Finite Group Databasebeta

← C137×#23972 #46873358

Subgroups — C137×#23972 #46873358

Order 35072.

1516 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C137C211yesmaximal, characteristic, complemented
2C2×#449×C137C211yesmaximal, characteristic, complemented
3C2×#417×C137C211yesmaximal, characteristic, complemented
4#2407×C137C211yesmaximal, characteristic, complemented
5#2024×C137C211yesmaximal, characteristic, complemented
6#2023×C137C211yesmaximal, characteristic, complemented
7#2000×C137C211yesmaximal, characteristic, complemented
8#1999×C137C211yesmaximal, characteristic, complemented
9#1895×C137C211yesmaximal, characteristic, complemented
10#1879×C137C211yesmaximal, characteristic, complemented
11#1877×C137C211yesmaximal, characteristic, complemented
12#1874×C137C211yesmaximal, characteristic, complemented
13#1872×C137C211yesmaximal, characteristic, complemented
14#1870×C137C211yesmaximal, characteristic, complemented
15#1824×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137—21no—
17C22×#41×C137C2211yescharacteristic
18C22×SD16×C137C2211yescharacteristic
19C22×D8×C137C2211yescharacteristic
20C22×M16×C137C2211yescharacteristic
21#547×C137—24no—
22#547×C137—24no—
23C2×C4⋊Q8×C137C2211yescharacteristic
24C2×#123×C137—21no—
25C2×#123×C137—21no—
26C2×C22⋊Q8×C137—21no—
27C2×C22⋊Q8×C137C2211yescharacteristic
28C2×#121×C137C2211yescharacteristic
29C2×#121×C137C2211yescharacteristic
30C2×#121×C137C2211yescharacteristic
31C2×C4×D4×C137C2211yescharacteristic
32C2×C4×D4×C137C2211yescharacteristic
33C22×C4⋊C4×C137C2211yescharacteristic
34C22×C4⋊C4×C137C2211yescharacteristic
35#449×C137—24no—
36#417×C137—24no—
37C2×#103×C137C2211yescharacteristic
38C2×#103×C137C2211yescharacteristic
39C2×#103×C137C2211yescharacteristic
40C2×#102×C137C2211yescharacteristic
41C2×#102×C137C2211yescharacteristic
42C2×#102×C137C2211yescharacteristic
43C2×#102×C137C2211yescharacteristic
44C2×#102×C137C2211yescharacteristic
45C2×C22⋊C8×C137C2211yescharacteristic
46C2×C22⋊C8×C137C2211yescharacteristic
47C2×C22⋊C8×C137C2211yescharacteristic
48#394×C137—21no—
49#392×C137—21no—
50#391×C137C2211yescharacteristic
51#390×C137C2211yescharacteristic
52#386×C137—21no—
53#385×C137—21no—
54#380×C137C2211yescharacteristic
55#340×C137C2211yescharacteristic
56#340×C137C2211yescharacteristic
57#340×C137C2211yescharacteristic
58#340×C137C2211yescharacteristic
59#340×C137C2211yescharacteristic
60#340×C137C2211yescharacteristic
61#336×C137C2211yescharacteristic
62#336×C137C2211yescharacteristic
63C2×#41×C137—28no—
64C2×#41×C137—22no—
65C2×#41×C137—22no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—41no—
69C2×#41×C137—41no—
70C2×#41×C137—44no—
71C2×#41×C137—44no—
72C22×Q8×C137—21no—
73C22×Q8×C137C2311yescharacteristic
74C22×D4×C137—21no—
75C22×D4×C137—21no—
76C22×D4×C137—21no—
77C22×D4×C137—21no—
78C22×D4×C137D411yescharacteristic
79C22×D4×C137C2311yescharacteristic
80C22×D4×C137C2311yescharacteristic
81C23×C4×C137—21no—
82C23×C4×C137—21no—
83C23×C4×C137—21no—
84C23×C4×C137—21no—
85C23×C4×C137C2311yescharacteristic
86C23×C4×C137C2311yescharacteristic
87C2×SD16×C137—22no—
88C2×SD16×C137—22no—
89C2×SD16×C137—41no—
90C2×D8×C137—22no—
91C2×D8×C137—22no—
92C2×D8×C137—41no—
93C2×M16×C137—22no—
94C2×M16×C137—41no—
95C2×M16×C137—41no—
96C22×C8×C137C2311yescharacteristic
97C22×C8×C137C2311yescharacteristic
98C22×C8×C137C2311yescharacteristic
99C22×C8×C137C2311yescharacteristic
100C4⋊Q8×C137—22no—
101C4⋊Q8×C137—22no—
102#123×C137—28no—
103#123×C137—28no—
104C22⋊Q8×C137—28no—
105C22⋊Q8×C137—22no—
106C22⋊Q8×C137—41no—
107#121×C137—22no—
108#121×C137—22no—
109#121×C137—22no—
110#121×C137—22no—
111#121×C137—41no—
112#121×C137D414yescomplemented
113C4×D4×C137—22no—
114C4×D4×C137—22no—
115C4×D4×C137—22no—
116C4×D4×C137—22no—
117C2×C4⋊C4×C137—21no—
118C2×C4⋊C4×C137—21no—
119C2×C4⋊C4×C137—22no—
120C2×C4⋊C4×C137—21no—
121C2×C4⋊C4×C137—22no—
122C2×C4⋊C4×C137—22no—
123C2×C4⋊C4×C137—21no—
124C2×C4⋊C4×C137D411yescharacteristic
125C2×C4⋊C4×C137D414yescomplemented
126C2×C4⋊C4×C137C2311yescharacteristic
127C2×C4⋊C4×C137C2311yescharacteristic
128C2×C4⋊C4×C137C2311yescharacteristic
129C2×C4⋊C4×C137C2311yescharacteristic
130C2×C4⋊C4×C137C2311yescharacteristic
131C2×C22⋊C4×C137—21no—
132C2×C22⋊C4×C137—21no—
133C2×C22⋊C4×C137—21no—
134C2×C22⋊C4×C137—21no—
135C2×C22⋊C4×C137—21no—
136C2×C22⋊C4×C137—21no—
137C2×C22⋊C4×C137—21no—
138C2×C22⋊C4×C137—21no—
139C2×C22⋊C4×C137D411yescharacteristic
140C2×C22⋊C4×C137D411yescharacteristic
141C2×C42×C137C2311yescharacteristic
142#103×C137—22no—
143#103×C137—22no—
144#103×C137—22no—
145#102×C137—22no—
146#102×C137—22no—
147#102×C137—22no—
148#102×C137—41no—
149#102×C137—41no—
150C22⋊C8×C137—22no—
151C22⋊C8×C137—41no—
152C22⋊C8×C137—41no—
153#95×C137—21no—
154#95×C137—21no—
155#95×C137—21no—
156C24×C137—21no—
157C24×C137—21no—
158C24×C137C2×D411yescharacteristic
159C24×C137C2×D411yescharacteristic
160#41×C137—28no—
161#41×C137—44no—
162#41×C137—44no—
163#41×C137—44no—
164#41×C137—432no—
165C2×Q8×C137—24no—
166C2×Q8×C137—21no—
167C2×Q8×C137—21no—
168C2×Q8×C137—21no—
169C2×Q8×C137—21no—
170C2×Q8×C137—21no—
171C2×Q8×C137—42no—
172C2×Q8×C137—42no—
173C2×Q8×C137#4112yescomplemented
174C2×D4×C137—22no—
175C2×D4×C137—22no—
176C2×D4×C137—24no—
177C2×D4×C137—24no—
178C2×D4×C137—22no—
179C2×D4×C137—21no—
180C2×D4×C137—21no—
181C2×D4×C137—21no—
182C2×D4×C137—21no—
183C2×D4×C137—21no—
184C2×D4×C137—21no—
185C2×D4×C137—21no—
186C2×D4×C137—21no—
187C2×D4×C137—21no—
188C2×D4×C137—21no—
189C2×D4×C137—42no—
190C2×D4×C137—42no—
191C2×D4×C137—42no—
192C2×D4×C137—42no—
193C2×D4×C137—42no—
194C2×D4×C137—42no—
195C2×D4×C137—42no—
196C2×D4×C137—42no—
197C2×D4×C137—42no—
198C2×D4×C137—81no—
199C2×D4×C137C2×D412yes—
200C2×D4×C137#4112yescomplemented
201C22×C4×C137—21no—
202C22×C4×C137—21no—
203C22×C4×C137—21no—
204C22×C4×C137—21no—
205C22×C4×C137—24no—
206C22×C4×C137—24no—
207C22×C4×C137—24no—
208C22×C4×C137—21no—
209C22×C4×C137—21no—
210C22×C4×C137—21no—
211C22×C4×C137—21no—
212C22×C4×C137—21no—
213C22×C4×C137—21no—
214C22×C4×C137—21no—
215C22×C4×C137—21no—
216C22×C4×C137—21no—
217C22×C4×C137—21no—
218C22×C4×C137—21no—
219C22×C4×C137—21no—
220C22×C4×C137—42no—
221C22×C4×C137—42no—
222C22×C4×C137—42no—
223C22×C4×C137—42no—
224C22×C4×C137—42no—
225C22×C4×C137—42no—
226C22×C4×C137—42no—
227C22×C4×C137—42no—
228C22×C4×C137—42no—
229C22×C4×C137C2×D411yescharacteristic
230C22×C4×C137C2×D411yescharacteristic
231C22×C4×C137C2×D411yescharacteristic
232C22×C4×C137C2×D412yes—
233C22×C4×C137C2×D412yes—
234C22×C4×C137C2×D411yescharacteristic
235C22×C4×C137C2411yescharacteristic
236SD16×C137—44no—
237D8×C137—44no—
238M16×C137—44no—
239C2×C8×C137—21no—
240C2×C8×C137—21no—
241C2×C8×C137—21no—
242C2×C8×C137—21no—
243C2×C8×C137—21no—
244C2×C8×C137—21no—
245C2×C8×C137—21no—
246C2×C8×C137—21no—
247C2×C8×C137—21no—
248C2×C8×C137—21no—
249C2×C8×C137—21no—
250C2×C8×C137—21no—
251C4⋊C4×C137—24no—
252C4⋊C4×C137—24no—
253C4⋊C4×C137—24no—
254C4⋊C4×C137—22no—
255C4⋊C4×C137—21no—
256C4⋊C4×C137—21no—
257C4⋊C4×C137—21no—
258C4⋊C4×C137—21no—
259C4⋊C4×C137—21no—
260C4⋊C4×C137—21no—
261C4⋊C4×C137—21no—
262C4⋊C4×C137—42no—
263C4⋊C4×C137C2×D412yes—
264C4⋊C4×C137C2×D412yes—
265C4⋊C4×C137C2×D412yes—
266C22⋊C4×C137—24no—
267C22⋊C4×C137—24no—
268C22⋊C4×C137—22no—
269C22⋊C4×C137—24no—
270C22⋊C4×C137—22no—
271C22⋊C4×C137—42no—
272C22⋊C4×C137—42no—
273C22⋊C4×C137—42no—
274C22⋊C4×C137—81no—
275C22⋊C4×C137—81no—
276C42×C137—21no—
277C42×C137—21no—
278C23×C137—21no—
279C23×C137—21no—
280C23×C137—21no—
281C23×C137—21no—
282C23×C137—21no—
283C23×C137—21no—
284C23×C137—21no—
285C23×C137—21no—
286C23×C137—21no—
287C23×C137—21no—
288C23×C137—21no—
289C23×C137—21no—
290C23×C137—22no—
291C23×C137—22no—
292C23×C137—41no—
293C23×C137—41no—
294C23×C137—41no—
295C23×C137—41no—
296C23×C137—41no—
297C23×C137—41no—
298C23×C137—41no—
299C23×C137—41no—
300C23×C137—41no—
301C23×C137—41no—
302C23×C137—41no—
303C23×C137—41no—
304C23×C137#12012yes—
305C23×C137AGL(1,ℤ/8)12yes—
306C23×C137C22×D411yescharacteristic
307Q8×C137—22no—
308Q8×C137—22no—
309Q8×C137—48no—
310Q8×C137—41no—
311Q8×C137—41no—
312D4×C137—28no—
313D4×C137—22no—
314D4×C137—22no—
315D4×C137—22no—
316D4×C137—22no—
317D4×C137—48no—
318D4×C137—48no—
319D4×C137—48no—
320D4×C137—41no—
321D4×C137—41no—
322D4×C137—41no—
323D4×C137—41no—
324D4×C137—84no—
325C2×C4×C137—21no—
326C2×C4×C137—21no—
327C2×C4×C137—21no—
328C2×C4×C137—21no—
329C2×C4×C137—22no—
330C2×C4×C137—22no—
331C2×C4×C137—22no—
332C2×C4×C137—22no—
333C2×C4×C137—21no—
334C2×C4×C137—21no—
335C2×C4×C137—22no—
336C2×C4×C137—22no—
337C2×C4×C137—22no—
338C2×C4×C137—21no—
339C2×C4×C137—22no—
340C2×C4×C137—21no—
341C2×C4×C137—21no—
342C2×C4×C137—21no—
343C2×C4×C137—48no—
344C2×C4×C137—48no—
345C2×C4×C137—48no—
346C2×C4×C137—48no—
347C2×C4×C137—41no—
348C2×C4×C137—41no—
349C2×C4×C137—41no—
350C2×C4×C137—41no—
351C2×C4×C137—41no—
352C2×C4×C137—41no—
353C2×C4×C137—41no—
354C2×C4×C137—41no—
355C2×C4×C137—41no—
356C2×C4×C137—41no—
357C2×C4×C137—41no—
358C2×C4×C137—41no—
359C2×C4×C137—41no—
360C2×C4×C137—41no—
361C2×C4×C137—41no—
362C2×C4×C137—41no—
363C2×C4×C137—41no—
364C2×C4×C137—41no—
365C2×C4×C137#12012yes—
366C2×C4×C137AGL(1,ℤ/8)12yes—
367C2×C4×C137C22×D411yescharacteristic
368C2×C4×C137C22×D411yescharacteristic
369C2×C4×C137C2×#4111yescharacteristic
370C2×C4×C137C2×#4111yescharacteristic
371C2×C4×C137H(5,𝔽2)11yescharacteristic
372C2×C4×C137H(5,𝔽2)11yescharacteristic
373C8×C137—41no—
374C8×C137—41no—
375C8×C137—41no—
376C8×C137—41no—
377C22×C137—22no—
378C22×C137—22no—
379C22×C137—22no—
380C22×C137—22no—
381C22×C137—22no—
382C22×C137—22no—
383C22×C137—41no—
384C22×C137—41no—
385C22×C137—41no—
386C22×C137—41no—
387C22×C137—41no—
388C22×C137—41no—
389C22×C137—41no—
390C22×C137—41no—
391C22×C137—42no—
392C22×C137—42no—
393C22×C137—42no—
394C22×C137—42no—
395C22×C137—42no—
396C22×C137—42no—
397C22×C137—81no—
398C22×C137—81no—
399C22×C137—81no—
400C22×C137—81no—
401C22×C137—81no—
402C22×C137—81no—
403C22×C137—81no—
404C22×C137—81no—
405C22×C137C2×#12011yescharacteristic
406C22×C137#54611yescharacteristic
407C22×C137#54611yescharacteristic
408C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
410C22×C137#57711yescharacteristic
411C22×C137#57811yescharacteristic
412C4×C137—22no—
413C4×C137—22no—
414C4×C137—41no—
415C4×C137—42no—
416C4×C137—42no—
417C4×C137—42no—
418C4×C137—42no—
419C4×C137—41no—
420C4×C137—81no—
421C4×C137—81no—
422C4×C137#52511yescharacteristic
423C4×C137#53511yescharacteristic
424C4×C137#54611yescharacteristic
425C4×C137#54611yescharacteristic
426C2×C137—42no—
427C2×C137—42no—
428C2×C137—82no—
429C2×C137—82no—
430C2×C137#240411yescharacteristic
431C2×C137#300311yescharacteristic
432C2×C137#301311yescharacteristic
433C2×C137#330611yescharacteristic
434C2×C137#330811yescharacteristic
435C2×C137#333011yescharacteristic
436C2×C137#333211yescharacteristic
437#23972C13711yesmaximal, characteristic, direct product factor, Sylow
438C137#2397211yescharacteristic, direct product factor, Sylow
439C2×#547C2×C13711yescharacteristic, complemented
440C2×#449C2×C13711yescharacteristic, complemented
441C2×#417C2×C13711yescharacteristic, complemented
442#2407C2×C13711yescharacteristic, complemented
443#2024C2×C13711yescharacteristic, complemented
444#2023C2×C13711yescharacteristic, complemented
445#2000C2×C13711yescharacteristic, complemented
446#1999C2×C13711yescharacteristic, complemented
447#1895C2×C13711yescharacteristic, complemented
448#1879C2×C13711yescharacteristic, complemented
449#1877C2×C13711yescharacteristic, complemented
450#1874C2×C13711yescharacteristic, complemented
451#1872C2×C13711yescharacteristic, complemented
452#1870C2×C13711yescharacteristic, complemented
453#1824C2×C13711yescharacteristic, complemented
454C22×#41—21no—
455C22×#41C22×C13711yescharacteristic
456C22×SD16C22×C13711yescharacteristic
457C22×D8C22×C13711yescharacteristic
458C22×M16C22×C13711yescharacteristic
459#547—24no—
460#547—24no—
461C2×C4⋊Q8C22×C13711yescharacteristic
462C2×#123—21no—
463C2×#123—21no—
464C2×C22⋊Q8—21no—
465C2×C22⋊Q8C22×C13711yescharacteristic
466C2×#121C22×C13711yescharacteristic
467C2×#121C22×C13711yescharacteristic
468C2×#121C22×C13711yescharacteristic
469C2×C4×D4C22×C13711yescharacteristic
470C2×C4×D4C22×C13711yescharacteristic
471C22×C4⋊C4C22×C13711yescharacteristic
472C22×C4⋊C4C22×C13711yescharacteristic
473#449—24no—
474#417—24no—
475C2×#103C22×C13711yescharacteristic
476C2×#103C22×C13711yescharacteristic
477C2×#103C22×C13711yescharacteristic
478C2×#102C22×C13711yescharacteristic
479C2×#102C22×C13711yescharacteristic
480C2×#102C22×C13711yescharacteristic
481C2×#102C22×C13711yescharacteristic
482C2×#102C22×C13711yescharacteristic
483C2×C22⋊C8C22×C13711yescharacteristic
484C2×C22⋊C8C22×C13711yescharacteristic
485C2×C22⋊C8C22×C13711yescharacteristic
486#394—21no—
487#392—21no—
488#391C22×C13711yescharacteristic
489#390C22×C13711yescharacteristic
490#386—21no—
491#385—21no—
492#380C22×C13711yescharacteristic
493#340C22×C13711yescharacteristic
494#340C22×C13711yescharacteristic
495#340C22×C13711yescharacteristic
496#340C22×C13711yescharacteristic
497#340C22×C13711yescharacteristic
498#340C22×C13711yescharacteristic
499#336C22×C13711yescharacteristic
500#336C22×C13711yescharacteristic
501C2×#41—28no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—44no—
509C2×#41—44no—
510C22×Q8—21no—
511C22×Q8C23×C13711yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4D4×C13711yescharacteristic
517C22×D4C23×C13711yescharacteristic
518C22×D4C23×C13711yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C23×C13711yescharacteristic
524C23×C4C23×C13711yescharacteristic
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×D8—22no—
529C2×D8—22no—
530C2×D8—41no—
531C2×M16—22no—
532C2×M16—41no—
533C2×M16—41no—
534C22×C8C23×C13711yescharacteristic
535C22×C8C23×C13711yescharacteristic
536C22×C8C23×C13711yescharacteristic
537C22×C8C23×C13711yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540#123—28no—
541#123—28no—
542C22⋊Q8—28no—
543C22⋊Q8—22no—
544C22⋊Q8—41no—
545#121—22no—
546#121—22no—
547#121—22no—
548#121—22no—
549#121—41no—
550#121D4×C13714yescomplemented
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4D4×C13711yescharacteristic
563C2×C4⋊C4D4×C13714yescomplemented
564C2×C4⋊C4C23×C13711yescharacteristic
565C2×C4⋊C4C23×C13711yescharacteristic
566C2×C4⋊C4C23×C13711yescharacteristic
567C2×C4⋊C4C23×C13711yescharacteristic
568C2×C4⋊C4C23×C13711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4D4×C13711yescharacteristic
578C2×C22⋊C4D4×C13711yescharacteristic
579C2×C42C23×C13711yescharacteristic
580#103—22no—
581#103—22no—
582#103—22no—
583#102—22no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588C22⋊C8—22no—
589C22⋊C8—41no—
590C22⋊C8—41no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—21no—
595C24—21no—
596C24C2×D4×C13711yescharacteristic
597C24C2×D4×C13711yescharacteristic
598#41—28no—
599#41—44no—
600#41—44no—
601#41—44no—
602#41—432no—
603C2×Q8—24no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8#41×C13712yescomplemented
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4C2×D4×C13712yes—
638C2×D4#41×C13712yescomplemented
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C13711yescharacteristic
668C22×C4C2×D4×C13711yescharacteristic
669C22×C4C2×D4×C13711yescharacteristic
670C22×C4C2×D4×C13712yes—
671C22×C4C2×D4×C13712yes—
672C22×C4C2×D4×C13711yescharacteristic
673C22×C4C24×C13711yescharacteristic
674SD16—44no—
675D8—44no—
676M16—44no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—42no—
701C4⋊C4C2×D4×C13712yes—
702C4⋊C4C2×D4×C13712yes—
703C4⋊C4C2×D4×C13712yes—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—22no—
707C22⋊C4—24no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C42—21no—
715C42—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23#120×C13712yes—
743C23AGL(1,ℤ/8)×C13712yes—
744C23C22×D4×C13711yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—48no—
748Q8—41no—
749Q8—41no—
750D4—28no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—41no—
762D4—84no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—48no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4#120×C13712yes—
804C2×C4AGL(1,ℤ/8)×C13712yes—
805C2×C4C22×D4×C13711yescharacteristic
806C2×C4C22×D4×C13711yescharacteristic
807C2×C4C2×#41×C13711yescharacteristic
808C2×C4C2×#41×C13711yescharacteristic
809C2×C4H(5,𝔽2)×C13711yescharacteristic
810C2×C4H(5,𝔽2)×C13711yescharacteristic
811C8—41no—
812C8—41no—
813C8—41no—
814C8—41no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#120×C13711yescharacteristic
844C22#546×C13711yescharacteristic
845C22#546×C13711yescharacteristic
846C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
847C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
848C22#577×C13711yescharacteristic
849C22#578×C13711yescharacteristic
850C4—22no—
851C4—22no—
852C4—41no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—41no—
858C4—81no—
859C4—81no—
860C4#525×C13711yescharacteristic
861C4#535×C13711yescharacteristic
862C4#546×C13711yescharacteristic
863C4#546×C13711yescharacteristic
864C2—42no—
865C2—42no—
866C2—82no—
867C2—82no—
868C2#2404×C13711yescharacteristic
869C2#3003×C13711yescharacteristic
870C2#3013×C13711yescharacteristic
871C2#3306×C13711yescharacteristic
872C2#3308×C13711yescharacteristic
873C2#3330×C13711yescharacteristic
874C2#3332×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×#547×C137C2semidirect
2. C2×#449×C137C2semidirect
3. C2×#417×C137C2semidirect
4. #2407×C137C2semidirect
5. #2024×C137C2semidirect
6. #2023×C137C2semidirect
7. #2000×C137C2semidirect
8. #1999×C137C2semidirect
9. #1895×C137C2semidirect
10. #1879×C137C2semidirect
11. #1877×C137C2semidirect
12. #1874×C137C2semidirect
13. #1872×C137C2semidirect
14. #1870×C137C2semidirect
15. #1824×C137C2semidirect
112. #121×C137D4semidirect
125. C2×C4⋊C4×C137D4semidirect
173. C2×Q8×C137#41semidirect
200. C2×D4×C137#41semidirect
437. #23972C137direct (N × H)
438. C137#23972direct (N × H)
439. C2×#547C2×C137semidirect
440. C2×#449C2×C137semidirect
441. C2×#417C2×C137semidirect
442. #2407C2×C137semidirect
443. #2024C2×C137semidirect
444. #2023C2×C137semidirect
445. #2000C2×C137semidirect
446. #1999C2×C137semidirect
447. #1895C2×C137semidirect
448. #1879C2×C137semidirect
449. #1877C2×C137semidirect
450. #1874C2×C137semidirect
451. #1872C2×C137semidirect
452. #1870C2×C137semidirect
453. #1824C2×C137semidirect
550. #121D4×C137semidirect
563. C2×C4⋊C4D4×C137semidirect
611. C2×Q8#41×C137semidirect
638. C2×D4#41×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1372
C2×#449×C1372
C2×#417×C1372
#2407×C1372
#2024×C1372
#2023×C1372
#2000×C1372
#1999×C1372
#1895×C1372
#1879×C1372
#1877×C1372
#1874×C1372
#1872×C1372
#1870×C1372
#1824×C1372
#23972137