Finite Group Databasebeta

← #29587119

Subgroups — #29587119

Order 15616.

1110 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519704C211yesmaximal, characteristic
2#21448310C211yesmaximal, characteristic
3C2×C4×#11758196C211yesmaximal, characteristic, complemented
4C2×#16839523C211yesmaximal, characteristic, complemented
5C2×#16839522C211yesmaximal, characteristic, complemented
6#21445512C211yesmaximal, characteristic, complemented
7C22×#104×C61C211yesmaximal, characteristic
8C22×#11758194C2211yescharacteristic
9C2×#14519736C2211yescharacteristic
10C22×#11758196—21no—
11C22×C4×Dic61C2211yescharacteristic
12C22×C4×Dic61C2211yescharacteristic
13C2×#14519704—22no—
14C2×#14519704—22no—
15C2×#14519704—22no—
16#16839669C412yescomplemented
17#16839665C412yescomplemented
18#16839642—21no—
19#16839642—21no—
20C4×#11758196—22no—
21C4×#11758196—22no—
22C4×C22⋊Dic61—22no—
23C2×#14519684—21no—
24#16839523—22no—
25#16839522—22no—
26#16839516—22no—
27C22×#41×C61C2211yescharacteristic
28C22×M16×C61C2211yescharacteristic
29C22×C42×C61C2211yescharacteristic
30C2×#104×C61—22no—
31C2×#104×C61—22no—
32C2×#104×C61—22no—
33C23×Dic61—21no—
34C23×Dic61D411yescharacteristic
35C23×Dic61D411yescharacteristic
36C2×#11758194—21no—
37C2×#11758194—21no—
38C2×#11758194—21no—
39C2×#11758194—21no—
40C2×#11758194—21no—
41C2×#11758194D412yes—
42C22×#92418—21no—
43#14519736—21no—
44#14519736—21no—
45#14519736—21no—
46#14519736—21no—
47C2×C4⋊Dic61C2×C412yes—
48C2×#11758196—28no—
49C2×#11758196—24no—
50C2×C22⋊Dic61—21no—
51C2×C22⋊Dic61—22no—
52C2×C22⋊Dic61—22no—
53C2×C4×Dic61—21no—
54C2×C4×Dic61—21no—
55C2×C4×Dic61—21no—
56C2×C4×Dic61—21no—
57C2×C4×Dic61—21no—
58C2×C4×Dic61—21no—
59C2×C4×Dic61—21no—
60C2×C4×Dic61—21no—
61C2×C4×Dic61—21no—
62C2×C4×Dic61—21no—
63C2×C4×Dic61C2×C412yes—
64C2×C4×Dic61D412yes—
65C2×C4×Dic61D412yes—
66#14519704—28no—
67#14519684—24no—
68#14519684—22no—
69#14519684—22no—
70C2×#41×C61—21no—
71C2×#41×C61—21no—
72C2×#41×C61—21no—
73C2×#41×C61—21no—
74C2×#41×C61—21no—
75C2×#41×C61—21no—
76C2×#41×C61—21no—
77C2×#41×C61—21no—
78C2×#41×C61—21no—
79C2×#41×C61—21no—
80C2×#41×C61D412yes—
81C2×#41×C61Q812yes—
82C22×Q8×C61C2×C411yescharacteristic
83C22×D4×C61—21no—
84C22×D4×C61C2×C411yescharacteristic
85C23×C4×C61—21no—
86C23×C4×C61—21no—
87C23×C4×C61C2311yescharacteristic
88C2×M16×C61—21no—
89C2×M16×C61—21no—
90C2×M16×C61—21no—
91C2×M16×C61—21no—
92C2×M16×C61—21no—
93C2×M16×C61D412yes—
94C22×C8×C61—21no—
95C2×C42×C61—21no—
96C2×C42×C61—21no—
97C2×C42×C61—21no—
98C2×C42×C61—21no—
99C2×C42×C61—21no—
100C2×C42×C61D412yes—
101#104×C61—28no—
102C24×C61—21no—
103C24×C61C2×D411yescharacteristic
104#41×C61—22no—
105#41×C61—22no—
106#41×C61—22no—
107#41×C61—22no—
108#41×C61—22no—
109#41×C61—22no—
110#41×C61—22no—
111#41×C61—22no—
112#41×C61—41no—
113#41×C61—41no—
114#41×C61—41no—
115#41×C61—41no—
116#41×C61—41no—
117#41×C61—41no—
118#41×C61—41no—
119#41×C61—41no—
120C2×Q8×C61—21no—
121C2×Q8×C61—21no—
122C2×Q8×C61—21no—
123C2×Q8×C61—21no—
124C2×Q8×C61—21no—
125C2×Q8×C61C4⋊C412yescomplemented
126C2×D4×C61—22no—
127C2×D4×C61—22no—
128C2×D4×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—21no—
131C2×D4×C61—21no—
132C2×D4×C61—21no—
133C2×D4×C61—41no—
134C2×D4×C61—41no—
135C2×D4×C61—41no—
136C2×D4×C61—41no—
137C2×D4×C61C4⋊C412yescomplemented
138C22×C4×C61—24no—
139C22×C4×C61—21no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—42no—
144C22×C4×C61—41no—
145C22×C4×C61—41no—
146C22×C4×C61—41no—
147C22×C4×C61—41no—
148C22×C4×C61—41no—
149C22×C4×C61—41no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61C2×D411yescharacteristic
153C22×C4×C61C2×D411yescharacteristic
154C22×C4×C61C2×D411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×Q811yescharacteristic
158C22×C4×C61#4111yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C22×C4×C61#4111yescharacteristic
161C22×C4×C61#4111yescharacteristic
162C22×C4×C61#4111yescharacteristic
163C22×C4×C61#4111yescharacteristic
164C22×Dic61—21no—
165C22×Dic61—21no—
166C22×Dic61—24no—
167C22×Dic61—24no—
168C22×Dic61—22no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—22no—
172C22×Dic61—42no—
173C22×Dic61—42no—
174C22×Dic61—41no—
175C22×Dic61—41no—
176C22×Dic61C22⋊C412yes—
177C22×Dic61C22⋊C412yes—
178M16×C61—22no—
179M16×C61—22no—
180M16×C61—41no—
181M16×C61—41no—
182C2×C8×C61—22no—
183C2×C8×C61—41no—
184C2×C8×C61—41no—
185C42×C61—22no—
186C42×C61—22no—
187C42×C61—41no—
188C42×C61—41no—
189C22⋊Dic61—44no—
190C22⋊Dic61—41no—
191C22⋊Dic61—41no—
192C22⋊Dic61—44no—
193C4⋊Dic61—22no—
194C4⋊Dic61—22no—
195#11758196—216no—
196C4×Dic61—22no—
197C4×Dic61—22no—
198C4×Dic61—22no—
199C4×Dic61—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—41no—
203C4×Dic61—41no—
204C4×Dic61—41no—
205C4×Dic61—41no—
206#11758194—22no—
207#11758194—22no—
208#11758194—41no—
209#11758194—41no—
210C2×#92418—22no—
211C2×#92418—41no—
212C2×#92418—41no—
213C23×C61—22no—
214C23×C61—22no—
215C23×C61—22no—
216C23×C61—41no—
217C23×C61—41no—
218C23×C61—42no—
219C23×C61—42no—
220C23×C61C2×C22⋊C411yescharacteristic
221C23×C61#12011yescharacteristic
222C23×C61#12111yescharacteristic
223C23×C61C22⋊Q811yescharacteristic
224C23×C61#12311yescharacteristic
225C23×C61#12411yescharacteristic
226C23×C61#12711yescharacteristic
227Q8×C61—22no—
228Q8×C61—22no—
229Q8×C61—41no—
230Q8×C61—41no—
231D4×C61—22no—
232D4×C61—22no—
233D4×C61—42no—
234D4×C61—42no—
235D4×C61—42no—
236D4×C61—42no—
237D4×C61—41no—
238D4×C61—41no—
239C2×C4×C61—24no—
240C2×C4×C61—22no—
241C2×C4×C61—44no—
242C2×C4×C61—42no—
243C2×C4×C61—44no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—42no—
247C2×C4×C61—42no—
248C2×C4×C61—42no—
249C2×C4×C61—42no—
250C2×C4×C61—42no—
251C2×C4×C61C2×C4⋊C411yescharacteristic
252C2×C4×C61#11711yescharacteristic
253C2×C4×C61C4×D411yescharacteristic
254C2×C4×C61C4×D411yescharacteristic
255C2×C4×C61C4×D411yescharacteristic
256C2×C4×C61C4×D411yescharacteristic
257C2×C4×C61#12011yescharacteristic
258C2×C4×C61#12011yescharacteristic
259C2×C4×C61#12111yescharacteristic
260C2×C4×C61#12111yescharacteristic
261C2×C4×C61#12111yescharacteristic
262C2×C4×C61#12111yescharacteristic
263C2×C4×C61#12111yescharacteristic
264C2×C4×C61#12111yescharacteristic
265C2×C4×C61#12111yescharacteristic
266C2×C4×C61C22⋊Q811yescharacteristic
267C2×C4×C61C22⋊Q811yescharacteristic
268C2×C4×C61C22⋊Q811yescharacteristic
269C2×C4×C61C22⋊Q811yescharacteristic
270C2×C4×C61C22⋊Q811yescharacteristic
271C2×C4×C61#12311yescharacteristic
272C2×C4×C61#12311yescharacteristic
273C2×C4×C61#12311yescharacteristic
274C2×C4×C61#12311yescharacteristic
275C2×C4×C61#12411yescharacteristic
276C2×C4×C61#12411yescharacteristic
277C2×C4×C61#12611yescharacteristic
278C2×C4×C61#12611yescharacteristic
279C2×Dic61—24no—
280C2×Dic61—24no—
281C2×Dic61—22no—
282C2×Dic61—22no—
283C2×Dic61—24no—
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—44no—
288C2×Dic61—42no—
289C2×Dic61—44no—
290C2×Dic61—42no—
291C2×Dic61—42no—
292C2×Dic61—42no—
293C2×Dic61—42no—
294C2×Dic61—42no—
295C2×Dic61—42no—
296C2×Dic61#10414yescomplemented
297C8×C61—42no—
298#92418—42no—
299#11075—611nomaximal, Sylow
300C22×C61—22no—
301C22×C61—22no—
302C22×C61—21no—
303C22×C61—21no—
304C22×C61—21no—
305C22×C61—21no—
306C22×C61—22no—
307C22×C61—22no—
308C22×C61—44no—
309C22×C61—42no—
310C22×C61—81no—
311C22×C61—81no—
312C22×C61—82no—
313C22×C61#38011yescharacteristic
314C22×C61#38611yescharacteristic
315C22×C61#39011yescharacteristic
316C22×C61#39211yescharacteristic
317C22×C61#39311yescharacteristic
318C22×C61#39711yescharacteristic
319C22×C61#39911yescharacteristic
320C22×C61C2×#10412yes—
321C22×C61#42112yes—
322C4×C61—44no—
323C4×C61—42no—
324C4×C61#38511yescharacteristic
325C4×C61#38511yescharacteristic
326C4×C61#38811yescharacteristic
327C4×C61#38811yescharacteristic
328C4×C61#39411yescharacteristic
329C4×C61#39411yescharacteristic
330C4×C61#39611yescharacteristic
331C4×C61#39611yescharacteristic
332Dic61—24no—
333Dic61—44no—
334Dic61—42no—
335Dic61—82no—
336C22×#104—611no—
337C22×#104D6111yescharacteristic
338#2297—611no—
339C2×C4×C4⋊C4—611no—
340C2×#339—611no—
341C2×#339—611no—
342#1728—611no—
343C2×C61—21no—
344C2×C61—21no—
345C2×C61—21no—
346C2×C61—21no—
347C2×C61—82no—
348C2×C61#143911yescharacteristic
349C2×C61#180612yes—
350C2×C61#189611yescharacteristic
351C2×C61#189711yescharacteristic
352C2×C61#198012yes—
353C22×#41C2×D6111yescharacteristic
354C22×M16—611no—
355C22×M16C2×D6111yescharacteristic
356C2×#117—611no—
357C22×C4⋊C4—1221no—
358C22×C42—611no—
359C22×C42—611no—
360C22×C42C2×D6111yescharacteristic
361C2×#104—22no—
362C2×#104—22no—
363C2×#104—22no—
364C2×#104—1222no—
365C2×#104—1222no—
366C2×#104—1222no—
367#391—612no—
368#390—612no—
369#386—1221no—
370#386—1221no—
371C4×C4⋊C4—1222no—
372C4×C4⋊C4—1222no—
373C4×C22⋊C4—1222no—
374C2×#95—1221no—
375#339—1222no—
376#339—1222no—
377#336—1222no—
378C61#1107511yescharacteristic, complemented, Sylow
379C2×#41—21no—
380C2×#41—21no—
381C2×#41—21no—
382C2×#41—21no—
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—21no—
386C2×#41—21no—
387C2×#41—21no—
388C2×#41—21no—
389C2×#41Dic12212yes—
390C2×#41C22⋊D6112yes—
391C22×Q8C4×D6111yescharacteristic
392C22×D4—21no—
393C22×D4C4×D6111yescharacteristic
394C23×C4—21no—
395C23×C4—21no—
396C23×C4—611no—
397C23×C4—611no—
398C23×C4—1221no—
399C23×C4C22×D6111yescharacteristic
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16—21no—
404C2×M16—21no—
405C2×M16—612no—
406C2×M16—1221no—
407C2×M16—1221no—
408C2×M16—1221no—
409C2×M16—1221no—
410C2×M16—1221no—
411C2×M16C22⋊D6112yes—
412C22×C8—21no—
413C22×C8—1221no—
414#117—1221no—
415#117—1221no—
416#117—1221no—
417#117—1221no—
418C2×C4⋊C4—612no—
419C2×C4⋊C4—1224no—
420C2×C4⋊C4—1228no—
421C2×C22⋊C4—1222no—
422C2×C22⋊C4—1222no—
423C2×C22⋊C4—1221no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—612no—
430C2×C42—612no—
431C2×C42—612no—
432C2×C42—1221no—
433C2×C42—1221no—
434C2×C42—1221no—
435C2×C42—1221no—
436C2×C42—1221no—
437C2×C42—1221no—
438C2×C42—1221no—
439C2×C42—1221no—
440C2×C42—1221no—
441C2×C42—1221no—
442C2×C42C22⋊D6112yes—
443#104—28no—
444#104—1228no—
445#95—1222no—
446#95—1222no—
447#95—1224no—
448C24—21no—
449C24D4×D6111yescharacteristic
450#41—22no—
451#41—22no—
452#41—22no—
453#41—22no—
454#41—22no—
455#41—22no—
456#41—22no—
457#41—22no—
458#41—41no—
459#41—41no—
460#41—41no—
461#41—41no—
462#41—41no—
463#41—41no—
464#41—41no—
465#41—41no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8#1175819612yescomplemented
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—41no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4#1175819612yescomplemented
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—42no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—612no—
497C22×C4—612no—
498C22×C4—1224no—
499C22×C4—1221no—
500C22×C4—1221no—
501C22×C4—1224no—
502C22×C4—1221no—
503C22×C4—1222no—
504C22×C4—1221no—
505C22×C4—1222no—
506C22×C4—2442no—
507C22×C4—2442no—
508C22×C4—2441no—
509C22×C4—2441no—
510C22×C4C2×Dic12211yescharacteristic
511C22×C4C2×C4×D6111yescharacteristic
512C22×C4#1175822211yescharacteristic
513C22×C4#1175822211yescharacteristic
514C22×C4D4×D6111yescharacteristic
515C22×C4D4×D6111yescharacteristic
516C22×C4D4×D6111yescharacteristic
517C22×C4#1175822411yescharacteristic
518C22×C4#1175822411yescharacteristic
519C22×C4#1175822411yescharacteristic
520C22×C4#1175822411yescharacteristic
521C22×C4C2×C22⋊D6111yescharacteristic
522C22×C4C2×C22⋊D6111yescharacteristic
523C22×C4C2×C22⋊D6111yescharacteristic
524M16—22no—
525M16—22no—
526M16—41no—
527M16—41no—
528M16—1222no—
529M16—1222no—
530M16—2441no—
531M16—2441no—
532C2×C8—22no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—1222no—
536C2×C8—2441no—
537C2×C8—2441no—
538C4⋊C4—12216no—
539C4⋊C4—1222no—
540C4⋊C4—1222no—
541C22⋊C4—2444no—
542C22⋊C4—2444no—
543C22⋊C4—2441no—
544C22⋊C4—2441no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—41no—
549C42—1222no—
550C42—1222no—
551C42—1222no—
552C42—1222no—
553C42—1222no—
554C42—1222no—
555C42—2441no—
556C42—2441no—
557C42—2441no—
558C42—2441no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—42no—
563C23—42no—
564C23—41no—
565C23—41no—
566C23C22⋊C4×D6111yescharacteristic
567C23#1451974511yescharacteristic
568C23#1451974911yescharacteristic
569C23#1451975411yescharacteristic
570C23#1451975911yescharacteristic
571C23#1451976311yescharacteristic
572C23#1451977311yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—22no—
578D4—22no—
579D4—42no—
580D4—42no—
581D4—42no—
582D4—42no—
583D4—41no—
584D4—41no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—44no—
588C2×C4—42no—
589C2×C4—44no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—614no—
598C2×C4—1224no—
599C2×C4—1224no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1224no—
603C2×C4—1222no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—2442no—
607C2×C4—2442no—
608C2×C4—2442no—
609C2×C4—2444no—
610C2×C4—2442no—
611C2×C4—2444no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2442no—
615C2×C4C2×#1175819611yescharacteristic
616C2×C4#1451973311yescharacteristic
617C2×C4#1451973711yescharacteristic
618C2×C4#1451973711yescharacteristic
619C2×C4C4×C22⋊D6111yescharacteristic
620C2×C4C4×C22⋊D6111yescharacteristic
621C2×C4#1451974511yescharacteristic
622C2×C4#1451974611yescharacteristic
623C2×C4#1451974811yescharacteristic
624C2×C4#1451974811yescharacteristic
625C2×C4#1451974911yescharacteristic
626C2×C4#1451974911yescharacteristic
627C2×C4#1451974911yescharacteristic
628C2×C4#1451975011yescharacteristic
629C2×C4#1451975011yescharacteristic
630C2×C4#1451975411yescharacteristic
631C2×C4#1451975411yescharacteristic
632C2×C4#1451975411yescharacteristic
633C2×C4#1451975611yescharacteristic
634C2×C4#1451975611yescharacteristic
635C2×C4#1451975811yescharacteristic
636C2×C4#1451975811yescharacteristic
637C2×C4#1451975911yescharacteristic
638C2×C4#1451976011yescharacteristic
639C2×C4#1451976311yescharacteristic
640C2×C4#1451976411yescharacteristic
641C2×C4#1451977011yescharacteristic
642C2×C4#1451977011yescharacteristic
643C8—42no—
644C8—2442no—
645C22—22no—
646C22—22no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—22no—
652C22—22no—
653C22—44no—
654C22—42no—
655C22—82no—
656C22—81no—
657C22—81no—
658C22#1683962011yescharacteristic
659C22#1683963811yescharacteristic
660C22#1683966211yescharacteristic
661C22#1683967011yescharacteristic
662C22#1683967411yescharacteristic
663C22#1683969011yescharacteristic
664C22#1683969811yescharacteristic
665C22#104×D6112yes—
666C22#1683977712yes—
667C4—44no—
668C4—42no—
669C4—1224no—
670C4—4882no—
671C4—2444no—
672C4—2442no—
673C4#1683963411yescharacteristic
674C4#1683963511yescharacteristic
675C4#1683965011yescharacteristic
676C4#1683965611yescharacteristic
677C4#1683967611yescharacteristic
678C4#1683967711yescharacteristic
679C4#1683968511yescharacteristic
680C4#1683968511yescharacteristic
681C2—21no—
682C2—21no—
683C2—21no—
684C2—21no—
685C2—82no—
686C2#2144406211yescharacteristic
687C2#2144583712yes—
688C2#2144625911yescharacteristic
689C2#2144626411yescharacteristic
690C2#2144673612yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC22×#104×C61C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#41×C61C22
cosocleC23×C4×C61C23
hypercenterC22×#104D61
hypocenterC61#11075
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11758196C2semidirect
4. C2×#16839523C2semidirect
5. C2×#16839522C2semidirect
6. #21445512C2semidirect
16. #16839669C4semidirect
17. #16839665C4semidirect
125. C2×Q8×C61C4⋊C4semidirect
137. C2×D4×C61C4⋊C4semidirect
296. C2×Dic61#104semidirect
378. C61#11075semidirect
471. C2×Q8#11758196semidirect
483. C2×D4#11758196semidirect

Maximal subgroups

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

subgroupindex
C22×#145197042
#214483102
C2×C4×#117581962
C2×#168395232
C2×#168395222
#214455122
C22×#104×C612
#1107561