Finite Group Databasebeta

← C137×#24044 #46873430

Subgroups — C137×#24044 #46873430

Order 35072.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C137C211yesmaximal, characteristic
2C2×#482×C137C211yesmaximal, characteristic, complemented
3C2×#418×C137C211yesmaximal, characteristic, complemented
4#2485×C137C211yesmaximal, characteristic, complemented
5#2041×C137C211yesmaximal, characteristic, complemented
6#2041×C137C211yesmaximal, characteristic, complemented
7#2034×C137C211yesmaximal, characteristic, complemented
8#2033×C137C211yesmaximal, characteristic, complemented
9#1895×C137C211yesmaximal, characteristic, complemented
10#1870×C137C211yesmaximal, characteristic, complemented
11#1864×C137C211yesmaximal, characteristic, complemented
12#1862×C137C211yesmaximal, characteristic, complemented
13#1786×C137C211yesmaximal, characteristic, complemented
14#1786×C137C211yesmaximal, characteristic, complemented
15#1786×C137C211yesmaximal, characteristic, complemented
16C23×D4×C137—21no—
17C23×D4×C137C2211yescharacteristic
18C23×D4×C137C2211yescharacteristic
19C22×M16×C137C2211yescharacteristic, complemented
20D42×C137—24no—
21D42×C137—24no—
22C2×#127×C137C2211yescharacteristic
23C2×#121×C137—21no—
24C2×#121×C137C2211yescharacteristic
25C2×#121×C137C2211yescharacteristic
26C2×#120×C137—21no—
27C2×#120×C137—21no—
28C2×C4×D4×C137C2211yescharacteristic
29C2×C4×D4×C137C2211yescharacteristic
30C2×#117×C137C2211yescharacteristic, complemented
31#482×C137—24no—
32C2×#107×C137C2211yescharacteristic, complemented
33C2×#106×C137C2211yescharacteristic, complemented
34#418×C137—24no—
35C2×#102×C137C2211yescharacteristic
36C2×#102×C137C2211yescharacteristic
37C2×#102×C137C2211yescharacteristic
38C2×#102×C137C2211yescharacteristic
39C2×#102×C137C2211yescharacteristic, complemented
40C2×#102×C137C2211yescharacteristic, complemented
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×C22⋊C8×C137C2211yescharacteristic, complemented
48C2×C22⋊C8×C137C2211yescharacteristic, complemented
49C2×C22⋊C8×C137C2211yescharacteristic, complemented
50#397×C137—21no—
51#394×C137—21no—
52#389×C137C2211yescharacteristic, complemented
53#389×C137C2211yescharacteristic, complemented
54#388×C137—21no—
55#387×C137—21no—
56#380×C137C2211yescharacteristic, complemented
57#380×C137C2211yescharacteristic, complemented
58#380×C137C2211yescharacteristic, complemented
59#340×C137C2211yescharacteristic, complemented
60#340×C137C2211yescharacteristic, complemented
61#336×C137C2211yescharacteristic, complemented
62#336×C137C2211yescharacteristic, complemented
63C25×C137—21no—
64C25×C137—21no—
65C22×D4×C137—22no—
66C22×D4×C137—22no—
67C22×D4×C137—28no—
68C22×D4×C137—21no—
69C22×D4×C137—21no—
70C22×D4×C137—22no—
71C22×D4×C137—22no—
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—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×C137D411yescharacteristic
86C22×D4×C137D414yes—
87C22×D4×C137C2311yescharacteristic
88C22×D4×C137C2311yescharacteristic
89C22×D4×C137C2311yescharacteristic
90C23×C4×C137—21no—
91C23×C4×C137C2311yescharacteristic
92C23×C4×C137C2311yescharacteristic
93C2×M16×C137—22no—
94C2×M16×C137—41no—
95C2×M16×C137—41no—
96C22×C8×C137C2311yescharacteristic
97C22×C8×C137C2311yescharacteristic
98C22×C8×C137C2311yescharacteristic
99C22×C8×C137C2311yescharacteristic
100#127×C137—22no—
101#127×C137—22no—
102#121×C137—28no—
103#121×C137—22no—
104#121×C137—22no—
105#121×C137—22no—
106#121×C137D414yes—
107#120×C137—28no—
108#120×C137—28no—
109C4×D4×C137—22no—
110C4×D4×C137—22no—
111C4×D4×C137—22no—
112C4×D4×C137—22no—
113#117×C137—22no—
114#117×C137—22no—
115C2×C4⋊C4×C137—21no—
116C2×C4⋊C4×C137—21no—
117C2×C4⋊C4×C137D411yescharacteristic
118C2×C4⋊C4×C137C2311yescharacteristic
119C2×C4⋊C4×C137C2311yescharacteristic
120C2×C4⋊C4×C137C2311yescharacteristic
121C2×C4⋊C4×C137C2311yescharacteristic
122C2×C4⋊C4×C137C2311yescharacteristic
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×C137D411yescharacteristic
131C2×C22⋊C4×C137D411yescharacteristic
132C2×C42×C137—21no—
133C2×C42×C137C2311yescharacteristic
134#107×C137—22no—
135#106×C137—22no—
136#102×C137—22no—
137#102×C137—22no—
138#102×C137—22no—
139#102×C137—22no—
140#102×C137—22no—
141#102×C137—22no—
142#102×C137—22no—
143#102×C137—22no—
144#102×C137—41no—
145#102×C137—41no—
146#102×C137—41no—
147#102×C137—41no—
148C22⋊C8×C137—22no—
149C22⋊C8×C137—41no—
150C22⋊C8×C137—41no—
151#95×C137—21no—
152#95×C137—21no—
153#95×C137—21no—
154#95×C137—21no—
155#95×C137—21no—
156C24×C137—21no—
157C24×C137—24no—
158C24×C137—21no—
159C24×C137—21no—
160C24×C137—24no—
161C24×C137—42no—
162C24×C137—42no—
163C24×C137—42no—
164C24×C137—42no—
165C24×C137—42no—
166C24×C137—42no—
167C24×C137—42no—
168C24×C137—42no—
169C24×C137—81no—
170C24×C137—81no—
171C24×C137—81no—
172C24×C137—81no—
173C24×C137C2×D411yescharacteristic
174C24×C137C2×D411yescharacteristic
175C2×D4×C137—22no—
176C2×D4×C137—22no—
177C2×D4×C137—28no—
178C2×D4×C137—24no—
179C2×D4×C137—24no—
180C2×D4×C137—24no—
181C2×D4×C137—24no—
182C2×D4×C137—24no—
183C2×D4×C137—24no—
184C2×D4×C137—22no—
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—21no—
193C2×D4×C137—21no—
194C2×D4×C137—21no—
195C2×D4×C137—21no—
196C2×D4×C137—21no—
197C2×D4×C137—21no—
198C2×D4×C137—44no—
199C2×D4×C137—44no—
200C2×D4×C137—44no—
201C2×D4×C137—42no—
202C2×D4×C137—42no—
203C2×D4×C137—42no—
204C2×D4×C137—42no—
205C2×D4×C137—42no—
206C2×D4×C137—44no—
207C2×D4×C137—44no—
208C2×D4×C137—432no—
209C2×D4×C137—44no—
210C2×D4×C137—42no—
211C2×D4×C137—42no—
212C2×D4×C137—42no—
213C2×D4×C137—42no—
214C2×D4×C137—44no—
215C2×D4×C137—42no—
216C2×D4×C137—81no—
217C2×D4×C137—81no—
218C2×D4×C137C2×D412yes—
219C2×D4×C137C2×D412yes—
220C2×D4×C137C2×D412yes—
221C2×D4×C137#4112yes—
222C2×D4×C137#4112yes—
223C22×C4×C137—21no—
224C22×C4×C137—21no—
225C22×C4×C137—21no—
226C22×C4×C137—21no—
227C22×C4×C137—24no—
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—21no—
239C22×C4×C137—42no—
240C22×C4×C137—42no—
241C22×C4×C137C2×D411yescharacteristic
242C22×C4×C137C2×D411yescharacteristic
243C22×C4×C137C2×D411yescharacteristic
244C22×C4×C137C2×D412yes—
245C22×C4×C137C2×D412yes—
246C22×C4×C137C2×D411yescharacteristic
247C22×C4×C137C2411yescharacteristic
248M16×C137—44no—
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—21no—
257C2×C8×C137—21no—
258C2×C8×C137—21no—
259C2×C8×C137—21no—
260C2×C8×C137—21no—
261C4⋊C4×C137—22no—
262C4⋊C4×C137—21no—
263C4⋊C4×C137—21no—
264C4⋊C4×C137—21no—
265C4⋊C4×C137—21no—
266C4⋊C4×C137—21no—
267C4⋊C4×C137—21no—
268C4⋊C4×C137—21no—
269C4⋊C4×C137—21no—
270C4⋊C4×C137—21no—
271C4⋊C4×C137—42no—
272C4⋊C4×C137—81no—
273C4⋊C4×C137C2×D412yes—
274C22⋊C4×C137—24no—
275C22⋊C4×C137—24no—
276C22⋊C4×C137—22no—
277C22⋊C4×C137—24no—
278C22⋊C4×C137—22no—
279C22⋊C4×C137—42no—
280C22⋊C4×C137—42no—
281C22⋊C4×C137—81no—
282C22⋊C4×C137—81no—
283C42×C137—21no—
284C42×C137—21no—
285C42×C137—42no—
286C23×C137—21no—
287C23×C137—22no—
288C23×C137—21no—
289C23×C137—21no—
290C23×C137—21no—
291C23×C137—21no—
292C23×C137—22no—
293C23×C137—22no—
294C23×C137—21no—
295C23×C137—21no—
296C23×C137—21no—
297C23×C137—21no—
298C23×C137—21no—
299C23×C137—21no—
300C23×C137—21no—
301C23×C137—22no—
302C23×C137—22no—
303C23×C137—48no—
304C23×C137—48no—
305C23×C137—48no—
306C23×C137—48no—
307C23×C137—41no—
308C23×C137—41no—
309C23×C137—41no—
310C23×C137—41no—
311C23×C137—41no—
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—84no—
324C23×C137—84no—
325C23×C137—84no—
326C23×C137—84no—
327C23×C137—84no—
328C23×C137—84no—
329C23×C137—84no—
330C23×C137—84no—
331C23×C137—84no—
332C23×C137—84no—
333C23×C137#12012yes—
334C23×C137AGL(1,ℤ/8)12yes—
335C23×C137C22×D411yescharacteristic
336D4×C137—28no—
337D4×C137—22no—
338D4×C137—22no—
339D4×C137—22no—
340D4×C137—22no—
341D4×C137—22no—
342D4×C137—22no—
343D4×C137—22no—
344D4×C137—48no—
345D4×C137—48no—
346D4×C137—48no—
347D4×C137—48no—
348D4×C137—48no—
349D4×C137—41no—
350D4×C137—41no—
351D4×C137—41no—
352D4×C137—41no—
353D4×C137—84no—
354D4×C137#12314yes—
355C2×C4×C137—21no—
356C2×C4×C137—21no—
357C2×C4×C137—21no—
358C2×C4×C137—21no—
359C2×C4×C137—22no—
360C2×C4×C137—22no—
361C2×C4×C137—22no—
362C2×C4×C137—22no—
363C2×C4×C137—21no—
364C2×C4×C137—21no—
365C2×C4×C137—22no—
366C2×C4×C137—21no—
367C2×C4×C137—21no—
368C2×C4×C137—21no—
369C2×C4×C137—21no—
370C2×C4×C137—48no—
371C2×C4×C137—41no—
372C2×C4×C137—41no—
373C2×C4×C137—41no—
374C2×C4×C137—41no—
375C2×C4×C137—41no—
376C2×C4×C137—41no—
377C2×C4×C137—41no—
378C2×C4×C137—41no—
379C2×C4×C137—41no—
380C2×C4×C137—41no—
381C2×C4×C137—41no—
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#12012yes—
390C2×C4×C137AGL(1,ℤ/8)12yes—
391C2×C4×C137C22×D411yescharacteristic
392C2×C4×C137C22×D411yescharacteristic
393C2×C4×C137C2×#4111yescharacteristic
394C2×C4×C137C2×#4111yescharacteristic
395C2×C4×C137H(5,𝔽2)11yescharacteristic
396C2×C4×C137H(5,𝔽2)11yescharacteristic
397C8×C137—41no—
398C8×C137—41no—
399C8×C137—41no—
400C8×C137—41no—
401C22×C137—22no—
402C22×C137—24no—
403C22×C137—22no—
404C22×C137—22no—
405C22×C137—22no—
406C22×C137—22no—
407C22×C137—22no—
408C22×C137—41no—
409C22×C137—42no—
410C22×C137—41no—
411C22×C137—42no—
412C22×C137—41no—
413C22×C137—42no—
414C22×C137—41no—
415C22×C137—42no—
416C22×C137—41no—
417C22×C137—41no—
418C22×C137—42no—
419C22×C137—41no—
420C22×C137—41no—
421C22×C137—42no—
422C22×C137—42no—
423C22×C137—42no—
424C22×C137—42no—
425C22×C137—42no—
426C22×C137—42no—
427C22×C137—42no—
428C22×C137—816no—
429C22×C137—816no—
430C22×C137—81no—
431C22×C137—81no—
432C22×C137—81no—
433C22×C137—81no—
434C22×C137—81no—
435C22×C137—81no—
436C22×C137—81no—
437C22×C137—81no—
438C22×C137C2×#12011yescharacteristic
439C22×C137#54611yescharacteristic
440C22×C137#54611yescharacteristic
441C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C137#57611yescharacteristic
444C22×C137#57711yescharacteristic
445C4×C137—22no—
446C4×C137—22no—
447C4×C137—41no—
448C4×C137—42no—
449C4×C137—41no—
450C4×C137—81no—
451C4×C137—81no—
452C4×C137—81no—
453C4×C137—81no—
454C4×C137C2×#12311yescharacteristic
455C4×C137#53411yescharacteristic
456C4×C137#54611yescharacteristic
457C4×C137#54611yescharacteristic
458C2×C137—42no—
459C2×C137—42no—
460C2×C137—44no—
461C2×C137—82no—
462C2×C137—82no—
463C2×C137#240511yescharacteristic
464C2×C137#300311yescharacteristic
465C2×C137#301211yescharacteristic
466C2×C137#331011yescharacteristic
467C2×C137#331811yescharacteristic
468C2×C137#332411yescharacteristic
469C2×C137#332511yescharacteristic
470#24044C13711yesmaximal, characteristic, direct product factor, Sylow
471C137#2404411yescharacteristic, direct product factor, Sylow
472C2×D42C2×C13711yescharacteristic
473C2×#482C2×C13711yescharacteristic, complemented
474C2×#418C2×C13711yescharacteristic, complemented
475#2485C2×C13711yescharacteristic, complemented
476#2041C2×C13711yescharacteristic, complemented
477#2041C2×C13711yescharacteristic, complemented
478#2034C2×C13711yescharacteristic, complemented
479#2033C2×C13711yescharacteristic, complemented
480#1895C2×C13711yescharacteristic, complemented
481#1870C2×C13711yescharacteristic, complemented
482#1864C2×C13711yescharacteristic, complemented
483#1862C2×C13711yescharacteristic, complemented
484#1786C2×C13711yescharacteristic, complemented
485#1786C2×C13711yescharacteristic, complemented
486#1786C2×C13711yescharacteristic, complemented
487C23×D4—21no—
488C23×D4C22×C13711yescharacteristic
489C23×D4C22×C13711yescharacteristic
490C22×M16C22×C13711yescharacteristic, complemented
491D42—24no—
492D42—24no—
493C2×#127C22×C13711yescharacteristic
494C2×#121—21no—
495C2×#121C22×C13711yescharacteristic
496C2×#121C22×C13711yescharacteristic
497C2×#120—21no—
498C2×#120—21no—
499C2×C4×D4C22×C13711yescharacteristic
500C2×C4×D4C22×C13711yescharacteristic
501C2×#117C22×C13711yescharacteristic, complemented
502#482—24no—
503C2×#107C22×C13711yescharacteristic, complemented
504C2×#106C22×C13711yescharacteristic, complemented
505#418—24no—
506C2×#102C22×C13711yescharacteristic
507C2×#102C22×C13711yescharacteristic
508C2×#102C22×C13711yescharacteristic
509C2×#102C22×C13711yescharacteristic
510C2×#102C22×C13711yescharacteristic, complemented
511C2×#102C22×C13711yescharacteristic, complemented
512C2×#102C22×C13711yescharacteristic, complemented
513C2×#102C22×C13711yescharacteristic, complemented
514C2×#102C22×C13711yescharacteristic, complemented
515C2×#102C22×C13711yescharacteristic, complemented
516C2×#102C22×C13711yescharacteristic, complemented
517C2×#102C22×C13711yescharacteristic, complemented
518C2×C22⋊C8C22×C13711yescharacteristic, complemented
519C2×C22⋊C8C22×C13711yescharacteristic, complemented
520C2×C22⋊C8C22×C13711yescharacteristic, complemented
521#397—21no—
522#394—21no—
523#389C22×C13711yescharacteristic, complemented
524#389C22×C13711yescharacteristic, complemented
525#388—21no—
526#387—21no—
527#380C22×C13711yescharacteristic, complemented
528#380C22×C13711yescharacteristic, complemented
529#380C22×C13711yescharacteristic, complemented
530#340C22×C13711yescharacteristic, complemented
531#340C22×C13711yescharacteristic, complemented
532#336C22×C13711yescharacteristic, complemented
533#336C22×C13711yescharacteristic, complemented
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4D4×C13711yescharacteristic
557C22×D4D4×C13714yes—
558C22×D4C23×C13711yescharacteristic
559C22×D4C23×C13711yescharacteristic
560C22×D4C23×C13711yescharacteristic
561C23×C4—21no—
562C23×C4C23×C13711yescharacteristic
563C23×C4C23×C13711yescharacteristic
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C13711yescharacteristic
568C22×C8C23×C13711yescharacteristic
569C22×C8C23×C13711yescharacteristic
570C22×C8C23×C13711yescharacteristic
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121D4×C13714yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C13711yescharacteristic
589C2×C4⋊C4C23×C13711yescharacteristic
590C2×C4⋊C4C23×C13711yescharacteristic
591C2×C4⋊C4C23×C13711yescharacteristic
592C2×C4⋊C4C23×C13711yescharacteristic
593C2×C4⋊C4C23×C13711yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C13711yescharacteristic
602C2×C22⋊C4D4×C13711yescharacteristic
603C2×C42—21no—
604C2×C42C23×C13711yescharacteristic
605#107—22no—
606#106—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C13711yescharacteristic
645C24C2×D4×C13711yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C13712yes—
690C2×D4C2×D4×C13712yes—
691C2×D4C2×D4×C13712yes—
692C2×D4#41×C13712yes—
693C2×D4#41×C13712yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C13711yescharacteristic
713C22×C4C2×D4×C13711yescharacteristic
714C22×C4C2×D4×C13711yescharacteristic
715C22×C4C2×D4×C13712yes—
716C22×C4C2×D4×C13712yes—
717C22×C4C2×D4×C13711yescharacteristic
718C22×C4C24×C13711yescharacteristic
719M16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C13712yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#120×C13712yes—
805C23AGL(1,ℤ/8)×C13712yes—
806C23C22×D4×C13711yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#123×C13714yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4#120×C13712yes—
861C2×C4AGL(1,ℤ/8)×C13712yes—
862C2×C4C22×D4×C13711yescharacteristic
863C2×C4C22×D4×C13711yescharacteristic
864C2×C4C2×#41×C13711yescharacteristic
865C2×C4C2×#41×C13711yescharacteristic
866C2×C4H(5,𝔽2)×C13711yescharacteristic
867C2×C4H(5,𝔽2)×C13711yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—24no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—42no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C13711yescharacteristic
910C22#546×C13711yescharacteristic
911C22#546×C13711yescharacteristic
912C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
913C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
914C22#576×C13711yescharacteristic
915C22#577×C13711yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—42no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×#123×C13711yescharacteristic
926C4#534×C13711yescharacteristic
927C4#546×C13711yescharacteristic
928C4#546×C13711yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2#2405×C13711yescharacteristic
935C2#3003×C13711yescharacteristic
936C2#3012×C13711yescharacteristic
937C2#3310×C13711yescharacteristic
938C2#3318×C13711yescharacteristic
939C2#3324×C13711yescharacteristic
940C2#3325×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC2×D42×C137C2
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
2. C2×#482×C137C2semidirect
3. C2×#418×C137C2semidirect
4. #2485×C137C2semidirect
5. #2041×C137C2semidirect
6. #2041×C137C2semidirect
7. #2034×C137C2semidirect
8. #2033×C137C2semidirect
9. #1895×C137C2semidirect
10. #1870×C137C2semidirect
11. #1864×C137C2semidirect
12. #1862×C137C2semidirect
13. #1786×C137C2semidirect
14. #1786×C137C2semidirect
15. #1786×C137C2semidirect
19. C22×M16×C137C22semidirect
30. C2×#117×C137C22semidirect
32. C2×#107×C137C22semidirect
33. C2×#106×C137C22semidirect
39. C2×#102×C137C22semidirect
40. C2×#102×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×C22⋊C8×C137C22semidirect
48. C2×C22⋊C8×C137C22semidirect
49. C2×C22⋊C8×C137C22semidirect
52. #389×C137C22semidirect
53. #389×C137C22semidirect
56. #380×C137C22semidirect
57. #380×C137C22semidirect
58. #380×C137C22semidirect
59. #340×C137C22semidirect
60. #340×C137C22semidirect
61. #336×C137C22semidirect
62. #336×C137C22semidirect
470. #24044C137direct (N × H)
471. C137#24044direct (N × H)
473. C2×#482C2×C137semidirect
474. C2×#418C2×C137semidirect
475. #2485C2×C137semidirect
476. #2041C2×C137semidirect
477. #2041C2×C137semidirect
478. #2034C2×C137semidirect
479. #2033C2×C137semidirect
480. #1895C2×C137semidirect
481. #1870C2×C137semidirect
482. #1864C2×C137semidirect
483. #1862C2×C137semidirect
484. #1786C2×C137semidirect
485. #1786C2×C137semidirect
486. #1786C2×C137semidirect
490. C22×M16C22×C137semidirect
501. C2×#117C22×C137semidirect
503. C2×#107C22×C137semidirect
504. C2×#106C22×C137semidirect
510. C2×#102C22×C137semidirect
511. C2×#102C22×C137semidirect
512. C2×#102C22×C137semidirect
513. C2×#102C22×C137semidirect
514. C2×#102C22×C137semidirect
515. C2×#102C22×C137semidirect
516. C2×#102C22×C137semidirect
517. C2×#102C22×C137semidirect
518. C2×C22⋊C8C22×C137semidirect
519. C2×C22⋊C8C22×C137semidirect
520. C2×C22⋊C8C22×C137semidirect
523. #389C22×C137semidirect
524. #389C22×C137semidirect
527. #380C22×C137semidirect
528. #380C22×C137semidirect
529. #380C22×C137semidirect
530. #340C22×C137semidirect
531. #340C22×C137semidirect
532. #336C22×C137semidirect
533. #336C22×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×#482×C1372
C2×#418×C1372
#2485×C1372
#2041×C1372
#2034×C1372
#2033×C1372
#1895×C1372
#1870×C1372
#1864×C1372
#1862×C1372
#1786×C1372
#24044137