Finite Group Databasebeta

← #29646022

Subgroups — #29646022

Order 15616.

1268 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840307C211yesmaximal, characteristic
2#21454448C211yesmaximal, characteristic, complemented
3C2×#16839812C211yesmaximal, characteristic, complemented
4#21444180C211yesmaximal, characteristic, complemented
5#21444179C211yesmaximal, characteristic, complemented
6#21444178C211yesmaximal, characteristic, complemented
7#21444169C214yesmaximal, complemented
8#21444138C214yesmaximal, complemented
9C61×#1471C211yesmaximal, characteristic, complemented
10C22×#11758224C412yes—
11#16840307—21no—
12#16840307—21no—
13#16840307—21no—
14#16840307—21no—
15#16840307—21no—
16#16840307—21no—
17#16840307—21no—
18#16840307—21no—
19C2×#14519776C411yescharacteristic
20C2×#14519773C411yescharacteristic
21C2×#14519763C2212yes—
22C2×#14519751C2211yescharacteristic
23C2×#14519749C412yes—
24C2×D4×Dic61C411yescharacteristic
25C2×#14519739C411yescharacteristic
26C2×#14519737C2212yes—
27C22×C4×Dic61C2211yescharacteristic
28#16839816—21no—
29#16839816C2212yes—
30#16839812—21no—
31#16839812—21no—
32#16839812—21no—
33#16839812C2212yes—
34#16839812C2212yes—
35#16839812C2212yes—
36#16839785—21no—
37C2×#14519706—21no—
38#16839726C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40M16×Dic61—21no—
41C2×C8×Dic61—21no—
42#16839486C2214yes—
43#16839485C2214yes—
44#16839485C2214yes—
45C2×#121×C61C2211yescharacteristic
46C61×#407C2211yescharacteristic
47C2×C22⋊C8×C61C2211yescharacteristic
48C61×#323C2214yes—
49C2×#11758224—22no—
50C2×#11758224—22no—
51C2×#11758224—22no—
52C2×#11758224—22no—
53C2×#11758224—48no—
54C22×Dic122C2×C412yes—
55C22×D244C2×C411yescharacteristic
56C22×C22⋊D61C2×C412yes—
57C22×C22⋊D61C2×C412yes—
58C22×C22⋊D61C2×C412yes—
59C23×Dic61C2×C411yescharacteristic
60C23×Dic61C2×C411yescharacteristic
61C23×Dic61C2×C412yes—
62C22×C4×D61C2×C412yes—
63C2×#11758194—21no—
64C22×#92418—21no—
65#14519776—21no—
66#14519776—21no—
67#14519776—21no—
68#14519776—21no—
69#14519773—21no—
70#14519773—21no—
71#14519773—21no—
72#14519773—21no—
73#14519763—22no—
74#14519763—22no—
75#14519763—22no—
76#14519763—22no—
77#14519751—21no—
78#14519751—21no—
79#14519751—21no—
80#14519751—21no—
81#14519749—22no—
82#14519749—22no—
83#14519749—22no—
84#14519749—22no—
85D4×Dic61—21no—
86D4×Dic61—21no—
87D4×Dic61—21no—
88D4×Dic61—21no—
89#14519739—21no—
90#14519739—21no—
91#14519739—21no—
92#14519739—21no—
93#14519737—22no—
94#14519737—22no—
95#14519737—22no—
96#14519737—22no—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×#11758196C2×C412yes—
99C2×C22⋊Dic61C2×C412yes—
100C2×#11758198C2×C412yes—
101C2×#11758198C2312yes—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61D411yescharacteristic
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C2×C4×Dic61C2311yescharacteristic
114#14519706—22no—
115#14519706—22no—
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418—21no—
119C22⋊#92418—21no—
120C22⋊#92418C2312yes—
121C22⋊#92418C2312yes—
122#14519687—22no—
123C8×Dic61—22no—
124C8×Dic61—22no—
125C8×Dic61—22no—
126C22×D4×C61C2×C411yescharacteristic
127C22×D4×C61C2×C412yes—
128C23×C4×C61C2311yescharacteristic
129C2×M16×C61—21no—
130C22×C8×C61—21no—
131#121×C61—21no—
132#121×C61—21no—
133#121×C61—21no—
134#121×C61—21no—
135C2×C4⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2312yes—
137C22⋊C8×C61—21no—
138C22⋊C8×C61—21no—
139C22⋊C8×C61C2312yes—
140C22⋊C8×C61C2312yes—
141C24×C61C22×C411yescharacteristic
142C24×C61C22×C412yes—
143C23×D61C22×C412yes—
144C2×D4×C61—22no—
145C2×D4×C61—22no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—42no—
149C2×D4×C61—44no—
150C22×C4×C61—42no—
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C412yes—
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C2×C22⋊D61—28no—
165C2×C22⋊D61—44no—
166C2×C22⋊D61—44no—
167C22×Dic61—24no—
168C22×Dic61—24no—
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—44no—
172C22×Dic61C22⋊C411yescharacteristic
173C22×Dic61C22⋊C411yescharacteristic
174C22×Dic61C22⋊C411yescharacteristic
175C22×Dic61C22⋊C411yescharacteristic
176C22×Dic61C22⋊C411yescharacteristic
177C22×Dic61C22⋊C411yescharacteristic
178C22×Dic61C22⋊C411yescharacteristic
179C22×Dic61C22⋊C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C412yes—
184C22×Dic61C22×C411yescharacteristic
185#11758224—48no—
186#11758224—48no—
187#11758224—48no—
188#11758224—48no—
189C2×D244—21no—
190C2×D244—21no—
191C2×D244—42no—
192C2×C4×D61—22no—
193C2×C4×D61—22no—
194C2×C4×D61—44no—
195C2×Dic122—22no—
196C2×Dic122—22no—
197C2×Dic122—44no—
198M16×C61—42no—
199C2×C8×C61—22no—
200C2×C8×C61—22no—
201C2×C8×C61—42no—
202C4⋊C4×C61—21no—
203C4⋊C4×C61—21no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—22no—
206C22⋊Dic61—22no—
207C22⋊Dic61—22no—
208#11758198—22no—
209#11758198—22no—
210#11758198—22no—
211#11758198—22no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214#11758196—22no—
215#11758196—22no—
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22⋊C411yescharacteristic
221C4×Dic61C22⋊C411yescharacteristic
222C4×Dic61C22⋊C411yescharacteristic
223C4×Dic61C22⋊C411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C4×Dic61C2×D411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C4×Dic61C2×D411yescharacteristic
228C4×Dic61C2×D411yescharacteristic
229C4×Dic61C2×D411yescharacteristic
230C4×Dic61C2×D411yescharacteristic
231C4×Dic61C2×D411yescharacteristic
232#11758194—42no—
233C2×#92418—22no—
234C2×#92418—22no—
235C2×#92418—42no—
236C23×C61—22no—
237C23×C61—22no—
238C23×C61—22no—
239C23×C61—24no—
240C23×C61—41no—
241C23×C61—42no—
242C23×C61—42no—
243C23×C61C2×C22⋊C411yescharacteristic
244C23×C61C2×C22⋊C411yescharacteristic
245C23×C61C23×C411yescharacteristic
246C22×D61—22no—
247C22×D61—24no—
248C22×D61—42no—
249C22×D61—42no—
250D4×C61—42no—
251D4×C61—44no—
252D4×C61—44no—
253D4×C61—42no—
254C2×C4×C61—22no—
255C2×C4×C61—22no—
256C2×C4×C61—22no—
257C2×C4×C61—22no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—42no—
262C2×C4×C61C2×C22⋊C411yescharacteristic
263C2×C4×C61C2×C22⋊C411yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C22×D411yescharacteristic
266C22⋊D61—44no—
267C22⋊D61—44no—
268C22⋊D61—44no—
269C22⋊D61—44no—
270C22⋊D61—44no—
271C22⋊D61—44no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—22no—
279C2×Dic61—22no—
280C2×Dic61—22no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—44no—
284C2×Dic61—44no—
285C2×Dic61—42no—
286C2×Dic61#10014yes—
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292C2×Dic61C2×C22⋊C411yescharacteristic
293C2×Dic61C2×C22⋊C411yescharacteristic
294C2×Dic61C2×C22⋊C411yescharacteristic
295C2×Dic61#13114yes—
296D244—42no—
297D244—42no—
298C4×D61—44no—
299C4×D61—44no—
300Dic122—44no—
301Dic122—44no—
302C8×C61—42no—
303C8×C61—42no—
304#92418—42no—
305#92418—42no—
306#17384—611nomaximal, Sylow
307C22×C61—21no—
308C22×C61—21no—
309C22×C61—21no—
310C22×C61—21no—
311C22×C61—21no—
312C22×C61—21no—
313C22×C61—21no—
314C22×C61—44no—
315C22×C61—42no—
316C22×C61—42no—
317C22×C61—42no—
318C22×C61—84no—
319C22×C61C2×#10012yes—
320C22×C61C22×C22⋊C411yescharacteristic
321C22×C61C2×#13112yes—
322C2×D61—42no—
323C2×D61—42no—
324C2×D61—42no—
325C2×D61—84no—
326C4×C61—21no—
327C4×C61—21no—
328C4×C61—21no—
329C4×C61—42no—
330C4×C61#41012yes—
331Dic61—21no—
332Dic61—21no—
333Dic61—21no—
334Dic61—21no—
335Dic61—42no—
336Dic61#40812yes—
337Dic61#40812yes—
338Dic61C2×#10012yes—
339Dic61C2×#10012yes—
340C2×#532—611no—
341#2920—611no—
342C2×#431—611no—
343#1471—611no—
344#1471—611no—
345#1471—611no—
346#1471D6111yescharacteristic, complemented
347#1469—614no—
348#1460—614no—
349C2×C61—22no—
350C2×C61—22no—
351C2×C61—41no—
352C2×C61—82no—
353C2×C61C2×#40811yescharacteristic
354C2×C61C2×#41011yescharacteristic
355C2×C61C22×#10011yescharacteristic
356D61—82no—
357C22×#41—612no—
358#532—1221no—
359#532—1221no—
360#532—1221no—
361#532—1221no—
362#532—1221no—
363#532—1221no—
364#532—1221no—
365#532—1221no—
366C2×C4⋊Q8—611no—
367C2×#127—611no—
368C2×#124—612no—
369C2×#121—612no—
370C2×#121—611no—
371C2×#121C2×D6111yescharacteristic
372C2×C4×D4—611no—
373C2×C4×D4—611no—
374C2×C4×D4—612no—
375C22×C42—611no—
376#432—612no—
377#432—1221no—
378#431—612no—
379#431—612no—
380#431—612no—
381#431—1221no—
382#431—1221no—
383#431—1221no—
384#423—1221no—
385C2×C4⋊C8—1221no—
386#407—611no—
387#407C2×D6111yescharacteristic
388C2×C22⋊C8—611no—
389C2×C22⋊C8C2×D6111yescharacteristic
390C4×M16—1221no—
391C2×C4×C8—1221no—
392#323—614no—
393#323—614no—
394#323—614no—
395#323C2×D6114yes—
396C61#1738411yescharacteristic, complemented, Sylow
397C2×#41—1222no—
398C2×#41—1222no—
399C2×#41—1222no—
400C2×#41—1222no—
401C2×#41—2448no—
402C22×Q8—612no—
403C22×D4—612no—
404C22×D4—612no—
405C22×D4—612no—
406C22×D4—611no—
407C22×D4C4×D6111yescharacteristic
408C22×D4C4×D6112yes—
409C23×C4—611no—
410C23×C4—611no—
411C23×C4—612no—
412C23×C4—612no—
413C23×C4C22×D6111yescharacteristic
414C2×M16—21no—
415C2×M16—1221no—
416C22×C8—21no—
417C22×C8—1221no—
418C4⋊Q8—1221no—
419C4⋊Q8—1221no—
420C4⋊Q8—1221no—
421C4⋊Q8—1221no—
422#127—1221no—
423#127—1221no—
424#127—1221no—
425#127—1221no—
426#124—1222no—
427#124—1222no—
428#124—1222no—
429#124—1222no—
430#121—21no—
431#121—21no—
432#121—21no—
433#121—21no—
434#121—1222no—
435#121—1222no—
436#121—1222no—
437#121—1222no—
438#121—1221no—
439#121—1221no—
440#121—1221no—
441#121—1221no—
442C4×D4—1222no—
443C4×D4—1222no—
444C4×D4—1222no—
445C4×D4—1222no—
446C4×D4—1221no—
447C4×D4—1221no—
448C4×D4—1221no—
449C4×D4—1221no—
450C4×D4—1221no—
451C4×D4—1221no—
452C4×D4—1221no—
453C4×D4—1221no—
454C2×C4⋊C4—612no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4C4×D6111yescharacteristic
457C2×C22⋊C4—612no—
458C2×C22⋊C4—612no—
459C2×C22⋊C4—612no—
460C2×C22⋊C4C22×D6112yes—
461C2×C42—611no—
462C2×C42—611no—
463C2×C42—611no—
464C2×C42—611no—
465C2×C42—611no—
466C2×C42—611no—
467C2×C42—611no—
468C2×C42—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—611no—
473C4⋊C8—1222no—
474C4⋊C8—1222no—
475C4⋊C8—1222no—
476C4⋊C8—1222no—
477C22⋊C8—21no—
478C22⋊C8—21no—
479C22⋊C8—612no—
480C22⋊C8—612no—
481C22⋊C8—1221no—
482C22⋊C8—1221no—
483C22⋊C8C22×D6112yes—
484C22⋊C8C22×D6112yes—
485#97—1222no—
486C4×C8—1222no—
487C4×C8—1222no—
488C4×C8—1222no—
489C24—612no—
490C24C2×C4×D6111yescharacteristic
491C24C2×C4×D6112yes—
492#41—2448no—
493#41—2448no—
494#41—2448no—
495#41—2448no—
496C2×Q8—1222no—
497C2×Q8—1222no—
498C2×Q8—2444no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—44no—
505C2×D4—1222no—
506C2×D4—1222no—
507C2×D4—1222no—
508C2×D4—1222no—
509C2×D4—1228no—
510C2×D4—1222no—
511C2×D4—1222no—
512C2×D4—1221no—
513C2×D4—1221no—
514C2×D4—2442no—
515C2×D4—2444no—
516C2×D4—2444no—
517C22×C4—42no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—611no—
521C22×C4—611no—
522C22×C4—611no—
523C22×C4—611no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—612no—
531C22×C4—1222no—
532C22×C4—1222no—
533C22×C4—1224no—
534C22×C4—1224no—
535C22×C4—1222no—
536C22×C4—1222no—
537C22×C4—2444no—
538C22×C4—2444no—
539C22×C4C2×C4×D6111yescharacteristic
540C22×C4C2×C4×D6112yes—
541C22×C4D4×D6111yescharacteristic
542C22×C4D4×D6111yescharacteristic
543C22×C4D4×D6111yescharacteristic
544C22×C4D4×D6111yescharacteristic
545C22×C4C23×D6111yescharacteristic
546M16—42no—
547M16—2442no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—42no—
551C2×C8—1222no—
552C2×C8—1222no—
553C2×C8—2442no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—1222no—
557C4⋊C4—1222no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—1222no—
563C22⋊C4—1222no—
564C22⋊C4—1222no—
565C22⋊C4—1222no—
566C22⋊C4—1222no—
567C22⋊C4—1222no—
568C42—611no—
569C42—611no—
570C42—611no—
571C42—611no—
572C42—611no—
573C42—611no—
574C42—611no—
575C42—611no—
576C42—611no—
577C42—611no—
578C42—611no—
579C42—611no—
580C42—611no—
581C42—611no—
582C42—611no—
583C42—611no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—41no—
589C23—42no—
590C23—42no—
591C23—1224no—
592C23—1222no—
593C23—2442no—
594C23—2442no—
595C23C22⋊C4×D6111yescharacteristic
596C23C22⋊C4×D6111yescharacteristic
597C23C22×C4×D6111yescharacteristic
598Q8—2444no—
599Q8—2444no—
600D4—42no—
601D4—44no—
602D4—44no—
603D4—42no—
604D4—2442no—
605D4—2444no—
606D4—2444no—
607D4—2444no—
608D4—2444no—
609D4—2444no—
610D4—2444no—
611D4—2442no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—611no—
621C2×C4—611no—
622C2×C4—611no—
623C2×C4—611no—
624C2×C4—614no—
625C2×C4—614no—
626C2×C4—611no—
627C2×C4—611no—
628C2×C4—611no—
629C2×C4—611no—
630C2×C4—1222no—
631C2×C4—1222no—
632C2×C4—1222no—
633C2×C4—1222no—
634C2×C4—1222no—
635C2×C4—1222no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—1222no—
639C2×C4—1222no—
640C2×C4—1222no—
641C2×C4—2444no—
642C2×C4—2444no—
643C2×C4—2444no—
644C2×C4—2444no—
645C2×C4—2442no—
646C2×C4C22⋊C4×D6111yescharacteristic
647C2×C4C22⋊C4×D6111yescharacteristic
648C2×C4C2×D4×D6111yescharacteristic
649C2×C4C2×D4×D6111yescharacteristic
650C8—42no—
651C8—42no—
652C8—2442no—
653C8—2442no—
654C22—21no—
655C22—21no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—44no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—84no—
666C22—4884no—
667C22—2442no—
668C22—2442no—
669C22—2442no—
670C22#100×D6112yes—
671C22C2×C22⋊C4×D6111yescharacteristic
672C22#131×D6112yes—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—42no—
677C4—612no—
678C4—612no—
679C4—612no—
680C4—612no—
681C4—1221no—
682C4—1221no—
683C4—1221no—
684C4—1221no—
685C4—2442no—
686C4#1683973412yes—
687C2—22no—
688C2—22no—
689C2—41no—
690C2—82no—
691C2—4882no—
692C2#408×D6111yescharacteristic
693C2C2×#1683973411yescharacteristic
694C2C2×#100×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1471C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840307C2
cosocleC22×C4×C61C24
hypercenter#1471D61
hypocenterC61#17384
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1471

Complements

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

NH ≅ G/Ntype
2. #21454448C2semidirect
3. C2×#16839812C2semidirect
4. #21444180C2semidirect
5. #21444179C2semidirect
6. #21444178C2semidirect
7. #21444169C2semidirect
8. #21444138C2semidirect
9. C61×#1471C2semidirect
346. #1471D61semidirect
396. C61#17384semidirect

Maximal subgroups

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

subgroupindex
C2×#168403072
#214544482
C2×#168398122
#214441802
#214441792
#214441782
#214441692
#214441382
C61×#14712
#1738461