Finite Group Databasebeta

← C137×#22419 #46871805

Subgroups — C137×#22419 #46871805

Order 35072.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C137C211yesmaximal, characteristic
2C2×#435×C137C211yesmaximal, characteristic, complemented
3C2×#417×C137C211yesmaximal, characteristic, complemented
4C22×#102×C137C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C137C211yesmaximal, characteristic, complemented
6#1983×C137C211yesmaximal, characteristic, complemented
7#1959×C137C211yesmaximal, characteristic, complemented
8#1895×C137C211yesmaximal, characteristic, complemented
9#1892×C137C211yesmaximal, characteristic, complemented
10#1874×C137C211yesmaximal, characteristic, complemented
11#1872×C137C211yesmaximal, characteristic, complemented
12#1802×C137C211yesmaximal, characteristic, complemented
13#1788×C137C211yesmaximal, characteristic, complemented
14#1786×C137C211yesmaximal, characteristic, complemented
15#1762×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C22×M16×C137C2211yescharacteristic, complemented
19C23×C8×C137C2211yescharacteristic
20#546×C137—24no—
21#546×C137C418yescomplemented
22C2×#124×C137C2211yescharacteristic
23C2×#123×C137—21no—
24C2×C22⋊Q8×C137C2211yescharacteristic
25C2×#121×C137—21no—
26C2×#121×C137C2211yescharacteristic
27C2×#120×C137—21no—
28C2×C4×D4×C137—21no—
29C2×C4×D4×C137C2211yescharacteristic
30C2×C4×D4×C137C2211yescharacteristic
31C22×C4⋊C4×C137C2211yescharacteristic
32C22×C4⋊C4×C137C2211yescharacteristic, complemented
33C22×C22⋊C4×C137—21no—
34#435×C137—24no—
35C2×C4⋊C8×C137C2211yescharacteristic, complemented
36#417×C137—24no—
37C2×#103×C137C2211yescharacteristic, complemented
38C2×#103×C137C2211yescharacteristic, complemented
39C2×#103×C137C2211yescharacteristic, complemented
40C2×#103×C137C2211yescharacteristic, complemented
41C2×#102×C137—24no—
42C2×#102×C137C2211yescharacteristic
43C2×#102×C137C2211yescharacteristic
44C2×#102×C137C2211yescharacteristic
45C2×#102×C137C2211yescharacteristic
46C2×#102×C137C2211yescharacteristic
47C2×#102×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic
49C2×#102×C137C2211yescharacteristic
50C2×C22⋊C8×C137C2211yescharacteristic
51C2×C22⋊C8×C137C2211yescharacteristic, complemented
52C2×#97×C137C2211yescharacteristic, complemented
53#389×C137—21no—
54#385×C137—21no—
55#385×C137—21no—
56#384×C137C2211yescharacteristic, complemented
57#380×C137C2211yescharacteristic
58#380×C137C2211yescharacteristic, complemented
59C4×C4⋊C4×C137C2211yescharacteristic, complemented
60#340×C137C2211yescharacteristic, complemented
61#340×C137C2211yescharacteristic, complemented
62#340×C137C2211yescharacteristic, complemented
63#340×C137C2211yescharacteristic, complemented
64C25×C137—21no—
65C2×#41×C137—22no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—41no—
69C2×#41×C137—41no—
70C2×#41×C137C2×C414yescomplemented
71C22×Q8×C137C2311yescharacteristic
72C22×D4×C137—22no—
73C22×D4×C137—22no—
74C22×D4×C137—21no—
75C22×D4×C137—21no—
76C22×D4×C137—21no—
77C22×D4×C137—22no—
78C22×D4×C137—41no—
79C22×D4×C137—41no—
80C22×D4×C137C2×C414yescomplemented
81C22×D4×C137D411yescharacteristic
82C22×D4×C137C2311yescharacteristic
83C22×D4×C137C2311yescharacteristic
84C23×C4×C137—21no—
85C23×C4×C137—21no—
86C23×C4×C137—21no—
87C23×C4×C137—21no—
88C23×C4×C137C2311yescharacteristic
89C23×C4×C137C2311yescharacteristic
90C2×M16×C137—22no—
91C2×M16×C137—22no—
92C2×M16×C137—41no—
93C22×C8×C137—22no—
94C22×C8×C137—22no—
95C22×C8×C137—41no—
96C22×C8×C137C2311yescharacteristic
97C22×C8×C137C2311yescharacteristic
98C22×C8×C137C2311yescharacteristic
99C22×C8×C137C2311yescharacteristic
100#124×C137—22no—
101#124×C137C2×C414yescomplemented
102#123×C137—28no—
103C22⋊Q8×C137—22no—
104C22⋊Q8×C137C2×C414yescomplemented
105#121×C137—22no—
106#121×C137—28no—
107#121×C137C2×C414yescomplemented
108#120×C137—28no—
109C4×D4×C137—22no—
110C4×D4×C137—44no—
111C4×D4×C137C2×C414yes—
112C4×D4×C137C2×C414yescomplemented
113C4×D4×C137D414yes—
114C2×C4⋊C4×C137—21no—
115C2×C4⋊C4×C137—22no—
116C2×C4⋊C4×C137—22no—
117C2×C4⋊C4×C137—21no—
118C2×C4⋊C4×C137—21no—
119C2×C4⋊C4×C137—21no—
120C2×C4⋊C4×C137—21no—
121C2×C4⋊C4×C137—41no—
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—28no—
135C2×C22⋊C4×C137—21no—
136C2×C22⋊C4×C137—21no—
137C2×C22⋊C4×C137D411yescharacteristic
138C2×C22⋊C4×C137D411yescharacteristic
139C2×C42×C137—21no—
140C2×C42×C137C2311yescharacteristic
141C4⋊C8×C137—22no—
142#103×C137—22no—
143#103×C137—22no—
144#103×C137—41no—
145#103×C137—41no—
146#102×C137—22no—
147#102×C137—22no—
148#102×C137—22no—
149#102×C137—22no—
150#102×C137—22no—
151#102×C137—41no—
152#102×C137—41no—
153#102×C137D414yescomplemented
154C22⋊C8×C137—22no—
155C22⋊C8×C137—22no—
156#97×C137—22no—
157#95×C137—21no—
158#95×C137—21no—
159#95×C137—21no—
160C24×C137—21no—
161C24×C137—21no—
162C24×C137—24no—
163C24×C137—42no—
164C24×C137—42no—
165C24×C137—42no—
166C24×C137—42no—
167C24×C137—81no—
168C24×C137—81no—
169C24×C137C2×D411yescharacteristic
170C24×C137C2×D411yescharacteristic
171#41×C137—28no—
172#41×C137—44no—
173#41×C137—44no—
174#41×C137—44no—
175C2×Q8×C137—21no—
176C2×Q8×C137—21no—
177C2×Q8×C137—21no—
178C2×Q8×C137—21no—
179C2×Q8×C137—21no—
180C2×Q8×C137C22×C412yes—
181C2×D4×C137—22no—
182C2×D4×C137—22no—
183C2×D4×C137—28no—
184C2×D4×C137—24no—
185C2×D4×C137—24no—
186C2×D4×C137—24no—
187C2×D4×C137—21no—
188C2×D4×C137—21no—
189C2×D4×C137—21no—
190C2×D4×C137—21no—
191C2×D4×C137—21no—
192C2×D4×C137—21no—
193C2×D4×C137—21no—
194C2×D4×C137—21no—
195C2×D4×C137—44no—
196C2×D4×C137—44no—
197C2×D4×C137—44no—
198C2×D4×C137—42no—
199C2×D4×C137—42no—
200C2×D4×C137—42no—
201C2×D4×C137—42no—
202C2×D4×C137—81no—
203C2×D4×C137—81no—
204C2×D4×C137C22⋊C414yes—
205C2×D4×C137C22×C412yes—
206C2×D4×C137C22×C412yes—
207C2×D4×C137C2×D412yes—
208C2×D4×C137#4112yes—
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—24no—
221C22×C4×C137—24no—
222C22×C4×C137—21no—
223C22×C4×C137—21no—
224C22×C4×C137—21no—
225C22×C4×C137—42no—
226C22×C4×C137—42no—
227C22×C4×C137—42no—
228C22×C4×C137—42no—
229C22×C4×C137—42no—
230C22×C4×C137—42no—
231C22×C4×C137—81no—
232C22×C4×C137—81no—
233C22×C4×C137—81no—
234C22×C4×C137—81no—
235C22×C4×C137C22×C412yes—
236C22×C4×C137C22×C412yes—
237C22×C4×C137C2×D411yescharacteristic
238C22×C4×C137C2×D411yescharacteristic
239C22×C4×C137C2×D411yescharacteristic
240C22×C4×C137C2×D411yescharacteristic
241C22×C4×C137C2×D412yes—
242C22×C4×C137C2×D412yes—
243C22×C4×C137C2411yescharacteristic
244M16×C137—44no—
245C2×C8×C137—21no—
246C2×C8×C137—21no—
247C2×C8×C137—21no—
248C2×C8×C137—21no—
249C2×C8×C137—21no—
250C2×C8×C137—21no—
251C2×C8×C137—21no—
252C2×C8×C137—21no—
253C2×C8×C137—21no—
254C2×C8×C137—21no—
255C2×C8×C137—21no—
256C2×C8×C137—44no—
257C2×C8×C137C2×D412yes—
258C4⋊C4×C137—24no—
259C4⋊C4×C137—21no—
260C4⋊C4×C137—21no—
261C4⋊C4×C137—21no—
262C4⋊C4×C137—21no—
263C4⋊C4×C137—21no—
264C4⋊C4×C137—21no—
265C4⋊C4×C137—21no—
266C4⋊C4×C137—21no—
267C4⋊C4×C137—42no—
268C4⋊C4×C137—42no—
269C4⋊C4×C137—42no—
270C4⋊C4×C137—81no—
271C4⋊C4×C137C22⋊C414yes—
272C4⋊C4×C137C22×C412yes—
273C4⋊C4×C137C2×D412yes—
274C22⋊C4×C137—24no—
275C22⋊C4×C137—24no—
276C22⋊C4×C137—24no—
277C22⋊C4×C137—24no—
278C22⋊C4×C137—24no—
279C22⋊C4×C137—42no—
280C22⋊C4×C137—42no—
281C22⋊C4×C137C22⋊C414yes—
282C22⋊C4×C137C22⋊C414yes—
283C42×C137—42no—
284C42×C137C22×C412yes—
285C42×C137C2×D412yes—
286C23×C137—21no—
287C23×C137—21no—
288C23×C137—21no—
289C23×C137—21no—
290C23×C137—22no—
291C23×C137—21no—
292C23×C137—22no—
293C23×C137—21no—
294C23×C137—22no—
295C23×C137—21no—
296C23×C137—21no—
297C23×C137—21no—
298C23×C137—21no—
299C23×C137—22no—
300C23×C137—48no—
301C23×C137—41no—
302C23×C137—41no—
303C23×C137—41no—
304C23×C137—41no—
305C23×C137—41no—
306C23×C137—41no—
307C23×C137—41no—
308C23×C137—41no—
309C23×C137—41no—
310C23×C137—41no—
311C23×C137—48no—
312C23×C137—84no—
313C23×C137—84no—
314C23×C137—84no—
315C23×C137—84no—
316C23×C137—84no—
317C23×C137C2×C22⋊C412yes—
318C23×C137C2×C22⋊C412yes—
319C23×C137AGL(1,ℤ/8)12yes—
320C23×C137#13712yes—
321C23×C137C22×D411yescharacteristic
322Q8×C137—22no—
323Q8×C137—22no—
324Q8×C137—41no—
325Q8×C137—41no—
326D4×C137—28no—
327D4×C137—22no—
328D4×C137—22no—
329D4×C137—22no—
330D4×C137—22no—
331D4×C137—22no—
332D4×C137—48no—
333D4×C137—48no—
334D4×C137—41no—
335D4×C137—41no—
336D4×C137—84no—
337D4×C137C4×D414yescomplemented
338C2×C4×C137—21no—
339C2×C4×C137—21no—
340C2×C4×C137—21no—
341C2×C4×C137—21no—
342C2×C4×C137—21no—
343C2×C4×C137—21no—
344C2×C4×C137—21no—
345C2×C4×C137—21no—
346C2×C4×C137—22no—
347C2×C4×C137—22no—
348C2×C4×C137—22no—
349C2×C4×C137—22no—
350C2×C4×C137—22no—
351C2×C4×C137—22no—
352C2×C4×C137—22no—
353C2×C4×C137—22no—
354C2×C4×C137—22no—
355C2×C4×C137—22no—
356C2×C4×C137—22no—
357C2×C4×C137—48no—
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—41no—
366C2×C4×C137—41no—
367C2×C4×C137—41no—
368C2×C4×C137—41no—
369C2×C4×C137—41no—
370C2×C4×C137—41no—
371C2×C4×C137—41no—
372C2×C4×C137—41no—
373C2×C4×C137—84no—
374C2×C4×C137—84no—
375C2×C4×C137—84no—
376C2×C4×C137C2×C22⋊C412yes—
377C2×C4×C137C2×C22⋊C412yes—
378C2×C4×C137C2×C22⋊C412yes—
379C2×C4×C137C2×C22⋊C412yes—
380C2×C4×C137C23×C411yescharacteristic
381C2×C4×C137C22×D411yescharacteristic
382C2×C4×C137C22×D411yescharacteristic
383C2×C4×C137C2×#4111yescharacteristic
384C2×C4×C137H(5,𝔽2)11yescharacteristic
385C2×C4×C137H(5,𝔽2)11yescharacteristic
386C8×C137—22no—
387C8×C137—41no—
388C8×C137—41no—
389C8×C137—41no—
390C22×C137—22no—
391C22×C137—22no—
392C22×C137—22no—
393C22×C137—22no—
394C22×C137—22no—
395C22×C137—22no—
396C22×C137—22no—
397C22×C137—24no—
398C22×C137—22no—
399C22×C137—22no—
400C22×C137—42no—
401C22×C137—42no—
402C22×C137—41no—
403C22×C137—42no—
404C22×C137—41no—
405C22×C137—42no—
406C22×C137—41no—
407C22×C137—42no—
408C22×C137—41no—
409C22×C137—42no—
410C22×C137—42no—
411C22×C137—42no—
412C22×C137—42no—
413C22×C137—816no—
414C22×C137—81no—
415C22×C137—81no—
416C22×C137—81no—
417C22×C137—81no—
418C22×C137#41714yescomplemented
419C22×C137C22×C22⋊C411yescharacteristic
420C22×C137D4211yescharacteristic
421C22×C137#54611yescharacteristic
422C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C137C2×#13711yescharacteristic
424C22×C137#57611yescharacteristic
425C22×C137#57711yescharacteristic
426C4×C137—22no—
427C4×C137—22no—
428C4×C137—22no—
429C4×C137—22no—
430C4×C137—42no—
431C4×C137—42no—
432C4×C137—42no—
433C4×C137—81no—
434C4×C137—81no—
435C4×C137—81no—
436C4×C137C2×C4×D411yescharacteristic
437C4×C137#51811yescharacteristic
438C4×C137D4211yescharacteristic
439C4×C137#54611yescharacteristic
440C2×C137—24no—
441C2×C137—42no—
442C2×C137—44no—
443C2×C137—82no—
444C2×C137D4×C22⋊C411yescharacteristic
445C2×C137C2×#41711yescharacteristic
446C2×C137#289711yescharacteristic
447C2×C137#326411yescharacteristic
448C2×C137#326611yescharacteristic
449C2×C137#330611yescharacteristic
450C2×C137#331411yescharacteristic
451#22419C13711yesmaximal, characteristic, direct product factor, Sylow
452C137#2241911yescharacteristic, direct product factor, Sylow
453C2×#546C2×C13711yescharacteristic
454C2×#435C2×C13711yescharacteristic, complemented
455C2×#417C2×C13711yescharacteristic, complemented
456C22×#102C2×C13711yescharacteristic, complemented
457D4×C4⋊C4C2×C13711yescharacteristic, complemented
458#1983C2×C13711yescharacteristic, complemented
459#1959C2×C13711yescharacteristic, complemented
460#1895C2×C13711yescharacteristic, complemented
461#1892C2×C13711yescharacteristic, complemented
462#1874C2×C13711yescharacteristic, complemented
463#1872C2×C13711yescharacteristic, complemented
464#1802C2×C13711yescharacteristic, complemented
465#1788C2×C13711yescharacteristic, complemented
466#1786C2×C13711yescharacteristic, complemented
467#1762C2×C13711yescharacteristic, complemented
468C22×#41C22×C13711yescharacteristic
469C23×D4C22×C13711yescharacteristic
470C22×M16C22×C13711yescharacteristic, complemented
471C23×C8C22×C13711yescharacteristic
472#546—24no—
473#546C4×C13718yescomplemented
474C2×#124C22×C13711yescharacteristic
475C2×#123—21no—
476C2×C22⋊Q8C22×C13711yescharacteristic
477C2×#121—21no—
478C2×#121C22×C13711yescharacteristic
479C2×#120—21no—
480C2×C4×D4—21no—
481C2×C4×D4C22×C13711yescharacteristic
482C2×C4×D4C22×C13711yescharacteristic
483C22×C4⋊C4C22×C13711yescharacteristic
484C22×C4⋊C4C22×C13711yescharacteristic, complemented
485C22×C22⋊C4—21no—
486#435—24no—
487C2×C4⋊C8C22×C13711yescharacteristic, complemented
488#417—24no—
489C2×#103C22×C13711yescharacteristic, complemented
490C2×#103C22×C13711yescharacteristic, complemented
491C2×#103C22×C13711yescharacteristic, complemented
492C2×#103C22×C13711yescharacteristic, complemented
493C2×#102—24no—
494C2×#102C22×C13711yescharacteristic
495C2×#102C22×C13711yescharacteristic
496C2×#102C22×C13711yescharacteristic
497C2×#102C22×C13711yescharacteristic
498C2×#102C22×C13711yescharacteristic
499C2×#102C22×C13711yescharacteristic
500C2×#102C22×C13711yescharacteristic
501C2×#102C22×C13711yescharacteristic
502C2×C22⋊C8C22×C13711yescharacteristic
503C2×C22⋊C8C22×C13711yescharacteristic, complemented
504C2×#97C22×C13711yescharacteristic, complemented
505#389—21no—
506#385—21no—
507#385—21no—
508#384C22×C13711yescharacteristic, complemented
509#380C22×C13711yescharacteristic
510#380C22×C13711yescharacteristic, complemented
511C4×C4⋊C4C22×C13711yescharacteristic, complemented
512#340C22×C13711yescharacteristic, complemented
513#340C22×C13711yescharacteristic, complemented
514#340C22×C13711yescharacteristic, complemented
515#340C22×C13711yescharacteristic, complemented
516C25—21no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—41no—
521C2×#41—41no—
522C2×#41C2×C4×C13714yescomplemented
523C22×Q8C23×C13711yescharacteristic
524C22×D4—22no—
525C22×D4—22no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4C2×C4×C13714yescomplemented
533C22×D4D4×C13711yescharacteristic
534C22×D4C23×C13711yescharacteristic
535C22×D4C23×C13711yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C23×C13711yescharacteristic
541C23×C4C23×C13711yescharacteristic
542C2×M16—22no—
543C2×M16—22no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—22no—
547C22×C8—41no—
548C22×C8C23×C13711yescharacteristic
549C22×C8C23×C13711yescharacteristic
550C22×C8C23×C13711yescharacteristic
551C22×C8C23×C13711yescharacteristic
552#124—22no—
553#124C2×C4×C13714yescomplemented
554#123—28no—
555C22⋊Q8—22no—
556C22⋊Q8C2×C4×C13714yescomplemented
557#121—22no—
558#121—28no—
559#121C2×C4×C13714yescomplemented
560#120—28no—
561C4×D4—22no—
562C4×D4—44no—
563C4×D4C2×C4×C13714yes—
564C4×D4C2×C4×C13714yescomplemented
565C4×D4D4×C13714yes—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4D4×C13711yescharacteristic
576C2×C4⋊C4C23×C13711yescharacteristic
577C2×C4⋊C4C23×C13711yescharacteristic
578C2×C4⋊C4C23×C13711yescharacteristic
579C2×C4⋊C4C23×C13711yescharacteristic
580C2×C4⋊C4C23×C13711yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—28no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C13711yescharacteristic
590C2×C22⋊C4D4×C13711yescharacteristic
591C2×C42—21no—
592C2×C42C23×C13711yescharacteristic
593C4⋊C8—22no—
594#103—22no—
595#103—22no—
596#103—41no—
597#103—41no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604#102—41no—
605#102D4×C13714yescomplemented
606C22⋊C8—22no—
607C22⋊C8—22no—
608#97—22no—
609#95—21no—
610#95—21no—
611#95—21no—
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×D4×C13711yescharacteristic
622C24C2×D4×C13711yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×C4×C13712yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊C4×C13714yes—
657C2×D4C22×C4×C13712yes—
658C2×D4C22×C4×C13712yes—
659C2×D4C2×D4×C13712yes—
660C2×D4#41×C13712yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—81no—
684C22×C4—81no—
685C22×C4—81no—
686C22×C4—81no—
687C22×C4C22×C4×C13712yes—
688C22×C4C22×C4×C13712yes—
689C22×C4C2×D4×C13711yescharacteristic
690C22×C4C2×D4×C13711yescharacteristic
691C22×C4C2×D4×C13711yescharacteristic
692C22×C4C2×D4×C13711yescharacteristic
693C22×C4C2×D4×C13712yes—
694C22×C4C2×D4×C13712yes—
695C22×C4C24×C13711yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8C2×D4×C13712yes—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—81no—
723C4⋊C4C22⋊C4×C13714yes—
724C4⋊C4C22×C4×C13712yes—
725C4⋊C4C2×D4×C13712yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4C22⋊C4×C13714yes—
734C22⋊C4C22⋊C4×C13714yes—
735C42—42no—
736C42C22×C4×C13712yes—
737C42C2×D4×C13712yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊C4×C13712yes—
770C23C2×C22⋊C4×C13712yes—
771C23AGL(1,ℤ/8)×C13712yes—
772C23#137×C13712yes—
773C23C22×D4×C13711yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4C4×D4×C13714yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—84no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4C2×C22⋊C4×C13712yes—
829C2×C4C2×C22⋊C4×C13712yes—
830C2×C4C2×C22⋊C4×C13712yes—
831C2×C4C2×C22⋊C4×C13712yes—
832C2×C4C23×C4×C13711yescharacteristic
833C2×C4C22×D4×C13711yescharacteristic
834C2×C4C22×D4×C13711yescharacteristic
835C2×C4C2×#41×C13711yescharacteristic
836C2×C4H(5,𝔽2)×C13711yescharacteristic
837C2×C4H(5,𝔽2)×C13711yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22#417×C13714yescomplemented
871C22C22×C22⋊C4×C13711yescharacteristic
872C22D42×C13711yescharacteristic
873C22#546×C13711yescharacteristic
874C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
875C22C2×#137×C13711yescharacteristic
876C22#576×C13711yescharacteristic
877C22#577×C13711yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4C2×C4×D4×C13711yescharacteristic
889C4#518×C13711yescharacteristic
890C4D42×C13711yescharacteristic
891C4#546×C13711yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊C4×C13711yescharacteristic
897C2C2×#417×C13711yescharacteristic
898C2#2897×C13711yescharacteristic
899C2#3264×C13711yescharacteristic
900C2#3266×C13711yescharacteristic
901C2#3306×C13711yescharacteristic
902C2#3314×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutatorC2×C4C23×C4×C137
Frattini, cosocleC22×C4C24×C137
prime radicalC2×#546×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×#417×C137C2semidirect
4. C22×#102×C137C2semidirect
5. D4×C4⋊C4×C137C2semidirect
6. #1983×C137C2semidirect
7. #1959×C137C2semidirect
8. #1895×C137C2semidirect
9. #1892×C137C2semidirect
10. #1874×C137C2semidirect
11. #1872×C137C2semidirect
12. #1802×C137C2semidirect
13. #1788×C137C2semidirect
14. #1786×C137C2semidirect
15. #1762×C137C2semidirect
18. C22×M16×C137C22semidirect
21. #546×C137C4semidirect
32. C22×C4⋊C4×C137C22semidirect
35. C2×C4⋊C8×C137C22semidirect
37. C2×#103×C137C22semidirect
38. C2×#103×C137C22semidirect
39. C2×#103×C137C22semidirect
40. C2×#103×C137C22semidirect
51. C2×C22⋊C8×C137C22semidirect
52. C2×#97×C137C22semidirect
56. #384×C137C22semidirect
58. #380×C137C22semidirect
59. C4×C4⋊C4×C137C22semidirect
60. #340×C137C22semidirect
61. #340×C137C22semidirect
62. #340×C137C22semidirect
63. #340×C137C22semidirect
70. C2×#41×C137C2×C4semidirect
80. C22×D4×C137C2×C4semidirect
101. #124×C137C2×C4semidirect
104. C22⋊Q8×C137C2×C4semidirect
107. #121×C137C2×C4semidirect
112. C4×D4×C137C2×C4semidirect
153. #102×C137D4semidirect
337. D4×C137C4×D4semidirect
418. C22×C137#417semidirect
451. #22419C137direct (N × H)
452. C137#22419direct (N × H)
454. C2×#435C2×C137semidirect
455. C2×#417C2×C137semidirect
456. C22×#102C2×C137semidirect
457. D4×C4⋊C4C2×C137semidirect
458. #1983C2×C137semidirect
459. #1959C2×C137semidirect
460. #1895C2×C137semidirect
461. #1892C2×C137semidirect
462. #1874C2×C137semidirect
463. #1872C2×C137semidirect
464. #1802C2×C137semidirect
465. #1788C2×C137semidirect
466. #1786C2×C137semidirect
467. #1762C2×C137semidirect
470. C22×M16C22×C137semidirect
473. #546C4×C137semidirect
484. C22×C4⋊C4C22×C137semidirect
487. C2×C4⋊C8C22×C137semidirect
489. C2×#103C22×C137semidirect
490. C2×#103C22×C137semidirect
491. C2×#103C22×C137semidirect
492. C2×#103C22×C137semidirect
503. C2×C22⋊C8C22×C137semidirect
504. C2×#97C22×C137semidirect
508. #384C22×C137semidirect
510. #380C22×C137semidirect
511. C4×C4⋊C4C22×C137semidirect
512. #340C22×C137semidirect
513. #340C22×C137semidirect
514. #340C22×C137semidirect
515. #340C22×C137semidirect
522. C2×#41C2×C4×C137semidirect
532. C22×D4C2×C4×C137semidirect
553. #124C2×C4×C137semidirect
556. C22⋊Q8C2×C4×C137semidirect
559. #121C2×C4×C137semidirect
564. C4×D4C2×C4×C137semidirect
605. #102D4×C137semidirect
789. D4C4×D4×C137semidirect
870. C22#417×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×#435×C1372
C2×#417×C1372
C22×#102×C1372
D4×C4⋊C4×C1372
#1983×C1372
#1959×C1372
#1895×C1372
#1892×C1372
#1874×C1372
#1872×C1372
#1802×C1372
#1788×C1372
#1786×C1372
#1762×C1372
#22419137