Finite Group Databasebeta

← C137×#24451 #46873837

Subgroups — C137×#24451 #46873837

Order 35072.

1580 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C137C211yesmaximal, characteristic, complemented
2C2×#469×C137C211yesmaximal, characteristic, complemented
3C2×#449×C137C211yesmaximal, characteristic, complemented
4C2×#449×C137C211yesmaximal, characteristic, complemented
5C2×#417×C137C211yesmaximal, characteristic, complemented
6#2416×C137C211yesmaximal, characteristic, complemented
7#2041×C137C211yesmaximal, characteristic, complemented
8#2034×C137C211yesmaximal, characteristic, complemented
9#2011×C137C211yesmaximal, characteristic, complemented
10#1999×C137C211yesmaximal, characteristic, complemented
11#1880×C137C211yesmaximal, characteristic, complemented
12#1874×C137C211yesmaximal, characteristic, complemented
13#1870×C137C211yesmaximal, characteristic, complemented
14#1865×C137C211yesmaximal, characteristic, complemented
15#1788×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C22×#41×C137C2211yescharacteristic
18C22×SD16×C137C2211yescharacteristic
19C22×D8×C137C2211yescharacteristic
20C22×D8×C137C2211yescharacteristic
21C22×M16×C137C2211yescharacteristic
22#550×C137—24no—
23#550×C137—24no—
24C2×#127×C137—21no—
25C2×#127×C137C2211yescharacteristic
26C2×#121×C137—21no—
27C2×#121×C137—21no—
28C2×#121×C137—21no—
29C2×#121×C137C2211yescharacteristic
30C2×#121×C137C2211yescharacteristic
31C2×#121×C137C2211yescharacteristic
32C2×#121×C137C2211yescharacteristic
33C2×C4×Q8×C137C2211yescharacteristic
34C2×C4×D4×C137—21no—
35C2×C4×D4×C137C2211yescharacteristic
36C22×C4⋊C4×C137C2211yescharacteristic
37#469×C137—24no—
38#449×C137—24no—
39#449×C137—24no—
40C2×#106×C137C2211yescharacteristic
41#417×C137—24no—
42C2×#103×C137C2211yescharacteristic
43C2×#103×C137C2211yescharacteristic
44C2×#103×C137C2211yescharacteristic
45C2×#102×C137C2211yescharacteristic
46C2×#102×C137C2211yescharacteristic
47C2×#102×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic
49C2×#102×C137C2211yescharacteristic
50C2×#102×C137C2211yescharacteristic
51C2×#102×C137C2211yescharacteristic
52C2×C22⋊C8×C137C2211yescharacteristic
53C2×C22⋊C8×C137C2211yescharacteristic
54C2×C22⋊C8×C137C2211yescharacteristic
55#396×C137—21no—
56#394×C137—21no—
57#390×C137C2211yescharacteristic
58#389×C137C2211yescharacteristic
59#386×C137—21no—
60#380×C137C2211yescharacteristic
61#340×C137C2211yescharacteristic
62#340×C137C2211yescharacteristic
63#336×C137C2211yescharacteristic
64#336×C137C2211yescharacteristic
65C2×#41×C137—22no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—22no—
69C2×#41×C137—22no—
70C2×#41×C137—22no—
71C2×#41×C137—22no—
72C2×#41×C137—41no—
73C2×#41×C137—41no—
74C2×#41×C137—41no—
75C2×#41×C137—41no—
76C2×#41×C137D414yescomplemented
77C22×Q8×C137C2311yescharacteristic
78C22×D4×C137—21no—
79C22×D4×C137—21no—
80C22×D4×C137—21no—
81C22×D4×C137—21no—
82C22×D4×C137—21no—
83C22×D4×C137—21no—
84C22×D4×C137—21no—
85C22×D4×C137—21no—
86C22×D4×C137D411yescharacteristic
87C22×D4×C137C2311yescharacteristic
88C22×D4×C137C2311yescharacteristic
89C22×D4×C137C2311yescharacteristic
90C23×C4×C137—21no—
91C23×C4×C137—21no—
92C23×C4×C137—21no—
93C23×C4×C137C2311yescharacteristic
94C23×C4×C137C2311yescharacteristic
95C2×SD16×C137—22no—
96C2×SD16×C137—22no—
97C2×SD16×C137—22no—
98C2×D8×C137—22no—
99C2×D8×C137—22no—
100C2×D8×C137—22no—
101C2×D8×C137—41no—
102C2×D8×C137—41no—
103C2×D8×C137—41no—
104C2×M16×C137—22no—
105C2×M16×C137—22no—
106C2×M16×C137—41no—
107C22×C8×C137C2311yescharacteristic
108C22×C8×C137C2311yescharacteristic
109C22×C8×C137C2311yescharacteristic
110C22×C8×C137C2311yescharacteristic
111#127×C137—28no—
112#127×C137—22no—
113#127×C137—22no—
114#121×C137—28no—
115#121×C137—28no—
116#121×C137—22no—
117#121×C137—22no—
118#121×C137—22no—
119#121×C137—22no—
120#121×C137—22no—
121#121×C137—22no—
122#121×C137—41no—
123#121×C137—44no—
124#121×C137D414yescomplemented
125C4×Q8×C137—22no—
126C4×Q8×C137—22no—
127C4×D4×C137—28no—
128C4×D4×C137—22no—
129C4×D4×C137—22no—
130C2×C4⋊C4×C137—21no—
131C2×C4⋊C4×C137—22no—
132C2×C4⋊C4×C137—21no—
133C2×C4⋊C4×C137—21no—
134C2×C4⋊C4×C137—41no—
135C2×C4⋊C4×C137D411yescharacteristic
136C2×C4⋊C4×C137C2311yescharacteristic
137C2×C4⋊C4×C137C2311yescharacteristic
138C2×C4⋊C4×C137C2311yescharacteristic
139C2×C4⋊C4×C137C2311yescharacteristic
140C2×C22⋊C4×C137—21no—
141C2×C22⋊C4×C137—21no—
142C2×C22⋊C4×C137—21no—
143C2×C22⋊C4×C137—21no—
144C2×C22⋊C4×C137—21no—
145C2×C22⋊C4×C137—21no—
146C2×C22⋊C4×C137—21no—
147C2×C22⋊C4×C137D411yescharacteristic
148C2×C22⋊C4×C137D411yescharacteristic
149C2×C42×C137—21no—
150C2×C42×C137C2311yescharacteristic
151#106×C137—22no—
152#103×C137—22no—
153#103×C137—22no—
154#103×C137D414yescomplemented
155#102×C137—22no—
156#102×C137—22no—
157#102×C137—22no—
158#102×C137—22no—
159#102×C137—22no—
160#102×C137—22no—
161#102×C137—41no—
162C22⋊C8×C137—22no—
163C22⋊C8×C137—22no—
164C22⋊C8×C137—41no—
165#95×C137—21no—
166#95×C137—21no—
167C24×C137—21no—
168C24×C137—21no—
169C24×C137—21no—
170C24×C137C2×D411yescharacteristic
171C24×C137C2×D411yescharacteristic
172#41×C137—28no—
173#41×C137—44no—
174#41×C137—44no—
175#41×C137—44no—
176#41×C137—44no—
177#41×C137—44no—
178#41×C137—44no—
179#41×C137—44no—
180C2×Q8×C137—21no—
181C2×Q8×C137—21no—
182C2×Q8×C137—21no—
183C2×Q8×C137C2×D412yes—
184C2×Q8×C137C2×D412yes—
185C2×Q8×C137#4112yes—
186C2×D4×C137—24no—
187C2×D4×C137—24no—
188C2×D4×C137—22no—
189C2×D4×C137—24no—
190C2×D4×C137—24no—
191C2×D4×C137—24no—
192C2×D4×C137—24no—
193C2×D4×C137—22no—
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—21no—
204C2×D4×C137—21no—
205C2×D4×C137—21no—
206C2×D4×C137—21no—
207C2×D4×C137—21no—
208C2×D4×C137—21no—
209C2×D4×C137—21no—
210C2×D4×C137—41no—
211C2×D4×C137—42no—
212C2×D4×C137—42no—
213C2×D4×C137—42no—
214C2×D4×C137—42no—
215C2×D4×C137—42no—
216C2×D4×C137—42no—
217C2×D4×C137—42no—
218C2×D4×C137—42no—
219C2×D4×C137—42no—
220C2×D4×C137—42no—
221C2×D4×C137—42no—
222C2×D4×C137—81no—
223C2×D4×C137—81no—
224C2×D4×C137—81no—
225C2×D4×C137—81no—
226C2×D4×C137—81no—
227C2×D4×C137—81no—
228C2×D4×C137—81no—
229C2×D4×C137C2×D412yes—
230C2×D4×C137C2×D412yes—
231C22×C4×C137—21no—
232C22×C4×C137—21no—
233C22×C4×C137—21no—
234C22×C4×C137—21no—
235C22×C4×C137—21no—
236C22×C4×C137—24no—
237C22×C4×C137—21no—
238C22×C4×C137—21no—
239C22×C4×C137—24no—
240C22×C4×C137—21no—
241C22×C4×C137—21no—
242C22×C4×C137—21no—
243C22×C4×C137—21no—
244C22×C4×C137—21no—
245C22×C4×C137—21no—
246C22×C4×C137—21no—
247C22×C4×C137—21no—
248C22×C4×C137—42no—
249C22×C4×C137—42no—
250C22×C4×C137—42no—
251C22×C4×C137—42no—
252C22×C4×C137—42no—
253C22×C4×C137—42no—
254C22×C4×C137—81no—
255C22×C4×C137C2×D411yescharacteristic
256C22×C4×C137C2×D411yescharacteristic
257C22×C4×C137C2×D411yescharacteristic
258C22×C4×C137C2×D412yes—
259C22×C4×C137C2×D412yes—
260C22×C4×C137C2×D411yescharacteristic
261C22×C4×C137C2411yescharacteristic
262SD16×C137—44no—
263D8×C137—44no—
264D8×C137—44no—
265M16×C137—44no—
266C2×C8×C137—21no—
267C2×C8×C137—21no—
268C2×C8×C137—21no—
269C2×C8×C137—21no—
270C2×C8×C137—21no—
271C2×C8×C137—21no—
272C2×C8×C137—21no—
273C2×C8×C137—21no—
274C2×C8×C137—21no—
275C2×C8×C137—21no—
276C2×C8×C137—21no—
277C2×C8×C137C2×D412yes—
278C4⋊C4×C137—24no—
279C4⋊C4×C137—22no—
280C4⋊C4×C137—21no—
281C4⋊C4×C137—21no—
282C4⋊C4×C137—21no—
283C4⋊C4×C137—21no—
284C4⋊C4×C137—21no—
285C4⋊C4×C137—21no—
286C4⋊C4×C137—42no—
287C4⋊C4×C137—42no—
288C4⋊C4×C137C2×D412yes—
289C4⋊C4×C137C2×D412yes—
290C22⋊C4×C137—24no—
291C22⋊C4×C137—22no—
292C22⋊C4×C137—24no—
293C22⋊C4×C137—22no—
294C22⋊C4×C137—42no—
295C22⋊C4×C137—42no—
296C22⋊C4×C137—42no—
297C22⋊C4×C137—42no—
298C22⋊C4×C137—81no—
299C42×C137—24no—
300C42×C137—21no—
301C42×C137—21no—
302C23×C137—21no—
303C23×C137—21no—
304C23×C137—21no—
305C23×C137—21no—
306C23×C137—21no—
307C23×C137—21no—
308C23×C137—21no—
309C23×C137—22no—
310C23×C137—22no—
311C23×C137—21no—
312C23×C137—21no—
313C23×C137—21no—
314C23×C137—21no—
315C23×C137—21no—
316C23×C137—21no—
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—41no—
329C23×C137—41no—
330C23×C137—41no—
331C23×C137—41no—
332C23×C137—41no—
333C23×C137—41no—
334C23×C137—41no—
335C23×C137—41no—
336C23×C137#12012yes—
337C23×C137C22×D411yescharacteristic
338Q8×C137—22no—
339Q8×C137—22no—
340Q8×C137—22no—
341Q8×C137#12114yescomplemented
342D4×C137—22no—
343D4×C137—22no—
344D4×C137—22no—
345D4×C137—22no—
346D4×C137—44no—
347D4×C137—48no—
348D4×C137—48no—
349D4×C137—48no—
350D4×C137—41no—
351D4×C137—41no—
352D4×C137—41no—
353D4×C137—41no—
354D4×C137—41no—
355D4×C137—41no—
356D4×C137—41no—
357D4×C137—41no—
358D4×C137—84no—
359D4×C137—84no—
360D4×C137—84no—
361D4×C137—84no—
362D4×C137—84no—
363C2×C4×C137—21no—
364C2×C4×C137—22no—
365C2×C4×C137—21no—
366C2×C4×C137—22no—
367C2×C4×C137—21no—
368C2×C4×C137—22no—
369C2×C4×C137—21no—
370C2×C4×C137—22no—
371C2×C4×C137—22no—
372C2×C4×C137—22no—
373C2×C4×C137—22no—
374C2×C4×C137—21no—
375C2×C4×C137—22no—
376C2×C4×C137—21no—
377C2×C4×C137—21no—
378C2×C4×C137—22no—
379C2×C4×C137—21no—
380C2×C4×C137—21no—
381C2×C4×C137—21no—
382C2×C4×C137—48no—
383C2×C4×C137—48no—
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—41no—
396C2×C4×C137—41no—
397C2×C4×C137—41no—
398C2×C4×C137—84no—
399C2×C4×C137#12012yes—
400C2×C4×C137AGL(1,ℤ/8)12yes—
401C2×C4×C137C22×D411yescharacteristic
402C2×C4×C137C22×D411yescharacteristic
403C2×C4×C137C22×D411yescharacteristic
404C2×C4×C137C2×#4111yescharacteristic
405C2×C4×C137H(5,𝔽2)11yescharacteristic
406C2×C4×C137H(5,𝔽2)11yescharacteristic
407C8×C137—22no—
408C8×C137—41no—
409C8×C137—41no—
410C8×C137—41no—
411C22×C137—22no—
412C22×C137—22no—
413C22×C137—22no—
414C22×C137—41no—
415C22×C137—41no—
416C22×C137—41no—
417C22×C137—41no—
418C22×C137—41no—
419C22×C137—42no—
420C22×C137—42no—
421C22×C137—41no—
422C22×C137—41no—
423C22×C137—42no—
424C22×C137—42no—
425C22×C137—41no—
426C22×C137—42no—
427C22×C137—42no—
428C22×C137—41no—
429C22×C137—41no—
430C22×C137—41no—
431C22×C137—81no—
432C22×C137—81no—
433C22×C137—81no—
434C22×C137—81no—
435C22×C137—81no—
436C22×C137—81no—
437C22×C137—81no—
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×C137C2×#12011yescharacteristic
447C22×C137D4211yescharacteristic
448C22×C137#54611yescharacteristic
449C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C137#57511yescharacteristic
451C22×C137#57611yescharacteristic
452C22×C137#57711yescharacteristic
453C4×C137—22no—
454C4×C137—24no—
455C4×C137—22no—
456C4×C137—41no—
457C4×C137—41no—
458C4×C137—42no—
459C4×C137—42no—
460C4×C137—81no—
461C4×C137—81no—
462C4×C137C2×#12111yescharacteristic
463C4×C137#53411yescharacteristic
464C4×C137D4211yescharacteristic
465C4×C137#54611yescharacteristic
466C2×C137—42no—
467C2×C137—81no—
468C2×C137—82no—
469C2×C137—82no—
470C2×C137—161no—
471C2×C137#241011yescharacteristic
472C2×C137#300611yescharacteristic
473C2×C137#301211yescharacteristic
474C2×C137#327111yescharacteristic
475C2×C137#327411yescharacteristic
476C2×C137#330911yescharacteristic
477C2×C137#333211yescharacteristic
478#24451C13711yesmaximal, characteristic, direct product factor, Sylow
479C137#2445111yescharacteristic, direct product factor, Sylow
480C2×#550C2×C13711yescharacteristic, complemented
481C2×#469C2×C13711yescharacteristic, complemented
482C2×#449C2×C13711yescharacteristic, complemented
483C2×#449C2×C13711yescharacteristic, complemented
484C2×#417C2×C13711yescharacteristic, complemented
485#2416C2×C13711yescharacteristic, complemented
486#2041C2×C13711yescharacteristic, complemented
487#2034C2×C13711yescharacteristic, complemented
488#2011C2×C13711yescharacteristic, complemented
489#1999C2×C13711yescharacteristic, complemented
490#1880C2×C13711yescharacteristic, complemented
491#1874C2×C13711yescharacteristic, complemented
492#1870C2×C13711yescharacteristic, complemented
493#1865C2×C13711yescharacteristic, complemented
494#1788C2×C13711yescharacteristic, complemented
495C22×#41C22×C13711yescharacteristic
496C22×#41C22×C13711yescharacteristic
497C22×SD16C22×C13711yescharacteristic
498C22×D8C22×C13711yescharacteristic
499C22×D8C22×C13711yescharacteristic
500C22×M16C22×C13711yescharacteristic
501#550—24no—
502#550—24no—
503C2×#127—21no—
504C2×#127C22×C13711yescharacteristic
505C2×#121—21no—
506C2×#121—21no—
507C2×#121—21no—
508C2×#121C22×C13711yescharacteristic
509C2×#121C22×C13711yescharacteristic
510C2×#121C22×C13711yescharacteristic
511C2×#121C22×C13711yescharacteristic
512C2×C4×Q8C22×C13711yescharacteristic
513C2×C4×D4—21no—
514C2×C4×D4C22×C13711yescharacteristic
515C22×C4⋊C4C22×C13711yescharacteristic
516#469—24no—
517#449—24no—
518#449—24no—
519C2×#106C22×C13711yescharacteristic
520#417—24no—
521C2×#103C22×C13711yescharacteristic
522C2×#103C22×C13711yescharacteristic
523C2×#103C22×C13711yescharacteristic
524C2×#102C22×C13711yescharacteristic
525C2×#102C22×C13711yescharacteristic
526C2×#102C22×C13711yescharacteristic
527C2×#102C22×C13711yescharacteristic
528C2×#102C22×C13711yescharacteristic
529C2×#102C22×C13711yescharacteristic
530C2×#102C22×C13711yescharacteristic
531C2×C22⋊C8C22×C13711yescharacteristic
532C2×C22⋊C8C22×C13711yescharacteristic
533C2×C22⋊C8C22×C13711yescharacteristic
534#396—21no—
535#394—21no—
536#390C22×C13711yescharacteristic
537#389C22×C13711yescharacteristic
538#386—21no—
539#380C22×C13711yescharacteristic
540#340C22×C13711yescharacteristic
541#340C22×C13711yescharacteristic
542#336C22×C13711yescharacteristic
543#336C22×C13711yescharacteristic
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41D4×C13714yescomplemented
556C22×Q8C23×C13711yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4D4×C13711yescharacteristic
566C22×D4C23×C13711yescharacteristic
567C22×D4C23×C13711yescharacteristic
568C22×D4C23×C13711yescharacteristic
569C23×C4—21no—
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C13711yescharacteristic
573C23×C4C23×C13711yescharacteristic
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8—41no—
582C2×D8—41no—
583C2×M16—22no—
584C2×M16—22no—
585C2×M16—41no—
586C22×C8C23×C13711yescharacteristic
587C22×C8C23×C13711yescharacteristic
588C22×C8C23×C13711yescharacteristic
589C22×C8C23×C13711yescharacteristic
590#127—28no—
591#127—22no—
592#127—22no—
593#121—28no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—41no—
602#121—44no—
603#121D4×C13714yescomplemented
604C4×Q8—22no—
605C4×Q8—22no—
606C4×D4—28no—
607C4×D4—22no—
608C4×D4—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4D4×C13711yescharacteristic
615C2×C4⋊C4C23×C13711yescharacteristic
616C2×C4⋊C4C23×C13711yescharacteristic
617C2×C4⋊C4C23×C13711yescharacteristic
618C2×C4⋊C4C23×C13711yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C13711yescharacteristic
627C2×C22⋊C4D4×C13711yescharacteristic
628C2×C42—21no—
629C2×C42C23×C13711yescharacteristic
630#106—22no—
631#103—22no—
632#103—22no—
633#103D4×C13714yescomplemented
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24C2×D4×C13711yescharacteristic
650C24C2×D4×C13711yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656#41—44no—
657#41—44no—
658#41—44no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8C2×D4×C13712yes—
663C2×Q8C2×D4×C13712yes—
664C2×Q8#41×C13712yes—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
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—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—41no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4C2×D4×C13712yes—
709C2×D4C2×D4×C13712yes—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—81no—
734C22×C4C2×D4×C13711yescharacteristic
735C22×C4C2×D4×C13711yescharacteristic
736C22×C4C2×D4×C13711yescharacteristic
737C22×C4C2×D4×C13712yes—
738C22×C4C2×D4×C13712yes—
739C22×C4C2×D4×C13711yescharacteristic
740C22×C4C24×C13711yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744M16—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8C2×D4×C13712yes—
757C4⋊C4—24no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4C2×D4×C13712yes—
768C4⋊C4C2×D4×C13712yes—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—81no—
778C42—24no—
779C42—21no—
780C42—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—41no—
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—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23#120×C13712yes—
816C23C22×D4×C13711yescharacteristic
817Q8—22no—
818Q8—22no—
819Q8—22no—
820Q8#121×C13714yescomplemented
821D4—22no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—44no—
826D4—48no—
827D4—48no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—84no—
838D4—84no—
839D4—84no—
840D4—84no—
841D4—84no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—48no—
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—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4#120×C13712yes—
879C2×C4AGL(1,ℤ/8)×C13712yes—
880C2×C4C22×D4×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—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—41no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22C2×#120×C13711yescharacteristic
926C22D42×C13711yescharacteristic
927C22#546×C13711yescharacteristic
928C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
929C22#575×C13711yescharacteristic
930C22#576×C13711yescharacteristic
931C22#577×C13711yescharacteristic
932C4—22no—
933C4—24no—
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—42no—
939C4—81no—
940C4—81no—
941C4C2×#121×C13711yescharacteristic
942C4#534×C13711yescharacteristic
943C4D42×C13711yescharacteristic
944C4#546×C13711yescharacteristic
945C2—42no—
946C2—81no—
947C2—82no—
948C2—82no—
949C2—161no—
950C2#2410×C13711yescharacteristic
951C2#3006×C13711yescharacteristic
952C2#3012×C13711yescharacteristic
953C2#3271×C13711yescharacteristic
954C2#3274×C13711yescharacteristic
955C2#3309×C13711yescharacteristic
956C2#3332×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C4×D4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#550×C137C2semidirect
2. C2×#469×C137C2semidirect
3. C2×#449×C137C2semidirect
4. C2×#449×C137C2semidirect
5. C2×#417×C137C2semidirect
6. #2416×C137C2semidirect
7. #2041×C137C2semidirect
8. #2034×C137C2semidirect
9. #2011×C137C2semidirect
10. #1999×C137C2semidirect
11. #1880×C137C2semidirect
12. #1874×C137C2semidirect
13. #1870×C137C2semidirect
14. #1865×C137C2semidirect
15. #1788×C137C2semidirect
76. C2×#41×C137D4semidirect
124. #121×C137D4semidirect
154. #103×C137D4semidirect
341. Q8×C137#121semidirect
478. #24451C137direct (N × H)
479. C137#24451direct (N × H)
480. C2×#550C2×C137semidirect
481. C2×#469C2×C137semidirect
482. C2×#449C2×C137semidirect
483. C2×#449C2×C137semidirect
484. C2×#417C2×C137semidirect
485. #2416C2×C137semidirect
486. #2041C2×C137semidirect
487. #2034C2×C137semidirect
488. #2011C2×C137semidirect
489. #1999C2×C137semidirect
490. #1880C2×C137semidirect
491. #1874C2×C137semidirect
492. #1870C2×C137semidirect
493. #1865C2×C137semidirect
494. #1788C2×C137semidirect
555. C2×#41D4×C137semidirect
603. #121D4×C137semidirect
633. #103D4×C137semidirect
820. Q8#121×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1372
C2×#469×C1372
C2×#449×C1372
C2×#417×C1372
#2416×C1372
#2041×C1372
#2034×C1372
#2011×C1372
#1999×C1372
#1880×C1372
#1874×C1372
#1870×C1372
#1865×C1372
#1788×C1372
#24451137