Finite Group Databasebeta

← #29680218

Subgroups — #29680218

Order 15616.

894 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839719C211yesmaximal, characteristic
2#21448444C211yesmaximal, characteristic
3#21448440C211yesmaximal, characteristic
4#21445953C211yesmaximal, characteristic, complemented
5#21445951C211yesmaximal, characteristic, complemented
6#21445951C211yesmaximal, characteristic, complemented
7#21445949C211yesmaximal, characteristic, complemented
8#21445948C211yesmaximal, characteristic, complemented
9#21445946C211yesmaximal, characteristic, complemented
10#21445945C211yesmaximal, characteristic, complemented
11#21445537C211yesmaximal, characteristic
12#21445537C211yesmaximal, characteristic
13#21445534C211yesmaximal, characteristic
14#340×D61C211yesmaximal, characteristic
15C61×#1836C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519735C2211yescharacteristic
19C2×#14519735C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21C2×C4⋊C4×D61C2211yescharacteristic
22C2×C4⋊C4×D61C2211yescharacteristic
23#16839719C418yescomplemented
24C2×#14519687C2211yescharacteristic
25C2×C4×#92418C2211yescharacteristic
26C2×C8×Dic61C2211yescharacteristic
27#16839659—21no—
28#16839659—21no—
29#16839657—21no—
30#16839657—21no—
31#16839636—21no—
32#16839636—21no—
33#16839633—21no—
34#16839633—21no—
35#16839632C2211yescharacteristic
36#16839631C2211yescharacteristic
37#16839631C2211yescharacteristic
38#16839628C2211yescharacteristic
39#16839627C2211yescharacteristic
40#16839627C2211yescharacteristic
41#16839525C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×#97×C61C2211yescharacteristic
54C61×#384C2211yescharacteristic
55C61×#382C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×C4×D61—21no—
61C22×C4×D61—21no—
62C22×C4×D61C2311yescharacteristic
63C2×#11758189—22no—
64C2×#11758189—22no—
65C2×#11758189C2×C414yes—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C2×C8×D61—22no—
69C2×C8×D61—22no—
70C2×C8×D61C2×C414yes—
71#14519735—22no—
72#14519735—22no—
73#14519735—22no—
74#14519735—22no—
75#14519734C2×C414yes—
76#14519734Q814yes—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758196D411yescharacteristic
90C2×#11758196D411yescharacteristic
91C4⋊C4×D61—22no—
92C4⋊C4×D61—22no—
93C4⋊C4×D61—22no—
94C4⋊C4×D61—22no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198D411yescharacteristic
98C2×#11758198D411yescharacteristic
99C2×C4×Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61C2311yescharacteristic
102#14519687C2×C414yescomplemented
103C4×#92418C2×C414yescomplemented
104C8×Dic61C2×C414yescomplemented
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111C22×C8×C61C2311yescharacteristic
112C22×C8×C61C2311yescharacteristic
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61—21no—
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C42×C61C2311yescharacteristic
120#97×C61C2×C414yescomplemented
121#95×C61—21no—
122#95×C61—21no—
123C23×D61C2×D411yescharacteristic
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2411yescharacteristic
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C22×Dic61C2×D411yescharacteristic
136C22×Dic61C2×D411yescharacteristic
137C22×Dic61C2×D411yescharacteristic
138C2×C4×D61—42no—
139C2×C4×D61—42no—
140C2×C4×D61—81no—
141C2×C4×D61—81no—
142C2×C4×D61—81no—
143C2×C4×D61—81no—
144C2×C4×D61C22×C412yes—
145C2×C4×D61C2×Q812yes—
146C2×C4×D61#4112yes—
147C2×C4×D61#4112yes—
148C2×C4×D61#4112yes—
149C2×C4×D61#4112yes—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61C22×C412yes—
155C2×C8×C61C22×C412yes—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—81no—
165C4⋊C4×C61—81no—
166C42×C61C22×C412yes—
167C42×C61C2×Q812yes—
168#11758198—42no—
169#11758198—42no—
170#11758198C4⋊C414yes—
171#11758198C4⋊C414yes—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—81no—
181C4⋊Dic61—81no—
182#11758196—42no—
183#11758196—42no—
184#11758196—81no—
185#11758196—81no—
186#11758196—81no—
187#11758196—81no—
188#11758196C4⋊C414yes—
189#11758196C4⋊C414yes—
190C4×Dic61—42no—
191C4×Dic61—42no—
192C4×Dic61C22×C412yes—
193C4×Dic61C2×Q812yes—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C22×C412yes—
199C2×#92418C22×C412yes—
200#11758189—28no—
201C8×D61—28no—
202C23×C61C22×D411yescharacteristic
203C22×D61—21no—
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61C2×C4⋊C412yes—
208C22×D61#12412yes—
209C22×D61#12412yes—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61C2×C4⋊C412yes—
227C2×C4×C61C2×C4⋊C412yes—
228C2×C4×C61C23×C411yescharacteristic
229C2×C4×C61C22×Q811yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61C2×C4⋊C412yes—
251C2×Dic61C2×C4⋊C412yes—
252C2×Dic61C2×C4⋊C412yes—
253C2×Dic61#12412yes—
254C2×Dic61#12412yes—
255C4×D61—84no—
256C4×D61—84no—
257C4×D61#11714yes—
258C4×D61#11714yes—
259C4×D61#12514yes—
260C4×D61#12514yes—
261C8×C61—22no—
262C8×C61—22no—
263#92418—22no—
264#92418—22no—
265#20763—611nomaximal, Sylow
266C22×C61C22×C4⋊C411yescharacteristic
267C22×C61C2×#12411yescharacteristic
268C22×C61C2×#12411yescharacteristic
269C22×C61#57611yescharacteristic
270C22×C61#57711yescharacteristic
271C22×C61#57711yescharacteristic
272C22×C61#57811yescharacteristic
273C2×D61—22no—
274C2×D61—22no—
275C2×D61—22no—
276C2×D61—22no—
277C2×D61—22no—
278C2×D61—22no—
279C2×D61#38214yes—
280C4×C61—22no—
281C4×C61—22no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61—81no—
286C4×C61C2×#11711yescharacteristic
287C4×C61C2×#11711yescharacteristic
288C4×C61C2×#12511yescharacteristic
289C4×C61C2×#12511yescharacteristic
290Dic61—22no—
291Dic61—22no—
292Dic61—81no—
293Dic61—81no—
294Dic61—81no—
295Dic61—81no—
296Dic61#38214yes—
297C2×#405—611no—
298#2317—611no—
299#2317—611no—
300#1836—611no—
301#1836—611no—
302#1836—611no—
303#1836D6111yescharacteristic, complemented
304#1835—611no—
305#1835—611no—
306#1834—611no—
307#1834—611no—
308#1736—611no—
309#1736—611no—
310#1735—611no—
311C2×#340—611no—
312C2×C61C2×#38211yescharacteristic
313C2×C61#291211yescharacteristic
314C2×C61#291311yescharacteristic
315C2×C61#313611yescharacteristic
316C2×C61#313611yescharacteristic
317C2×C61#313711yescharacteristic
318C2×C61#313711yescharacteristic
319D61—24no—
320C22×M16—611no—
321C23×C8—611no—
322C2×#117—611no—
323C2×#117—611no—
324C2×#117—611no—
325C22×C4⋊C4—611no—
326C22×C4⋊C4—611no—
327#405—618no—
328C2×#97—611no—
329C2×#97C2×D6111yescharacteristic
330C2×C4×C8—611no—
331C2×C4×C8—611no—
332#389—1221no—
333#389—1221no—
334#389—1221no—
335#389—1221no—
336#385—1221no—
337#385—1221no—
338#385—1221no—
339#385—1221no—
340#384—611no—
341#384—611no—
342#384—611no—
343#384C2×D6111yescharacteristic
344#382—611no—
345#382—611no—
346#382—611no—
347#382C2×D6111yescharacteristic
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340—611no—
357#340—611no—
358#340—611no—
359#340—611no—
360#340C2×D6111yescharacteristic
361#340C2×D6111yescharacteristic
362#340C2×D6111yescharacteristic
363#340C2×D6111yescharacteristic
364C61#2076311yescharacteristic, complemented, Sylow
365C23×C4—611no—
366C23×C4—1221no—
367C23×C4—1221no—
368C2×M16—614no—
369C2×M16—1222no—
370C2×M16—1222no—
371C22×C8—611no—
372C22×C8—611no—
373C22×C8—614no—
374C22×C8—1222no—
375C22×C8—1222no—
376C22×C8C22×D6111yescharacteristic
377C22×C8C22×D6111yescharacteristic
378#117—614no—
379#117—614no—
380#117—1222no—
381#117—1222no—
382#117—1222no—
383#117—1222no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—611no—
390C2×C4⋊C4—611no—
391C2×C4⋊C4—611no—
392C2×C4⋊C4—1222no—
393C2×C4⋊C4—1222no—
394C2×C4⋊C4—1222no—
395C2×C4⋊C4—1222no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1221no—
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4C22×D6111yescharacteristic
405C2×C4⋊C4C22×D6111yescharacteristic
406C2×C4⋊C4C22×D6111yescharacteristic
407C2×C4⋊C4C22×D6111yescharacteristic
408C2×C22⋊C4—611no—
409C2×C22⋊C4—611no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C42—611no—
413C2×C42—1221no—
414C2×C42—1221no—
415C2×C42C22×D6111yescharacteristic
416#97—614no—
417#97C4×D6114yescomplemented
418C4×C8—614no—
419C4×C8—614no—
420#95—21no—
421#95—21no—
422#95—1221no—
423#95—1221no—
424#95—1221no—
425#95—1221no—
426#95—1221no—
427#95—1221no—
428C24—611no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—611no—
434C22×C4—612no—
435C22×C4—612no—
436C22×C4—612no—
437C22×C4—612no—
438C22×C4—612no—
439C22×C4—612no—
440C22×C4—611no—
441C22×C4—611no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—4881no—
447C22×C4—4881no—
448C22×C4—4881no—
449C22×C4—4881no—
450C22×C4—2442no—
451C22×C4—2442no—
452C22×C4D4×D6111yescharacteristic
453C22×C4D4×D6111yescharacteristic
454C22×C4C23×D6111yescharacteristic
455M16—1228no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—612no—
461C2×C8—612no—
462C2×C8—1228no—
463C2×C8—1221no—
464C2×C8—1221no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8C2×C4×D6112yes—
468C2×C8C2×C4×D6112yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—614no—
480C4⋊C4—614no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—4881no—
490C4⋊C4—4881no—
491C4⋊C4—4881no—
492C4⋊C4—4881no—
493C4⋊C4—4881no—
494C4⋊C4—4881no—
495C4⋊C4—2442no—
496C4⋊C4—2442no—
497C22⋊C4—614no—
498C22⋊C4—614no—
499C22⋊C4—2442no—
500C22⋊C4—2442no—
501C42—612no—
502C42—612no—
503C42—2442no—
504C42—2442no—
505C42C2×C4×D6112yes—
506C42Q8×D6112yes—
507C23—612no—
508C23—612no—
509C23—612no—
510C23—1221no—
511C23—1221no—
512C23—1221no—
513C23—1221no—
514C23C2×D4×D6111yescharacteristic
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—612no—
532C2×C4—612no—
533C2×C4—612no—
534C2×C4—614no—
535C2×C4—614no—
536C2×C4—614no—
537C2×C4—614no—
538C2×C4—612no—
539C2×C4—612no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—4884no—
545C2×C4—4884no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4C4⋊C4×D6112yes—
559C2×C4C4⋊C4×D6112yes—
560C2×C4C22×C4×D6111yescharacteristic
561C2×C4C2×Q8×D6111yescharacteristic
562C2×C4#41×D6111yescharacteristic
563C2×C4#41×D6111yescharacteristic
564C2×C4#41×D6111yescharacteristic
565C2×C4#41×D6111yescharacteristic
566C8—22no—
567C8—22no—
568C8—1222no—
569C8—1222no—
570C22—614no—
571C22—1222no—
572C22—1222no—
573C22—1222no—
574C22—1222no—
575C22—1222no—
576C22—1222no—
577C22C2×C4⋊C4×D6111yescharacteristic
578C22#124×D6111yescharacteristic
579C22#124×D6111yescharacteristic
580C22#1684056611yescharacteristic
581C22#1684057111yescharacteristic
582C22#1684057211yescharacteristic
583C22#1684057811yescharacteristic
584C4—22no—
585C4—22no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—614no—
591C4—1222no—
592C4—1222no—
593C4—4881no—
594C4—4881no—
595C4—4881no—
596C4—4881no—
597C4#117×D6111yescharacteristic
598C4#117×D6111yescharacteristic
599C4#125×D6111yescharacteristic
600C4#125×D6111yescharacteristic
601C2—1224no—
602C2#382×D6111yescharacteristic
603C2#2145441311yescharacteristic
604C2#2145441811yescharacteristic
605C2#2145617011yescharacteristic
606C2#2145617411yescharacteristic
607C2#2145618111yescharacteristic
608C2#2145618511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1836C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1836D61
hypocenterC61#20763
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1836

Complements

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

NH ≅ G/Ntype
4. #21445953C2semidirect
5. #21445951C2semidirect
6. #21445951C2semidirect
7. #21445949C2semidirect
8. #21445948C2semidirect
9. #21445946C2semidirect
10. #21445945C2semidirect
15. C61×#1836C2semidirect
23. #16839719C4semidirect
102. #14519687C2×C4semidirect
103. C4×#92418C2×C4semidirect
104. C8×Dic61C2×C4semidirect
120. #97×C61C2×C4semidirect
303. #1836D61semidirect
364. C61#20763semidirect
417. #97C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168397192
#214484442
#214484402
#214459532
#214459512
#214459492
#214459482
#214459462
#214459452
#214455372
#214455342
#340×D612
C61×#18362
#2076361