Finite Group Databasebeta

← #29721408

Subgroups — #29721408

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840053C211yesmaximal, characteristic, complemented
2C2×#16839822C211yesmaximal, characteristic, complemented
3#21451643C211yesmaximal, characteristic, complemented
4#21448513C211yesmaximal, characteristic
5#21447254C211yesmaximal, characteristic, complemented
6#21447254C211yesmaximal, characteristic, complemented
7#21447010C211yesmaximal, characteristic
8#21447003C211yesmaximal, characteristic
9#21446771C211yesmaximal, characteristic, complemented
10#21446558C211yesmaximal, characteristic, complemented
11#21446548C211yesmaximal, characteristic, complemented
12#21446517C211yesmaximal, characteristic, complemented
13#21446503C211yesmaximal, characteristic, complemented
14#21445826C211yesmaximal, characteristic, complemented
15C61×#1949C211yesmaximal, characteristic, complemented
16C2×#14519777C2211yescharacteristic
17C2×#14519752C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519734C2211yescharacteristic
20#16840053—24no—
21#16839822—24no—
22C2×#14519709C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519699C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×#14519697C2211yescharacteristic
29C2×#14519689C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519687C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839702—21no—
34#16839699—21no—
35#16839683—21no—
36#16839675—21no—
37#16839664—21no—
38#16839663C2211yescharacteristic
39#16839661C2211yescharacteristic
40#16839661C2211yescharacteristic
41#16839661C2211yescharacteristic
42#16839653—21no—
43#16839640—21no—
44#16839636—21no—
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47#16839619C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C61×#382C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122—21no—
62C22×D244—21no—
63C22×D244C2311yescharacteristic
64C22×C4×D61—21no—
65C22×C4×D61C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519777—22no—
69#14519777—22no—
70#14519752—22no—
71#14519752—22no—
72C4×D244—22no—
73C4×D244—22no—
74#14519734—22no—
75#14519734—22no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196D411yescharacteristic
84C2×#11758196D411yescharacteristic
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198D411yescharacteristic
93C2×#11758198D411yescharacteristic
94C2×C4×Dic61C2311yescharacteristic
95#14519709—22no—
96#14519709—22no—
97C4⋊#92418—22no—
98#14519699—22no—
99#14519699—22no—
100#14519697—22no—
101#14519697—22no—
102#14519689—22no—
103#14519689—22no—
104#14519687—22no—
105C8×Dic61—22no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C42×C61—21no—
119C2×C42×C61C2311yescharacteristic
120#107×C61—22no—
121#106×C61—22no—
122C4⋊C8×C61D414yescomplemented
123#95×C61—21no—
124#95×C61—21no—
125#95×C61—21no—
126C23×D61—21no—
127C23×D61C2×D411yescharacteristic
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—21no—
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2411yescharacteristic
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—24no—
147C2×D244—81no—
148C2×D244—81no—
149C2×D244#4112yes—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—42no—
157C2×C4×D61—81no—
158C2×C4×D61—81no—
159C2×Dic122—42no—
160C2×Dic122—81no—
161C2×Dic122—81no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61C2×D412yes—
167C2×C8×C61C2×D412yes—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61#4112yes—
176C42×C61—81no—
177C42×C61C2×D412yes—
178C42×C61#4112yes—
179#11758198—24no—
180#11758198—22no—
181#11758198—22no—
182#11758198—42no—
183#11758198—81no—
184#11758198—81no—
185#11758198—81no—
186#11758198—81no—
187#11758198—81no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—42no—
195C4⋊Dic61—81no—
196C4⋊Dic61—81no—
197C4⋊Dic61—81no—
198#11758196—22no—
199#11758196—22no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418—21no—
208C23×C61C22×D411yescharacteristic
209C22×D61—21no—
210C22×D61—22no—
211C22×D61—21no—
212C22×D61—21no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
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—22no—
228C2×C4×C61—41no—
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#12112yes—
240C2×C4×C61#12112yes—
241C2×C4×C61C22×D411yescharacteristic
242C2×C4×C61C2×#4111yescharacteristic
243C2×C4×C61C2×#4111yescharacteristic
244C2×C4×C61C2×#4111yescharacteristic
245C2×C4×C612−1+411yescharacteristic
246C2×C4×C612−1+411yescharacteristic
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
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—
269D244—84no—
270C4×D61—41no—
271C4×D61—41no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—84no—
275Dic122—84no—
276C8×C61—22no—
277C8×C61—22no—
278#92418—41no—
279#92418—41no—
280#24716—611nomaximal, Sylow
281C22×C61C2×#12111yescharacteristic
282C22×C61#52511yescharacteristic
283C22×C61#53611yescharacteristic
284C22×C61#57611yescharacteristic
285C22×C61#57711yescharacteristic
286C22×C61#57711yescharacteristic
287C22×C61#57711yescharacteristic
288C2×D61—41no—
289C2×D61—42no—
290C2×D61—41no—
291C2×D61—42no—
292C2×D61—41no—
293C2×D61—42no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—81no—
299C2×D61—81no—
300C2×D61—81no—
301C2×D61—81no—
302C4×C61—22no—
303C4×C61—22no—
304C4×C61—42no—
305C4×C61—81no—
306C4×C61—81no—
307C4×C61—81no—
308C4×C61#54711yescharacteristic
309C4×C61#54811yescharacteristic
310C4×C61#55211yescharacteristic
311C4×C61#55611yescharacteristic
312Dic61—41no—
313Dic61—41no—
314Dic61—41no—
315Dic61—81no—
316Dic61—81no—
317Dic61—81no—
318C2×#476—611no—
319C2×#433—611no—
320#2628—611no—
321#2324—611no—
322#2077—611no—
323#2077—611no—
324#2034—611no—
325#2033—611no—
326#1988—611no—
327#1949D6111yescharacteristic, complemented
328#1943—611no—
329#1941—611no—
330#1936—611no—
331#1934—611no—
332#1804—611no—
333C2×C61#241511yescharacteristic
334C2×C61#305711yescharacteristic
335C2×C61#306211yescharacteristic
336C2×C61#311811yescharacteristic
337C2×C61#312511yescharacteristic
338C2×C61#324111yescharacteristic
339C2×C61#324411yescharacteristic
340D61—81no—
341D61—82no—
342C2×C4⋊Q8—611no—
343C2×#121—611no—
344C2×C4×D4—611no—
345C2×#117—611no—
346#476—1224no—
347#433—1224no—
348C2×#107C2×D6111yescharacteristic
349C2×#106—611no—
350C2×#106—611no—
351C2×#106C2×D6111yescharacteristic
352C2×C4⋊C8—611no—
353C2×C4⋊C8C2×D6111yescharacteristic
354C2×#102—611no—
355C2×#102—611no—
356C2×#102—611no—
357C2×#102—611no—
358C2×C22⋊C8—611no—
359C2×C22⋊C8—611no—
360C2×#97—611no—
361C2×C4×C8—611no—
362#400—1221no—
363#399—1221no—
364#395—1221no—
365#393—1221no—
366#390—611no—
367#390—1221no—
368#389—611no—
369#389—611no—
370#389—611no—
371#388—1221no—
372#386—1221no—
373#385—1221no—
374#382C2×D6111yescharacteristic
375#380—611no—
376#380—611no—
377#380—611no—
378C4×C4⋊C4C2×D6111yescharacteristic
379#340—611no—
380#340—611no—
381#340—611no—
382#340—611no—
383#340—611no—
384#340—611no—
385#340C2×D6111yescharacteristic
386#340C2×D6111yescharacteristic
387C61#2471611yescharacteristic, complemented, Sylow
388C22×Q8—1221no—
389C22×D4—611no—
390C22×D4—1221no—
391C23×C4—611no—
392C23×C4—1221no—
393C22×C8—611no—
394C22×C8—611no—
395C22×C8C22×D6111yescharacteristic
396C22×C8C22×D6111yescharacteristic
397C4⋊Q8—1222no—
398C4⋊Q8—1222no—
399#121—1222no—
400#121—1222no—
401C4×D4—1222no—
402C4×D4—1222no—
403#117—1222no—
404#117—1222no—
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⋊C4C22×D6111yescharacteristic
415C2×C4⋊C4C22×D6111yescharacteristic
416C2×C4⋊C4C22×D6111yescharacteristic
417C2×C4⋊C4C22×D6111yescharacteristic
418C2×C22⋊C4—611no—
419C2×C22⋊C4—611no—
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⋊C4—1221no—
427C2×C42—21no—
428C2×C42—611no—
429C2×C42C22×D6111yescharacteristic
430#107—22no—
431#106—22no—
432#106—1222no—
433#106—1222no—
434C4⋊C8—1222no—
435C4⋊C8D24414yescomplemented
436#102—1222no—
437#102—1222no—
438#102—1222no—
439#102—1222no—
440C22⋊C8—1222no—
441C22⋊C8—1222no—
442#97—1222no—
443C4×C8—1222no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—1221no—
448#95—1221no—
449#95—1221no—
450#95—1221no—
451#95—1221no—
452#95—1221no—
453C24—611no—
454C24—1221no—
455C2×Q8—4881no—
456C2×Q8—4881no—
457C2×Q8—2442no—
458C2×D4—612no—
459C2×D4—1224no—
460C2×D4—1221no—
461C2×D4—1221no—
462C2×D4—1221no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4—4881no—
466C2×D4—4881no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—4881no—
484C22×C4—4881no—
485C22×C4—2442no—
486C22×C4D4×D6111yescharacteristic
487C22×C4D4×D6111yescharacteristic
488C22×C4C23×D6111yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—1221no—
497C2×C8—1221no—
498C2×C8—1221no—
499C2×C8C2×D24412yes—
500C2×C8C2×D24412yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1221no—
511C4⋊C4—1221no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C4⋊C4—4881no—
517C4⋊C4—4881no—
518C4⋊C4—4881no—
519C4⋊C4—2442no—
520C4⋊C4#1175822412yes—
521C22⋊C4—1224no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—4881no—
525C22⋊C4—4881no—
526C22⋊C4—4881no—
527C22⋊C4—4881no—
528C22⋊C4—4881no—
529C22⋊C4—2442no—
530C42—81no—
531C42—1221no—
532C42—1221no—
533C42C2×D24412yes—
534C42#1175822612yes—
535C23—1221no—
536C23—1222no—
537C23—1221no—
538C23—1221no—
539C23—1221no—
540C23—1221no—
541C23—1221no—
542C23—1221no—
543C23—2441no—
544C23—2441no—
545C23—2441no—
546C23—2441no—
547C23—2441no—
548C23—2441no—
549C23C2×D4×D6111yescharacteristic
550Q8—4884no—
551D4—1222no—
552D4—1222no—
553D4—4884no—
554D4—2441no—
555D4—2441no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—4884no—
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—2441no—
594C2×C4—2441no—
595C2×C4#1451975212yes—
596C2×C4#1451975212yes—
597C2×C4C22×D24411yescharacteristic
598C2×C4#41×D6111yescharacteristic
599C2×C4C2×#1175822411yescharacteristic
600C2×C4C2×#1175822611yescharacteristic
601C2×C4#1451982411yescharacteristic
602C2×C4#1451982511yescharacteristic
603C8—22no—
604C8—22no—
605C8—2441no—
606C8—2441no—
607C22—4881no—
608C22—4881no—
609C22—4881no—
610C22—4881no—
611C22—2441no—
612C22—2442no—
613C22—2441no—
614C22—2441no—
615C22—2442no—
616C22—2441no—
617C22—2441no—
618C22—2441no—
619C22—2442no—
620C22—2441no—
621C22C2×#1451975211yescharacteristic
622C22#1684027211yescharacteristic
623C22#1684033511yescharacteristic
624C22#1684056611yescharacteristic
625C22#1684056911yescharacteristic
626C22#1684056911yescharacteristic
627C22#1684057111yescharacteristic
628C4—22no—
629C4—22no—
630C4—42no—
631C4—81no—
632C4—81no—
633C4—81no—
634C4—4881no—
635C4—4881no—
636C4—4881no—
637C4—2441no—
638C4—2441no—
639C4—2441no—
640C4#1684041611yescharacteristic
641C4#1684042411yescharacteristic
642C4#1684045011yescharacteristic
643C4#1684048611yescharacteristic
644C2—4882no—
645C2—4881no—
646C2#2144924611yescharacteristic
647C2#2145545911yescharacteristic
648C2#2145550011yescharacteristic
649C2#2145600211yescharacteristic
650C2#2145609511yescharacteristic
651C2#2145707711yescharacteristic
652C2#2145712411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1949C2
socleC23×C61C22×D4
prime radicalC2×#14519752C22
hypercenter#1949D61
hypocenterC61#24716
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
1. C2×#16840053C2semidirect
2. C2×#16839822C2semidirect
3. #21451643C2semidirect
5. #21447254C2semidirect
6. #21447254C2semidirect
9. #21446771C2semidirect
10. #21446558C2semidirect
11. #21446548C2semidirect
12. #21446517C2semidirect
13. #21446503C2semidirect
14. #21445826C2semidirect
15. C61×#1949C2semidirect
122. C4⋊C8×C61D4semidirect
327. #1949D61semidirect
387. C61#24716semidirect
435. C4⋊C8D244semidirect

Maximal subgroups

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

subgroupindex
C2×#168400532
C2×#168398222
#214516432
#214485132
#214472542
#214470102
#214470032
#214467712
#214465582
#214465482
#214465172
#214465032
#214458262
C61×#19492
#2471661