Finite Group Databasebeta

← #29730183

Subgroups — #29730183

Order 15616.

850 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840069C211yesmaximal, characteristic, complemented
2C2×C8×D244C211yesmaximal, characteristic
3#21450980C211yesmaximal, characteristic
4#21450724C211yesmaximal, characteristic
5#21447257C211yesmaximal, characteristic, complemented
6#21447246C211yesmaximal, characteristic, complemented
7#21447020C211yesmaximal, characteristic, complemented
8#21447013C211yesmaximal, characteristic, complemented
9#21446784C211yesmaximal, characteristic, complemented
10#21446587C211yesmaximal, characteristic, complemented
11#21446239C211yesmaximal, characteristic, complemented
12#21446239C211yesmaximal, characteristic, complemented
13#21445847C211yesmaximal, characteristic, complemented
14#21445843C211yesmaximal, characteristic, complemented
15C4×#103×C61C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C2×#14519769C2211yescharacteristic
19C2×#14519753C2211yescharacteristic
20C2×#14519753C2211yescharacteristic
21C2×C4×D244C2211yescharacteristic
22#16840069—24no—
23C8×D244—24no—
24C2×#14519710C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33#16839702—21no—
34#16839692—21no—
35#16839680—21no—
36#16839679—21no—
37#16839653—21no—
38#16839653—21no—
39#16839653—21no—
40#16839653—21no—
41#16839628C2211yescharacteristic
42#16839619C2211yescharacteristic
43#16839619C2211yescharacteristic
44#16839619C2211yescharacteristic
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47#16839619C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×C4×Q8×C61C2211yescharacteristic
55C2×#103×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×C4×C8×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×D244D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C2×C8×D61—22no—
67C2×C8×D61—22no—
68C2×C8×D61—22no—
69C2×C8×D61—22no—
70C2×C8×D61—41no—
71C2×C8×D61—41no—
72#14519769—22no—
73#14519769—22no—
74#14519753—22no—
75#14519753—22no—
76#14519753—41no—
77#14519753—41no—
78C4×D244—22no—
79C4×D244—22no—
80C2×C4⋊Dic61D411yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—21no—
96C2×#11758198—21no—
97C2×#11758198D411yescharacteristic
98C2×#11758198D411yescharacteristic
99#14519710—22no—
100#14519710—41no—
101#14519708—22no—
102#14519708—41no—
103C4⋊#92418D414yes—
104#14519701—22no—
105#14519701—22no—
106#14519689—22no—
107#14519689—22no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116C22×Q8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C22×C8×C61C2311yescharacteristic
119C4×Q8×C61—22no—
120C4×Q8×C61—22no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61C2311yescharacteristic
123C2×C4⋊C4×C61C2311yescharacteristic
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C42×C61—21no—
126C2×C42×C61—21no—
127C2×C42×C61C2311yescharacteristic
128#103×C61—22no—
129#103×C61—22no—
130C4×C8×C61—22no—
131#95×C61—21no—
132C23×D61C2×D411yescharacteristic
133C23×D61C2×D411yescharacteristic
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×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
153C2×D244—22no—
154C2×D244—22no—
155C2×D244—22no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C8×C61—21no—
169C2×C8×C61—21no—
170C2×C8×C61—21no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61#4112yes—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—21no—
176C4⋊C4×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—42no—
181C42×C61—42no—
182C42×C61—81no—
183C42×C61C2×D412yes—
184C42×C61#4112yes—
185#11758198—22no—
186#11758198—22no—
187#11758198—42no—
188#11758198—42no—
189#11758198—42no—
190#11758198—42no—
191#11758198—42no—
192#11758198—42no—
193#11758198—81no—
194#11758198—81no—
195C4⋊Dic61—22no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204#11758196—42no—
205#11758196—42no—
206#11758196—42no—
207#11758196—42no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418C2×D412yes—
213C2×#92418C2×D412yes—
214C8×D61—44no—
215C8×D61—44no—
216C23×C61C22×D411yescharacteristic
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61—21no—
225C22×D61—21no—
226C22×D61—21no—
227C22×D61—21no—
228C22×D61—21no—
229C22×D61#13512yes—
230C22×D61#13512yes—
231Q8×C61—22no—
232Q8×C61—22no—
233Q8×C61—41no—
234Q8×C61—41no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—22no—
240C2×C4×C61—41no—
241C2×C4×C61—41no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61#12112yes—
252C2×C4×C61#12112yes—
253C2×C4×C61C22×D411yescharacteristic
254C2×C4×C61C2×#4111yescharacteristic
255C2×C4×C61C2×#4111yescharacteristic
256C2×C4×C61C2×#4111yescharacteristic
257C2×C4×C61H(5,𝔽2)11yescharacteristic
258C2×C4×C612−1+411yescharacteristic
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61—21no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—41no—
266C2×Dic61—41no—
267C2×Dic61—41no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277D244—28no—
278C4×D61—41no—
279C4×D61—41no—
280C4×D61—41no—
281C4×D61—41no—
282C4×D61—41no—
283C4×D61—41no—
284C4×D61—41no—
285C4×D61—41no—
286C8×C61—22no—
287C8×C61—41no—
288#92418—22no—
289#92418—22no—
290#25343—611nomaximal, Sylow
291C22×C61C2×#12111yescharacteristic
292C22×C61#54611yescharacteristic
293C22×C61#54711yescharacteristic
294C22×C61C2×#13511yescharacteristic
295C22×C61C2×#13511yescharacteristic
296C22×C61#57711yescharacteristic
297C22×C61#57811yescharacteristic
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—22no—
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—41no—
305C2×D61—41no—
306C2×D61—41no—
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C4×C61—22no—
313C4×C61—22no—
314C4×C61—42no—
315C4×C61—81no—
316C4×C61—81no—
317C4×C61—81no—
318C4×C61#52911yescharacteristic
319C4×C61#54211yescharacteristic
320C4×C61#54611yescharacteristic
321C4×C61#54811yescharacteristic
322Dic61—41no—
323Dic61—41no—
324Dic61—81no—
325Dic61—81no—
326Dic61—81no—
327Dic61—81no—
328C2×#479—611no—
329C2×C8×D4—611no—
330#2562—611no—
331#2536—611no—
332#2077—611no—
333#2075—611no—
334#2036—611no—
335#2035—611no—
336#1991—611no—
337#1949—611no—
338#1892—611no—
339#1892—611no—
340#1808—611no—
341#1807—611no—
342C4×#103D6111yescharacteristic, complemented
343C2×C61#242711yescharacteristic
344C2×C61#305011yescharacteristic
345C2×C61#306311yescharacteristic
346C2×C61#330011yescharacteristic
347C2×C61#330111yescharacteristic
348C2×C61#333611yescharacteristic
349C2×C61#333711yescharacteristic
350D61—42no—
351D61—42no—
352C23×C8—611no—
353C23×C8—611no—
354C2×#125—611no—
355C2×C22⋊Q8—611no—
356C2×C22⋊Q8—611no—
357C2×C4×Q8C2×D6111yescharacteristic
358C2×C4×D4—611no—
359#479—1224no—
360C8×D4—1224no—
361C2×#107—611no—
362C2×#107—611no—
363C2×#106—611no—
364C2×#106—611no—
365C2×C4⋊C8—611no—
366C2×#103—611no—
367C2×#103—611no—
368C2×#103C2×D6111yescharacteristic
369C2×#103C2×D6111yescharacteristic
370C2×C22⋊C8—611no—
371C2×C22⋊C8—611no—
372C2×C4×C8C2×D6111yescharacteristic
373#400—1221no—
374#398—1221no—
375#394—1221no—
376#394—1221no—
377#388—1221no—
378#388—1221no—
379#388—1221no—
380#388—1221no—
381#382—611no—
382#380—611no—
383#380—611no—
384#380—611no—
385#380—611no—
386#380—611no—
387#380—611no—
388C4×C4⋊C4C2×D6111yescharacteristic
389#340—611no—
390#340—611no—
391#340—611no—
392#340—611no—
393#340—611no—
394#340—611no—
395#340C2×D6111yescharacteristic
396#340C2×D6111yescharacteristic
397C61#2534311yescharacteristic, complemented, Sylow
398C22×Q8C22×D6111yescharacteristic
399C22×D4—611no—
400C23×C4—611no—
401C23×C4—611no—
402C22×C8—611no—
403C22×C8—611no—
404C22×C8—1222no—
405C22×C8—1222no—
406C22×C8—1222no—
407C22×C8—1222no—
408C22×C8—2441no—
409C22×C8—2441no—
410C22×C8C22×D6111yescharacteristic
411C22×C8C22×D6111yescharacteristic
412#125—1222no—
413#125—1222no—
414C22⋊Q8—1222no—
415C22⋊Q8—1222no—
416C22⋊Q8—2441no—
417C22⋊Q8—2441no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×D4—1222no—
421C4×D4—1222no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—611no—
424C2×C4⋊C4—611no—
425C2×C4⋊C4—611no—
426C2×C4⋊C4—611no—
427C2×C4⋊C4—611no—
428C2×C4⋊C4—1221no—
429C2×C4⋊C4—1221no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4C22×D6111yescharacteristic
433C2×C4⋊C4C22×D6111yescharacteristic
434C2×C4⋊C4C22×D6111yescharacteristic
435C2×C22⋊C4—611no—
436C2×C22⋊C4—611no—
437C2×C22⋊C4—1221no—
438C2×C22⋊C4—1221no—
439C2×C22⋊C4—1221no—
440C2×C22⋊C4—1221no—
441C2×C22⋊C4—1221no—
442C2×C22⋊C4—1221no—
443C2×C22⋊C4—1221no—
444C2×C22⋊C4—1221no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42C22×D6111yescharacteristic
448#107—1222no—
449#107—2441no—
450#106—1222no—
451#106—2441no—
452C4⋊C8—614no—
453#103—22no—
454#103—22no—
455#103—1222no—
456#103—1222no—
457C22⋊C8—1222no—
458C22⋊C8—1222no—
459C4×C8—22no—
460#95—21no—
461#95—1221no—
462#95—1221no—
463#95—1221no—
464#95—1221no—
465#95—1221no—
466#95—1221no—
467#95—1221no—
468#95—1221no—
469C24—611no—
470C24—611no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8#1175822212yes—
477C2×D4—1222no—
478C2×D4—1222no—
479C2×D4—1222no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1221no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1221no—
492C22×C4—1221no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1221no—
502C22×C4D4×D6111yescharacteristic
503C22×C4D4×D6111yescharacteristic
504C22×C4C23×D6111yescharacteristic
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—612no—
511C2×C8—612no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—2444no—
517C2×C8—2444no—
518C2×C8#1175822212yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—1222no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C4⋊C4—2442no—
536C4⋊C4—2442no—
537C4⋊C4—2442no—
538C4⋊C4—2442no—
539C22⋊C4—1222no—
540C22⋊C4—1222no—
541C22⋊C4—4881no—
542C22⋊C4—4881no—
543C22⋊C4—2442no—
544C22⋊C4—2442no—
545C22⋊C4—2442no—
546C22⋊C4—2442no—
547C22⋊C4—2442no—
548C22⋊C4—2442no—
549C42—42no—
550C42—81no—
551C42#1175822212yes—
552C42D4×D6112yes—
553C23—612no—
554C23—612no—
555C23—1221no—
556C23—1221no—
557C23—1221no—
558C23—1221no—
559C23—1221no—
560C23—1221no—
561C23—1221no—
562C23—1221no—
563C23—1221no—
564C23—1221no—
565C23—1221no—
566C23—1221no—
567C23C2×D4×D6111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—1228no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
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—1221no—
590C2×C4—1221no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
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×C4—2441no—
604C2×C4—2441no—
605C2×C4—2441no—
606C2×C4—2441no—
607C2×C4—2441no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2441no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4#1451975012yes—
616C2×C4#1451975012yes—
617C2×C4C2×D4×D6111yescharacteristic
618C2×C4C2×#1175822211yescharacteristic
619C2×C4C2×#1175822211yescharacteristic
620C2×C4C2×#1175822211yescharacteristic
621C2×C4#1451982311yescharacteristic
622C2×C4#1451982411yescharacteristic
623C8—22no—
624C8—41no—
625C8—1222no—
626C8—1222no—
627C22—1222no—
628C22—1222no—
629C22—1222no—
630C22—1222no—
631C22—1222no—
632C22—1222no—
633C22—2441no—
634C22—2441no—
635C22—2441no—
636C22—2441no—
637C22—2441no—
638C22—2441no—
639C22—2441no—
640C22—2441no—
641C22C2×#1451975011yescharacteristic
642C22#1684040811yescharacteristic
643C22#1684041711yescharacteristic
644C22#135×D6111yescharacteristic
645C22#135×D6111yescharacteristic
646C22#1684056811yescharacteristic
647C22#1684057511yescharacteristic
648C4—22no—
649C4—22no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—4881no—
655C4—4881no—
656C4—4881no—
657C4—4881no—
658C4—2441no—
659C4—2441no—
660C4#1684029611yescharacteristic
661C4#1684038311yescharacteristic
662C4#1684040811yescharacteristic
663C4#1684042111yescharacteristic
664C2—2442no—
665C2—2442no—
666C2#2144939611yescharacteristic
667C2#2145539911yescharacteristic
668C2#2145550811yescharacteristic
669C2#2145771111yescharacteristic
670C2#2145772611yescharacteristic
671C2#2145818911yescharacteristic
672C2#2145820311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC4×#103×C61C2
socleC23×C61C22×D4
prime radicalC22×D244D4
hypercenterC4×#103D61
hypocenterC61#25343
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
1. C2×#16840069C2semidirect
5. #21447257C2semidirect
6. #21447246C2semidirect
7. #21447020C2semidirect
8. #21447013C2semidirect
9. #21446784C2semidirect
10. #21446587C2semidirect
11. #21446239C2semidirect
12. #21446239C2semidirect
13. #21445847C2semidirect
14. #21445843C2semidirect
15. C4×#103×C61C2semidirect
342. C4×#103D61semidirect
397. C61#25343semidirect

Maximal subgroups

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

subgroupindex
C2×#168400692
C2×C8×D2442
#214509802
#214507242
#214472572
#214472462
#214470202
#214470132
#214467842
#214465872
#214462392
#214458472
#214458432
C4×#103×C612
#2534361