Finite Group Databasebeta

← C137×#24440 #46873826

Subgroups — C137×#24440 #46873826

Order 35072.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C137C211yesmaximal, characteristic, complemented
2C2×#469×C137C211yesmaximal, characteristic, complemented
3C2×#447×C137C211yesmaximal, characteristic, complemented
4C2×#447×C137C211yesmaximal, characteristic, complemented
5C2×#418×C137C211yesmaximal, characteristic, complemented
6#2414×C137C211yesmaximal, characteristic, complemented
7#2041×C137C211yesmaximal, characteristic, complemented
8#2034×C137C211yesmaximal, characteristic, complemented
9#2011×C137C211yesmaximal, characteristic, complemented
10#1999×C137C211yesmaximal, characteristic, complemented
11#1879×C137C211yesmaximal, characteristic, complemented
12#1875×C137C211yesmaximal, characteristic, complemented
13#1870×C137C211yesmaximal, characteristic, complemented
14#1864×C137C211yesmaximal, characteristic, complemented
15#1786×C137C211yesmaximal, characteristic, complemented
16C23×D4×C137—21no—
17C23×D4×C137C2211yescharacteristic
18C23×D4×C137C2211yescharacteristic
19C22×D8×C137C2211yescharacteristic
20C22×D8×C137C2211yescharacteristic, complemented
21C22×D8×C137C2211yescharacteristic, complemented
22C22×M16×C137C2211yescharacteristic, complemented
23D42×C137—24no—
24D42×C137—24no—
25C2×#127×C137C2211yescharacteristic
26C2×#121×C137—21no—
27C2×#121×C137C2211yescharacteristic
28C2×#121×C137C2211yescharacteristic
29C2×#121×C137C2211yescharacteristic, complemented
30C2×#121×C137C2211yescharacteristic, complemented
31C2×#120×C137—21no—
32C2×#120×C137—21no—
33C2×C4×D4×C137C2211yescharacteristic
34C2×C4×D4×C137C2211yescharacteristic
35C2×#117×C137C2211yescharacteristic, complemented
36#469×C137—24no—
37#447×C137—24no—
38#447×C137—24no—
39C2×#106×C137C2211yescharacteristic, complemented
40#418×C137—24no—
41C2×#102×C137C2211yescharacteristic
42C2×#102×C137C2211yescharacteristic
43C2×#102×C137C2211yescharacteristic
44C2×#102×C137C2211yescharacteristic, complemented
45C2×#102×C137C2211yescharacteristic, complemented
46C2×#102×C137C2211yescharacteristic, complemented
47C2×#102×C137C2211yescharacteristic, complemented
48C2×#102×C137C2211yescharacteristic, complemented
49C2×#102×C137C2211yescharacteristic, complemented
50C2×#102×C137C2211yescharacteristic, complemented
51C2×C22⋊C8×C137C2211yescharacteristic, complemented
52C2×C22⋊C8×C137C2211yescharacteristic, complemented
53C2×C22⋊C8×C137C2211yescharacteristic, complemented
54#394×C137—21no—
55#392×C137—21no—
56#390×C137—21no—
57#390×C137C2211yescharacteristic, complemented
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—
66C25×C137—21no—
67C22×D4×C137—22no—
68C22×D4×C137—22no—
69C22×D4×C137—28no—
70C22×D4×C137—21no—
71C22×D4×C137—21no—
72C22×D4×C137—22no—
73C22×D4×C137—22no—
74C22×D4×C137—22no—
75C22×D4×C137—22no—
76C22×D4×C137—21no—
77C22×D4×C137—21no—
78C22×D4×C137—21no—
79C22×D4×C137—21no—
80C22×D4×C137—21no—
81C22×D4×C137—22no—
82C22×D4×C137—21no—
83C22×D4×C137—41no—
84C22×D4×C137—41no—
85C22×D4×C137—41no—
86C22×D4×C137—41no—
87C22×D4×C137—44no—
88C22×D4×C137—44no—
89C22×D4×C137D411yescharacteristic
90C22×D4×C137D414yescomplemented
91C22×D4×C137C2311yescharacteristic
92C22×D4×C137C2311yescharacteristic
93C22×D4×C137C2311yescharacteristic
94C22×D4×C137C2311yescharacteristic
95C23×C4×C137—21no—
96C23×C4×C137C2311yescharacteristic
97C23×C4×C137C2311yescharacteristic
98C2×D8×C137—22no—
99C2×D8×C137—22no—
100C2×D8×C137—22no—
101C2×D8×C137—22no—
102C2×D8×C137—22no—
103C2×D8×C137—22no—
104C2×D8×C137—41no—
105C2×D8×C137—41no—
106C2×D8×C137—41no—
107C2×M16×C137—22no—
108C2×M16×C137—22no—
109C2×M16×C137—41no—
110C22×C8×C137C2311yescharacteristic
111C22×C8×C137C2311yescharacteristic
112C22×C8×C137C2311yescharacteristic
113C22×C8×C137C2311yescharacteristic
114#127×C137—22no—
115#127×C137—22no—
116#121×C137—28no—
117#121×C137—22no—
118#121×C137—22no—
119#121×C137—22no—
120#121×C137—22no—
121#121×C137—22no—
122#121×C137—22no—
123#121×C137—41no—
124#121×C137D414yescomplemented
125#120×C137—28no—
126#120×C137—28no—
127C4×D4×C137—22no—
128C4×D4×C137—22no—
129C4×D4×C137—22no—
130C4×D4×C137—22no—
131#117×C137—22no—
132#117×C137—41no—
133C2×C4⋊C4×C137—21no—
134C2×C4⋊C4×C137D411yescharacteristic
135C2×C4⋊C4×C137C2311yescharacteristic
136C2×C4⋊C4×C137C2311yescharacteristic
137C2×C4⋊C4×C137C2311yescharacteristic
138C2×C4⋊C4×C137C2311yescharacteristic
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×C137—21no—
145C2×C22⋊C4×C137—21no—
146C2×C22⋊C4×C137—21no—
147C2×C22⋊C4×C137—21no—
148C2×C22⋊C4×C137D411yescharacteristic
149C2×C22⋊C4×C137D411yescharacteristic
150C2×C42×C137—21no—
151C2×C42×C137C2311yescharacteristic
152#106×C137—22no—
153#102×C137—22no—
154#102×C137—22no—
155#102×C137—22no—
156#102×C137—22no—
157#102×C137—22no—
158#102×C137—22no—
159#102×C137—22no—
160#102×C137—22no—
161#102×C137—41no—
162#102×C137D414yescomplemented
163C22⋊C8×C137—22no—
164C22⋊C8×C137—22no—
165C22⋊C8×C137—41no—
166#95×C137—21no—
167#95×C137—21no—
168C24×C137—21no—
169C24×C137—24no—
170C24×C137—21no—
171C24×C137—21no—
172C24×C137—24no—
173C24×C137—21no—
174C24×C137—42no—
175C24×C137—42no—
176C24×C137—42no—
177C24×C137—42no—
178C24×C137—42no—
179C24×C137—42no—
180C24×C137—42no—
181C24×C137—42no—
182C24×C137—81no—
183C24×C137—81no—
184C24×C137—81no—
185C24×C137—81no—
186C24×C137C2×D411yescharacteristic
187C24×C137C2×D411yescharacteristic
188C2×D4×C137—22no—
189C2×D4×C137—22no—
190C2×D4×C137—28no—
191C2×D4×C137—24no—
192C2×D4×C137—24no—
193C2×D4×C137—24no—
194C2×D4×C137—24no—
195C2×D4×C137—24no—
196C2×D4×C137—24no—
197C2×D4×C137—22no—
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—21no—
207C2×D4×C137—21no—
208C2×D4×C137—21no—
209C2×D4×C137—21no—
210C2×D4×C137—21no—
211C2×D4×C137—21no—
212C2×D4×C137—21no—
213C2×D4×C137—21no—
214C2×D4×C137—21no—
215C2×D4×C137—21no—
216C2×D4×C137—21no—
217C2×D4×C137—44no—
218C2×D4×C137—44no—
219C2×D4×C137—44no—
220C2×D4×C137—42no—
221C2×D4×C137—42no—
222C2×D4×C137—42no—
223C2×D4×C137—42no—
224C2×D4×C137—42no—
225C2×D4×C137—42no—
226C2×D4×C137—44no—
227C2×D4×C137—44no—
228C2×D4×C137—432no—
229C2×D4×C137—44no—
230C2×D4×C137—42no—
231C2×D4×C137—42no—
232C2×D4×C137—42no—
233C2×D4×C137—42no—
234C2×D4×C137—44no—
235C2×D4×C137—42no—
236C2×D4×C137—42no—
237C2×D4×C137—42no—
238C2×D4×C137—81no—
239C2×D4×C137—81no—
240C2×D4×C137—81no—
241C2×D4×C137—81no—
242C2×D4×C137—81no—
243C2×D4×C137C2×D412yes—
244C2×D4×C137C2×D412yes—
245C2×D4×C137C2×D412yes—
246C2×D4×C137C2×D412yes—
247C2×D4×C137#4112yes—
248C22×C4×C137—21no—
249C22×C4×C137—21no—
250C22×C4×C137—21no—
251C22×C4×C137—21no—
252C22×C4×C137—24no—
253C22×C4×C137—21no—
254C22×C4×C137—21no—
255C22×C4×C137—21no—
256C22×C4×C137—21no—
257C22×C4×C137—21no—
258C22×C4×C137—21no—
259C22×C4×C137—21no—
260C22×C4×C137—21no—
261C22×C4×C137—21no—
262C22×C4×C137—21no—
263C22×C4×C137—42no—
264C22×C4×C137—42no—
265C22×C4×C137C2×D411yescharacteristic
266C22×C4×C137C2×D411yescharacteristic
267C22×C4×C137C2×D411yescharacteristic
268C22×C4×C137C2×D412yes—
269C22×C4×C137C2×D412yes—
270C22×C4×C137C2×D411yescharacteristic
271C22×C4×C137C2411yescharacteristic
272D8×C137—44no—
273D8×C137—44no—
274D8×C137—44no—
275M16×C137—44no—
276C2×C8×C137—21no—
277C2×C8×C137—21no—
278C2×C8×C137—21no—
279C2×C8×C137—21no—
280C2×C8×C137—21no—
281C2×C8×C137—21no—
282C2×C8×C137—21no—
283C2×C8×C137—21no—
284C2×C8×C137—21no—
285C2×C8×C137—21no—
286C2×C8×C137—21no—
287C2×C8×C137C2×D412yescomplemented
288C4⋊C4×C137—22no—
289C4⋊C4×C137—21no—
290C4⋊C4×C137—21no—
291C4⋊C4×C137—21no—
292C4⋊C4×C137—21no—
293C4⋊C4×C137—21no—
294C4⋊C4×C137—21no—
295C4⋊C4×C137—81no—
296C4⋊C4×C137C2×D412yes—
297C4⋊C4×C137C2×D412yescomplemented
298C22⋊C4×C137—24no—
299C22⋊C4×C137—24no—
300C22⋊C4×C137—22no—
301C22⋊C4×C137—24no—
302C22⋊C4×C137—22no—
303C22⋊C4×C137—42no—
304C22⋊C4×C137—42no—
305C22⋊C4×C137—42no—
306C22⋊C4×C137—42no—
307C22⋊C4×C137—81no—
308C22⋊C4×C137—81no—
309C42×C137—21no—
310C42×C137—21no—
311C42×C137—42no—
312C23×C137—21no—
313C23×C137—22no—
314C23×C137—21no—
315C23×C137—21no—
316C23×C137—22no—
317C23×C137—21no—
318C23×C137—21no—
319C23×C137—22no—
320C23×C137—21no—
321C23×C137—21no—
322C23×C137—21no—
323C23×C137—21no—
324C23×C137—21no—
325C23×C137—21no—
326C23×C137—21no—
327C23×C137—22no—
328C23×C137—22no—
329C23×C137—48no—
330C23×C137—48no—
331C23×C137—48no—
332C23×C137—48no—
333C23×C137—41no—
334C23×C137—41no—
335C23×C137—41no—
336C23×C137—41no—
337C23×C137—41no—
338C23×C137—41no—
339C23×C137—41no—
340C23×C137—41no—
341C23×C137—41no—
342C23×C137—41no—
343C23×C137—41no—
344C23×C137—41no—
345C23×C137—41no—
346C23×C137—41no—
347C23×C137—41no—
348C23×C137—41no—
349C23×C137—41no—
350C23×C137—41no—
351C23×C137—41no—
352C23×C137—41no—
353C23×C137—41no—
354C23×C137—41no—
355C23×C137—41no—
356C23×C137—84no—
357C23×C137—84no—
358C23×C137—84no—
359C23×C137—84no—
360C23×C137—84no—
361C23×C137—84no—
362C23×C137—84no—
363C23×C137—84no—
364C23×C137—84no—
365C23×C137—84no—
366C23×C137#12012yes—
367C23×C137AGL(1,ℤ/8)12yes—
368C23×C137C22×D411yescharacteristic
369D4×C137—28no—
370D4×C137—22no—
371D4×C137—22no—
372D4×C137—22no—
373D4×C137—22no—
374D4×C137—22no—
375D4×C137—22no—
376D4×C137—22no—
377D4×C137—48no—
378D4×C137—48no—
379D4×C137—48no—
380D4×C137—48no—
381D4×C137—48no—
382D4×C137—41no—
383D4×C137—41no—
384D4×C137—41no—
385D4×C137—41no—
386D4×C137—41no—
387D4×C137—41no—
388D4×C137—41no—
389D4×C137—41no—
390D4×C137—84no—
391D4×C137—84no—
392D4×C137—84no—
393D4×C137#12114yes—
394C2×C4×C137—21no—
395C2×C4×C137—21no—
396C2×C4×C137—21no—
397C2×C4×C137—21no—
398C2×C4×C137—22no—
399C2×C4×C137—22no—
400C2×C4×C137—22no—
401C2×C4×C137—22no—
402C2×C4×C137—21no—
403C2×C4×C137—21no—
404C2×C4×C137—22no—
405C2×C4×C137—22no—
406C2×C4×C137—21no—
407C2×C4×C137—21no—
408C2×C4×C137—21no—
409C2×C4×C137—21no—
410C2×C4×C137—48no—
411C2×C4×C137—41no—
412C2×C4×C137—41no—
413C2×C4×C137—41no—
414C2×C4×C137—41no—
415C2×C4×C137—41no—
416C2×C4×C137—41no—
417C2×C4×C137—41no—
418C2×C4×C137—41no—
419C2×C4×C137—41no—
420C2×C4×C137—41no—
421C2×C4×C137—41no—
422C2×C4×C137—41no—
423C2×C4×C137—41no—
424C2×C4×C137—41no—
425C2×C4×C137#12012yes—
426C2×C4×C137AGL(1,ℤ/8)12yes—
427C2×C4×C137C22×D411yescharacteristic
428C2×C4×C137C22×D411yescharacteristic
429C2×C4×C137C22×D411yescharacteristic
430C2×C4×C137C2×#4111yescharacteristic
431C2×C4×C137H(5,𝔽2)11yescharacteristic
432C2×C4×C137H(5,𝔽2)11yescharacteristic
433C8×C137—22no—
434C8×C137—41no—
435C8×C137—41no—
436C8×C137—41no—
437C22×C137—22no—
438C22×C137—24no—
439C22×C137—22no—
440C22×C137—22no—
441C22×C137—22no—
442C22×C137—22no—
443C22×C137—22no—
444C22×C137—41no—
445C22×C137—42no—
446C22×C137—41no—
447C22×C137—42no—
448C22×C137—41no—
449C22×C137—42no—
450C22×C137—41no—
451C22×C137—41no—
452C22×C137—42no—
453C22×C137—41no—
454C22×C137—42no—
455C22×C137—41no—
456C22×C137—41no—
457C22×C137—42no—
458C22×C137—42no—
459C22×C137—42no—
460C22×C137—42no—
461C22×C137—42no—
462C22×C137—42no—
463C22×C137—42no—
464C22×C137—816no—
465C22×C137—816no—
466C22×C137—81no—
467C22×C137—81no—
468C22×C137—81no—
469C22×C137—81no—
470C22×C137—81no—
471C22×C137—81no—
472C22×C137—81no—
473C22×C137—81no—
474C22×C137—81no—
475C22×C137—81no—
476C22×C137—81no—
477C22×C137—81no—
478C22×C137—81no—
479C22×C137—81no—
480C22×C137—81no—
481C22×C137C2×#12011yescharacteristic
482C22×C137D4211yescharacteristic
483C22×C137#54611yescharacteristic
484C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
485C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
486C22×C137#57611yescharacteristic
487C22×C137#57611yescharacteristic
488C4×C137—22no—
489C4×C137—22no—
490C4×C137—41no—
491C4×C137—42no—
492C4×C137—41no—
493C4×C137—42no—
494C4×C137—81no—
495C4×C137—81no—
496C4×C137C2×#12111yescharacteristic
497C4×C137#53411yescharacteristic
498C4×C137D4211yescharacteristic
499C4×C137#54611yescharacteristic
500C2×C137—42no—
501C2×C137—42no—
502C2×C137—44no—
503C2×C137—82no—
504C2×C137—82no—
505C2×C137—161no—
506C2×C137#241011yescharacteristic
507C2×C137#300311yescharacteristic
508C2×C137#300811yescharacteristic
509C2×C137#326411yescharacteristic
510C2×C137#327411yescharacteristic
511C2×C137#331811yescharacteristic
512C2×C137#332511yescharacteristic
513#24440C13711yesmaximal, characteristic, direct product factor, Sylow
514C137#2444011yescharacteristic, direct product factor, Sylow
515C2×D42C2×C13711yescharacteristic, complemented
516C2×#469C2×C13711yescharacteristic, complemented
517C2×#447C2×C13711yescharacteristic, complemented
518C2×#447C2×C13711yescharacteristic, complemented
519C2×#418C2×C13711yescharacteristic, complemented
520#2414C2×C13711yescharacteristic, complemented
521#2041C2×C13711yescharacteristic, complemented
522#2034C2×C13711yescharacteristic, complemented
523#2011C2×C13711yescharacteristic, complemented
524#1999C2×C13711yescharacteristic, complemented
525#1879C2×C13711yescharacteristic, complemented
526#1875C2×C13711yescharacteristic, complemented
527#1870C2×C13711yescharacteristic, complemented
528#1864C2×C13711yescharacteristic, complemented
529#1786C2×C13711yescharacteristic, complemented
530C23×D4—21no—
531C23×D4C22×C13711yescharacteristic
532C23×D4C22×C13711yescharacteristic
533C22×D8C22×C13711yescharacteristic
534C22×D8C22×C13711yescharacteristic, complemented
535C22×D8C22×C13711yescharacteristic, complemented
536C22×M16C22×C13711yescharacteristic, complemented
537D42—24no—
538D42—24no—
539C2×#127C22×C13711yescharacteristic
540C2×#121—21no—
541C2×#121C22×C13711yescharacteristic
542C2×#121C22×C13711yescharacteristic
543C2×#121C22×C13711yescharacteristic, complemented
544C2×#121C22×C13711yescharacteristic, complemented
545C2×#120—21no—
546C2×#120—21no—
547C2×C4×D4C22×C13711yescharacteristic
548C2×C4×D4C22×C13711yescharacteristic
549C2×#117C22×C13711yescharacteristic, complemented
550#469—24no—
551#447—24no—
552#447—24no—
553C2×#106C22×C13711yescharacteristic, complemented
554#418—24no—
555C2×#102C22×C13711yescharacteristic
556C2×#102C22×C13711yescharacteristic
557C2×#102C22×C13711yescharacteristic
558C2×#102C22×C13711yescharacteristic, complemented
559C2×#102C22×C13711yescharacteristic, complemented
560C2×#102C22×C13711yescharacteristic, complemented
561C2×#102C22×C13711yescharacteristic, complemented
562C2×#102C22×C13711yescharacteristic, complemented
563C2×#102C22×C13711yescharacteristic, complemented
564C2×#102C22×C13711yescharacteristic, complemented
565C2×C22⋊C8C22×C13711yescharacteristic, complemented
566C2×C22⋊C8C22×C13711yescharacteristic, complemented
567C2×C22⋊C8C22×C13711yescharacteristic, complemented
568#394—21no—
569#392—21no—
570#390—21no—
571#390C22×C13711yescharacteristic, complemented
572#389C22×C13711yescharacteristic, complemented
573#388—21no—
574#380C22×C13711yescharacteristic, complemented
575#340C22×C13711yescharacteristic, complemented
576#340C22×C13711yescharacteristic, complemented
577#336C22×C13711yescharacteristic, complemented
578#336C22×C13711yescharacteristic, complemented
579C25—21no—
580C25—21no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—28no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—41no—
598C22×D4—41no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—44no—
602C22×D4—44no—
603C22×D4D4×C13711yescharacteristic
604C22×D4D4×C13714yescomplemented
605C22×D4C23×C13711yescharacteristic
606C22×D4C23×C13711yescharacteristic
607C22×D4C23×C13711yescharacteristic
608C22×D4C23×C13711yescharacteristic
609C23×C4—21no—
610C23×C4C23×C13711yescharacteristic
611C23×C4C23×C13711yescharacteristic
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—41no—
619C2×D8—41no—
620C2×D8—41no—
621C2×M16—22no—
622C2×M16—22no—
623C2×M16—41no—
624C22×C8C23×C13711yescharacteristic
625C22×C8C23×C13711yescharacteristic
626C22×C8C23×C13711yescharacteristic
627C22×C8C23×C13711yescharacteristic
628#127—22no—
629#127—22no—
630#121—28no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—22no—
637#121—41no—
638#121D4×C13714yescomplemented
639#120—28no—
640#120—28no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—22no—
646#117—41no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4D4×C13711yescharacteristic
649C2×C4⋊C4C23×C13711yescharacteristic
650C2×C4⋊C4C23×C13711yescharacteristic
651C2×C4⋊C4C23×C13711yescharacteristic
652C2×C4⋊C4C23×C13711yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C13711yescharacteristic
663C2×C22⋊C4D4×C13711yescharacteristic
664C2×C42—21no—
665C2×C42C23×C13711yescharacteristic
666#106—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—41no—
676#102D4×C13714yescomplemented
677C22⋊C8—22no—
678C22⋊C8—22no—
679C22⋊C8—41no—
680#95—21no—
681#95—21no—
682C24—21no—
683C24—24no—
684C24—21no—
685C24—21no—
686C24—24no—
687C24—21no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24—81no—
700C24C2×D4×C13711yescharacteristic
701C24C2×D4×C13711yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—432no—
743C2×D4—44no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4—81no—
757C2×D4C2×D4×C13712yes—
758C2×D4C2×D4×C13712yes—
759C2×D4C2×D4×C13712yes—
760C2×D4C2×D4×C13712yes—
761C2×D4#41×C13712yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2×D4×C13711yescharacteristic
780C22×C4C2×D4×C13711yescharacteristic
781C22×C4C2×D4×C13711yescharacteristic
782C22×C4C2×D4×C13712yes—
783C22×C4C2×D4×C13712yes—
784C22×C4C2×D4×C13711yescharacteristic
785C22×C4C24×C13711yescharacteristic
786D8—44no—
787D8—44no—
788D8—44no—
789M16—44no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8C2×D4×C13712yescomplemented
802C4⋊C4—22no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—81no—
810C4⋊C4C2×D4×C13712yes—
811C4⋊C4C2×D4×C13712yescomplemented
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—22no—
815C22⋊C4—24no—
816C22⋊C4—22no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—81no—
822C22⋊C4—81no—
823C42—21no—
824C42—21no—
825C42—42no—
826C23—21no—
827C23—22no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—22no—
843C23—48no—
844C23—48no—
845C23—48no—
846C23—48no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23#120×C13712yes—
881C23AGL(1,ℤ/8)×C13712yes—
882C23C22×D4×C13711yescharacteristic
883D4—28no—
884D4—22no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4#121×C13714yes—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—48no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4#120×C13712yes—
940C2×C4AGL(1,ℤ/8)×C13712yes—
941C2×C4C22×D4×C13711yescharacteristic
942C2×C4C22×D4×C13711yescharacteristic
943C2×C4C22×D4×C13711yescharacteristic
944C2×C4C2×#41×C13711yescharacteristic
945C2×C4H(5,𝔽2)×C13711yescharacteristic
946C2×C4H(5,𝔽2)×C13711yescharacteristic
947C8—22no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—22no—
953C22—24no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22C2×#120×C13711yescharacteristic
996C22D42×C13711yescharacteristic
997C22#546×C13711yescharacteristic
998C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
999C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
1000C22#576×C13711yescharacteristic
1001C22#576×C13711yescharacteristic
1002C4—22no—
1003C4—22no—
1004C4—41no—
1005C4—42no—
1006C4—41no—
1007C4—42no—
1008C4—81no—
1009C4—81no—
1010C4C2×#121×C13711yescharacteristic
1011C4#534×C13711yescharacteristic
1012C4D42×C13711yescharacteristic
1013C4#546×C13711yescharacteristic
1014C2—42no—
1015C2—42no—
1016C2—44no—
1017C2—82no—
1018C2—82no—
1019C2—161no—
1020C2#2410×C13711yescharacteristic
1021C2#3003×C13711yescharacteristic
1022C2#3008×C13711yescharacteristic
1023C2#3264×C13711yescharacteristic
1024C2#3274×C13711yescharacteristic
1025C2#3318×C13711yescharacteristic
1026C2#3325×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
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
1. C2×D42×C137C2semidirect
2. C2×#469×C137C2semidirect
3. C2×#447×C137C2semidirect
4. C2×#447×C137C2semidirect
5. C2×#418×C137C2semidirect
6. #2414×C137C2semidirect
7. #2041×C137C2semidirect
8. #2034×C137C2semidirect
9. #2011×C137C2semidirect
10. #1999×C137C2semidirect
11. #1879×C137C2semidirect
12. #1875×C137C2semidirect
13. #1870×C137C2semidirect
14. #1864×C137C2semidirect
15. #1786×C137C2semidirect
20. C22×D8×C137C22semidirect
21. C22×D8×C137C22semidirect
22. C22×M16×C137C22semidirect
29. C2×#121×C137C22semidirect
30. C2×#121×C137C22semidirect
35. C2×#117×C137C22semidirect
39. C2×#106×C137C22semidirect
44. C2×#102×C137C22semidirect
45. C2×#102×C137C22semidirect
46. C2×#102×C137C22semidirect
47. C2×#102×C137C22semidirect
48. C2×#102×C137C22semidirect
49. C2×#102×C137C22semidirect
50. C2×#102×C137C22semidirect
51. C2×C22⋊C8×C137C22semidirect
52. C2×C22⋊C8×C137C22semidirect
53. C2×C22⋊C8×C137C22semidirect
57. #390×C137C22semidirect
58. #389×C137C22semidirect
60. #380×C137C22semidirect
61. #340×C137C22semidirect
62. #340×C137C22semidirect
63. #336×C137C22semidirect
64. #336×C137C22semidirect
90. C22×D4×C137D4semidirect
124. #121×C137D4semidirect
162. #102×C137D4semidirect
287. C2×C8×C137C2×D4semidirect
297. C4⋊C4×C137C2×D4semidirect
513. #24440C137direct (N × H)
514. C137#24440direct (N × H)
515. C2×D42C2×C137semidirect
516. C2×#469C2×C137semidirect
517. C2×#447C2×C137semidirect
518. C2×#447C2×C137semidirect
519. C2×#418C2×C137semidirect
520. #2414C2×C137semidirect
521. #2041C2×C137semidirect
522. #2034C2×C137semidirect
523. #2011C2×C137semidirect
524. #1999C2×C137semidirect
525. #1879C2×C137semidirect
526. #1875C2×C137semidirect
527. #1870C2×C137semidirect
528. #1864C2×C137semidirect
529. #1786C2×C137semidirect
534. C22×D8C22×C137semidirect
535. C22×D8C22×C137semidirect
536. C22×M16C22×C137semidirect
543. C2×#121C22×C137semidirect
544. C2×#121C22×C137semidirect
549. C2×#117C22×C137semidirect
553. C2×#106C22×C137semidirect
558. C2×#102C22×C137semidirect
559. C2×#102C22×C137semidirect
560. C2×#102C22×C137semidirect
561. C2×#102C22×C137semidirect
562. C2×#102C22×C137semidirect
563. C2×#102C22×C137semidirect
564. C2×#102C22×C137semidirect
565. C2×C22⋊C8C22×C137semidirect
566. C2×C22⋊C8C22×C137semidirect
567. C2×C22⋊C8C22×C137semidirect
571. #390C22×C137semidirect
572. #389C22×C137semidirect
574. #380C22×C137semidirect
575. #340C22×C137semidirect
576. #340C22×C137semidirect
577. #336C22×C137semidirect
578. #336C22×C137semidirect
604. C22×D4D4×C137semidirect
638. #121D4×C137semidirect
676. #102D4×C137semidirect
801. C2×C8C2×D4×C137semidirect
811. C4⋊C4C2×D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1372
C2×#469×C1372
C2×#447×C1372
C2×#418×C1372
#2414×C1372
#2041×C1372
#2034×C1372
#2011×C1372
#1999×C1372
#1879×C1372
#1875×C1372
#1870×C1372
#1864×C1372
#1786×C1372
#24440137