Finite Group Databasebeta

← C2×#1859×C137 #46870247

Subgroups — C2×#1859×C137 #46870247

Order 35072.

1566 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#520×C137C211yesmaximal, characteristic
2C2×#428×C137C211yesmaximal, characteristic, complemented
3C22×#104×C137C211yesmaximal, characteristic
4C2×#417×C137C211yesmaximal, characteristic
5C2×#384×C137C211yesmaximal, characteristic, complemented
6#1859×C137C218yesmaximal, direct product factor
7C2×#343×C137C211yesmaximal, characteristic, complemented
8C2×#339×C137C211yesmaximal, characteristic, complemented
9C22×#41×C137C2211yescharacteristic
10C22×M16×C137C2211yescharacteristic
11C22×M16×C137C2211yescharacteristic
12#520×C137—22no—
13#520×C137—22no—
14#520×C137—22no—
15#520×C137C2214yes—
16C2×C4×Q8×C137—21no—
17C2×C4×D4×C137—21no—
18C2×C4×D4×C137—22no—
19C2×#117×C137—21no—
20C2×#117×C137C2211yescharacteristic
21C22×C4⋊C4×C137—21no—
22C22×C4⋊C4×C137—22no—
23C22×C4⋊C4×C137C2211yescharacteristic
24C22×C4⋊C4×C137C2211yescharacteristic
25C22×C42×C137C2211yescharacteristic
26#428×C137—22no—
27#428×C137C2214yescomplemented
28C2×#107×C137—21no—
29C2×#106×C137—21no—
30C2×#104×C137C418yescomplemented
31C2×#104×C137C2214yes—
32#417×C137—22no—
33#417×C137C2214yes—
34C2×#103×C137—21no—
35C2×#102×C137—21no—
36#384×C137—22no—
37#384×C137C2214yescomplemented
38#343×C137C2214yescomplemented
39#339×C137C2214yescomplemented
40C2×#41×C137—21no—
41C2×#41×C137—21no—
42C2×#41×C137—22no—
43C2×#41×C137—22no—
44C2×#41×C137C2×C414yes—
45C2×#41×C137D412yes—
46C2×#41×C137Q814yes—
47C2×#41×C137C2312yes—
48C22×Q8×C137D411yescharacteristic
49C22×D4×C137—21no—
50C22×D4×C137D411yescharacteristic
51C23×C4×C137—21no—
52C23×C4×C137—21no—
53C23×C4×C137—22no—
54C23×C4×C137—21no—
55C23×C4×C137D412yes—
56C23×C4×C137C2311yescharacteristic
57C2×M16×C137—21no—
58C2×M16×C137—22no—
59C2×M16×C137—21no—
60C2×M16×C137—22no—
61C2×M16×C137—22no—
62C2×M16×C137C2×C414yescomplemented
63C2×M16×C137C2312yes—
64C2×M16×C137C2312yes—
65C22×C8×C137—21no—
66C22×C8×C137—21no—
67C4×Q8×C137—24no—
68C4×Q8×C137—24no—
69C4×D4×C137—28no—
70C4×D4×C137—24no—
71C4×D4×C137—24no—
72C4×D4×C137—28no—
73#117×C137—24no—
74#117×C137—21no—
75#117×C137—21no—
76#117×C137—24no—
77#117×C137D412yes—
78#117×C137C2312yes—
79C2×C4⋊C4×C137—22no—
80C2×C4⋊C4×C137—24no—
81C2×C4⋊C4×C137—21no—
82C2×C4⋊C4×C137—21no—
83C2×C4⋊C4×C137—21no—
84C2×C4⋊C4×C137—21no—
85C2×C4⋊C4×C137—24no—
86C2×C4⋊C4×C137—21no—
87C2×C4⋊C4×C137—21no—
88C2×C4⋊C4×C137—21no—
89C2×C4⋊C4×C137—21no—
90C2×C4⋊C4×C137—21no—
91C2×C4⋊C4×C137—28no—
92C2×C4⋊C4×C137—48no—
93C2×C4⋊C4×C137D412yes—
94C2×C4⋊C4×C137D411yescharacteristic
95C2×C4⋊C4×C137D411yescharacteristic
96C2×C4⋊C4×C137C2312yes—
97C2×C4⋊C4×C137C2312yes—
98C2×C22⋊C4×C137—22no—
99C2×C22⋊C4×C137—21no—
100C2×C42×C137—22no—
101C2×C42×C137—21no—
102C2×C42×C137—21no—
103C2×C42×C137—22no—
104C2×C42×C137C2×C414yescomplemented
105C2×C42×C137C2312yes—
106#107×C137—24no—
107#106×C137—24no—
108#104×C137C2×C4116yescomplemented
109#103×C137—24no—
110#102×C137—24no—
111C24×C137—21no—
112C24×C137C2×D411yescharacteristic
113#41×C137—24no—
114#41×C137—24no—
115#41×C137—24no—
116#41×C137—24no—
117#41×C137—24no—
118#41×C137—22no—
119#41×C137—22no—
120#41×C137C4⋊C418yescomplemented
121#41×C137C22×C414yes—
122#41×C137C2×Q814yes—
123C2×Q8×C137—21no—
124C2×Q8×C137—22no—
125C2×Q8×C137C4⋊C414yescomplemented
126C2×Q8×C137C2×D412yes—
127C2×D4×C137—24no—
128C2×D4×C137—22no—
129C2×D4×C137—24no—
130C2×D4×C137—22no—
131C2×D4×C137—21no—
132C2×D4×C137—22no—
133C2×D4×C137C4⋊C414yescomplemented
134C2×D4×C137C2×D412yes—
135C22×C4×C137—24no—
136C22×C4×C137—24no—
137C22×C4×C137—24no—
138C22×C4×C137—21no—
139C22×C4×C137—22no—
140C22×C4×C137—24no—
141C22×C4×C137—22no—
142C22×C4×C137—24no—
143C22×C4×C137—22no—
144C22×C4×C137—21no—
145C22×C4×C137—22no—
146C22×C4×C137—21no—
147C22×C4×C137—28no—
148C22×C4×C137—22no—
149C22×C4×C137—22no—
150C22×C4×C137—44no—
151C22×C4×C137—44no—
152C22×C4×C137—41no—
153C22×C4×C137—41no—
154C22×C4×C137—84no—
155C22×C4×C137C22×C412yes—
156C22×C4×C137C2×D414yes—
157C22×C4×C137C2×D411yescharacteristic
158C22×C4×C137C2×D411yescharacteristic
159C22×C4×C137C2×D411yescharacteristic
160C22×C4×C137C2×D411yescharacteristic
161C22×C4×C137C2×D411yescharacteristic
162C22×C4×C137C2×Q812yes—
163C22×C4×C137#4112yes—
164C22×C4×C137#4112yes—
165C22×C4×C137C2411yescharacteristic
166M16×C137—24no—
167M16×C137—22no—
168M16×C137—22no—
169M16×C137—22no—
170M16×C137—42no—
171M16×C137C22×C414yescomplemented
172C2×C8×C137—24no—
173C2×C8×C137—22no—
174C2×C8×C137—22no—
175C2×C8×C137—42no—
176C4⋊C4×C137—28no—
177C4⋊C4×C137—22no—
178C4⋊C4×C137—21no—
179C4⋊C4×C137—22no—
180C4⋊C4×C137—21no—
181C4⋊C4×C137—22no—
182C4⋊C4×C137—22no—
183C4⋊C4×C137—22no—
184C4⋊C4×C137—22no—
185C4⋊C4×C137—416no—
186C4⋊C4×C137—41no—
187C4⋊C4×C137—41no—
188C4⋊C4×C137C2×D412yes—
189C4⋊C4×C137C2×D412yes—
190C22⋊C4×C137—28no—
191C22⋊C4×C137—22no—
192C22⋊C4×C137—22no—
193C42×C137—28no—
194C42×C137—24no—
195C42×C137—22no—
196C42×C137—22no—
197C42×C137—22no—
198C42×C137C22×C414yescomplemented
199C23×C137—22no—
200C23×C137—22no—
201C23×C137—22no—
202C23×C137—24no—
203C23×C137—42no—
204C23×C137—42no—
205C23×C137C4×D412yes—
206C23×C137#12011yescharacteristic
207C23×C137#12011yescharacteristic
208C23×C137C22⋊Q812yes—
209C23×C137C22×D411yescharacteristic
210Q8×C137—22no—
211Q8×C137—24no—
212Q8×C137C2×C4⋊C414yescomplemented
213D4×C137—24no—
214D4×C137—24no—
215D4×C137—28no—
216D4×C137—22no—
217D4×C137—24no—
218D4×C137C2×C4⋊C414yescomplemented
219C2×C4×C137—24no—
220C2×C4×C137—216no—
221C2×C4×C137—24no—
222C2×C4×C137—24no—
223C2×C4×C137—22no—
224C2×C4×C137—24no—
225C2×C4×C137—24no—
226C2×C4×C137—24no—
227C2×C4×C137—28no—
228C2×C4×C137—22no—
229C2×C4×C137—24no—
230C2×C4×C137—22no—
231C2×C4×C137—44no—
232C2×C4×C137—42no—
233C2×C4×C137—42no—
234C2×C4×C137—44no—
235C2×C4×C137—44no—
236C2×C4×C137—42no—
237C2×C4×C137—82no—
238C2×C4×C137—88no—
239C2×C4×C137—82no—
240C2×C4×C137—82no—
241C2×C4×C137C2×C4⋊C412yes—
242C2×C4×C137C2×C4⋊C412yes—
243C2×C4×C137C4×D412yes—
244C2×C4×C137C4×D412yes—
245C2×C4×C137C4×D412yes—
246C2×C4×C137#12011yescharacteristic
247C2×C4×C137#12011yescharacteristic
248C2×C4×C137C22⋊Q812yes—
249C2×C4×C137C22⋊Q812yes—
250C2×C4×C137C22⋊Q812yes—
251C2×C4×C137#12312yes—
252C2×C4×C137#12312yes—
253C2×C4×C137C23×C411yescharacteristic
254C2×C4×C137C22×D411yescharacteristic
255C2×C4×C137C22×D411yescharacteristic
256C2×C4×C137C22×Q811yescharacteristic
257C2×C4×C137C2×#4111yescharacteristic
258C2×C4×C137C2×#4111yescharacteristic
259C8×C137—24no—
260C8×C137—42no—
261C22×C137—24no—
262C22×C137—24no—
263C22×C137—21no—
264C22×C137—21no—
265C22×C137—21no—
266C22×C137—21no—
267C22×C137—24no—
268C22×C137—48no—
269C22×C137—42no—
270C22×C137—42no—
271C22×C137#38512yes—
272C22×C137#38512yes—
273C22×C137#45312yes—
274C22×C137#45612yes—
275C22×C137C2×C4×D411yescharacteristic
276C22×C137C2×#12011yescharacteristic
277C22×C137C2×C22⋊Q811yescharacteristic
278C4×C137—28no—
279C4×C137—24no—
280C4×C137—44no—
281C4×C137—42no—
282C4×C137—42no—
283C4×C137—82no—
284C4×C137#38512yes—
285C4×C137#38512yes—
286C4×C137C22×C4⋊C411yescharacteristic
287C4×C137C2×C4×D411yescharacteristic
288C4×C137C2×C22⋊Q811yescharacteristic
289C4×C137C2×#12311yescharacteristic
290C2×C137—21no—
291C2×C137—21no—
292C2×C137—22no—
293C2×C137—44no—
294C2×C137#185914yesdirect product factor
295C2×C137C2×#38511yescharacteristic
296C2×C137C2×#45311yescharacteristic
297C2×C137C2×#45611yescharacteristic
298C2×#1859C13711yesmaximal, characteristic, direct product factor, Sylow
299C137C2×#185911yescharacteristic, direct product factor, Sylow
300C2×#520C2×C13711yescharacteristic
301C2×#428C2×C13711yescharacteristic, complemented
302C22×#104C2×C13711yescharacteristic
303C2×#417C2×C13711yescharacteristic
304C2×#384C2×C13711yescharacteristic, complemented
305#1859C2×C13718yesdirect product factor
306C2×#343C2×C13711yescharacteristic, complemented
307C2×#339C2×C13711yescharacteristic, complemented
308C22×#41C22×C13711yescharacteristic
309C22×M16C22×C13711yescharacteristic
310C22×M16C22×C13711yescharacteristic
311#520—22no—
312#520—22no—
313#520—22no—
314#520C22×C13714yes—
315C2×C4×Q8—21no—
316C2×C4×D4—21no—
317C2×C4×D4—22no—
318C2×#117—21no—
319C2×#117C22×C13711yescharacteristic
320C22×C4⋊C4—21no—
321C22×C4⋊C4—22no—
322C22×C4⋊C4C22×C13711yescharacteristic
323C22×C4⋊C4C22×C13711yescharacteristic
324C22×C42C22×C13711yescharacteristic
325#428—22no—
326#428C22×C13714yescomplemented
327C2×#107—21no—
328C2×#106—21no—
329C2×#104C4×C13718yescomplemented
330C2×#104C22×C13714yes—
331#417—22no—
332#417C22×C13714yes—
333C2×#103—21no—
334C2×#102—21no—
335#384—22no—
336#384C22×C13714yescomplemented
337#343C22×C13714yescomplemented
338#339C22×C13714yescomplemented
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41C2×C4×C13714yes—
344C2×#41D4×C13712yes—
345C2×#41Q8×C13714yes—
346C2×#41C23×C13712yes—
347C22×Q8D4×C13711yescharacteristic
348C22×D4—21no—
349C22×D4D4×C13711yescharacteristic
350C23×C4—21no—
351C23×C4—21no—
352C23×C4—22no—
353C23×C4—21no—
354C23×C4D4×C13712yes—
355C23×C4C23×C13711yescharacteristic
356C2×M16—21no—
357C2×M16—22no—
358C2×M16—21no—
359C2×M16—22no—
360C2×M16—22no—
361C2×M16C2×C4×C13714yescomplemented
362C2×M16C23×C13712yes—
363C2×M16C23×C13712yes—
364C22×C8—21no—
365C22×C8—21no—
366C4×Q8—24no—
367C4×Q8—24no—
368C4×D4—28no—
369C4×D4—24no—
370C4×D4—24no—
371C4×D4—28no—
372#117—24no—
373#117—21no—
374#117—21no—
375#117—24no—
376#117D4×C13712yes—
377#117C23×C13712yes—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—48no—
392C2×C4⋊C4D4×C13712yes—
393C2×C4⋊C4D4×C13711yescharacteristic
394C2×C4⋊C4D4×C13711yescharacteristic
395C2×C4⋊C4C23×C13712yes—
396C2×C4⋊C4C23×C13712yes—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—21no—
399C2×C42—22no—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—22no—
403C2×C42C2×C4×C13714yescomplemented
404C2×C42C23×C13712yes—
405#107—24no—
406#106—24no—
407#104C2×C4×C137116yescomplemented
408#103—24no—
409#102—24no—
410C24—21no—
411C24C2×D4×C13711yescharacteristic
412#41—24no—
413#41—24no—
414#41—24no—
415#41—24no—
416#41—24no—
417#41—22no—
418#41—22no—
419#41C4⋊C4×C13718yescomplemented
420#41C22×C4×C13714yes—
421#41C2×Q8×C13714yes—
422C2×Q8—21no—
423C2×Q8—22no—
424C2×Q8C4⋊C4×C13714yescomplemented
425C2×Q8C2×D4×C13712yes—
426C2×D4—24no—
427C2×D4—22no—
428C2×D4—24no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—22no—
432C2×D4C4⋊C4×C13714yescomplemented
433C2×D4C2×D4×C13712yes—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—28no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—84no—
454C22×C4C22×C4×C13712yes—
455C22×C4C2×D4×C13714yes—
456C22×C4C2×D4×C13711yescharacteristic
457C22×C4C2×D4×C13711yescharacteristic
458C22×C4C2×D4×C13711yescharacteristic
459C22×C4C2×D4×C13711yescharacteristic
460C22×C4C2×D4×C13711yescharacteristic
461C22×C4C2×Q8×C13712yes—
462C22×C4#41×C13712yes—
463C22×C4#41×C13712yes—
464C22×C4C24×C13711yescharacteristic
465M16—24no—
466M16—22no—
467M16—22no—
468M16—22no—
469M16—42no—
470M16C22×C4×C13714yescomplemented
471C2×C8—24no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—42no—
475C4⋊C4—28no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—416no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4C2×D4×C13712yes—
488C4⋊C4C2×D4×C13712yes—
489C22⋊C4—28no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C42—28no—
493C42—24no—
494C42—22no—
495C42—22no—
496C42—22no—
497C42C22×C4×C13714yescomplemented
498C23—22no—
499C23—22no—
500C23—24no—
501C23—22no—
502C23—42no—
503C23—42no—
504C23C4×D4×C13712yes—
505C23#120×C13711yescharacteristic
506C23#120×C13711yescharacteristic
507C23C22⋊Q8×C13712yes—
508C23C22×D4×C13711yescharacteristic
509Q8—24no—
510Q8—22no—
511Q8C2×C4⋊C4×C13714yescomplemented
512D4—28no—
513D4—24no—
514D4—24no—
515D4—24no—
516D4—22no—
517D4C2×C4⋊C4×C13714yescomplemented
518C2×C4—24no—
519C2×C4—216no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—28no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—44no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—44no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—82no—
537C2×C4—88no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4C2×C4⋊C4×C13712yes—
541C2×C4C2×C4⋊C4×C13712yes—
542C2×C4C4×D4×C13712yes—
543C2×C4C4×D4×C13712yes—
544C2×C4C4×D4×C13712yes—
545C2×C4#120×C13711yescharacteristic
546C2×C4#120×C13711yescharacteristic
547C2×C4C22⋊Q8×C13712yes—
548C2×C4C22⋊Q8×C13712yes—
549C2×C4C22⋊Q8×C13712yes—
550C2×C4#123×C13712yes—
551C2×C4#123×C13712yes—
552C2×C4C23×C4×C13711yescharacteristic
553C2×C4C22×D4×C13711yescharacteristic
554C2×C4C22×D4×C13711yescharacteristic
555C2×C4C22×Q8×C13711yescharacteristic
556C2×C4C2×#41×C13711yescharacteristic
557C2×C4C2×#41×C13711yescharacteristic
558C8—24no—
559C8—42no—
560C22—24no—
561C22—24no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—24no—
567C22—48no—
568C22—42no—
569C22—42no—
570C22#385×C13712yes—
571C22#385×C13712yes—
572C22#453×C13712yes—
573C22#456×C13712yes—
574C22C2×C4×D4×C13711yescharacteristic
575C22C2×#120×C13711yescharacteristic
576C22C2×C22⋊Q8×C13711yescharacteristic
577C4—28no—
578C4—24no—
579C4—44no—
580C4—42no—
581C4—42no—
582C4—82no—
583C4#385×C13712yes—
584C4#385×C13712yes—
585C4C22×C4⋊C4×C13711yescharacteristic
586C4C2×C4×D4×C13711yescharacteristic
587C4C2×C22⋊Q8×C13711yescharacteristic
588C4C2×#123×C13711yescharacteristic
589C2—21no—
590C2—22no—
591C2—21no—
592C2—44no—
593C2#1859×C13714yesdirect product factor
594C2C2×#385×C13711yescharacteristic
595C2C2×#453×C13711yescharacteristic
596C2C2×#456×C13711yescharacteristic
subgroupG/H
center, socleC23×C137#120
commutatorC2×C4C23×C4×C137
Frattini, cosocleC22×C4C24×C137
prime radicalC22×#41×C137C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#428×C137C2semidirect
5. C2×#384×C137C2semidirect
6. #1859×C137C2direct (N × H)
7. C2×#343×C137C2semidirect
8. C2×#339×C137C2semidirect
27. #428×C137C22semidirect
30. C2×#104×C137C4semidirect
37. #384×C137C22semidirect
38. #343×C137C22semidirect
39. #339×C137C22semidirect
62. C2×M16×C137C2×C4semidirect
104. C2×C42×C137C2×C4semidirect
108. #104×C137C2×C4semidirect
120. #41×C137C4⋊C4semidirect
125. C2×Q8×C137C4⋊C4semidirect
133. C2×D4×C137C4⋊C4semidirect
171. M16×C137C22×C4semidirect
198. C42×C137C22×C4semidirect
212. Q8×C137C2×C4⋊C4semidirect
218. D4×C137C2×C4⋊C4semidirect
294. C2×C137#1859direct (N × H)
298. C2×#1859C137direct (N × H)
299. C137C2×#1859direct (N × H)
301. C2×#428C2×C137semidirect
304. C2×#384C2×C137semidirect
305. #1859C2×C137direct (N × H)
306. C2×#343C2×C137semidirect
307. C2×#339C2×C137semidirect
326. #428C22×C137semidirect
329. C2×#104C4×C137semidirect
336. #384C22×C137semidirect
337. #343C22×C137semidirect
338. #339C22×C137semidirect
361. C2×M16C2×C4×C137semidirect
403. C2×C42C2×C4×C137semidirect
407. #104C2×C4×C137semidirect
419. #41C4⋊C4×C137semidirect
424. C2×Q8C4⋊C4×C137semidirect
432. C2×D4C4⋊C4×C137semidirect
470. M16C22×C4×C137semidirect
497. C42C22×C4×C137semidirect
511. Q8C2×C4⋊C4×C137semidirect
517. D4C2×C4⋊C4×C137semidirect
593. C2#1859×C137direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#520×C1372
C2×#428×C1372
C22×#104×C1372
C2×#417×C1372
C2×#384×C1372
#1859×C1372
C2×#343×C1372
C2×#339×C1372
C2×#1859137