Finite Group Databasebeta

← #29730154

Subgroups — #29730154

Order 15616.

894 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840045C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D61C211yesmaximal, characteristic
3#21450813C211yesmaximal, characteristic
4#21450738C211yesmaximal, characteristic
5#21447255C211yesmaximal, characteristic, complemented
6#21447254C211yesmaximal, characteristic, complemented
7#21447014C211yesmaximal, characteristic, complemented
8#21447012C211yesmaximal, characteristic, complemented
9#21446778C211yesmaximal, characteristic, complemented
10#21446581C211yesmaximal, characteristic, complemented
11#21446239C211yesmaximal, characteristic, complemented
12#21445844C211yesmaximal, characteristic, complemented
13#21445843C211yesmaximal, characteristic, complemented
14#103×Dic61C211yesmaximal, characteristic, complemented
15C61×#1892C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C2×#14519776C2211yescharacteristic
18C2×#14519763—21no—
19C2×#14519753C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22#16840045—24no—
23C8×C22⋊D61—24no—
24C2×#14519709C2211yescharacteristic
25C2×#14519709C2211yescharacteristic
26C2×#14519708C2211yescharacteristic
27C2×#14519708C2211yescharacteristic
28C2×#14519706C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×#14519689C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34#16839691—21no—
35#16839690—21no—
36#16839685—21no—
37#16839684—21no—
38#16839666—21no—
39#16839662—21no—
40#16839657—21no—
41#16839631C2211yescharacteristic
42#16839622C2211yescharacteristic
43#16839622C2211yescharacteristic
44#16839619C2211yescharacteristic
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47C4⋊C4×Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C23×C8×C61C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C2×#103×C61C2211yescharacteristic
57C2×#103×C61C2211yescharacteristic
58C61×#380C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122—21no—
62C22×C22⋊D61D411yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C2×C8×D61—22no—
67C2×C8×D61—22no—
68C2×C8×D61—41no—
69#14519776—22no—
70#14519776—22no—
71#14519763—44no—
72#14519753—22no—
73#14519753—41no—
74Q8×Dic61—22no—
75Q8×Dic61—22no—
76C4×C22⋊D61—22no—
77C4×C22⋊D61—22no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×#11758196D411yescharacteristic
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61D411yescharacteristic
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198D411yescharacteristic
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61C2311yescharacteristic
99#14519709—22no—
100#14519709—41no—
101#14519708—22no—
102#14519708—41no—
103#14519706D414yes—
104#14519701—22no—
105#14519701—22no—
106C22⋊#92418—22no—
107#14519689—22no—
108C8×Dic61—22no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684—21no—
115C22×Q8×C61C2311yescharacteristic
116C23×C4×C61C2311yescharacteristic
117C22×C8×C61—22no—
118C22×C8×C61—22no—
119C22×C8×C61—41no—
120C22×C8×C61C2311yescharacteristic
121C22×C8×C61C2311yescharacteristic
122C22⋊Q8×C61—22no—
123C22⋊Q8×C61—41no—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C4⋊C4×C61C2311yescharacteristic
128C2×C22⋊C4×C61—21no—
129C2×C22⋊C4×C61—21no—
130#103×C61—22no—
131#103×C61—22no—
132#95×C61—21no—
133C24×C61C2×D411yescharacteristic
134C23×D61C2×D411yescharacteristic
135C2×Q8×C61—21no—
136C2×Q8×C61—21no—
137C2×Q8×C61—21no—
138C2×Q8×C61—21no—
139C2×Q8×C61—21no—
140C2×Q8×C61#4112yes—
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×C61—21no—
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C2×C22⋊D61—22no—
154C2×C22⋊D61—22no—
155C2×C22⋊D61SD1614yes—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
162C22×Dic61C2×D411yescharacteristic
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×Dic122—42no—
170C2×Dic122—42no—
171C2×Dic122—42no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—44no—
177C2×C8×C61C2×D412yes—
178C2×C8×C61#4112yes—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—42no—
186C22⋊C4×C61—42no—
187C22⋊C4×C61—42no—
188C22⋊Dic61—22no—
189C22⋊Dic61—42no—
190C22⋊Dic61—81no—
191#11758198—22no—
192#11758198—42no—
193#11758198—42no—
194#11758198—42no—
195#11758198—81no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—21no—
204C4⋊Dic61—42no—
205#11758196—22no—
206#11758196—42no—
207#11758196—42no—
208#11758196—42no—
209#11758196—81no—
210C4×Dic61—42no—
211C4×Dic61—42no—
212C4×Dic61C2×D412yes—
213C4×Dic61#4112yes—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418C2×D412yes—
220C8×D61—44no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61—21no—
227C23×C61C2×SD1612yes—
228C23×C61C22×D411yescharacteristic
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61—21no—
235C22×D61C2×SD1612yes—
236Q8×C61—22no—
237Q8×C61—22no—
238Q8×C61—41no—
239Q8×C61—41no—
240C2×C4×C61—21no—
241C2×C4×C61—22no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
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—41no—
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×C61C22×D411yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61H(5,𝔽2)11yescharacteristic
264C2×C4×C612−1+411yescharacteristic
265C22⋊D61—28no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—41no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61#12112yes—
284C2×Dic61#12112yes—
285C2×Dic61C2×SD1612yes—
286C2×Dic61#13512yes—
287C4×D61—41no—
288C4×D61—41no—
289C4×D61—41no—
290C4×D61—41no—
291Dic122—84no—
292C8×C61—22no—
293C8×C61—22no—
294#92418—22no—
295#92418—41no—
296#25341—611nomaximal, Sylow
297C22×C61—22no—
298C22×C61—22no—
299C22×C61—22no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61—41no—
304C22×C61C2×#12111yescharacteristic
305C22×C61#54611yescharacteristic
306C22×C61#54711yescharacteristic
307C22×C61C22×SD1611yescharacteristic
308C22×C61C2×#13511yescharacteristic
309C22×C61#57711yescharacteristic
310C22×C61#57811yescharacteristic
311C2×D61—22no—
312C2×D61—22no—
313C2×D61—22no—
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C2×D61—41no—
318C4×C61—41no—
319C4×C61—42no—
320C4×C61—81no—
321C4×C61—81no—
322C4×C61—81no—
323C4×C61#52911yescharacteristic
324C4×C61#54211yescharacteristic
325C4×C61#54611yescharacteristic
326C4×C61#54811yescharacteristic
327Dic61—22no—
328Dic61—41no—
329Dic61—81no—
330Dic61—81no—
331Dic61—81no—
332Dic61—81no—
333Dic61#46514yes—
334C2×#475—611no—
335C2×C8×D4—611no—
336#2547—611no—
337#2538—611no—
338#2077—611no—
339#2077—611no—
340#2035—611no—
341#2035—611no—
342#1990—611no—
343#1948—611no—
344#1892—611no—
345#1892D6111yescharacteristic, complemented
346#1807—611no—
347#1807—611no—
348C4×#103—611no—
349C2×C61—42no—
350C2×C61#242711yescharacteristic
351C2×C61C2×#46511yescharacteristic
352C2×C61#306311yescharacteristic
353C2×C61#329811yescharacteristic
354C2×C61#330411yescharacteristic
355C2×C61#333511yescharacteristic
356C2×C61#334211yescharacteristic
357D61—42no—
358C23×C8—611no—
359C23×C8C2×D6111yescharacteristic
360C2×C4⋊Q8—611no—
361C2×#124—1221no—
362C2×C22⋊Q8—611no—
363C2×C22⋊Q8C2×D6111yescharacteristic
364C2×C4×Q8—611no—
365C2×C4×D4—611no—
366#475—1224no—
367C8×D4—1224no—
368C2×#106—611no—
369C2×#106—611no—
370C2×#106—611no—
371C2×#106—611no—
372C2×C4⋊C8—611no—
373C2×#103—611no—
374C2×#103—611no—
375C2×#103C2×D6111yescharacteristic
376C2×#103C2×D6111yescharacteristic
377C2×C22⋊C8—611no—
378C2×C22⋊C8—611no—
379C2×C4×C8—611no—
380#397—1221no—
381#397—1221no—
382#396—1221no—
383#396—1221no—
384#391—1221no—
385#390—1221no—
386#389—1221no—
387#384—611no—
388#380—611no—
389#380—611no—
390#380—611no—
391#380—611no—
392#380—611no—
393#380C2×D6111yescharacteristic
394C4×C4⋊C4—611no—
395#340—611no—
396#340—611no—
397#340—611no—
398#340—611no—
399#340—611no—
400#340—611no—
401#340C2×D6111yescharacteristic
402#340C2×D6111yescharacteristic
403C61#2534111yescharacteristic, complemented, Sylow
404C22×Q8—1221no—
405C22×Q8C22×D6111yescharacteristic
406C22×D4—611no—
407C23×C4—611no—
408C23×C4C22×D6111yescharacteristic
409C22×C8—22no—
410C22×C8—22no—
411C22×C8—41no—
412C22×C8—611no—
413C22×C8—611no—
414C22×C8—1222no—
415C22×C8—1222no—
416C22×C8—2441no—
417C22×C8C22×D6111yescharacteristic
418C22×C8C22×D6111yescharacteristic
419C4⋊Q8—1222no—
420C4⋊Q8—1222no—
421#124—2444no—
422C22⋊Q8—22no—
423C22⋊Q8—41no—
424C22⋊Q8—1222no—
425C22⋊Q8—2441no—
426C4×Q8—1222no—
427C4×Q8—1222no—
428C4×D4—1222no—
429C4×D4—1222no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—611no—
435C2×C4⋊C4—611no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4—1221no—
440C2×C4⋊C4—1221no—
441C2×C4⋊C4C22×D6111yescharacteristic
442C2×C4⋊C4C22×D6111yescharacteristic
443C2×C4⋊C4C22×D6111yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—611no—
447C2×C22⋊C4—611no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C22⋊C4—1221no—
451C2×C22⋊C4—1221no—
452C2×C22⋊C4—1221no—
453C2×C22⋊C4—1221no—
454C2×C42—611no—
455C2×C42—1221no—
456C2×C42—1221no—
457#106—1222no—
458#106—1222no—
459#106—2441no—
460#106—2441no—
461C4⋊C8—614no—
462#103—22no—
463#103—22no—
464#103—1222no—
465#103—1222no—
466C22⋊C8—1222no—
467C22⋊C8—1222no—
468C4×C8—1222no—
469#95—21no—
470#95—1221no—
471#95—1221no—
472#95—1221no—
473#95—1221no—
474#95—1221no—
475#95—1221no—
476C24—611no—
477C24D4×D6111yescharacteristic
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—2442no—
484C2×Q8—2442no—
485C2×Q8—2442no—
486C2×Q8#1175822212yes—
487C2×D4—614no—
488C2×D4—1222no—
489C2×D4—1222no—
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—21no—
500C22×C4—611no—
501C22×C4—611no—
502C22×C4—611no—
503C22×C4—1221no—
504C22×C4—1221no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4D4×D6111yescharacteristic
514C22×C4C23×D6111yescharacteristic
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—44no—
520C2×C8—612no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—1221no—
525C2×C8—1221no—
526C2×C8—2444no—
527C2×C8D4×D6112yes—
528C2×C8#1175822412yes—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—1222no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—1221no—
541C4⋊C4—1221no—
542C4⋊C4—1221no—
543C4⋊C4—1221no—
544C4⋊C4—1221no—
545C4⋊C4—4881no—
546C4⋊C4—2442no—
547C4⋊C4—2442no—
548C4⋊C4—2442no—
549C4⋊C4—2442no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—1222no—
553C22⋊C4—1222no—
554C22⋊C4—4881no—
555C22⋊C4—4881no—
556C22⋊C4—2442no—
557C22⋊C4—2442no—
558C22⋊C4—2442no—
559C22⋊C4—2442no—
560C42—612no—
561C42—612no—
562C42—2442no—
563C42—2442no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—612no—
571C23—1221no—
572C23—1221no—
573C23—1221no—
574C23—1221no—
575C23—1221no—
576C23—1221no—
577C23SD16×D6112yes—
578C23C2×D4×D6111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—41no—
582Q8—41no—
583Q8—4884no—
584D4—1228no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—612no—
605C2×C4—612no—
606C2×C4—612no—
607C2×C4—612no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—1221no—
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—2441no—
622C2×C4—2441no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4—2441no—
628C2×C4—2441no—
629C2×C4C2×D4×D6111yescharacteristic
630C2×C4#41×D6111yescharacteristic
631C2×C4C2×#1175822411yescharacteristic
632C2×C4C2×#1175822211yescharacteristic
633C2×C4#1451982211yescharacteristic
634C2×C4#1451982411yescharacteristic
635C8—22no—
636C8—22no—
637C8—1222no—
638C8—2441no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—1222no—
647C22—1222no—
648C22—1222no—
649C22—2441no—
650C22—2441no—
651C22—2441no—
652C22—2441no—
653C22#121×D6111yescharacteristic
654C22#1684040211yescharacteristic
655C22#1684041211yescharacteristic
656C22C2×SD16×D6111yescharacteristic
657C22#135×D6111yescharacteristic
658C22#1684056911yescharacteristic
659C22#1684057511yescharacteristic
660C4—41no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—614no—
666C4—1222no—
667C4—4881no—
668C4—4881no—
669C4—4881no—
670C4—4881no—
671C4—2441no—
672C4#1684029211yescharacteristic
673C4#1684038011yescharacteristic
674C4#1684039911yescharacteristic
675C4#1684042111yescharacteristic
676C2—42no—
677C2—2442no—
678C2#2144939311yescharacteristic
679C2#465×D6111yescharacteristic
680C2#2145550911yescharacteristic
681C2#2145768011yescharacteristic
682C2#2145775411yescharacteristic
683C2#2145817111yescharacteristic
684C2#2145824611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1892C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#1892D61
hypocenterC61#25341
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
1. C2×#16840045C2semidirect
5. #21447255C2semidirect
6. #21447254C2semidirect
7. #21447014C2semidirect
8. #21447012C2semidirect
9. #21446778C2semidirect
10. #21446581C2semidirect
11. #21446239C2semidirect
12. #21445844C2semidirect
13. #21445843C2semidirect
14. #103×Dic61C2semidirect
15. C61×#1892C2semidirect
345. #1892D61semidirect
403. C61#25341semidirect

Maximal subgroups

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

subgroupindex
C2×#168400452
C2×C8×C22⋊D612
#214508132
#214507382
#214472552
#214472542
#214470142
#214470122
#214467782
#214465812
#214462392
#214458442
#214458432
#103×Dic612
C61×#18922
#2534161