Finite Group Databasebeta

← #29587356

Subgroups — #29587356

Order 15616.

864 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839780C211yesmaximal, characteristic
2C2×#16839778C211yesmaximal, characteristic
3C2×#16839735C211yesmaximal, characteristic
4#21445557C211yesmaximal, characteristic, complemented
5#21445551C211yesmaximal, characteristic, complemented
6C2×#16839518C211yesmaximal, characteristic, complemented
7C61×#2911C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C2×#14519736C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839780—22no—
13#16839780—22no—
14#16839778—22no—
15#16839778—22no—
16C2×#14519705—22no—
17C2×#14519703C414yescomplemented
18#16839735—22no—
19#16839735—22no—
20C2×#14519691—22no—
21#16839530—22no—
22#16839528—22no—
23#16839518—22no—
24C22×M16×C61C2211yescharacteristic
25C2×#117×C61C2211yescharacteristic
26C2×#117×C61C2211yescharacteristic
27C61×#428—22no—
28C61×#428—22no—
29C61×#427—22no—
30C2×#11758222—21no—
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×#11758222C2×C412yes—
41C2×#11758222D412yes—
42C22×Dic122Q811yescharacteristic
43C22×D244Q811yescharacteristic
44C22×C22⋊D61—21no—
45C22×C4×D61—21no—
46C2×#11758194—21no—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194D412yes—
52C22×#92418—21no—
53#14519736—21no—
54#14519736—21no—
55#14519736—21no—
56#14519736—21no—
57#14519736—21no—
58#14519736—21no—
59#14519736—21no—
60#14519736—21no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—21no—
63C2×C22⋊Dic61—21no—
64C2×C22⋊Dic61D412yes—
65C2×C4×Dic61—21no—
66C2×C4×Dic61C2×C412yes—
67#14519705—28no—
68#14519703—28no—
69#14519691—28no—
70C23×C4×C61C2311yescharacteristic
71C2×M16×C61—21no—
72C2×M16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61C2×C412yes—
75C2×M16×C61D412yes—
76C2×M16×C61D412yes—
77C22×C8×C61—21no—
78#117×C61—21no—
79#117×C61—21no—
80#117×C61—21no—
81#117×C61—21no—
82#117×C61—21no—
83#117×C61—21no—
84#117×C61D412yes—
85#117×C61D412yes—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C22⋊C4×C61—21no—
89C2×C22⋊C4×C61—21no—
90C2×C42×C61—21no—
91C2×C42×C61—21no—
92#107×C61—24no—
93#106×C61—24no—
94C24×C61C2×D411yescharacteristic
95C23×D61—21no—
96C22×C4×C61—41no—
97C22×C4×C61—41no—
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×Q811yescharacteristic
106C22×C4×C61#4111yescharacteristic
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—22no—
120C22×Dic61—22no—
121#11758222—22no—
122#11758222—22no—
123#11758222—22no—
124#11758222—22no—
125#11758222—22no—
126#11758222—22no—
127#11758222—22no—
128#11758222—22no—
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×D244C4⋊C412yes—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—41no—
146C2×C4×D61—41no—
147C2×C4×D61—41no—
148C2×C4×D61—41no—
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122C4⋊C412yes—
155M16×C61—22no—
156M16×C61—22no—
157M16×C61—22no—
158M16×C61C22⋊C414yes—
159C2×C8×C61—22no—
160C2×C8×C61—22no—
161C2×C8×C61—22no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61—41no—
165C4⋊C4×C61—41no—
166C22⋊C4×C61—22no—
167C22⋊C4×C61—22no—
168C22⋊C4×C61—41no—
169C22⋊C4×C61—41no—
170C42×C61—22no—
171C42×C61—22no—
172C42×C61—41no—
173C42×C61—41no—
174C22⋊Dic61—22no—
175C22⋊Dic61—22no—
176C22⋊Dic61—41no—
177C22⋊Dic61—41no—
178C4⋊Dic61—41no—
179C4⋊Dic61—41no—
180C4⋊Dic61—41no—
181C4⋊Dic61—41no—
182C4×Dic61—22no—
183C4×Dic61—22no—
184C4×Dic61—41no—
185C4×Dic61—41no—
186#11758194—22no—
187#11758194—22no—
188#11758194—41no—
189#11758194—41no—
190C2×#92418—22no—
191C2×#92418—41no—
192C2×#92418—41no—
193C23×C61—81no—
194C23×C61C4×D411yescharacteristic
195C23×C61#12011yescharacteristic
196C23×C61#12111yescharacteristic
197C23×C61#12111yescharacteristic
198C23×C61C22⋊Q811yescharacteristic
199C23×C61#12311yescharacteristic
200C23×C61#12711yescharacteristic
201C22×D61—22no—
202C22×D61—41no—
203C22×D61—41no—
204C22×D61—82no—
205C2×C4×C61—42no—
206C2×C4×C61—42no—
207C2×C4×C61—82no—
208C2×C4×C61—82no—
209C2×C4×C61C2×C22⋊C411yescharacteristic
210C2×C4×C61C2×C4⋊C411yescharacteristic
211C2×C4×C61#11711yescharacteristic
212C2×C4×C61C4×D411yescharacteristic
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
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×C61C22⋊Q811yescharacteristic
224C2×C4×C61C22⋊Q811yescharacteristic
225C2×C4×C61C22⋊Q811yescharacteristic
226C2×C4×C61C22⋊Q811yescharacteristic
227C2×C4×C61C22⋊Q811yescharacteristic
228C2×C4×C61#12311yescharacteristic
229C2×C4×C61#12311yescharacteristic
230C2×C4×C61#12311yescharacteristic
231C2×C4×C61#12311yescharacteristic
232C2×C4×C61#12411yescharacteristic
233C2×C4×C61#12411yescharacteristic
234C2×C4×C61#12411yescharacteristic
235C2×C4×C61#12611yescharacteristic
236C2×C4×C61#12611yescharacteristic
237C22⋊D61—42no—
238C22⋊D61—42no—
239C22⋊D61—42no—
240C22⋊D61—42no—
241C2×Dic61—22no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—82no—
247C2×Dic61—82no—
248D244—22no—
249D244—22no—
250D244—41no—
251D244—41no—
252C4×D61—42no—
253C4×D61—42no—
254C4×D61—42no—
255C4×D61—42no—
256Dic122—22no—
257Dic122—22no—
258Dic122—41no—
259Dic122—41no—
260C8×C61—24no—
261#92418—42no—
262#11115—611nomaximal, Sylow
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—41no—
269C22×C61—41no—
270C22×C61#38511yescharacteristic
271C22×C61#38811yescharacteristic
272C22×C61#39011yescharacteristic
273C22×C61#39211yescharacteristic
274C22×C61#39411yescharacteristic
275C22×C61#39611yescharacteristic
276C22×C61#39911yescharacteristic
277C2×D61—42no—
278C2×D61—82no—
279C2×D61—82no—
280C2×D61—82no—
281C4×C61—82no—
282C4×C61—82no—
283C4×C61#38011yescharacteristic
284C4×C61#38511yescharacteristic
285C4×C61#38611yescharacteristic
286C4×C61#38811yescharacteristic
287C4×C61#39311yescharacteristic
288C4×C61#39411yescharacteristic
289C4×C61#39611yescharacteristic
290C4×C61#39711yescharacteristic
291Dic61—42no—
292Dic61—82no—
293Dic61—82no—
294#2911D6111yescharacteristic, complemented
295C2×#421—611no—
296C2×#421—611no—
297C2×#410—611no—
298#1742—611no—
299#1740—611no—
300C2×H(3,ℤ/4)—611no—
301C2×C61—21no—
302C2×C61—21no—
303C2×C61—21no—
304C2×C61—21no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61#143911yescharacteristic
309D61—82no—
310C22×#41—611no—
311C22×M16—611no—
312C22×M16C2×D6111yescharacteristic
313C2×#117—611no—
314C2×#117—611no—
315C2×#117C2×D6111yescharacteristic
316C2×#117C2×D6111yescharacteristic
317#428—22no—
318#428—22no—
319#427—22no—
320#421—1222no—
321#421—1222no—
322#421—1222no—
323#421—1222no—
324C2×#104—614no—
325C2×#104—1222no—
326#410—1222no—
327#410—1222no—
328C2×#99—1222no—
329#343—1222no—
330#342—1222no—
331H(3,ℤ/4)—1222no—
332C61#1111511yescharacteristic, complemented, Sylow
333C2×#41—612no—
334C2×#41—612no—
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—
344C2×#41—1221no—
345C22×Q8—611no—
346C22×D4—611no—
347C22×D4—1221no—
348C23×C4—1221no—
349C23×C4C22×D6111yescharacteristic
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—612no—
354C2×M16—1221no—
355C2×M16—1221no—
356C2×M16—1221no—
357C2×M16—1221no—
358C2×M16—1221no—
359C2×M16C4×D6112yes—
360C2×M16D24412yes—
361C2×M16C22⋊D6112yes—
362C22×C8—21no—
363C22×C8—1221no—
364#117—21no—
365#117—21no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—1221no—
371#117—1221no—
372#117—1221no—
373#117—1221no—
374#117—1221no—
375#117—1221no—
376#117—1221no—
377#117—1221no—
378#117C22⋊D6112yes—
379#117C22⋊D6112yes—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—612no—
387C2×C22⋊C4—1221no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—612no—
391C2×C42—1221no—
392#107—24no—
393#106—24no—
394#104—1228no—
395#104—1228no—
396#99—1228no—
397C24—1221no—
398C24D4×D6111yescharacteristic
399#41—1222no—
400#41—1222no—
401#41—1222no—
402#41—1222no—
403#41—1222no—
404#41—1222no—
405#41—1222no—
406#41—1222no—
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—612no—
416C2×Q8—1221no—
417C2×Q8—1221no—
418C2×Q8—1221no—
419C2×Q8—1221no—
420C2×Q8—1221no—
421C2×D4—612no—
422C2×D4—1222no—
423C2×D4—1222no—
424C2×D4—1221no—
425C2×D4—1221no—
426C2×D4—1221no—
427C2×D4—1221no—
428C2×D4—1221no—
429C2×D4—2441no—
430C2×D4—2441no—
431C2×D4—2441no—
432C2×D4—2441no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—1221no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—2441no—
441C22×C4—2441no—
442C22×C4—2441no—
443C22×C4—2441no—
444C22×C4C2×C4×D6111yescharacteristic
445C22×C4C2×D24411yescharacteristic
446C22×C4#1175822211yescharacteristic
447C22×C4#1175822211yescharacteristic
448C22×C4D4×D6111yescharacteristic
449C22×C4D4×D6111yescharacteristic
450C22×C4#1175822411yescharacteristic
451C22×C4Q8×D6111yescharacteristic
452C22×C4#1175822611yescharacteristic
453C22×C4#1175822611yescharacteristic
454C22×C4#1175822611yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456C22×C4C2×C22⋊D6111yescharacteristic
457C22×C4C2×C22⋊D6111yescharacteristic
458M16—22no—
459M16—22no—
460M16—22no—
461M16—1222no—
462M16—1222no—
463M16—2441no—
464M16—2441no—
465M16#1175819814yes—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—1222no—
470C2×C8—2441no—
471C2×C8—2441no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—2441no—
477C4⋊C4—2441no—
478C4⋊C4—2441no—
479C4⋊C4—2441no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—1222no—
485C22⋊C4—1222no—
486C22⋊C4—2441no—
487C22⋊C4—2441no—
488C42—22no—
489C42—22no—
490C42—41no—
491C42—41no—
492C42—1222no—
493C42—1222no—
494C42—2441no—
495C42—2441no—
496C23—81no—
497C23—1222no—
498C23—4882no—
499C23—2441no—
500C23—2441no—
501C23#1451973911yescharacteristic
502C23#1451974511yescharacteristic
503C23#1451974911yescharacteristic
504C23#1451975211yescharacteristic
505C23#1451975511yescharacteristic
506C23#1451976211yescharacteristic
507C23#1451977311yescharacteristic
508Q8—1222no—
509Q8—1222no—
510Q8—2441no—
511Q8—2441no—
512D4—1222no—
513D4—1222no—
514D4—2442no—
515D4—2442no—
516D4—2442no—
517D4—2442no—
518D4—2441no—
519D4—2441no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—1222no—
525C2×C4—4882no—
526C2×C4—4882no—
527C2×C4—2442no—
528C2×C4—2442no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2442no—
532C2×C4—2442no—
533C2×C4—2442no—
534C2×C4—2442no—
535C2×C4C2×#1175819811yescharacteristic
536C2×C4C4⋊C4×D6111yescharacteristic
537C2×C4#1451973511yescharacteristic
538C2×C4C4×C22⋊D6111yescharacteristic
539C2×C4C4×C22⋊D6111yescharacteristic
540C2×C4#1451973911yescharacteristic
541C2×C4#1451974511yescharacteristic
542C2×C4#1451974611yescharacteristic
543C2×C4#1451974811yescharacteristic
544C2×C4#1451974911yescharacteristic
545C2×C4#1451975111yescharacteristic
546C2×C4#1451975111yescharacteristic
547C2×C4#1451975211yescharacteristic
548C2×C4#1451975211yescharacteristic
549C2×C4#1451975311yescharacteristic
550C2×C4#1451975311yescharacteristic
551C2×C4#1451975311yescharacteristic
552C2×C4#1451975511yescharacteristic
553C2×C4#1451975711yescharacteristic
554C2×C4#1451976011yescharacteristic
555C2×C4#1451976211yescharacteristic
556C2×C4#1451976211yescharacteristic
557C2×C4#1451976211yescharacteristic
558C2×C4#1451976611yescharacteristic
559C2×C4#1451976611yescharacteristic
560C2×C4#1451976611yescharacteristic
561C2×C4#1451977211yescharacteristic
562C2×C4#1451977211yescharacteristic
563C8—24no—
564C8—2442no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—4882no—
573C22—4882no—
574C22—4882no—
575C22—2442no—
576C22#1683963311yescharacteristic
577C22#1683965211yescharacteristic
578C22#1683966311yescharacteristic
579C22#1683967011yescharacteristic
580C22#1683967911yescharacteristic
581C22#1683968411yescharacteristic
582C22#1683969711yescharacteristic
583C4—82no—
584C4—82no—
585C4—4882no—
586C4—4882no—
587C4—2442no—
588C4#1683961911yescharacteristic
589C4#1683963311yescharacteristic
590C4#1683964111yescharacteristic
591C4#1683965211yescharacteristic
592C4#1683967311yescharacteristic
593C4#1683967911yescharacteristic
594C4#1683968411yescharacteristic
595C4#1683968811yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—21no—
603C2—4882no—
604C2#2144406111yescharacteristic
subgroupG/H
centerC4#16839652
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2911C2
socleC2×C61#1439
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#2911D61
hypocenterC61#11115
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2911

Complements

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

NH ≅ G/Ntype
4. #21445557C2semidirect
5. #21445551C2semidirect
6. C2×#16839518C2semidirect
7. C61×#2911C2semidirect
17. C2×#14519703C4semidirect
294. #2911D61semidirect
332. C61#11115semidirect

Maximal subgroups

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

subgroupindex
C2×#168397802
C2×#168397782
C2×#168397352
#214455572
#214455512
C2×#168395182
C61×#29112
#1111561