Finite Group Databasebeta

← #29686376

Subgroups — #29686376

Order 15616.

980 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
1C2×#16839981C211yesmaximal, characteristic
2C2×#16839862C211yesmaximal, characteristic
3C2×C4×#11758202C211yesmaximal, characteristic, complemented
4#21448182C211yesmaximal, characteristic, complemented
5#21446752C211yesmaximal, characteristic
6#21446575C211yesmaximal, characteristic, complemented
7#21446457C211yesmaximal, characteristic, complemented
8#21446436C211yesmaximal, characteristic
9#21446177C211yesmaximal, characteristic
10#21446163C211yesmaximal, characteristic, complemented
11#21445821C211yesmaximal, characteristic, complemented
12#21445676C211yesmaximal, characteristic, complemented
13#21445649C211yesmaximal, characteristic, complemented
14C4×#14519698C211yesmaximal, characteristic
15C61×#2326C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20C2×C4×Dic122C2211yescharacteristic
21#16839981C418yescomplemented
22#16839862—24no—
23C4×#11758202—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519700C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic
38C4×C4⋊Dic61C2211yescharacteristic
39C4×C4⋊Dic61C2211yescharacteristic
40C4×C4⋊Dic61C2211yescharacteristic
41#16839613—21no—
42#16839613—21no—
43#16839613—21no—
44#16839607—21no—
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51C2×#124×C61C2211yescharacteristic
52C2×C4×Q8×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C61×#391C2211yescharacteristic
55C61×#390C2211yescharacteristic
56C61×#388—21no—
57C61×#388—21no—
58C61×#385—21no—
59C61×#385—21no—
60C61×#384C2211yescharacteristic
61C61×#376C2211yescharacteristic
62C22×Dic122C2311yescharacteristic
63C2×#11758202—22no—
64C2×#11758202—22no—
65C2×#11758202C2×C414yescomplemented
66C2×#11758200—22no—
67C2×#11758200—22no—
68C2×#11758200C2×C414yes—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C4×Dic122—22no—
74C4×Dic122—22no—
75C4×Dic122—22no—
76C4×Dic122—22no—
77C4×Dic122C2×C414yescomplemented
78C4×Dic122D414yes—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91#14519710—22no—
92#14519710—22no—
93C4⋊#92418—22no—
94C4⋊#92418C2×C414yescomplemented
95#14519701—22no—
96#14519701—22no—
97#14519701C2×C414yescomplemented
98#14519700—22no—
99#14519700—22no—
100#14519698—22no—
101#14519698—22no—
102#14519698C2×C414yes—
103#14519688—22no—
104C4×#92418—22no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108C22×Q8×C61C2311yescharacteristic
109C22×D4×C61C2311yescharacteristic
110C23×C4×C61—21no—
111#124×C61—22no—
112#124×C61C2×C414yes—
113C4×Q8×C61—22no—
114C4×Q8×C61—22no—
115C4×D4×C61—22no—
116C4×D4×C61—22no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C22⋊C4×C61—21no—
123C2×C22⋊C4×C61—21no—
124C2×C22⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C42×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C2×C42×C61C2311yescharacteristic
130C2×C42×C61C2311yescharacteristic
131#95×C61—21no—
132#95×C61—21no—
133#95×C61D411yescharacteristic
134#95×C61D411yescharacteristic
135#95×C61D411yescharacteristic
136#95×C61D411yescharacteristic
137C24×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61C22×C412yes—
144C2×D4×C61—21no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61C22×C412yes—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—42no—
154C22×C4×C61—81no—
155C22×C4×C61—81no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2×D411yescharacteristic
162C22×C4×C61C2411yescharacteristic
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122C22×C412yes—
171C2×Dic122C2×D412yes—
172C2×Dic122#4112yes—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—42no—
178C4⋊C4×C61—81no—
179C4⋊C4×C61—81no—
180C22⋊C4×C61—24no—
181C22⋊C4×C61—24no—
182C22⋊C4×C61—42no—
183C22⋊C4×C61—81no—
184C22⋊C4×C61—81no—
185C42×C61—21no—
186C42×C61—21no—
187C42×C61—42no—
188C42×C61C22×C412yes—
189C42×C61C2×D412yes—
190C42×C61#4112yes—
191C42×C61#4112yes—
192#11758202—28no—
193#11758200—28no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61C22×C412yes—
198C4⋊Dic61C2×D412yes—
199C4⋊Dic61#4112yes—
200#11758196—24no—
201#11758196—24no—
202#11758196—24no—
203C4×Dic61—24no—
204C4×Dic61—24no—
205C4×Dic61—24no—
206C4×Dic61—81no—
207C4×Dic61—81no—
208C4×Dic61—81no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418C22×C412yes—
220C2×#92418C22×C412yes—
221C23×C61—22no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61—41no—
228C23×C61C22×D411yescharacteristic
229Q8×C61—22no—
230Q8×C61—22no—
231Q8×C61—41no—
232Q8×C61—41no—
233D4×C61—22no—
234D4×C61—22no—
235D4×C61—41no—
236D4×C61—41no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61—22no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—84no—
261C2×C4×C61C4×D412yes—
262C2×C4×C61C4×D412yes—
263C2×C4×C61#12112yes—
264C2×C4×C61#12112yes—
265C2×C4×C61C23×C411yescharacteristic
266C2×C4×C61C22×D411yescharacteristic
267C2×C4×C61C2×#4111yescharacteristic
268C2×C4×C61C2×#4111yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×Dic61—22no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283Dic122—22no—
284Dic122—22no—
285Dic122—22no—
286Dic122C4×D414yes—
287#92418—22no—
288#92418—22no—
289#92418—41no—
290#92418—41no—
291#21512—611nomaximal, Sylow
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—81no—
296C22×C61—81no—
297C22×C61—81no—
298C22×C61—81no—
299C22×C61C2×C4×D411yescharacteristic
300C22×C61C2×#12111yescharacteristic
301C22×C61#52511yescharacteristic
302C22×C61#57611yescharacteristic
303C22×C61#57711yescharacteristic
304C22×C61#57811yescharacteristic
305C22×C61#57811yescharacteristic
306C4×C61—22no—
307C4×C61—22no—
308C4×C61—22no—
309C4×C61—22no—
310C4×C61—41no—
311C4×C61—41no—
312C4×C61—42no—
313C4×C61—81no—
314C4×C61—81no—
315C4×C61C2×C4×D411yescharacteristic
316C4×C61C4×#4111yescharacteristic
317C4×C61#52911yescharacteristic
318C4×C61#53211yescharacteristic
319Dic61—24no—
320Dic61—42no—
321Dic61—42no—
322Dic61—42no—
323C2×#464—611no—
324C2×#440—611no—
325C2×C4×Q16—611no—
326#2326D6111yescharacteristic
327#2276—611no—
328#1983—611no—
329#1947—611no—
330#1928—611no—
331#1925—611no—
332#1880—611no—
333#1878—611no—
334#1803—611no—
335#1768—611no—
336#1763—611no—
337C4×#102—611no—
338C2×C61—82no—
339C2×C61C4×#12111yescharacteristic
340C2×C61#294711yescharacteristic
341C2×C61#295111yescharacteristic
342C2×C61#304411yescharacteristic
343C2×C61#304511yescharacteristic
344C2×C61#312111yescharacteristic
345C2×C61#312411yescharacteristic
346C22×Q16—611no—
347C22×SD16—611no—
348C2×#124C2×D6111yescharacteristic
349C2×C4×Q8—611no—
350C2×C4×Q8—611no—
351C2×C4×Q8—611no—
352C2×C4×Q8C2×D6111yescharacteristic
353C2×C4×D4C2×D6111yescharacteristic
354#464—618no—
355#440—1224no—
356C4×Q16—1224no—
357C2×#107—611no—
358C2×#107—611no—
359C2×C4⋊C8—611no—
360C2×C4⋊C8—611no—
361C2×#103—611no—
362C2×#103—611no—
363C2×#103—611no—
364C2×#103—611no—
365C2×#103—611no—
366C2×#102—611no—
367C2×#102—611no—
368C2×#102—611no—
369C2×#97—611no—
370C2×C4×C8—611no—
371#391C2×D6111yescharacteristic
372#390C2×D6111yescharacteristic
373#388—21no—
374#388—21no—
375#385—21no—
376#385—21no—
377#384C2×D6111yescharacteristic
378C4×C4⋊C4—611no—
379C4×C4⋊C4—611no—
380C4×C4⋊C4—611no—
381C4×C4⋊C4—1221no—
382C4×C4⋊C4—1221no—
383C4×C4⋊C4—1221no—
384#376—1221no—
385#376C2×D6111yescharacteristic
386#340—611no—
387#340—611no—
388#340—611no—
389#340—611no—
390#336—611no—
391#336—611no—
392C61#2151211yescharacteristic, complemented, Sylow
393C22×Q8—611no—
394C22×Q8C22×D6111yescharacteristic
395C22×D4C22×D6111yescharacteristic
396C23×C4—21no—
397C2×Q16—614no—
398C2×Q16—1222no—
399C2×Q16—1222no—
400C2×SD16—614no—
401C2×SD16—1222no—
402C2×SD16—1222no—
403C22×C8—611no—
404C22×C8—611no—
405C22×C8—611no—
406C22×C8—611no—
407#124—22no—
408#124C4×D6114yes—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—614no—
412C4×Q8—614no—
413C4×Q8—1222no—
414C4×Q8—1222no—
415C4×Q8—1222no—
416C4×Q8—1222no—
417C4×D4—22no—
418C4×D4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4C22×D6111yescharacteristic
429C2×C4⋊C4C22×D6111yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C42—21no—
436C2×C42—1221no—
437C2×C42—1221no—
438C2×C42—1221no—
439C2×C42—1221no—
440C2×C42—1221no—
441C2×C42—1221no—
442C2×C42C22×D6111yescharacteristic
443C2×C42C22×D6111yescharacteristic
444C2×C42C22×D6111yescharacteristic
445#107—1222no—
446#107—1222no—
447C4⋊C8—614no—
448C4⋊C8—1222no—
449#103—614no—
450#103—1222no—
451#103—1222no—
452#103—1222no—
453#103—1222no—
454#102—614no—
455#102—1222no—
456#102—1222no—
457#97—1222no—
458C4×C8—1222no—
459#95—21no—
460#95—21no—
461#95—1221no—
462#95—1221no—
463#95—1221no—
464#95C22⋊D6111yescharacteristic
465#95C22⋊D6111yescharacteristic
466#95C22⋊D6111yescharacteristic
467#95C22⋊D6111yescharacteristic
468C24—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—612no—
475C2×Q8—612no—
476C2×Q8—612no—
477C2×Q8—1221no—
478C2×Q8—1221no—
479C2×Q8—1221no—
480C2×Q8C2×C4×D6112yes—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4C2×C4×D6112yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—81no—
492C22×C4—81no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4C2×C22⋊D6111yescharacteristic
498C22×C4C2×C22⋊D6111yescharacteristic
499C22×C4C2×C22⋊D6111yescharacteristic
500C22×C4C2×C22⋊D6111yescharacteristic
501C22×C4C2×C22⋊D6111yescharacteristic
502C22×C4C2×C22⋊D6111yescharacteristic
503C22×C4C23×D6111yescharacteristic
504Q16—1228no—
505SD16—1228no—
506C2×C8—612no—
507C2×C8—612no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—81no—
524C4⋊C4—81no—
525C4⋊C4—612no—
526C4⋊C4—612no—
527C4⋊C4—612no—
528C4⋊C4—1224no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—1224no—
533C4⋊C4—1224no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—42no—
537C22⋊C4—81no—
538C22⋊C4—81no—
539C42—21no—
540C42—21no—
541C42—42no—
542C42—1224no—
543C42—1224no—
544C42—1224no—
545C42—4881no—
546C42—4881no—
547C42—4881no—
548C42C2×C4×D6112yes—
549C42#1175822212yes—
550C42D4×D6112yes—
551C42#1175822412yes—
552C23—22no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23C22×C22⋊D6111yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—41no—
563Q8—41no—
564Q8—614no—
565Q8—1222no—
566Q8—1222no—
567Q8—1222no—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—1222no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—2441no—
603C2×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4C4×C22⋊D6112yes—
609C2×C4C4×C22⋊D6112yes—
610C2×C4#1451974812yes—
611C2×C4#1451974812yes—
612C2×C4C22×C4×D6111yescharacteristic
613C2×C4C2×D4×D6111yescharacteristic
614C2×C4#41×D6111yescharacteristic
615C2×C4#41×D6111yescharacteristic
616C2×C4C2×#1175822411yescharacteristic
617C2×C4C2×#1175822211yescharacteristic
618C8—1222no—
619C8—1222no—
620C8—2441no—
621C8—2441no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—81no—
629C22C2×C4×C22⋊D6111yescharacteristic
630C22C2×#1451974811yescharacteristic
631C22#1684026911yescharacteristic
632C22#1684056511yescharacteristic
633C22#1684057311yescharacteristic
634C22#1684057711yescharacteristic
635C22#1684057711yescharacteristic
636C4—22no—
637C4—22no—
638C4—22no—
639C4—22no—
640C4—42no—
641C4—41no—
642C4—41no—
643C4—81no—
644C4—81no—
645C4—1224no—
646C4—2442no—
647C4—2442no—
648C4—2442no—
649C4C4×D4×D6111yescharacteristic
650C4C4×#1175822411yescharacteristic
651C4#1684029411yescharacteristic
652C4#1684030911yescharacteristic
653C2—82no—
654C2C4×#1451974811yescharacteristic
655C2#2145465811yescharacteristic
656C2#2145469211yescharacteristic
657C2#2145534511yescharacteristic
658C2#2145535411yescharacteristic
659C2#2145604211yescharacteristic
660C2#2145607511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2326C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenter#2326D61
hypocenterC61#21512
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ #376 ◁ #2326

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758202C2semidirect
4. #21448182C2semidirect
6. #21446575C2semidirect
7. #21446457C2semidirect
10. #21446163C2semidirect
11. #21445821C2semidirect
12. #21445676C2semidirect
13. #21445649C2semidirect
21. #16839981C4semidirect
65. C2×#11758202C2×C4semidirect
77. C4×Dic122C2×C4semidirect
94. C4⋊#92418C2×C4semidirect
97. #14519701C2×C4semidirect
392. C61#21512semidirect

Maximal subgroups

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

subgroupindex
C2×#168399812
C2×#168398622
C2×C4×#117582022
#214481822
#214467522
#214465752
#214464572
#214464362
#214461772
#214461632
#214458212
#214456762
#214456492
C4×#145196982
C61×#23262
#2151261