Finite Group Databasebeta

← #29730143

Subgroups — #29730143

Order 15616.

874 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840055C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D61C211yesmaximal, characteristic
3#21450989C211yesmaximal, characteristic
4#21450738C211yesmaximal, characteristic
5#21447250C211yesmaximal, characteristic, complemented
6#21447249C211yesmaximal, characteristic, complemented
7#21447021C211yesmaximal, characteristic, complemented
8#21447019C211yesmaximal, characteristic, complemented
9#21446778C211yesmaximal, characteristic, complemented
10#21446576C211yesmaximal, characteristic, complemented
11#21446239C211yesmaximal, characteristic, complemented
12#21445848C211yesmaximal, characteristic, complemented
13#21445847C211yesmaximal, characteristic, complemented
14#103×Dic61C211yesmaximal, characteristic, complemented
15C61×#1892C211yesmaximal, characteristic, complemented
16C22×C8×D61C2211yescharacteristic
17C2×#14519776C2211yescharacteristic
18C2×#14519753C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×C4×C22⋊D61C2211yescharacteristic
21#16840055—24no—
22C8×C22⋊D61—24no—
23C2×#14519711C2211yescharacteristic
24C2×#14519711C2211yescharacteristic
25C2×#14519710C2211yescharacteristic
26C2×#14519710C2211yescharacteristic
27C2×#14519706C2211yescharacteristic
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×C8×Dic61C2211yescharacteristic
33#16839685—21no—
34#16839684—21no—
35#16839675—21no—
36#16839674—21no—
37#16839662—21no—
38#16839662—21no—
39#16839657—21no—
40#16839631C2211yescharacteristic
41#16839626—21no—
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#14519753—22no—
72#14519753—41no—
73Q8×Dic61—22no—
74Q8×Dic61—22no—
75C4×C22⋊D61—22no—
76C4×C22⋊D61—22no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×#11758196—21no—
83C2×#11758196—21no—
84C2×#11758196—21no—
85C2×#11758196—21no—
86C2×#11758196D411yescharacteristic
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61D411yescharacteristic
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—21no—
93C2×#11758198—21no—
94C2×#11758198D411yescharacteristic
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61C2311yescharacteristic
98#14519711—22no—
99#14519711—41no—
100#14519710—22no—
101#14519710—41no—
102#14519706D414yes—
103#14519701—22no—
104#14519701—22no—
105C22⋊#92418—22no—
106#14519689—22no—
107C8×Dic61—22no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114C22×Q8×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C22×C8×C61—22no—
117C22×C8×C61—22no—
118C22×C8×C61—41no—
119C22×C8×C61C2311yescharacteristic
120C22×C8×C61C2311yescharacteristic
121C22⋊Q8×C61—22no—
122C22⋊Q8×C61—41no—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61C2311yescharacteristic
125C2×C4⋊C4×C61C2311yescharacteristic
126C2×C4⋊C4×C61C2311yescharacteristic
127C2×C22⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129#103×C61—22no—
130#103×C61—22no—
131#95×C61—21no—
132C24×C61C2×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×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×C61C2411yescharacteristic
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61Q1614yes—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61—21no—
159C22×Dic61C2×D411yescharacteristic
160C22×Dic61C2×D411yescharacteristic
161C22×Dic61C2×D411yescharacteristic
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×Dic122—42no—
169C2×Dic122—81no—
170C2×Dic122—81no—
171C2×C8×C61—21no—
172C2×C8×C61—21no—
173C2×C8×C61—21no—
174C2×C8×C61—21no—
175C2×C8×C61—44no—
176C2×C8×C61C2×D412yes—
177C2×C8×C61#4112yes—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—42no—
185C22⋊C4×C61—42no—
186C22⋊C4×C61—81no—
187C22⋊Dic61—22no—
188C22⋊Dic61—81no—
189C22⋊Dic61—81no—
190#11758198—22no—
191#11758198—42no—
192#11758198—81no—
193#11758198—81no—
194#11758198—81no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—21no—
203C4⋊Dic61—42no—
204#11758196—22no—
205#11758196—42no—
206#11758196—42no—
207#11758196—42no—
208#11758196—81no—
209C4×Dic61—42no—
210C4×Dic61—42no—
211C4×Dic61C2×D412yes—
212C4×Dic61#4112yes—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418C2×D412yes—
219C8×D61—44no—
220C23×C61—21no—
221C23×C61—21no—
222C23×C61—21no—
223C23×C61—21no—
224C23×C61—21no—
225C23×C61—21no—
226C23×C61C2×Q1612yes—
227C23×C61C22×D411yescharacteristic
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—21no—
231C22×D61—21no—
232C22×D61—21no—
233C22×D61—21no—
234C22×D61C2×Q1612yes—
235Q8×C61—22no—
236Q8×C61—22no—
237Q8×C61—41no—
238Q8×C61—41no—
239C2×C4×C61—21no—
240C2×C4×C61—22no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
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—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×C61C22×D411yescharacteristic
259C2×C4×C61C2×#4111yescharacteristic
260C2×C4×C61C2×#4111yescharacteristic
261C2×C4×C61C2×#4111yescharacteristic
262C2×C4×C61H(5,𝔽2)11yescharacteristic
263C2×C4×C612−1+411yescharacteristic
264C22⋊D61—28no—
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—41no—
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#12112yes—
283C2×Dic61#12112yes—
284C2×Dic61C2×Q1612yes—
285C2×Dic61#13512yes—
286C4×D61—41no—
287C4×D61—41no—
288C4×D61—41no—
289C4×D61—41no—
290Dic122—84no—
291C8×C61—22no—
292C8×C61—22no—
293#92418—22no—
294#92418—41no—
295#25340—611nomaximal, Sylow
296C22×C61—22no—
297C22×C61—22no—
298C22×C61—22no—
299C22×C61—41no—
300C22×C61—41no—
301C22×C61—41no—
302C22×C61—41no—
303C22×C61C2×#12111yescharacteristic
304C22×C61#54611yescharacteristic
305C22×C61#54711yescharacteristic
306C22×C61C22×Q1611yescharacteristic
307C22×C61C2×#13511yescharacteristic
308C22×C61#57611yescharacteristic
309C22×C61#57711yescharacteristic
310C2×D61—22no—
311C2×D61—22no—
312C2×D61—22no—
313C2×D61—41no—
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C4×C61—41no—
318C4×C61—42no—
319C4×C61—81no—
320C4×C61—81no—
321C4×C61—81no—
322C4×C61#52911yescharacteristic
323C4×C61#54211yescharacteristic
324C4×C61#54611yescharacteristic
325C4×C61#54811yescharacteristic
326Dic61—22no—
327Dic61—41no—
328Dic61—81no—
329Dic61—81no—
330Dic61—81no—
331Dic61—81no—
332Dic61#46714yes—
333C2×#477—611no—
334C2×C8×D4—611no—
335#2563—611no—
336#2538—611no—
337#2076—611no—
338#2076—611no—
339#2036—611no—
340#2036—611no—
341#1990—611no—
342#1947—611no—
343#1892—611no—
344#1892D6111yescharacteristic, complemented
345#1808—611no—
346#1808—611no—
347C4×#103—611no—
348C2×C61—42no—
349C2×C61#242711yescharacteristic
350C2×C61C2×#46711yescharacteristic
351C2×C61#306211yescharacteristic
352C2×C61#329911yescharacteristic
353C2×C61#330511yescharacteristic
354C2×C61#333811yescharacteristic
355C2×C61#334011yescharacteristic
356D61—42no—
357C23×C8—611no—
358C23×C8C2×D6111yescharacteristic
359C2×C4⋊Q8—611no—
360C2×C22⋊Q8—611no—
361C2×C22⋊Q8C2×D6111yescharacteristic
362C2×C4×Q8—611no—
363C2×C4×D4—611no—
364#477—1224no—
365C8×D4—1224no—
366C2×#107—611no—
367C2×#107—611no—
368C2×#107—611no—
369C2×#107—611no—
370C2×C4⋊C8—611no—
371C2×#103—611no—
372C2×#103—611no—
373C2×#103C2×D6111yescharacteristic
374C2×#103C2×D6111yescharacteristic
375C2×C22⋊C8—611no—
376C2×C22⋊C8—611no—
377C2×C4×C8—611no—
378#396—1221no—
379#396—1221no—
380#393—1221no—
381#393—1221no—
382#390—1221no—
383#390—1221no—
384#389—1221no—
385#384—611no—
386#382—1221no—
387#380—611no—
388#380—611no—
389#380—611no—
390#380—611no—
391#380—611no—
392#380C2×D6111yescharacteristic
393C4×C4⋊C4—611no—
394#340—611no—
395#340—611no—
396#340—611no—
397#340—611no—
398#340—611no—
399#340—611no—
400#340C2×D6111yescharacteristic
401#340C2×D6111yescharacteristic
402C61#2534011yescharacteristic, complemented, Sylow
403C22×Q8—1221no—
404C22×Q8C22×D6111yescharacteristic
405C22×D4—611no—
406C23×C4—611no—
407C23×C4C22×D6111yescharacteristic
408C22×C8—22no—
409C22×C8—22no—
410C22×C8—41no—
411C22×C8—611no—
412C22×C8—611no—
413C22×C8—1222no—
414C22×C8—1222no—
415C22×C8—2441no—
416C22×C8C22×D6111yescharacteristic
417C22×C8C22×D6111yescharacteristic
418C4⋊Q8—1222no—
419C4⋊Q8—1222no—
420C22⋊Q8—22no—
421C22⋊Q8—41no—
422C22⋊Q8—1222no—
423C22⋊Q8—2441no—
424C4×Q8—1222no—
425C4×Q8—1222no—
426C4×D4—1222no—
427C4×D4—1222no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—611no—
430C2×C4⋊C4—611no—
431C2×C4⋊C4—611no—
432C2×C4⋊C4—611no—
433C2×C4⋊C4—611no—
434C2×C4⋊C4—1221no—
435C2×C4⋊C4—1221no—
436C2×C4⋊C4—1221no—
437C2×C4⋊C4—1221no—
438C2×C4⋊C4—1221no—
439C2×C4⋊C4C22×D6111yescharacteristic
440C2×C4⋊C4C22×D6111yescharacteristic
441C2×C4⋊C4C22×D6111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—611no—
445C2×C22⋊C4—611no—
446C2×C22⋊C4—1221no—
447C2×C22⋊C4—1221no—
448C2×C22⋊C4—1221no—
449C2×C22⋊C4—1221no—
450C2×C22⋊C4—1221no—
451C2×C22⋊C4—1221no—
452C2×C42—611no—
453C2×C42—1221no—
454C2×C42—1221no—
455#107—1222no—
456#107—1222no—
457#107—2441no—
458#107—2441no—
459C4⋊C8—614no—
460#103—22no—
461#103—22no—
462#103—1222no—
463#103—1222no—
464C22⋊C8—1222no—
465C22⋊C8—1222no—
466C4×C8—1222no—
467#95—21no—
468#95—1221no—
469#95—1221no—
470#95—1221no—
471#95—1221no—
472#95—1221no—
473#95—1221no—
474C24—611no—
475C24D4×D6111yescharacteristic
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—4881no—
482C2×Q8—4881no—
483C2×Q8—2442no—
484C2×Q8#1175822212yes—
485C2×D4—614no—
486C2×D4—1222no—
487C2×D4—1222no—
488C22×C4—21no—
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—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—1221no—
502C22×C4—1221no—
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×C4D4×D6111yescharacteristic
512C22×C4C23×D6111yescharacteristic
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—44no—
518C2×C8—612no—
519C2×C8—1221no—
520C2×C8—1221no—
521C2×C8—1221no—
522C2×C8—1221no—
523C2×C8—1221no—
524C2×C8—2444no—
525C2×C8D4×D6112yes—
526C2×C8#1175822412yes—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—1222no—
535C4⋊C4—1221no—
536C4⋊C4—1221no—
537C4⋊C4—1221no—
538C4⋊C4—1221no—
539C4⋊C4—1221no—
540C4⋊C4—1221no—
541C4⋊C4—1221no—
542C4⋊C4—1221no—
543C4⋊C4—4881no—
544C4⋊C4—2442no—
545C4⋊C4—2442no—
546C4⋊C4—2442no—
547C4⋊C4—2442no—
548C22⋊C4—42no—
549C22⋊C4—81no—
550C22⋊C4—1222no—
551C22⋊C4—1222no—
552C22⋊C4—4881no—
553C22⋊C4—4881no—
554C22⋊C4—4881no—
555C22⋊C4—4881no—
556C22⋊C4—4881no—
557C22⋊C4—2442no—
558C42—612no—
559C42—612no—
560C42—2442no—
561C42—2442no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—612no—
569C23—1221no—
570C23—1221no—
571C23—1221no—
572C23—1221no—
573C23—1221no—
574C23—1221no—
575C23Q16×D6112yes—
576C23C2×D4×D6111yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—41no—
580Q8—41no—
581Q8—4884no—
582D4—1228no—
583C2×C4—21no—
584C2×C4—22no—
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—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—612no—
603C2×C4—612no—
604C2×C4—612no—
605C2×C4—612no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—2441no—
612C2×C4—2441no—
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×C4C2×D4×D6111yescharacteristic
628C2×C4#41×D6111yescharacteristic
629C2×C4C2×#1175822411yescharacteristic
630C2×C4C2×#1175822211yescharacteristic
631C2×C4#1451982211yescharacteristic
632C2×C4#1451982411yescharacteristic
633C8—22no—
634C8—22no—
635C8—1222no—
636C8—2441no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—1222no—
645C22—1222no—
646C22—1222no—
647C22—2441no—
648C22—2441no—
649C22—2441no—
650C22—2441no—
651C22#121×D6111yescharacteristic
652C22#1684040211yescharacteristic
653C22#1684041211yescharacteristic
654C22C2×Q16×D6111yescharacteristic
655C22#135×D6111yescharacteristic
656C22#1684056411yescharacteristic
657C22#1684056811yescharacteristic
658C4—41no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—614no—
664C4—1222no—
665C4—4881no—
666C4—4881no—
667C4—4881no—
668C4—4881no—
669C4—2441no—
670C4#1684029211yescharacteristic
671C4#1684038011yescharacteristic
672C4#1684039911yescharacteristic
673C4#1684042111yescharacteristic
674C2—42no—
675C2—2442no—
676C2#2144939311yescharacteristic
677C2#467×D6111yescharacteristic
678C2#2145549211yescharacteristic
679C2#2145769111yescharacteristic
680C2#2145776511yescharacteristic
681C2#2145820811yescharacteristic
682C2#2145822711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1892C2
socleC23×C61C22×D4
prime radicalC22×C22⋊D61D4
hypercenter#1892D61
hypocenterC61#25340
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×#16840055C2semidirect
5. #21447250C2semidirect
6. #21447249C2semidirect
7. #21447021C2semidirect
8. #21447019C2semidirect
9. #21446778C2semidirect
10. #21446576C2semidirect
11. #21446239C2semidirect
12. #21445848C2semidirect
13. #21445847C2semidirect
14. #103×Dic61C2semidirect
15. C61×#1892C2semidirect
344. #1892D61semidirect
402. C61#25340semidirect

Maximal subgroups

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

subgroupindex
C2×#168400552
C2×C8×C22⋊D612
#214509892
#214507382
#214472502
#214472492
#214470212
#214470192
#214467782
#214465762
#214462392
#214458482
#214458472
#103×Dic612
C61×#18922
#2534061