Finite Group Databasebeta

← #29684393

Subgroups — #29684393

Order 15616.

814 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
1#21448470C211yesmaximal, characteristic, complemented
2#21448462C211yesmaximal, characteristic
3#21446702C211yesmaximal, characteristic
4#21446675C211yesmaximal, characteristic
5#21446558C211yesmaximal, characteristic, complemented
6#21446553C211yesmaximal, characteristic, complemented
7#21446518C211yesmaximal, characteristic
8#21446511C211yesmaximal, characteristic, complemented
9#21446504C211yesmaximal, characteristic
10#21446497C211yesmaximal, characteristic, complemented
11#21445716C211yesmaximal, characteristic, complemented
12C4×#14519701C211yesmaximal, characteristic, complemented
13C4×#14519698C211yesmaximal, characteristic
14#21445507C211yesmaximal, characteristic, complemented
15C2×C61×#440C211yesmaximal, characteristic
16C2×#14519711C2211yescharacteristic
17C2×#14519709C2211yescharacteristic
18C2×#14519701C2211yescharacteristic
19C2×#14519701C2211yescharacteristic
20C2×#14519698C2211yescharacteristic
21C2×#14519698C2211yescharacteristic
22C2×#14519687C2211yescharacteristic
23C2×#14519687C2211yescharacteristic
24C2×C4×#92418C2211yescharacteristic
25C2×C8×Dic61C2211yescharacteristic
26C2×C8×Dic61C2211yescharacteristic
27#16839669C2211yescharacteristic
28#16839669C2211yescharacteristic
29#16839665C2211yescharacteristic
30#16839665C2211yescharacteristic
31#16839661C2211yescharacteristic
32#16839661C2211yescharacteristic
33#16839661C2211yescharacteristic
34#16839661C2211yescharacteristic
35#16839655—21no—
36#16839655—21no—
37#16839648—21no—
38#16839648—21no—
39#16839630—21no—
40#16839628—21no—
41#16839625—21no—
42#16839622—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44C4×C4⋊Dic61C2211yescharacteristic
45#16839608C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C22×SD16×C61C2211yescharacteristic
53C2×C4×Q8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C61×#440C418yescomplemented
56C2×#107×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C2×#97×C61C2211yescharacteristic
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C22⋊Dic61—21no—
71C2×C22⋊Dic61—21no—
72C2×C22⋊Dic61—21no—
73C2×C22⋊Dic61—21no—
74C2×C4×Dic61—21no—
75C2×C4×Dic61—21no—
76C2×C4×Dic61C2311yescharacteristic
77C2×C4×Dic61C2311yescharacteristic
78#14519711—22no—
79#14519709—22no—
80#14519701—22no—
81#14519701—22no—
82#14519698—22no—
83#14519698—22no—
84#14519687—22no—
85#14519687—22no—
86C4×#92418—22no—
87C8×Dic61—22no—
88C8×Dic61—22no—
89#14519684—21no—
90#14519684—21no—
91#14519684—21no—
92#14519684—21no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684D411yescharacteristic
100#14519684D411yescharacteristic
101#14519684D411yescharacteristic
102#14519684D411yescharacteristic
103C22×Q8×C61C2311yescharacteristic
104C22×D4×C61C2311yescharacteristic
105C23×C4×C61—21no—
106C2×SD16×C61—22no—
107C2×SD16×C61—22no—
108C2×SD16×C61C2×C414yes—
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C4×Q8×C61—22no—
112C4×Q8×C61C2×C414yes—
113C4×D4×C61—22no—
114C4×D4×C61C2×C414yes—
115C2×C4⋊C4×C61—21no—
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—21no—
119C2×C42×C61—21no—
120C2×C42×C61C2311yescharacteristic
121#107×C61C2×C414yes—
122#103×C61C2×C414yes—
123#102×C61C2×C414yes—
124#97×C61C2×C414yes—
125C24×C61—21no—
126C2×Q8×C61—21no—
127C2×Q8×C61—21no—
128C2×Q8×C61—21no—
129C2×Q8×C61—21no—
130C2×Q8×C61—21no—
131C2×Q8×C61C22×C412yes—
132C2×D4×C61—21no—
133C2×D4×C61—21no—
134C2×D4×C61—21no—
135C2×D4×C61—21no—
136C2×D4×C61—21no—
137C2×D4×C61C22×C412yes—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—24no—
142C22×C4×C61—81no—
143C22×C4×C61—81no—
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C22×Dic61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C22×Dic61—21no—
151C22×Dic61C2×D411yescharacteristic
152C22×Dic61C2×D411yescharacteristic
153C22×Dic61C2×D411yescharacteristic
154C22×Dic61C2×D411yescharacteristic
155SD16×C61—28no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61C22×C412yes—
159C2×C8×C61C22×C412yes—
160C2×C8×C61#4112yes—
161C2×C8×C61#4112yes—
162C4⋊C4×C61—24no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61C22×C412yes—
166C4⋊C4×C61C22×C412yes—
167C22⋊C4×C61—24no—
168C42×C61—24no—
169C42×C61C22×C412yes—
170C42×C61#4112yes—
171C22⋊Dic61—81no—
172C22⋊Dic61—81no—
173C22⋊Dic61—81no—
174C22⋊Dic61—81no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—81no—
184C4⋊Dic61—81no—
185C4⋊Dic61—81no—
186C4⋊Dic61—81no—
187C4×Dic61—21no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—81no—
192C4×Dic61—81no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418#4112yes—
198C2×#92418#4112yes—
199C23×C61—22no—
200C23×C61—41no—
201C23×C61—41no—
202C23×C61—41no—
203C23×C61—41no—
204C23×C61—41no—
205C23×C61—41no—
206C23×C61C22×D411yescharacteristic
207Q8×C61—22no—
208Q8×C61—22no—
209Q8×C61—41no—
210Q8×C61—41no—
211D4×C61—22no—
212D4×C61—22no—
213D4×C61—41no—
214D4×C61—41no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—22no—
220C2×C4×C61—22no—
221C2×C4×C61—22no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—84no—
229C2×C4×C61C4×D412yes—
230C2×C4×C61C4×D412yes—
231C2×C4×C61C23×C411yescharacteristic
232C2×C4×C61C2×#4111yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C2×C4×C61C2×#4111yescharacteristic
235C2×C4×C61C2×#4111yescharacteristic
236C2×C4×C61C2×#4111yescharacteristic
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—21no—
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
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—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C8×C61—22no—
262C8×C61#11714yes—
263#92418—22no—
264#92418—22no—
265#21291—611nomaximal, Sylow
266C22×C61—42no—
267C22×C61—42no—
268C22×C61—42no—
269C22×C61—81no—
270C22×C61—81no—
271C22×C61—81no—
272C22×C61—81no—
273C22×C61C2×C4×D411yescharacteristic
274C22×C61#53211yescharacteristic
275C22×C61#53211yescharacteristic
276C22×C61#57611yescharacteristic
277C22×C61#57711yescharacteristic
278C22×C61#57711yescharacteristic
279C22×C61#57811yescharacteristic
280C4×C61—22no—
281C4×C61—22no—
282C4×C61—42no—
283C4×C61—42no—
284C4×C61—42no—
285C4×C61C2×#11711yescharacteristic
286C4×C61C4×#4111yescharacteristic
287C4×C61#52911yescharacteristic
288C4×C61#52911yescharacteristic
289Dic61—41no—
290Dic61—41no—
291Dic61—41no—
292Dic61—41no—
293Dic61—81no—
294Dic61—81no—
295Dic61—81no—
296Dic61—81no—
297C2×#440D6111yescharacteristic
298#2320—611no—
299#2319—611no—
300#1973—611no—
301#1968—611no—
302#1943—611no—
303#1942—611no—
304#1936—611no—
305#1935—611no—
306#1934—611no—
307#1933—611no—
308#1776—611no—
309C4×#103—611no—
310C4×#102—611no—
311#1726—611no—
312C2×C61—82no—
313C2×C61#229311yescharacteristic
314C2×C61#294611yescharacteristic
315C2×C61#294711yescharacteristic
316C2×C61#317411yescharacteristic
317C2×C61#317511yescharacteristic
318C2×C61#317811yescharacteristic
319C2×C61#317911yescharacteristic
320C22×SD16C2×D6111yescharacteristic
321C2×C4×Q8C2×D6111yescharacteristic
322C2×C4×D4C2×D6111yescharacteristic
323#440Dic6118yescomplemented
324C2×#107—611no—
325C2×#107C2×D6111yescharacteristic
326C2×#106—611no—
327C2×#103—611no—
328C2×#103—611no—
329C2×#103C2×D6111yescharacteristic
330C2×#102—611no—
331C2×#102—611no—
332C2×#102C2×D6111yescharacteristic
333C2×#97—611no—
334C2×#97—611no—
335C2×#97C2×D6111yescharacteristic
336C2×C4×C8—611no—
337C2×C4×C8—611no—
338C2×C4×C8—611no—
339#391—611no—
340#391—611no—
341#390—611no—
342#390—611no—
343#389—611no—
344#389—611no—
345#389—611no—
346#389—611no—
347#388—1221no—
348#388—1221no—
349#387—1221no—
350#387—1221no—
351#383—1221no—
352#382—1221no—
353#381—1221no—
354#380—1221no—
355C4×C4⋊C4—611no—
356C4×C4⋊C4—611no—
357#376—611no—
358#340—611no—
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340—611no—
364C61#2129111yescharacteristic, complemented, Sylow
365C22×Q8C22×D6111yescharacteristic
366C22×D4C22×D6111yescharacteristic
367C23×C4—21no—
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16C2×Dic6114yes—
371C22×C8—611no—
372C22×C8—611no—
373C22×C8C22×D6111yescharacteristic
374C22×C8C22×D6111yescharacteristic
375C4×Q8—22no—
376C4×Q8C2×Dic6114yes—
377C4×D4—22no—
378C4×D4C2×Dic6114yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—611no—
381C2×C4⋊C4—611no—
382C2×C4⋊C4—611no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4C22×D6111yescharacteristic
389C2×C4⋊C4C22×D6111yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—1221no—
394C2×C22⋊C4—1221no—
395C2×C42—21no—
396C2×C42—611no—
397C2×C42—611no—
398C2×C42—1221no—
399C2×C42—1221no—
400C2×C42C22×D6111yescharacteristic
401#107—1222no—
402#107C2×Dic6114yes—
403#106—1222no—
404#103—1222no—
405#103—1222no—
406#103C2×Dic6114yes—
407#102—1222no—
408#102—1222no—
409#102C2×Dic6114yes—
410#97—1222no—
411#97—1222no—
412#97C2×Dic6114yes—
413C4×C8—1222no—
414C4×C8—1222no—
415C4×C8—1222no—
416#95—611no—
417#95—611no—
418#95—611no—
419#95—611no—
420#95—1221no—
421#95—1221no—
422#95—1221no—
423#95—1221no—
424#95—1221no—
425#95—1221no—
426#95—1221no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430C24—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8C22×Dic6112yes—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4C22×Dic6112yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—81no—
448C22×C4—81no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4D4×D6111yescharacteristic
458C22×C4D4×D6111yescharacteristic
459C22×C4C23×D6111yescharacteristic
460SD16—28no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—612no—
464C2×C8—612no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8#1175822212yes—
470C2×C8#1175822212yes—
471C2×C8C22×Dic6112yes—
472C2×C8C22×Dic6112yes—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—24no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1221no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—4881no—
485C4⋊C4—4881no—
486C4⋊C4—4881no—
487C4⋊C4—4881no—
488C4⋊C4C22×Dic6112yes—
489C4⋊C4C22×Dic6112yes—
490C22⋊C4—24no—
491C22⋊C4—4881no—
492C22⋊C4—4881no—
493C22⋊C4—4881no—
494C22⋊C4—4881no—
495C42—24no—
496C42—1221no—
497C42—1221no—
498C42—1221no—
499C42—1221no—
500C42—4881no—
501C42—4881no—
502C42#1175822412yes—
503C42C22×Dic6112yes—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23C2×D4×D6111yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—84no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
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×C4D4×Dic6112yes—
559C2×C4D4×Dic6112yes—
560C2×C4C23×Dic6111yescharacteristic
561C2×C4#41×D6111yescharacteristic
562C2×C4#41×D6111yescharacteristic
563C2×C4C2×#1175822411yescharacteristic
564C2×C4C2×#1175822211yescharacteristic
565C2×C4C2×#1175822211yescharacteristic
566C8—22no—
567C8—1222no—
568C8—1222no—
569C8#1451973614yes—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22C2×D4×Dic6111yescharacteristic
578C22#1684030911yescharacteristic
579C22#1684030911yescharacteristic
580C22#1684056611yescharacteristic
581C22#1684057111yescharacteristic
582C22#1684057211yescharacteristic
583C22#1684057811yescharacteristic
584C4—22no—
585C4—22no—
586C4—42no—
587C4—42no—
588C4—42no—
589C4—4881no—
590C4—4881no—
591C4—4881no—
592C4—4881no—
593C4—2441no—
594C4—2441no—
595C4—2441no—
596C4—2441no—
597C4C2×#1451973611yescharacteristic
598C4#41×Dic6111yescharacteristic
599C4#1684029411yescharacteristic
600C4#1684029411yescharacteristic
601C2—82no—
602C2#2144828411yescharacteristic
603C2#2145465211yescharacteristic
604C2#2145466311yescharacteristic
605C2#2145644511yescharacteristic
606C2#2145645611yescharacteristic
607C2#2145648511yescharacteristic
608C2#2145650011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#440C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenterC2×#440D61
hypocenterC61#21291
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. #21448470C2semidirect
5. #21446558C2semidirect
6. #21446553C2semidirect
8. #21446511C2semidirect
10. #21446497C2semidirect
11. #21445716C2semidirect
12. C4×#14519701C2semidirect
14. #21445507C2semidirect
55. C61×#440C4semidirect
323. #440Dic61semidirect
364. C61#21291semidirect

Maximal subgroups

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

subgroupindex
#214484702
#214484622
#214467022
#214466752
#214465582
#214465532
#214465182
#214465112
#214465042
#214464972
#214457162
C4×#145197012
C4×#145196982
#214455072
C2×C61×#4402
#2129161