Finite Group Databasebeta

← C137×#22423 #46871809

Subgroups — C137×#22423 #46871809

Order 35072.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C137C211yesmaximal, characteristic
2C2×#435×C137C211yesmaximal, characteristic, complemented
3C2×#418×C137C211yesmaximal, characteristic, complemented
4C22×#102×C137C211yesmaximal, characteristic, complemented
5#2352×C137C211yesmaximal, characteristic, complemented
6#1982×C137C211yesmaximal, characteristic, complemented
7#1961×C137C211yesmaximal, characteristic, complemented
8#1895×C137C211yesmaximal, characteristic, complemented
9#1893×C137C211yesmaximal, characteristic, complemented
10#1875×C137C211yesmaximal, characteristic, complemented
11#1874×C137C211yesmaximal, characteristic, complemented
12#1804×C137C211yesmaximal, characteristic, complemented
13#1786×C137C211yesmaximal, characteristic, complemented
14#1786×C137C211yesmaximal, characteristic, complemented
15#1762×C137C211yesmaximal, characteristic, complemented
16C23×D4×C137—21no—
17C23×D4×C137C2211yescharacteristic
18C23×D4×C137C2211yescharacteristic
19C22×M16×C137C2211yescharacteristic, complemented
20C23×C8×C137C2211yescharacteristic, complemented
21D42×C137—24no—
22D42×C137C418yescomplemented
23C2×#127×C137C2211yescharacteristic
24C2×#121×C137—21no—
25C2×#121×C137C2211yescharacteristic
26C2×#121×C137C2211yescharacteristic
27C2×#120×C137—21no—
28C2×#120×C137—21no—
29C2×C4×D4×C137C2211yescharacteristic
30C2×C4×D4×C137C2211yescharacteristic
31C2×#117×C137C2211yescharacteristic, complemented
32C22×C4⋊C4×C137C2211yescharacteristic, complemented
33#435×C137—24no—
34C2×C4⋊C8×C137C2211yescharacteristic, complemented
35#418×C137—24no—
36C2×#102×C137—24no—
37C2×#102×C137C2211yescharacteristic
38C2×#102×C137C2211yescharacteristic
39C2×#102×C137C2211yescharacteristic
40C2×#102×C137C2211yescharacteristic
41C2×#102×C137C2211yescharacteristic, complemented
42C2×#102×C137C2211yescharacteristic, complemented
43C2×#102×C137C2211yescharacteristic, complemented
44C2×#102×C137C2211yescharacteristic, complemented
45C2×#102×C137C2211yescharacteristic, complemented
46C2×#102×C137C2211yescharacteristic, complemented
47C2×#102×C137C2211yescharacteristic, complemented
48C2×#102×C137C2211yescharacteristic, complemented
49C2×C22⋊C8×C137C2211yescharacteristic, complemented
50C2×C22⋊C8×C137C2211yescharacteristic, complemented
51C2×#97×C137C2211yescharacteristic, complemented
52#388×C137—21no—
53#387×C137—21no—
54#386×C137—21no—
55#382×C137C2211yescharacteristic, complemented
56#380×C137C2211yescharacteristic, complemented
57#380×C137C2211yescharacteristic, complemented
58C4×C4⋊C4×C137C2211yescharacteristic, complemented
59C4×C22⋊C4×C137—21no—
60#340×C137C2211yescharacteristic, complemented
61#340×C137C2211yescharacteristic, complemented
62#340×C137C2211yescharacteristic, complemented
63#340×C137C2211yescharacteristic, complemented
64C25×C137—21no—
65C25×C137—21no—
66C22×D4×C137—22no—
67C22×D4×C137—22no—
68C22×D4×C137—22no—
69C22×D4×C137—22no—
70C22×D4×C137—21no—
71C22×D4×C137—21no—
72C22×D4×C137—28no—
73C22×D4×C137—21no—
74C22×D4×C137—21no—
75C22×D4×C137—21no—
76C22×D4×C137—22no—
77C22×D4×C137—22no—
78C22×D4×C137—21no—
79C22×D4×C137—41no—
80C22×D4×C137—41no—
81C22×D4×C137—41no—
82C22×D4×C137—41no—
83C22×D4×C137—44no—
84C22×D4×C137—44no—
85C22×D4×C137C2×C414yes—
86C22×D4×C137C2×C414yescomplemented
87C22×D4×C137D411yescharacteristic
88C22×D4×C137C2311yescharacteristic
89C22×D4×C137C2311yescharacteristic
90C22×D4×C137C2311yescharacteristic
91C23×C4×C137—21no—
92C23×C4×C137—21no—
93C23×C4×C137C2311yescharacteristic
94C23×C4×C137C2311yescharacteristic
95C2×M16×C137—22no—
96C2×M16×C137—22no—
97C2×M16×C137—41no—
98C22×C8×C137—22no—
99C22×C8×C137—22no—
100C22×C8×C137—41no—
101C22×C8×C137C2311yescharacteristic
102C22×C8×C137C2311yescharacteristic
103C22×C8×C137C2311yescharacteristic
104C22×C8×C137C2311yescharacteristic
105#127×C137—22no—
106#127×C137C2×C414yescomplemented
107#121×C137—22no—
108#121×C137—22no—
109#121×C137—28no—
110#121×C137C2×C414yes—
111#121×C137C2×C414yescomplemented
112#120×C137—28no—
113#120×C137—28no—
114C4×D4×C137—22no—
115C4×D4×C137C2×C414yes—
116C4×D4×C137C2×C414yescomplemented
117C4×D4×C137D414yes—
118#117×C137—22no—
119#117×C137—41no—
120C2×C4⋊C4×C137—22no—
121C2×C4⋊C4×C137—21no—
122C2×C4⋊C4×C137—41no—
123C2×C4⋊C4×C137D411yescharacteristic
124C2×C4⋊C4×C137C2311yescharacteristic
125C2×C4⋊C4×C137C2311yescharacteristic
126C2×C4⋊C4×C137C2311yescharacteristic
127C2×C4⋊C4×C137C2311yescharacteristic
128C2×C4⋊C4×C137C2311yescharacteristic
129C2×C22⋊C4×C137—21no—
130C2×C22⋊C4×C137—21no—
131C2×C22⋊C4×C137—21no—
132C2×C22⋊C4×C137—21no—
133C2×C22⋊C4×C137—21no—
134C2×C22⋊C4×C137—21no—
135C2×C22⋊C4×C137D411yescharacteristic
136C2×C22⋊C4×C137D411yescharacteristic
137C2×C42×C137—21no—
138C2×C42×C137—21no—
139C2×C42×C137C2311yescharacteristic
140C4⋊C8×C137—22no—
141#102×C137—22no—
142#102×C137—22no—
143#102×C137—22no—
144#102×C137—22no—
145#102×C137—22no—
146#102×C137—22no—
147#102×C137—22no—
148#102×C137—41no—
149#102×C137—41no—
150#102×C137—41no—
151#102×C137—41no—
152#102×C137D414yescomplemented
153C22⋊C8×C137—22no—
154C22⋊C8×C137—22no—
155#97×C137—22no—
156#95×C137—21no—
157#95×C137—21no—
158#95×C137—21no—
159#95×C137—21no—
160#95×C137—21no—
161C24×C137—21no—
162C24×C137—21no—
163C24×C137—21no—
164C24×C137—24no—
165C24×C137—24no—
166C24×C137—42no—
167C24×C137—42no—
168C24×C137—42no—
169C24×C137—42no—
170C24×C137—42no—
171C24×C137—42no—
172C24×C137—42no—
173C24×C137—42no—
174C24×C137—81no—
175C24×C137—81no—
176C24×C137—81no—
177C24×C137—81no—
178C24×C137C2×D411yescharacteristic
179C24×C137C2×D411yescharacteristic
180C2×D4×C137—22no—
181C2×D4×C137—22no—
182C2×D4×C137—28no—
183C2×D4×C137—28no—
184C2×D4×C137—24no—
185C2×D4×C137—24no—
186C2×D4×C137—24no—
187C2×D4×C137—24no—
188C2×D4×C137—24no—
189C2×D4×C137—24no—
190C2×D4×C137—21no—
191C2×D4×C137—21no—
192C2×D4×C137—21no—
193C2×D4×C137—21no—
194C2×D4×C137—21no—
195C2×D4×C137—21no—
196C2×D4×C137—21no—
197C2×D4×C137—21no—
198C2×D4×C137—21no—
199C2×D4×C137—21no—
200C2×D4×C137—21no—
201C2×D4×C137—21no—
202C2×D4×C137—21no—
203C2×D4×C137—44no—
204C2×D4×C137—44no—
205C2×D4×C137—44no—
206C2×D4×C137—44no—
207C2×D4×C137—44no—
208C2×D4×C137—44no—
209C2×D4×C137—42no—
210C2×D4×C137—42no—
211C2×D4×C137—42no—
212C2×D4×C137—42no—
213C2×D4×C137—42no—
214C2×D4×C137—42no—
215C2×D4×C137—432no—
216C2×D4×C137—42no—
217C2×D4×C137—42no—
218C2×D4×C137—42no—
219C2×D4×C137—42no—
220C2×D4×C137—81no—
221C2×D4×C137—81no—
222C2×D4×C137C22⋊C414yes—
223C2×D4×C137C22×C412yes—
224C2×D4×C137C22×C412yes—
225C2×D4×C137C22×C412yes—
226C2×D4×C137C2×D412yes—
227C2×D4×C137#4112yes—
228C22×C4×C137—21no—
229C22×C4×C137—21no—
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—24no—
239C22×C4×C137—21no—
240C22×C4×C137—21no—
241C22×C4×C137—21no—
242C22×C4×C137—42no—
243C22×C4×C137—42no—
244C22×C4×C137—42no—
245C22×C4×C137—42no—
246C22×C4×C137—81no—
247C22×C4×C137C22×C412yes—
248C22×C4×C137C22×C412yes—
249C22×C4×C137C2×D411yescharacteristic
250C22×C4×C137C2×D411yescharacteristic
251C22×C4×C137C2×D411yescharacteristic
252C22×C4×C137C2×D411yescharacteristic
253C22×C4×C137C2×D412yes—
254C22×C4×C137C2×D412yes—
255C22×C4×C137C2411yescharacteristic
256M16×C137—44no—
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×C137—21no—
266C2×C8×C137—21no—
267C2×C8×C137—21no—
268C2×C8×C137—44no—
269C2×C8×C137C2×D412yescomplemented
270C4⋊C4×C137—21no—
271C4⋊C4×C137—21no—
272C4⋊C4×C137—21no—
273C4⋊C4×C137—21no—
274C4⋊C4×C137—21no—
275C4⋊C4×C137—21no—
276C4⋊C4×C137—21no—
277C4⋊C4×C137—21no—
278C4⋊C4×C137—42no—
279C4⋊C4×C137C22⋊C414yes—
280C4⋊C4×C137C22×C412yes—
281C4⋊C4×C137C2×D412yescomplemented
282C22⋊C4×C137—24no—
283C22⋊C4×C137—24no—
284C22⋊C4×C137—24no—
285C22⋊C4×C137—42no—
286C22⋊C4×C137—42no—
287C22⋊C4×C137—81no—
288C22⋊C4×C137C22⋊C414yes—
289C22⋊C4×C137C22⋊C414yes—
290C42×C137—42no—
291C42×C137—81no—
292C42×C137C22×C412yes—
293C42×C137C2×D412yes—
294C23×C137—21no—
295C23×C137—21no—
296C23×C137—21no—
297C23×C137—21no—
298C23×C137—22no—
299C23×C137—21no—
300C23×C137—22no—
301C23×C137—21no—
302C23×C137—22no—
303C23×C137—21no—
304C23×C137—21no—
305C23×C137—21no—
306C23×C137—21no—
307C23×C137—22no—
308C23×C137—22no—
309C23×C137—48no—
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—41no—
323C23×C137—41no—
324C23×C137—41no—
325C23×C137—41no—
326C23×C137—41no—
327C23×C137—41no—
328C23×C137—48no—
329C23×C137—84no—
330C23×C137—84no—
331C23×C137—84no—
332C23×C137—84no—
333C23×C137—84no—
334C23×C137—84no—
335C23×C137—84no—
336C23×C137—84no—
337C23×C137—84no—
338C23×C137—84no—
339C23×C137C2×C22⋊C412yes—
340C23×C137C2×C22⋊C412yes—
341C23×C137AGL(1,ℤ/8)12yes—
342C23×C137AGL(1,ℤ/8)12yes—
343C23×C137C22×D411yescharacteristic
344D4×C137—28no—
345D4×C137—22no—
346D4×C137—22no—
347D4×C137—22no—
348D4×C137—22no—
349D4×C137—22no—
350D4×C137—22no—
351D4×C137—22no—
352D4×C137—48no—
353D4×C137—48no—
354D4×C137—48no—
355D4×C137—48no—
356D4×C137—48no—
357D4×C137—41no—
358D4×C137—41no—
359D4×C137—41no—
360D4×C137—41no—
361D4×C137—84no—
362D4×C137C4×D414yes—
363C2×C4×C137—21no—
364C2×C4×C137—21no—
365C2×C4×C137—21no—
366C2×C4×C137—21no—
367C2×C4×C137—21no—
368C2×C4×C137—21no—
369C2×C4×C137—21no—
370C2×C4×C137—21no—
371C2×C4×C137—22no—
372C2×C4×C137—22no—
373C2×C4×C137—22no—
374C2×C4×C137—22no—
375C2×C4×C137—22no—
376C2×C4×C137—22no—
377C2×C4×C137—22no—
378C2×C4×C137—22no—
379C2×C4×C137—22no—
380C2×C4×C137—22no—
381C2×C4×C137—48no—
382C2×C4×C137—41no—
383C2×C4×C137—41no—
384C2×C4×C137—41no—
385C2×C4×C137—41no—
386C2×C4×C137—41no—
387C2×C4×C137—41no—
388C2×C4×C137—41no—
389C2×C4×C137—41no—
390C2×C4×C137—41no—
391C2×C4×C137—41no—
392C2×C4×C137—41no—
393C2×C4×C137—41no—
394C2×C4×C137—41no—
395C2×C4×C137—84no—
396C2×C4×C137C2×C22⋊C412yes—
397C2×C4×C137C2×C22⋊C412yes—
398C2×C4×C137C2×C22⋊C412yes—
399C2×C4×C137C2×C22⋊C412yes—
400C2×C4×C137C23×C411yescharacteristic
401C2×C4×C137C22×D411yescharacteristic
402C2×C4×C137C22×D411yescharacteristic
403C2×C4×C137C2×#4111yescharacteristic
404C2×C4×C137H(5,𝔽2)11yescharacteristic
405C2×C4×C137H(5,𝔽2)11yescharacteristic
406C8×C137—22no—
407C8×C137—41no—
408C8×C137—41no—
409C8×C137—41no—
410C22×C137—22no—
411C22×C137—22no—
412C22×C137—22no—
413C22×C137—22no—
414C22×C137—22no—
415C22×C137—22no—
416C22×C137—22no—
417C22×C137—24no—
418C22×C137—22no—
419C22×C137—22no—
420C22×C137—42no—
421C22×C137—42no—
422C22×C137—41no—
423C22×C137—42no—
424C22×C137—41no—
425C22×C137—42no—
426C22×C137—41no—
427C22×C137—42no—
428C22×C137—41no—
429C22×C137—42no—
430C22×C137—42no—
431C22×C137—42no—
432C22×C137—42no—
433C22×C137—42no—
434C22×C137—42no—
435C22×C137—42no—
436C22×C137—816no—
437C22×C137—816no—
438C22×C137—81no—
439C22×C137—81no—
440C22×C137—81no—
441C22×C137—81no—
442C22×C137—81no—
443C22×C137—81no—
444C22×C137—81no—
445C22×C137—81no—
446C22×C137#41814yescomplemented
447C22×C137C22×C22⋊C411yescharacteristic
448C22×C137D4211yescharacteristic
449C22×C137#54611yescharacteristic
450C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
452C22×C137#57611yescharacteristic
453C22×C137#57711yescharacteristic
454C4×C137—22no—
455C4×C137—22no—
456C4×C137—22no—
457C4×C137—22no—
458C4×C137—42no—
459C4×C137—42no—
460C4×C137—81no—
461C4×C137—81no—
462C4×C137—81no—
463C4×C137C2×C4×D411yescharacteristic
464C4×C137#51811yescharacteristic
465C4×C137D4211yescharacteristic
466C4×C137#54611yescharacteristic
467C2×C137—24no—
468C2×C137—42no—
469C2×C137—44no—
470C2×C137—82no—
471C2×C137—82no—
472C2×C137D4×C22⋊C411yescharacteristic
473C2×C137C2×#41811yescharacteristic
474C2×C137#289711yescharacteristic
475C2×C137#326411yescharacteristic
476C2×C137#326511yescharacteristic
477C2×C137#331011yescharacteristic
478C2×C137#331811yescharacteristic
479#22423C13711yesmaximal, characteristic, direct product factor, Sylow
480C137#2242311yescharacteristic, direct product factor, Sylow
481C2×D42C2×C13711yescharacteristic
482C2×#435C2×C13711yescharacteristic, complemented
483C2×#418C2×C13711yescharacteristic, complemented
484C22×#102C2×C13711yescharacteristic, complemented
485#2352C2×C13711yescharacteristic, complemented
486#1982C2×C13711yescharacteristic, complemented
487#1961C2×C13711yescharacteristic, complemented
488#1895C2×C13711yescharacteristic, complemented
489#1893C2×C13711yescharacteristic, complemented
490#1875C2×C13711yescharacteristic, complemented
491#1874C2×C13711yescharacteristic, complemented
492#1804C2×C13711yescharacteristic, complemented
493#1786C2×C13711yescharacteristic, complemented
494#1786C2×C13711yescharacteristic, complemented
495#1762C2×C13711yescharacteristic, complemented
496C23×D4—21no—
497C23×D4C22×C13711yescharacteristic
498C23×D4C22×C13711yescharacteristic
499C22×M16C22×C13711yescharacteristic, complemented
500C23×C8C22×C13711yescharacteristic, complemented
501D42—24no—
502D42C4×C13718yescomplemented
503C2×#127C22×C13711yescharacteristic
504C2×#121—21no—
505C2×#121C22×C13711yescharacteristic
506C2×#121C22×C13711yescharacteristic
507C2×#120—21no—
508C2×#120—21no—
509C2×C4×D4C22×C13711yescharacteristic
510C2×C4×D4C22×C13711yescharacteristic
511C2×#117C22×C13711yescharacteristic, complemented
512C22×C4⋊C4C22×C13711yescharacteristic, complemented
513#435—24no—
514C2×C4⋊C8C22×C13711yescharacteristic, complemented
515#418—24no—
516C2×#102—24no—
517C2×#102C22×C13711yescharacteristic
518C2×#102C22×C13711yescharacteristic
519C2×#102C22×C13711yescharacteristic
520C2×#102C22×C13711yescharacteristic
521C2×#102C22×C13711yescharacteristic, complemented
522C2×#102C22×C13711yescharacteristic, complemented
523C2×#102C22×C13711yescharacteristic, complemented
524C2×#102C22×C13711yescharacteristic, complemented
525C2×#102C22×C13711yescharacteristic, complemented
526C2×#102C22×C13711yescharacteristic, complemented
527C2×#102C22×C13711yescharacteristic, complemented
528C2×#102C22×C13711yescharacteristic, complemented
529C2×C22⋊C8C22×C13711yescharacteristic, complemented
530C2×C22⋊C8C22×C13711yescharacteristic, complemented
531C2×#97C22×C13711yescharacteristic, complemented
532#388—21no—
533#387—21no—
534#386—21no—
535#382C22×C13711yescharacteristic, complemented
536#380C22×C13711yescharacteristic, complemented
537#380C22×C13711yescharacteristic, complemented
538C4×C4⋊C4C22×C13711yescharacteristic, complemented
539C4×C22⋊C4—21no—
540#340C22×C13711yescharacteristic, complemented
541#340C22×C13711yescharacteristic, complemented
542#340C22×C13711yescharacteristic, complemented
543#340C22×C13711yescharacteristic, complemented
544C25—21no—
545C25—21no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—28no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—21no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4—44no—
564C22×D4—44no—
565C22×D4C2×C4×C13714yes—
566C22×D4C2×C4×C13714yescomplemented
567C22×D4D4×C13711yescharacteristic
568C22×D4C23×C13711yescharacteristic
569C22×D4C23×C13711yescharacteristic
570C22×D4C23×C13711yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4C23×C13711yescharacteristic
574C23×C4C23×C13711yescharacteristic
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C23×C13711yescharacteristic
582C22×C8C23×C13711yescharacteristic
583C22×C8C23×C13711yescharacteristic
584C22×C8C23×C13711yescharacteristic
585#127—22no—
586#127C2×C4×C13714yescomplemented
587#121—22no—
588#121—22no—
589#121—28no—
590#121C2×C4×C13714yes—
591#121C2×C4×C13714yescomplemented
592#120—28no—
593#120—28no—
594C4×D4—22no—
595C4×D4C2×C4×C13714yes—
596C4×D4C2×C4×C13714yescomplemented
597C4×D4D4×C13714yes—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4D4×C13711yescharacteristic
604C2×C4⋊C4C23×C13711yescharacteristic
605C2×C4⋊C4C23×C13711yescharacteristic
606C2×C4⋊C4C23×C13711yescharacteristic
607C2×C4⋊C4C23×C13711yescharacteristic
608C2×C4⋊C4C23×C13711yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4D4×C13711yescharacteristic
616C2×C22⋊C4D4×C13711yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C23×C13711yescharacteristic
620C4⋊C8—22no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630#102—41no—
631#102—41no—
632#102D4×C13714yescomplemented
633C22⋊C8—22no—
634C22⋊C8—22no—
635#97—22no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×D4×C13711yescharacteristic
659C24C2×D4×C13711yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊C4×C13714yes—
703C2×D4C22×C4×C13712yes—
704C2×D4C22×C4×C13712yes—
705C2×D4C22×C4×C13712yes—
706C2×D4C2×D4×C13712yes—
707C2×D4#41×C13712yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—81no—
727C22×C4C22×C4×C13712yes—
728C22×C4C22×C4×C13712yes—
729C22×C4C2×D4×C13711yescharacteristic
730C22×C4C2×D4×C13711yescharacteristic
731C22×C4C2×D4×C13711yescharacteristic
732C22×C4C2×D4×C13711yescharacteristic
733C22×C4C2×D4×C13712yes—
734C22×C4C2×D4×C13712yes—
735C22×C4C24×C13711yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—44no—
749C2×C8C2×D4×C13712yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—42no—
759C4⋊C4C22⋊C4×C13714yes—
760C4⋊C4C22×C4×C13712yes—
761C4⋊C4C2×D4×C13712yescomplemented
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4C22⋊C4×C13714yes—
769C22⋊C4C22⋊C4×C13714yes—
770C42—42no—
771C42—81no—
772C42C22×C4×C13712yes—
773C42C2×D4×C13712yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C22⋊C4×C13712yes—
820C23C2×C22⋊C4×C13712yes—
821C23AGL(1,ℤ/8)×C13712yes—
822C23AGL(1,ℤ/8)×C13712yes—
823C23C22×D4×C13711yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4C4×D4×C13714yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—84no—
876C2×C4C2×C22⋊C4×C13712yes—
877C2×C4C2×C22⋊C4×C13712yes—
878C2×C4C2×C22⋊C4×C13712yes—
879C2×C4C2×C22⋊C4×C13712yes—
880C2×C4C23×C4×C13711yescharacteristic
881C2×C4C22×D4×C13711yescharacteristic
882C2×C4C22×D4×C13711yescharacteristic
883C2×C4C2×#41×C13711yescharacteristic
884C2×C4H(5,𝔽2)×C13711yescharacteristic
885C2×C4H(5,𝔽2)×C13711yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22#418×C13714yescomplemented
927C22C22×C22⋊C4×C13711yescharacteristic
928C22D42×C13711yescharacteristic
929C22#546×C13711yescharacteristic
930C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
931C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
932C22#576×C13711yescharacteristic
933C22#577×C13711yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×C4×D4×C13711yescharacteristic
944C4#518×C13711yescharacteristic
945C4D42×C13711yescharacteristic
946C4#546×C13711yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊C4×C13711yescharacteristic
953C2C2×#418×C13711yescharacteristic
954C2#2897×C13711yescharacteristic
955C2#3264×C13711yescharacteristic
956C2#3265×C13711yescharacteristic
957C2#3310×C13711yescharacteristic
958C2#3318×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutatorC2×C4C23×C4×C137
Frattini, cosocleC22×C4C24×C137
prime radicalC2×D42×C137C2
LCSG ▷ C2×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×#435×C137C2semidirect
3. C2×#418×C137C2semidirect
4. C22×#102×C137C2semidirect
5. #2352×C137C2semidirect
6. #1982×C137C2semidirect
7. #1961×C137C2semidirect
8. #1895×C137C2semidirect
9. #1893×C137C2semidirect
10. #1875×C137C2semidirect
11. #1874×C137C2semidirect
12. #1804×C137C2semidirect
13. #1786×C137C2semidirect
14. #1786×C137C2semidirect
15. #1762×C137C2semidirect
19. C22×M16×C137C22semidirect
20. C23×C8×C137C22semidirect
22. D42×C137C4semidirect
31. C2×#117×C137C22semidirect
32. C22×C4⋊C4×C137C22semidirect
34. C2×C4⋊C8×C137C22semidirect
41. C2×#102×C137C22semidirect
42. C2×#102×C137C22semidirect
43. C2×#102×C137C22semidirect
44. C2×#102×C137C22semidirect
45. C2×#102×C137C22semidirect
46. C2×#102×C137C22semidirect
47. C2×#102×C137C22semidirect
48. C2×#102×C137C22semidirect
49. C2×C22⋊C8×C137C22semidirect
50. C2×C22⋊C8×C137C22semidirect
51. C2×#97×C137C22semidirect
55. #382×C137C22semidirect
56. #380×C137C22semidirect
57. #380×C137C22semidirect
58. C4×C4⋊C4×C137C22semidirect
60. #340×C137C22semidirect
61. #340×C137C22semidirect
62. #340×C137C22semidirect
63. #340×C137C22semidirect
86. C22×D4×C137C2×C4semidirect
106. #127×C137C2×C4semidirect
111. #121×C137C2×C4semidirect
116. C4×D4×C137C2×C4semidirect
152. #102×C137D4semidirect
269. C2×C8×C137C2×D4semidirect
281. C4⋊C4×C137C2×D4semidirect
446. C22×C137#418semidirect
479. #22423C137direct (N × H)
480. C137#22423direct (N × H)
482. C2×#435C2×C137semidirect
483. C2×#418C2×C137semidirect
484. C22×#102C2×C137semidirect
485. #2352C2×C137semidirect
486. #1982C2×C137semidirect
487. #1961C2×C137semidirect
488. #1895C2×C137semidirect
489. #1893C2×C137semidirect
490. #1875C2×C137semidirect
491. #1874C2×C137semidirect
492. #1804C2×C137semidirect
493. #1786C2×C137semidirect
494. #1786C2×C137semidirect
495. #1762C2×C137semidirect
499. C22×M16C22×C137semidirect
500. C23×C8C22×C137semidirect
502. D42C4×C137semidirect
511. C2×#117C22×C137semidirect
512. C22×C4⋊C4C22×C137semidirect
514. C2×C4⋊C8C22×C137semidirect
521. C2×#102C22×C137semidirect
522. C2×#102C22×C137semidirect
523. C2×#102C22×C137semidirect
524. C2×#102C22×C137semidirect
525. C2×#102C22×C137semidirect
526. C2×#102C22×C137semidirect
527. C2×#102C22×C137semidirect
528. C2×#102C22×C137semidirect
529. C2×C22⋊C8C22×C137semidirect
530. C2×C22⋊C8C22×C137semidirect
531. C2×#97C22×C137semidirect
535. #382C22×C137semidirect
536. #380C22×C137semidirect
537. #380C22×C137semidirect
538. C4×C4⋊C4C22×C137semidirect
540. #340C22×C137semidirect
541. #340C22×C137semidirect
542. #340C22×C137semidirect
543. #340C22×C137semidirect
566. C22×D4C2×C4×C137semidirect
586. #127C2×C4×C137semidirect
591. #121C2×C4×C137semidirect
596. C4×D4C2×C4×C137semidirect
632. #102D4×C137semidirect
749. C2×C8C2×D4×C137semidirect
761. C4⋊C4C2×D4×C137semidirect
926. C22#418×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×#435×C1372
C2×#418×C1372
C22×#102×C1372
#2352×C1372
#1982×C1372
#1961×C1372
#1895×C1372
#1893×C1372
#1875×C1372
#1874×C1372
#1804×C1372
#1786×C1372
#1762×C1372
#22423137