Finite Group Databasebeta

← #29650139

Subgroups — #29650139

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455848C211yesmaximal, characteristic
2#21454898C211yesmaximal, characteristic, complemented
3#21454896C211yesmaximal, characteristic
4#21444699C211yesmaximal, characteristic, complemented
5#21444662C211yesmaximal, characteristic, complemented
6#21444660C211yesmaximal, characteristic, complemented
7SD16⋊#92418C211yesmaximal, characteristic, complemented
8#21444630C211yesmaximal, characteristic, complemented
9#21444622C211yesmaximal, characteristic, complemented
10#21444616C211yesmaximal, characteristic, complemented
11#21444598C211yesmaximal, characteristic, complemented
12#21444264C211yesmaximal, characteristic, complemented
13#21444234C211yesmaximal, characteristic
14#21444117C211yesmaximal, characteristic, complemented
15C61×#1588C211yesmaximal, characteristic, complemented
16#16840309C2211yescharacteristic
17C4×Q8×D61C2211yescharacteristic
18#16840082C411yescharacteristic
19#16840079C411yescharacteristic
20#16840046C411yescharacteristic
21#16840045C411yescharacteristic
22#16839961C411yescharacteristic
23#16839960C411yescharacteristic
24#16839902C411yescharacteristic
25#16839899C411yescharacteristic
26Q8×#92418C2211yescharacteristic
27C8×Dic122—21no—
28C8×Dic122C2211yescharacteristic
29#16839886—21no—
30#16839886C2211yescharacteristic
31C4×#11758190C2211yescharacteristic
32C4×#11758201C2211yescharacteristic
33C4×#11758200C2211yescharacteristic
34#16839841C2211yescharacteristic
35#16839831—21no—
36#16839830—21no—
37D4×#92418C2211yescharacteristic
38#16839827C2211yescharacteristic
39#16839818C2211yescharacteristic
40#16839814—21no—
41#16839814C2211yescharacteristic
42#16839813—21no—
43#16839813C2211yescharacteristic
44#16839813C2211yescharacteristic
45#16839730—21no—
46#16839727—21no—
47C4×#11758189C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839491C2211yescharacteristic
55D4⋊#92418C2211yescharacteristic
56#16839489C2211yescharacteristic
57#16839483C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C8×Q8×C61C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C61×#436C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758222—21no—
68C2×Q8×D61C2×C411yescharacteristic
69C2×#11758190C2×C411yescharacteristic
70C2×#11758200C2×C411yescharacteristic
71C2×#11758201C2×C411yescharacteristic
72C2×#11758189—21no—
73C2×#11758189—21no—
74C22×#92418—21no—
75C2×C8×D61—21no—
76#14519776C2×C411yescharacteristic
77#14519773C2×C411yescharacteristic
78#14519763—21no—
79#14519752C2×C411yescharacteristic
80#14519750—21no—
81#14519748C2×C411yescharacteristic
82Q8×Dic61C2×C411yescharacteristic
83C4×Dic122—21no—
84C4×Dic122C2311yescharacteristic
85#14519742—21no—
86#14519742C2×C411yescharacteristic
87C4×D244C2311yescharacteristic
88C4×C22⋊D61—21no—
89C4⋊C4×D61—21no—
90C4⋊C4×D61C2×C411yescharacteristic
91C42×D61—21no—
92C42×D61C2311yescharacteristic
93#14519709C2×C411yescharacteristic
94#14519708C2×C411yescharacteristic
95#14519708C2×C411yescharacteristic
96C4⋊#92418—21no—
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519706—21no—
100#14519706—21no—
101#14519706C2×C411yescharacteristic
102#14519706C2×C411yescharacteristic
103#14519706D411yescharacteristic
104#14519706D411yescharacteristic
105#14519702C2×C411yescharacteristic
106#14519701C2×C411yescharacteristic
107#14519700C2×C411yescharacteristic
108#14519699C2×C411yescharacteristic
109#14519698C2×C411yescharacteristic
110#14519697C2×C411yescharacteristic
111C22⋊#92418—21no—
112#14519689—21no—
113#14519689—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689C2×C411yescharacteristic
117#14519689C2×C411yescharacteristic
118#14519689D411yescharacteristic
119#14519689D411yescharacteristic
120#14519687—21no—
121#14519687—21no—
122C4×#92418—21no—
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C2×SD16×C61C2×C411yescharacteristic
130C2×M16×C61—21no—
131C4×Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#106×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C2×C22⋊D61—21no—
148C2×C22⋊D61—21no—
149C2×C22⋊D61—21no—
150Q8×D61—22no—
151Q8×D61—22no—
152#11758222—81no—
153#11758222—81no—
154C2×D244—21no—
155C2×D244C22×C411yescharacteristic
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61C22×C411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61#4111yescharacteristic
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122C22×C411yescharacteristic
165SD16×C61—22no—
166M16×C61—81no—
167C2×C8×C61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61C22×C411yescharacteristic
171C2×C8×C61C22×C411yescharacteristic
172C2×C8×C61C2×D411yescharacteristic
173C2×C8×C61C2×D411yescharacteristic
174C4⋊C4×C61—21no—
175C4⋊C4×C61C22×C411yescharacteristic
176C4⋊C4×C61C22×C411yescharacteristic
177C22⋊C4×C61—21no—
178C42×C61—21no—
179C42×C61C2411yescharacteristic
180C22⋊Dic61—21no—
181#11758201—22no—
182#11758200—22no—
183#11758198—21no—
184#11758198—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61C22×C411yescharacteristic
187C4⋊Dic61C22×C411yescharacteristic
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61C22×C411yescharacteristic
196C4×Dic61C2×D411yescharacteristic
197C4×Dic61#4111yescharacteristic
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—81no—
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206#11758190—22no—
207#11758189—42no—
208#11758189—81no—
209C8×D61—81no—
210C23×C61—21no—
211C22×D61—21no—
212C22×D61C4×D411yescharacteristic
213Q8×C61—21no—
214Q8×C61#13112yes—
215D4×C61—21no—
216D4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61C23×C411yescharacteristic
223C2×C4×C61C22×D411yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C22⋊D61—81no—
226C22⋊D61—81no—
227C22⋊D61—81no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61C4×D411yescharacteristic
232C2×Dic61C4×D411yescharacteristic
233C2×Dic61C4×D411yescharacteristic
234D244—21no—
235D244—21no—
236D244—81no—
237C4×D61—24no—
238C4×D61—21no—
239C4×D61—21no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—41no—
243C4×D61—41no—
244C4×D61—41no—
245C4×D61—81no—
246Dic122—24no—
247Dic122—21no—
248Dic122—81no—
249Dic122#13112yes—
250C8×C61—22no—
251C8×C61—21no—
252C8×C61—21no—
253C8×C61—21no—
254C8×C61—21no—
255C8×C61—41no—
256C8×C61—41no—
257#92418—21no—
258#92418—21no—
259#92418—21no—
260#92418—21no—
261#92418—41no—
262#92418—41no—
263#92418—41no—
264#17923—611nomaximal, Sylow
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61C2×C4×D411yescharacteristic
269C2×D61—21no—
270C2×D61—21no—
271C2×D61—21no—
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C4×C61—22no—
276C4×C61—21no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61C2×#13111yescharacteristic
280C4×C61C2×#13111yescharacteristic
281C4×C61#57711yescharacteristic
282C4×C61#57711yescharacteristic
283Dic61—21no—
284Dic61—22no—
285Dic61—21no—
286Dic61—21no—
287Dic61—41no—
288Dic61—41no—
289#3103—611no—
290#2982—611no—
291#2981—611no—
292#1588—611no—
293#1588D6111yescharacteristic, complemented
294#1583—611no—
295#1583—611no—
296SD16⋊C8—611no—
297SD16⋊C8—611no—
298C8×SD16—611no—
299C8×SD16—611no—
300#1572—611no—
301#1491—611no—
302#1484—611no—
303#1453—611no—
304C2×C61—81no—
305C2×C61#292911yescharacteristic
306C2×C61#294911yescharacteristic
307C2×C61#295611yescharacteristic
308D61—41no—
309D61—81no—
310#532—611no—
311C2×C4×Q8—611no—
312#481—611no—
313#481—611no—
314#475—611no—
315#475—611no—
316#460—611no—
317#460—611no—
318#448—611no—
319#448—611no—
320C8×Q8—611no—
321C8×Q8—611no—
322C8×Q8—611no—
323C8×Q8—1221no—
324C8×Q8—1221no—
325C8×Q8C2×D6111yescharacteristic
326C4×SD16—611no—
327C4×SD16—611no—
328C4×SD16—611no—
329C4×SD16C2×D6111yescharacteristic
330#436—611no—
331#436C2×D6111yescharacteristic
332#435—1221no—
333#435—1221no—
334C8×D4—611no—
335C8×D4—611no—
336#432—611no—
337#431—611no—
338#431—611no—
339#431—611no—
340#431—1221no—
341#431—1221no—
342#408—1221no—
343#408—1221no—
344C4×M16—611no—
345#335—611no—
346#335C2×D6111yescharacteristic
347#334—611no—
348#334—611no—
349Q8⋊C8—611no—
350Q8⋊C8—611no—
351Q8⋊C8—611no—
352Q8⋊C8C2×D6111yescharacteristic
353D4⋊C8—611no—
354D4⋊C8—611no—
355D4⋊C8—611no—
356D4⋊C8C2×D6111yescharacteristic
357#322—611no—
358#322—611no—
359#322C2×D6111yescharacteristic
360C82—611no—
361C61#1792311yescharacteristic, complemented, Sylow
362C2×#41—1221no—
363C22×Q8—611no—
364C2×SD16—611no—
365C2×SD16—611no—
366C2×SD16—611no—
367C2×SD16C4×D6111yescharacteristic
368C2×M16—21no—
369C2×M16—1221no—
370C2×M16—1221no—
371C22×C8—1221no—
372C22×C8—1221no—
373C4⋊Q8—611no—
374#127—611no—
375#124—1221no—
376#121—611no—
377#121—611no—
378#121—1221no—
379C4×Q8—611no—
380C4×Q8—611no—
381C4×Q8—611no—
382C4×Q8—1221no—
383C4×Q8—1221no—
384C4×Q8C22×D6111yescharacteristic
385C4×D4—611no—
386C4×D4—1221no—
387C4×D4C22×D6111yescharacteristic
388C2×C4⋊C4—611no—
389C2×C4⋊C4—1221no—
390C2×C42—611no—
391C2×C42—1221no—
392#106—611no—
393#106—611no—
394#106—611no—
395#106C4×D6111yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—611no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8C22×D6111yescharacteristic
407C4⋊C8C22×D6111yescharacteristic
408#103—611no—
409#103—611no—
410#103—611no—
411#103C4×D6111yescharacteristic
412#102—611no—
413#102—611no—
414#102—611no—
415#102C4×D6111yescharacteristic
416C22⋊C8—21no—
417C22⋊C8—611no—
418C22⋊C8—611no—
419C22⋊C8—611no—
420C22⋊C8—611no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426#97—1221no—
427#97—1221no—
428C4×C8—21no—
429C4×C8—611no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—1221no—
433C4×C8—1221no—
434C4×C8—1221no—
435C4×C8—1221no—
436C4×C8C22×D6111yescharacteristic
437C4×C8C22×D6111yescharacteristic
438C4×C8C22×D6111yescharacteristic
439#41—4881no—
440#41—4881no—
441C2×Q8—611no—
442C2×Q8—1221no—
443C2×Q8—1221no—
444C2×Q8—1222no—
445C2×Q8—1222no—
446C2×Q8C2×C4×D6111yescharacteristic
447C2×D4—611no—
448C2×D4—1221no—
449C2×D4—1221no—
450C2×D4—1221no—
451C2×D4—1221no—
452C2×D4C2×C4×D6111yescharacteristic
453C22×C4—21no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460SD16—22no—
461SD16—1222no—
462SD16—1222no—
463SD16—1222no—
464M16—81no—
465M16—4881no—
466M16—2442no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—611no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—611no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—1221no—
477C2×C8—4881no—
478C2×C8—4881no—
479C2×C8C2×C4×D6111yescharacteristic
480C2×C8C2×C4×D6111yescharacteristic
481C2×C8D4×D6111yescharacteristic
482C2×C8D4×D6111yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—611no—
485C4⋊C4—611no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4C2×C4×D6111yescharacteristic
492C4⋊C4C2×C4×D6111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—1221no—
495C22⋊C4—1221no—
496C22⋊C4—1221no—
497C42—21no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—1221no—
502C42—1221no—
503C42—1221no—
504C42C23×D6111yescharacteristic
505C23—21no—
506C23—611no—
507C23—1221no—
508Q8—21no—
509Q8—612no—
510Q8—1224no—
511Q8—1221no—
512Q8—4881no—
513Q8#1451978512yes—
514D4—21no—
515D4—21no—
516D4—1221no—
517D4—1221no—
518D4—4881no—
519D4—4881no—
520D4—4881no—
521D4—4881no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—611no—
530C2×C4—1224no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—4881no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4C22×C4×D6111yescharacteristic
543C2×C4C2×D4×D6111yescharacteristic
544C2×C4#41×D6111yescharacteristic
545C8—22no—
546C8—21no—
547C8—21no—
548C8—21no—
549C8—21no—
550C8—41no—
551C8—41no—
552C8—1221no—
553C8—1221no—
554C8—1221no—
555C8—1221no—
556C8—2441no—
557C8—2441no—
558C8—2441no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—1221no—
563C22—1221no—
564C22—1221no—
565C22—2441no—
566C22—2441no—
567C22—2441no—
568C22C4×D4×D6111yescharacteristic
569C4—21no—
570C4—22no—
571C4—41no—
572C4—41no—
573C4—1221no—
574C4—1221no—
575C4—1221no—
576C4—1222no—
577C4—2441no—
578C4—2441no—
579C4#131×D6111yescharacteristic
580C4C2×#1451978511yescharacteristic
581C4#1684057111yescharacteristic
582C4#1684057211yescharacteristic
583C2—81no—
584C2—4881no—
585C2—2441no—
586C2#2145451011yescharacteristic
587C2#2145467511yescharacteristic
588C2#2145472411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1588C2
socleC22×C61C2×C4×D4
prime radical#16840309C22
cosocleC42×C61C24
hypercenter#1588D61
hypocenterC61#17923
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1588

Complements

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

NH ≅ G/Ntype
2. #21454898C2semidirect
4. #21444699C2semidirect
5. #21444662C2semidirect
6. #21444660C2semidirect
7. SD16⋊#92418C2semidirect
8. #21444630C2semidirect
9. #21444622C2semidirect
10. #21444616C2semidirect
11. #21444598C2semidirect
12. #21444264C2semidirect
14. #21444117C2semidirect
15. C61×#1588C2semidirect
293. #1588D61semidirect
361. C61#17923semidirect

Maximal subgroups

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

subgroupindex
#214558482
#214548982
#214548962
#214446992
#214446622
#214446602
SD16⋊#924182
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#214446162
#214445982
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#214442342
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C61×#15882
#1792361