Finite Group Databasebeta

← #29585454

Subgroups — #29585454

Order 15616.

1180 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic
2C2×#16839735C211yesmaximal, characteristic
3C2×#16839735C211yesmaximal, characteristic
4#21445530C211yesmaximal, characteristic, complemented
5#21445529C211yesmaximal, characteristic, complemented
6#21445528C211yesmaximal, characteristic, complemented
7C61×#1733C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9#16840528—22no—
10#16840528—22no—
11#16840528—22no—
12#16840528—22no—
13C2×#14519785—22no—
14C2×#14519783—22no—
15C22×#11758194C2211yescharacteristic
16C2×M16×D61C414yescomplemented
17C2×#14519736C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19#16839735—22no—
20#16839735—22no—
21#16839735C414yescomplemented
22#16839735C414yescomplemented
23C2×#14519691—22no—
24C2×#14519691—22no—
25#16839523—22no—
26#16839522—22no—
27#16839521—22no—
28C22×M16×C61C2211yescharacteristic
29C2×#117×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C61×#339—22no—
32C2×#11758222—21no—
33C2×#11758222—21no—
34C2×#11758222—21no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222C2×C412yes—
41C2×#11758222C2×C412yes—
42C2×#11758222D412yes—
43C2×#11758222D412yes—
44C22×Dic122Q811yescharacteristic
45C22×D244Q811yescharacteristic
46C22×C22⋊D61D412yes—
47C22×C4×D61C2×C412yes—
48#14519785—28no—
49#14519785—28no—
50#14519783—28no—
51#14519783—28no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194C2×C412yes—
56C2×#11758194D412yes—
57C2×#11758194D412yes—
58C2×#11758189—24no—
59M16×D61—28no—
60M16×D61—28no—
61C22×#92418—21no—
62C2×C8×D61—24no—
63#14519736—21no—
64#14519736—21no—
65#14519736—21no—
66#14519736—21no—
67#14519736—21no—
68#14519736—21no—
69#14519736C2×C412yes—
70#14519736C2×C412yes—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C22⋊Dic61—21no—
74C2×C22⋊Dic61—21no—
75C2×C4×Dic61—21no—
76C2×C4×Dic61—21no—
77#14519691—28no—
78#14519691—28no—
79C23×C4×C61C2311yescharacteristic
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61C2×C412yes—
84C2×M16×C61D412yes—
85C2×M16×C61D412yes—
86C22×C8×C61—21no—
87#117×C61—21no—
88#117×C61—21no—
89#117×C61—21no—
90#117×C61—21no—
91#117×C61—21no—
92#117×C61—21no—
93#117×C61C2×C412yes—
94#117×C61C2×C412yes—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61—21no—
97C2×C22⋊C4×C61—21no—
98C2×C22⋊C4×C61—21no—
99C2×C42×C61—21no—
100C2×C42×C61—21no—
101C24×C61C2×D411yescharacteristic
102C23×D61C4⋊C412yes—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61C22×C411yescharacteristic
106C22×C4×C61C22×C411yescharacteristic
107C22×C4×C61C22×C411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×Q811yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C22×C4×C61#4111yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C2×C22⋊D61—22no—
120C2×C22⋊D61—22no—
121C2×C22⋊D61—22no—
122C2×C22⋊D61—22no—
123C2×C22⋊D61C22⋊C414yes—
124C2×C22⋊D61C22⋊C414yes—
125C22×Dic61—41no—
126C22×Dic61—41no—
127C22×Dic61C4⋊C412yes—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—22no—
133#11758222—22no—
134#11758222—22no—
135#11758222—22no—
136#11758222—22no—
137#11758222—22no—
138#11758222—22no—
139#11758222—22no—
140#11758222—22no—
141#11758222—22no—
142#11758222—22no—
143#11758222—22no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244C4⋊C412yes—
149C2×D244C4⋊C412yes—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61C4214yes—
155C2×C4×D61C22⋊C414yes—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122C4⋊C412yes—
161C2×Dic122C4⋊C412yes—
162M16×C61—22no—
163M16×C61—22no—
164M16×C61—22no—
165M16×C61C22⋊C414yes—
166C2×C8×C61—22no—
167C2×C8×C61—22no—
168C2×C8×C61—22no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61—41no—
173C22⋊C4×C61—22no—
174C22⋊C4×C61—22no—
175C22⋊C4×C61—41no—
176C22⋊C4×C61—41no—
177C42×C61—22no—
178C42×C61—22no—
179C42×C61—41no—
180C42×C61—41no—
181C22⋊Dic61—22no—
182C22⋊Dic61—22no—
183C22⋊Dic61—41no—
184C22⋊Dic61—41no—
185C4⋊Dic61—22no—
186C4⋊Dic61—22no—
187C4⋊Dic61—41no—
188C4⋊Dic61—41no—
189C4×Dic61—22no—
190C4×Dic61—22no—
191C4×Dic61—41no—
192C4×Dic61—41no—
193#11758194—22no—
194#11758194—22no—
195#11758194—22no—
196#11758194C22⋊C414yes—
197C2×#92418—22no—
198C2×#92418—22no—
199C2×#92418—22no—
200#11758189—216no—
201C8×D61—216no—
202C23×C61—81no—
203C23×C61C2×C22⋊C411yescharacteristic
204C23×C61C2×C22⋊C411yescharacteristic
205C23×C61C2×C4⋊C411yescharacteristic
206C23×C61#12111yescharacteristic
207C23×C61#12111yescharacteristic
208C23×C61#12111yescharacteristic
209C23×C61#12111yescharacteristic
210C22×D61—22no—
211C22×D61—22no—
212C22×D61—82no—
213C22×D61#9514yes—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—82no—
217C2×C4×C61—82no—
218C2×C4×C61C2×C4211yescharacteristic
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61C2×C4⋊C411yescharacteristic
223C2×C4×C61C2×C4⋊C411yescharacteristic
224C2×C4×C61#11711yescharacteristic
225C2×C4×C61#11711yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C4×D411yescharacteristic
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61C4×D411yescharacteristic
234C2×C4×C61#12011yescharacteristic
235C2×C4×C61#12011yescharacteristic
236C2×C4×C61#12011yescharacteristic
237C2×C4×C61#12011yescharacteristic
238C2×C4×C61C22⋊Q811yescharacteristic
239C2×C4×C61C22⋊Q811yescharacteristic
240C2×C4×C61C22⋊Q811yescharacteristic
241C2×C4×C61C22⋊Q811yescharacteristic
242C2×C4×C61#12311yescharacteristic
243C2×C4×C61#12311yescharacteristic
244C2×C4×C61#12311yescharacteristic
245C2×C4×C61#12311yescharacteristic
246C22⋊D61—24no—
247C22⋊D61—24no—
248C22⋊D61—24no—
249C22⋊D61—24no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61—82no—
255C2×Dic61—82no—
256C2×Dic61#9514yes—
257D244—22no—
258D244—22no—
259D244—22no—
260D244—22no—
261C4×D61—24no—
262C4×D61—24no—
263C4×D61—24no—
264C4×D61—24no—
265Dic122—22no—
266Dic122—22no—
267Dic122—22no—
268Dic122—22no—
269C8×C61—24no—
270#92418—24no—
271#10766—611nomaximal, Sylow
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61C2×#9511yescharacteristic
280C22×C61#38011yescharacteristic
281C22×C61#38011yescharacteristic
282C22×C61#38611yescharacteristic
283C22×C61#38611yescharacteristic
284C22×C61#38611yescharacteristic
285C22×C61#38611yescharacteristic
286C2×D61—24no—
287C2×D61—44no—
288C2×D61—82no—
289C2×D61—82no—
290C4×C61—82no—
291C4×C61—82no—
292C4×C61C4×C22⋊C411yescharacteristic
293C4×C61C4×C22⋊C411yescharacteristic
294C4×C61#37911yescharacteristic
295C4×C61#38111yescharacteristic
296C4×C61#38511yescharacteristic
297C4×C61#38511yescharacteristic
298C4×C61#38511yescharacteristic
299C4×C61#38511yescharacteristic
300Dic61—24no—
301Dic61—82no—
302Dic61—82no—
303C2×#568—611no—
304C2×#410—611no—
305C2×#410—611no—
306#1733—611no—
307#1733—611no—
308#1733—611no—
309#1733D6111yescharacteristic, complemented
310C2×C61—21no—
311C2×C61—21no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61—21no—
315C2×C61—21no—
316C2×C61—21no—
317C2×C61C22⋊#9511yescharacteristic
318D61—44no—
319C22×#41—611no—
320#568—1222no—
321#568—1222no—
322#568—1222no—
323#568—1222no—
324C2×#131—1222no—
325C2×#131—1222no—
326C22×M16—611no—
327C22×M16—614no—
328C22×M16C2×D6111yescharacteristic
329C2×#117—611no—
330C2×#117—611no—
331C2×#117C2×D6111yescharacteristic
332C2×#117C2×D6111yescharacteristic
333#410—614no—
334#410—614no—
335#410—1222no—
336#410—1222no—
337C2×#99—1222no—
338C2×#99—1222no—
339#339—22no—
340#339—1222no—
341#339—1222no—
342#339—1222no—
343C61#1076611yescharacteristic, complemented, Sylow
344C2×#41—612no—
345C2×#41—612no—
346C2×#41—612no—
347C2×#41—612no—
348C2×#41—1221no—
349C2×#41—1221no—
350C2×#41—1221no—
351C2×#41—1221no—
352C2×#41—1221no—
353C2×#41—1221no—
354C2×#41—1221no—
355C2×#41—1221no—
356C22×Q8—611no—
357C22×D4—612no—
358C22×D4—611no—
359C23×C4—612no—
360C23×C4C22×D6111yescharacteristic
361#131—1228no—
362#131—1228no—
363#131—1228no—
364#131—1228no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—612no—
369C2×M16—612no—
370C2×M16—612no—
371C2×M16—1224no—
372C2×M16—1228no—
373C2×M16—1221no—
374C2×M16—1221no—
375C2×M16—1221no—
376C2×M16—1228no—
377C2×M16C4×D6112yes—
378C2×M16D24412yes—
379C2×M16C22⋊D6112yes—
380C22×C8—21no—
381C22×C8—1224no—
382C22×C8—1221no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—612no—
390#117—612no—
391#117—1221no—
392#117—1221no—
393#117—1221no—
394#117—1221no—
395#117—1221no—
396#117—1221no—
397#117C4×D6112yes—
398#117C4×D6112yes—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4—1221no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—1221no—
410C2×C42—1221no—
411#99—1228no—
412#99—1228no—
413C24—612no—
414C24D4×D6111yescharacteristic
415#41—1222no—
416#41—1222no—
417#41—1222no—
418#41—1222no—
419#41—1222no—
420#41—1222no—
421#41—1222no—
422#41—1222no—
423#41—1222no—
424#41—1222no—
425#41—1222no—
426#41—1222no—
427#41—1222no—
428#41—1222no—
429#41—1222no—
430#41—1222no—
431C2×Q8—612no—
432C2×Q8—612no—
433C2×Q8—1221no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×D4—614no—
438C2×D4—614no—
439C2×D4—612no—
440C2×D4—612no—
441C2×D4—1222no—
442C2×D4—1222no—
443C2×D4—1222no—
444C2×D4—1222no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—612no—
452C22×C4—614no—
453C22×C4—614no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—2441no—
459C22×C4—2441no—
460C22×C4C2×C4×D6111yescharacteristic
461C22×C4C2×C4×D6111yescharacteristic
462C22×C4C2×C4×D6111yescharacteristic
463C22×C4C2×D24411yescharacteristic
464C22×C4#1175822211yescharacteristic
465C22×C4#1175822211yescharacteristic
466C22×C4D4×D6111yescharacteristic
467C22×C4D4×D6111yescharacteristic
468C22×C4D4×D6111yescharacteristic
469C22×C4D4×D6111yescharacteristic
470C22×C4#1175822411yescharacteristic
471C22×C4Q8×D6111yescharacteristic
472C22×C4#1175822611yescharacteristic
473C22×C4C2×C22⋊D6111yescharacteristic
474M16—22no—
475M16—22no—
476M16—22no—
477M16—614no—
478M16—12216no—
479M16—1222no—
480M16—1222no—
481M16—1222no—
482M16#1175819814yes—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—12216no—
487C2×C8—1222no—
488C2×C8—1222no—
489C2×C8—1222no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—2441no—
497C4⋊C4—2441no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—1222no—
503C22⋊C4—1222no—
504C22⋊C4—2441no—
505C22⋊C4—2441no—
506C42—22no—
507C42—22no—
508C42—41no—
509C42—41no—
510C42—1222no—
511C42—1222no—
512C42—2441no—
513C42—2441no—
514C23—81no—
515C23—614no—
516C23—1222no—
517C23—1222no—
518C23—4882no—
519C23C22⋊C4×D6111yescharacteristic
520C23C22⋊C4×D6111yescharacteristic
521C23C4⋊C4×D6111yescharacteristic
522C23#1451974811yescharacteristic
523C23#1451975011yescharacteristic
524C23#1451975011yescharacteristic
525C23#1451975211yescharacteristic
526Q8—1222no—
527Q8—1222no—
528Q8—1222no—
529Q8—1222no—
530D4—1224no—
531D4—1224no—
532D4—1224no—
533D4—1224no—
534D4—1222no—
535D4—1222no—
536D4—1222no—
537D4—1222no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—614no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1224no—
546C2×C4—1224no—
547C2×C4—1224no—
548C2×C4—1224no—
549C2×C4—4882no—
550C2×C4—4882no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4C42×D6111yescharacteristic
554C2×C4C22⋊C4×D6111yescharacteristic
555C2×C4C22⋊C4×D6111yescharacteristic
556C2×C4C2×#1175819811yescharacteristic
557C2×C4C4⋊C4×D6111yescharacteristic
558C2×C4C4⋊C4×D6111yescharacteristic
559C2×C4#1451973411yescharacteristic
560C2×C4#1451973511yescharacteristic
561C2×C4#1451973711yescharacteristic
562C2×C4#1451973711yescharacteristic
563C2×C4C4×C22⋊D6111yescharacteristic
564C2×C4C4×C22⋊D6111yescharacteristic
565C2×C4#1451973911yescharacteristic
566C2×C4#1451973911yescharacteristic
567C2×C4C4×D24411yescharacteristic
568C2×C4C4×D24411yescharacteristic
569C2×C4#1451974511yescharacteristic
570C2×C4#1451974511yescharacteristic
571C2×C4#1451974711yescharacteristic
572C2×C4#1451974711yescharacteristic
573C2×C4#1451975311yescharacteristic
574C2×C4#1451975511yescharacteristic
575C2×C4#1451975511yescharacteristic
576C2×C4#1451975711yescharacteristic
577C2×C4#1451975911yescharacteristic
578C2×C4#1451975911yescharacteristic
579C2×C4#1451976211yescharacteristic
580C2×C4#1451976211yescharacteristic
581C8—24no—
582C8—1224no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—1224no—
591C22—4882no—
592C22—4882no—
593C22—2444no—
594C22#95×D6111yescharacteristic
595C22#1683961911yescharacteristic
596C22#1683962111yescharacteristic
597C22#1683963811yescharacteristic
598C22#1683963811yescharacteristic
599C22#1683964011yescharacteristic
600C22#1683964011yescharacteristic
601C4—82no—
602C4—82no—
603C4—1224no—
604C4—4882no—
605C4—4882no—
606C4#1683960911yescharacteristic
607C4C4×#1175819811yescharacteristic
608C4#1683961711yescharacteristic
609C4#1683962411yescharacteristic
610C4#1683963311yescharacteristic
611C4#1683963311yescharacteristic
612C4#1683963611yescharacteristic
613C4#1683963611yescharacteristic
614C2—21no—
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—21no—
621C2—2444no—
622C2#2144404011yescharacteristic
subgroupG/H
centerC4#16839617
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1733C2
socleC2×C61C22⋊#95
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#1733D61
hypocenterC61#10766
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. #21445530C2semidirect
5. #21445529C2semidirect
6. #21445528C2semidirect
7. C61×#1733C2semidirect
16. C2×M16×D61C4semidirect
21. #16839735C4semidirect
22. #16839735C4semidirect
309. #1733D61semidirect
343. C61#10766semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
C2×#168397352
#214455302
#214455292
#214455282
C61×#17332
#1076661