Finite Group Databasebeta

← #29709558

Subgroups — #29709558

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758201C211yesmaximal, characteristic, complemented
2C2×#16839823C211yesmaximal, characteristic, complemented
3#21448512C211yesmaximal, characteristic
4#21447320C211yesmaximal, characteristic, complemented
5#21447255C211yesmaximal, characteristic, complemented
6#21447200C211yesmaximal, characteristic, complemented
7#21447190C211yesmaximal, characteristic, complemented
8#21447134C211yesmaximal, characteristic, complemented
9#21447012C211yesmaximal, characteristic, complemented
10#21447008C211yesmaximal, characteristic
11#21446820C211yesmaximal, characteristic
12C4×#14519708C211yesmaximal, characteristic, complemented
13#21445649C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic, complemented
15C61×#2323C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×#14519751C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C4×#11758201—24no—
20#16839823—24no—
21C2×#14519708C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519697C2211yescharacteristic
30C2×#14519697C2211yescharacteristic
31C2×#14519697C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×#14519688C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic
36#16839664C2211yescharacteristic
37#16839662—21no—
38#16839660C2211yescharacteristic
39#16839652—21no—
40#16839638—21no—
41#16839633—21no—
42#16839622C2211yescharacteristic
43C4×C4⋊Dic61C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50C2×C22⋊Q8×C61C2211yescharacteristic
51C2×C4×Q8×C61C2211yescharacteristic
52C2×#117×C61C2211yescharacteristic
53C61×#391C2211yescharacteristic
54C61×#389—21no—
55C61×#389C2211yescharacteristic
56C61×#388—21no—
57C61×#388—21no—
58C61×#387—21no—
59C61×#380C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C22×D244C2311yescharacteristic
62C22×C22⋊D61—21no—
63C22×C4×D61—21no—
64C2×#11758201—22no—
65C2×#11758201—22no—
66C2×#11758201—22no—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71#14519751—22no—
72#14519751—22no—
73C4×D244—22no—
74C4×D244—22no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×C22⋊Dic61—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×C4×Dic61—21no—
85#14519708—22no—
86#14519708—22no—
87#14519708—22no—
88C4⋊#92418—22no—
89C4⋊#92418—22no—
90#14519701—22no—
91#14519701—22no—
92#14519701—22no—
93#14519697—22no—
94#14519697—22no—
95#14519697—22no—
96C22⋊#92418—22no—
97C22⋊#92418—22no—
98#14519688—22no—
99C4×#92418D414yescomplemented
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103C22×Q8×C61C2311yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C22⋊Q8×C61—22no—
106C22⋊Q8×C61—22no—
107C4×Q8×C61—22no—
108C4×Q8×C61—22no—
109#117×C61—22no—
110#117×C61—22no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61—21no—
114C2×C4⋊C4×C61D411yescharacteristic
115C2×C4⋊C4×C61D411yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C22⋊C4×C61—21no—
120C2×C22⋊C4×C61—21no—
121C2×C22⋊C4×C61D411yescharacteristic
122C2×C22⋊C4×C61D411yescharacteristic
123C2×C42×C61—21no—
124C2×C42×C61—21no—
125C2×C42×C61C2311yescharacteristic
126C2×C42×C61C2311yescharacteristic
127#95×C61—21no—
128#95×C61—21no—
129#95×C61—21no—
130#95×C61—21no—
131#95×C61—21no—
132C24×C61C2×D411yescharacteristic
133C23×D61—21no—
134C2×Q8×C61—21no—
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61#4112yes—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—21no—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—24no—
157C2×C22⋊D61—81no—
158C2×C22⋊D61—81no—
159C22×Dic61—21no—
160C22×Dic61—21no—
161C22×Dic61—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244—21no—
166C2×D244—21no—
167C2×D244#4112yes—
168C2×C4×D61—42no—
169C2×C4×D61—81no—
170C2×C4×D61—81no—
171C4⋊C4×C61—24no—
172C4⋊C4×C61—22no—
173C4⋊C4×C61—22no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—42no—
180C4⋊C4×C61—81no—
181C4⋊C4×C61#4112yes—
182C22⋊C4×C61—24no—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—81no—
186C42×C61—21no—
187C42×C61—21no—
188C42×C61—42no—
189C42×C61—81no—
190C42×C61C2×D412yes—
191C42×C61#4112yes—
192C22⋊Dic61—81no—
193#11758201—28no—
194#11758198—24no—
195#11758198—42no—
196#11758198—81no—
197#11758198—81no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61#4112yes—
204#11758196—81no—
205C4×Dic61—81no—
206C2×#92418—21no—
207C2×#92418—21no—
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×#92418C2×D412yes—
217C2×#92418C2×D412yes—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61C22×D411yescharacteristic
226C22×D61—22no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61—41no—
230C22×D61—41no—
231C22×D61—41no—
232C22×D61—41no—
233Q8×C61—22no—
234Q8×C61—22no—
235Q8×C61—41no—
236Q8×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—22no—
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—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61#12112yes—
267C2×C4×C61#12112yes—
268C2×C4×C61C22×D411yescharacteristic
269C2×C4×C61C2×#4111yescharacteristic
270C2×C4×C61C2×#4111yescharacteristic
271C2×C4×C61C2×#4111yescharacteristic
272C2×C4×C61C2×#4111yescharacteristic
273C2×C4×C61C2×#4111yescharacteristic
274C22⋊D61—84no—
275C2×Dic61—22no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—41no—
284D244—22no—
285D244—22no—
286D244—41no—
287D244—41no—
288C4×D61—84no—
289#92418—22no—
290#92418—22no—
291#92418—41no—
292#92418—41no—
293#23707—611nomaximal, Sylow
294C22×C61—41no—
295C22×C61—41no—
296C22×C61—41no—
297C22×C61—41no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61C2×#12111yescharacteristic
302C22×C61#52511yescharacteristic
303C22×C61#52511yescharacteristic
304C22×C61#57711yescharacteristic
305C22×C61#57711yescharacteristic
306C22×C61#57711yescharacteristic
307C22×C61#57711yescharacteristic
308C2×D61—42no—
309C2×D61—42no—
310C2×D61—42no—
311C2×D61—81no—
312C2×D61—81no—
313C2×D61—81no—
314C2×D61—81no—
315C4×C61—22no—
316C4×C61—22no—
317C4×C61—42no—
318C4×C61—41no—
319C4×C61—42no—
320C4×C61—41no—
321C4×C61—41no—
322C4×C61—81no—
323C4×C61—81no—
324C4×C61#52511yescharacteristic
325C4×C61#52911yescharacteristic
326C4×C61#52911yescharacteristic
327C4×C61#53211yescharacteristic
328Dic61—42no—
329Dic61—81no—
330Dic61—81no—
331C2×C4×SD16—611no—
332C2×#433—611no—
333#2324—611no—
334#2323D6111yescharacteristic, complemented
335#2088—611no—
336#2077—611no—
337#2066—611no—
338#2065—611no—
339#2055—611no—
340#2035—611no—
341#2034—611no—
342#2000—611no—
343C4×#106—611no—
344#1763—611no—
345#1762—611no—
346C2×C61—81no—
347C2×C61#239211yescharacteristic
348C2×C61#305711yescharacteristic
349C2×C61#306011yescharacteristic
350C2×C61#312311yescharacteristic
351C2×C61#312511yescharacteristic
352C2×C61#312511yescharacteristic
353C2×C61#312611yescharacteristic
354D61—82no—
355C22×SD16—611no—
356C2×C22⋊Q8C2×D6111yescharacteristic
357C2×#121—611no—
358C2×C4×Q8C2×D6111yescharacteristic
359C2×C4×D4—611no—
360C2×#117C2×D6111yescharacteristic
361C4×SD16—1224no—
362#433—1224no—
363C2×#106—611no—
364C2×#106—611no—
365C2×#106—611no—
366C2×C4⋊C8—611no—
367C2×C4⋊C8—611no—
368C2×#103—611no—
369C2×#103—611no—
370C2×#103—611no—
371C2×#102—611no—
372C2×#102—611no—
373C2×#102—611no—
374C2×C22⋊C8—611no—
375C2×C22⋊C8—611no—
376C2×#97—611no—
377C2×C4×C8—611no—
378#391C2×D6111yescharacteristic
379#390—611no—
380#390—1221no—
381#389—21no—
382#389—611no—
383#389C2×D6111yescharacteristic
384#388—21no—
385#388—21no—
386#388—1221no—
387#387—21no—
388#386—1221no—
389#385—1221no—
390#380—611no—
391#380C2×D6111yescharacteristic
392C4×C4⋊C4—611no—
393C4×C4⋊C4C2×D6111yescharacteristic
394#340—611no—
395#340—611no—
396#340—611no—
397#340—611no—
398#340—611no—
399#340—611no—
400C61#2370711yescharacteristic, complemented, Sylow
401C22×Q8C22×D6111yescharacteristic
402C22×D4—611no—
403C22×D4—1221no—
404C23×C4—1221no—
405C23×C4C22×D6111yescharacteristic
406C2×SD16—1222no—
407C2×SD16—1222no—
408C2×SD16—1222no—
409C22×C8—611no—
410C22×C8—611no—
411C22×C8—611no—
412C22×C8—611no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415#121—1222no—
416#121—1222no—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×D4—1222no—
420C4×D4—1222no—
421#117—22no—
422#117—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—611no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4C22⋊D6111yescharacteristic
431C2×C4⋊C4C22⋊D6111yescharacteristic
432C2×C4⋊C4C22×D6111yescharacteristic
433C2×C4⋊C4C22×D6111yescharacteristic
434C2×C4⋊C4C22×D6111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—1221no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4C22⋊D6111yescharacteristic
443C2×C22⋊C4C22⋊D6111yescharacteristic
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—1221no—
447C2×C42C22×D6111yescharacteristic
448C2×C42C22×D6111yescharacteristic
449#106—1222no—
450#106—1222no—
451#106—1222no—
452C4⋊C8—1222no—
453C4⋊C8—1222no—
454#103—1222no—
455#103—1222no—
456#103—1222no—
457#102—1222no—
458#102—1222no—
459#102—1222no—
460C22⋊C8—1222no—
461C22⋊C8—1222no—
462#97—1222no—
463C4×C8—614no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—1221no—
470#95—1221no—
471#95—1221no—
472C24—1221no—
473C24C2×C22⋊D6111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8#1175822212yes—
480C2×D4—612no—
481C2×D4—1224no—
482C2×D4—1221no—
483C2×D4—1221no—
484C2×D4—1221no—
485C2×D4—1221no—
486C2×D4—1221no—
487C2×D4—4881no—
488C2×D4—4881no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4—4881no—
503C22×C4—4881no—
504C22×C4—2442no—
505C22×C4C2×C22⋊D6111yescharacteristic
506C22×C4C2×C22⋊D6111yescharacteristic
507C22×C4C2×C22⋊D6111yescharacteristic
508C22×C4C2×C22⋊D6111yescharacteristic
509C22×C4C2×C22⋊D6111yescharacteristic
510C22×C4C23×D6111yescharacteristic
511SD16—1228no—
512C2×C8—612no—
513C2×C8—612no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C4⋊C4—24no—
525C4⋊C4—21no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4—612no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—4881no—
541C4⋊C4#1175822212yes—
542C22⋊C4—24no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—81no—
546C22⋊C4—1224no—
547C22⋊C4—4881no—
548C22⋊C4—4881no—
549C22⋊C4—4881no—
550C22⋊C4—2442no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—81no—
555C42—4881no—
556C42D4×D6112yes—
557C42#1175822412yes—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—1222no—
566C23—2441no—
567C23—2441no—
568C23—2441no—
569C23—2441no—
570C23—2441no—
571C23—2441no—
572C23C22×C22⋊D6111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—1222no—
578D4—1222no—
579D4—4884no—
580D4—2441no—
581D4—2441no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—1222no—
612C2×C4—4884no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4#1451974912yes—
622C2×C4#1451974912yes—
623C2×C4C2×D4×D6111yescharacteristic
624C2×C4#41×D6111yescharacteristic
625C2×C4#41×D6111yescharacteristic
626C2×C4C2×#1175822411yescharacteristic
627C2×C4C2×#1175822211yescharacteristic
628C2×C4C2×#1175822211yescharacteristic
629C8—1222no—
630C8—1222no—
631C8—2441no—
632C8—2441no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—4881no—
641C22—4881no—
642C22—4881no—
643C22—4881no—
644C22—2442no—
645C22—2442no—
646C22—2442no—
647C22C2×#1451974911yescharacteristic
648C22#1684026911yescharacteristic
649C22#1684027311yescharacteristic
650C22#1684057011yescharacteristic
651C22#1684057011yescharacteristic
652C22#1684057011yescharacteristic
653C22#1684057311yescharacteristic
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—42no—
659C4—41no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—4881no—
664C4—4881no—
665C4—2442no—
666C4#1684027111yescharacteristic
667C4#1684029211yescharacteristic
668C4#1684029411yescharacteristic
669C4#1684030911yescharacteristic
670C2—81no—
671C2—4882no—
672C2#2144906111yescharacteristic
673C2#2145546011yescharacteristic
674C2#2145547811yescharacteristic
675C2#2145606611yescharacteristic
676C2#2145609011yescharacteristic
677C2#2145609611yescharacteristic
678C2#2145611011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2323C2
socleC23×C61C22×D4
prime radicalC2×#14519751C22
hypercenter#2323D61
hypocenterC61#23707
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
1. C2×C4×#11758201C2semidirect
2. C2×#16839823C2semidirect
4. #21447320C2semidirect
5. #21447255C2semidirect
6. #21447200C2semidirect
7. #21447190C2semidirect
8. #21447134C2semidirect
9. #21447012C2semidirect
12. C4×#14519708C2semidirect
13. #21445649C2semidirect
14. #21445647C2semidirect
15. C61×#2323C2semidirect
99. C4×#92418D4semidirect
334. #2323D61semidirect
400. C61#23707semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117582012
C2×#168398232
#214485122
#214473202
#214472552
#214472002
#214471902
#214471342
#214470122
#214470082
#214468202
C4×#145197082
#214456492
#214456472
C61×#23232
#2370761