Finite Group Databasebeta

← #29587299

Subgroups — #29587299

Order 15616.

866 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×#16839798C211yesmaximal, characteristic, complemented
2C2×#16839780C211yesmaximal, characteristic
3C2×#16839778C211yesmaximal, characteristic
4C2×#16839730C211yesmaximal, characteristic
5C2×#16839534C211yesmaximal, characteristic, complemented
6C2×#16839526C211yesmaximal, characteristic, complemented
7C2×C61×#344C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C22×#11758194C2211yescharacteristic
10C23×#92418C2211yescharacteristic
11C2×#14519736C2211yescharacteristic
12#16839798—22no—
13#16839798—22no—
14C2×#14519710—21no—
15C2×#14519708—21no—
16#16839780—22no—
17#16839780—22no—
18#16839778—22no—
19#16839778—22no—
20C2×#14519705—22no—
21C2×#14519703—22no—
22#16839730—21no—
23#16839730—21no—
24#16839730C414yescomplemented
25C2×#14519689—22no—
26#16839534—22no—
27#16839526—22no—
28C22×M16×C61C2211yescharacteristic
29C22×M16×C61C2211yescharacteristic
30C2×#117×C61C2211yescharacteristic
31C61×#344—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×#11758222D412yes—
44C22×Dic122Q811yescharacteristic
45C22×D244Q811yescharacteristic
46C22×C22⋊D61—21no—
47C22×C4×D61—21no—
48C2×#11758194—21no—
49C2×#11758194—21no—
50C2×#11758194—21no—
51C2×#11758194—21no—
52C2×#11758194—21no—
53C2×#11758194D412yes—
54C22×#92418—21no—
55C22×#92418—21no—
56C22×#92418—21no—
57C22×#92418—21no—
58C22×#92418—21no—
59C22×#92418C2×C412yes—
60C22×#92418D412yes—
61C22×#92418D411yescharacteristic
62C22×#92418D411yescharacteristic
63#14519736—21no—
64#14519736—21no—
65#14519736—21no—
66#14519736D412yes—
67C2×C4⋊Dic61—21no—
68C2×C22⋊Dic61—21no—
69C2×C4×Dic61—21no—
70#14519710—24no—
71#14519708—24no—
72#14519705—28no—
73#14519703—28no—
74#14519689—24no—
75#14519689—24no—
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—
91#117×C61—21no—
92#117×C61—21no—
93#117×C61—21no—
94#117×C61D412yes—
95C2×C4⋊C4×C61—21no—
96C2×C22⋊C4×C61—21no—
97C2×C42×C61—21no—
98C24×C61#4111yescharacteristic
99C23×D61—21no—
100C22×C4×C61—41no—
101C22×C4×C61C22×C411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
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
115C2×C22⋊D61—22no—
116C2×C22⋊D61—22no—
117C2×C22⋊D61—41no—
118C2×C22⋊D61—41no—
119C2×C22⋊D61—41no—
120C2×C22⋊D61—41no—
121C22×Dic61—21no—
122C22×Dic61—41no—
123#11758222—22no—
124#11758222—22no—
125#11758222—22no—
126#11758222—22no—
127#11758222—22no—
128#11758222—22no—
129#11758222—22no—
130#11758222—22no—
131#11758222—41no—
132#11758222—41no—
133#11758222—41no—
134#11758222—41no—
135#11758222—41no—
136#11758222—41no—
137#11758222—41no—
138#11758222—41no—
139C2×D244—21no—
140C2×D244—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244C4⋊C412yes—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—41no—
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122C4⋊C412yes—
157M16×C61—22no—
158M16×C61—22no—
159M16×C61—22no—
160M16×C61—22no—
161M16×C61—41no—
162M16×C61—41no—
163M16×C61—41no—
164M16×C61—41no—
165C2×C8×C61—22no—
166C2×C8×C61—22no—
167C2×C8×C61—41no—
168C2×C8×C61—41no—
169C2×C8×C61—41no—
170C2×C8×C61—41no—
171C4⋊C4×C61—22no—
172C4⋊C4×C61—41no—
173C22⋊C4×C61—22no—
174C22⋊C4×C61—41no—
175C42×C61—22no—
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—
187C2×#92418—22no—
188C2×#92418—22no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—22no—
192C2×#92418—22no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—22no—
196C2×#92418—41no—
197C2×#92418—41no—
198C2×#92418C22⋊C412yes—
199C2×#92418C22⋊C412yes—
200C23×C61—42no—
201C23×C61#11711yescharacteristic
202C23×C61#12111yescharacteristic
203C23×C61#12111yescharacteristic
204C23×C61#12111yescharacteristic
205C23×C61C22⋊Q811yescharacteristic
206C23×C61#12611yescharacteristic
207C23×C61#12611yescharacteristic
208C22×D61—22no—
209C22×D61—44no—
210C22×D61—41no—
211C22×D61—41no—
212C2×C4×C61—42no—
213C2×C4×C61—82no—
214C2×C4×C61C2×C22⋊C411yescharacteristic
215C2×C4×C61C2×C4⋊C411yescharacteristic
216C2×C4×C61C4×D411yescharacteristic
217C2×C4×C61C4×D411yescharacteristic
218C2×C4×C61C4×D411yescharacteristic
219C2×C4×C61C4×D411yescharacteristic
220C2×C4×C61#12011yescharacteristic
221C2×C4×C61#12011yescharacteristic
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×C61C22⋊Q811yescharacteristic
229C2×C4×C61C22⋊Q811yescharacteristic
230C2×C4×C61C22⋊Q811yescharacteristic
231C2×C4×C61C22⋊Q811yescharacteristic
232C2×C4×C61C22⋊Q811yescharacteristic
233C2×C4×C61#12311yescharacteristic
234C2×C4×C61#12311yescharacteristic
235C2×C4×C61#12311yescharacteristic
236C2×C4×C61#12311yescharacteristic
237C2×C4×C61#12311yescharacteristic
238C2×C4×C61#12411yescharacteristic
239C2×C4×C61#12411yescharacteristic
240C2×C4×C61#12411yescharacteristic
241C2×C4×C61#12711yescharacteristic
242C22⋊D61—42no—
243C22⋊D61—42no—
244C22⋊D61—42no—
245C22⋊D61—42no—
246C2×Dic61—22no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—42no—
250C2×Dic61—82no—
251D244—22no—
252D244—22no—
253D244—41no—
254D244—41no—
255C4×D61—42no—
256C4×D61—42no—
257C4×D61—42no—
258C4×D61—42no—
259Dic122—22no—
260Dic122—22no—
261Dic122—41no—
262Dic122—41no—
263C8×C61—42no—
264C8×C61—42no—
265#92418—22no—
266#92418—22no—
267#92418—42no—
268#11104—611nomaximal, Sylow
269C22×C61—22no—
270C22×C61—22no—
271C22×C61—22no—
272C22×C61—41no—
273C22×C61—41no—
274C22×C61—41no—
275C22×C61—41no—
276C22×C61#38011yescharacteristic
277C22×C61#38811yescharacteristic
278C22×C61#38811yescharacteristic
279C22×C61#39211yescharacteristic
280C22×C61#39611yescharacteristic
281C22×C61#39611yescharacteristic
282C22×C61#39711yescharacteristic
283C2×D61—44no—
284C2×D61—42no—
285C2×D61—82no—
286C2×D61—82no—
287C4×C61—82no—
288C4×C61#38511yescharacteristic
289C4×C61#38511yescharacteristic
290C4×C61#38611yescharacteristic
291C4×C61#39011yescharacteristic
292C4×C61#39311yescharacteristic
293C4×C61#39411yescharacteristic
294C4×C61#39411yescharacteristic
295C4×C61#39911yescharacteristic
296Dic61—42no—
297Dic61—82no—
298C2×#427—611no—
299C2×#421—611no—
300C2×#421—611no—
301C2×#408—611no—
302C2×#344—611no—
303C2×#344D6111yescharacteristic, complemented
304C2×#341—611no—
305C2×C61—21no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61—21no—
309C2×C61—21no—
310C2×C61—21no—
311C2×C61#143911yescharacteristic
312C2×C61#181412yes—
313D61—82no—
314C22×#41—611no—
315C22×M16—611no—
316C22×M16C2×D6111yescharacteristic
317C22×M16C2×D6111yescharacteristic
318C23×C8—611no—
319C2×#117—611no—
320C2×#117C2×D6111yescharacteristic
321#427—1222no—
322#427—1222no—
323C2×#107—1221no—
324C2×#106—1221no—
325#421—1222no—
326#421—1222no—
327#421—1222no—
328#421—1222no—
329C2×#104—1222no—
330C2×#104—1222no—
331#408—614no—
332#408—1221no—
333#408—1221no—
334C2×C22⋊C8—1222no—
335#344—22no—
336#344—1222no—
337#341—1222no—
338C61#1110411yescharacteristic, complemented, Sylow
339C2×#41—612no—
340C2×#41—612no—
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—
350C2×#41—1221no—
351C22×Q8—611no—
352C22×D4—611no—
353C22×D4—1221no—
354C23×C4—1221no—
355C23×C4C22×D6111yescharacteristic
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—612no—
367C2×M16—1221no—
368C2×M16—1221no—
369C2×M16—1221no—
370C2×M16—1221no—
371C2×M16—1221no—
372C2×M16C4×D6112yes—
373C2×M16C22⋊D6112yes—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—612no—
377C22×C8—612no—
378C22×C8—611no—
379C22×C8—611no—
380C22×C8—1221no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117—612no—
389#117—1221no—
390#117—1221no—
391#117—1221no—
392#117D24412yes—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—1221no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—1221no—
397C2×C42—21no—
398C2×C42—1221no—
399#107—1224no—
400#106—1224no—
401#104—1228no—
402#104—1228no—
403C22⋊C8—1224no—
404C22⋊C8—1224no—
405C24—1221no—
406C24#1175822211yescharacteristic
407#41—1222no—
408#41—1222no—
409#41—1222no—
410#41—1222no—
411#41—1222no—
412#41—1222no—
413#41—1222no—
414#41—1222no—
415#41—2441no—
416#41—2441no—
417#41—2441no—
418#41—2441no—
419#41—2441no—
420#41—2441no—
421#41—2441no—
422#41—2441no—
423C2×Q8—612no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×Q8—1221no—
429C2×D4—612no—
430C2×D4—1222no—
431C2×D4—1222no—
432C2×D4—1221no—
433C2×D4—1221no—
434C2×D4—1221no—
435C2×D4—1221no—
436C2×D4—1221no—
437C2×D4—2441no—
438C2×D4—2441no—
439C2×D4—2441no—
440C2×D4—2441no—
441C22×C4—41no—
442C22×C4—1221no—
443C22×C4—1222no—
444C22×C4—1222no—
445C22×C4—2441no—
446C22×C4—2441no—
447C22×C4—2441no—
448C22×C4—2441no—
449C22×C4—2441no—
450C22×C4C2×C4×D6111yescharacteristic
451C22×C4C2×D24411yescharacteristic
452C22×C4#1175822211yescharacteristic
453C22×C4#1175822211yescharacteristic
454C22×C4#1175822211yescharacteristic
455C22×C4D4×D6111yescharacteristic
456C22×C4D4×D6111yescharacteristic
457C22×C4D4×D6111yescharacteristic
458C22×C4D4×D6111yescharacteristic
459C22×C4D4×D6111yescharacteristic
460C22×C4#1175822411yescharacteristic
461C22×C4Q8×D6111yescharacteristic
462C22×C4#1175822611yescharacteristic
463C22×C4C2×C22⋊D6111yescharacteristic
464M16—22no—
465M16—22no—
466M16—22no—
467M16—22no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—41no—
472M16—1222no—
473M16—1222no—
474M16—2441no—
475M16—2441no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—612no—
483C2×C8—612no—
484C2×C8—1222no—
485C2×C8—1222no—
486C2×C8—1221no—
487C2×C8—1221no—
488C2×C8—1222no—
489C2×C8—1222no—
490C2×C8—1221no—
491C2×C8—1221no—
492C2×C8—1222no—
493C2×C8—2441no—
494C2×C8—2441no—
495C4⋊C4—22no—
496C4⋊C4—41no—
497C4⋊C4—1222no—
498C4⋊C4—2441no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C22⋊C4—1222no—
502C22⋊C4—2441no—
503C42—22no—
504C42—41no—
505C42—1222no—
506C42—2441no—
507C23—42no—
508C23—1222no—
509C23—2444no—
510C23—2441no—
511C23—2441no—
512C23#1451973411yescharacteristic
513C23#1451975011yescharacteristic
514C23#1451975011yescharacteristic
515C23#1451975111yescharacteristic
516C23#1451975511yescharacteristic
517C23#1451977111yescharacteristic
518C23#1451977211yescharacteristic
519Q8—1222no—
520Q8—1222no—
521Q8—2441no—
522Q8—2441no—
523D4—1222no—
524D4—1222no—
525D4—2442no—
526D4—2442no—
527D4—2442no—
528D4—2442no—
529D4—2441no—
530D4—2441no—
531C2×C4—42no—
532C2×C4—82no—
533C2×C4—1222no—
534C2×C4—4882no—
535C2×C4—2442no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4C22⋊C4×D6111yescharacteristic
543C2×C4C4⋊C4×D6111yescharacteristic
544C2×C4#1451973711yescharacteristic
545C2×C4C4×C22⋊D6111yescharacteristic
546C2×C4#1451973911yescharacteristic
547C2×C4C4×D24411yescharacteristic
548C2×C4#1451974511yescharacteristic
549C2×C4#1451974711yescharacteristic
550C2×C4#1451974711yescharacteristic
551C2×C4#1451974911yescharacteristic
552C2×C4#1451975011yescharacteristic
553C2×C4#1451975011yescharacteristic
554C2×C4#1451975011yescharacteristic
555C2×C4#1451975211yescharacteristic
556C2×C4#1451975311yescharacteristic
557C2×C4#1451975511yescharacteristic
558C2×C4#1451975511yescharacteristic
559C2×C4#1451975511yescharacteristic
560C2×C4#1451975711yescharacteristic
561C2×C4#1451975911yescharacteristic
562C2×C4#1451976011yescharacteristic
563C2×C4#1451976211yescharacteristic
564C2×C4#1451976211yescharacteristic
565C2×C4#1451976211yescharacteristic
566C2×C4#1451976311yescharacteristic
567C2×C4#1451976311yescharacteristic
568C2×C4#1451976511yescharacteristic
569C2×C4#1451977311yescharacteristic
570C8—42no—
571C8—42no—
572C8—1222no—
573C8—1222no—
574C8—2442no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—4882no—
583C22—4882no—
584C22—2442no—
585C22—2444no—
586C22#1683962111yescharacteristic
587C22#1683965111yescharacteristic
588C22#1683965311yescharacteristic
589C22#1683967111yescharacteristic
590C22#1683968411yescharacteristic
591C22#1683968611yescharacteristic
592C22#1683969111yescharacteristic
593C4—82no—
594C4—4882no—
595C4—2442no—
596C4#1683963311yescharacteristic
597C4#1683963611yescharacteristic
598C4#1683964011yescharacteristic
599C4#1683966211yescharacteristic
600C4#1683967511yescharacteristic
601C4#1683967711yescharacteristic
602C4#1683968011yescharacteristic
603C4#1683969711yescharacteristic
604C2—21no—
605C2—21no—
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—4882no—
611C2#2144406311yescharacteristic
612C2#2144587212yes—
subgroupG/H
centerC2×C4#14519750
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#344C2
socleC22×C61#380
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#344D61
hypocenterC61#11104
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#16839798C2semidirect
5. C2×#16839534C2semidirect
6. C2×#16839526C2semidirect
7. C2×C61×#344C2semidirect
24. #16839730C4semidirect
303. C2×#344D61semidirect
338. C61#11104semidirect

Maximal subgroups

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

subgroupindex
C2×#168397982
C2×#168397802
C2×#168397782
C2×#168397302
C2×#168395342
C2×#168395262
C2×C61×#3442
#1110461