Finite Group Databasebeta

← #30620349

Subgroups — #30620349

Order 15616.

1062 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462557C212yesmaximal
2#21462012C212yesmaximal, complemented
3#21461847C212yesmaximal, complemented
4#21461846C212yesmaximal, complemented
5#21461721C211yesmaximal, characteristic, complemented
6#21461720C211yesmaximal, characteristic, complemented
7#21461686C211yesmaximal, characteristic, complemented
8#21461572C211yesmaximal, characteristic, complemented
9#21461525C211yesmaximal, characteristic, complemented
10#21461524C211yesmaximal, characteristic, complemented
11C2×#16840479C211yesmaximal, characteristic
12C2×D61⋊M16C2212yes—
13C22×#11758217C2212yes—
14#16840795—22no—
15#16840794—22no—
16#16840791—22no—
17#16840789—22no—
18#16840765C2212yes—
19C2×#14519838C2212yes—
20C2×#14519838C2212yes—
21#16840734C2212yes—
22#16840732C2212yes—
23C4×#11758217C2212yes—
24#16840642C2211yescharacteristic
25#16840642C2212yes—
26#16840642C2211yescharacteristic
27#16840642C2212yes—
28#16840642C2211yescharacteristic
29#16840642C2211yescharacteristic
30#16840642C2212yes—
31#16840642C2212yes—
32#16840479—22no—
33#16840479—22no—
34#16840479—22no—
35#16840479—22no—
36C2×#14519776C2211yescharacteristic
37C2×#14519772C411yescharacteristic
38C2×#14519772C411yescharacteristic
39C2×#14519770C411yescharacteristic
40C2×#14519763C411yescharacteristic
41C2×#14519763C411yescharacteristic
42C2×#14519755C2211yescharacteristic
43C2×#14519754C2211yescharacteristic
44C2×C4×Dic122C411yescharacteristic
45C2×#14519742C411yescharacteristic
46C2×#14519742C2211yescharacteristic
47C2×#14519737C2211yescharacteristic
48C2×#14519734C2211yescharacteristic
49C2×#14519733C2211yescharacteristic
50C2×#126×C61C411yescharacteristic
51C2×#11758213—22no—
52D61⋊M16—24no—
53D61⋊M16—42no—
54C2×#11758217—22no—
55C2×#11758217—24no—
56C2×#11758217—42no—
57C2×#11758217C2312yes—
58C2×#11758217C2312yes—
59C2×#11758217C2312yes—
60C2×#11758217C2312yes—
61C2×D61⋊C8—22no—
62C22×#92420—22no—
63#14519844—22no—
64C4⋊#92420—22no—
65#14519838—24no—
66#14519838—42no—
67#14519834—22no—
68#14519834—22no—
69C22⋊#92420—22no—
70C22⋊#92420—22no—
71#14519832—22no—
72C4×#92420—22no—
73C22×Dic122C2×C411yescharacteristic
74C22×Dic122C2×C411yescharacteristic
75C22×Dic122C2311yescharacteristic
76C22×C22⋊D61C2×C411yescharacteristic
77C23×Dic61C2311yescharacteristic
78C22×C4×D61C2311yescharacteristic
79#14519776—22no—
80#14519776—22no—
81#14519772—22no—
82#14519772—22no—
83#14519772—22no—
84#14519772—22no—
85#14519770—22no—
86#14519770—22no—
87#14519763—22no—
88#14519763—22no—
89#14519763—22no—
90#14519763—22no—
91#14519755—22no—
92#14519755—22no—
93#14519754—22no—
94#14519754—22no—
95C4×Dic122—21no—
96C4×Dic122—21no—
97C4×Dic122—21no—
98C4×Dic122—21no—
99#14519742—21no—
100#14519742—21no—
101#14519742—21no—
102#14519742—21no—
103#14519742—22no—
104#14519742—22no—
105#14519737D412yes—
106#14519737D412yes—
107#14519737D412yes—
108#14519737D412yes—
109#14519734—22no—
110#14519734—22no—
111#14519733—22no—
112#14519733—22no—
113C2×C4⋊Dic61C2×C411yescharacteristic
114C2×C4⋊Dic61C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C2×#11758196C2×C411yescharacteristic
117C2×#11758196C2×C411yescharacteristic
118C2×#11758196C2×C411yescharacteristic
119C2×#11758196C2311yescharacteristic
120C2×#11758196C2311yescharacteristic
121C2×#11758196C2311yescharacteristic
122C2×C22⋊Dic61C2×C411yescharacteristic
123C2×C22⋊Dic61C2×C411yescharacteristic
124C2×#11758198C2×C411yescharacteristic
125C2×#11758198C2×C411yescharacteristic
126C2×#11758198C2×C411yescharacteristic
127C2×#11758198C2×C411yescharacteristic
128C2×#11758198C2×C411yescharacteristic
129C2×C4×Dic61C2×C411yescharacteristic
130C2×C4×Dic61C2×C411yescharacteristic
131C2×C4×Dic61C2×C411yescharacteristic
132C2×C4×Dic61C2×C411yescharacteristic
133C2×C4×Dic61C2×C411yescharacteristic
134C2×C4×Dic61C2311yescharacteristic
135#126×C61—22no—
136#126×C61—22no—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C4⋊C4×C61C2×C411yescharacteristic
139C2×C4⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic
143C2×C42×C61C2×C411yescharacteristic
144C24×C61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C2×C22⋊D61—42no—
153C2×C22⋊D61C22⋊C412yes—
154C2×C22⋊D61C22⋊C412yes—
155C22×Dic61—22no—
156C22×Dic61—21no—
157C22×Dic61—21no—
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C22×Dic61C22×C411yescharacteristic
164C22×Dic61C2×D412yes—
165C22×Dic61C2×D412yes—
166C22×Dic61C2411yescharacteristic
167C2×C4×D61—22no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61C2×D412yes—
171C2×C4×D61C2×D412yes—
172C2×Dic122—21no—
173C2×Dic122—21no—
174C2×Dic122—21no—
175C2×Dic122—21no—
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×Dic122—21no—
179C2×Dic122—21no—
180C2×Dic122—42no—
181C2×Dic122—42no—
182#11758217—22no—
183#11758217—22no—
184#11758217—22no—
185#11758217—22no—
186#11758217—22no—
187#11758217—22no—
188#11758217—22no—
189#11758217—44no—
190#11758217#4114yes—
191C2×#92420—22no—
192C2×#92420—22no—
193C2×#92420—22no—
194C2×#92420—22no—
195C2×#92420—44no—
196#11758213—44no—
197D61⋊C8—44no—
198C4⋊C4×C61—21no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—22no—
201C4⋊C4×C61—22no—
202C22⋊C4×C61—22no—
203C22⋊C4×C61—22no—
204C22⋊C4×C61C22⋊C412yes—
205C22⋊C4×C61C22⋊C412yes—
206C42×C61—21no—
207C42×C61—21no—
208C22⋊Dic61—22no—
209C22⋊Dic61—22no—
210#11758198—22no—
211#11758198—22no—
212#11758198—22no—
213#11758198—22no—
214#11758198C22⋊C412yes—
215#11758198C22⋊C412yes—
216C4⋊Dic61—22no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219#11758196—22no—
220#11758196—21no—
221#11758196—21no—
222#11758196—21no—
223#11758196—21no—
224#11758196—22no—
225#11758196—22no—
226#11758196—22no—
227#11758196C22⋊C411yescharacteristic
228#11758196C22⋊C411yescharacteristic
229#11758196C22⋊C411yescharacteristic
230#11758196C22⋊C411yescharacteristic
231C4×Dic61—21no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—21no—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—21no—
241C4×Dic61C2×D412yes—
242C4×Dic61C2×D412yes—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—41no—
246C23×C61—41no—
247C23×C61C2×C22⋊C412yes—
248C23×C61C23×C411yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61C2×C22⋊C412yes—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—41no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—41no—
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61C2×C22⋊C411yescharacteristic
268C2×C4×C61C2×C22⋊C412yes—
269C22⋊D61—24no—
270C22⋊D61—42no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—22no—
274C2×Dic61—22no—
275C2×Dic61—22no—
276C2×Dic61—22no—
277C2×Dic61—22no—
278C2×Dic61—21no—
279C2×Dic61—21no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61C2×C22⋊C411yescharacteristic
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C22×D412yes—
292C2×Dic61C2×#4112yes—
293C2×Dic61H(5,𝔽2)11yescharacteristic
294C2×Dic612−1+411yescharacteristic
295C4×D61—22no—
296C4×D61—22no—
297C4×D61—22no—
298C4×D61—22no—
299Dic122—42no—
300Dic122—42no—
301Dic122—42no—
302Dic122—42no—
303Dic122—42no—
304Dic122—42no—
305#92420—24no—
306#92420—42no—
307#92420—42no—
308#92420—42no—
309#22484—611nomaximal, Sylow
310C22×C61—21no—
311C22×C61—21no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—22no—
315C22×C61—81no—
316C22×C61—81no—
317C22×C61C22×C22⋊C411yescharacteristic
318C22×C61C4×#4111yescharacteristic
319C22×C61#52011yescharacteristic
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—22no—
323C2×D61—81no—
324C2×D61—81no—
325C4×C61—21no—
326C4×C61—21no—
327C4×C61—22no—
328C4×C61—41no—
329C4×C61—41no—
330C4×C61—41no—
331C4×C61—41no—
332Dic61—21no—
333Dic61—21no—
334Dic61—21no—
335Dic61—41no—
336Dic61—41no—
337Dic61—41no—
338Dic61—41no—
339Dic61#41312yes—
340Dic61#54612yes—
341Dic61#54712yes—
342C2×#556—611no—
343D4×M16—612no—
344#1997—612no—
345#1901—612no—
346#1901—612no—
347#1822—611no—
348#1822—611no—
349#1801—611no—
350C4×#101—611no—
351#1742—611no—
352#1742—611no—
353C2×C61—21no—
354C2×C61—21no—
355C2×C61—42no—
356C2×C61#233911yescharacteristic
357C2×C61C2×#41311yescharacteristic
358C2×C61#288911yescharacteristic
359D61—42no—
360C22×M16—612no—
361C22×M16—612no—
362#556—1222no—
363#556—1222no—
364#556—1222no—
365#556—1222no—
366C2×C4⋊Q8—611no—
367C2×#126—611no—
368C2×#126—611no—
369C2×#126—611no—
370C2×#126#692311yescharacteristic
371C2×#124—611no—
372C2×#124—611no—
373C2×C22⋊Q8—611no—
374C2×C22⋊Q8—611no—
375C2×C4×Q8—611no—
376C2×C4×Q8—611no—
377C2×C4×Q8—611no—
378C2×C4×D4—611no—
379C2×#117—611no—
380C2×#117—611no—
381#436—1222no—
382#435—1222no—
383#435—1222no—
384C8×D4—1222no—
385#423—612no—
386C2×#101—612no—
387C2×#101—612no—
388#407—612no—
389#407—612no—
390C4×M16—612no—
391#343—611no—
392#343—611no—
393#343—611no—
394#343—612no—
395#343—612no—
396#343—612no—
397#343—612no—
398#343—611no—
399C61#2248411yescharacteristic, complemented, Sylow
400C22×Q8—611no—
401C22×Q8—611no—
402C22×Q8—611no—
403C22×D4—611no—
404C23×C4—611no—
405C23×C4—611no—
406C2×M16—612no—
407C2×M16—612no—
408C2×M16—612no—
409C2×M16—612no—
410C2×M16—1222no—
411C2×M16—1222no—
412C2×M16—1224no—
413C2×M16—1224no—
414C2×M16—2442no—
415C2×M16—2442no—
416C22×C8—1222no—
417C22×C8—1222no—
418C4⋊Q8—1222no—
419C4⋊Q8—1222no—
420#126—22no—
421#126—22no—
422#126—1222no—
423#126—1222no—
424#126—1222no—
425#126—1222no—
426#126—1222no—
427#126—1222no—
428#124—1222no—
429#124—1222no—
430#124—1222no—
431#124—1222no—
432C22⋊Q8—1222no—
433C22⋊Q8—1222no—
434C22⋊Q8—1222no—
435C22⋊Q8—1222no—
436C4×Q8—1221no—
437C4×Q8—1221no—
438C4×Q8—1221no—
439C4×Q8—1221no—
440C4×Q8—1222no—
441C4×Q8—1222no—
442C4×Q8—1221no—
443C4×Q8—1221no—
444C4×Q8—1221no—
445C4×Q8—1221no—
446C4×D4—612no—
447C4×D4—612no—
448C4×D4—612no—
449C4×D4—612no—
450#117—1222no—
451#117—1222no—
452#117—1222no—
453#117—1222no—
454C2×C4⋊C4—611no—
455C2×C4⋊C4—611no—
456C2×C4⋊C4—611no—
457C2×C4⋊C4—611no—
458C2×C4⋊C4—611no—
459C2×C4⋊C4—611no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4C2×#692311yescharacteristic
464C2×C4⋊C4C2×#692311yescharacteristic
465C2×C4⋊C4C2×#692311yescharacteristic
466C2×C22⋊C4—611no—
467C2×C22⋊C4—611no—
468C2×C22⋊C4—611no—
469C2×C22⋊C4—611no—
470C2×C22⋊C4—611no—
471C2×C22⋊C4—611no—
472C2×C22⋊C4—611no—
473C2×C22⋊C4C2×#692311yescharacteristic
474C2×C22⋊C4C2×#692311yescharacteristic
475C2×C22⋊C4C2×#692311yescharacteristic
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—611no—
480C2×C42—611no—
481C2×C42—611no—
482C2×C42C2×#692311yescharacteristic
483C4⋊C8—1222no—
484C4⋊C8—1222no—
485#101—1224no—
486#101—2442no—
487C22⋊C8—1222no—
488C22⋊C8—1222no—
489C22⋊C8—1222no—
490C22⋊C8—1222no—
491#97—1222no—
492C4×C8—1222no—
493C24—611no—
494C24C22×#692311yescharacteristic
495C2×Q8—1222no—
496C2×Q8—1221no—
497C2×Q8—1222no—
498C2×Q8—1221no—
499C2×Q8—1221no—
500C2×Q8—1221no—
501C2×Q8—1221no—
502C2×Q8—1221no—
503C2×Q8—2442no—
504C2×Q8—2442no—
505C2×D4—612no—
506C2×D4—612no—
507C2×D4—2442no—
508C22×C4—611no—
509C22×C4—612no—
510C22×C4—612no—
511C22×C4—611no—
512C22×C4—611no—
513C22×C4—612no—
514C22×C4—612no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—1222no—
520C22×C4—1221no—
521C22×C4—1221no—
522C22×C4—1222no—
523C22×C4—1221no—
524C22×C4—1221no—
525C22×C4C22×#692311yescharacteristic
526C22×C4C22×#692311yescharacteristic
527C22×C4C22×#692311yescharacteristic
528C22×C4C22×#692311yescharacteristic
529C22×C4C22×#692311yescharacteristic
530C22×C4C22×#692311yescharacteristic
531M16—614no—
532M16—1222no—
533M16—1222no—
534M16—1222no—
535M16—1222no—
536M16—1222no—
537M16—1222no—
538M16—1222no—
539M16—2444no—
540M16—2444no—
541C2×C8—1222no—
542C2×C8—1222no—
543C2×C8—1222no—
544C2×C8—1222no—
545C2×C8—2444no—
546C2×C8—2444no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—611no—
552C4⋊C4—611no—
553C4⋊C4—611no—
554C4⋊C4—611no—
555C4⋊C4—1222no—
556C4⋊C4—1222no—
557C4⋊C4—1222no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1222no—
565C4⋊C4—1222no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—612no—
569C22⋊C4—612no—
570C22⋊C4—1222no—
571C22⋊C4—1222no—
572C22⋊C4—1222no—
573C22⋊C4—1222no—
574C22⋊C4—1222no—
575C22⋊C4—1222no—
576C22⋊C4C22⋊#692312yes—
577C22⋊C4C22⋊#692312yes—
578C42—21no—
579C42—21no—
580C42—612no—
581C42—612no—
582C42—1221no—
583C42—1221no—
584C42—1221no—
585C42—1221no—
586C42—1221no—
587C42—1221no—
588C42—1221no—
589C42—1221no—
590C42—1221no—
591C42—1221no—
592C23—21no—
593C23—21no—
594C23—41no—
595C23—41no—
596C23—612no—
597C23—1221no—
598C23—1221no—
599C23—2441no—
600C23—2441no—
601C23C2×C22⋊#692312yes—
602C23C23×#692311yescharacteristic
603Q8—2442no—
604Q8—2442no—
605Q8—2442no—
606Q8—2442no—
607Q8—2442no—
608Q8—2442no—
609D4—1224no—
610D4—2442no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—611no—
624C2×C4—612no—
625C2×C4—612no—
626C2×C4—611no—
627C2×C4—611no—
628C2×C4—611no—
629C2×C4—611no—
630C2×C4—611no—
631C2×C4—1222no—
632C2×C4—1222no—
633C2×C4—1222no—
634C2×C4—1222no—
635C2×C4—1222no—
636C2×C4—1222no—
637C2×C4—1222no—
638C2×C4—1222no—
639C2×C4—1222no—
640C2×C4—1221no—
641C2×C4—1221no—
642C2×C4—1221no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—2441no—
649C2×C4—2441no—
650C2×C4—2441no—
651C2×C4C2×C22⋊#692311yescharacteristic
652C2×C4C2×C22⋊#692311yescharacteristic
653C2×C4C2×C22⋊#692312yes—
654C8—1224no—
655C8—2442no—
656C8—2442no—
657C8—2442no—
658C22—21no—
659C22—21no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—81no—
664C22—81no—
665C22—1222no—
666C22—1222no—
667C22—1222no—
668C22—4881no—
669C22—4881no—
670C22C22×C22⋊#692311yescharacteristic
671C22#41×#692311yescharacteristic
672C22#1684083111yescharacteristic
673C4—21no—
674C4—21no—
675C4—22no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—612no—
681C4—612no—
682C4—612no—
683C4—1221no—
684C4—1221no—
685C4—1221no—
686C4—2441no—
687C4—2441no—
688C4—2441no—
689C4—2441no—
690C2—21no—
691C2—21no—
692C2—42no—
693C2—2442no—
694C2#2146232211yescharacteristic
695C2D61⋊#41311yescharacteristic
696C2#2146243111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#126×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×Dic61C24
hypercenterC2×#126#6923
hypocenterC61#22484
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
2. #21462012C2semidirect
3. #21461847C2semidirect
4. #21461846C2semidirect
5. #21461721C2semidirect
6. #21461720C2semidirect
7. #21461686C2semidirect
8. #21461572C2semidirect
9. #21461525C2semidirect
10. #21461524C2semidirect
399. C61#22484semidirect

Maximal subgroups

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

subgroupindex
#214625572
#214620122
#214618472
#214618462
#214617212
#214617202
#214616862
#214615722
#214615252
#214615242
C2×#168404792
#2248461