Finite Group Databasebeta

← #29587309

Subgroups — #29587309

Order 15616.

910 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519708C211yesmaximal, characteristic, complemented
2C2×#16839764C211yesmaximal, characteristic
3C2×#16839761C211yesmaximal, characteristic
4C2×#16839730C211yesmaximal, characteristic
5C2×#16839530C211yesmaximal, characteristic, complemented
6C2×#16839526C211yesmaximal, characteristic, complemented
7C2×C61×#343C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C23×#92418C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C2×#14519708—22no—
13C2×#14519708—22no—
14C2×#14519708—22no—
15#16839764—22no—
16#16839764—22no—
17#16839761—22no—
18#16839761—22no—
19C2×#14519702—21no—
20C2×#14519700—21no—
21C2×#14519699—21no—
22C2×#14519697—21no—
23#16839730—22no—
24#16839730C414yescomplemented
25C2×#14519689—22no—
26#16839530—22no—
27#16839526—22no—
28C22×M16×C61C2211yescharacteristic
29C22×M16×C61C2211yescharacteristic
30C22×C4⋊C4×C61C2211yescharacteristic
31C61×#343—22no—
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×#11758222—21no—
42C2×#11758222C2×C412yes—
43C2×#11758222Q812yes—
44C22×Dic122D411yescharacteristic
45C22×D244D411yescharacteristic
46C22×C22⋊D61—21no—
47C23×Dic61—21no—
48C22×C4×D61—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194—21no—
54C2×#11758194D412yes—
55C22×#92418—21no—
56C22×#92418—21no—
57C22×#92418—21no—
58C22×#92418—21no—
59C22×#92418—21no—
60C22×#92418C2×C412yes—
61C22×#92418D412yes—
62C22×#92418D412yes—
63C2×C4⋊Dic61—21no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61—21no—
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61D412yes—
69#14519708—28no—
70#14519702—24no—
71#14519700—24no—
72#14519699—24no—
73#14519697—24no—
74#14519689—28no—
75C23×C4×C61—21no—
76C23×C4×C61C2311yescharacteristic
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61—21no—
81C2×M16×C61—21no—
82C2×M16×C61—21no—
83C2×M16×C61—21no—
84C2×M16×C61—21no—
85C2×M16×C61—21no—
86C2×M16×C61—21no—
87C2×M16×C61C2×C412yes—
88C2×M16×C61D412yes—
89C22×C8×C61—21no—
90C22×C8×C61—21no—
91C2×C4⋊C4×C61—21no—
92C2×C4⋊C4×C61—21no—
93C2×C4⋊C4×C61—21no—
94C2×C4⋊C4×C61—21no—
95C2×C4⋊C4×C61—21no—
96C2×C4⋊C4×C61D412yes—
97C24×C61#4111yescharacteristic
98C23×D61—21no—
99C22×C4×C61—22no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61—82no—
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
117C2×C22⋊D61—22no—
118C2×C22⋊D61—22no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C2×C22⋊D61—41no—
122C2×C22⋊D61—41no—
123C22×Dic61—21no—
124C22×Dic61—22no—
125C22×Dic61—41no—
126C22×Dic61—41no—
127C22×Dic61—82no—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—22no—
133#11758222—22no—
134#11758222—22no—
135#11758222—22no—
136#11758222—41no—
137#11758222—41no—
138#11758222—41no—
139#11758222—41no—
140#11758222—41no—
141#11758222—41no—
142#11758222—41no—
143#11758222—41no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244—21no—
147C2×D244—21no—
148C2×D244—21no—
149C2×D244C4⋊C412yes—
150C2×C4×D61—22no—
151C2×C4×D61—22no—
152C2×C4×D61—41no—
153C2×C4×D61—41no—
154C2×C4×D61—41no—
155C2×C4×D61—41no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122C4⋊C412yes—
162M16×C61—22no—
163M16×C61—22no—
164M16×C61—22no—
165M16×C61—22no—
166M16×C61—41no—
167M16×C61—41no—
168M16×C61—41no—
169M16×C61—41no—
170C2×C8×C61—22no—
171C2×C8×C61—22no—
172C2×C8×C61—41no—
173C2×C8×C61—41no—
174C2×C8×C61—41no—
175C2×C8×C61—41no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61—41no—
179C4⋊C4×C61—41no—
180C4⋊Dic61—22no—
181C4⋊Dic61—22no—
182C4⋊Dic61—41no—
183C4⋊Dic61—41no—
184#11758194—22no—
185#11758194—22no—
186#11758194—41no—
187#11758194—41no—
188C2×#92418—22no—
189C2×#92418—22no—
190C2×#92418—22no—
191C2×#92418—22no—
192C2×#92418—22no—
193C2×#92418—22no—
194C2×#92418—22no—
195C2×#92418—41no—
196C2×#92418—41no—
197C2×#92418C22⋊C414yes—
198C23×C61—22no—
199C23×C61—22no—
200C23×C61#11711yescharacteristic
201C23×C61#12111yescharacteristic
202C23×C61#12111yescharacteristic
203C23×C61#12111yescharacteristic
204C23×C61C22⋊Q811yescharacteristic
205C23×C61#12611yescharacteristic
206C23×C61#12611yescharacteristic
207C22×D61—22no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—42no—
211C22×D61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—82no—
214C2×C4×C61—82no—
215C2×C4×C61—82no—
216C2×C4×C61C2×C22⋊C411yescharacteristic
217C2×C4×C61C2×C4⋊C411yescharacteristic
218C2×C4×C61C4×D411yescharacteristic
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×C61C22⋊Q811yescharacteristic
231C2×C4×C61C22⋊Q811yescharacteristic
232C2×C4×C61C22⋊Q811yescharacteristic
233C2×C4×C61C22⋊Q811yescharacteristic
234C2×C4×C61C22⋊Q811yescharacteristic
235C2×C4×C61#12311yescharacteristic
236C2×C4×C61#12311yescharacteristic
237C2×C4×C61#12311yescharacteristic
238C2×C4×C61#12311yescharacteristic
239C2×C4×C61#12311yescharacteristic
240C2×C4×C61#12411yescharacteristic
241C2×C4×C61#12411yescharacteristic
242C2×C4×C61#12411yescharacteristic
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—
253C2×Dic61—82no—
254C2×Dic61—82no—
255D244—22no—
256D244—22no—
257D244—41no—
258D244—41no—
259C4×D61—42no—
260C4×D61—42no—
261C4×D61—42no—
262C4×D61—42no—
263Dic122—22no—
264Dic122—22no—
265Dic122—41no—
266Dic122—41no—
267C8×C61—42no—
268C8×C61—42no—
269#92418—24no—
270#92418—42no—
271#11106—611nomaximal, Sylow
272C22×C61—22no—
273C22×C61—22no—
274C22×C61—22no—
275C22×C61—22no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61#38011yescharacteristic
281C22×C61#38811yescharacteristic
282C22×C61#38811yescharacteristic
283C22×C61#39211yescharacteristic
284C22×C61#39611yescharacteristic
285C22×C61#39611yescharacteristic
286C22×C61#39711yescharacteristic
287C22×C61#47112yes—
288C22×C61#47112yes—
289C2×D61—44no—
290C2×D61—42no—
291C2×D61—82no—
292C2×D61—81no—
293C2×D61—81no—
294C4×C61—82no—
295C4×C61#38511yescharacteristic
296C4×C61#38511yescharacteristic
297C4×C61#38611yescharacteristic
298C4×C61#39011yescharacteristic
299C4×C61#39311yescharacteristic
300C4×C61#39411yescharacteristic
301C4×C61#39411yescharacteristic
302C4×C61#39911yescharacteristic
303Dic61—42no—
304Dic61—82no—
305C22×#106—611no—
306C2×#417—611no—
307C2×#417—611no—
308C2×#408—611no—
309C2×#343—611no—
310C2×#343D6111yescharacteristic, complemented
311C2×#341—611no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61—21no—
315C2×C61—21no—
316C2×C61#143911yescharacteristic
317C2×C61#181512yes—
318C2×C61#201911yescharacteristic
319C2×C61#201911yescharacteristic
320C2×C61#207912yes—
321D61—82no—
322C22×#41—611no—
323C22×M16—611no—
324C22×M16C2×D6111yescharacteristic
325C22×M16C2×D6111yescharacteristic
326C23×C8—611no—
327C22×C4⋊C4—611no—
328C22×C4⋊C4C2×D6111yescharacteristic
329C2×#106—1222no—
330C2×#106—1222no—
331C2×#106—1222no—
332#417—1222no—
333#417—1222no—
334#417—1222no—
335#417—1222no—
336C2×#103—1221no—
337C2×#103—1221no—
338C2×#102—1221no—
339C2×#102—1221no—
340#408—614no—
341#408—1222no—
342C2×C22⋊C8—1222no—
343#343—22no—
344#343—1222no—
345#341—1222no—
346C61#1110611yescharacteristic, complemented, Sylow
347C2×#41—612no—
348C2×#41—612no—
349C2×#41—1221no—
350C2×#41—1221no—
351C2×#41—1221no—
352C2×#41—1221no—
353C2×#41—1221no—
354C2×#41—1221no—
355C2×#41—1221no—
356C2×#41—1221no—
357C2×#41—1221no—
358C2×#41—1221no—
359C22×Q8—611no—
360C22×D4—611no—
361C22×D4—1221no—
362C23×C4—21no—
363C23×C4—1221no—
364C23×C4—1221no—
365C23×C4C22×D6111yescharacteristic
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—612no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16—1221no—
382C2×M16C4×D6112yes—
383C2×M16C22⋊D6112yes—
384C22×C8—21no—
385C22×C8—21no—
386C22×C8—612no—
387C22×C8—612no—
388C22×C8—612no—
389C22×C8—1221no—
390C22×C8—1221no—
391C22×C8—1221no—
392C22×C8—1221no—
393C22×C8—1221no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—612no—
400C2×C4⋊C4—1221no—
401C2×C4⋊C4—1221no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4D24412yes—
406#106—1228no—
407#103—1224no—
408#103—1224no—
409#102—1224no—
410#102—1224no—
411C22⋊C8—1228no—
412C24—1221no—
413C24#1175822211yescharacteristic
414#41—1222no—
415#41—1222no—
416#41—1222no—
417#41—1222no—
418#41—1222no—
419#41—1222no—
420#41—1222no—
421#41—1222no—
422#41—2441no—
423#41—2441no—
424#41—2441no—
425#41—2441no—
426#41—2441no—
427#41—2441no—
428#41—2441no—
429#41—2441no—
430C2×Q8—612no—
431C2×Q8—1221no—
432C2×Q8—1221no—
433C2×Q8—1221no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×D4—612no—
437C2×D4—1222no—
438C2×D4—1222no—
439C2×D4—1221no—
440C2×D4—1221no—
441C2×D4—1221no—
442C2×D4—1221no—
443C2×D4—1221no—
444C2×D4—2441no—
445C2×D4—2441no—
446C2×D4—2441no—
447C2×D4—2441no—
448C22×C4—22no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—82no—
452C22×C4—1221no—
453C22×C4—1222no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—4882no—
457C22×C4—2441no—
458C22×C4—2441no—
459C22×C4—2441no—
460C22×C4—2441no—
461C22×C4—2441no—
462C22×C4—2441no—
463C22×C4C2×C4×D6111yescharacteristic
464C22×C4C2×D24411yescharacteristic
465C22×C4#1175822211yescharacteristic
466C22×C4#1175822211yescharacteristic
467C22×C4#1175822211yescharacteristic
468C22×C4D4×D6111yescharacteristic
469C22×C4D4×D6111yescharacteristic
470C22×C4D4×D6111yescharacteristic
471C22×C4D4×D6111yescharacteristic
472C22×C4D4×D6111yescharacteristic
473C22×C4#1175822411yescharacteristic
474C22×C4Q8×D6111yescharacteristic
475C22×C4#1175822611yescharacteristic
476C22×C4C2×C22⋊D6111yescharacteristic
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—1222no—
486M16—1222no—
487M16—2441no—
488M16—2441no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—614no—
496C2×C8—1222no—
497C2×C8—1222no—
498C2×C8—1222no—
499C2×C8—1222no—
500C2×C8—1222no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—2441no—
504C2×C8—2441no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—2441no—
512C4⋊C4—2441no—
513C23—22no—
514C23—22no—
515C23—1222no—
516C23—2441no—
517C23—2442no—
518C23—2442no—
519C23—2441no—
520C23#1451973411yescharacteristic
521C23#1451975011yescharacteristic
522C23#1451975011yescharacteristic
523C23#1451975111yescharacteristic
524C23#1451975511yescharacteristic
525C23#1451977111yescharacteristic
526C23#1451977211yescharacteristic
527Q8—1222no—
528Q8—1222no—
529Q8—2441no—
530Q8—2441no—
531D4—1222no—
532D4—1222no—
533D4—2442no—
534D4—2442no—
535D4—2442no—
536D4—2442no—
537D4—2441no—
538D4—2441no—
539C2×C4—42no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4—1222no—
544C2×C4—4882no—
545C2×C4—4882no—
546C2×C4—4882no—
547C2×C4—2442no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2442no—
551C2×C4—2442no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4C22⋊C4×D6111yescharacteristic
555C2×C4C4⋊C4×D6111yescharacteristic
556C2×C4#1451973711yescharacteristic
557C2×C4C4×C22⋊D6111yescharacteristic
558C2×C4#1451973911yescharacteristic
559C2×C4C4×D24411yescharacteristic
560C2×C4#1451974511yescharacteristic
561C2×C4#1451974711yescharacteristic
562C2×C4#1451974711yescharacteristic
563C2×C4#1451974911yescharacteristic
564C2×C4#1451975011yescharacteristic
565C2×C4#1451975011yescharacteristic
566C2×C4#1451975011yescharacteristic
567C2×C4#1451975211yescharacteristic
568C2×C4#1451975311yescharacteristic
569C2×C4#1451975511yescharacteristic
570C2×C4#1451975511yescharacteristic
571C2×C4#1451975511yescharacteristic
572C2×C4#1451975711yescharacteristic
573C2×C4#1451975911yescharacteristic
574C2×C4#1451976011yescharacteristic
575C2×C4#1451976211yescharacteristic
576C2×C4#1451976211yescharacteristic
577C2×C4#1451976211yescharacteristic
578C2×C4#1451976311yescharacteristic
579C2×C4#1451976311yescharacteristic
580C2×C4#1451976511yescharacteristic
581C2×C4#1451977311yescharacteristic
582C8—42no—
583C8—42no—
584C8—1224no—
585C8—2442no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—22no—
594C22—4881no—
595C22—4881no—
596C22—4882no—
597C22—2442no—
598C22—2444no—
599C22#1683962111yescharacteristic
600C22#1683965111yescharacteristic
601C22#1683965311yescharacteristic
602C22#1683967111yescharacteristic
603C22#1683968411yescharacteristic
604C22#1683968611yescharacteristic
605C22#1683969111yescharacteristic
606C22#1684002412yes—
607C22#1684002812yes—
608C4—82no—
609C4—4882no—
610C4—2442no—
611C4#1683963311yescharacteristic
612C4#1683963611yescharacteristic
613C4#1683964011yescharacteristic
614C4#1683966211yescharacteristic
615C4#1683967511yescharacteristic
616C4#1683967711yescharacteristic
617C4#1683968011yescharacteristic
618C4#1683969711yescharacteristic
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—4882no—
624C2#2144406311yescharacteristic
625C2#2144587712yes—
626C2#2144693211yescharacteristic
627C2#2144693511yescharacteristic
628C2#2144726812yes—
subgroupG/H
centerC23#14519750
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#343C2
socleC23×C61#121
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#343D61
hypocenterC61#11106
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
1. C22×#14519708C2semidirect
5. C2×#16839530C2semidirect
6. C2×#16839526C2semidirect
7. C2×C61×#343C2semidirect
24. #16839730C4semidirect
310. C2×#343D61semidirect
346. C61#11106semidirect

Maximal subgroups

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

subgroupindex
C22×#145197082
C2×#168397642
C2×#168397612
C2×#168397302
C2×#168395302
C2×#168395262
C2×C61×#3432
#1110661