Finite Group Databasebeta

← #29587032

Subgroups — #29587032

Order 15616.

1006 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839766C211yesmaximal, characteristic
2C22×#14519699C211yesmaximal, characteristic
3C22×#14519693C211yesmaximal, characteristic
4C2×#16839530C211yesmaximal, characteristic, complemented
5C2×#16839527C211yesmaximal, characteristic, complemented
6#21445540C211yesmaximal, characteristic, complemented
7C2×C61×#424C211yesmaximal, characteristic, complemented
8C23×D244C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12#16839766—22no—
13#16839766C414yescomplemented
14C2×#14519699—22no—
15C2×#14519699—22no—
16C2×#14519699—22no—
17C2×#14519697—22no—
18C2×#14519693—22no—
19C2×#14519693—22no—
20C2×#14519693—22no—
21#16839530—22no—
22#16839527—22no—
23#16839524—22no—
24C22×M16×C61C2211yescharacteristic
25C23×C8×C61C2211yescharacteristic
26C2×#117×C61C2211yescharacteristic
27C61×#424—22no—
28C61×#424—22no—
29C2×C4⋊C8×C61—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×Dic61—21no—
46C2×#11758194—21no—
47C2×#11758194—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194—21no—
55C2×#11758194—21no—
56C2×#11758194C2×C412yes—
57C2×#11758194D412yes—
58C22×#92418—21no—
59C22×#92418—21no—
60C2×C4⋊Dic61—21no—
61C2×C4⋊Dic61—21no—
62C2×C4⋊Dic61—21no—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61D412yes—
66#14519699—28no—
67#14519697—28no—
68#14519693—28no—
69C23×C4×C61C2311yescharacteristic
70C2×M16×C61—21no—
71C2×M16×C61—21no—
72C2×M16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61—21no—
75C2×M16×C61D412yes—
76C22×C8×C61—21no—
77C22×C8×C61—21no—
78C22×C8×C61—21no—
79C22×C8×C61—21no—
80C22×C8×C61—21no—
81C22×C8×C61—21no—
82C22×C8×C61—21no—
83C22×C8×C61D412yes—
84#117×C61—21no—
85#117×C61—21no—
86#117×C61C2×C412yes—
87#117×C61D412yes—
88C2×C4⋊C4×C61D412yes—
89C2×C22⋊C4×C61—21no—
90C2×C42×C61—21no—
91C4⋊C8×C61—28no—
92C24×C61#4111yescharacteristic
93C23×D61—22no—
94C23×D61—22no—
95C23×D61—22no—
96C23×D61—41no—
97C23×D61—41no—
98C23×D61—41no—
99C23×D61—41no—
100C23×D61—82no—
101C23×D61—82no—
102C22×C4×C61—22no—
103C22×C4×C61C22×C411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×D411yescharacteristic
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×Q811yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C22×Dic61—22no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C22×Dic61—82no—
121C2×D244—22no—
122C2×D244—22no—
123C2×D244—22no—
124C2×D244—22no—
125C2×D244—22no—
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—22no—
130C2×D244—22no—
131C2×D244—22no—
132C2×D244—22no—
133C2×D244—22no—
134C2×D244—22no—
135C2×D244—22no—
136C2×D244—41no—
137C2×D244—41no—
138C2×D244—41no—
139C2×D244—41no—
140C2×D244—41no—
141C2×D244—41no—
142C2×D244—41no—
143C2×D244—41no—
144C2×D244—41no—
145C2×D244—41no—
146C2×D244—41no—
147C2×D244—41no—
148C2×D244C4⋊C414yes—
149M16×C61—22no—
150M16×C61—22no—
151M16×C61—41no—
152M16×C61—41no—
153C2×C8×C61—22no—
154C2×C8×C61—22no—
155C2×C8×C61—22no—
156C2×C8×C61—22no—
157C2×C8×C61—41no—
158C2×C8×C61—41no—
159C2×C8×C61—41no—
160C2×C8×C61—41no—
161C2×C8×C61—41no—
162C2×C8×C61—41no—
163C4⋊C4×C61—22no—
164C4⋊C4×C61C22⋊C414yes—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—22no—
167C42×C61—22no—
168C42×C61—22no—
169C4⋊Dic61—22no—
170C4⋊Dic61—22no—
171C4⋊Dic61—41no—
172C4⋊Dic61—41no—
173#11758194—22no—
174#11758194—22no—
175#11758194—22no—
176#11758194—22no—
177#11758194—41no—
178#11758194—41no—
179#11758194—41no—
180#11758194—41no—
181C2×#92418—22no—
182C2×#92418—22no—
183C2×#92418—41no—
184C2×#92418—41no—
185C2×#92418—41no—
186C2×#92418—41no—
187C23×C61—22no—
188C23×C61—22no—
189C23×C61C4×D411yescharacteristic
190C23×C61#12111yescharacteristic
191C23×C61C22⋊Q811yescharacteristic
192C23×C61#12311yescharacteristic
193C23×C61#12311yescharacteristic
194C23×C61#12311yescharacteristic
195C23×C61#12611yescharacteristic
196C22×D61—24no—
197C22×D61—42no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—84no—
204C22×D61—84no—
205C22×D61—82no—
206C22×D61—82no—
207C22×D61—82no—
208C22×D61—82no—
209C22×D61—84no—
210C22×D61—84no—
211C22×D61—82no—
212C22×D61—82no—
213C2×C4×C61—24no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61C2×C22⋊C411yescharacteristic
217C2×C4×C61C2×C4⋊C411yescharacteristic
218C2×C4×C61#11711yescharacteristic
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61C4×D411yescharacteristic
221C2×C4×C61C4×D411yescharacteristic
222C2×C4×C61#12011yescharacteristic
223C2×C4×C61#12011yescharacteristic
224C2×C4×C61#12011yescharacteristic
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61#12111yescharacteristic
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61C22⋊Q811yescharacteristic
233C2×C4×C61C22⋊Q811yescharacteristic
234C2×C4×C61C22⋊Q811yescharacteristic
235C2×C4×C61C22⋊Q811yescharacteristic
236C2×C4×C61C22⋊Q811yescharacteristic
237C2×C4×C61#12311yescharacteristic
238C2×C4×C61#12311yescharacteristic
239C2×C4×C61#12411yescharacteristic
240C2×C4×C61#12411yescharacteristic
241C2×C4×C61#12411yescharacteristic
242C2×C4×C61#12611yescharacteristic
243C2×C4×C61#12711yescharacteristic
244C2×Dic61—42no—
245C2×Dic61—82no—
246C2×Dic61—82no—
247C2×Dic61—82no—
248D244—24no—
249D244—24no—
250D244—42no—
251D244—42no—
252D244—42no—
253D244—42no—
254D244—42no—
255D244—42no—
256C8×C61—42no—
257C8×C61—42no—
258#92418—42no—
259#92418—42no—
260#11061—611nomaximal, Sylow
261C22×C61—22no—
262C22×C61—22no—
263C22×C61—22no—
264C22×C61—22no—
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—21no—
269C22×C61#38511yescharacteristic
270C22×C61#38611yescharacteristic
271C22×C61#38811yescharacteristic
272C22×C61#39411yescharacteristic
273C22×C61#39611yescharacteristic
274C22×C61#39711yescharacteristic
275C22×C61#39911yescharacteristic
276C22×C61#47112yes—
277C22×C61#47212yes—
278C2×D61—44no—
279C2×D61—84no—
280C2×D61—84no—
281C2×D61—84no—
282C2×D61—84no—
283C2×D61—84no—
284C2×D61—82no—
285C2×D61—82no—
286C2×D61—84no—
287C4×C61—44no—
288C4×C61#38011yescharacteristic
289C4×C61#38511yescharacteristic
290C4×C61#38811yescharacteristic
291C4×C61#39011yescharacteristic
292C4×C61#39211yescharacteristic
293C4×C61#39311yescharacteristic
294C4×C61#39411yescharacteristic
295C4×C61#39611yescharacteristic
296Dic61—82no—
297C2×#424D6111yescharacteristic, complemented
298C2×#418—611no—
299C22×#102—611no—
300C22×#100—611no—
301C2×#343—611no—
302C2×#341—611no—
303#1736—611no—
304C2×C61—21no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61#143911yescharacteristic
309C2×C61#190712yes—
310C2×C61#204511yescharacteristic
311C2×C61#204611yescharacteristic
312C2×C61#206312yes—
313D61—84no—
314C23×D4—611no—
315C22×M16—611no—
316C22×M16—611no—
317C22×M16C2×D6111yescharacteristic
318C23×C8C2×D6111yescharacteristic
319C2×#117C2×D6111yescharacteristic
320C22×C4⋊C4—611no—
321#424—22no—
322#424—22no—
323C2×C4⋊C8—22no—
324#418—614no—
325#418—1222no—
326C2×#102—1222no—
327C2×#102—1222no—
328C2×#102—1222no—
329C2×#102—1222no—
330C2×#100—1222no—
331C2×#100—1222no—
332C2×#100—1222no—
333#343—1222no—
334#341—1222no—
335#340—1222no—
336C61#1106111yescharacteristic, complemented, Sylow
337C25—1221no—
338C22×D4—612no—
339C22×D4—612no—
340C22×D4—612no—
341C22×D4—1221no—
342C22×D4—1221no—
343C22×D4—1221no—
344C22×D4—1221no—
345C22×D4—1221no—
346C22×D4—1221no—
347C22×D4—1221no—
348C22×D4—1221no—
349C22×D4—1221no—
350C22×D4—1221no—
351C22×D4—1221no—
352C23×C4—1221no—
353C23×C4C22×D6111yescharacteristic
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—612no—
360C2×M16—612no—
361C2×M16—1221no—
362C2×M16—1221no—
363C2×M16—1221no—
364C2×M16—1221no—
365C2×M16—1221no—
366C2×M16—1221no—
367C2×M16—1221no—
368C2×M16—1221no—
369C2×M16—1221no—
370C2×M16—1221no—
371C2×M16C22⋊D6112yes—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—1221no—
380C22×C8—1221no—
381C22×C8C22⋊D6112yes—
382#117—21no—
383#117—21no—
384#117C4×D6112yes—
385#117C22⋊D6112yes—
386C2×C4⋊C4—612no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4D24412yes—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395C4⋊C8—28no—
396#102—1228no—
397#102—1228no—
398#100—1228no—
399C24—1222no—
400C24—1222no—
401C24—1222no—
402C24—4882no—
403C24—4882no—
404C24—2441no—
405C24—2441no—
406C24—2441no—
407C24—2441no—
408C24#1175822211yescharacteristic
409C2×D4—614no—
410C2×D4—1222no—
411C2×D4—1222no—
412C2×D4—1222no—
413C2×D4—1222no—
414C2×D4—1222no—
415C2×D4—1222no—
416C2×D4—1222no—
417C2×D4—1222no—
418C2×D4—1222no—
419C2×D4—1222no—
420C2×D4—1222no—
421C2×D4—1222no—
422C2×D4—1222no—
423C2×D4—1222no—
424C2×D4—1222no—
425C2×D4—2441no—
426C2×D4—2441no—
427C2×D4—2441no—
428C2×D4—2441no—
429C2×D4—2441no—
430C2×D4—2441no—
431C2×D4—2441no—
432C2×D4—2441no—
433C2×D4—2441no—
434C2×D4—2441no—
435C2×D4—2441no—
436C2×D4—2441no—
437C22×C4—22no—
438C22×C4—1222no—
439C22×C4—4882no—
440C22×C4—2441no—
441C22×C4—2441no—
442C22×C4C2×C4×D6111yescharacteristic
443C22×C4C2×D24411yescharacteristic
444C22×C4#1175822211yescharacteristic
445C22×C4D4×D6111yescharacteristic
446C22×C4D4×D6111yescharacteristic
447C22×C4D4×D6111yescharacteristic
448C22×C4#1175822411yescharacteristic
449C22×C4Q8×D6111yescharacteristic
450C22×C4#1175822611yescharacteristic
451C22×C4#1175822611yescharacteristic
452C22×C4#1175822611yescharacteristic
453C22×C4C2×C22⋊D6111yescharacteristic
454C22×C4C2×C22⋊D6111yescharacteristic
455C22×C4C2×C22⋊D6111yescharacteristic
456M16—22no—
457M16—22no—
458M16—41no—
459M16—41no—
460M16—1222no—
461M16—1222no—
462M16—1222no—
463M16—1222no—
464M16—2441no—
465M16—2441no—
466M16—2441no—
467M16—2441no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—1222no—
479C2×C8—1222no—
480C2×C8—2441no—
481C2×C8—2441no—
482C2×C8—2441no—
483C2×C8—2441no—
484C4⋊C4—22no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—2441no—
488C4⋊C4—2441no—
489C4⋊C4#1175819814yes—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C42—22no—
493C42—22no—
494C23—22no—
495C23—22no—
496C23—1224no—
497C23—4884no—
498C23—4882no—
499C23—4882no—
500C23—4884no—
501C23—4884no—
502C23—4882no—
503C23—4882no—
504C23—4884no—
505C23—4882no—
506C23—4882no—
507C23—2442no—
508C23—2442no—
509C23—2442no—
510C23—2442no—
511C23—2442no—
512C23—2442no—
513C23C4×C22⋊D6111yescharacteristic
514C23#1451975111yescharacteristic
515C23#1451975511yescharacteristic
516C23#1451976011yescharacteristic
517C23#1451976211yescharacteristic
518C23#1451976211yescharacteristic
519C23#1451977211yescharacteristic
520D4—1224no—
521D4—1224no—
522D4—2442no—
523D4—2442no—
524D4—2442no—
525D4—2442no—
526D4—2442no—
527D4—2442no—
528C2×C4—24no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—4882no—
532C2×C4—4882no—
533C2×C4—4882no—
534C2×C4—2442no—
535C2×C4C2×#1175819811yescharacteristic
536C2×C4C4⋊C4×D6111yescharacteristic
537C2×C4#1451973511yescharacteristic
538C2×C4C4×C22⋊D6111yescharacteristic
539C2×C4#1451973911yescharacteristic
540C2×C4#1451973911yescharacteristic
541C2×C4#1451974511yescharacteristic
542C2×C4#1451974511yescharacteristic
543C2×C4#1451974611yescharacteristic
544C2×C4#1451974811yescharacteristic
545C2×C4#1451974911yescharacteristic
546C2×C4#1451974911yescharacteristic
547C2×C4#1451975111yescharacteristic
548C2×C4#1451975211yescharacteristic
549C2×C4#1451975211yescharacteristic
550C2×C4#1451975211yescharacteristic
551C2×C4#1451975311yescharacteristic
552C2×C4#1451975311yescharacteristic
553C2×C4#1451975311yescharacteristic
554C2×C4#1451975511yescharacteristic
555C2×C4#1451975711yescharacteristic
556C2×C4#1451976211yescharacteristic
557C2×C4#1451976211yescharacteristic
558C2×C4#1451976611yescharacteristic
559C2×C4#1451976611yescharacteristic
560C2×C4#1451976611yescharacteristic
561C2×C4#1451977211yescharacteristic
562C2×C4#1451977311yescharacteristic
563C8—42no—
564C8—42no—
565C8—2442no—
566C8—2442no—
567C22—22no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—22no—
575C22—4884no—
576C22—4884no—
577C22—4884no—
578C22—4884no—
579C22—4884no—
580C22—4882no—
581C22—4882no—
582C22—4884no—
583C22—2444no—
584C22#1683963311yescharacteristic
585C22#1683964111yescharacteristic
586C22#1683965211yescharacteristic
587C22#1683967911yescharacteristic
588C22#1683968411yescharacteristic
589C22#1683968811yescharacteristic
590C22#1683969711yescharacteristic
591C22#1684002512yes—
592C22#1684003212yes—
593C4—44no—
594C4—4882no—
595C4#1683961911yescharacteristic
596C4#1683963311yescharacteristic
597C4#1683965211yescharacteristic
598C4#1683966311yescharacteristic
599C4#1683967011yescharacteristic
600C4#1683967311yescharacteristic
601C4#1683967911yescharacteristic
602C4#1683968411yescharacteristic
603C2—21no—
604C2—21no—
605C2—21no—
606C2—21no—
607C2—4884no—
608C2#2144406111yescharacteristic
609C2#2144632712yes—
610C2#2144707511yescharacteristic
611C2#2144708211yescharacteristic
612C2#2144717812yes—
subgroupG/H
centerC23#14519751
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#424C2
socleC23×C61#121
prime radicalC23×D244C22
cosocleC23×C4×C61C23
hypercenterC2×#424D61
hypocenterC61#11061
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
4. C2×#16839530C2semidirect
5. C2×#16839527C2semidirect
6. #21445540C2semidirect
7. C2×C61×#424C2semidirect
13. #16839766C4semidirect
297. C2×#424D61semidirect
336. C61#11061semidirect

Maximal subgroups

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

subgroupindex
C2×#168397662
C22×#145196992
C22×#145196932
C2×#168395302
C2×#168395272
#214455402
C2×C61×#4242
#1106161