Finite Group Databasebeta

← #29587182

Subgroups — #29587182

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839780C211yesmaximal, characteristic
2C22×#14519705C211yesmaximal, characteristic
3C2×#16839735C211yesmaximal, characteristic
4C2×#16839532C211yesmaximal, characteristic, complemented
5C2×#16839522C211yesmaximal, characteristic, complemented
6C2×#16839518C211yesmaximal, characteristic, complemented
7C61×#2296C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839780—22no—
13#16839780C414yescomplemented
14C2×#14519705—22no—
15C2×#14519705—22no—
16C2×#14519705—22no—
17C2×#14519705—22no—
18#16839735—22no—
19#16839735—22no—
20C2×#14519691—22no—
21#16839532—22no—
22#16839522—22no—
23#16839518—22no—
24C2×#117×C61C2211yescharacteristic
25C2×#117×C61C2211yescharacteristic
26C22×C42×C61C2211yescharacteristic
27C61×#389—22no—
28C61×#385—22no—
29C4×C4⋊C4×C61—22no—
30C2×#11758222—21no—
31C2×#11758222—21no—
32C2×#11758222—21no—
33C2×#11758222—21no—
34C2×#11758222—21no—
35C2×#11758222—21no—
36C2×#11758222—21no—
37C2×#11758222—21no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222C2×C412yes—
41C2×#11758222D412yes—
42C22×Dic122Q811yescharacteristic
43C22×D244Q811yescharacteristic
44C22×C22⋊D61—21no—
45C22×C4×D61—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—
60#14519736—21no—
61#14519736—21no—
62#14519736—21no—
63#14519736D412yes—
64C2×C4⋊Dic61—21no—
65C2×C22⋊Dic61—21no—
66C2×C4×Dic61—21no—
67#14519705—28no—
68#14519705—28no—
69#14519691—28no—
70C23×C4×C61—21no—
71C23×C4×C61C2311yescharacteristic
72#117×C61—21no—
73#117×C61—21no—
74#117×C61—21no—
75#117×C61—21no—
76#117×C61—21no—
77#117×C61—21no—
78#117×C61C2×C412yes—
79#117×C61D412yes—
80C2×C4⋊C4×C61—21no—
81C2×C4⋊C4×C61—24no—
82C2×C4⋊C4×C61—21no—
83C2×C22⋊C4×C61—21no—
84C2×C22⋊C4×C61D412yes—
85C2×C42×C61—21no—
86C2×C42×C61—21no—
87C2×C42×C61—21no—
88C2×C42×C61—21no—
89C2×C42×C61—21no—
90C2×C42×C61—21no—
91C2×C42×C61D412yes—
92C2×C42×C61D412yes—
93#95×C61—24no—
94C24×C61C2×D411yescharacteristic
95C23×D61—21no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—44no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61C2×Q811yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C22×C4×C61#4111yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C2×C22⋊D61—22no—
117C2×C22⋊D61—22no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C22×Dic61—21no—
123C22×Dic61—41no—
124#11758222—22no—
125#11758222—22no—
126#11758222—22no—
127#11758222—22no—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—41no—
133#11758222—41no—
134#11758222—41no—
135#11758222—41no—
136#11758222—41no—
137#11758222—41no—
138#11758222—41no—
139#11758222—41no—
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244C4⋊C412yescomplemented
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×C4×D61—41no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122C4⋊C412yescomplemented
158C4⋊C4×C61—22no—
159C4⋊C4×C61—22no—
160C4⋊C4×C61—48no—
161C4⋊C4×C61—41no—
162C4⋊C4×C61—41no—
163C22⋊C4×C61—22no—
164C22⋊C4×C61—22no—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—22no—
167C42×C61—22no—
168C42×C61—22no—
169C42×C61—22no—
170C42×C61—41no—
171C42×C61—41no—
172C42×C61—41no—
173C42×C61—41no—
174C42×C61C22⋊C414yes—
175C22⋊Dic61—22no—
176C22⋊Dic61—41no—
177C4⋊Dic61—22no—
178C4⋊Dic61—41no—
179C4×Dic61—22no—
180C4×Dic61—41no—
181#11758194—22no—
182#11758194—22no—
183#11758194—22no—
184#11758194—22no—
185#11758194—41no—
186#11758194—41no—
187#11758194—41no—
188#11758194—41no—
189C2×#92418—22no—
190C2×#92418—22no—
191C2×#92418—41no—
192C2×#92418—41no—
193C2×#92418—41no—
194C2×#92418—41no—
195C23×C61—42no—
196C23×C61C4×D411yescharacteristic
197C23×C61#12011yescharacteristic
198C23×C61#12011yescharacteristic
199C23×C61#12111yescharacteristic
200C23×C61#12111yescharacteristic
201C23×C61C22⋊Q811yescharacteristic
202C23×C61#12411yescharacteristic
203C22×D61—22no—
204C22×D61—41no—
205C22×D61—41no—
206C22×D61—82no—
207C2×C4×C61—24no—
208C2×C4×C61—24no—
209C2×C4×C61—44no—
210C2×C4×C61—42no—
211C2×C4×C61—44no—
212C2×C4×C61—44no—
213C2×C4×C61—42no—
214C2×C4×C61—44no—
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#12111yescharacteristic
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61C22⋊Q811yescharacteristic
230C2×C4×C61C22⋊Q811yescharacteristic
231C2×C4×C61C22⋊Q811yescharacteristic
232C2×C4×C61C22⋊Q811yescharacteristic
233C2×C4×C61C22⋊Q811yescharacteristic
234C2×C4×C61#12311yescharacteristic
235C2×C4×C61#12311yescharacteristic
236C2×C4×C61#12311yescharacteristic
237C2×C4×C61#12311yescharacteristic
238C2×C4×C61#12311yescharacteristic
239C2×C4×C61#12411yescharacteristic
240C2×C4×C61#12411yescharacteristic
241C2×C4×C61#12611yescharacteristic
242C2×C4×C61#12611yescharacteristic
243C2×C4×C61#12711yescharacteristic
244C22⋊D61—42no—
245C22⋊D61—42no—
246C22⋊D61—42no—
247C22⋊D61—42no—
248C2×Dic61—22no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—42no—
252C2×Dic61—82no—
253D244—22no—
254D244—22no—
255D244—41no—
256D244—41no—
257C4×D61—42no—
258C4×D61—42no—
259C4×D61—42no—
260C4×D61—42no—
261Dic122—22no—
262Dic122—22no—
263Dic122—41no—
264Dic122—41no—
265#92418—42no—
266#92418—42no—
267#11085—611nomaximal, Sylow
268C22×C61—22no—
269C22×C61—22no—
270C22×C61—22no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61#38511yescharacteristic
276C22×C61#38611yescharacteristic
277C22×C61#38811yescharacteristic
278C22×C61#39211yescharacteristic
279C22×C61#39311yescharacteristic
280C22×C61#39411yescharacteristic
281C22×C61#39611yescharacteristic
282C2×D61—42no—
283C2×D61—82no—
284C2×D61—82no—
285C2×D61—82no—
286C4×C61—44no—
287C4×C61—44no—
288C4×C61—82no—
289C4×C61#38011yescharacteristic
290C4×C61#38511yescharacteristic
291C4×C61#38811yescharacteristic
292C4×C61#39011yescharacteristic
293C4×C61#39411yescharacteristic
294C4×C61#39611yescharacteristic
295C4×C61#39711yescharacteristic
296C4×C61#39911yescharacteristic
297Dic61—42no—
298Dic61—82no—
299C2×#421—611no—
300C22×#104—611no—
301C2×#410—611no—
302#2296D6111yescharacteristic, complemented
303C2×#344—611no—
304C2×#339—611no—
305C2×H(3,ℤ/4)—611no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61—21no—
309C2×C61—21no—
310C2×C61—21no—
311C2×C61—21no—
312C2×C61#143911yescharacteristic
313C2×C61#203112yes—
314D61—82no—
315C22×#41—611no—
316C22×M16—611no—
317C22×M16—611no—
318C2×#117—611no—
319C2×#117C2×D6111yescharacteristic
320C2×#117C2×D6111yescharacteristic
321C22×C42C2×D6111yescharacteristic
322#421—614no—
323#421—1222no—
324C2×#104—1222no—
325C2×#104—1222no—
326C2×#104—1222no—
327C2×#104—1222no—
328#410—1222no—
329#410—1222no—
330C2×#99—1222no—
331#389—22no—
332#385—22no—
333C4×C4⋊C4—22no—
334#344—1222no—
335#339—1222no—
336H(3,ℤ/4)—1222no—
337C61#1108511yescharacteristic, complemented, Sylow
338C2×#41—612no—
339C2×#41—612no—
340C2×#41—1221no—
341C2×#41—1221no—
342C2×#41—1221no—
343C2×#41—1221no—
344C2×#41—1221no—
345C2×#41—1221no—
346C2×#41—1221no—
347C2×#41—1221no—
348C2×#41—1221no—
349C2×#41—1221no—
350C22×Q8—611no—
351C22×D4—611no—
352C22×D4—1221no—
353C23×C4—21no—
354C23×C4—1221no—
355C23×C4C22×D6111yescharacteristic
356C2×M16—612no—
357C2×M16—612no—
358C2×M16—1221no—
359C2×M16—1221no—
360C2×M16—1221no—
361C2×M16—1221no—
362C2×M16—1221no—
363C2×M16—1221no—
364C2×M16—1221no—
365C2×M16—1221no—
366C2×M16—1221no—
367C2×M16—1221no—
368C22×C8—1221no—
369C22×C8—1221no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—612no—
377#117—1221no—
378#117—1221no—
379#117—1221no—
380#117C4×D6112yes—
381#117D24412yes—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—1221no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—1221no—
388C2×C22⋊C4C22⋊D6112yes—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—1221no—
396C2×C42C22⋊D6112yes—
397C2×C42C22⋊D6112yes—
398#104—1228no—
399#104—1228no—
400#99—1228no—
401#95—24no—
402C24—1221no—
403C24C2×C22⋊D6111yescharacteristic
404#41—1222no—
405#41—1222no—
406#41—1222no—
407#41—1222no—
408#41—1222no—
409#41—1222no—
410#41—1222no—
411#41—1222no—
412#41—2441no—
413#41—2441no—
414#41—2441no—
415#41—2441no—
416#41—2441no—
417#41—2441no—
418#41—2441no—
419#41—2441no—
420C2×Q8—612no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×D4—612no—
427C2×D4—1222no—
428C2×D4—1222no—
429C2×D4—1221no—
430C2×D4—1221no—
431C2×D4—1221no—
432C2×D4—1221no—
433C2×D4—1221no—
434C2×D4—2441no—
435C2×D4—2441no—
436C2×D4—2441no—
437C2×D4—2441no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—44no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—1221no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—2441no—
448C22×C4—2441no—
449C22×C4—2441no—
450C22×C4—2441no—
451C22×C4—2441no—
452C22×C4C2×C4×D6111yescharacteristic
453C22×C4C2×D24411yescharacteristic
454C22×C4#1175822211yescharacteristic
455C22×C4#1175822211yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C22×C4D4×D6111yescharacteristic
459C22×C4#1175822411yescharacteristic
460C22×C4Q8×D6111yescharacteristic
461C22×C4#1175822611yescharacteristic
462C22×C4#1175822611yescharacteristic
463C22×C4#1175822611yescharacteristic
464C22×C4C2×C22⋊D6111yescharacteristic
465C22×C4C2×C22⋊D6111yescharacteristic
466M16—1222no—
467M16—1222no—
468M16—1222no—
469M16—1222no—
470M16—2441no—
471M16—2441no—
472M16—2441no—
473M16—2441no—
474C2×C8—1222no—
475C2×C8—1222no—
476C2×C8—2441no—
477C2×C8—2441no—
478C2×C8—2441no—
479C2×C8—2441no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—48no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—1222no—
486C4⋊C4—2441no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—1222no—
492C22⋊C4—2441no—
493C42—22no—
494C42—22no—
495C42—22no—
496C42—41no—
497C42—41no—
498C42—41no—
499C42—41no—
500C42—1222no—
501C42—2441no—
502C42#1175819814yes—
503C23—42no—
504C23—1222no—
505C23—4882no—
506C23—2441no—
507C23—2441no—
508C23C4×C22⋊D6111yescharacteristic
509C23#1451974511yescharacteristic
510C23#1451974611yescharacteristic
511C23#1451974911yescharacteristic
512C23#1451975111yescharacteristic
513C23#1451975311yescharacteristic
514C23#1451976611yescharacteristic
515Q8—1222no—
516Q8—1222no—
517Q8—2441no—
518Q8—2441no—
519D4—1222no—
520D4—1222no—
521D4—2442no—
522D4—2442no—
523D4—2442no—
524D4—2442no—
525D4—2441no—
526D4—2441no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—1222no—
537C2×C4—4882no—
538C2×C4—2442no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2442no—
542C2×C4—2442no—
543C2×C4—2442no—
544C2×C4—2442no—
545C2×C4C2×#1175819811yescharacteristic
546C2×C4C4⋊C4×D6111yescharacteristic
547C2×C4#1451973511yescharacteristic
548C2×C4C4×C22⋊D6111yescharacteristic
549C2×C4#1451973911yescharacteristic
550C2×C4#1451973911yescharacteristic
551C2×C4#1451974511yescharacteristic
552C2×C4#1451974811yescharacteristic
553C2×C4#1451974911yescharacteristic
554C2×C4#1451975111yescharacteristic
555C2×C4#1451975211yescharacteristic
556C2×C4#1451975211yescharacteristic
557C2×C4#1451975211yescharacteristic
558C2×C4#1451975311yescharacteristic
559C2×C4#1451975311yescharacteristic
560C2×C4#1451975511yescharacteristic
561C2×C4#1451975511yescharacteristic
562C2×C4#1451975711yescharacteristic
563C2×C4#1451976011yescharacteristic
564C2×C4#1451976211yescharacteristic
565C2×C4#1451976211yescharacteristic
566C2×C4#1451976211yescharacteristic
567C2×C4#1451976211yescharacteristic
568C2×C4#1451976611yescharacteristic
569C2×C4#1451976611yescharacteristic
570C2×C4#1451977211yescharacteristic
571C2×C4#1451977211yescharacteristic
572C2×C4#1451977311yescharacteristic
573C8—2442no—
574C8—2442no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—4882no—
583C22—4882no—
584C22—4882no—
585C22—2442no—
586C22#1683963311yescharacteristic
587C22#1683964111yescharacteristic
588C22#1683965211yescharacteristic
589C22#1683967011yescharacteristic
590C22#1683967311yescharacteristic
591C22#1683967911yescharacteristic
592C22#1683968411yescharacteristic
593C4—44no—
594C4—44no—
595C4—82no—
596C4—4882no—
597C4—2442no—
598C4#1683961911yescharacteristic
599C4#1683963311yescharacteristic
600C4#1683965211yescharacteristic
601C4#1683966311yescharacteristic
602C4#1683967911yescharacteristic
603C4#1683968411yescharacteristic
604C4#1683968811yescharacteristic
605C4#1683969711yescharacteristic
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—4882no—
613C2#2144406111yescharacteristic
614C2#2144698812yes—
subgroupG/H
centerC2×C4#14519766
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2296C2
socleC22×C61#393
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#2296D61
hypocenterC61#11085
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2296

Complements

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

NH ≅ G/Ntype
4. C2×#16839532C2semidirect
5. C2×#16839522C2semidirect
6. C2×#16839518C2semidirect
7. C61×#2296C2semidirect
13. #16839780C4semidirect
145. C2×D244C4⋊C4semidirect
157. C2×Dic122C4⋊C4semidirect
302. #2296D61semidirect
337. C61#11085semidirect

Maximal subgroups

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

subgroupindex
C2×#168397802
C22×#145197052
C2×#168397352
C2×#168395322
C2×#168395222
C2×#168395182
C61×#22962
#1108561