Finite Group Databasebeta

← #29586991

Subgroups — #29586991

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839768C211yesmaximal, characteristic
2C2×#16839766C211yesmaximal, characteristic
3#21448435C211yesmaximal, characteristic, complemented
4C2×#16839664C211yesmaximal, characteristic
5C2×#16839530C211yesmaximal, characteristic, complemented
6C2×#16839522C211yesmaximal, characteristic, complemented
7C2×C61×#339C211yesmaximal, characteristic, complemented
8C23×D244C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C2×#14519736C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C22×#11758198—22no—
13#16839768—22no—
14#16839768—22no—
15#16839766—22no—
16#16839766—22no—
17C2×#14519699—22no—
18C2×#14519697—22no—
19#16839664—22no—
20#16839664C414yescomplemented
21#16839660—22no—
22#16839658—22no—
23#16839620—22no—
24#16839530—22no—
25#16839522—22no—
26C22×M16×C61C2211yescharacteristic
27C2×#117×C61C2211yescharacteristic
28C22×C42×C61C2211yescharacteristic
29C61×#339—22no—
30C24×D61—21no—
31C22×D244—21no—
32C22×D244—21no—
33C22×D244—21no—
34C22×D244—21no—
35C22×D244—21no—
36C22×D244—21no—
37C22×D244—21no—
38C22×D244—21no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244C2×C412yes—
43C22×D244D412yes—
44C22×D244Q812yes—
45C23×Dic61D412yes—
46C2×#11758194—21no—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194D412yes—
52C22×#92418—21no—
53#14519736—21no—
54#14519736—21no—
55#14519736—21no—
56#14519736—21no—
57C2×C4⋊Dic61—21no—
58C2×C4⋊Dic61—21no—
59C2×C4⋊Dic61—21no—
60C2×C4⋊Dic61—21no—
61C2×C4⋊Dic61C2×C412yes—
62C2×C4⋊Dic61D412yes—
63C2×C4⋊Dic61D412yes—
64C2×#11758196—24no—
65C2×C22⋊Dic61—21no—
66C2×#11758198—28no—
67C2×#11758198—48no—
68C2×C4×Dic61—21no—
69#14519699—28no—
70#14519697—28no—
71#14519684—24no—
72C23×C4×C61—21no—
73C23×C4×C61C2311yescharacteristic
74C2×M16×C61—21no—
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61D412yes—
80C22×C8×C61—21no—
81#117×C61—21no—
82#117×C61—21no—
83#117×C61—21no—
84#117×C61—21no—
85C2×C4⋊C4×C61D412yes—
86C2×C22⋊C4×C61—21no—
87C2×C42×C61—21no—
88C2×C42×C61—21no—
89C2×C42×C61—21no—
90C2×C42×C61—21no—
91C2×C42×C61—21no—
92C2×C42×C61—21no—
93C2×C42×C61C2×C412yes—
94C24×C61C2×D411yescharacteristic
95C23×D61—22no—
96C23×D61—22no—
97C23×D61—22no—
98C23×D61—44no—
99C23×D61—44no—
100C23×D61—41no—
101C23×D61—41no—
102C23×D61—41no—
103C23×D61—41no—
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
124C22×Dic61—22no—
125C22×Dic61—22no—
126C22×Dic61—22no—
127C22×Dic61—44no—
128C22×Dic61C22⋊C414yes—
129C2×D244—22no—
130C2×D244—22no—
131C2×D244—22no—
132C2×D244—22no—
133C2×D244—22no—
134C2×D244—22no—
135C2×D244—22no—
136C2×D244—22no—
137C2×D244—22no—
138C2×D244—22no—
139C2×D244—22no—
140C2×D244—22no—
141C2×D244—22no—
142C2×D244—22no—
143C2×D244—22no—
144C2×D244—41no—
145C2×D244—41no—
146C2×D244—41no—
147C2×D244—41no—
148C2×D244—41no—
149C2×D244—41no—
150C2×D244—41no—
151C2×D244—41no—
152C2×D244—41no—
153C2×D244—41no—
154C2×D244—41no—
155C2×D244—41no—
156C2×D244C4⋊C414yescomplemented
157M16×C61—22no—
158M16×C61—22no—
159M16×C61—41no—
160M16×C61—41no—
161C2×C8×C61—22no—
162C2×C8×C61—41no—
163C2×C8×C61—41no—
164C4⋊C4×C61—22no—
165C4⋊C4×C61—22no—
166C22⋊C4×C61—41no—
167C22⋊C4×C61—41no—
168C42×C61—22no—
169C42×C61—22no—
170C42×C61—41no—
171C42×C61—41no—
172C42×C61—41no—
173C42×C61—41no—
174C22⋊Dic61—41no—
175C22⋊Dic61—41no—
176#11758198—416no—
177C4⋊Dic61—22no—
178C4⋊Dic61—22no—
179C4⋊Dic61—22no—
180C4⋊Dic61—22no—
181C4⋊Dic61—22no—
182C4⋊Dic61—22no—
183#11758196—84no—
184C4×Dic61—41no—
185C4×Dic61—41no—
186#11758194—22no—
187#11758194—22no—
188#11758194—41no—
189#11758194—41no—
190C2×#92418—22no—
191C2×#92418—41no—
192C2×#92418—41no—
193C23×C61—22no—
194C23×C61—22no—
195C23×C61C2×C22⋊C411yescharacteristic
196C23×C61#12011yescharacteristic
197C23×C61#12111yescharacteristic
198C23×C61C22⋊Q811yescharacteristic
199C23×C61#12311yescharacteristic
200C23×C61#12411yescharacteristic
201C23×C61#12711yescharacteristic
202C22×D61—24no—
203C22×D61—44no—
204C22×D61—44no—
205C22×D61—48no—
206C22×D61—48no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—42no—
212C22×D61—42no—
213C22×D61—82no—
214C22×D61—82no—
215C22×D61—84no—
216C22×D61—84no—
217C22×D61—82no—
218C22×D61—82no—
219C2×C4×C61—24no—
220C2×C4×C61—42no—
221C2×C4×C61—44no—
222C2×C4×C61—44no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61—42no—
227C2×C4×C61C2×C4⋊C411yescharacteristic
228C2×C4×C61#11711yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×C4×C61C4×D411yescharacteristic
232C2×C4×C61C4×D411yescharacteristic
233C2×C4×C61#12011yescharacteristic
234C2×C4×C61#12011yescharacteristic
235C2×C4×C61#12111yescharacteristic
236C2×C4×C61#12111yescharacteristic
237C2×C4×C61#12111yescharacteristic
238C2×C4×C61#12111yescharacteristic
239C2×C4×C61#12111yescharacteristic
240C2×C4×C61#12111yescharacteristic
241C2×C4×C61#12111yescharacteristic
242C2×C4×C61C22⋊Q811yescharacteristic
243C2×C4×C61C22⋊Q811yescharacteristic
244C2×C4×C61C22⋊Q811yescharacteristic
245C2×C4×C61C22⋊Q811yescharacteristic
246C2×C4×C61C22⋊Q811yescharacteristic
247C2×C4×C61#12311yescharacteristic
248C2×C4×C61#12311yescharacteristic
249C2×C4×C61#12311yescharacteristic
250C2×C4×C61#12311yescharacteristic
251C2×C4×C61#12411yescharacteristic
252C2×C4×C61#12411yescharacteristic
253C2×C4×C61#12611yescharacteristic
254C2×C4×C61#12611yescharacteristic
255C2×Dic61—24no—
256C2×Dic61—44no—
257C2×Dic61—44no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61—82no—
262D244—24no—
263D244—24no—
264D244—42no—
265D244—42no—
266D244—42no—
267D244—42no—
268D244—42no—
269D244—42no—
270C8×C61—42no—
271#92418—42no—
272#11054—611nomaximal, Sylow
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—22no—
278C22×C61—22no—
279C22×C61—22no—
280C22×C61—22no—
281C22×C61#38011yescharacteristic
282C22×C61#38611yescharacteristic
283C22×C61#39011yescharacteristic
284C22×C61#39211yescharacteristic
285C22×C61#39311yescharacteristic
286C22×C61#39711yescharacteristic
287C22×C61#39911yescharacteristic
288C22×C61#45312yes—
289C22×C61#45412yes—
290C2×D61—48no—
291C2×D61—44no—
292C2×D61—84no—
293C2×D61—84no—
294C2×D61—84no—
295C2×D61—82no—
296C2×D61—82no—
297C2×D61—84no—
298C2×D61—84no—
299C4×C61—44no—
300C4×C61—82no—
301C4×C61#38511yescharacteristic
302C4×C61#38511yescharacteristic
303C4×C61#38811yescharacteristic
304C4×C61#38811yescharacteristic
305C4×C61#39411yescharacteristic
306C4×C61#39411yescharacteristic
307C4×C61#39611yescharacteristic
308C4×C61#39611yescharacteristic
309Dic61—44no—
310Dic61—82no—
311C2×#418—611no—
312C2×#418—611no—
313#2316—611no—
314C2×#390—611no—
315C2×#343—611no—
316C2×#339—611no—
317C2×#339D6111yescharacteristic, complemented
318C2×C61—21no—
319C2×C61—21no—
320C2×C61—21no—
321C2×C61—21no—
322C2×C61#143911yescharacteristic
323C2×C61#188711yescharacteristic
324C2×C61#188811yescharacteristic
325C2×C61#200612yes—
326C2×C61#202712yes—
327D61—84no—
328C23×D4—611no—
329C22×M16—611no—
330C22×M16C2×D6111yescharacteristic
331C2×#117—611no—
332C2×#117C2×D6111yescharacteristic
333C22×C4⋊C4—611no—
334C22×C22⋊C4—1222no—
335C22×C42C2×D6111yescharacteristic
336#418—1222no—
337#418—1222no—
338#418—1222no—
339#418—1222no—
340C2×#102—1222no—
341C2×#102—1222no—
342#390—614no—
343#390—1222no—
344#389—1222no—
345#389—1222no—
346#380—1222no—
347#343—1222no—
348#339—22no—
349#339—1222no—
350C61#1105411yescharacteristic, complemented, Sylow
351C25—1221no—
352C22×D4—612no—
353C22×D4—612no—
354C22×D4—612no—
355C22×D4—1221no—
356C22×D4—1221no—
357C22×D4—1221no—
358C22×D4—1221no—
359C22×D4—1221no—
360C22×D4—1221no—
361C22×D4—1221no—
362C22×D4—1221no—
363C22×D4—1221no—
364C22×D4—1221no—
365C22×D4—1221no—
366C23×C4—21no—
367C23×C4—612no—
368C23×C4C22×D6111yescharacteristic
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—612no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16C22⋊D6112yes—
381C22×C8—21no—
382C22×C8—1221no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—1221no—
388#117—1221no—
389#117—1221no—
390#117—1221no—
391C2×C4⋊C4—612no—
392C2×C4⋊C4—612no—
393C2×C4⋊C4—612no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4—1221no—
397C2×C4⋊C4—1221no—
398C2×C4⋊C4—1224no—
399C2×C4⋊C4D24412yes—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—1228no—
402C2×C22⋊C4—1221no—
403C2×C22⋊C4—2448no—
404C2×C42—21no—
405C2×C42—21no—
406C2×C42—21no—
407C2×C42—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—1221no—
411C2×C42C4×D6112yes—
412#102—1228no—
413#102—1228no—
414#95—1224no—
415C24—1222no—
416C24—1222no—
417C24—1222no—
418C24—2444no—
419C24—2444no—
420C24—2441no—
421C24—2441no—
422C24—2441no—
423C24—2441no—
424C24D4×D6111yescharacteristic
425C2×D4—614no—
426C2×D4—1222no—
427C2×D4—1222no—
428C2×D4—1222no—
429C2×D4—1222no—
430C2×D4—1222no—
431C2×D4—1222no—
432C2×D4—1222no—
433C2×D4—1222no—
434C2×D4—1222no—
435C2×D4—1222no—
436C2×D4—1222no—
437C2×D4—1222no—
438C2×D4—1222no—
439C2×D4—1222no—
440C2×D4—1222no—
441C2×D4—2441no—
442C2×D4—2441no—
443C2×D4—2441no—
444C2×D4—2441no—
445C2×D4—2441no—
446C2×D4—2441no—
447C2×D4—2441no—
448C2×D4—2441no—
449C2×D4—2441no—
450C2×D4—2441no—
451C2×D4—2441no—
452C2×D4—2441no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—42no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—614no—
460C22×C4—1222no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—2444no—
464C22×C4C2×C4×D6111yescharacteristic
465C22×C4C2×D24411yescharacteristic
466C22×C4#1175822211yescharacteristic
467C22×C4#1175822211yescharacteristic
468C22×C4#1175822211yescharacteristic
469C22×C4#1175822211yescharacteristic
470C22×C4D4×D6111yescharacteristic
471C22×C4D4×D6111yescharacteristic
472C22×C4D4×D6111yescharacteristic
473C22×C4D4×D6111yescharacteristic
474C22×C4#1175822411yescharacteristic
475C22×C4Q8×D6111yescharacteristic
476C22×C4#1175822611yescharacteristic
477C22×C4C2×C22⋊D6111yescharacteristic
478M16—22no—
479M16—22no—
480M16—41no—
481M16—41no—
482M16—1222no—
483M16—1222no—
484M16—2441no—
485M16—2441no—
486C2×C8—22no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—1222no—
490C2×C8—2441no—
491C2×C8—2441no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—4884no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—24416no—
504C22⋊C4—2441no—
505C22⋊C4—2441no—
506C42—22no—
507C42—22no—
508C42—41no—
509C42—41no—
510C42—41no—
511C42—41no—
512C42—2441no—
513C42—2441no—
514C23—22no—
515C23—22no—
516C23—1224no—
517C23—4884no—
518C23—4882no—
519C23—4882no—
520C23—4884no—
521C23—4882no—
522C23—4882no—
523C23—2444no—
524C23—2448no—
525C23—2444no—
526C23—2448no—
527C23—2442no—
528C23—2442no—
529C23—2442no—
530C23—2442no—
531C23—2442no—
532C23—2442no—
533C23C22⋊C4×D6111yescharacteristic
534C23#1451974711yescharacteristic
535C23#1451975011yescharacteristic
536C23#1451975511yescharacteristic
537C23#1451976211yescharacteristic
538C23#1451976311yescharacteristic
539C23#1451977311yescharacteristic
540D4—1224no—
541D4—1224no—
542D4—2442no—
543D4—2442no—
544D4—2442no—
545D4—2442no—
546D4—2442no—
547D4—2442no—
548C2×C4—24no—
549C2×C4—44no—
550C2×C4—42no—
551C2×C4—44no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—1224no—
557C2×C4—4882no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2442no—
561C2×C4—2444no—
562C2×C4—2444no—
563C2×C4C4⋊C4×D6111yescharacteristic
564C2×C4#1451973411yescharacteristic
565C2×C4#1451973711yescharacteristic
566C2×C4C4×C22⋊D6111yescharacteristic
567C2×C4#1451973911yescharacteristic
568C2×C4C4×D24411yescharacteristic
569C2×C4#1451974511yescharacteristic
570C2×C4#1451974711yescharacteristic
571C2×C4#1451974911yescharacteristic
572C2×C4#1451975011yescharacteristic
573C2×C4#1451975011yescharacteristic
574C2×C4#1451975011yescharacteristic
575C2×C4#1451975011yescharacteristic
576C2×C4#1451975111yescharacteristic
577C2×C4#1451975211yescharacteristic
578C2×C4#1451975311yescharacteristic
579C2×C4#1451975511yescharacteristic
580C2×C4#1451975511yescharacteristic
581C2×C4#1451975511yescharacteristic
582C2×C4#1451975711yescharacteristic
583C2×C4#1451975911yescharacteristic
584C2×C4#1451976011yescharacteristic
585C2×C4#1451976211yescharacteristic
586C2×C4#1451976211yescharacteristic
587C2×C4#1451976311yescharacteristic
588C2×C4#1451976511yescharacteristic
589C2×C4#1451977111yescharacteristic
590C2×C4#1451977211yescharacteristic
591C8—42no—
592C8—2442no—
593C22—22no—
594C22—22no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—22no—
600C22—22no—
601C22—4884no—
602C22—4884no—
603C22—4884no—
604C22—4884no—
605C22—4882no—
606C22—4882no—
607C22—4884no—
608C22—2448no—
609C22—2444no—
610C22#1683962111yescharacteristic
611C22#1683964011yescharacteristic
612C22#1683966211yescharacteristic
613C22#1683967111yescharacteristic
614C22#1683967511yescharacteristic
615C22#1683969111yescharacteristic
616C22#1683969711yescharacteristic
617C22#1683993112yes—
618C22#1683993612yes—
619C4—44no—
620C4—82no—
621C4—4882no—
622C4—2444no—
623C4#1683963311yescharacteristic
624C4#1683963611yescharacteristic
625C4#1683965111yescharacteristic
626C4#1683965311yescharacteristic
627C4#1683967711yescharacteristic
628C4#1683968011yescharacteristic
629C4#1683968411yescharacteristic
630C4#1683968611yescharacteristic
631C2—21no—
632C2—21no—
633C2—21no—
634C2—21no—
635C2—4884no—
636C2#2144406311yescharacteristic
637C2#2144621611yescharacteristic
638C2#2144622111yescharacteristic
639C2#2144686212yes—
640C2#2144697412yes—
subgroupG/H
centerC23#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#339C2
socleC23×C61#120
prime radicalC23×D244C22
cosocleC23×C4×C61C23
hypercenterC2×#339D61
hypocenterC61#11054
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
3. #21448435C2semidirect
5. C2×#16839530C2semidirect
6. C2×#16839522C2semidirect
7. C2×C61×#339C2semidirect
20. #16839664C4semidirect
156. C2×D244C4⋊C4semidirect
317. C2×#339D61semidirect
350. C61#11054semidirect

Maximal subgroups

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

subgroupindex
C2×#168397682
C2×#168397662
#214484352
C2×#168396642
C2×#168395302
C2×#168395222
C2×C61×#3392
#1105461