C2×#14519769C2211yescharacteristic
17#16840069—24no—
18#16839823—24no—
19C2×#14519710C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519701C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519688C2211yescharacteristic
32C2×C4×#92418C2211yescharacteristic
33#16839695—21no—
34#16839695—21no—
35#16839685—21no—
36#16839685—21no—
37#16839660C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839632C2211yescharacteristic
40#16839622C2211yescharacteristic
41#16839622C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C2×C22⋊Q8×C61C2211yescharacteristic
51C2×C4×Q8×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C61×#391C2211yescharacteristic
54C61×#389—21no—
55C61×#389C2211yescharacteristic
56C61×#388—21no—
57C61×#388—21no—
58C61×#387—21no—
59C61×#380C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519769—22no—
66#14519769—22no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×C22⋊Dic61—21no—
78C2×C22⋊Dic61—21no—
79#14519710—22no—
80#14519710—22no—
81#14519710—22no—
82#14519708—22no—
83C4⋊#92418—22no—
84C4⋊#92418D414yes—
85#14519701—22no—
86#14519701—22no—
87#14519701—22no—
88#14519701—22no—
89C22⋊#92418—22no—
90C22⋊#92418—22no—
91#14519688—22no—
92C4×#92418—22no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97C22×Q8×C61C2311yescharacteristic
98C23×C4×C61C2311yescharacteristic
99C22⋊Q8×C61—22no—
100C22⋊Q8×C61—22no—
101C4×Q8×C61—22no—
102C4×Q8×C61—22no—
103#117×C61—22no—
104#117×C61—22no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61D411yescharacteristic
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C22⋊C4×C61—21no—
114C2×C22⋊C4×C61—21no—
115C2×C22⋊C4×C61D411yescharacteristic
116C2×C22⋊C4×C61D411yescharacteristic
117C2×C42×C61—21no—
118C2×C42×C61—21no—
119C2×C42×C61C2311yescharacteristic
120C2×C42×C61C2311yescharacteristic
121#95×C61—21no—
122#95×C61—21no—
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126C24×C61C2×D411yescharacteristic
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61—21no—
132C2×Q8×C61#4112yes—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2411yescharacteristic
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—21no—
153C4⋊C4×C61—24no—
154C4⋊C4×C61—22no—
155C4⋊C4×C61—22no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—42no—
162C4⋊C4×C61—81no—
163C4⋊C4×C61#4112yes—
164C22⋊C4×C61—24no—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—22no—
167C22⋊C4×C61—81no—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—42no—
171C42×C61—81no—
172C42×C61C2×D412yes—
173C42×C61#4112yes—
174C22⋊Dic61—81no—
175C22⋊Dic61—81no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—81no—
185C4⋊Dic61—81no—
186#11758196—42no—
187#11758196—42no—
188#11758196—81no—
189#11758196—81no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418C2×D412yes—
201C2×#92418C2×D412yes—
202C23×C61—21no—
203C23×C61—21no—
204C23×C61—21no—
205C23×C61—21no—
206C23×C61—21no—
207C23×C61—21no—
208C23×C61—21no—
209C23×C61C22×D411yescharacteristic
210Q8×C61—22no—
211Q8×C61—22no—
212Q8×C61—41no—
213Q8×C61—41no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—22no—
222C2×C4×C61—22no—
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—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61#12112yes—
244C2×C4×C61#12112yes—
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61C2×#4111yescharacteristic
249C2×C4×C612−1+411yescharacteristic
250C2×C4×C612−1+411yescharacteristic
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—
263#92418—22no—
264#92418—22no—
265#92418—41no—
266#92418—41no—
267#24715—611nomaximal, Sylow
268C22×C61—41no—
269C22×C61—41no—
270C22×C61—41no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61C2×#12111yescharacteristic
276C22×C61#52511yescharacteristic
277C22×C61#53611yescharacteristic
278C22×C61#57611yescharacteristic
279C22×C61#57711yescharacteristic
280C22×C61#57811yescharacteristic
281C22×C61#57811yescharacteristic
282C4×C61—22no—
283C4×C61—22no—
284C4×C61—42no—
285C4×C61—41no—
286C4×C61—42no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—81no—
290C4×C61—81no—
291C4×C61#54711yescharacteristic
292C4×C61#54811yescharacteristic
293C4×C61#55211yescharacteristic
294C4×C61#55611yescharacteristic
295Dic61—81no—
296Dic61—81no—
297Dic61—81no—
298Dic61—81no—
299C2×#479—611no—
300C2×#433—611no—
301#2629—611no—
302#2323D6111yescharacteristic
303#2077—611no—
304#2075—611no—
305#2036—611no—
306#2036—611no—
307#1989—611no—
308#1947—611no—
309#1943—611no—
310#1942—611no—
311#1935—611no—
312#1933—611no—
313#1803—611no—
314C2×C61—81no—
315C2×C61#241511yescharacteristic
316C2×C61#306111yescharacteristic
317C2×C61#306311yescharacteristic
318C2×C61#311911yescharacteristic
319C2×C61#312711yescharacteristic
320C2×C61#324211yescharacteristic
321C2×C61#324311yescharacteristic
322C2×#125—611no—
323C2×C22⋊Q8C2×D6111yescharacteristic
324C2×C4×Q8C2×D6111yescharacteristic
325C2×#117C2×D6111yescharacteristic
326#479—1224no—
327#433—1224no—
328C2×#107—611no—
329C2×#107—611no—
330C2×#107—611no—
331C2×#106—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8—611no—
334C2×#103—611no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#103—611no—
338C2×C22⋊C8—611no—
339C2×C22⋊C8—611no—
340C2×#97—611no—
341C2×C4×C8—611no—
342#398—1221no—
343#398—1221no—
344#396—1221no—
345#396—1221no—
346#391C2×D6111yescharacteristic
347#389—21no—
348#389—611no—
349#389—611no—
350#389C2×D6111yescharacteristic
351#388—21no—
352#388—21no—
353#387—21no—
354#384—611no—
355#380—611no—
356#380—611no—
357#380C2×D6111yescharacteristic
358C4×C4⋊C4C2×D6111yescharacteristic
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364#340—611no—
365#340—611no—
366#340—611no—
367C61#2471511yescharacteristic, complemented, Sylow
368C22×Q8C22×D6111yescharacteristic
369C23×C4C22×D6111yescharacteristic
370C22×C8—611no—
371C22×C8—611no—
372C22×C8—611no—
373C22×C8—611no—
374#125—1222no—
375#125—1222no—
376C22⋊Q8—22no—
377C22⋊Q8—22no—
378C4×Q8—22no—
379C4×Q8—22no—
380#117—22no—
381#117—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4C22⋊D6111yescharacteristic
396C2×C4⋊C4C22⋊D6111yescharacteristic
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C4⋊C4C22×D6111yescharacteristic
399C2×C4⋊C4C22×D6111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4C22⋊D6111yescharacteristic
405C2×C22⋊C4C22⋊D6111yescharacteristic
406C2×C42—21no—
407C2×C42—21no—
408C2×C42C22×D6111yescharacteristic
409C2×C42C22×D6111yescharacteristic
410#107—1222no—
411#107—1222no—
412#107—1222no—
413#106—1222no—
414C4⋊C8—614no—
415C4⋊C8—1222no—
416#103—1222no—
417#103—1222no—
418#103—1222no—
419#103—1222no—
420C22⋊C8—1222no—
421C22⋊C8—1222no—
422#97—1222no—
423C4×C8—1222no—
424#95—21no—
425#95—21no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433C24C2×C22⋊D6111yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8#1175822212yes—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4C2×C22⋊D6111yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456C22×C4C2×C22⋊D6111yescharacteristic
457C22×C4C2×C22⋊D6111yescharacteristic
458C22×C4C2×C22⋊D6111yescharacteristic
459C22×C4C23×D6111yescharacteristic
460C2×C8—612no—
461C2×C8—612no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—4881no—
491C4⋊C4—4881no—
492C4⋊C4—4881no—
493C4⋊C4—4881no—
494C4⋊C4—2442no—
495C4⋊C4—2442no—
496C4⋊C4#1175822212yes—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—81no—
501C22⋊C4—4881no—
502C22⋊C4—4881no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—81no—
507C42D4×D6112yes—
508C42#1175822412yes—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23C22×C22⋊D6111yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—41no—
520Q8—41no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4#1451974912yes—
563C2×C4#1451974912yes—
564C2×C4C2×D4×D6111yescharacteristic
565C2×C4C2×#1175822411yescharacteristic
566C2×C4C2×#1175822211yescharacteristic
567C2×C4C2×#1175822211yescharacteristic
568C2×C4#1451982411yescharacteristic
569C2×C4#1451982411yescharacteristic
570C8—1222no—
571C8—1222no—
572C8—2441no—
573C8—2441no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C2×#1451974911yescharacteristic
582C22#1684027311yescharacteristic
583C22#1684033311yescharacteristic
584C22#1684056511yescharacteristic
585C22#1684057011yescharacteristic
586C22#1684057711yescharacteristic
587C22#1684057711yescharacteristic
588C4—22no—
589C4—22no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—41no—
594C4—42no—
595C4—81no—
596C4—81no—
597C4—4881no—
598C4—4881no—
599C4—4881no—
600C4—4881no—
601C4#1684041711yescharacteristic
602C4#1684042111yescharacteristic
603C4#1684045211yescharacteristic
604C4#1684048211yescharacteristic
605C2—81no—
606C2#2144924811yescharacteristic
607C2#2145548611yescharacteristic
608C2#2145550611yescharacteristic
609C2#2145601811yescharacteristic
610C2#2145611911yescharacteristic
611C2#2145708111yescharacteristic
612C2#2145709611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2323C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#2323D61
hypocenterC61#24715
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
1. C2×#16840069C2semidirect
8. #21446776C2semidirect
9. #21446577C2semidirect
10. #21446554C2semidirect
11. #21446549C2semidirect
12. #21446512C2semidirect
13. #21446498C2semidirect
14. #21445824C2semidirect
367. C61#24715semidirect

Maximal subgroups

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

subgroupindex
C2×#168400692
C2×#168398232
#214516492
#214472562
#214472452
#214470192
#214467762
#214465772
#214465542
#214465492
#214465122
#214464982
#214458242
C61×#23232
#2471561