Finite Group Databasebeta

← #29689587

Subgroups — #29689587

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459224C211yesmaximal, characteristic
2#21454454C211yesmaximal, characteristic
3#21448315C211yesmaximal, characteristic
4#21446798C212yesmaximal, complemented
5#21446794C212yesmaximal, complemented
6#21446761C212yesmaximal, complemented
7#21446761C212yesmaximal, complemented
8#21445919C211yesmaximal, characteristic
9#21445918C211yesmaximal, characteristic
10#21445916C211yesmaximal, characteristic
11C61×#1826C211yesmaximal, characteristic
12#16840393C412yescomplemented
13#16840393C412yescomplemented
14#16840390—21no—
15#16840390—21no—
16#16840390C412yescomplemented
17#16840390C412yescomplemented
18#16840388—21no—
19#16840388—21no—
20#16840319—22no—
21#16840315—22no—
22#16840315C2212yes—
23#16840315C2212yes—
24C2×#14519736C2211yescharacteristic
25C2×#14519736C2211yescharacteristic
26#16839820—22no—
27#16839820—22no—
28#16839785C2212yes—
29#16839726C2211yescharacteristic
30M16×Dic61C2212yes—
31#16839656—21no—
32#16839650—21no—
33#16839647—21no—
34#16839645—21no—
35C4×#11758196C2211yescharacteristic
36C4×#11758196C2211yescharacteristic
37C4×C22⋊Dic61C2211yescharacteristic
38#16839608C2211yescharacteristic
39C42×Dic61C2211yescharacteristic
40#16839523C2212yes—
41#16839523C2212yes—
42#16839522C2212yes—
43#16839522C2212yes—
44#16839521C2212yes—
45#16839521C2212yes—
46C2×#117×C61C2211yescharacteristic
47C61×#407C2211yescharacteristic
48C4×C22⋊C4×C61C2211yescharacteristic
49C61×#339C2212yes—
50C61×#339C2212yes—
51C2×#11758194C2312yes—
52#14519777—22no—
53#14519777—22no—
54#14519776—22no—
55#14519776—22no—
56#14519776C2×C412yes—
57#14519776C2×C412yes—
58#14519776C2×C412yes—
59#14519776C2×C412yes—
60#14519769—22no—
61#14519769—22no—
62#14519768—22no—
63#14519768—22no—
64#14519768C2×C412yes—
65#14519768C2×C412yes—
66#14519768C2×C412yes—
67#14519768C2×C412yes—
68#14519756—22no—
69#14519756—22no—
70#14519756—22no—
71#14519756—22no—
72#14519754—22no—
73#14519754—22no—
74#14519754—22no—
75#14519754—22no—
76#14519754—22no—
77#14519754—22no—
78#14519754—22no—
79#14519754—22no—
80C4×Dic122—22no—
81C4×Dic122—22no—
82C4×Dic122—22no—
83C4×Dic122—22no—
84#14519736—21no—
85#14519736—21no—
86#14519736C2×C412yes—
87#14519736C2×C412yes—
88#14519736C2×C412yes—
89#14519736D412yes—
90#14519736D412yes—
91#14519736C2312yes—
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61D411yescharacteristic
95C2×C4⋊Dic61D411yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C22⋊Dic61D411yescharacteristic
101C2×C22⋊Dic61D411yescharacteristic
102C2×C4×Dic61—21no—
103C2×C4×Dic61—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61C2311yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109#14519706—24no—
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112#14519687—22no—
113C8×Dic61—22no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117#14519684—21no—
118#14519684—21no—
119C23×C4×C61C2311yescharacteristic
120C2×M16×C61C2312yes—
121#117×C61—21no—
122#117×C61—21no—
123#117×C61C2×C412yes—
124#117×C61C2312yes—
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C42×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132C22⋊C8×C61—21no—
133C22⋊C8×C61—21no—
134#95×C61—21no—
135C24×C61C2×D411yescharacteristic
136C22×C4×C61—22no—
137C22×C4×C61—22no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2411yescharacteristic
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155C22×Dic61C2×D411yescharacteristic
156C2×Dic122—22no—
157C2×Dic122—22no—
158C2×Dic122—22no—
159C2×Dic122—22no—
160M16×C61—22no—
161M16×C61—22no—
162C2×C8×C61—22no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61C22×C412yes—
166C4⋊C4×C61C22×C412yes—
167C22⋊C4×C61—22no—
168C22⋊C4×C61—22no—
169C22⋊C4×C61—42no—
170C42×C61—22no—
171C42×C61—22no—
172C42×C61—22no—
173C42×C61—22no—
174C22⋊Dic61—22no—
175C22⋊Dic61—22no—
176C22⋊Dic61—42no—
177C22⋊Dic61C22⋊C412yes—
178C22⋊Dic61C22⋊C412yes—
179C22⋊Dic61C22⋊C412yes—
180C22⋊Dic61C22⋊C412yes—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—22no—
184C4⋊Dic61—22no—
185C4⋊Dic61—22no—
186C4⋊Dic61—22no—
187C4⋊Dic61C22⋊C412yes—
188C4⋊Dic61C22⋊C412yes—
189C4⋊Dic61C22⋊C412yes—
190C4⋊Dic61C22⋊C412yes—
191C4⋊Dic61C22×C412yes—
192C4⋊Dic61C22×C412yes—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—42no—
202#11758196—42no—
203C4×Dic61—22no—
204C4×Dic61—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61—42no—
208C4×Dic61—42no—
209C4×Dic61C22×C412yes—
210C4×Dic61C22×C412yes—
211C4×Dic61C2×D412yes—
212C4×Dic61C2×D412yes—
213#11758194—22no—
214#11758194—22no—
215C2×#92418—22no—
216C23×C61—21no—
217C23×C61—21no—
218C23×C61—41no—
219C23×C61—41no—
220C23×C61C2×C22⋊C411yescharacteristic
221C23×C61C2×C22⋊C411yescharacteristic
222C23×C61C22×D411yescharacteristic
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—81no—
238C2×C4×C61—81no—
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C23×C411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C612−1+412yes—
244C2×C4×C612−1+412yes—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—81no—
258C2×Dic61—81no—
259C2×Dic61C2×C22⋊C412yes—
260C2×Dic61C2×C22⋊C412yes—
261C2×Dic61C2×C22⋊C412yes—
262C2×Dic61C2×C22⋊C412yes—
263Dic122—82no—
264Dic122—82no—
265Dic122—82no—
266Dic122—82no—
267C8×C61—42no—
268#92418—42no—
269#21846—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—81no—
279C22×C61—81no—
280C22×C61C22×C22⋊C411yescharacteristic
281C22×C61#53611yescharacteristic
282C22×C61#53611yescharacteristic
283C4×C61—21no—
284C4×C61—21no—
285C4×C61—42no—
286C4×C61—42no—
287C4×C61—42no—
288C4×C61—81no—
289C4×C61#51912yes—
290C4×C61#53612yes—
291Dic61—22no—
292Dic61—22no—
293Dic61—22no—
294Dic61—22no—
295Dic61—42no—
296Dic61—42no—
297Dic61—42no—
298Dic61—81no—
299#3458—611no—
300#2921—611no—
301#2298—611no—
302#1995—612no—
303#1994—612no—
304#1986—612no—
305#1986—612no—
306#1826—611no—
307#1826—611no—
308#1826—611no—
309#1826D6111yescharacteristic
310C2×C61—21no—
311C2×C61—21no—
312C2×C61—41no—
313C2×C61—41no—
314C2×C61#231011yescharacteristic
315C2×C61#290111yescharacteristic
316C2×C61#290111yescharacteristic
317#544—612no—
318#544—612no—
319#544—612no—
320#544—612no—
321#544—1221no—
322#544—1221no—
323#543—1221no—
324#543—1221no—
325#533—612no—
326#533—612no—
327#533—1222no—
328#533—1222no—
329C2×#117—611no—
330C2×#117—611no—
331C2×#117C2×D6111yescharacteristic
332#433—1222no—
333#433—1222no—
334#423—612no—
335#407—611no—
336#407C2×D6111yescharacteristic
337C4×M16—612no—
338#388—1221no—
339#388—1221no—
340#387—1221no—
341#387—1221no—
342C4×C4⋊C4—611no—
343C4×C4⋊C4—611no—
344C4×C22⋊C4—611no—
345C4×C22⋊C4C2×D6111yescharacteristic
346#376—611no—
347C43—611no—
348#339—612no—
349#339—612no—
350#339—612no—
351#339—612no—
352#339—612no—
353#339—612no—
354#339C2×D6112yes—
355#339C2×D6112yes—
356C61#2184611yescharacteristic, complemented, Sylow
357C23×C4C22×D6111yescharacteristic
358C2×M16—612no—
359C2×M16C22×D6112yes—
360C4⋊Q8—612no—
361C4⋊Q8—612no—
362C4⋊Q8—612no—
363C4⋊Q8—612no—
364C4⋊Q8—1222no—
365C4⋊Q8—1222no—
366C4⋊Q8—1222no—
367C4⋊Q8—1222no—
368#125—612no—
369#125—612no—
370#125—612no—
371#125—612no—
372#125—1222no—
373#125—1222no—
374#125—1222no—
375#125—1222no—
376C22⋊Q8—1222no—
377C22⋊Q8—1222no—
378C22⋊Q8—1222no—
379C22⋊Q8—1222no—
380C22⋊Q8—1222no—
381C22⋊Q8—1222no—
382C22⋊Q8—1222no—
383C22⋊Q8—1222no—
384C22⋊Q8—1222no—
385C22⋊Q8—1222no—
386C22⋊Q8—1222no—
387C22⋊Q8—1222no—
388C4×Q8—1222no—
389C4×Q8—1222no—
390C4×Q8—1222no—
391C4×Q8—1222no—
392#117—21no—
393#117—21no—
394#117—612no—
395#117—612no—
396#117—612no—
397#117—612no—
398#117—612no—
399#117—612no—
400#117—1221no—
401#117—1221no—
402#117C4×D6112yes—
403#117C22×D6112yes—
404C2×C4⋊C4—611no—
405C2×C4⋊C4—611no—
406C2×C4⋊C4—611no—
407C2×C4⋊C4—611no—
408C2×C4⋊C4—1221no—
409C2×C4⋊C4—1221no—
410C2×C4⋊C4C4×D6111yescharacteristic
411C2×C4⋊C4C4×D6111yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—611no—
415C2×C22⋊C4—611no—
416C2×C22⋊C4—1221no—
417C2×C22⋊C4—1221no—
418C2×C42—21no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—1221no—
424C2×C42—1221no—
425C2×C42—1221no—
426C2×C42C22×D6111yescharacteristic
427C2×C42C22×D6111yescharacteristic
428C4⋊C8—1224no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433#97—1222no—
434C4×C8—1222no—
435#95—21no—
436#95—1221no—
437#95—1221no—
438#95—1221no—
439#95—1221no—
440#95—1221no—
441C24D4×D6111yescharacteristic
442C2×Q8—1222no—
443C2×Q8—1222no—
444C2×Q8—1222no—
445C2×Q8—1222no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—1221no—
457C22×C4—1221no—
458C22×C4—1221no—
459C22×C4—1221no—
460C22×C4C2×C4×D6111yescharacteristic
461C22×C4C2×C4×D6111yescharacteristic
462C22×C4D4×D6111yescharacteristic
463C22×C4D4×D6111yescharacteristic
464C22×C4D4×D6111yescharacteristic
465C22×C4C23×D6111yescharacteristic
466M16—22no—
467M16—22no—
468M16—1222no—
469M16—1222no—
470C2×C8—22no—
471C2×C8—1222no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—612no—
475C4⋊C4—612no—
476C4⋊C4—612no—
477C4⋊C4—612no—
478C4⋊C4—612no—
479C4⋊C4—612no—
480C4⋊C4—1222no—
481C4⋊C4—1222no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—1222no—
491C4⋊C4—1222no—
492C4⋊C4—1221no—
493C4⋊C4—1221no—
494C4⋊C4—2442no—
495C4⋊C4—2442no—
496C4⋊C4C2×C4×D6112yes—
497C4⋊C4C2×C4×D6112yes—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—42no—
501C22⋊C4—612no—
502C22⋊C4—612no—
503C22⋊C4—612no—
504C22⋊C4—612no—
505C22⋊C4—1222no—
506C22⋊C4—1222no—
507C22⋊C4—2442no—
508C42—22no—
509C42—22no—
510C42—22no—
511C42—22no—
512C42—612no—
513C42—612no—
514C42—612no—
515C42—612no—
516C42—1222no—
517C42—1222no—
518C42—1222no—
519C42—1222no—
520C42—2442no—
521C42—2442no—
522C23—21no—
523C23—21no—
524C23—41no—
525C23—41no—
526C23C22⋊C4×D6111yescharacteristic
527C23C22⋊C4×D6111yescharacteristic
528C23C2×D4×D6111yescharacteristic
529Q8—4882no—
530Q8—4882no—
531Q8—4882no—
532Q8—4882no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—612no—
550C2×C4—612no—
551C2×C4—612no—
552C2×C4—612no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—4881no—
557C2×C4—4881no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4—2441no—
563C2×C4—2441no—
564C2×C4—2441no—
565C2×C4—2441no—
566C2×C4—2441no—
567C2×C4C22⋊C4×D6111yescharacteristic
568C2×C4C22⋊C4×D6111yescharacteristic
569C2×C4C22×C4×D6111yescharacteristic
570C2×C4C2×D4×D6111yescharacteristic
571C2×C4#1451982412yes—
572C2×C4#1451982412yes—
573C8—42no—
574C8—2442no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—81no—
584C22—81no—
585C22C2×C22⋊C4×D6111yescharacteristic
586C22#1684033411yescharacteristic
587C22#1684033411yescharacteristic
588C4—21no—
589C4—21no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—81no—
594C4—1222no—
595C4—1222no—
596C4—1222no—
597C4—1222no—
598C4—4881no—
599C4—2442no—
600C4—2442no—
601C4—2442no—
602C4#1684023912yes—
603C4#1684033412yes—
604C2—21no—
605C2—21no—
606C2—41no—
607C2—41no—
608C2#2144840411yescharacteristic
609C2#2145436311yescharacteristic
610C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1826C2
socleC22×C61C22×C22⋊C4
prime radicalC24×C61C2×D4
cosocleC22×C4×C61C24
hypercenter#1826D61
hypocenterC61#21846
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #21446798C2semidirect
5. #21446794C2semidirect
6. #21446761C2semidirect
7. #21446761C2semidirect
12. #16840393C4semidirect
13. #16840393C4semidirect
16. #16840390C4semidirect
17. #16840390C4semidirect
356. C61#21846semidirect

Maximal subgroups

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

subgroupindex
#214592242
#214544542
#214483152
#214467982
#214467942
#214467612
#214459192
#214459182
#214459162
C61×#18262
#2184661