Finite Group Databasebeta

← #29587060

Subgroups — #29587060

Order 15616.

870 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839778C211yesmaximal, characteristic
2#21454336C211yesmaximal, characteristic
3C2×#16839730C211yesmaximal, characteristic
4C2×#16839533C211yesmaximal, characteristic, complemented
5C2×#16839526C211yesmaximal, characteristic, complemented
6#21445535C211yesmaximal, characteristic, complemented
7C61×#2905C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C23×#92418C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839778—22no—
13#16839778—22no—
14C2×#14519703—22no—
15#16839770C412yescomplemented
16#16839766C412yescomplemented
17#16839761—22no—
18#16839756—22no—
19#16839730—22no—
20#16839730—22no—
21C2×#14519689—22no—
22#16839533—22no—
23#16839526—22no—
24#16839524—22no—
25C22×M16×C61C2211yescharacteristic
26C22×M16×C61C2211yescharacteristic
27C2×#117×C61C2211yescharacteristic
28C61×#424—22no—
29C61×#424—22no—
30C61×#423—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×#11758222D412yes—
42C2×#11758222Q812yes—
43C22×Dic122C2×C411yescharacteristic
44C22×D244C2×C411yescharacteristic
45C22×C22⋊D61—21no—
46C22×C4×D61—21no—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194C2×C412yes—
53C22×#92418—21no—
54C22×#92418—21no—
55C22×#92418—21no—
56C22×#92418—21no—
57C22×#92418—21no—
58C22×#92418—21no—
59C22×#92418—21no—
60C22×#92418D412yes—
61#14519736—21no—
62#14519736—21no—
63#14519736—21no—
64#14519736D412yes—
65C2×C4⋊Dic61—21no—
66C2×C22⋊Dic61—21no—
67C2×C4×Dic61—21no—
68#14519703—28no—
69#14519700—24no—
70#14519697—24no—
71#14519689—28no—
72C23×C4×C61C2311yescharacteristic
73C2×M16×C61—21no—
74C2×M16×C61—21no—
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×C61—21no—
84C2×M16×C61D412yes—
85C22×C8×C61—21no—
86C22×C8×C61D412yes—
87#117×C61—21no—
88#117×C61—21no—
89#117×C61C2×C412yes—
90#117×C61D412yes—
91C2×C4⋊C4×C61D412yes—
92C2×C22⋊C4×C61—21no—
93C2×C42×C61—21no—
94C4⋊C8×C61—28no—
95C24×C61#4111yescharacteristic
96C23×D61—21no—
97C22×C4×C61—22no—
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×Q811yescharacteristic
107C22×C4×C61#4111yescharacteristic
108C22×C4×C61#4111yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C2×C22⋊D61—22no—
113C2×C22⋊D61—22no—
114C2×C22⋊D61—41no—
115C2×C22⋊D61—41no—
116C2×C22⋊D61—41no—
117C2×C22⋊D61—41no—
118C22×Dic61—21no—
119C22×Dic61—41no—
120#11758222—22no—
121#11758222—22no—
122#11758222—22no—
123#11758222—22no—
124#11758222—22no—
125#11758222—22no—
126#11758222—22no—
127#11758222—22no—
128#11758222—41no—
129#11758222—41no—
130#11758222—41no—
131#11758222—41no—
132#11758222—41no—
133#11758222—41no—
134#11758222—41no—
135#11758222—41no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244—21no—
141C2×D244C4⋊C412yes—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—41no—
145C2×C4×D61—41no—
146C2×C4×D61—41no—
147C2×C4×D61—41no—
148C2×Dic122—21no—
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122C4⋊C412yes—
154M16×C61—22no—
155M16×C61—22no—
156M16×C61—41no—
157M16×C61—41no—
158M16×C61—41no—
159M16×C61—41no—
160M16×C61—41no—
161M16×C61—41no—
162C2×C8×C61—22no—
163C2×C8×C61—22no—
164C2×C8×C61—22no—
165C2×C8×C61—22no—
166C2×C8×C61—41no—
167C2×C8×C61—41no—
168C4⋊C4×C61—22no—
169C4⋊C4×C61C22⋊C414yes—
170C22⋊C4×C61—22no—
171C22⋊C4×C61—22no—
172C42×C61—22no—
173C42×C61—22no—
174C22⋊Dic61—22no—
175C22⋊Dic61—41no—
176C4⋊Dic61—22no—
177C4⋊Dic61—41no—
178C4×Dic61—22no—
179C4×Dic61—41no—
180#11758194—22no—
181#11758194—22no—
182#11758194—41no—
183#11758194—41no—
184C2×#92418—22no—
185C2×#92418—22no—
186C2×#92418—22no—
187C2×#92418—22no—
188C2×#92418—41no—
189C2×#92418—41no—
190C2×#92418—41no—
191C2×#92418—41no—
192C2×#92418—41no—
193C2×#92418—41no—
194C23×C61—42no—
195C23×C61C4×D411yescharacteristic
196C23×C61#12111yescharacteristic
197C23×C61C22⋊Q811yescharacteristic
198C23×C61#12311yescharacteristic
199C23×C61#12311yescharacteristic
200C23×C61#12311yescharacteristic
201C23×C61#12611yescharacteristic
202C22×D61—22no—
203C22×D61—44no—
204C22×D61—41no—
205C22×D61—41no—
206C2×C4×C61—24no—
207C2×C4×C61—82no—
208C2×C4×C61C2×C22⋊C411yescharacteristic
209C2×C4×C61C2×C4⋊C411yescharacteristic
210C2×C4×C61#11711yescharacteristic
211C2×C4×C61C4×D411yescharacteristic
212C2×C4×C61C4×D411yescharacteristic
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61#12011yescharacteristic
215C2×C4×C61#12011yescharacteristic
216C2×C4×C61#12011yescharacteristic
217C2×C4×C61#12111yescharacteristic
218C2×C4×C61#12111yescharacteristic
219C2×C4×C61#12111yescharacteristic
220C2×C4×C61#12111yescharacteristic
221C2×C4×C61#12111yescharacteristic
222C2×C4×C61#12111yescharacteristic
223C2×C4×C61#12111yescharacteristic
224C2×C4×C61C22⋊Q811yescharacteristic
225C2×C4×C61C22⋊Q811yescharacteristic
226C2×C4×C61C22⋊Q811yescharacteristic
227C2×C4×C61C22⋊Q811yescharacteristic
228C2×C4×C61C22⋊Q811yescharacteristic
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#12711yescharacteristic
236C22⋊D61—42no—
237C22⋊D61—42no—
238C22⋊D61—42no—
239C22⋊D61—42no—
240C2×Dic61—22no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—42no—
244C2×Dic61—82no—
245D244—22no—
246D244—22no—
247D244—41no—
248D244—41no—
249C4×D61—42no—
250C4×D61—42no—
251C4×D61—42no—
252C4×D61—42no—
253Dic122—22no—
254Dic122—22no—
255Dic122—41no—
256Dic122—41no—
257C8×C61—42no—
258C8×C61—42no—
259#92418—42no—
260#92418—42no—
261#11065—611nomaximal, Sylow
262C22×C61—22no—
263C22×C61—22no—
264C22×C61—22no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61#38511yescharacteristic
270C22×C61#38611yescharacteristic
271C22×C61#38811yescharacteristic
272C22×C61#39411yescharacteristic
273C22×C61#39611yescharacteristic
274C22×C61#39711yescharacteristic
275C22×C61#39911yescharacteristic
276C2×D61—44no—
277C2×D61—42no—
278C2×D61—82no—
279C2×D61—82no—
280C4×C61—44no—
281C4×C61#38011yescharacteristic
282C4×C61#38511yescharacteristic
283C4×C61#38811yescharacteristic
284C4×C61#39011yescharacteristic
285C4×C61#39211yescharacteristic
286C4×C61#39311yescharacteristic
287C4×C61#39411yescharacteristic
288C4×C61#39611yescharacteristic
289Dic61—42no—
290Dic61—82no—
291#2905D6111yescharacteristic, complemented
292C2×#421—611no—
293#2896—611no—
294C2×#408—611no—
295C2×#344—611no—
296C2×#341—611no—
297#1735—611no—
298C2×C61—21no—
299C2×C61—21no—
300C2×C61—21no—
301C2×C61—21no—
302C2×C61—21no—
303C2×C61—21no—
304C2×C61#143911yescharacteristic
305C2×C61#188112yes—
306D61—82no—
307C22×#41—611no—
308C22×M16—611no—
309C22×M16C2×D6111yescharacteristic
310C22×M16C2×D6111yescharacteristic
311C23×C8—611no—
312C2×#117—611no—
313C2×#117C2×D6111yescharacteristic
314#424—22no—
315#424—22no—
316#423—22no—
317#421—1222no—
318#421—1222no—
319C2×#104—1222no—
320#419—612no—
321#418—612no—
322#417—1222no—
323#416—1222no—
324#408—1222no—
325#408—1222no—
326C2×C22⋊C8—1222no—
327#344—1222no—
328#341—1222no—
329#340—1222no—
330C61#1106511yescharacteristic, complemented, Sylow
331C2×#41—612no—
332C2×#41—612no—
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—
343C22×Q8—611no—
344C22×D4—611no—
345C22×D4—1221no—
346C23×C4—1221no—
347C23×C4C22×D6111yescharacteristic
348C2×M16—21no—
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—21no—
358C2×M16—21no—
359C2×M16—612no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16—1221no—
363C2×M16—1221no—
364C2×M16—1221no—
365C2×M16C22⋊D6112yes—
366C22×C8—21no—
367C22×C8—612no—
368C22×C8—1221no—
369C22×C8—1221no—
370C22×C8—1221no—
371C22×C8—1221no—
372C22×C8—1221no—
373C22×C8—1221no—
374C22×C8—1221no—
375C22×C8C22⋊D6112yes—
376#117—21no—
377#117—21no—
378#117—612no—
379#117—1221no—
380#117—1221no—
381#117—1221no—
382#117C4×D6112yes—
383#117C22⋊D6112yes—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4D24412yes—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—1221no—
388C2×C42—21no—
389C2×C42—1221no—
390C4⋊C8—28no—
391#104—1228no—
392#103—1224no—
393#102—1224no—
394C22⋊C8—1228no—
395C24—1221no—
396C24#1175822211yescharacteristic
397#41—1222no—
398#41—1222no—
399#41—1222no—
400#41—1222no—
401#41—1222no—
402#41—1222no—
403#41—1222no—
404#41—1222no—
405#41—2441no—
406#41—2441no—
407#41—2441no—
408#41—2441no—
409#41—2441no—
410#41—2441no—
411#41—2441no—
412#41—2441no—
413C2×Q8—612no—
414C2×Q8—1221no—
415C2×Q8—1221no—
416C2×Q8—1221no—
417C2×Q8—1221no—
418C2×Q8—1221no—
419C2×D4—612no—
420C2×D4—1222no—
421C2×D4—1222no—
422C2×D4—1221no—
423C2×D4—1221no—
424C2×D4—1221no—
425C2×D4—1221no—
426C2×D4—1221no—
427C2×D4—2441no—
428C2×D4—2441no—
429C2×D4—2441no—
430C2×D4—2441no—
431C22×C4—22no—
432C22×C4—1221no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—2441no—
436C22×C4—2441no—
437C22×C4—2441no—
438C22×C4—2441no—
439C22×C4—2441no—
440C22×C4C2×C4×D6111yescharacteristic
441C22×C4C2×D24411yescharacteristic
442C22×C4#1175822211yescharacteristic
443C22×C4D4×D6111yescharacteristic
444C22×C4D4×D6111yescharacteristic
445C22×C4D4×D6111yescharacteristic
446C22×C4#1175822411yescharacteristic
447C22×C4Q8×D6111yescharacteristic
448C22×C4#1175822611yescharacteristic
449C22×C4#1175822611yescharacteristic
450C22×C4#1175822611yescharacteristic
451C22×C4C2×C22⋊D6111yescharacteristic
452C22×C4C2×C22⋊D6111yescharacteristic
453C22×C4C2×C22⋊D6111yescharacteristic
454M16—22no—
455M16—22no—
456M16—41no—
457M16—41no—
458M16—41no—
459M16—41no—
460M16—41no—
461M16—41no—
462M16—1222no—
463M16—1222no—
464M16—2441no—
465M16—2441no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—1222no—
473C2×C8—1222no—
474C2×C8—1222no—
475C2×C8—1222no—
476C2×C8—2441no—
477C2×C8—2441no—
478C2×C8—2441no—
479C2×C8—2441no—
480C2×C8—2441no—
481C2×C8—2441no—
482C4⋊C4—22no—
483C4⋊C4—1222no—
484C4⋊C4—2441no—
485C4⋊C4#1175819814yes—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—1222no—
489C22⋊C4—2441no—
490C42—22no—
491C42—22no—
492C42—1222no—
493C42—2441no—
494C23—42no—
495C23—1222no—
496C23—2444no—
497C23—2441no—
498C23—2441no—
499C23C4×C22⋊D6111yescharacteristic
500C23#1451975111yescharacteristic
501C23#1451975511yescharacteristic
502C23#1451976011yescharacteristic
503C23#1451976211yescharacteristic
504C23#1451976211yescharacteristic
505C23#1451977211yescharacteristic
506Q8—1222no—
507Q8—1222no—
508Q8—2441no—
509Q8—2441no—
510D4—1222no—
511D4—1222no—
512D4—2442no—
513D4—2442no—
514D4—2442no—
515D4—2442no—
516D4—2441no—
517D4—2441no—
518C2×C4—24no—
519C2×C4—82no—
520C2×C4—1222no—
521C2×C4—4882no—
522C2×C4—2442no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2442no—
526C2×C4—2442no—
527C2×C4—2442no—
528C2×C4—2442no—
529C2×C4C2×#1175819811yescharacteristic
530C2×C4C4⋊C4×D6111yescharacteristic
531C2×C4#1451973511yescharacteristic
532C2×C4C4×C22⋊D6111yescharacteristic
533C2×C4#1451973911yescharacteristic
534C2×C4#1451973911yescharacteristic
535C2×C4#1451974511yescharacteristic
536C2×C4#1451974511yescharacteristic
537C2×C4#1451974611yescharacteristic
538C2×C4#1451974811yescharacteristic
539C2×C4#1451974911yescharacteristic
540C2×C4#1451974911yescharacteristic
541C2×C4#1451975111yescharacteristic
542C2×C4#1451975211yescharacteristic
543C2×C4#1451975211yescharacteristic
544C2×C4#1451975211yescharacteristic
545C2×C4#1451975311yescharacteristic
546C2×C4#1451975311yescharacteristic
547C2×C4#1451975311yescharacteristic
548C2×C4#1451975511yescharacteristic
549C2×C4#1451975711yescharacteristic
550C2×C4#1451976211yescharacteristic
551C2×C4#1451976211yescharacteristic
552C2×C4#1451976611yescharacteristic
553C2×C4#1451976611yescharacteristic
554C2×C4#1451976611yescharacteristic
555C2×C4#1451977211yescharacteristic
556C2×C4#1451977311yescharacteristic
557C8—42no—
558C8—42no—
559C8—2442no—
560C8—2442no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—4882no—
569C22—4882no—
570C22—2444no—
571C22—2442no—
572C22#1683963311yescharacteristic
573C22#1683964111yescharacteristic
574C22#1683965211yescharacteristic
575C22#1683967911yescharacteristic
576C22#1683968411yescharacteristic
577C22#1683968811yescharacteristic
578C22#1683969711yescharacteristic
579C4—44no—
580C4—4882no—
581C4—2442no—
582C4#1683961911yescharacteristic
583C4#1683963311yescharacteristic
584C4#1683965211yescharacteristic
585C4#1683966311yescharacteristic
586C4#1683967011yescharacteristic
587C4#1683967311yescharacteristic
588C4#1683967911yescharacteristic
589C4#1683968411yescharacteristic
590C2—21no—
591C2—21no—
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—4882no—
597C2#2144406111yescharacteristic
598C2#2144618112yes—
subgroupG/H
centerC2×C4#14519746
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2905C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#2905D61
hypocenterC61#11065
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2905

Complements

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

NH ≅ G/Ntype
4. C2×#16839533C2semidirect
5. C2×#16839526C2semidirect
6. #21445535C2semidirect
7. C61×#2905C2semidirect
15. #16839770C4semidirect
16. #16839766C4semidirect
291. #2905D61semidirect
330. C61#11065semidirect

Maximal subgroups

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

subgroupindex
C2×#168397782
#214543362
C2×#168397302
C2×#168395332
C2×#168395262
#214455352
C61×#29052
#1106561