Finite Group Databasebeta

← #29586358

Subgroups — #29586358

Order 15616.

904 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839744C211yesmaximal, characteristic
2C2×#16839735C211yesmaximal, characteristic
3#21454263C211yesmaximal, characteristic
4#21454237C211yesmaximal, characteristic, complemented
5C2×#16839534C211yesmaximal, characteristic, complemented
6C2×#16839532C211yesmaximal, characteristic, complemented
7C61×#1742C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839744—22no—
13#16839744—22no—
14C2×#14519695C412yescomplemented
15C2×#14519693C412yescomplemented
16#16839735—22no—
17#16839735—22no—
18C2×#14519691C414yes—
19#16839730—22no—
20#16839728—22no—
21#16839725C414yescomplemented
22#16839720—22no—
23#16839717—22no—
24M16×Dic61—22no—
25#16839534—22no—
26#16839532—22no—
27C22×M16×C61C2211yescharacteristic
28C22×M16×C61C2211yescharacteristic
29C2×#117×C61C2211yescharacteristic
30C61×#343—22no—
31C2×#11758222—21no—
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×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C22×Dic122C2×C411yescharacteristic
44C22×D244C2×C411yescharacteristic
45C22×C22⋊D61C2×C412yes—
46C22×C4×D61C2×C412yes—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194C2×C412yes—
57C2×#11758194C2×C412yes—
58C2×#11758194D412yes—
59C22×#92418—21no—
60C22×#92418D412yes—
61#14519736—21no—
62#14519736—21no—
63#14519736D412yes—
64#14519736D412yes—
65C2×C4⋊Dic61—21no—
66C2×C22⋊Dic61C2×C412yes—
67C2×C4×Dic61—21no—
68#14519695—24no—
69#14519693—24no—
70#14519691—28no—
71#14519689—28no—
72#14519687—24no—
73C8×Dic61—24no—
74C23×C4×C61C2311yescharacteristic
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61C2×C412yes—
84C2×M16×C61C2×C412yes—
85C2×M16×C61D412yes—
86C2×M16×C61D412yes—
87C22×C8×C61—21no—
88C22×C8×C61—21no—
89#117×C61—21no—
90#117×C61—21no—
91#117×C61—21no—
92#117×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C22⋊C4×C61C2×C412yes—
95C2×C42×C61—21no—
96C24×C61C22×C411yescharacteristic
97C23×D61C4212yes—
98C22×C4×C61—22no—
99C22×C4×C61C22×C411yescharacteristic
100C22×C4×C61C22×C411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61#4111yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C2×C22⋊D61—22no—
114C2×C22⋊D61—22no—
115C2×C22⋊D61—22no—
116C2×C22⋊D61—22no—
117C2×C22⋊D61—22no—
118C2×C22⋊D61—22no—
119C22×Dic61—22no—
120C22×Dic61C4212yes—
121#11758222—41no—
122#11758222—41no—
123#11758222—41no—
124#11758222—41no—
125#11758222—41no—
126#11758222—41no—
127#11758222—41no—
128#11758222—41no—
129#11758222—41no—
130#11758222—41no—
131#11758222—41no—
132#11758222—41no—
133#11758222—41no—
134#11758222—41no—
135#11758222—41no—
136#11758222—41no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155M16×C61—22no—
156M16×C61—22no—
157M16×C61—22no—
158M16×C61—22no—
159M16×C61—22no—
160M16×C61—41no—
161M16×C61—41no—
162M16×C61C22⋊C414yes—
163C2×C8×C61—22no—
164C2×C8×C61—22no—
165C2×C8×C61—22no—
166C2×C8×C61—22no—
167C2×C8×C61—41no—
168C2×C8×C61—41no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C22⋊C4×C61—22no—
172C22⋊C4×C61—22no—
173C42×C61—41no—
174C42×C61—41no—
175C22⋊Dic61—22no—
176C22⋊Dic61C22⋊C414yes—
177C4⋊Dic61—22no—
178C4⋊Dic61—22no—
179C4×Dic61—22no—
180C4×Dic61—22no—
181#11758194—22no—
182#11758194—22no—
183#11758194—22no—
184#11758194—22no—
185#11758194—22no—
186#11758194—22no—
187#11758194—41no—
188#11758194—41no—
189C2×#92418—22no—
190C2×#92418—22no—
191C2×#92418—22no—
192C2×#92418—41no—
193C2×#92418—41no—
194C2×#92418C22⋊C414yes—
195C23×C61—81no—
196C23×C61C2×C4211yescharacteristic
197C23×C61C2×C22⋊C411yescharacteristic
198C23×C61#11711yescharacteristic
199C23×C61C4×D411yescharacteristic
200C23×C61C4×D411yescharacteristic
201C23×C61C4×D411yescharacteristic
202C23×C61C4×D411yescharacteristic
203C22×D61—22no—
204C22×D61—22no—
205C22×D61—22no—
206C22×D61—82no—
207C2×C4×C61—42no—
208C2×C4×C61—82no—
209C2×C4×C61C2×C22⋊C411yescharacteristic
210C2×C4×C61C2×C22⋊C411yescharacteristic
211C2×C4×C61#11711yescharacteristic
212C2×C4×C61#11711yescharacteristic
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C4×D411yescharacteristic
217C2×C4×C61C4×D411yescharacteristic
218C2×C4×C61C4×D411yescharacteristic
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61#12011yescharacteristic
222C2×C4×C61#12111yescharacteristic
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61#12311yescharacteristic
229C2×C4×C61#12311yescharacteristic
230C2×C4×C61#12311yescharacteristic
231C2×C4×C61#12411yescharacteristic
232C2×C4×C61#12411yescharacteristic
233C2×C4×C61#12411yescharacteristic
234C2×C4×C61#12611yescharacteristic
235C2×C4×C61#12611yescharacteristic
236C2×C4×C61#12711yescharacteristic
237C22⋊D61—42no—
238C22⋊D61—42no—
239C22⋊D61—42no—
240C22⋊D61—42no—
241C2×Dic61—22no—
242C2×Dic61—22no—
243C2×Dic61—22no—
244C2×Dic61—24no—
245C2×Dic61—82no—
246D244—41no—
247D244—41no—
248D244—41no—
249D244—41no—
250C4×D61—42no—
251C4×D61—42no—
252C4×D61—42no—
253C4×D61—42no—
254Dic122—41no—
255Dic122—41no—
256Dic122—41no—
257Dic122—41no—
258C8×C61—24no—
259C8×C61—42no—
260#92418—24no—
261#92418—42no—
262#10941—611nomaximal, Sylow
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61C4×C22⋊C411yescharacteristic
271C22×C61C4×C22⋊C411yescharacteristic
272C22×C61C4×C22⋊C411yescharacteristic
273C22×C61#38611yescharacteristic
274C22×C61#38811yescharacteristic
275C22×C61#38811yescharacteristic
276C22×C61#39011yescharacteristic
277C2×D61—44no—
278C2×D61—42no—
279C2×D61—82no—
280C2×D61—82no—
281C4×C61—82no—
282C4×C61#38611yescharacteristic
283C4×C61#38611yescharacteristic
284C4×C61#38811yescharacteristic
285C4×C61#38811yescharacteristic
286C4×C61#38811yescharacteristic
287C4×C61#38811yescharacteristic
288C4×C61#39011yescharacteristic
289C4×C61#39011yescharacteristic
290Dic61—44no—
291Dic61—42no—
292C2×#413—611no—
293C2×#410—611no—
294#2879—611no—
295#2873—611no—
296C2×#344—611no—
297C2×#344—611no—
298#1742D6111yescharacteristic, complemented
299C2×C61—21no—
300C2×C61—21no—
301C2×C61—21no—
302C2×C61—21no—
303C2×C61—21no—
304C2×C61—21no—
305C2×C61—21no—
306C2×C61#143711yescharacteristic
307D61—82no—
308C22×#41—611no—
309C22×M16—611no—
310C22×M16—611no—
311C22×M16C2×D6111yescharacteristic
312C22×M16C2×D6111yescharacteristic
313C2×#117—611no—
314C2×#117C2×D6111yescharacteristic
315#413—1222no—
316#413—1222no—
317C2×#101—612no—
318C2×#100—612no—
319#410—1222no—
320#410—1222no—
321C2×#99—614no—
322#408—1222no—
323#408—1222no—
324#407—614no—
325#405—1222no—
326#405—1222no—
327C4×M16—1222no—
328#344—1222no—
329#344—1222no—
330#343—22no—
331C61#1094111yescharacteristic, complemented, Sylow
332C2×#41—1221no—
333C2×#41—1221no—
334C2×#41—1221no—
335C2×#41—1221no—
336C2×#41—1221no—
337C2×#41—1221no—
338C2×#41—1221no—
339C2×#41—1221no—
340C2×#41—1221no—
341C2×#41—1221no—
342C2×#41—1221no—
343C2×#41—1221no—
344C22×Q8—611no—
345C22×D4—612no—
346C22×D4—611no—
347C23×C4—612no—
348C23×C4C22×D6111yescharacteristic
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—612no—
358C2×M16—612no—
359C2×M16—612no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16—1221no—
363C2×M16—1221no—
364C2×M16—1221no—
365C2×M16—1221no—
366C2×M16—1221no—
367C2×M16—1221no—
368C2×M16—1221no—
369C2×M16C4×D6112yes—
370C2×M16C4×D6112yes—
371C2×M16D24412yes—
372C2×M16C22⋊D6112yes—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—612no—
376C22×C8—1221no—
377#117—21no—
378#117—21no—
379#117—21no—
380#117—21no—
381#117—612no—
382#117—612no—
383#117—1221no—
384#117—1221no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—1221no—
387C2×C22⋊C4—612no—
388C2×C22⋊C4C4×D6112yes—
389C2×C42—21no—
390C2×C42—1221no—
391#101—1224no—
392#100—1224no—
393#99—1228no—
394C22⋊C8—1228no—
395#97—1224no—
396C4×C8—1224no—
397C24—612no—
398C24C2×C4×D6111yescharacteristic
399#41—2441no—
400#41—2441no—
401#41—2441no—
402#41—2441no—
403#41—2441no—
404#41—2441no—
405#41—2441no—
406#41—2441no—
407#41—2441no—
408#41—2441no—
409#41—2441no—
410#41—2441no—
411#41—2441no—
412#41—2441no—
413#41—2441no—
414#41—2441no—
415C2×Q8—1221no—
416C2×Q8—1221no—
417C2×Q8—1221no—
418C2×Q8—1221no—
419C2×Q8—1221no—
420C2×Q8—1221no—
421C2×D4—1222no—
422C2×D4—1222no—
423C2×D4—1222no—
424C2×D4—1222no—
425C2×D4—1222no—
426C2×D4—1222no—
427C2×D4—1221no—
428C2×D4—1221no—
429C2×D4—1221no—
430C2×D4—1221no—
431C2×D4—1221no—
432C2×D4—1221no—
433C22×C4—22no—
434C22×C4—612no—
435C22×C4—1222no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4C2×C4×D6111yescharacteristic
443C22×C4C2×C4×D6111yescharacteristic
444C22×C4C2×D24411yescharacteristic
445C22×C4#1175822211yescharacteristic
446C22×C4#1175822211yescharacteristic
447C22×C4D4×D6111yescharacteristic
448C22×C4D4×D6111yescharacteristic
449C22×C4D4×D6111yescharacteristic
450C22×C4D4×D6111yescharacteristic
451C22×C4#1175822411yescharacteristic
452C22×C4#1175822411yescharacteristic
453C22×C4#1175822611yescharacteristic
454C22×C4#1175822611yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—41no—
462M16—41no—
463M16—1222no—
464M16—1222no—
465M16—1222no—
466M16—1222no—
467M16—1222no—
468M16—1222no—
469M16—2441no—
470M16—2441no—
471M16#1175819814yes—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—614no—
479C2×C8—1222no—
480C2×C8—1222no—
481C2×C8—1222no—
482C2×C8—2441no—
483C2×C8—2441no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—614no—
491C22⋊C4—1222no—
492C42—41no—
493C42—41no—
494C42—1222no—
495C42—1222no—
496C23—81no—
497C23—1222no—
498C23—1222no—
499C23—1222no—
500C23—4882no—
501C23C42×D6111yescharacteristic
502C23C22⋊C4×D6111yescharacteristic
503C23#1451973511yescharacteristic
504C23#1451973711yescharacteristic
505C23C4×C22⋊D6111yescharacteristic
506C23#1451973911yescharacteristic
507C23C4×D24411yescharacteristic
508Q8—2441no—
509Q8—2441no—
510Q8—2441no—
511Q8—2441no—
512D4—2442no—
513D4—2442no—
514D4—2442no—
515D4—2442no—
516D4—2441no—
517D4—2441no—
518D4—2441no—
519D4—2441no—
520C2×C4—42no—
521C2×C4—82no—
522C2×C4—1222no—
523C2×C4—1222no—
524C2×C4—1222no—
525C2×C4—1224no—
526C2×C4—4882no—
527C2×C4—2442no—
528C2×C4—2442no—
529C2×C4—2442no—
530C2×C4—2442no—
531C2×C4C22⋊C4×D6111yescharacteristic
532C2×C4C2×#1175819811yescharacteristic
533C2×C4#1451973411yescharacteristic
534C2×C4#1451973511yescharacteristic
535C2×C4#1451973711yescharacteristic
536C2×C4#1451973711yescharacteristic
537C2×C4#1451973711yescharacteristic
538C2×C4C4×C22⋊D6111yescharacteristic
539C2×C4#1451973911yescharacteristic
540C2×C4#1451973911yescharacteristic
541C2×C4#1451973911yescharacteristic
542C2×C4C4×D24411yescharacteristic
543C2×C4#1451974711yescharacteristic
544C2×C4#1451974911yescharacteristic
545C2×C4#1451974911yescharacteristic
546C2×C4#1451975011yescharacteristic
547C2×C4#1451975011yescharacteristic
548C2×C4#1451975211yescharacteristic
549C2×C4#1451975211yescharacteristic
550C2×C4#1451976111yescharacteristic
551C2×C4#1451976211yescharacteristic
552C2×C4#1451976211yescharacteristic
553C2×C4#1451976311yescharacteristic
554C2×C4#1451976311yescharacteristic
555C2×C4#1451976611yescharacteristic
556C2×C4#1451977211yescharacteristic
557C2×C4#1451977211yescharacteristic
558C2×C4#1451977311yescharacteristic
559C8—24no—
560C8—42no—
561C8—1224no—
562C8—2442no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—4882no—
571C22—4882no—
572C22—2444no—
573C22—2442no—
574C22#1683960911yescharacteristic
575C22#1683960911yescharacteristic
576C22C4×#1175819811yescharacteristic
577C22#1683964011yescharacteristic
578C22#1683965211yescharacteristic
579C22#1683965411yescharacteristic
580C22#1683966211yescharacteristic
581C4—82no—
582C4—2444no—
583C4—2442no—
584C4#1683963911yescharacteristic
585C4#1683964011yescharacteristic
586C4#1683965111yescharacteristic
587C4#1683965111yescharacteristic
588C4#1683965211yescharacteristic
589C4#1683965411yescharacteristic
590C4#1683966211yescharacteristic
591C4#1683966311yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—4882no—
600C2#2144405511yescharacteristic
subgroupG/H
centerC4#16839640
commutatorC23×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1742C2
socleC2×C61#1437
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#1742D61
hypocenterC61#10941
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1742

Complements

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

NH ≅ G/Ntype
4. #21454237C2semidirect
5. C2×#16839534C2semidirect
6. C2×#16839532C2semidirect
7. C61×#1742C2semidirect
14. C2×#14519695C4semidirect
15. C2×#14519693C4semidirect
21. #16839725C4semidirect
298. #1742D61semidirect
331. C61#10941semidirect

Maximal subgroups

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

subgroupindex
C2×#168397442
C2×#168397352
#214542632
#214542372
C2×#168395342
C2×#168395322
C61×#17422
#1094161