Finite Group Databasebeta

← #29587120

Subgroups — #29587120

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×#14519705C211yesmaximal, characteristic
2C22×#14519703C211yesmaximal, characteristic
3#21448307C211yesmaximal, characteristic
4C2×C4×#11758196C211yesmaximal, characteristic, complemented
5C2×#16839521C211yesmaximal, characteristic, complemented
6#21445512C211yesmaximal, characteristic, complemented
7C2×C61×#339C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758196—21no—
11C22×C4×Dic61C2211yescharacteristic
12C22×C4×Dic61C2211yescharacteristic
13C2×#14519705—22no—
14C2×#14519705—22no—
15C2×#14519705—22no—
16C2×#14519703—22no—
17C2×#14519703—22no—
18C2×#14519703—22no—
19#16839667C412yescomplemented
20#16839663C412yescomplemented
21#16839639—21no—
22#16839639—21no—
23C4×#11758196—22no—
24C4×#11758196—22no—
25C4×#11758198—22no—
26C2×#14519684—21no—
27#16839521—22no—
28#16839516—22no—
29C22×M16×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C22×C42×C61C2211yescharacteristic
32C61×#339—22no—
33C2×#11758222—21no—
34C2×#11758222—21no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222D412yes—
44C2×#11758222Q812yes—
45C22×Dic122C2×C411yescharacteristic
46C22×D244C2×C411yescharacteristic
47C22×C22⋊D61—21no—
48C23×Dic61—21no—
49C23×Dic61D411yescharacteristic
50C23×Dic61D411yescharacteristic
51C22×C4×D61—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194—21no—
57C2×#11758194D412yes—
58C22×#92418—21no—
59C2×#11758196—28no—
60C2×#11758196—24no—
61C2×#11758198—22no—
62C2×#11758198—22no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61—21no—
69C2×C4×Dic61—21no—
70C2×C4×Dic61—21no—
71C2×C4×Dic61—21no—
72C2×C4×Dic61C2×C412yes—
73C2×C4×Dic61D412yes—
74C2×C4×Dic61D412yes—
75#14519705—28no—
76#14519703—28no—
77#14519684—24no—
78#14519684—22no—
79#14519684—22no—
80C23×C4×C61—21no—
81C23×C4×C61C2311yescharacteristic
82C2×M16×C61—21no—
83C2×M16×C61—21no—
84C2×M16×C61—21no—
85C2×M16×C61—21no—
86C2×M16×C61—21no—
87C2×M16×C61D412yes—
88C22×C8×C61—21no—
89#117×C61—21no—
90#117×C61—21no—
91#117×C61—21no—
92#117×C61—21no—
93C2×C4⋊C4×C61C2×C412yes—
94C2×C22⋊C4×C61—21no—
95C2×C42×C61—21no—
96C2×C42×C61—21no—
97C2×C42×C61—21no—
98C2×C42×C61—21no—
99C2×C42×C61—21no—
100C2×C42×C61—21no—
101C2×C42×C61D412yes—
102C24×C61C2×D411yescharacteristic
103C23×D61—21no—
104C22×C4×C61—24no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—42no—
108C22×C4×C61—41no—
109C22×C4×C61—41no—
110C22×C4×C61C22×C411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×Q811yescharacteristic
118C22×C4×C61#4111yescharacteristic
119C22×C4×C61#4111yescharacteristic
120C22×C4×C61#4111yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C22×C4×C61#4111yescharacteristic
124C2×C22⋊D61—22no—
125C2×C22⋊D61—22no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61—41no—
128C2×C22⋊D61—41no—
129C2×C22⋊D61—41no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—24no—
133C22×Dic61—24no—
134C22×Dic61—21no—
135C22×Dic61—22no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—42no—
139C22×Dic61—42no—
140C22×Dic61—41no—
141C22×Dic61—41no—
142C22×Dic61C22⋊C412yes—
143C22×Dic61C22⋊C412yes—
144#11758222—22no—
145#11758222—22no—
146#11758222—22no—
147#11758222—22no—
148#11758222—22no—
149#11758222—22no—
150#11758222—22no—
151#11758222—22no—
152#11758222—41no—
153#11758222—41no—
154#11758222—41no—
155#11758222—41no—
156#11758222—41no—
157#11758222—41no—
158#11758222—41no—
159#11758222—41no—
160C2×D244—21no—
161C2×D244—21no—
162C2×D244—21no—
163C2×D244—21no—
164C2×D244—21no—
165C2×D244C4⋊C412yescomplemented
166C2×C4×D61—22no—
167C2×C4×D61—22no—
168C2×C4×D61—41no—
169C2×C4×D61—41no—
170C2×C4×D61—41no—
171C2×C4×D61—41no—
172C2×Dic122—21no—
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—21no—
177C2×Dic122C4⋊C412yescomplemented
178M16×C61—22no—
179M16×C61—22no—
180M16×C61—41no—
181M16×C61—41no—
182C2×C8×C61—22no—
183C2×C8×C61—41no—
184C2×C8×C61—41no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—22no—
187C22⋊C4×C61—41no—
188C22⋊C4×C61—41no—
189C42×C61—22no—
190C42×C61—22no—
191C42×C61—41no—
192C42×C61—41no—
193C42×C61—41no—
194C42×C61—41no—
195#11758198—44no—
196#11758198—44no—
197#11758196—216no—
198C4×Dic61—22no—
199C4×Dic61—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61—22no—
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×C61C2×C22⋊C411yescharacteristic
216C23×C61#12011yescharacteristic
217C23×C61#12111yescharacteristic
218C23×C61C22⋊Q811yescharacteristic
219C23×C61#12311yescharacteristic
220C23×C61#12411yescharacteristic
221C23×C61#12711yescharacteristic
222C22×D61—22no—
223C22×D61—41no—
224C22×D61—41no—
225C22×D61—42no—
226C22×D61—42no—
227C2×C4×C61—24no—
228C2×C4×C61—44no—
229C2×C4×C61—42no—
230C2×C4×C61—44no—
231C2×C4×C61—42no—
232C2×C4×C61—42no—
233C2×C4×C61—42no—
234C2×C4×C61—42no—
235C2×C4×C61C2×C4⋊C411yescharacteristic
236C2×C4×C61#11711yescharacteristic
237C2×C4×C61C4×D411yescharacteristic
238C2×C4×C61C4×D411yescharacteristic
239C2×C4×C61C4×D411yescharacteristic
240C2×C4×C61C4×D411yescharacteristic
241C2×C4×C61#12011yescharacteristic
242C2×C4×C61#12011yescharacteristic
243C2×C4×C61#12111yescharacteristic
244C2×C4×C61#12111yescharacteristic
245C2×C4×C61#12111yescharacteristic
246C2×C4×C61#12111yescharacteristic
247C2×C4×C61#12111yescharacteristic
248C2×C4×C61#12111yescharacteristic
249C2×C4×C61#12111yescharacteristic
250C2×C4×C61C22⋊Q811yescharacteristic
251C2×C4×C61C22⋊Q811yescharacteristic
252C2×C4×C61C22⋊Q811yescharacteristic
253C2×C4×C61C22⋊Q811yescharacteristic
254C2×C4×C61C22⋊Q811yescharacteristic
255C2×C4×C61#12311yescharacteristic
256C2×C4×C61#12311yescharacteristic
257C2×C4×C61#12311yescharacteristic
258C2×C4×C61#12311yescharacteristic
259C2×C4×C61#12411yescharacteristic
260C2×C4×C61#12411yescharacteristic
261C2×C4×C61#12611yescharacteristic
262C2×C4×C61#12611yescharacteristic
263C22⋊D61—42no—
264C22⋊D61—42no—
265C22⋊D61—42no—
266C22⋊D61—42no—
267C2×Dic61—24no—
268C2×Dic61—24no—
269C2×Dic61—22no—
270C2×Dic61—22no—
271C2×Dic61—24no—
272C2×Dic61—22no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—44no—
277C2×Dic61—42no—
278C2×Dic61—44no—
279C2×Dic61—42no—
280C2×Dic61—42no—
281C2×Dic61—41no—
282C2×Dic61—41no—
283C2×Dic61—42no—
284C2×Dic61#10414yescomplemented
285D244—22no—
286D244—22no—
287D244—41no—
288D244—41no—
289C4×D61—42no—
290C4×D61—42no—
291C4×D61—42no—
292C4×D61—42no—
293Dic122—22no—
294Dic122—22no—
295Dic122—41no—
296Dic122—41no—
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#38011yescharacteristic
309C22×C61#38611yescharacteristic
310C22×C61#39011yescharacteristic
311C22×C61#39211yescharacteristic
312C22×C61#39311yescharacteristic
313C22×C61#39711yescharacteristic
314C22×C61#39911yescharacteristic
315C22×C61C2×#10412yes—
316C22×C61#42112yes—
317C2×D61—44no—
318C2×D61—42no—
319C2×D61—81no—
320C2×D61—81no—
321C2×D61—82no—
322C4×C61—44no—
323C4×C61—82no—
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—42no—
336C22×#104—611no—
337C22×#104—611no—
338#2297—611no—
339C2×C4×C4⋊C4—611no—
340C2×#339—611no—
341C2×#339D6111yescharacteristic, complemented
342#1728—611no—
343C2×C61—21no—
344C2×C61—21no—
345C2×C61—21no—
346C2×C61—21no—
347C2×C61#143911yescharacteristic
348C2×C61#180612yes—
349C2×C61#189611yescharacteristic
350C2×C61#189711yescharacteristic
351C2×C61#198012yes—
352D61—82no—
353C22×#41—611no—
354C22×M16—611no—
355C22×M16C2×D6111yescharacteristic
356C2×#117C2×D6111yescharacteristic
357C22×C4⋊C4—1221no—
358C22×C42—611no—
359C22×C42—611no—
360C22×C42C2×D6111yescharacteristic
361C2×#104—1222no—
362C2×#104—1222no—
363C2×#104—1222no—
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—22no—
376#339—1222no—
377#336—1222no—
378C61#1107511yescharacteristic, complemented, Sylow
379C2×#41—612no—
380C2×#41—612no—
381C2×#41—1221no—
382C2×#41—1221no—
383C2×#41—1221no—
384C2×#41—1221no—
385C2×#41—1221no—
386C2×#41—1221no—
387C2×#41—1221no—
388C2×#41—1221no—
389C2×#41—1221no—
390C2×#41—1221no—
391C22×Q8—611no—
392C22×D4—611no—
393C22×D4—1221no—
394C23×C4—21no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—1221no—
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—21no—
415#117—21no—
416#117—21no—
417#117—21no—
418C2×C4⋊C4—1224no—
419C2×C4⋊C4—1228no—
420C2×C4⋊C4C4×D6112yes—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—1222no—
423C2×C22⋊C4—1222no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—21no—
430C2×C42—612no—
431C2×C42—612no—
432C2×C42—612no—
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×C42D24412yes—
443#104—1228no—
444#104—1228no—
445#95—1222no—
446#95—1222no—
447#95—1224no—
448C24—1221no—
449C24D4×D6111yescharacteristic
450#41—1222no—
451#41—1222no—
452#41—1222no—
453#41—1222no—
454#41—1222no—
455#41—1222no—
456#41—1222no—
457#41—1222no—
458#41—2441no—
459#41—2441no—
460#41—2441no—
461#41—2441no—
462#41—2441no—
463#41—2441no—
464#41—2441no—
465#41—2441no—
466C2×Q8—612no—
467C2×Q8—1221no—
468C2×Q8—1221no—
469C2×Q8—1221no—
470C2×Q8—1221no—
471C2×Q8—1221no—
472C2×D4—612no—
473C2×D4—1222no—
474C2×D4—1222no—
475C2×D4—1221no—
476C2×D4—1221no—
477C2×D4—1221no—
478C2×D4—1221no—
479C2×D4—1221no—
480C2×D4—2441no—
481C2×D4—2441no—
482C2×D4—2441no—
483C2×D4—2441no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—42no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—612no—
491C22×C4—612no—
492C22×C4—1224no—
493C22×C4—1221no—
494C22×C4—1221no—
495C22×C4—1224no—
496C22×C4—1221no—
497C22×C4—1221no—
498C22×C4—1222no—
499C22×C4—1221no—
500C22×C4—1222no—
501C22×C4—1222no—
502C22×C4—2442no—
503C22×C4—2442no—
504C22×C4—2441no—
505C22×C4—2441no—
506C22×C4—2441no—
507C22×C4—2441no—
508C22×C4—2441no—
509C22×C4—2441no—
510C22×C4C2×C4×D6111yescharacteristic
511C22×C4C2×D24411yescharacteristic
512C22×C4#1175822211yescharacteristic
513C22×C4#1175822211yescharacteristic
514C22×C4#1175822211yescharacteristic
515C22×C4#1175822211yescharacteristic
516C22×C4D4×D6111yescharacteristic
517C22×C4D4×D6111yescharacteristic
518C22×C4D4×D6111yescharacteristic
519C22×C4D4×D6111yescharacteristic
520C22×C4#1175822411yescharacteristic
521C22×C4Q8×D6111yescharacteristic
522C22×C4#1175822611yescharacteristic
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—22no—
539C4⋊C4—22no—
540C4⋊C4—12216no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C22⋊C4—2444no—
544C22⋊C4—2444no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—41no—
549C42—41no—
550C42—41no—
551C42—1222no—
552C42—1222no—
553C42—1222no—
554C42—1222no—
555C42—1222no—
556C42—1222no—
557C42—2441no—
558C42—2441no—
559C23—22no—
560C23—22no—
561C23—1222no—
562C23—2442no—
563C23—2442no—
564C23—2441no—
565C23—2441no—
566C23C22⋊C4×D6111yescharacteristic
567C23#1451974711yescharacteristic
568C23#1451975011yescharacteristic
569C23#1451975511yescharacteristic
570C23#1451976211yescharacteristic
571C23#1451976311yescharacteristic
572C23#1451977311yescharacteristic
573Q8—1222no—
574Q8—1222no—
575Q8—2441no—
576Q8—2441no—
577D4—1222no—
578D4—1222no—
579D4—2442no—
580D4—2442no—
581D4—2442no—
582D4—2442no—
583D4—2441no—
584D4—2441no—
585C2×C4—24no—
586C2×C4—44no—
587C2×C4—42no—
588C2×C4—44no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—614no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1222no—
597C2×C4—1222no—
598C2×C4—1224no—
599C2×C4—1222no—
600C2×C4—1222no—
601C2×C4—1222no—
602C2×C4—1222no—
603C2×C4—2444no—
604C2×C4—2442no—
605C2×C4—2444no—
606C2×C4—2442no—
607C2×C4—2442no—
608C2×C4—2441no—
609C2×C4—2441no—
610C2×C4—2442no—
611C2×C4—2442no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4—2442no—
615C2×C4C4⋊C4×D6111yescharacteristic
616C2×C4#1451973411yescharacteristic
617C2×C4#1451973711yescharacteristic
618C2×C4C4×C22⋊D6111yescharacteristic
619C2×C4#1451973911yescharacteristic
620C2×C4C4×D24411yescharacteristic
621C2×C4#1451974511yescharacteristic
622C2×C4#1451974711yescharacteristic
623C2×C4#1451974911yescharacteristic
624C2×C4#1451975011yescharacteristic
625C2×C4#1451975011yescharacteristic
626C2×C4#1451975011yescharacteristic
627C2×C4#1451975011yescharacteristic
628C2×C4#1451975111yescharacteristic
629C2×C4#1451975211yescharacteristic
630C2×C4#1451975311yescharacteristic
631C2×C4#1451975511yescharacteristic
632C2×C4#1451975511yescharacteristic
633C2×C4#1451975511yescharacteristic
634C2×C4#1451975711yescharacteristic
635C2×C4#1451975911yescharacteristic
636C2×C4#1451976011yescharacteristic
637C2×C4#1451976211yescharacteristic
638C2×C4#1451976211yescharacteristic
639C2×C4#1451976311yescharacteristic
640C2×C4#1451976511yescharacteristic
641C2×C4#1451977111yescharacteristic
642C2×C4#1451977211yescharacteristic
643C8—42no—
644C8—2442no—
645C22—22no—
646C22—22no—
647C22—21no—
648C22—21no—
649C22—21no—
650C22—21no—
651C22—22no—
652C22—22no—
653C22—4882no—
654C22—4881no—
655C22—4881no—
656C22—2444no—
657C22—2442no—
658C22#1683962111yescharacteristic
659C22#1683964011yescharacteristic
660C22#1683966211yescharacteristic
661C22#1683967111yescharacteristic
662C22#1683967511yescharacteristic
663C22#1683969111yescharacteristic
664C22#1683969711yescharacteristic
665C22#104×D6112yes—
666C22#1683977712yes—
667C4—44no—
668C4—82no—
669C4—1224no—
670C4—2444no—
671C4—2442no—
672C4—2442no—
673C4#1683963311yescharacteristic
674C4#1683963611yescharacteristic
675C4#1683965111yescharacteristic
676C4#1683965311yescharacteristic
677C4#1683967711yescharacteristic
678C4#1683968011yescharacteristic
679C4#1683968411yescharacteristic
680C4#1683968611yescharacteristic
681C2—21no—
682C2—21no—
683C2—21no—
684C2—21no—
685C2—4882no—
686C2#2144406311yescharacteristic
687C2#2144583812yes—
688C2#2144626111yescharacteristic
689C2#2144626611yescharacteristic
690C2#2144673612yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#339C2
socleC23×C61C2×C22⋊C4
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#339D61
hypocenterC61#11075
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×C4×#11758196C2semidirect
5. C2×#16839521C2semidirect
6. #21445512C2semidirect
7. C2×C61×#339C2semidirect
19. #16839667C4semidirect
20. #16839663C4semidirect
165. C2×D244C4⋊C4semidirect
177. C2×Dic122C4⋊C4semidirect
284. C2×Dic61#104semidirect
341. C2×#339D61semidirect
378. C61#11075semidirect

Maximal subgroups

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

subgroupindex
C22×#145197052
C22×#145197032
#214483072
C2×C4×#117581962
C2×#168395212
#214455122
C2×C61×#3392
#1107561