Finite Group Databasebeta

← C137×#24442 #46873828

Subgroups — C137×#24442 #46873828

Order 35072.

1570 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C137C211yesmaximal, characteristic
2C2×#470×C137C211yesmaximal, characteristic, complemented
3C2×#452×C137C211yesmaximal, characteristic, complemented
4C2×#450×C137C211yesmaximal, characteristic, complemented
5C2×#418×C137C211yesmaximal, characteristic, complemented
6#2415×C137C211yesmaximal, characteristic, complemented
7#2042×C137C211yesmaximal, characteristic, complemented
8#2034×C137C211yesmaximal, characteristic, complemented
9#2015×C137C211yesmaximal, characteristic, complemented
10#2000×C137C211yesmaximal, characteristic, complemented
11#1877×C137C211yesmaximal, characteristic, complemented
12#1873×C137C211yesmaximal, characteristic, complemented
13#1870×C137C211yesmaximal, characteristic, complemented
14#1864×C137C211yesmaximal, characteristic, complemented
15#1788×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C22×Q16×C137C2211yescharacteristic, complemented
19C22×SD16×C137C2211yescharacteristic
20C22×SD16×C137C2211yescharacteristic
21C22×M16×C137C2211yescharacteristic
22#546×C137—24no—
23#546×C137—24no—
24C2×#124×C137C2211yescharacteristic
25C2×#123×C137—21no—
26C2×C22⋊Q8×C137C2211yescharacteristic
27C2×C22⋊Q8×C137C2211yescharacteristic
28C2×C22⋊Q8×C137C2211yescharacteristic, complemented
29C2×#121×C137—21no—
30C2×#121×C137C2211yescharacteristic
31C2×#120×C137—21no—
32C2×C4×D4×C137C2211yescharacteristic
33C2×C4×D4×C137C2211yescharacteristic
34C2×#117×C137C2211yescharacteristic
35C22×C22⋊C4×C137—21no—
36#470×C137—24no—
37#452×C137—24no—
38#450×C137—24no—
39C2×#106×C137C2211yescharacteristic, complemented
40#418×C137—24no—
41C2×#103×C137C2211yescharacteristic, complemented
42C2×#103×C137C2211yescharacteristic, complemented
43C2×#103×C137C2211yescharacteristic, complemented
44C2×#103×C137C2211yescharacteristic, complemented
45C2×#102×C137C2211yescharacteristic
46C2×#102×C137C2211yescharacteristic
47C2×#102×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic
49C2×#102×C137C2211yescharacteristic
50C2×#102×C137C2211yescharacteristic
51C2×C22⋊C8×C137C2211yescharacteristic
52C2×C22⋊C8×C137C2211yescharacteristic, complemented
53C2×C22⋊C8×C137C2211yescharacteristic, complemented
54#397×C137—21no—
55#394×C137—21no—
56#391×C137C2211yescharacteristic, complemented
57#389×C137—21no—
58#389×C137C2211yescharacteristic, complemented
59#388×C137—21no—
60#380×C137C2211yescharacteristic, complemented
61#340×C137C2211yescharacteristic, complemented
62#340×C137C2211yescharacteristic, complemented
63#336×C137C2211yescharacteristic, complemented
64#336×C137C2211yescharacteristic, complemented
65C25×C137—21no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—22no—
69C2×#41×C137—22no—
70C2×#41×C137—41no—
71C2×#41×C137—41no—
72C22×Q8×C137C2311yescharacteristic
73C22×Q8×C137C2311yescharacteristic
74C22×D4×C137—22no—
75C22×D4×C137—22no—
76C22×D4×C137—21no—
77C22×D4×C137—21no—
78C22×D4×C137—21no—
79C22×D4×C137—22no—
80C22×D4×C137—41no—
81C22×D4×C137—41no—
82C22×D4×C137D414yes—
83C22×D4×C137D411yescharacteristic
84C22×D4×C137C2311yescharacteristic
85C22×D4×C137C2311yescharacteristic
86C23×C4×C137—21no—
87C23×C4×C137—21no—
88C23×C4×C137C2311yescharacteristic
89C23×C4×C137C2311yescharacteristic
90C2×Q16×C137—22no—
91C2×Q16×C137—22no—
92C2×Q16×C137—41no—
93C2×SD16×C137—22no—
94C2×SD16×C137—22no—
95C2×SD16×C137—22no—
96C2×SD16×C137—22no—
97C2×SD16×C137—41no—
98C2×SD16×C137—41no—
99C2×M16×C137—22no—
100C2×M16×C137—22no—
101C2×M16×C137—41no—
102C22×C8×C137C2311yescharacteristic
103C22×C8×C137C2311yescharacteristic
104C22×C8×C137C2311yescharacteristic
105C22×C8×C137C2311yescharacteristic
106#124×C137—22no—
107#124×C137—22no—
108#123×C137—28no—
109C22⋊Q8×C137—22no—
110C22⋊Q8×C137—22no—
111C22⋊Q8×C137—22no—
112C22⋊Q8×C137—22no—
113C22⋊Q8×C137—41no—
114C22⋊Q8×C137D414yes—
115#121×C137—28no—
116#121×C137—22no—
117#121×C137—22no—
118#120×C137—28no—
119C4×D4×C137—22no—
120C4×D4×C137—22no—
121C4×D4×C137—22no—
122C4×D4×C137—22no—
123#117×C137—22no—
124#117×C137—41no—
125C2×C4⋊C4×C137—21no—
126C2×C4⋊C4×C137—21no—
127C2×C4⋊C4×C137—21no—
128C2×C4⋊C4×C137—21no—
129C2×C4⋊C4×C137D411yescharacteristic
130C2×C4⋊C4×C137C2311yescharacteristic
131C2×C4⋊C4×C137C2311yescharacteristic
132C2×C4⋊C4×C137C2311yescharacteristic
133C2×C4⋊C4×C137C2311yescharacteristic
134C2×C22⋊C4×C137—28no—
135C2×C22⋊C4×C137—21no—
136C2×C22⋊C4×C137—21no—
137C2×C22⋊C4×C137—21no—
138C2×C22⋊C4×C137—21no—
139C2×C22⋊C4×C137—21no—
140C2×C22⋊C4×C137—21no—
141C2×C22⋊C4×C137—21no—
142C2×C22⋊C4×C137—21no—
143C2×C22⋊C4×C137—21no—
144C2×C22⋊C4×C137D411yescharacteristic
145C2×C22⋊C4×C137D411yescharacteristic
146C2×C42×C137—21no—
147C2×C42×C137C2311yescharacteristic
148#106×C137—22no—
149#103×C137—22no—
150#103×C137—22no—
151#103×C137—22no—
152#103×C137—41no—
153#102×C137—22no—
154#102×C137—22no—
155#102×C137—22no—
156#102×C137—22no—
157#102×C137—22no—
158#102×C137D414yescomplemented
159C22⋊C8×C137—22no—
160C22⋊C8×C137—22no—
161C22⋊C8×C137—41no—
162#95×C137—21no—
163#95×C137—21no—
164#95×C137—21no—
165#95×C137—21no—
166C24×C137—21no—
167C24×C137—21no—
168C24×C137—24no—
169C24×C137—42no—
170C24×C137—42no—
171C24×C137—42no—
172C24×C137—42no—
173C24×C137—81no—
174C24×C137—81no—
175C24×C137C2×D411yescharacteristic
176C24×C137C2×D411yescharacteristic
177#41×C137—44no—
178#41×C137—44no—
179#41×C137—44no—
180#41×C137—44no—
181C2×Q8×C137—21no—
182C2×Q8×C137—21no—
183C2×Q8×C137—21no—
184C2×Q8×C137—21no—
185C2×Q8×C137—21no—
186C2×Q8×C137—21no—
187C2×Q8×C137—21no—
188C2×Q8×C137—21no—
189C2×Q8×C137—21no—
190C2×Q8×C137—21no—
191C2×Q8×C137—21no—
192C2×Q8×C137C2×D412yes—
193C2×D4×C137—28no—
194C2×D4×C137—24no—
195C2×D4×C137—22no—
196C2×D4×C137—24no—
197C2×D4×C137—24no—
198C2×D4×C137—21no—
199C2×D4×C137—21no—
200C2×D4×C137—21no—
201C2×D4×C137—21no—
202C2×D4×C137—21no—
203C2×D4×C137—21no—
204C2×D4×C137—21no—
205C2×D4×C137—21no—
206C2×D4×C137—44no—
207C2×D4×C137—44no—
208C2×D4×C137—44no—
209C2×D4×C137—41no—
210C2×D4×C137—41no—
211C2×D4×C137—42no—
212C2×D4×C137—42no—
213C2×D4×C137—42no—
214C2×D4×C137—42no—
215C2×D4×C137—81no—
216C2×D4×C137—81no—
217C2×D4×C137C2×D412yes—
218C2×D4×C137C2×D412yes—
219C2×D4×C137C2×D412yes—
220C2×D4×C137#4112yes—
221C22×C4×C137—21no—
222C22×C4×C137—21no—
223C22×C4×C137—21no—
224C22×C4×C137—21no—
225C22×C4×C137—24no—
226C22×C4×C137—21no—
227C22×C4×C137—21no—
228C22×C4×C137—21no—
229C22×C4×C137—24no—
230C22×C4×C137—21no—
231C22×C4×C137—21no—
232C22×C4×C137—21no—
233C22×C4×C137—21no—
234C22×C4×C137—21no—
235C22×C4×C137—21no—
236C22×C4×C137—21no—
237C22×C4×C137—21no—
238C22×C4×C137—21no—
239C22×C4×C137—42no—
240C22×C4×C137—42no—
241C22×C4×C137—81no—
242C22×C4×C137—81no—
243C22×C4×C137C2×D411yescharacteristic
244C22×C4×C137C2×D411yescharacteristic
245C22×C4×C137C2×D411yescharacteristic
246C22×C4×C137C2×D411yescharacteristic
247C22×C4×C137C2×D412yes—
248C22×C4×C137C2×D412yes—
249C22×C4×C137C2411yescharacteristic
250Q16×C137—44no—
251SD16×C137—44no—
252SD16×C137—44no—
253M16×C137—44no—
254C2×C8×C137—21no—
255C2×C8×C137—21no—
256C2×C8×C137—21no—
257C2×C8×C137—21no—
258C2×C8×C137—21no—
259C2×C8×C137—21no—
260C2×C8×C137—21no—
261C2×C8×C137—21no—
262C2×C8×C137—21no—
263C2×C8×C137—21no—
264C2×C8×C137—21no—
265C2×C8×C137C2×D412yes—
266C4⋊C4×C137—24no—
267C4⋊C4×C137—22no—
268C4⋊C4×C137—21no—
269C4⋊C4×C137—21no—
270C4⋊C4×C137—21no—
271C4⋊C4×C137—21no—
272C4⋊C4×C137—21no—
273C4⋊C4×C137—21no—
274C4⋊C4×C137—42no—
275C4⋊C4×C137—42no—
276C4⋊C4×C137—42no—
277C4⋊C4×C137C2×D412yes—
278C4⋊C4×C137C2×D412yes—
279C22⋊C4×C137—24no—
280C22⋊C4×C137—24no—
281C22⋊C4×C137—24no—
282C22⋊C4×C137—24no—
283C22⋊C4×C137—22no—
284C22⋊C4×C137—24no—
285C22⋊C4×C137—22no—
286C22⋊C4×C137—42no—
287C22⋊C4×C137—42no—
288C22⋊C4×C137—42no—
289C22⋊C4×C137—42no—
290C42×C137—21no—
291C42×C137—21no—
292C42×C137—42no—
293C23×C137—22no—
294C23×C137—21no—
295C23×C137—22no—
296C23×C137—21no—
297C23×C137—22no—
298C23×C137—21no—
299C23×C137—21no—
300C23×C137—21no—
301C23×C137—21no—
302C23×C137—22no—
303C23×C137—21no—
304C23×C137—21no—
305C23×C137—21no—
306C23×C137—21no—
307C23×C137—21no—
308C23×C137—21no—
309C23×C137—21no—
310C23×C137—48no—
311C23×C137—48no—
312C23×C137—41no—
313C23×C137—41no—
314C23×C137—41no—
315C23×C137—41no—
316C23×C137—41no—
317C23×C137—41no—
318C23×C137—41no—
319C23×C137—41no—
320C23×C137—41no—
321C23×C137—41no—
322C23×C137—84no—
323C23×C137—84no—
324C23×C137—84no—
325C23×C137—84no—
326C23×C137—84no—
327C23×C137#12012yes—
328C23×C137C22×D411yescharacteristic
329Q8×C137—22no—
330Q8×C137—22no—
331Q8×C137—41no—
332Q8×C137—41no—
333Q8×C137—41no—
334Q8×C137—41no—
335Q8×C137—41no—
336Q8×C137—41no—
337D4×C137—22no—
338D4×C137—22no—
339D4×C137—22no—
340D4×C137—22no—
341D4×C137—22no—
342D4×C137—48no—
343D4×C137—44no—
344D4×C137—48no—
345D4×C137—41no—
346D4×C137—41no—
347D4×C137—84no—
348D4×C137#12114yes—
349C2×C4×C137—21no—
350C2×C4×C137—21no—
351C2×C4×C137—22no—
352C2×C4×C137—22no—
353C2×C4×C137—22no—
354C2×C4×C137—22no—
355C2×C4×C137—21no—
356C2×C4×C137—21no—
357C2×C4×C137—22no—
358C2×C4×C137—21no—
359C2×C4×C137—22no—
360C2×C4×C137—22no—
361C2×C4×C137—21no—
362C2×C4×C137—21no—
363C2×C4×C137—21no—
364C2×C4×C137—21no—
365C2×C4×C137—21no—
366C2×C4×C137—21no—
367C2×C4×C137—48no—
368C2×C4×C137—41no—
369C2×C4×C137—41no—
370C2×C4×C137—41no—
371C2×C4×C137—41no—
372C2×C4×C137—41no—
373C2×C4×C137—41no—
374C2×C4×C137—41no—
375C2×C4×C137—41no—
376C2×C4×C137—41no—
377C2×C4×C137—41no—
378C2×C4×C137—41no—
379C2×C4×C137—41no—
380C2×C4×C137—41no—
381C2×C4×C137—41no—
382C2×C4×C137—41no—
383C2×C4×C137—41no—
384C2×C4×C137—41no—
385C2×C4×C137—41no—
386C2×C4×C137—41no—
387C2×C4×C137—84no—
388C2×C4×C137#12012yes—
389C2×C4×C137C22×D411yescharacteristic
390C2×C4×C137C22×D411yescharacteristic
391C2×C4×C137C22×D411yescharacteristic
392C2×C4×C137C2×#4111yescharacteristic
393C2×C4×C137H(5,𝔽2)11yescharacteristic
394C2×C4×C137H(5,𝔽2)11yescharacteristic
395C8×C137—22no—
396C8×C137—41no—
397C8×C137—41no—
398C8×C137—41no—
399C22×C137—22no—
400C22×C137—24no—
401C22×C137—22no—
402C22×C137—22no—
403C22×C137—42no—
404C22×C137—42no—
405C22×C137—41no—
406C22×C137—42no—
407C22×C137—41no—
408C22×C137—42no—
409C22×C137—41no—
410C22×C137—42no—
411C22×C137—41no—
412C22×C137—42no—
413C22×C137—41no—
414C22×C137—42no—
415C22×C137—41no—
416C22×C137—42no—
417C22×C137—41no—
418C22×C137—42no—
419C22×C137—41no—
420C22×C137—41no—
421C22×C137—41no—
422C22×C137—41no—
423C22×C137—816no—
424C22×C137—81no—
425C22×C137—81no—
426C22×C137—81no—
427C22×C137—81no—
428C22×C137C2×#12011yescharacteristic
429C22×C137D4211yescharacteristic
430C22×C137#54611yescharacteristic
431C22×C137#57511yescharacteristic
432C22×C137#57511yescharacteristic
433C22×C137#57711yescharacteristic
434C22×C137#57711yescharacteristic
435C4×C137—22no—
436C4×C137—41no—
437C4×C137—42no—
438C4×C137—41no—
439C4×C137—41no—
440C4×C137—42no—
441C4×C137—42no—
442C4×C137—81no—
443C4×C137—81no—
444C4×C137—81no—
445C4×C137C2×#12111yescharacteristic
446C4×C137#53411yescharacteristic
447C4×C137D4211yescharacteristic
448C4×C137#54611yescharacteristic
449C2×C137—42no—
450C2×C137—44no—
451C2×C137—81no—
452C2×C137—82no—
453C2×C137#241011yescharacteristic
454C2×C137#300511yescharacteristic
455C2×C137#300911yescharacteristic
456C2×C137#326711yescharacteristic
457C2×C137#327511yescharacteristic
458C2×C137#331111yescharacteristic
459C2×C137#332311yescharacteristic
460#24442C13711yesmaximal, characteristic, direct product factor, Sylow
461C137#2444211yescharacteristic, direct product factor, Sylow
462C2×#546C2×C13711yescharacteristic
463C2×#470C2×C13711yescharacteristic, complemented
464C2×#452C2×C13711yescharacteristic, complemented
465C2×#450C2×C13711yescharacteristic, complemented
466C2×#418C2×C13711yescharacteristic, complemented
467#2415C2×C13711yescharacteristic, complemented
468#2042C2×C13711yescharacteristic, complemented
469#2034C2×C13711yescharacteristic, complemented
470#2015C2×C13711yescharacteristic, complemented
471#2000C2×C13711yescharacteristic, complemented
472#1877C2×C13711yescharacteristic, complemented
473#1873C2×C13711yescharacteristic, complemented
474#1870C2×C13711yescharacteristic, complemented
475#1864C2×C13711yescharacteristic, complemented
476#1788C2×C13711yescharacteristic, complemented
477C22×#41C22×C13711yescharacteristic
478C23×D4C22×C13711yescharacteristic
479C22×Q16C22×C13711yescharacteristic, complemented
480C22×SD16C22×C13711yescharacteristic
481C22×SD16C22×C13711yescharacteristic
482C22×M16C22×C13711yescharacteristic
483#546—24no—
484#546—24no—
485C2×#124C22×C13711yescharacteristic
486C2×#123—21no—
487C2×C22⋊Q8C22×C13711yescharacteristic
488C2×C22⋊Q8C22×C13711yescharacteristic
489C2×C22⋊Q8C22×C13711yescharacteristic, complemented
490C2×#121—21no—
491C2×#121C22×C13711yescharacteristic
492C2×#120—21no—
493C2×C4×D4C22×C13711yescharacteristic
494C2×C4×D4C22×C13711yescharacteristic
495C2×#117C22×C13711yescharacteristic
496C22×C22⋊C4—21no—
497#470—24no—
498#452—24no—
499#450—24no—
500C2×#106C22×C13711yescharacteristic, complemented
501#418—24no—
502C2×#103C22×C13711yescharacteristic, complemented
503C2×#103C22×C13711yescharacteristic, complemented
504C2×#103C22×C13711yescharacteristic, complemented
505C2×#103C22×C13711yescharacteristic, complemented
506C2×#102C22×C13711yescharacteristic
507C2×#102C22×C13711yescharacteristic
508C2×#102C22×C13711yescharacteristic
509C2×#102C22×C13711yescharacteristic
510C2×#102C22×C13711yescharacteristic
511C2×#102C22×C13711yescharacteristic
512C2×C22⋊C8C22×C13711yescharacteristic
513C2×C22⋊C8C22×C13711yescharacteristic, complemented
514C2×C22⋊C8C22×C13711yescharacteristic, complemented
515#397—21no—
516#394—21no—
517#391C22×C13711yescharacteristic, complemented
518#389—21no—
519#389C22×C13711yescharacteristic, complemented
520#388—21no—
521#380C22×C13711yescharacteristic, complemented
522#340C22×C13711yescharacteristic, complemented
523#340C22×C13711yescharacteristic, complemented
524#336C22×C13711yescharacteristic, complemented
525#336C22×C13711yescharacteristic, complemented
526C25—21no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C22×Q8C23×C13711yescharacteristic
534C22×Q8C23×C13711yescharacteristic
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4D4×C13714yes—
544C22×D4D4×C13711yescharacteristic
545C22×D4C23×C13711yescharacteristic
546C22×D4C23×C13711yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C23×C13711yescharacteristic
550C23×C4C23×C13711yescharacteristic
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—41no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C22×C8C23×C13711yescharacteristic
564C22×C8C23×C13711yescharacteristic
565C22×C8C23×C13711yescharacteristic
566C22×C8C23×C13711yescharacteristic
567#124—22no—
568#124—22no—
569#123—28no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575C22⋊Q8D4×C13714yes—
576#121—28no—
577#121—22no—
578#121—22no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—41no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4D4×C13711yescharacteristic
591C2×C4⋊C4C23×C13711yescharacteristic
592C2×C4⋊C4C23×C13711yescharacteristic
593C2×C4⋊C4C23×C13711yescharacteristic
594C2×C4⋊C4C23×C13711yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4D4×C13711yescharacteristic
606C2×C22⋊C4D4×C13711yescharacteristic
607C2×C42—21no—
608C2×C42C23×C13711yescharacteristic
609#106—22no—
610#103—22no—
611#103—22no—
612#103—22no—
613#103—41no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—22no—
619#102D4×C13714yescomplemented
620C22⋊C8—22no—
621C22⋊C8—22no—
622C22⋊C8—41no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—21no—
629C24—24no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—81no—
635C24—81no—
636C24C2×D4×C13711yescharacteristic
637C24C2×D4×C13711yescharacteristic
638#41—44no—
639#41—44no—
640#41—44no—
641#41—44no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8C2×D4×C13712yes—
654C2×D4—28no—
655C2×D4—24no—
656C2×D4—22no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—44no—
668C2×D4—44no—
669C2×D4—44no—
670C2×D4—41no—
671C2×D4—41no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4C2×D4×C13712yes—
679C2×D4C2×D4×C13712yes—
680C2×D4C2×D4×C13712yes—
681C2×D4#41×C13712yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—24no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—81no—
703C22×C4—81no—
704C22×C4C2×D4×C13711yescharacteristic
705C22×C4C2×D4×C13711yescharacteristic
706C22×C4C2×D4×C13711yescharacteristic
707C22×C4C2×D4×C13711yescharacteristic
708C22×C4C2×D4×C13712yes—
709C22×C4C2×D4×C13712yes—
710C22×C4C24×C13711yescharacteristic
711Q16—44no—
712SD16—44no—
713SD16—44no—
714M16—44no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8C2×D4×C13712yes—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4C2×D4×C13712yes—
739C4⋊C4C2×D4×C13712yes—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—24no—
746C22⋊C4—22no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C42—21no—
752C42—21no—
753C42—42no—
754C23—22no—
755C23—21no—
756C23—22no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—48no—
772C23—48no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23#120×C13712yes—
789C23C22×D4×C13711yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—41no—
795Q8—41no—
796Q8—41no—
797Q8—41no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—48no—
804D4—48no—
805D4—44no—
806D4—41no—
807D4—41no—
808D4—84no—
809D4#121×C13714yes—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—48no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—84no—
849C2×C4#120×C13712yes—
850C2×C4C22×D4×C13711yescharacteristic
851C2×C4C22×D4×C13711yescharacteristic
852C2×C4C22×D4×C13711yescharacteristic
853C2×C4C2×#41×C13711yescharacteristic
854C2×C4H(5,𝔽2)×C13711yescharacteristic
855C2×C4H(5,𝔽2)×C13711yescharacteristic
856C8—22no—
857C8—41no—
858C8—41no—
859C8—41no—
860C22—22no—
861C22—24no—
862C22—22no—
863C22—22no—
864C22—41no—
865C22—42no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—42no—
872C22—41no—
873C22—42no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—41no—
883C22—41no—
884C22—816no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22C2×#120×C13711yescharacteristic
890C22D42×C13711yescharacteristic
891C22#546×C13711yescharacteristic
892C22#575×C13711yescharacteristic
893C22#575×C13711yescharacteristic
894C22#577×C13711yescharacteristic
895C22#577×C13711yescharacteristic
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—42no—
902C4—42no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4C2×#121×C13711yescharacteristic
907C4#534×C13711yescharacteristic
908C4D42×C13711yescharacteristic
909C4#546×C13711yescharacteristic
910C2—42no—
911C2—44no—
912C2—81no—
913C2—82no—
914C2#2410×C13711yescharacteristic
915C2#3005×C13711yescharacteristic
916C2#3009×C13711yescharacteristic
917C2#3267×C13711yescharacteristic
918C2#3275×C13711yescharacteristic
919C2#3311×C13711yescharacteristic
920C2#3323×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC2×#546×C137C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C4×D4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#470×C137C2semidirect
3. C2×#452×C137C2semidirect
4. C2×#450×C137C2semidirect
5. C2×#418×C137C2semidirect
6. #2415×C137C2semidirect
7. #2042×C137C2semidirect
8. #2034×C137C2semidirect
9. #2015×C137C2semidirect
10. #2000×C137C2semidirect
11. #1877×C137C2semidirect
12. #1873×C137C2semidirect
13. #1870×C137C2semidirect
14. #1864×C137C2semidirect
15. #1788×C137C2semidirect
18. C22×Q16×C137C22semidirect
28. C2×C22⋊Q8×C137C22semidirect
39. C2×#106×C137C22semidirect
41. C2×#103×C137C22semidirect
42. C2×#103×C137C22semidirect
43. C2×#103×C137C22semidirect
44. C2×#103×C137C22semidirect
52. C2×C22⋊C8×C137C22semidirect
53. C2×C22⋊C8×C137C22semidirect
56. #391×C137C22semidirect
58. #389×C137C22semidirect
60. #380×C137C22semidirect
61. #340×C137C22semidirect
62. #340×C137C22semidirect
63. #336×C137C22semidirect
64. #336×C137C22semidirect
158. #102×C137D4semidirect
460. #24442C137direct (N × H)
461. C137#24442direct (N × H)
463. C2×#470C2×C137semidirect
464. C2×#452C2×C137semidirect
465. C2×#450C2×C137semidirect
466. C2×#418C2×C137semidirect
467. #2415C2×C137semidirect
468. #2042C2×C137semidirect
469. #2034C2×C137semidirect
470. #2015C2×C137semidirect
471. #2000C2×C137semidirect
472. #1877C2×C137semidirect
473. #1873C2×C137semidirect
474. #1870C2×C137semidirect
475. #1864C2×C137semidirect
476. #1788C2×C137semidirect
479. C22×Q16C22×C137semidirect
489. C2×C22⋊Q8C22×C137semidirect
500. C2×#106C22×C137semidirect
502. C2×#103C22×C137semidirect
503. C2×#103C22×C137semidirect
504. C2×#103C22×C137semidirect
505. C2×#103C22×C137semidirect
513. C2×C22⋊C8C22×C137semidirect
514. C2×C22⋊C8C22×C137semidirect
517. #391C22×C137semidirect
519. #389C22×C137semidirect
521. #380C22×C137semidirect
522. #340C22×C137semidirect
523. #340C22×C137semidirect
524. #336C22×C137semidirect
525. #336C22×C137semidirect
619. #102D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1372
C2×#470×C1372
C2×#452×C1372
C2×#450×C1372
C2×#418×C1372
#2415×C1372
#2042×C1372
#2034×C1372
#2015×C1372
#2000×C1372
#1877×C1372
#1873×C1372
#1870×C1372
#1864×C1372
#1788×C1372
#24442137