Finite Group Databasebeta

← #29729463

Subgroups — #29729463

Order 15616.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840132C211yesmaximal, characteristic, complemented
2C2×#16840059C211yesmaximal, characteristic
3#21450814C211yesmaximal, characteristic
4#21447211C211yesmaximal, characteristic, complemented
5#21447197C211yesmaximal, characteristic, complemented
6#21447060C211yesmaximal, characteristic
7#21447060C211yesmaximal, characteristic
8#21446751C211yesmaximal, characteristic
9#21446751C211yesmaximal, characteristic
10#21446742C211yesmaximal, characteristic, complemented
11#21446543C211yesmaximal, characteristic, complemented
12#21446460C211yesmaximal, characteristic, complemented
13#21446453C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic
15C61×#2370C211yesmaximal, characteristic, complemented
16C2×#14519777C2211yescharacteristic
17C2×#14519765C2211yescharacteristic
18C2×#14519765C2211yescharacteristic
19C2×C4×D244C2211yescharacteristic
20#16840132—24no—
21#16840059—24no—
22C2×#14519710C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×#14519700C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519700C2211yescharacteristic
34C2×#14519700C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37C2×#14519697C2211yescharacteristic
38C2×#14519697C2211yescharacteristic
39C2×#14519688C2211yescharacteristic
40#16839689—21no—
41#16839689—21no—
42#16839668C2211yescharacteristic
43#16839668C2211yescharacteristic
44#16839619—21no—
45#16839619—21no—
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839517C2211yescharacteristic
49#16839517C2211yescharacteristic
50C2×#125×C61C2211yescharacteristic
51C61×#389—21no—
52C61×#389C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#387—21no—
55C61×#387—21no—
56C4×C4⋊C4×C61—21no—
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C22×Dic122C2311yescharacteristic
63C22×D244C2311yescharacteristic
64C22×C4×D61—21no—
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69#14519777—22no—
70#14519777—22no—
71#14519765—22no—
72#14519765—22no—
73#14519765—41no—
74#14519765—41no—
75C4×D244—22no—
76C4×D244—22no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85#14519710—22no—
86#14519708—22no—
87C4⋊#92418—22no—
88C4⋊#92418—41no—
89C4⋊#92418—41no—
90#14519700—22no—
91#14519700—22no—
92#14519700—22no—
93#14519700—22no—
94#14519700—22no—
95#14519700—22no—
96#14519700—41no—
97#14519700—41no—
98#14519697—22no—
99#14519697—22no—
100#14519697—22no—
101#14519697—22no—
102#14519688—22no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#125×C61—22no—
108#125×C61D414yes—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61D411yescharacteristic
114C2×C4⋊C4×C61D411yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C42×C61—21no—
120C2×C42×C61—21no—
121C2×C42×C61—21no—
122C2×C42×C61C2311yescharacteristic
123C2×C42×C61C2311yescharacteristic
124C2×C42×C61C2311yescharacteristic
125#95×C61—21no—
126#95×C61—21no—
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61D411yescharacteristic
131#95×C61D411yescharacteristic
132C23×D61—21no—
133C22×C4×C61—21no—
134C22×C4×C61—21no—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2411yescharacteristic
144C22×Dic61—21no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244—21no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244#4112yes—
153C2×C4×D61—42no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—21no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C4⋊C4×C61—24no—
169C4⋊C4×C61—24no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—42no—
178C4⋊C4×C61—81no—
179C4⋊C4×C61C2×D412yes—
180C4⋊C4×C61C2×D412yes—
181C4⋊C4×C61#4112yes—
182C42×C61—21no—
183C42×C61—21no—
184C42×C61—21no—
185C42×C61—21no—
186C42×C61—42no—
187C42×C61—81no—
188C42×C61—81no—
189C42×C61C2×D412yes—
190C42×C61#4112yes—
191#11758198—42no—
192#11758198—42no—
193#11758198—42no—
194#11758198—42no—
195#11758198—42no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—42no—
199C4⋊Dic61—42no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C23×C61C22×D411yescharacteristic
213C22×D61—22no—
214C22×D61—41no—
215C22×D61—41no—
216C22×D61—41no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—41no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—21no—
229C2×C4×C61—21no—
230C2×C4×C61—22no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
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#12112yes—
249C2×C4×C61#12112yes—
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C2×#4111yescharacteristic
252C2×C4×C61C2×#4111yescharacteristic
253C2×C4×C61C2×#4111yescharacteristic
254C2×C4×C61H(5,𝔽2)11yescharacteristic
255C2×C4×C612−1+411yescharacteristic
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—
265D244—22no—
266D244—22no—
267D244—41no—
268D244—41no—
269C4×D61—84no—
270Dic122—41no—
271Dic122—41no—
272Dic122—41no—
273Dic122—41no—
274Dic122—41no—
275Dic122—41no—
276Dic122—41no—
277Dic122—41no—
278#92418—41no—
279#92418—41no—
280#92418—41no—
281#92418—41no—
282#25289—611nomaximal, Sylow
283C22×C61C2×#12111yescharacteristic
284C22×C61#54611yescharacteristic
285C22×C61#54811yescharacteristic
286C22×C61#57511yescharacteristic
287C22×C61#57511yescharacteristic
288C22×C61#57711yescharacteristic
289C22×C61#57811yescharacteristic
290C2×D61—42no—
291C2×D61—42no—
292C2×D61—42no—
293C2×D61—81no—
294C2×D61—81no—
295C2×D61—81no—
296C2×D61—81no—
297C4×C61—22no—
298C4×C61—22no—
299C4×C61—42no—
300C4×C61—42no—
301C4×C61—42no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—41no—
306C4×C61—81no—
307C4×C61#52911yescharacteristic
308C4×C61#54211yescharacteristic
309C4×C61#54811yescharacteristic
310C4×C61#55011yescharacteristic
311Dic61—81no—
312Dic61—81no—
313Dic61—81no—
314C2×#491—611no—
315C2×#478—611no—
316#2547—611no—
317#2370D6111yescharacteristic, complemented
318#2068—611no—
319#2066—611no—
320#2042—611no—
321#2042—611no—
322#1983—611no—
323#1983—611no—
324#1981—611no—
325#1940—611no—
326#1928—611no—
327#1927—611no—
328#1762—611no—
329C2×C61#242611yescharacteristic
330C2×C61#304011yescharacteristic
331C2×C61#304611yescharacteristic
332C2×C61#330711yescharacteristic
333C2×C61#331511yescharacteristic
334C2×C61#337611yescharacteristic
335C2×C61#337711yescharacteristic
336D61—82no—
337C2×C4⋊Q8—611no—
338C2×#125C2×D6111yescharacteristic
339C2×#124—611no—
340C2×#124—611no—
341C2×C4×D4—611no—
342#491—1224no—
343#478—1224no—
344C2×#107—611no—
345C2×#106—611no—
346C2×C4⋊C8—611no—
347C2×C4⋊C8—611no—
348C2×C4⋊C8—611no—
349C2×#103—611no—
350C2×#103—611no—
351C2×#103—611no—
352C2×#103—611no—
353C2×#103—611no—
354C2×#103—611no—
355C2×#103—611no—
356C2×#103—611no—
357C2×#102—611no—
358C2×#102—611no—
359C2×#102—611no—
360C2×#102—611no—
361C2×#97—611no—
362#397—1221no—
363#397—1221no—
364#391—611no—
365#391—611no—
366#389—21no—
367#389C2×D6111yescharacteristic
368#389C2×D6111yescharacteristic
369#387—21no—
370#387—21no—
371#380—1221no—
372#380—1221no—
373C4×C4⋊C4—21no—
374C4×C4⋊C4C2×D6111yescharacteristic
375C4×C4⋊C4C2×D6111yescharacteristic
376C4×C4⋊C4C2×D6111yescharacteristic
377C4×C4⋊C4C2×D6111yescharacteristic
378#340—611no—
379#340—611no—
380#336—611no—
381#336—611no—
382C61#2528911yescharacteristic, complemented, Sylow
383C22×Q8—611no—
384C22×Q8—611no—
385C22×D4—611no—
386C23×C4—1221no—
387C22×C8—611no—
388C22×C8—611no—
389C22×C8—611no—
390C22×C8—611no—
391C4⋊Q8—1222no—
392C4⋊Q8—1222no—
393#125—22no—
394#125D24414yes—
395#124—1222no—
396#124—1222no—
397#124—2441no—
398#124—2441no—
399C4×D4—1222no—
400C4×D4—1222no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4—1221no—
408C2×C4⋊C4C22⋊D6111yescharacteristic
409C2×C4⋊C4C22⋊D6111yescharacteristic
410C2×C4⋊C4C22×D6111yescharacteristic
411C2×C4⋊C4C22×D6111yescharacteristic
412C2×C4⋊C4C22×D6111yescharacteristic
413C2×C4⋊C4C22×D6111yescharacteristic
414C2×C22⋊C4—1221no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C22⋊C4—1221no—
419C2×C42—21no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42C22×D6111yescharacteristic
423C2×C42C22×D6111yescharacteristic
424C2×C42C22×D6111yescharacteristic
425#107—1222no—
426#106—1222no—
427C4⋊C8—1222no—
428C4⋊C8—2441no—
429C4⋊C8—2441no—
430#103—1222no—
431#103—1222no—
432#103—1222no—
433#103—1222no—
434#103—1222no—
435#103—1222no—
436#103—2441no—
437#103—2441no—
438#102—1222no—
439#102—1222no—
440#102—1222no—
441#102—1222no—
442#97—1222no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95C22⋊D6111yescharacteristic
453#95C22⋊D6111yescharacteristic
454C24—1221no—
455C2×Q8—1221no—
456C2×Q8—1221no—
457C2×Q8—1221no—
458C2×Q8—1221no—
459C2×Q8—1221no—
460C2×Q8—1221no—
461C2×Q8—1221no—
462C2×Q8—1221no—
463C2×Q8—1221no—
464C2×Q8—1221no—
465C2×Q8—1221no—
466C2×Q8—1221no—
467C2×D4—612no—
468C2×D4—1221no—
469C2×D4—1221no—
470C2×D4—1221no—
471C2×D4—1221no—
472C2×D4—1221no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—2442no—
481C22×C4—2442no—
482C22×C4—2442no—
483C22×C4C2×C22⋊D6111yescharacteristic
484C22×C4C2×C22⋊D6111yescharacteristic
485C22×C4C2×C22⋊D6111yescharacteristic
486C22×C4C2×C22⋊D6111yescharacteristic
487C22×C4C2×C22⋊D6111yescharacteristic
488C22×C4C2×C22⋊D6111yescharacteristic
489C22×C4C23×D6111yescharacteristic
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1221no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8—1221no—
500C2×C8—1221no—
501C2×C8—1221no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—42no—
512C4⋊C4—81no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—2442no—
516C4⋊C4—2442no—
517C4⋊C4C2×D24412yes—
518C4⋊C4C2×D24412yes—
519C4⋊C4#1175822612yes—
520C22⋊C4—2442no—
521C22⋊C4—2442no—
522C22⋊C4—2442no—
523C22⋊C4—2442no—
524C22⋊C4—2442no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—42no—
530C42—81no—
531C42—81no—
532C42C2×D24412yes—
533C42#1175822212yes—
534C23—1222no—
535C23—2441no—
536C23—2441no—
537C23—2441no—
538C23—2441no—
539C23—2441no—
540C23—2441no—
541C23C22×C22⋊D6111yescharacteristic
542Q8—2441no—
543Q8—2441no—
544Q8—2441no—
545Q8—2441no—
546Q8—2441no—
547Q8—2441no—
548Q8—2441no—
549Q8—2441no—
550D4—1222no—
551D4—1222no—
552D4—2441no—
553D4—2441no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
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—41no—
582C2×C4—4884no—
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#1451975112yes—
593C2×C4#1451975112yes—
594C2×C4C22×D24411yescharacteristic
595C2×C4#41×D6111yescharacteristic
596C2×C4C2×#1175822211yescharacteristic
597C2×C4C2×#1175822611yescharacteristic
598C2×C4#1451982311yescharacteristic
599C2×C4#1451982511yescharacteristic
600C8—2441no—
601C8—2441no—
602C8—2441no—
603C8—2441no—
604C22—4881no—
605C22—4881no—
606C22—4881no—
607C22—4881no—
608C22—2442no—
609C22—2442no—
610C22—2442no—
611C22C2×#1451975111yescharacteristic
612C22#1684040011yescharacteristic
613C22#1684042311yescharacteristic
614C22#1684056011yescharacteristic
615C22#1684056011yescharacteristic
616C22#1684057311yescharacteristic
617C22#1684057711yescharacteristic
618C4—22no—
619C4—22no—
620C4—42no—
621C4—41no—
622C4—41no—
623C4—42no—
624C4—42no—
625C4—41no—
626C4—41no—
627C4—81no—
628C4—4881no—
629C4—4881no—
630C4—4881no—
631C4#1684029911yescharacteristic
632C4#1684038411yescharacteristic
633C4#1684042411yescharacteristic
634C4#1684043411yescharacteristic
635C2—4882no—
636C2#2144937911yescharacteristic
637C2#2145531311yescharacteristic
638C2#2145536911yescharacteristic
639C2#2145778911yescharacteristic
640C2#2145790911yescharacteristic
641C2#2145864611yescharacteristic
642C2#2145866111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2370C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#2370D61
hypocenterC61#25289
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
1. C2×#16840132C2semidirect
4. #21447211C2semidirect
5. #21447197C2semidirect
10. #21446742C2semidirect
11. #21446543C2semidirect
12. #21446460C2semidirect
13. #21446453C2semidirect
15. C61×#2370C2semidirect
317. #2370D61semidirect
382. C61#25289semidirect

Maximal subgroups

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

subgroupindex
C2×#168401322
C2×#168400592
#214508142
#214472112
#214471972
#214470602
#214467512
#214467422
#214465432
#214464602
#214464532
#214456472
C61×#23702
#2528961