Finite Group Databasebeta

← #29687868

Subgroups — #29687868

Order 15616.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455601C211yesmaximal, characteristic
2#21454760C211yesmaximal, characteristic, complemented
3#21454248C211yesmaximal, characteristic
4#21446594C211yesmaximal, characteristic, complemented
5#21446421C211yesmaximal, characteristic, complemented
6#21446421C211yesmaximal, characteristic, complemented
7#21446095C211yesmaximal, characteristic
8#21446095C211yesmaximal, characteristic
9#21445840C211yesmaximal, characteristic
10#21445702C211yesmaximal, characteristic, complemented
11#21445697C211yesmaximal, characteristic, complemented
12#21445694C211yesmaximal, characteristic, complemented
13#21445660C211yesmaximal, characteristic
14#21445653C211yesmaximal, characteristic
15C61×#1986C211yesmaximal, characteristic, complemented
16C2×#14519785C2211yescharacteristic
17C2×#14519785C2211yescharacteristic
18C4×#11758222C2211yescharacteristic
19#16840066C411yescharacteristic, complemented
20#16840066C411yescharacteristic, complemented
21#16840059C411yescharacteristic, complemented
22#16840059C411yescharacteristic, complemented
23#16840054C411yescharacteristic, complemented
24#16840049C411yescharacteristic, complemented
25#16840044C411yescharacteristic, complemented
26#16840039C411yescharacteristic, complemented
27#16839893—21no—
28#16839893—21no—
29#16839893—21no—
30#16839893—21no—
31C2×#14519712C2211yescharacteristic
32C2×#14519712C2211yescharacteristic
33#16839798C2211yescharacteristic
34#16839798C2211yescharacteristic
35#16839789C2211yescharacteristic
36#16839789C2211yescharacteristic
37#16839786C2211yescharacteristic
38C2×C4⋊#92418C2211yescharacteristic
39C2×#14519705C2211yescharacteristic
40C2×#14519705C2211yescharacteristic
41#16839756C2211yescharacteristic
42#16839756C2211yescharacteristic
43#16839720C2211yescharacteristic
44#16839720C2211yescharacteristic
45#16839718C2211yescharacteristic
46#16839718C2211yescharacteristic
47#16839716—21no—
48#16839716—21no—
49#16839714—21no—
50C2×#14519688C2211yescharacteristic
51C2×#14519688C2211yescharacteristic
52#97×D61—21no—
53C2×C4×#92418C2211yescharacteristic
54#16839526C2211yescharacteristic
55#16839526C2211yescharacteristic
56#16839522C2211yescharacteristic
57#16839522C2211yescharacteristic
58#16839517C2211yescharacteristic
59#16839517C2211yescharacteristic
60C61×#533C2211yescharacteristic
61C4×M16×C61C2211yescharacteristic
62C4×C4⋊C4×C61C2211yescharacteristic
63C61×#339C2211yescharacteristic
64C61×#339C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519785—22no—
69#14519785—22no—
70#14519785—22no—
71#14519785Q814yescomplemented
72C2×#11758194C2311yescharacteristic
73C2×#11758194C2311yescharacteristic
74C2×#11758189—21no—
75C2×#11758189—21no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—21no—
81C2×C8×D61—21no—
82C4×Dic122C2×C411yescharacteristic
83C4×Dic122C2×C411yescharacteristic
84C4×D244C2×C411yescharacteristic
85C4×D244C2×C411yescharacteristic
86C4×C22⋊D61—21no—
87C4×C22⋊D61—21no—
88#14519736C2311yescharacteristic
89#14519734—21no—
90C42×D61—21no—
91#14519712—22no—
92#14519712—22no—
93#14519710C2×C411yescharacteristic
94#14519710C2×C411yescharacteristic
95#14519710C2×C411yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519708C2×C411yescharacteristic
98#14519708C2×C411yescharacteristic
99#14519708C2×C411yescharacteristic
100#14519708C2×C411yescharacteristic
101C4⋊#92418—21no—
102C4⋊#92418—21no—
103C4⋊#92418—21no—
104C4⋊#92418—21no—
105C4⋊#92418—21no—
106C4⋊#92418—21no—
107C4⋊#92418C2×C411yescharacteristic
108C4⋊#92418C2×C411yescharacteristic
109C4⋊#92418C2×C411yescharacteristic
110C4⋊#92418C2×C411yescharacteristic
111#14519705—22no—
112#14519705—22no—
113#14519700C2×C411yescharacteristic
114#14519700C2×C411yescharacteristic
115#14519700C2×C411yescharacteristic
116#14519700C2×C411yescharacteristic
117#14519697C2×C411yescharacteristic
118#14519697C2×C411yescharacteristic
119#14519697C2×C411yescharacteristic
120#14519697C2×C411yescharacteristic
121#14519688—21no—
122#14519688—21no—
123#14519688—22no—
124#14519688D411yescharacteristic
125#14519688D411yescharacteristic
126#14519688D411yescharacteristic
127#14519688D411yescharacteristic
128#14519687—21no—
129#14519687—21no—
130C4×#92418—21no—
131C4×#92418—21no—
132C4×#92418—22no—
133C8×Dic61—21no—
134C8×Dic61—21no—
135C2×M16×C61C2311yescharacteristic
136C2×M16×C61C2311yescharacteristic
137C4⋊Q8×C61C2×C411yescharacteristic
138C4⋊Q8×C61C2×C411yescharacteristic
139#125×C61C2×C411yescharacteristic
140#125×C61C2×C411yescharacteristic
141C22⋊Q8×C61—21no—
142C22⋊Q8×C61—21no—
143C4×Q8×C61—21no—
144C4×Q8×C61—21no—
145#117×C61C2311yescharacteristic
146#117×C61C2311yescharacteristic
147C2×C4⋊C4×C61—21no—
148C2×C42×C61C2311yescharacteristic
149C2×C42×C61C2311yescharacteristic
150C2×C42×C61C2311yescharacteristic
151#97×C61—21no—
152C4×C8×C61—21no—
153#95×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61#4111yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—21no—
162#11758222—21no—
163#11758222—21no—
164#11758222C2×Q812yes—
165#11758222#4112yes—
166C2×D244C22×C411yescharacteristic
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×Dic122C22×C411yescharacteristic
171M16×C61—21no—
172M16×C61—21no—
173M16×C61C2×Q812yes—
174M16×C61#4112yes—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—42no—
184C4⋊C4×C61C22×C411yescharacteristic
185C4⋊C4×C61C22×C411yescharacteristic
186C4⋊C4×C61C22×C411yescharacteristic
187C4⋊C4×C61C22×C411yescharacteristic
188C22⋊C4×C61—21no—
189C22⋊C4×C61—21no—
190C42×C61—21no—
191C42×C61—21no—
192C42×C61—21no—
193C42×C61—21no—
194C42×C61—21no—
195C42×C61—21no—
196C42×C61C22×C411yescharacteristic
197C42×C61C22×C411yescharacteristic
198C42×C61C2×D411yescharacteristic
199C42×C61C2×D411yescharacteristic
200C22⋊Dic61—21no—
201#11758198—21no—
202#11758198—21no—
203C4⋊Dic61C22×C411yescharacteristic
204C4⋊Dic61C22×C411yescharacteristic
205#11758196—21no—
206#11758196—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210#11758194—21no—
211#11758194—21no—
212#11758194—21no—
213#11758194—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418C22×C411yescharacteristic
223C2×#92418C22×C411yescharacteristic
224C2×#92418C22×C411yescharacteristic
225C2×#92418C22×C411yescharacteristic
226C2×#92418C2×D411yescharacteristic
227C2×#92418C2×D411yescharacteristic
228C2×#92418C2×D411yescharacteristic
229C2×#92418C2×D411yescharacteristic
230C2×#92418C2×Q812yes—
231C2×#92418#4112yes—
232#11758189—24no—
233#11758189—24no—
234C8×D61—24no—
235C8×D61—24no—
236C23×C61C2×#4111yescharacteristic
237C22×D61—21no—
238Q8×C61—81no—
239Q8×C61—81no—
240C2×C4×C61—22no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61C4×D411yescharacteristic
253C2×C4×C61C4×D411yescharacteristic
254C2×C4×C61C4×D411yescharacteristic
255C2×C4×C61C4×D411yescharacteristic
256C2×C4×C61C23×C411yescharacteristic
257C2×C4×C61C22×D411yescharacteristic
258C2×C4×C61C22×Q811yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C22⋊D61—22no—
263C22⋊D61—22no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267D244—21no—
268D244C4×Q812yes—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—81no—
272C4×D61—81no—
273Dic122—21no—
274Dic122C4×Q812yes—
275C8×C61—22no—
276C8×C61—22no—
277#92418—21no—
278#92418—21no—
279#92418—21no—
280#92418—21no—
281#92418—21no—
282#92418—21no—
283#92418—41no—
284#92418—41no—
285#92418C22⋊Q812yes—
286#92418C22⋊Q812yes—
287#21629—611nomaximal, Sylow
288C22×C61—21no—
289C22×C61—21no—
290C22×C61C2×C4×D411yescharacteristic
291C22×C61#52911yescharacteristic
292C22×C61#53311yescharacteristic
293C2×D61—22no—
294C2×D61—41no—
295C2×D61—41no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—42no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—41no—
305C4×C61—81no—
306C4×C61C2×C4×Q811yescharacteristic
307C4×C61C4×#4111yescharacteristic
308C4×C61C2×C22⋊Q811yescharacteristic
309C4×C61#52511yescharacteristic
310Dic61—22no—
311Dic61—41no—
312Dic61—41no—
313#3076—611no—
314#2961—611no—
315#2875—611no—
316#1986D6111yescharacteristic, complemented
317#1950—611no—
318#1922—611no—
319#1922—611no—
320#1866—611no—
321#1866—611no—
322#1806—611no—
323#1773—611no—
324#1772—611no—
325#1771—611no—
326#1765—611no—
327#1764—611no—
328C2×C61—21no—
329C2×C61—21no—
330C2×C61C4×C22⋊Q811yescharacteristic
331C2×C61#295611yescharacteristic
332C2×C61#295711yescharacteristic
333D61—42no—
334C2×#131—611no—
335C2×#131—611no—
336#533C2×D6111yescharacteristic
337C4×#41—611no—
338#479—611no—
339#479—611no—
340#478—611no—
341#478—611no—
342#477—611no—
343#476—611no—
344#475—611no—
345#474—611no—
346#446—1221no—
347#446—1221no—
348#446—1221no—
349#446—1221no—
350C2×#108—611no—
351C2×#108—611no—
352#427—611no—
353#427—611no—
354#424—611no—
355#424—611no—
356#423—611no—
357C2×C4⋊C8—611no—
358C2×#104—611no—
359C2×#104—611no—
360#416—611no—
361#416—611no—
362#405—611no—
363#405—611no—
364#405—611no—
365#405—611no—
366#405—1221no—
367#405—1221no—
368C4×M16—1221no—
369C4×M16C2×D6111yescharacteristic
370C2×#97—611no—
371C2×#97—611no—
372C2×#97—1221no—
373C2×C4×C8—611no—
374C4×C4⋊C4C2×D6111yescharacteristic
375#341—611no—
376#341—611no—
377#339—611no—
378#339—611no—
379#339C2×D6111yescharacteristic
380#339C2×D6111yescharacteristic
381#339C2×D6111yescharacteristic
382#339C2×D6111yescharacteristic
383#336—611no—
384#336—611no—
385C61#2162911yescharacteristic, complemented, Sylow
386C2×#41—611no—
387#131—614no—
388#131—1222no—
389#131—1222no—
390#131—1222no—
391C2×M16—611no—
392C2×M16—611no—
393C2×M16—1221no—
394C2×M16—1221no—
395C2×M16C22×D6111yescharacteristic
396C2×M16C22×D6111yescharacteristic
397C22×C8—611no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—1221no—
402C22×C8—1221no—
403C4⋊Q8C4×D6111yescharacteristic
404C4⋊Q8C4×D6111yescharacteristic
405#125C4×D6111yescharacteristic
406#125C4×D6111yescharacteristic
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—611no—
412C4×Q8—611no—
413C4×D4—611no—
414C4×D4—611no—
415C4×D4—1221no—
416C4×D4—1221no—
417#117—611no—
418#117—1221no—
419#117C22×D6111yescharacteristic
420#117C22×D6111yescharacteristic
421C2×C4⋊C4—21no—
422C2×C42—1221no—
423C2×C42C22×D6111yescharacteristic
424C2×C42C22×D6111yescharacteristic
425C2×C42C22×D6111yescharacteristic
426#108—1222no—
427#108—1222no—
428#107—611no—
429#107—611no—
430#107—611no—
431#107—611no—
432#106—611no—
433#106—611no—
434#106—611no—
435#106—611no—
436C4⋊C8—611no—
437C4⋊C8—611no—
438C4⋊C8—611no—
439C4⋊C8—611no—
440C4⋊C8—1221no—
441C4⋊C8—1221no—
442C4⋊C8—1221no—
443C4⋊C8—1221no—
444C4⋊C8—1221no—
445C4⋊C8—1221no—
446#104—1222no—
447#104—1222no—
448#103—611no—
449#103—611no—
450#103—611no—
451#103—611no—
452#102—611no—
453#102—611no—
454#102—611no—
455#102—611no—
456#97—21no—
457#97—611no—
458#97—611no—
459#97—611no—
460#97—611no—
461#97—1222no—
462#97—1221no—
463#97—1221no—
464#97—1221no—
465#97—1221no—
466C4×C8—21no—
467C4×C8—1222no—
468C4×C8—1221no—
469C4×C8—1221no—
470C4×C8—1221no—
471C4×C8—1221no—
472#95—21no—
473#41—612no—
474#41—612no—
475#41—1221no—
476#41—1221no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—611no—
480C2×D4—611no—
481C2×D4—1221no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4#1175822411yescharacteristic
488C22×C4#1175822411yescharacteristic
489C22×C4C23×D6111yescharacteristic
490M16—21no—
491M16—21no—
492M16—1224no—
493M16—1224no—
494M16—1221no—
495M16—1221no—
496M16—1221no—
497M16—1221no—
498M16Q8×D6112yes—
499M16#1175822612yes—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—611no—
503C2×C8—611no—
504C2×C8—612no—
505C2×C8—612no—
506C2×C8—611no—
507C2×C8—611no—
508C2×C8—611no—
509C2×C8—611no—
510C2×C8—611no—
511C2×C8—611no—
512C2×C8—1224no—
513C2×C8—1224no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—611no—
530C4⋊C4—611no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4C2×C4×D6111yescharacteristic
534C4⋊C4C2×C4×D6111yescharacteristic
535C4⋊C4C2×C4×D6111yescharacteristic
536C4⋊C4C2×C4×D6111yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—1221no—
540C22⋊C4—1221no—
541C22⋊C4—1221no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—1221no—
549C42—1221no—
550C42—1221no—
551C42C2×C4×D6111yescharacteristic
552C42C2×C4×D6111yescharacteristic
553C42D4×D6111yescharacteristic
554C42D4×D6111yescharacteristic
555C23—1221no—
556C23C2×#1175822411yescharacteristic
557Q8—81no—
558Q8—81no—
559Q8—612no—
560Q8—1221no—
561D4—612no—
562D4—1222no—
563D4—1222no—
564D4—1221no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—1221no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—4881no—
583C2×C4—4881no—
584C2×C4#1451973711yescharacteristic
585C2×C4#1451973711yescharacteristic
586C2×C4#1451973711yescharacteristic
587C2×C4#1451973711yescharacteristic
588C2×C4C22×C4×D6111yescharacteristic
589C2×C4C2×D4×D6111yescharacteristic
590C2×C4C2×Q8×D6111yescharacteristic
591C2×C4#41×D6111yescharacteristic
592C2×C4#41×D6111yescharacteristic
593C2×C4C2×#1175822611yescharacteristic
594C8—22no—
595C8—22no—
596C8—612no—
597C8—612no—
598C8—1221no—
599C8—1221no—
600C8—1221no—
601C8—1221no—
602C8—1221no—
603C8—1221no—
604C8—2441no—
605C8—2441no—
606C22—21no—
607C22—21no—
608C22—1222no—
609C22—2441no—
610C22—2441no—
611C22C2×#1451973711yescharacteristic
612C22#1684029111yescharacteristic
613C22#1684031711yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—1222no—
625C4—2441no—
626C4—2441no—
627C4C4×Q8×D6111yescharacteristic
628C4C4×#1175822611yescharacteristic
629C4C22⋊Q8×D6111yescharacteristic
630C4#1684027511yescharacteristic
631C2—21no—
632C2—21no—
633C2—2442no—
634C2#2144835711yescharacteristic
635C2#2145472511yescharacteristic
636C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1986C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758222C23
cosocleC22×C4×C61C24
hypercenter#1986D61
hypocenterC61#21629
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #21454760C2semidirect
4. #21446594C2semidirect
5. #21446421C2semidirect
6. #21446421C2semidirect
10. #21445702C2semidirect
11. #21445697C2semidirect
12. #21445694C2semidirect
15. C61×#1986C2semidirect
19. #16840066C4semidirect
20. #16840066C4semidirect
21. #16840059C4semidirect
22. #16840059C4semidirect
23. #16840054C4semidirect
24. #16840049C4semidirect
25. #16840044C4semidirect
26. #16840039C4semidirect
71. #14519785Q8semidirect
316. #1986D61semidirect
385. C61#21629semidirect

Maximal subgroups

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

subgroupindex
#214556012
#214547602
#214542482
#214465942
#214464212
#214460952
#214458402
#214457022
#214456972
#214456942
#214456602
#214456532
C61×#19862
#2162961