Finite Group Databasebeta

← #29698359

Subgroups — #29698359

Order 15616.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839862C211yesmaximal, characteristic
2C2×#16839862C211yesmaximal, characteristic
3C2×C4×#11758200C211yesmaximal, characteristic
4#21448739C211yesmaximal, characteristic, complemented
5#21446554C211yesmaximal, characteristic, complemented
6#21446549C211yesmaximal, characteristic, complemented
7#21446086C211yesmaximal, characteristic, complemented
8#21446080C211yesmaximal, characteristic
9#21446072C211yesmaximal, characteristic, complemented
10#21446066C211yesmaximal, characteristic
11#21445985C211yesmaximal, characteristic, complemented
12#21445829C211yesmaximal, characteristic
13#21445821C211yesmaximal, characteristic, complemented
14#21445694C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C61C211yesmaximal, characteristic
16C22×#11758200C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×C4×Dic122C2211yescharacteristic
19C2×C4×Dic122C2211yescharacteristic
20#16839862—24no—
21#16839862C418yescomplemented
22C4×#11758200—24no—
23C2×#14519710C2211yescharacteristic
24C2×#14519710C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519700C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519688C2211yescharacteristic
36C2×#14519688C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic
38#16839660C2211yescharacteristic
39#16839660C2211yescharacteristic
40#16839657—21no—
41#16839657—21no—
42#16839628C2211yescharacteristic
43#16839626—21no—
44#16839613—21no—
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839517C2211yescharacteristic
50#16839517C2211yescharacteristic
51C2×C4×D4×C61C2211yescharacteristic
52C2×C4×D4×C61C2211yescharacteristic
53C2×C4×D4×C61C2211yescharacteristic
54C22×C4⋊C4×C61—21no—
55C61×#389C2211yescharacteristic
56C61×#389C2211yescharacteristic
57C61×#385—21no—
58C61×#385—21no—
59C61×#384C2211yescharacteristic
60C61×#380—21no—
61C4×C4⋊C4×C61C2211yescharacteristic
62C22×Dic122C2311yescharacteristic
63C2×#11758200C2×C414yes—
64C2×#11758200D414yes—
65C2×#11758200Q814yes—
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C4×Dic122—22no—
71C4×Dic122—22no—
72C4×Dic122—22no—
73C4×Dic122—41no—
74C4×Dic122—41no—
75C4×Dic122C2×C414yescomplemented
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87#14519710—22no—
88#14519710—41no—
89#14519710C2×C414yescomplemented
90#14519708—22no—
91#14519708—41no—
92C4⋊#92418—22no—
93#14519700—22no—
94#14519700—22no—
95#14519700C2×C414yescomplemented
96#14519698—22no—
97#14519698—22no—
98#14519698C2×C414yes—
99#14519688—22no—
100#14519688C2×C414yescomplemented
101C4×#92418—22no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106C22×D4×C61C2311yescharacteristic
107C23×C4×C61—21no—
108C23×C4×C61—21no—
109C23×C4×C61—21no—
110C4×D4×C61—22no—
111C4×D4×C61—22no—
112C4×D4×C61—22no—
113C4×D4×C61—41no—
114C4×D4×C61—41no—
115C4×D4×C61C2×C414yes—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61—21no—
119C2×C4⋊C4×C61—21no—
120C2×C4⋊C4×C61—44no—
121C2×C4⋊C4×C61D411yescharacteristic
122C2×C4⋊C4×C61D411yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C42×C61C2311yescharacteristic
130C2×C42×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132#95×C61—21no—
133#95×C61—21no—
134#95×C61D411yescharacteristic
135#95×C61D411yescharacteristic
136C24×C61—21no—
137C2×D4×C61—21no—
138C2×D4×C61—21no—
139C2×D4×C61—21no—
140C2×D4×C61C22×C412yes—
141C2×D4×C61C2×D412yes—
142C2×D4×C61C2×Q812yes—
143C22×C4×C61—21no—
144C22×C4×C61—24no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—42no—
148C22×C4×C61—42no—
149C22×C4×C61—42no—
150C22×C4×C61—42no—
151C22×C4×C61—42no—
152C22×C4×C61—42no—
153C22×C4×C61—81no—
154C22×C4×C61—81no—
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61C2×D411yescharacteristic
159C22×C4×C61C2×D411yescharacteristic
160C22×C4×C61C2×D411yescharacteristic
161C22×C4×C61C2411yescharacteristic
162C22×Dic61—21no—
163C22×Dic61—21no—
164C22×Dic61—21no—
165C22×Dic61—21no—
166C2×Dic122—21no—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122C22×C412yes—
170C2×Dic122C2×D412yes—
171C2×Dic122C2×Q812yes—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—42no—
180C4⋊C4×C61—42no—
181C4⋊C4×C61—42no—
182C4⋊C4×C61—81no—
183C4⋊C4×C61C22×C412yes—
184C22⋊C4×C61—24no—
185C22⋊C4×C61—42no—
186C22⋊C4×C61—42no—
187C42×C61—21no—
188C42×C61—21no—
189C42×C61—21no—
190C42×C61—21no—
191C42×C61C22×C412yes—
192C42×C61#4112yes—
193#11758200C4⋊C4116yescomplemented
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61C22×C412yes—
200#11758196—24no—
201#11758196—42no—
202#11758196—42no—
203#11758196—42no—
204#11758196—42no—
205C4×Dic61—24no—
206C4×Dic61—42no—
207C4×Dic61—42no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418C22×C412yes—
217C2×#92418C22×C412yes—
218C2×#92418C2×D412yes—
219C2×#92418C2×Q812yes—
220C23×C61—22no—
221C23×C61—22no—
222C23×C61—22no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61—41no—
226C23×C61—41no—
227C23×C61C22×D411yescharacteristic
228D4×C61—22no—
229D4×C61—22no—
230D4×C61—22no—
231D4×C61C2×C4⋊C414yes—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—22no—
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—21no—
246C2×C4×C61—21no—
247C2×C4×C61—21no—
248C2×C4×C61—48no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61—84no—
258C2×C4×C61—84no—
259C2×C4×C61C4×D412yes—
260C2×C4×C61C4×D412yes—
261C2×C4×C61AGL(1,ℤ/8)12yes—
262C2×C4×C61C23×C411yescharacteristic
263C2×C4×C61C22×D411yescharacteristic
264C2×C4×C61C22×Q811yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61H(5,𝔽2)11yescharacteristic
267C2×C4×C612−1+411yescharacteristic
268C2×Dic61—22no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—22no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280Dic122—22no—
281Dic122—22no—
282Dic122—22no—
283Dic122C2×C4⋊C414yescomplemented
284#92418—22no—
285#92418—41no—
286#92418—41no—
287#92418C2×C4⋊C414yescomplemented
288#22677—611nomaximal, Sylow
289C22×C61—24no—
290C22×C61—42no—
291C22×C61—42no—
292C22×C61—42no—
293C22×C61—42no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61C2×C4×D411yescharacteristic
297C22×C61D4211yescharacteristic
298C22×C61D4×Q811yescharacteristic
299C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C61#57511yescharacteristic
301C22×C61#57711yescharacteristic
302C22×C61#57811yescharacteristic
303C4×C61—22no—
304C4×C61—22no—
305C4×C61—22no—
306C4×C61—42no—
307C4×C61—41no—
308C4×C61—41no—
309C4×C61—41no—
310C4×C61—81no—
311C4×C61—81no—
312C4×C61C22×C4⋊C411yescharacteristic
313C4×C61#52011yescharacteristic
314C4×C61#54711yescharacteristic
315C4×C61#55411yescharacteristic
316Dic61—24no—
317Dic61—42no—
318Dic61—81no—
319Dic61—81no—
320C2×#440—611no—
321C2×#440—611no—
322C2×C4×SD16—611no—
323#2351—611no—
324D4×C4⋊C4D6111yescharacteristic
325#1943—611no—
326#1942—611no—
327#1865—611no—
328#1864—611no—
329#1863—611no—
330#1862—611no—
331#1847—611no—
332#1804—611no—
333#1803—611no—
334#1771—611no—
335C2×C61—44no—
336C2×C61D4×C4⋊C411yescharacteristic
337C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
338C2×C61#294711yescharacteristic
339C2×C61#326511yescharacteristic
340C2×C61#326911yescharacteristic
341C2×C61#338611yescharacteristic
342C2×C61#338811yescharacteristic
343C22×SD16—611no—
344C2×C4×Q8—611no—
345C2×C4×Q8—611no—
346C2×C4×Q8—611no—
347C2×C4×D4C2×D6111yescharacteristic
348C2×C4×D4C2×D6111yescharacteristic
349C2×C4×D4C2×D6111yescharacteristic
350C22×C4⋊C4—21no—
351#440—618no—
352#440—1224no—
353C4×SD16—1224no—
354C2×#107—611no—
355C2×#107—611no—
356C2×#107—611no—
357C2×#106—611no—
358C2×#106—611no—
359C2×C4⋊C8—611no—
360C2×#103—611no—
361C2×#103—611no—
362C2×#103—611no—
363C2×#102—611no—
364C2×#102—611no—
365C2×#102—611no—
366C2×#97—611no—
367C2×#97—611no—
368C2×C4×C8—611no—
369#389—611no—
370#389—611no—
371#389—1221no—
372#389—1221no—
373#389C2×D6111yescharacteristic
374#389C2×D6111yescharacteristic
375#385—21no—
376#385—21no—
377#384C2×D6111yescharacteristic
378#382—611no—
379#382—1221no—
380#380—21no—
381C4×C4⋊C4—1221no—
382C4×C4⋊C4C2×D6111yescharacteristic
383#340—611no—
384#340—611no—
385#340—611no—
386#340—611no—
387#336—611no—
388#336—611no—
389C61#2267711yescharacteristic, complemented, Sylow
390C22×Q8—611no—
391C22×D4C22×D6111yescharacteristic
392C23×C4—21no—
393C23×C4—21no—
394C23×C4—21no—
395C2×SD16—614no—
396C2×SD16—614no—
397C2×SD16—614no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8—611no—
401C22×C8—611no—
402C4×Q8—614no—
403C4×Q8—1222no—
404C4×Q8—1222no—
405C4×Q8—1222no—
406C4×Q8—2441no—
407C4×Q8—2441no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—22no—
411C4×D4—41no—
412C4×D4—41no—
413C4×D4C4×D6114yes—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—44no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—1221no—
423C2×C4⋊C4—1221no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4C22⋊D6111yescharacteristic
428C2×C4⋊C4C22⋊D6111yescharacteristic
429C2×C4⋊C4C22×D6111yescharacteristic
430C2×C4⋊C4C22×D6111yescharacteristic
431C2×C4⋊C4C22×D6111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C42—1221no—
436C2×C42—1221no—
437C2×C42—1221no—
438C2×C42C22×D6111yescharacteristic
439C2×C42C22×D6111yescharacteristic
440C2×C42C22×D6111yescharacteristic
441#107—614no—
442#107—1222no—
443#107—2441no—
444#106—1222no—
445#106—2441no—
446C4⋊C8—1222no—
447#103—614no—
448#103—1222no—
449#103—1222no—
450#102—614no—
451#102—1222no—
452#102—1222no—
453#97—614no—
454#97—1222no—
455C4×C8—1222no—
456#95—21no—
457#95—21no—
458#95—1221no—
459#95—1221no—
460#95—1221no—
461#95—1221no—
462#95C22⋊D6111yescharacteristic
463#95C22⋊D6111yescharacteristic
464C24—21no—
465C2×Q8—612no—
466C2×Q8—612no—
467C2×Q8—612no—
468C2×Q8—1221no—
469C2×Q8—1221no—
470C2×Q8—1221no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4C2×C4×D6112yes—
475C2×D4D4×D6112yes—
476C2×D4Q8×D6112yes—
477C22×C4—21no—
478C22×C4—24no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4C2×C22⋊D6111yescharacteristic
494C22×C4C2×C22⋊D6111yescharacteristic
495C22×C4C2×C22⋊D6111yescharacteristic
496C22×C4C2×C22⋊D6111yescharacteristic
497C22×C4C2×C22⋊D6111yescharacteristic
498C22×C4C2×C22⋊D6111yescharacteristic
499C22×C4C23×D6111yescharacteristic
500SD16—6116no—
501C2×C8—612no—
502C2×C8—612no—
503C2×C8—612no—
504C2×C8—612no—
505C2×C8—1221no—
506C2×C8—1221no—
507C2×C8—1221no—
508C2×C8—1221no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—41no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—81no—
524C4⋊C4—612no—
525C4⋊C4—1221no—
526C4⋊C4—1224no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—2442no—
532C4⋊C4—2442no—
533C4⋊C4—2442no—
534C4⋊C4—2442no—
535C4⋊C4C2×C4×D6112yes—
536C22⋊C4—24no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—1224no—
544C42—2442no—
545C42—2442no—
546C42C2×C4×D6112yes—
547C42#1175822212yes—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23C22×C22⋊D6111yescharacteristic
556Q8—614no—
557Q8—1222no—
558Q8—1222no—
559Q8—1222no—
560D4—22no—
561D4—22no—
562D4—22no—
563D4C4⋊C4×D6114yes—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
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—48no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—84no—
591C2×C4—1222no—
592C2×C4—1222no—
593C2×C4—1222no—
594C2×C4—1222no—
595C2×C4—2441no—
596C2×C4—2441no—
597C2×C4—2441no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4—2441no—
601C2×C4—2441no—
602C2×C4—2441no—
603C2×C4C4×C22⋊D6112yes—
604C2×C4C4×C22⋊D6112yes—
605C2×C4#1451980312yes—
606C2×C4C22×C4×D6111yescharacteristic
607C2×C4C2×D4×D6111yescharacteristic
608C2×C4C2×Q8×D6111yescharacteristic
609C2×C4C2×#1175822211yescharacteristic
610C2×C4#1451982211yescharacteristic
611C2×C4#1451982511yescharacteristic
612C8—614no—
613C8—1222no—
614C8—2441no—
615C8—2441no—
616C22—24no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22C2×C4×C22⋊D6111yescharacteristic
624C22D4×C22⋊D6111yescharacteristic
625C22Q8×C22⋊D6111yescharacteristic
626C22C2×#1451980311yescharacteristic
627C22#1684056011yescharacteristic
628C22#1684057311yescharacteristic
629C22#1684057711yescharacteristic
630C4—22no—
631C4—22no—
632C4—22no—
633C4—42no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—1224no—
640C4—4881no—
641C4—4881no—
642C4—2442no—
643C4C2×C4⋊C4×D6111yescharacteristic
644C4#1684024311yescharacteristic
645C4#1684041311yescharacteristic
646C4#1684046711yescharacteristic
647C2—44no—
648C2C4⋊C4×C22⋊D6111yescharacteristic
649C2C4×#1451980311yescharacteristic
650C2#2145465811yescharacteristic
651C2#2145731011yescharacteristic
652C2#2145737011yescharacteristic
653C2#2145874011yescharacteristic
654C2#2145876411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×C4⋊C4×C61C2
socleC23×C61C22×D4
prime radicalC22×D4×C61C23
cosocleC22×C4×C61C24
hypercenterD4×C4⋊C4D61
hypocenterC61#22677
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #21448739C2semidirect
5. #21446554C2semidirect
6. #21446549C2semidirect
7. #21446086C2semidirect
9. #21446072C2semidirect
11. #21445985C2semidirect
13. #21445821C2semidirect
14. #21445694C2semidirect
21. #16839862C4semidirect
75. C4×Dic122C2×C4semidirect
89. #14519710C2×C4semidirect
95. #14519700C2×C4semidirect
100. #14519688C2×C4semidirect
193. #11758200C4⋊C4semidirect
283. Dic122C2×C4⋊C4semidirect
287. #92418C2×C4⋊C4semidirect
389. C61#22677semidirect

Maximal subgroups

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

subgroupindex
C2×#168398622
C2×C4×#117582002
#214487392
#214465542
#214465492
#214460862
#214460802
#214460722
#214460662
#214459852
#214458292
#214458212
#214456942
D4×C4⋊C4×C612
#2267761