Finite Group Databasebeta

← #29587004

Subgroups — #29587004

Order 15616.

910 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839780C211yesmaximal, characteristic
2C2×#16839761C211yesmaximal, characteristic
3C2×#16839735C211yesmaximal, characteristic
4C2×#16839532C211yesmaximal, characteristic, complemented
5#21445538C211yesmaximal, characteristic, complemented
6C2×#16839518C211yesmaximal, characteristic, complemented
7C61×#2316C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839780—22no—
13#16839780—22no—
14C2×#14519705—22no—
15#16839761—22no—
16#16839761—22no—
17C2×#14519700C412yescomplemented
18C2×#14519697C412yescomplemented
19#16839735—22no—
20#16839735—22no—
21C2×#14519691—22no—
22#16839532—22no—
23#16839524—22no—
24#16839518—22no—
25C2×#117×C61C2211yescharacteristic
26C2×#117×C61C2211yescharacteristic
27C22×C4⋊C4×C61C2211yescharacteristic
28C61×#389—22no—
29C61×#389—22no—
30C61×#380—22no—
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×#11758222—21no—
41C2×#11758222D412yes—
42C2×#11758222Q812yes—
43C22×Dic122C2×C411yescharacteristic
44C22×D244C2×C411yescharacteristic
45C22×C22⋊D61—21no—
46C22×C4×D61—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×#11758194—21no—
57C2×#11758194—21no—
58C2×#11758194D412yes—
59C22×#92418—21no—
60C22×#92418C2×C412yes—
61#14519736—21no—
62#14519736—21no—
63#14519736—21no—
64#14519736D412yes—
65C2×C4⋊Dic61—21no—
66C2×C22⋊Dic61—21no—
67C2×C4×Dic61—21no—
68#14519705—28no—
69#14519700—24no—
70#14519697—24no—
71#14519691—28no—
72C23×C4×C61—21no—
73C23×C4×C61C2311yescharacteristic
74#117×C61—21no—
75#117×C61—21no—
76#117×C61—21no—
77#117×C61—21no—
78#117×C61—21no—
79#117×C61—21no—
80#117×C61—21no—
81#117×C61—21no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61—21no—
84C2×C4⋊C4×C61—21no—
85C2×C4⋊C4×C61—21no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—24no—
88C2×C4⋊C4×C61C2×C412yes—
89C2×C4⋊C4×C61D412yes—
90C2×C4⋊C4×C61D412yes—
91C2×C22⋊C4×C61—21no—
92C2×C22⋊C4×C61D412yes—
93C2×C42×C61—21no—
94C2×C42×C61D412yes—
95#95×C61—24no—
96C24×C61C2×D411yescharacteristic
97C23×D61—21no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—82no—
104C22×C4×C61C22×C411yescharacteristic
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×C4×C61#4111yescharacteristic
118C2×C22⋊D61—22no—
119C2×C22⋊D61—22no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C22×Dic61—21no—
125C22×Dic61—41no—
126#11758222—22no—
127#11758222—22no—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—22no—
133#11758222—22no—
134#11758222—41no—
135#11758222—41no—
136#11758222—41no—
137#11758222—41no—
138#11758222—41no—
139#11758222—41no—
140#11758222—41no—
141#11758222—41no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244C4⋊C412yescomplemented
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—41no—
151C2×C4×D61—41no—
152C2×C4×D61—41no—
153C2×C4×D61—41no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122C4⋊C412yescomplemented
160C4⋊C4×C61—22no—
161C4⋊C4×C61—22no—
162C4⋊C4×C61—22no—
163C4⋊C4×C61—41no—
164C4⋊C4×C61—41no—
165C4⋊C4×C61—41no—
166C4⋊C4×C61—41no—
167C4⋊C4×C61—84no—
168C4⋊C4×C61C22⋊C414yes—
169C22⋊C4×C61—22no—
170C22⋊C4×C61—22no—
171C22⋊C4×C61—41no—
172C22⋊C4×C61—41no—
173C42×C61—22no—
174C42×C61—22no—
175C42×C61—41no—
176C42×C61—41no—
177C22⋊Dic61—22no—
178C22⋊Dic61—41no—
179C4⋊Dic61—22no—
180C4⋊Dic61—41no—
181C4×Dic61—22no—
182C4×Dic61—41no—
183#11758194—22no—
184#11758194—22no—
185#11758194—41no—
186#11758194—41no—
187#11758194—41no—
188#11758194—41no—
189#11758194—41no—
190#11758194—41no—
191C2×#92418—22no—
192C2×#92418—22no—
193C2×#92418—22no—
194C2×#92418—22no—
195C2×#92418—41no—
196C2×#92418—41no—
197C23×C61—41no—
198C23×C61—41no—
199C23×C61C4×D411yescharacteristic
200C23×C61#12011yescharacteristic
201C23×C61#12011yescharacteristic
202C23×C61#12111yescharacteristic
203C23×C61#12111yescharacteristic
204C23×C61C22⋊Q811yescharacteristic
205C23×C61#12411yescharacteristic
206C22×D61—22no—
207C22×D61—41no—
208C22×D61—41no—
209C22×D61—81no—
210C22×D61—81no—
211C2×C4×C61—24no—
212C2×C4×C61—44no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—82no—
220C2×C4×C61—82no—
221C2×C4×C61C2×C22⋊C411yescharacteristic
222C2×C4×C61C2×C4⋊C411yescharacteristic
223C2×C4×C61#11711yescharacteristic
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61#12011yescharacteristic
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61#12111yescharacteristic
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61#12111yescharacteristic
232C2×C4×C61#12111yescharacteristic
233C2×C4×C61#12111yescharacteristic
234C2×C4×C61C22⋊Q811yescharacteristic
235C2×C4×C61C22⋊Q811yescharacteristic
236C2×C4×C61C22⋊Q811yescharacteristic
237C2×C4×C61C22⋊Q811yescharacteristic
238C2×C4×C61C22⋊Q811yescharacteristic
239C2×C4×C61#12311yescharacteristic
240C2×C4×C61#12311yescharacteristic
241C2×C4×C61#12311yescharacteristic
242C2×C4×C61#12311yescharacteristic
243C2×C4×C61#12311yescharacteristic
244C2×C4×C61#12411yescharacteristic
245C2×C4×C61#12411yescharacteristic
246C2×C4×C61#12611yescharacteristic
247C2×C4×C61#12611yescharacteristic
248C2×C4×C61#12711yescharacteristic
249C22⋊D61—42no—
250C22⋊D61—42no—
251C22⋊D61—42no—
252C22⋊D61—42no—
253C2×Dic61—22no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—42no—
257C2×Dic61—81no—
258C2×Dic61—81no—
259D244—22no—
260D244—22no—
261D244—41no—
262D244—41no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—42no—
266C4×D61—42no—
267Dic122—22no—
268Dic122—22no—
269Dic122—41no—
270Dic122—41no—
271#92418—42no—
272#92418—42no—
273#11057—611nomaximal, Sylow
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—41no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61#38511yescharacteristic
285C22×C61#38611yescharacteristic
286C22×C61#38811yescharacteristic
287C22×C61#39211yescharacteristic
288C22×C61#39311yescharacteristic
289C22×C61#39411yescharacteristic
290C22×C61#39611yescharacteristic
291C2×D61—42no—
292C2×D61—82no—
293C2×D61—81no—
294C2×D61—81no—
295C2×D61—82no—
296C4×C61—44no—
297C4×C61—82no—
298C4×C61—82no—
299C4×C61#38011yescharacteristic
300C4×C61#38511yescharacteristic
301C4×C61#38811yescharacteristic
302C4×C61#39011yescharacteristic
303C4×C61#39411yescharacteristic
304C4×C61#39611yescharacteristic
305C4×C61#39711yescharacteristic
306C4×C61#39911yescharacteristic
307Dic61—42no—
308Dic61—82no—
309C2×#421—611no—
310C2×#417—611no—
311C2×#410—611no—
312#2316D6111yescharacteristic, complemented
313C2×#344—611no—
314#1736—611no—
315C2×H(3,ℤ/4)—611no—
316C2×C61—21no—
317C2×C61—21no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61—21no—
321C2×C61—21no—
322C2×C61#143911yescharacteristic
323C2×C61#190411yescharacteristic
324C2×C61#190511yescharacteristic
325D61—82no—
326C22×#41—611no—
327C22×M16—611no—
328C22×M16—611no—
329C2×#117—611no—
330C2×#117C2×D6111yescharacteristic
331C2×#117C2×D6111yescharacteristic
332C22×C4⋊C4C2×D6111yescharacteristic
333#421—1222no—
334#421—1222no—
335C2×#104—1222no—
336#417—1222no—
337#417—1222no—
338C2×#103—612no—
339C2×#102—612no—
340#410—1222no—
341#410—1222no—
342C2×#99—1222no—
343#389—22no—
344#389—22no—
345#380—22no—
346#344—1222no—
347#340—1222no—
348H(3,ℤ/4)—1222no—
349C61#1105711yescharacteristic, complemented, Sylow
350C2×#41—612no—
351C2×#41—612no—
352C2×#41—1221no—
353C2×#41—1221no—
354C2×#41—1221no—
355C2×#41—1221no—
356C2×#41—1221no—
357C2×#41—1221no—
358C2×#41—1221no—
359C2×#41—1221no—
360C2×#41—1221no—
361C2×#41—1221no—
362C22×Q8—611no—
363C22×D4—611no—
364C22×D4—1221no—
365C23×C4—21no—
366C23×C4—1221no—
367C23×C4C22×D6111yescharacteristic
368C2×M16—612no—
369C2×M16—1221no—
370C2×M16—1221no—
371C2×M16—1221no—
372C2×M16—1221no—
373C2×M16—1221no—
374C2×M16—1221no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C22×C8—612no—
381C22×C8—1221no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117—612no—
391#117—1221no—
392#117—1221no—
393#117—1221no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4C4×D6112yes—
402C2×C4⋊C4D24412yes—
403C2×C4⋊C4C22⋊D6112yes—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—1221no—
406C2×C22⋊C4C22⋊D6112yes—
407C2×C42—21no—
408C2×C42—1221no—
409C2×C42C22⋊D6112yes—
410#104—1228no—
411#103—1224no—
412#102—1224no—
413#99—1228no—
414#95—24no—
415C24—1221no—
416C24C2×C22⋊D6111yescharacteristic
417#41—1222no—
418#41—1222no—
419#41—1222no—
420#41—1222no—
421#41—1222no—
422#41—1222no—
423#41—1222no—
424#41—1222no—
425#41—2441no—
426#41—2441no—
427#41—2441no—
428#41—2441no—
429#41—2441no—
430#41—2441no—
431#41—2441no—
432#41—2441no—
433C2×Q8—612no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×D4—612no—
440C2×D4—1222no—
441C2×D4—1222no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—1221no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—2441no—
448C2×D4—2441no—
449C2×D4—2441no—
450C2×D4—2441no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—82no—
457C22×C4—1221no—
458C22×C4—1222no—
459C22×C4—1222no—
460C22×C4—2441no—
461C22×C4—2441no—
462C22×C4—2441no—
463C22×C4—2441no—
464C22×C4—2441no—
465C22×C4C2×C4×D6111yescharacteristic
466C22×C4C2×D24411yescharacteristic
467C22×C4#1175822211yescharacteristic
468C22×C4#1175822211yescharacteristic
469C22×C4D4×D6111yescharacteristic
470C22×C4D4×D6111yescharacteristic
471C22×C4D4×D6111yescharacteristic
472C22×C4#1175822411yescharacteristic
473C22×C4Q8×D6111yescharacteristic
474C22×C4#1175822611yescharacteristic
475C22×C4#1175822611yescharacteristic
476C22×C4#1175822611yescharacteristic
477C22×C4C2×C22⋊D6111yescharacteristic
478C22×C4C2×C22⋊D6111yescharacteristic
479M16—1222no—
480M16—1222no—
481M16—2441no—
482M16—2441no—
483M16—2441no—
484M16—2441no—
485M16—2441no—
486M16—2441no—
487C2×C8—1222no—
488C2×C8—1222no—
489C2×C8—1222no—
490C2×C8—1222no—
491C2×C8—2441no—
492C2×C8—2441no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4—84no—
501C4⋊C4—1222no—
502C4⋊C4—2441no—
503C4⋊C4#1175819814yes—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—1222no—
509C22⋊C4—2441no—
510C42—22no—
511C42—22no—
512C42—41no—
513C42—41no—
514C42—1222no—
515C42—2441no—
516C23—41no—
517C23—41no—
518C23—1222no—
519C23—4881no—
520C23—4881no—
521C23—2441no—
522C23—2441no—
523C23C4×C22⋊D6111yescharacteristic
524C23#1451974511yescharacteristic
525C23#1451974611yescharacteristic
526C23#1451974911yescharacteristic
527C23#1451975111yescharacteristic
528C23#1451975311yescharacteristic
529C23#1451976611yescharacteristic
530Q8—1222no—
531Q8—1222no—
532Q8—2441no—
533Q8—2441no—
534D4—1222no—
535D4—1222no—
536D4—2442no—
537D4—2442no—
538D4—2442no—
539D4—2442no—
540D4—2441no—
541D4—2441no—
542C2×C4—24no—
543C2×C4—44no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4—1222no—
553C2×C4—4881no—
554C2×C4—4881no—
555C2×C4—2442no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2442no—
559C2×C4—2442no—
560C2×C4—2442no—
561C2×C4—2442no—
562C2×C4C2×#1175819811yescharacteristic
563C2×C4C4⋊C4×D6111yescharacteristic
564C2×C4#1451973511yescharacteristic
565C2×C4C4×C22⋊D6111yescharacteristic
566C2×C4#1451973911yescharacteristic
567C2×C4#1451973911yescharacteristic
568C2×C4#1451974511yescharacteristic
569C2×C4#1451974811yescharacteristic
570C2×C4#1451974911yescharacteristic
571C2×C4#1451975111yescharacteristic
572C2×C4#1451975211yescharacteristic
573C2×C4#1451975211yescharacteristic
574C2×C4#1451975211yescharacteristic
575C2×C4#1451975311yescharacteristic
576C2×C4#1451975311yescharacteristic
577C2×C4#1451975511yescharacteristic
578C2×C4#1451975511yescharacteristic
579C2×C4#1451975711yescharacteristic
580C2×C4#1451976011yescharacteristic
581C2×C4#1451976211yescharacteristic
582C2×C4#1451976211yescharacteristic
583C2×C4#1451976211yescharacteristic
584C2×C4#1451976211yescharacteristic
585C2×C4#1451976611yescharacteristic
586C2×C4#1451976611yescharacteristic
587C2×C4#1451977211yescharacteristic
588C2×C4#1451977211yescharacteristic
589C2×C4#1451977311yescharacteristic
590C8—2442no—
591C8—2442no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—4882no—
603C22—4882no—
604C22—4881no—
605C22—4881no—
606C22—2442no—
607C22#1683963311yescharacteristic
608C22#1683964111yescharacteristic
609C22#1683965211yescharacteristic
610C22#1683967011yescharacteristic
611C22#1683967311yescharacteristic
612C22#1683967911yescharacteristic
613C22#1683968411yescharacteristic
614C4—44no—
615C4—82no—
616C4—82no—
617C4—4882no—
618C4—2442no—
619C4#1683961911yescharacteristic
620C4#1683963311yescharacteristic
621C4#1683965211yescharacteristic
622C4#1683966311yescharacteristic
623C4#1683967911yescharacteristic
624C4#1683968411yescharacteristic
625C4#1683968811yescharacteristic
626C4#1683969711yescharacteristic
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—21no—
633C2—4882no—
634C2#2144406111yescharacteristic
635C2#2144630611yescharacteristic
636C2#2144631311yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#2316C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenter#2316D61
hypocenterC61#11057
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
4. C2×#16839532C2semidirect
5. #21445538C2semidirect
6. C2×#16839518C2semidirect
7. C61×#2316C2semidirect
17. C2×#14519700C4semidirect
18. C2×#14519697C4semidirect
147. C2×D244C4⋊C4semidirect
159. C2×Dic122C4⋊C4semidirect
312. #2316D61semidirect
349. C61#11057semidirect

Maximal subgroups

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

subgroupindex
C2×#168397802
C2×#168397612
C2×#168397352
C2×#168395322
#214455382
C2×#168395182
C61×#23162
#1105761