Finite Group Databasebeta

← C137×#22442 #46871828

Subgroups — C137×#22442 #46871828

Order 35072.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C137C211yesmaximal, characteristic
2C2×#442×C137C211yesmaximal, characteristic, complemented
3C2×C4×D8×C137C211yesmaximal, characteristic, complemented
4#2339×C137C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C137C211yesmaximal, characteristic, complemented
6#1973×C137C211yesmaximal, characteristic, complemented
7#1968×C137C211yesmaximal, characteristic, complemented
8#1879×C137C211yesmaximal, characteristic, complemented
9#1879×C137C211yesmaximal, characteristic, complemented
10#1877×C137C211yesmaximal, characteristic, complemented
11#1877×C137C211yesmaximal, characteristic, complemented
12#1809×C137C211yesmaximal, characteristic, complemented
13#1788×C137C211yesmaximal, characteristic, complemented
14#1786×C137C211yesmaximal, characteristic, complemented
15#1753×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C137—24no—
19C2×AGL(1,ℤ/8)×C137—24no—
20C2×AGL(1,ℤ/8)×C137C418yescomplemented
21C22×SD16×C137C2211yescharacteristic
22C22×SD16×C137C2211yescharacteristic
23C22×D8×C137C2211yescharacteristic
24C22×D8×C137C2211yescharacteristic
25C22×M16×C137C2211yescharacteristic
26C2×C4×D4×C137C2211yescharacteristic
27C2×C4×D4×C137C2211yescharacteristic
28C2×C4×D4×C137C2211yescharacteristic, complemented
29C2×C4×D4×C137C2211yescharacteristic, complemented
30C22×C22⋊C4×C137—21no—
31#442×C137—24no—
32C4×D8×C137—24no—
33C2×#107×C137C2211yescharacteristic, complemented
34C2×#106×C137C2211yescharacteristic, complemented
35C2×#103×C137C2211yescharacteristic, complemented
36C2×#103×C137C2211yescharacteristic, complemented
37C2×#102×C137C2211yescharacteristic
38C2×#102×C137C2211yescharacteristic
39C2×#102×C137C2211yescharacteristic
40C2×#102×C137C2211yescharacteristic
41C2×#102×C137C2211yescharacteristic, complemented
42C2×#102×C137C2211yescharacteristic, complemented
43C2×C22⋊C8×C137C2211yescharacteristic
44C2×#97×C137C2211yescharacteristic, complemented
45C2×C4×C8×C137C2211yescharacteristic, complemented
46#391×C137C2211yescharacteristic, complemented
47#391×C137C2211yescharacteristic, complemented
48#390×C137C2211yescharacteristic
49#390×C137C2211yescharacteristic
50#386×C137—21no—
51#386×C137—21no—
52#386×C137—21no—
53#386×C137—21no—
54#381×C137—21no—
55#380×C137C2211yescharacteristic
56#380×C137C2211yescharacteristic
57#379×C137—21no—
58C4×C22⋊C4×C137C2211yescharacteristic
59C2×#95×C137—21no—
60#340×C137C2211yescharacteristic, complemented
61#340×C137C2211yescharacteristic, complemented
62#336×C137C2211yescharacteristic, complemented
63#336×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—22no—
77C22×D4×C137—41no—
78C22×D4×C137—41no—
79C22×D4×C137C2×C414yescomplemented
80C22×D4×C137C2311yescharacteristic
81C22×D4×C137C2311yescharacteristic
82C22×D4×C137C2311yescharacteristic
83C23×C4×C137—21no—
84C23×C4×C137—21no—
85C23×C4×C137—21no—
86C23×C4×C137—21no—
87C23×C4×C137—21no—
88C23×C4×C137C2311yescharacteristic
89AGL(1,ℤ/8)×C137—232no—
90C2×SD16×C137—22no—
91C2×SD16×C137—22no—
92C2×SD16×C137—22no—
93C2×SD16×C137—22no—
94C2×SD16×C137C2×C414yescomplemented
95C2×SD16×C137C2×C414yescomplemented
96C2×D8×C137—22no—
97C2×D8×C137—22no—
98C2×D8×C137C2×C414yes—
99C2×D8×C137C2×C414yescomplemented
100C2×D8×C137D414yes—
101C2×D8×C137D414yes—
102C2×M16×C137—22no—
103C2×M16×C137—22no—
104C2×M16×C137C2×C414yescomplemented
105C22×C8×C137C2311yescharacteristic
106C22×C8×C137C2311yescharacteristic
107C22×C8×C137C2311yescharacteristic
108C22×C8×C137C2311yescharacteristic
109C4×D4×C137—22no—
110C4×D4×C137—22no—
111C4×D4×C137—22no—
112C4×D4×C137—22no—
113C4×D4×C137—41no—
114C4×D4×C137—41no—
115C4×D4×C137—41no—
116C4×D4×C137—41no—
117C2×C4⋊C4×C137C2311yescharacteristic
118C2×C4⋊C4×C137C2311yescharacteristic
119C2×C4⋊C4×C137C2311yescharacteristic
120C2×C4⋊C4×C137C2311yescharacteristic
121C2×C22⋊C4×C137—21no—
122C2×C22⋊C4×C137—21no—
123C2×C22⋊C4×C137—21no—
124C2×C22⋊C4×C137—21no—
125C2×C22⋊C4×C137—21no—
126C2×C22⋊C4×C137—21no—
127C2×C22⋊C4×C137—21no—
128C2×C22⋊C4×C137—21no—
129C2×C22⋊C4×C137—21no—
130C2×C22⋊C4×C137—21no—
131C2×C22⋊C4×C137—44no—
132C2×C22⋊C4×C137D411yescharacteristic
133C2×C22⋊C4×C137D411yescharacteristic
134C2×C42×C137C2311yescharacteristic
135C2×C42×C137C2311yescharacteristic
136#107×C137—22no—
137#106×C137—22no—
138#103×C137—41no—
139#103×C137—41no—
140#102×C137—22no—
141#102×C137—22no—
142#102×C137—22no—
143#102×C137—22no—
144#102×C137—41no—
145#102×C137—41no—
146C22⋊C8×C137—22no—
147#97×C137—22no—
148C4×C8×C137—22no—
149#95×C137—21no—
150#95×C137—21no—
151#95×C137—21no—
152#95×C137—21no—
153#95×C137—21no—
154#95×C137—21no—
155#95×C137D411yescharacteristic
156#95×C137D411yescharacteristic
157C24×C137—21no—
158C24×C137—21no—
159C24×C137—21no—
160C24×C137—24no—
161C24×C137—42no—
162C24×C137—42no—
163C24×C137—42no—
164C24×C137—42no—
165C24×C137—81no—
166C24×C137—81no—
167C24×C137C2×D411yescharacteristic
168#41×C137—28no—
169#41×C137—44no—
170#41×C137—44no—
171#41×C137—44no—
172C2×Q8×C137—21no—
173C2×Q8×C137—21no—
174C2×Q8×C137—21no—
175C2×Q8×C137—21no—
176C2×Q8×C137—21no—
177C2×Q8×C137C22×C412yes—
178C2×D4×C137—28no—
179C2×D4×C137—24no—
180C2×D4×C137—24no—
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—21no—
190C2×D4×C137—21no—
191C2×D4×C137—21no—
192C2×D4×C137—44no—
193C2×D4×C137—44no—
194C2×D4×C137—44no—
195C2×D4×C137—42no—
196C2×D4×C137—42no—
197C2×D4×C137—42no—
198C2×D4×C137—42no—
199C2×D4×C137C22×C412yes—
200C2×D4×C137C22×C412yes—
201C2×D4×C137C22×C412yes—
202C2×D4×C137C2×D412yes—
203C2×D4×C137C2×D412yes—
204C2×D4×C137C2×D412yes—
205C2×D4×C137C2×D412yes—
206C22×C4×C137—21no—
207C22×C4×C137—21no—
208C22×C4×C137—21no—
209C22×C4×C137—21no—
210C22×C4×C137—21no—
211C22×C4×C137—24no—
212C22×C4×C137—21no—
213C22×C4×C137—21no—
214C22×C4×C137—21no—
215C22×C4×C137—21no—
216C22×C4×C137—42no—
217C22×C4×C137—42no—
218C22×C4×C137—42no—
219C22×C4×C137—42no—
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—81no—
227C22×C4×C137—81no—
228C22×C4×C137—81no—
229C22×C4×C137—81no—
230C22×C4×C137C22×C412yes—
231C22×C4×C137C2×D411yescharacteristic
232C22×C4×C137C2×D411yescharacteristic
233C22×C4×C137C2×D411yescharacteristic
234C22×C4×C137C2×D411yescharacteristic
235C22×C4×C137C2×D411yescharacteristic
236C22×C4×C137#4112yes—
237C22×C4×C137C2411yescharacteristic
238SD16×C137—28no—
239SD16×C137—28no—
240D8×C137—28no—
241D8×C137C22⋊C4116yescomplemented
242M16×C137—28no—
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—
251C2×C8×C137C22×C412yes—
252C2×C8×C137C22×C412yes—
253C2×C8×C137C2×D412yes—
254C2×C8×C137C2×D412yes—
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—21no—
263C22⋊C4×C137—22no—
264C22⋊C4×C137—41no—
265C22⋊C4×C137—42no—
266C22⋊C4×C137—42no—
267C22⋊C4×C137—42no—
268C22⋊C4×C137—42no—
269C22⋊C4×C137—42no—
270C22⋊C4×C137—42no—
271C22⋊C4×C137—42no—
272C22⋊C4×C137—81no—
273C22⋊C4×C137—81no—
274C22⋊C4×C137—81no—
275C42×C137—21no—
276C42×C137—21no—
277C42×C137—21no—
278C42×C137—21no—
279C23×C137—22no—
280C23×C137—22no—
281C23×C137—22no—
282C23×C137—22no—
283C23×C137—22no—
284C23×C137—22no—
285C23×C137—21no—
286C23×C137—21no—
287C23×C137—21no—
288C23×C137—21no—
289C23×C137—21no—
290C23×C137—21no—
291C23×C137—22no—
292C23×C137—48no—
293C23×C137—48no—
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—41no—
305C23×C137—41no—
306C23×C137—41no—
307C23×C137—41no—
308C23×C137—84no—
309C23×C137—84no—
310C23×C137—84no—
311C23×C137—84no—
312C23×C137—84no—
313C23×C137C4×D412yes—
314C23×C137C22×D411yescharacteristic
315Q8×C137—22no—
316Q8×C137—22no—
317Q8×C137—41no—
318Q8×C137—41no—
319D4×C137—22no—
320D4×C137—22no—
321D4×C137—22no—
322D4×C137—22no—
323D4×C137—22no—
324D4×C137—22no—
325D4×C137—22no—
326D4×C137—22no—
327D4×C137—48no—
328D4×C137—48no—
329D4×C137—41no—
330D4×C137—41no—
331D4×C137C2×C22⋊C414yes—
332D4×C137C2×C22⋊C414yescomplemented
333C2×C4×C137—21no—
334C2×C4×C137—21no—
335C2×C4×C137—21no—
336C2×C4×C137—21no—
337C2×C4×C137—22no—
338C2×C4×C137—22no—
339C2×C4×C137—22no—
340C2×C4×C137—22no—
341C2×C4×C137—22no—
342C2×C4×C137—21no—
343C2×C4×C137—21no—
344C2×C4×C137—21no—
345C2×C4×C137—21no—
346C2×C4×C137—21no—
347C2×C4×C137—21no—
348C2×C4×C137—21no—
349C2×C4×C137—21no—
350C2×C4×C137—21no—
351C2×C4×C137—48no—
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—41no—
366C2×C4×C137—84no—
367C2×C4×C137—84no—
368C2×C4×C137—84no—
369C2×C4×C137—84no—
370C2×C4×C137C4×D412yes—
371C2×C4×C137AGL(1,ℤ/8)12yescomplemented
372C2×C4×C137C23×C411yescharacteristic
373C2×C4×C137C22×D411yescharacteristic
374C2×C4×C137C22×D411yescharacteristic
375C2×C4×C137C2×#4111yescharacteristic
376C2×C4×C137H(5,𝔽2)11yescharacteristic
377C2×C4×C137H(5,𝔽2)11yescharacteristic
378C8×C137—22no—
379C8×C137—41no—
380C8×C137—41no—
381C8×C137C2×C22⋊C414yescomplemented
382C22×C137—22no—
383C22×C137—24no—
384C22×C137—24no—
385C22×C137—22no—
386C22×C137—22no—
387C22×C137—42no—
388C22×C137—42no—
389C22×C137—42no—
390C22×C137—42no—
391C22×C137—42no—
392C22×C137—42no—
393C22×C137—41no—
394C22×C137—41no—
395C22×C137—42no—
396C22×C137—42no—
397C22×C137—42no—
398C22×C137—41no—
399C22×C137—42no—
400C22×C137—42no—
401C22×C137—41no—
402C22×C137—42no—
403C22×C137—42no—
404C22×C137—42no—
405C22×C137—42no—
406C22×C137—816no—
407C22×C137—81no—
408C22×C137—81no—
409C22×C137—81no—
410C22×C137—81no—
411C22×C137C2×C4×D411yescharacteristic
412C22×C137D4211yescharacteristic
413C22×C137D4211yescharacteristic
414C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C137#57511yescharacteristic
416C22×C137#57611yescharacteristic
417C22×C137#57711yescharacteristic
418C4×C137—22no—
419C4×C137—22no—
420C4×C137—42no—
421C4×C137—41no—
422C4×C137—41no—
423C4×C137—41no—
424C4×C137—81no—
425C4×C137—81no—
426C4×C137—81no—
427C4×C137—81no—
428C4×C137C22×C22⋊C411yescharacteristic
429C4×C137#51811yescharacteristic
430C4×C137#54611yescharacteristic
431C4×C137#54611yescharacteristic
432C2×C137—42no—
433C2×C137—44no—
434C2×C137—44no—
435C2×C137—82no—
436C2×C137D4×C22⋊C411yescharacteristic
437C2×C137C4×AGL(1,ℤ/8)11yescharacteristic
438C2×C137#294611yescharacteristic
439C2×C137#326411yescharacteristic
440C2×C137#326711yescharacteristic
441C2×C137#327211yescharacteristic
442C2×C137#327311yescharacteristic
443#22442C13711yesmaximal, characteristic, direct product factor, Sylow
444C137#2244211yescharacteristic, direct product factor, Sylow
445C22×AGL(1,ℤ/8)C2×C13711yescharacteristic
446C2×#442C2×C13711yescharacteristic, complemented
447C2×C4×D8C2×C13711yescharacteristic, complemented
448#2339C2×C13711yescharacteristic, complemented
449D4×C22⋊C4C2×C13711yescharacteristic, complemented
450#1973C2×C13711yescharacteristic, complemented
451#1968C2×C13711yescharacteristic, complemented
452#1879C2×C13711yescharacteristic, complemented
453#1879C2×C13711yescharacteristic, complemented
454#1877C2×C13711yescharacteristic, complemented
455#1877C2×C13711yescharacteristic, complemented
456#1809C2×C13711yescharacteristic, complemented
457#1788C2×C13711yescharacteristic, complemented
458#1786C2×C13711yescharacteristic, complemented
459#1753C2×C13711yescharacteristic, complemented
460C22×#41C22×C13711yescharacteristic
461C23×D4C22×C13711yescharacteristic
462C2×AGL(1,ℤ/8)—24no—
463C2×AGL(1,ℤ/8)—24no—
464C2×AGL(1,ℤ/8)C4×C13718yescomplemented
465C22×SD16C22×C13711yescharacteristic
466C22×SD16C22×C13711yescharacteristic
467C22×D8C22×C13711yescharacteristic
468C22×D8C22×C13711yescharacteristic
469C22×M16C22×C13711yescharacteristic
470C2×C4×D4C22×C13711yescharacteristic
471C2×C4×D4C22×C13711yescharacteristic
472C2×C4×D4C22×C13711yescharacteristic, complemented
473C2×C4×D4C22×C13711yescharacteristic, complemented
474C22×C22⋊C4—21no—
475#442—24no—
476C4×D8—24no—
477C2×#107C22×C13711yescharacteristic, complemented
478C2×#106C22×C13711yescharacteristic, complemented
479C2×#103C22×C13711yescharacteristic, complemented
480C2×#103C22×C13711yescharacteristic, complemented
481C2×#102C22×C13711yescharacteristic
482C2×#102C22×C13711yescharacteristic
483C2×#102C22×C13711yescharacteristic
484C2×#102C22×C13711yescharacteristic
485C2×#102C22×C13711yescharacteristic, complemented
486C2×#102C22×C13711yescharacteristic, complemented
487C2×C22⋊C8C22×C13711yescharacteristic
488C2×#97C22×C13711yescharacteristic, complemented
489C2×C4×C8C22×C13711yescharacteristic, complemented
490#391C22×C13711yescharacteristic, complemented
491#391C22×C13711yescharacteristic, complemented
492#390C22×C13711yescharacteristic
493#390C22×C13711yescharacteristic
494#386—21no—
495#386—21no—
496#386—21no—
497#386—21no—
498#381—21no—
499#380C22×C13711yescharacteristic
500#380C22×C13711yescharacteristic
501#379—21no—
502C4×C22⋊C4C22×C13711yescharacteristic
503C2×#95—21no—
504#340C22×C13711yescharacteristic, complemented
505#340C22×C13711yescharacteristic, complemented
506#336C22×C13711yescharacteristic, complemented
507#336C22×C13711yescharacteristic, complemented
508C25—21no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41C2×C4×C13714yescomplemented
515C22×Q8C23×C13711yescharacteristic
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2×C4×C13714yescomplemented
524C22×D4C23×C13711yescharacteristic
525C22×D4C23×C13711yescharacteristic
526C22×D4C23×C13711yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C23×C13711yescharacteristic
533AGL(1,ℤ/8)—232no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16C2×C4×C13714yescomplemented
539C2×SD16C2×C4×C13714yescomplemented
540C2×D8—22no—
541C2×D8—22no—
542C2×D8C2×C4×C13714yes—
543C2×D8C2×C4×C13714yescomplemented
544C2×D8D4×C13714yes—
545C2×D8D4×C13714yes—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16C2×C4×C13714yescomplemented
549C22×C8C23×C13711yescharacteristic
550C22×C8C23×C13711yescharacteristic
551C22×C8C23×C13711yescharacteristic
552C22×C8C23×C13711yescharacteristic
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—41no—
561C2×C4⋊C4C23×C13711yescharacteristic
562C2×C4⋊C4C23×C13711yescharacteristic
563C2×C4⋊C4C23×C13711yescharacteristic
564C2×C4⋊C4C23×C13711yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
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—44no—
576C2×C22⋊C4D4×C13711yescharacteristic
577C2×C22⋊C4D4×C13711yescharacteristic
578C2×C42C23×C13711yescharacteristic
579C2×C42C23×C13711yescharacteristic
580#107—22no—
581#106—22no—
582#103—41no—
583#103—41no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102—41no—
590C22⋊C8—22no—
591#97—22no—
592C4×C8—22no—
593#95—21no—
594#95—21no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95D4×C13711yescharacteristic
600#95D4×C13711yescharacteristic
601C24—21no—
602C24—21no—
603C24—21no—
604C24—24no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—81no—
610C24—81no—
611C24C2×D4×C13711yescharacteristic
612#41—28no—
613#41—44no—
614#41—44no—
615#41—44no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8C22×C4×C13712yes—
622C2×D4—28no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4C22×C4×C13712yes—
644C2×D4C22×C4×C13712yes—
645C2×D4C22×C4×C13712yes—
646C2×D4C2×D4×C13712yes—
647C2×D4C2×D4×C13712yes—
648C2×D4C2×D4×C13712yes—
649C2×D4C2×D4×C13712yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—81no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4—81no—
674C22×C4C22×C4×C13712yes—
675C22×C4C2×D4×C13711yescharacteristic
676C22×C4C2×D4×C13711yescharacteristic
677C22×C4C2×D4×C13711yescharacteristic
678C22×C4C2×D4×C13711yescharacteristic
679C22×C4C2×D4×C13711yescharacteristic
680C22×C4#41×C13712yes—
681C22×C4C24×C13711yescharacteristic
682SD16—28no—
683SD16—28no—
684D8—28no—
685D8C22⋊C4×C137116yescomplemented
686M16—28no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8C22×C4×C13712yes—
696C2×C8C22×C4×C13712yes—
697C2×C8C2×D4×C13712yes—
698C2×C8C2×D4×C13712yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C22⋊C4—22no—
708C22⋊C4—41no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—81no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—48no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23C4×D4×C13712yes—
758C23C22×D4×C13711yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4C2×C22⋊C4×C13714yes—
776D4C2×C22⋊C4×C13714yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—84no—
814C2×C4C4×D4×C13712yes—
815C2×C4AGL(1,ℤ/8)×C13712yescomplemented
816C2×C4C23×C4×C13711yescharacteristic
817C2×C4C22×D4×C13711yescharacteristic
818C2×C4C22×D4×C13711yescharacteristic
819C2×C4C2×#41×C13711yescharacteristic
820C2×C4H(5,𝔽2)×C13711yescharacteristic
821C2×C4H(5,𝔽2)×C13711yescharacteristic
822C8—22no—
823C8—41no—
824C8—41no—
825C8C2×C22⋊C4×C13714yescomplemented
826C22—22no—
827C22—24no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—42no—
845C22—41no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22C2×C4×D4×C13711yescharacteristic
856C22D42×C13711yescharacteristic
857C22D42×C13711yescharacteristic
858C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
859C22#575×C13711yescharacteristic
860C22#576×C13711yescharacteristic
861C22#577×C13711yescharacteristic
862C4—22no—
863C4—22no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—81no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4C22×C22⋊C4×C13711yescharacteristic
873C4#518×C13711yescharacteristic
874C4#546×C13711yescharacteristic
875C4#546×C13711yescharacteristic
876C2—42no—
877C2—44no—
878C2—44no—
879C2—82no—
880C2D4×C22⋊C4×C13711yescharacteristic
881C2C4×AGL(1,ℤ/8)×C13711yescharacteristic
882C2#2946×C13711yescharacteristic
883C2#3264×C13711yescharacteristic
884C2#3267×C13711yescharacteristic
885C2#3272×C13711yescharacteristic
886C2#3273×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutatorC2×C4C23×C4×C137
Frattini, cosocleC22×C4C24×C137
prime radicalC22×AGL(1,ℤ/8)×C137C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C4×C22⋊C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#442×C137C2semidirect
3. C2×C4×D8×C137C2semidirect
4. #2339×C137C2semidirect
5. D4×C22⋊C4×C137C2semidirect
6. #1973×C137C2semidirect
7. #1968×C137C2semidirect
8. #1879×C137C2semidirect
9. #1879×C137C2semidirect
10. #1877×C137C2semidirect
11. #1877×C137C2semidirect
12. #1809×C137C2semidirect
13. #1788×C137C2semidirect
14. #1786×C137C2semidirect
15. #1753×C137C2semidirect
20. C2×AGL(1,ℤ/8)×C137C4semidirect
28. C2×C4×D4×C137C22semidirect
29. C2×C4×D4×C137C22semidirect
33. C2×#107×C137C22semidirect
34. C2×#106×C137C22semidirect
35. C2×#103×C137C22semidirect
36. C2×#103×C137C22semidirect
41. C2×#102×C137C22semidirect
42. C2×#102×C137C22semidirect
44. C2×#97×C137C22semidirect
45. C2×C4×C8×C137C22semidirect
46. #391×C137C22semidirect
47. #391×C137C22semidirect
60. #340×C137C22semidirect
61. #340×C137C22semidirect
62. #336×C137C22semidirect
63. #336×C137C22semidirect
70. C2×#41×C137C2×C4semidirect
79. C22×D4×C137C2×C4semidirect
94. C2×SD16×C137C2×C4semidirect
95. C2×SD16×C137C2×C4semidirect
99. C2×D8×C137C2×C4semidirect
104. C2×M16×C137C2×C4semidirect
241. D8×C137C22⋊C4semidirect
332. D4×C137C2×C22⋊C4semidirect
371. C2×C4×C137AGL(1,ℤ/8)semidirect
381. C8×C137C2×C22⋊C4semidirect
443. #22442C137direct (N × H)
444. C137#22442direct (N × H)
446. C2×#442C2×C137semidirect
447. C2×C4×D8C2×C137semidirect
448. #2339C2×C137semidirect
449. D4×C22⋊C4C2×C137semidirect
450. #1973C2×C137semidirect
451. #1968C2×C137semidirect
452. #1879C2×C137semidirect
453. #1879C2×C137semidirect
454. #1877C2×C137semidirect
455. #1877C2×C137semidirect
456. #1809C2×C137semidirect
457. #1788C2×C137semidirect
458. #1786C2×C137semidirect
459. #1753C2×C137semidirect
464. C2×AGL(1,ℤ/8)C4×C137semidirect
472. C2×C4×D4C22×C137semidirect
473. C2×C4×D4C22×C137semidirect
477. C2×#107C22×C137semidirect
478. C2×#106C22×C137semidirect
479. C2×#103C22×C137semidirect
480. C2×#103C22×C137semidirect
485. C2×#102C22×C137semidirect
486. C2×#102C22×C137semidirect
488. C2×#97C22×C137semidirect
489. C2×C4×C8C22×C137semidirect
490. #391C22×C137semidirect
491. #391C22×C137semidirect
504. #340C22×C137semidirect
505. #340C22×C137semidirect
506. #336C22×C137semidirect
507. #336C22×C137semidirect
514. C2×#41C2×C4×C137semidirect
523. C22×D4C2×C4×C137semidirect
538. C2×SD16C2×C4×C137semidirect
539. C2×SD16C2×C4×C137semidirect
543. C2×D8C2×C4×C137semidirect
548. C2×M16C2×C4×C137semidirect
685. D8C22⋊C4×C137semidirect
776. D4C2×C22⋊C4×C137semidirect
815. C2×C4AGL(1,ℤ/8)×C137semidirect
825. C8C2×C22⋊C4×C137semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1372
C2×#442×C1372
C2×C4×D8×C1372
#2339×C1372
D4×C22⋊C4×C1372
#1973×C1372
#1968×C1372
#1879×C1372
#1877×C1372
#1809×C1372
#1788×C1372
#1786×C1372
#1753×C1372
#22442137