Finite Group Databasebeta

← #29587238

Subgroups — #29587238

Order 15616.

910 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454336C211yesmaximal, characteristic
2C2×#16839761C211yesmaximal, characteristic
3C2×#16839735C211yesmaximal, characteristic
4C2×#16839532C211yesmaximal, characteristic, complemented
5#21445538C211yesmaximal, characteristic, complemented
6#21445528C211yesmaximal, characteristic, complemented
7C61×#2317C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839770—21no—
13#16839766—21no—
14#16839761—22no—
15#16839761—21no—
16#16839761—21no—
17#16839761—22no—
18#16839756—22no—
19C2×#14519700—21no—
20C2×#14519697—21no—
21#16839735—22no—
22#16839735C414yescomplemented
23C2×#14519691—22no—
24#16839532—22no—
25#16839524—22no—
26#16839521—22no—
27C2×#117×C61C2211yescharacteristic
28C2×#117×C61C2211yescharacteristic
29C22×C4⋊C4×C61C2211yescharacteristic
30C61×#389—22no—
31C61×#385—22no—
32C61×#384—21no—
33C61×#382—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—
43C2×#11758222—21no—
44C2×#11758222C2×C412yes—
45C2×#11758222Q812yes—
46C22×Dic122D411yescharacteristic
47C22×D244D411yescharacteristic
48C22×C22⋊D61—21no—
49C22×C4×D61—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194D412yes—
62C22×#92418—21no—
63C22×#92418D412yes—
64#14519736—21no—
65#14519736—21no—
66#14519736—21no—
67#14519736C2×C412yes—
68C2×C4⋊Dic61—21no—
69C2×C22⋊Dic61—21no—
70C2×C4×Dic61—21no—
71#14519700—24no—
72#14519700—22no—
73#14519700—22no—
74#14519697—24no—
75#14519697—22no—
76#14519697—22no—
77#14519691—28no—
78C23×C4×C61—21no—
79C23×C4×C61C2311yescharacteristic
80#117×C61—21no—
81#117×C61—21no—
82#117×C61—21no—
83#117×C61—21no—
84#117×C61—21no—
85#117×C61—21no—
86#117×C61C2×C412yes—
87#117×C61D412yes—
88C2×C4⋊C4×C61—21no—
89C2×C4⋊C4×C61—21no—
90C2×C4⋊C4×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—24no—
95C2×C4⋊C4×C61D411yescharacteristic
96C2×C4⋊C4×C61D411yescharacteristic
97C2×C4⋊C4×C61D412yes—
98C2×C22⋊C4×C61—21no—
99C2×C22⋊C4×C61D412yes—
100C2×C42×C61—21no—
101C2×C42×C61—21no—
102#95×C61—24no—
103C24×C61C2×D411yescharacteristic
104C23×D61—21no—
105C22×C4×C61—22no—
106C22×C4×C61—21no—
107C22×C4×C61—22no—
108C22×C4×C61—21no—
109C22×C4×C61—41no—
110C22×C4×C61—41no—
111C22×C4×C61—82no—
112C22×C4×C61C22×C411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×Q811yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C22×C4×C61#4111yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C22×C4×C61#4111yescharacteristic
126C2×C22⋊D61—22no—
127C2×C22⋊D61—22no—
128C2×C22⋊D61—41no—
129C2×C22⋊D61—41no—
130C2×C22⋊D61—41no—
131C2×C22⋊D61—41no—
132C22×Dic61—21no—
133C22×Dic61—41no—
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—41no—
143#11758222—41no—
144#11758222—41no—
145#11758222—41no—
146#11758222—41no—
147#11758222—41no—
148#11758222—41no—
149#11758222—41no—
150C2×D244—21no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—21no—
154C2×D244—21no—
155C2×D244C4⋊C412yescomplemented
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—41no—
159C2×C4×D61—41no—
160C2×C4×D61—41no—
161C2×C4×D61—41no—
162C2×Dic122—21no—
163C2×Dic122—21no—
164C2×Dic122—21no—
165C2×Dic122—21no—
166C2×Dic122—21no—
167C2×Dic122C4⋊C412yescomplemented
168C4⋊C4×C61—22no—
169C4⋊C4×C61—22no—
170C4⋊C4×C61—22no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—84no—
179C22⋊C4×C61—22no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C22⋊C4×C61C22⋊C414yes—
183C42×C61—22no—
184C42×C61—22no—
185C42×C61—41no—
186C42×C61—41no—
187C22⋊Dic61—22no—
188C22⋊Dic61—41no—
189C4⋊Dic61—22no—
190C4⋊Dic61—41no—
191C4×Dic61—22no—
192C4×Dic61—41no—
193#11758194—22no—
194#11758194—22no—
195#11758194—41no—
196#11758194—41no—
197#11758194—41no—
198#11758194—41no—
199#11758194—41no—
200#11758194—41no—
201C2×#92418—22no—
202C2×#92418—22no—
203C2×#92418—22no—
204C2×#92418—22no—
205C2×#92418—41no—
206C2×#92418—41no—
207C23×C61—41no—
208C23×C61—41no—
209C23×C61C2×C22⋊C411yescharacteristic
210C23×C61#12011yescharacteristic
211C23×C61#12111yescharacteristic
212C23×C61C22⋊Q811yescharacteristic
213C23×C61#12311yescharacteristic
214C23×C61#12411yescharacteristic
215C23×C61#12711yescharacteristic
216C22×D61—22no—
217C22×D61—41no—
218C22×D61—41no—
219C22×D61—81no—
220C22×D61—81no—
221C2×C4×C61—24no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—44no—
226C2×C4×C61—42no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—42no—
230C2×C4×C61—82no—
231C2×C4×C61—82no—
232C2×C4×C61C2×C4⋊C411yescharacteristic
233C2×C4×C61#11711yescharacteristic
234C2×C4×C61C4×D411yescharacteristic
235C2×C4×C61C4×D411yescharacteristic
236C2×C4×C61C4×D411yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61#12011yescharacteristic
239C2×C4×C61#12011yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61#12111yescharacteristic
243C2×C4×C61#12111yescharacteristic
244C2×C4×C61#12111yescharacteristic
245C2×C4×C61#12111yescharacteristic
246C2×C4×C61#12111yescharacteristic
247C2×C4×C61C22⋊Q811yescharacteristic
248C2×C4×C61C22⋊Q811yescharacteristic
249C2×C4×C61C22⋊Q811yescharacteristic
250C2×C4×C61C22⋊Q811yescharacteristic
251C2×C4×C61C22⋊Q811yescharacteristic
252C2×C4×C61#12311yescharacteristic
253C2×C4×C61#12311yescharacteristic
254C2×C4×C61#12311yescharacteristic
255C2×C4×C61#12311yescharacteristic
256C2×C4×C61#12411yescharacteristic
257C2×C4×C61#12411yescharacteristic
258C2×C4×C61#12611yescharacteristic
259C2×C4×C61#12611yescharacteristic
260C22⋊D61—42no—
261C22⋊D61—42no—
262C22⋊D61—42no—
263C22⋊D61—42no—
264C2×Dic61—22no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—42no—
268C2×Dic61—81no—
269C2×Dic61—81no—
270D244—22no—
271D244—22no—
272D244—41no—
273D244—41no—
274C4×D61—42no—
275C4×D61—42no—
276C4×D61—42no—
277C4×D61—42no—
278Dic122—22no—
279Dic122—22no—
280Dic122—41no—
281Dic122—41no—
282#92418—42no—
283#92418—42no—
284#11093—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—21no—
291C22×C61—41no—
292C22×C61—41no—
293C22×C61—41no—
294C22×C61—41no—
295C22×C61#38011yescharacteristic
296C22×C61#38611yescharacteristic
297C22×C61#39011yescharacteristic
298C22×C61#39211yescharacteristic
299C22×C61#39311yescharacteristic
300C22×C61#39711yescharacteristic
301C22×C61#39911yescharacteristic
302C2×D61—42no—
303C2×D61—82no—
304C2×D61—81no—
305C2×D61—81no—
306C2×D61—82no—
307C4×C61—44no—
308C4×C61—81no—
309C4×C61—82no—
310C4×C61—81no—
311C4×C61#38511yescharacteristic
312C4×C61#38511yescharacteristic
313C4×C61#38811yescharacteristic
314C4×C61#38811yescharacteristic
315C4×C61#39411yescharacteristic
316C4×C61#39411yescharacteristic
317C4×C61#39611yescharacteristic
318C4×C61#39611yescharacteristic
319Dic61—42no—
320Dic61—82no—
321#2896—611no—
322C2×#417—611no—
323C2×#410—611no—
324#2317D6111yescharacteristic, complemented
325C2×#344—611no—
326#1736—611no—
327#1733—611no—
328C2×C61—21no—
329C2×C61—21no—
330C2×C61—21no—
331C2×C61—21no—
332C2×C61—21no—
333C2×C61—21no—
334C2×C61#143911yescharacteristic
335C2×C61#200811yescharacteristic
336C2×C61#200911yescharacteristic
337D61—82no—
338C22×#41—611no—
339C22×M16—611no—
340C22×M16—611no—
341C2×#117—611no—
342C2×#117C2×D6111yescharacteristic
343C2×#117C2×D6111yescharacteristic
344C22×C4⋊C4C2×D6111yescharacteristic
345#419—1221no—
346#418—1221no—
347#417—1222no—
348#417—1222no—
349#417—1221no—
350#417—1221no—
351#416—1222no—
352C2×#103—1221no—
353C2×#102—1221no—
354#410—614no—
355#410—1222no—
356C2×#99—1222no—
357#389—22no—
358#385—22no—
359#384—21no—
360#382—21no—
361#344—1222no—
362#340—1222no—
363#339—1222no—
364C61#1109311yescharacteristic, complemented, Sylow
365C2×#41—612no—
366C2×#41—612no—
367C2×#41—1221no—
368C2×#41—1221no—
369C2×#41—1221no—
370C2×#41—1221no—
371C2×#41—1221no—
372C2×#41—1221no—
373C2×#41—1221no—
374C2×#41—1221no—
375C2×#41—1221no—
376C2×#41—1221no—
377C22×Q8—611no—
378C22×D4—611no—
379C22×D4—1221no—
380C23×C4—21no—
381C23×C4—1221no—
382C23×C4C22×D6111yescharacteristic
383C2×M16—612no—
384C2×M16—1221no—
385C2×M16—1221no—
386C2×M16—1221no—
387C2×M16—1221no—
388C2×M16—1221no—
389C2×M16—1221no—
390C2×M16—1221no—
391C2×M16—1221no—
392C2×M16—1221no—
393C2×M16—1221no—
394C2×M16—1221no—
395C22×C8—612no—
396C22×C8—1221no—
397#117—21no—
398#117—21no—
399#117—21no—
400#117—21no—
401#117—21no—
402#117—21no—
403#117—612no—
404#117—1221no—
405#117—1221no—
406#117—1221no—
407#117C4×D6112yes—
408#117D24412yes—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—1221no—
417C2×C4⋊C4C22⋊D6112yes—
418C2×C4⋊C4C22⋊D6111yescharacteristic
419C2×C4⋊C4C22⋊D6111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4C22⋊D6112yes—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—1221no—
426#103—1224no—
427#103—1222no—
428#103—1222no—
429#102—1224no—
430#102—1222no—
431#102—1222no—
432#99—1228no—
433#95—24no—
434C24—1221no—
435C24C2×C22⋊D6111yescharacteristic
436#41—1222no—
437#41—1222no—
438#41—1222no—
439#41—1222no—
440#41—1222no—
441#41—1222no—
442#41—1222no—
443#41—1222no—
444#41—2441no—
445#41—2441no—
446#41—2441no—
447#41—2441no—
448#41—2441no—
449#41—2441no—
450#41—2441no—
451#41—2441no—
452C2×Q8—612no—
453C2×Q8—1221no—
454C2×Q8—1221no—
455C2×Q8—1221no—
456C2×Q8—1221no—
457C2×Q8—1221no—
458C2×D4—612no—
459C2×D4—1222no—
460C2×D4—1222no—
461C2×D4—1221no—
462C2×D4—1221no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4—1221no—
466C2×D4—2441no—
467C2×D4—2441no—
468C2×D4—2441no—
469C2×D4—2441no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—82no—
477C22×C4—1221no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—2441no—
481C22×C4—2441no—
482C22×C4—2441no—
483C22×C4—2441no—
484C22×C4—2441no—
485C22×C4C2×C4×D6111yescharacteristic
486C22×C4C2×D24411yescharacteristic
487C22×C4#1175822211yescharacteristic
488C22×C4#1175822211yescharacteristic
489C22×C4D4×D6111yescharacteristic
490C22×C4D4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492C22×C4#1175822411yescharacteristic
493C22×C4Q8×D6111yescharacteristic
494C22×C4#1175822611yescharacteristic
495C22×C4#1175822611yescharacteristic
496C22×C4#1175822611yescharacteristic
497C22×C4C2×C22⋊D6111yescharacteristic
498C22×C4C2×C22⋊D6111yescharacteristic
499M16—1222no—
500M16—1222no—
501M16—2441no—
502M16—2441no—
503M16—2441no—
504M16—2441no—
505M16—2441no—
506M16—2441no—
507C2×C8—1222no—
508C2×C8—1222no—
509C2×C8—1222no—
510C2×C8—1222no—
511C2×C8—2441no—
512C2×C8—2441no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—84no—
524C4⋊C4—1222no—
525C4⋊C4—2441no—
526C22⋊C4—22no—
527C22⋊C4—41no—
528C22⋊C4—41no—
529C22⋊C4—1222no—
530C22⋊C4—2441no—
531C22⋊C4#1175819814yes—
532C42—22no—
533C42—22no—
534C42—41no—
535C42—41no—
536C42—1222no—
537C42—2441no—
538C23—41no—
539C23—41no—
540C23—1222no—
541C23—4881no—
542C23—4881no—
543C23—2441no—
544C23—2441no—
545C23C2×#1175819811yescharacteristic
546C23#1451974611yescharacteristic
547C23#1451974811yescharacteristic
548C23#1451975311yescharacteristic
549C23#1451976011yescharacteristic
550C23#1451976611yescharacteristic
551C23#1451977311yescharacteristic
552Q8—1222no—
553Q8—1222no—
554Q8—2441no—
555Q8—2441no—
556D4—1222no—
557D4—1222no—
558D4—2442no—
559D4—2442no—
560D4—2442no—
561D4—2442no—
562D4—2441no—
563D4—2441no—
564C2×C4—24no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—44no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—1222no—
576C2×C4—4881no—
577C2×C4—4881no—
578C2×C4—2442no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4C4⋊C4×D6111yescharacteristic
586C2×C4#1451973511yescharacteristic
587C2×C4C4×C22⋊D6111yescharacteristic
588C2×C4C4×C22⋊D6111yescharacteristic
589C2×C4#1451973911yescharacteristic
590C2×C4#1451973911yescharacteristic
591C2×C4#1451974511yescharacteristic
592C2×C4#1451974511yescharacteristic
593C2×C4#1451974911yescharacteristic
594C2×C4#1451974911yescharacteristic
595C2×C4#1451975111yescharacteristic
596C2×C4#1451975111yescharacteristic
597C2×C4#1451975211yescharacteristic
598C2×C4#1451975211yescharacteristic
599C2×C4#1451975211yescharacteristic
600C2×C4#1451975311yescharacteristic
601C2×C4#1451975311yescharacteristic
602C2×C4#1451975511yescharacteristic
603C2×C4#1451975511yescharacteristic
604C2×C4#1451975711yescharacteristic
605C2×C4#1451976211yescharacteristic
606C2×C4#1451976211yescharacteristic
607C2×C4#1451976211yescharacteristic
608C2×C4#1451976211yescharacteristic
609C2×C4#1451976611yescharacteristic
610C2×C4#1451976611yescharacteristic
611C2×C4#1451977211yescharacteristic
612C2×C4#1451977211yescharacteristic
613C8—2442no—
614C8—2442no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—21no—
620C22—21no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—4882no—
626C22—4882no—
627C22—4881no—
628C22—4881no—
629C22—2442no—
630C22#1683961911yescharacteristic
631C22#1683964111yescharacteristic
632C22#1683966311yescharacteristic
633C22#1683967011yescharacteristic
634C22#1683967311yescharacteristic
635C22#1683968811yescharacteristic
636C22#1683969711yescharacteristic
637C4—44no—
638C4—81no—
639C4—82no—
640C4—81no—
641C4—4882no—
642C4—2442no—
643C4#1683963311yescharacteristic
644C4#1683963311yescharacteristic
645C4#1683965211yescharacteristic
646C4#1683965211yescharacteristic
647C4#1683967911yescharacteristic
648C4#1683967911yescharacteristic
649C4#1683968411yescharacteristic
650C4#1683968411yescharacteristic
651C2—21no—
652C2—21no—
653C2—21no—
654C2—21no—
655C2—21no—
656C2—21no—
657C2—4882no—
658C2#2144406111yescharacteristic
659C2#2144687211yescharacteristic
660C2#2144687911yescharacteristic
subgroupG/H
centerC22#16839670
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2317C2
socleC22×C61#392
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#2317D61
hypocenterC61#11093
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2317

Complements

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

NH ≅ G/Ntype
4. C2×#16839532C2semidirect
5. #21445538C2semidirect
6. #21445528C2semidirect
7. C61×#2317C2semidirect
22. #16839735C4semidirect
155. C2×D244C4⋊C4semidirect
167. C2×Dic122C4⋊C4semidirect
324. #2317D61semidirect
364. C61#11093semidirect

Maximal subgroups

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

subgroupindex
#214543362
C2×#168397612
C2×#168397352
C2×#168395322
#214455382
#214455282
C61×#23172
#1109361