Finite Group Databasebeta

← #29587151

Subgroups — #29587151

Order 15616.

902 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839786C211yesmaximal, characteristic, complemented
2C2×#16839780C211yesmaximal, characteristic
3C22×#14519705C211yesmaximal, characteristic
4#21454263C211yesmaximal, characteristic
5C2×#16839532C211yesmaximal, characteristic, complemented
6#21445545C211yesmaximal, characteristic, complemented
7C2×C61×#339C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C22×#11758194C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12#16839786—22no—
13#16839786—22no—
14C2×C4⋊#92418—22no—
15#16839780—22no—
16#16839780—22no—
17C2×#14519705—22no—
18C2×#14519705—22no—
19C2×#14519705—22no—
20C2×#14519705C412yescomplemented
21C2×#14519705C412yescomplemented
22#16839730—22no—
23#16839728—22no—
24#16839725—22no—
25#16839532—22no—
26#16839526—22no—
27C22×M16×C61C2211yescharacteristic
28C2×#117×C61C2211yescharacteristic
29C22×C42×C61C2211yescharacteristic
30C61×#339—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×#11758222C2×C412yes—
42C2×#11758222D412yes—
43C22×Dic122Q811yescharacteristic
44C22×D244Q811yescharacteristic
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×#11758194—21no—
59C2×#11758194—21no—
60C2×#11758194—21no—
61C2×#11758194—21no—
62C2×#11758194—21no—
63C2×#11758194C2×C412yes—
64C2×#11758194D412yes—
65C22×#92418—21no—
66C22×#92418—21no—
67C22×#92418D412yes—
68C4⋊#92418—28no—
69#14519705—28no—
70#14519705—24no—
71#14519705—24no—
72#14519689—28no—
73C23×C4×C61—21no—
74C23×C4×C61C2311yescharacteristic
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C2×M16×C61—21no—
78C2×M16×C61—21no—
79C2×M16×C61—21no—
80C2×M16×C61D412yes—
81C22×C8×C61—21no—
82#117×C61—21no—
83#117×C61—21no—
84#117×C61—21no—
85#117×C61D412yes—
86C2×C4⋊C4×C61—21no—
87C2×C22⋊C4×C61—21no—
88C2×C42×C61—21no—
89C2×C42×C61—21no—
90C2×C42×C61—21no—
91C2×C42×C61—21no—
92C2×C42×C61C2×C411yescharacteristic
93C2×C42×C61C2×C411yescharacteristic
94C2×C42×C61D412yes—
95C2×C42×C61D412yes—
96C24×C61#4111yescharacteristic
97C23×D61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—44no—
103C22×C4×C61—41no—
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×D411yescharacteristic
112C22×C4×C61C2×Q811yescharacteristic
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—
125#11758222—22no—
126#11758222—22no—
127#11758222—22no—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—22no—
132#11758222—22no—
133#11758222—41no—
134#11758222—41no—
135#11758222—41no—
136#11758222—41no—
137#11758222—41no—
138#11758222—41no—
139#11758222—41no—
140#11758222—41no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244C4⋊C412yes—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×C4×D61—41no—
152C2×C4×D61—41no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122C4⋊C412yes—
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—41no—
162M16×C61—41no—
163C2×C8×C61—22no—
164C2×C8×C61—41no—
165C2×C8×C61—41no—
166C4⋊C4×C61—22no—
167C4⋊C4×C61—41no—
168C22⋊C4×C61—22no—
169C22⋊C4×C61—41no—
170C42×C61—21no—
171C42×C61—21no—
172C42×C61—22no—
173C42×C61—22no—
174C42×C61—22no—
175C42×C61—41no—
176C42×C61C22⋊C412yes—
177C42×C61C22⋊C412yes—
178#11758194—22no—
179#11758194—22no—
180#11758194—22no—
181#11758194—22no—
182#11758194—41no—
183#11758194—41no—
184#11758194—41no—
185#11758194—41no—
186#11758194—41no—
187#11758194—41no—
188#11758194—41no—
189#11758194—41no—
190C2×#92418—22no—
191C2×#92418—22no—
192C2×#92418—22no—
193C2×#92418—22no—
194C2×#92418—22no—
195C2×#92418—41no—
196C2×#92418—41no—
197C2×#92418—41no—
198C2×#92418—41no—
199C23×C61—42no—
200C23×C61C4×D411yescharacteristic
201C23×C61#12111yescharacteristic
202C23×C61C22⋊Q811yescharacteristic
203C23×C61#12311yescharacteristic
204C23×C61#12311yescharacteristic
205C23×C61#12311yescharacteristic
206C23×C61#12611yescharacteristic
207C22×D61—22no—
208C22×D61—41no—
209C22×D61—41no—
210C22×D61—82no—
211C2×C4×C61—24no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—44no—
215C2×C4×C61—44no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—82no—
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C2×C4⋊C411yescharacteristic
221C2×C4×C61#11711yescharacteristic
222C2×C4×C61C4×D411yescharacteristic
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61#12011yescharacteristic
226C2×C4×C61#12011yescharacteristic
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×C61#12111yescharacteristic
235C2×C4×C61C22⋊Q811yescharacteristic
236C2×C4×C61C22⋊Q811yescharacteristic
237C2×C4×C61C22⋊Q811yescharacteristic
238C2×C4×C61C22⋊Q811yescharacteristic
239C2×C4×C61C22⋊Q811yescharacteristic
240C2×C4×C61#12311yescharacteristic
241C2×C4×C61#12311yescharacteristic
242C2×C4×C61#12411yescharacteristic
243C2×C4×C61#12411yescharacteristic
244C2×C4×C61#12411yescharacteristic
245C2×C4×C61#12611yescharacteristic
246C2×C4×C61#12711yescharacteristic
247C22⋊D61—42no—
248C22⋊D61—42no—
249C22⋊D61—42no—
250C22⋊D61—42no—
251C2×Dic61—22no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254D244—22no—
255D244—22no—
256D244—41no—
257D244—41no—
258C4×D61—42no—
259C4×D61—42no—
260C4×D61—42no—
261C4×D61—42no—
262Dic122—22no—
263Dic122—22no—
264Dic122—41no—
265Dic122—41no—
266C8×C61—42no—
267#92418—42no—
268#92418—42no—
269#92418—42no—
270#11080—611nomaximal, Sylow
271C22×C61—22no—
272C22×C61—22no—
273C22×C61—22no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61#38511yescharacteristic
279C22×C61#38611yescharacteristic
280C22×C61#38811yescharacteristic
281C22×C61#39411yescharacteristic
282C22×C61#39611yescharacteristic
283C22×C61#39711yescharacteristic
284C22×C61#39911yescharacteristic
285C2×D61—44no—
286C2×D61—42no—
287C2×D61—82no—
288C2×D61—82no—
289C4×C61—24no—
290C4×C61—42no—
291C4×C61—82no—
292C4×C61#38011yescharacteristic
293C4×C61#38511yescharacteristic
294C4×C61#38811yescharacteristic
295C4×C61#39011yescharacteristic
296C4×C61#39211yescharacteristic
297C4×C61#39311yescharacteristic
298C4×C61#39411yescharacteristic
299C4×C61#39611yescharacteristic
300Dic61—42no—
301C2×#423—611no—
302C2×#421—611no—
303C22×#104—611no—
304#2879—611no—
305C2×#344—611no—
306#1738—611no—
307C2×#339D6111yescharacteristic, complemented
308C2×C61—21no—
309C2×C61—21no—
310C2×C61—21no—
311C2×C61—21no—
312C2×C61—21no—
313C2×C61—21no—
314C2×C61#143911yescharacteristic
315C2×C61#186112yes—
316D61—82no—
317C22×#41—611no—
318C22×M16—611no—
319C22×M16—611no—
320C22×M16—611no—
321C22×M16C2×D6111yescharacteristic
322C2×#117C2×D6111yescharacteristic
323C22×C42C2×D6111yescharacteristic
324#423—1222no—
325#423—1222no—
326C2×C4⋊C8—1222no—
327#421—1222no—
328#421—1222no—
329C2×#104—612no—
330C2×#104—612no—
331C2×#104—1222no—
332C2×#104—1222no—
333C2×#104—1222no—
334#408—1222no—
335#408—1222no—
336#407—1222no—
337#344—1222no—
338#341—1222no—
339#339—22no—
340C61#1108011yescharacteristic, complemented, Sylow
341C2×#41—612no—
342C2×#41—612no—
343C2×#41—1221no—
344C2×#41—1221no—
345C2×#41—1221no—
346C2×#41—1221no—
347C2×#41—1221no—
348C2×#41—1221no—
349C2×#41—1221no—
350C2×#41—1221no—
351C2×#41—1221no—
352C2×#41—1221no—
353C22×Q8—611no—
354C22×D4—611no—
355C22×D4—1221no—
356C23×C4—21no—
357C23×C4—1221no—
358C23×C4C22×D6111yescharacteristic
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—612no—
365C2×M16—612no—
366C2×M16—1221no—
367C2×M16—1221no—
368C2×M16—1221no—
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—
380C2×M16—1221no—
381C2×M16—1221no—
382C2×M16D24412yes—
383C22×C8—21no—
384C22×C8—612no—
385C22×C8—1221no—
386C22×C8—1221no—
387#117—21no—
388#117—21no—
389#117—21no—
390#117D24412yes—
391C2×C4⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42C4×D6111yescharacteristic
398C2×C42C4×D6111yescharacteristic
399C2×C42D24412yes—
400C2×C42C22⋊D6112yes—
401C4⋊C8—1228no—
402#104—1228no—
403#104—1224no—
404#104—1224no—
405C22⋊C8—1228no—
406C24—1221no—
407C24#1175822411yescharacteristic
408#41—1222no—
409#41—1222no—
410#41—1222no—
411#41—1222no—
412#41—1222no—
413#41—1222no—
414#41—1222no—
415#41—1222no—
416#41—2441no—
417#41—2441no—
418#41—2441no—
419#41—2441no—
420#41—2441no—
421#41—2441no—
422#41—2441no—
423#41—2441no—
424C2×Q8—612no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×Q8—1221no—
429C2×Q8—1221no—
430C2×D4—612no—
431C2×D4—1222no—
432C2×D4—1222no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—1221no—
436C2×D4—1221no—
437C2×D4—1221no—
438C2×D4—2441no—
439C2×D4—2441no—
440C2×D4—2441no—
441C2×D4—2441no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—44no—
447C22×C4—41no—
448C22×C4—1221no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—2441no—
452C22×C4—2441no—
453C22×C4—2441no—
454C22×C4—2441no—
455C22×C4C2×C4×D6111yescharacteristic
456C22×C4C2×D24411yescharacteristic
457C22×C4C2×D24411yescharacteristic
458C22×C4C2×D24411yescharacteristic
459C22×C4#1175822211yescharacteristic
460C22×C4#1175822211yescharacteristic
461C22×C4D4×D6111yescharacteristic
462C22×C4D4×D6111yescharacteristic
463C22×C4D4×D6111yescharacteristic
464C22×C4#1175822411yescharacteristic
465C22×C4#1175822411yescharacteristic
466C22×C4Q8×D6111yescharacteristic
467C22×C4#1175822611yescharacteristic
468C22×C4C2×C22⋊D6111yescharacteristic
469M16—22no—
470M16—22no—
471M16—41no—
472M16—41no—
473M16—1222no—
474M16—1222no—
475M16—1222no—
476M16—1222no—
477M16—2441no—
478M16—2441no—
479M16—2441no—
480M16—2441no—
481M16—2441no—
482M16—2441no—
483M16—2441no—
484M16—2441no—
485C2×C8—22no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—1222no—
489C2×C8—1222no—
490C2×C8—1222no—
491C2×C8—1222no—
492C2×C8—1222no—
493C2×C8—2441no—
494C2×C8—2441no—
495C2×C8—2441no—
496C2×C8—2441no—
497C4⋊C4—22no—
498C4⋊C4—41no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C42—21no—
502C42—21no—
503C42—22no—
504C42—22no—
505C42—22no—
506C42—41no—
507C42#1175819812yes—
508C42#1175819812yes—
509C23—42no—
510C23—1222no—
511C23—4882no—
512C23—2441no—
513C23—2441no—
514C23#1451973711yescharacteristic
515C23#1451974911yescharacteristic
516C23#1451975711yescharacteristic
517C23#1451975911yescharacteristic
518C23#1451976111yescharacteristic
519C23#1451976111yescharacteristic
520C23#1451977211yescharacteristic
521Q8—1222no—
522Q8—1222no—
523Q8—2441no—
524Q8—2441no—
525D4—1222no—
526D4—1222no—
527D4—2442no—
528D4—2442no—
529D4—2442no—
530D4—2442no—
531D4—2441no—
532D4—2441no—
533C2×C4—24no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—82no—
541C2×C4—1222no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2442no—
545C2×C4—2442no—
546C2×C4—2442no—
547C2×C4—2442no—
548C2×C4C2×#1175819811yescharacteristic
549C2×C4C4⋊C4×D6111yescharacteristic
550C2×C4#1451973511yescharacteristic
551C2×C4#1451973711yescharacteristic
552C2×C4C4×D24411yescharacteristic
553C2×C4C4×D24411yescharacteristic
554C2×C4#1451974711yescharacteristic
555C2×C4#1451974711yescharacteristic
556C2×C4#1451974711yescharacteristic
557C2×C4#1451974811yescharacteristic
558C2×C4#1451974911yescharacteristic
559C2×C4#1451975111yescharacteristic
560C2×C4#1451975111yescharacteristic
561C2×C4#1451975211yescharacteristic
562C2×C4#1451975211yescharacteristic
563C2×C4#1451975211yescharacteristic
564C2×C4#1451975311yescharacteristic
565C2×C4#1451975511yescharacteristic
566C2×C4#1451975511yescharacteristic
567C2×C4#1451975711yescharacteristic
568C2×C4#1451975711yescharacteristic
569C2×C4#1451975911yescharacteristic
570C2×C4#1451976111yescharacteristic
571C2×C4#1451976311yescharacteristic
572C2×C4#1451976311yescharacteristic
573C2×C4#1451976511yescharacteristic
574C2×C4#1451977211yescharacteristic
575C2×C4#1451977411yescharacteristic
576C8—42no—
577C8—2442no—
578C8—2442no—
579C8—2442no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—4882no—
588C22—4882no—
589C22—2444no—
590C22—2442no—
591C22#1683963611yescharacteristic
592C22#1683963911yescharacteristic
593C22#1683965411yescharacteristic
594C22#1683967811yescharacteristic
595C22#1683968411yescharacteristic
596C22#1683968911yescharacteristic
597C22#1683969911yescharacteristic
598C4—24no—
599C4—42no—
600C4—82no—
601C4—2442no—
602C4#1683961911yescharacteristic
603C4#1683963611yescharacteristic
604C4#1683965411yescharacteristic
605C4#1683966411yescharacteristic
606C4#1683967211yescharacteristic
607C4#1683967511yescharacteristic
608C4#1683967811yescharacteristic
609C4#1683968411yescharacteristic
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—4882no—
617C2#2144406511yescharacteristic
618C2#2144606012yes—
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#339C2
socleC22×C61#385
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#339D61
hypocenterC61#11080
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#16839786C2semidirect
5. C2×#16839532C2semidirect
6. #21445545C2semidirect
7. C2×C61×#339C2semidirect
20. C2×#14519705C4semidirect
21. C2×#14519705C4semidirect
307. C2×#339D61semidirect
340. C61#11080semidirect

Maximal subgroups

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

subgroupindex
C2×#168397862
C2×#168397802
C22×#145197052
#214542632
C2×#168395322
#214455452
C2×C61×#3392
#1108061