Finite Group Databasebeta

← C137×#23903 #46873289

Subgroups — C137×#23903 #46873289

Order 35072.

2096 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C137C211yesmaximal, characteristic, complemented
2C2×#534×C137C211yesmaximal, characteristic, complemented
3C2×#458×C137C211yesmaximal, characteristic, complemented
4C2×B(4,𝔽2)×C137C211yesmaximal, characteristic, complemented
5#2613×C137C212yesmaximal, complemented
6#2022×C137C212yesmaximal, complemented
7#2021×C137C212yesmaximal, complemented
8#1898×C137C212yesmaximal, complemented
9#1890×C137C211yesmaximal, characteristic, complemented
10#1889×C137C211yesmaximal, characteristic, complemented
11#1781×C137C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C137C2211yescharacteristic
13C23×D4×C137C2211yescharacteristic
14C23×D4×C137C2211yescharacteristic, complemented
15#546×C137—24no—
16D42×C137—24no—
17#535×C137—21no—
18#534×C137—21no—
19#534×C137—24no—
20#534×C137—24no—
21#534×C137C2212yes—
22#525×C137—21no—
23C2×#123×C137—21no—
24C2×#123×C137C2211yescharacteristic
25C2×#123×C137C2211yescharacteristic, complemented
26C2×#123×C137C2212yescomplemented
27C2×#121×C137—21no—
28C2×#121×C137—21no—
29C2×#120×C137—21no—
30C2×#120×C137—21no—
31C2×#120×C137C2211yescharacteristic
32C2×#120×C137C2212yes—
33C2×#120×C137C2211yescharacteristic, complemented
34C2×#120×C137C2212yescomplemented
35#518×C137C2211yescharacteristic
36C22×C22⋊C4×C137C2211yescharacteristic, complemented
37#458×C137—24no—
38B(4,𝔽2)×C137—24no—
39C2×#99×C137C2211yescharacteristic
40C2×#99×C137C2211yescharacteristic
41C2×#99×C137C2212yescomplemented
42C2×#99×C137C2212yescomplemented
43C2×#99×C137C2212yescomplemented
44#394×C137—24no—
45#392×C137—24no—
46#381×C137C2212yescomplemented
47#379×C137C2212yescomplemented
48#379×C137C2212yescomplemented
49#342×C137C2212yescomplemented
50#342×C137C2212yescomplemented
51C25×C137D411yescharacteristic, complemented
52C25×C137C2311yescharacteristic
53C25×C137C2311yescharacteristic
54H(5,𝔽2)×C137—22no—
55H(5,𝔽2)×C137—22no—
56H(5,𝔽2)×C137—42no—
57C2×#41×C137—21no—
58C2×#41×C137—22no—
59C22×D4×C137—21no—
60C22×D4×C137—21no—
61C22×D4×C137—21no—
62C22×D4×C137—22no—
63C22×D4×C137—24no—
64C22×D4×C137—22no—
65C22×D4×C137—22no—
66C22×D4×C137—21no—
67C22×D4×C137—21no—
68C22×D4×C137—22no—
69C22×D4×C137—22no—
70C22×D4×C137—24no—
71C22×D4×C137—22no—
72C22×D4×C137—22no—
73C22×D4×C137—42no—
74C22×D4×C137—42no—
75C22×D4×C137D411yescharacteristic, complemented
76C22×D4×C137D411yescharacteristic, complemented
77C22×D4×C137D414yescomplemented
78C22×D4×C137C2312yes—
79C22×D4×C137C2311yescharacteristic
80C22×D4×C137C2311yescharacteristic
81C23×C4×C137—21no—
82C23×C4×C137D411yescharacteristic, complemented
83C23×C4×C137C2311yescharacteristic
84#127×C137—22no—
85#124×C137—22no—
86#123×C137—28no—
87#123×C137—22no—
88#123×C137—22no—
89#123×C137—22no—
90#123×C137—22no—
91#123×C137—22no—
92#123×C137—22no—
93#123×C137—24no—
94#123×C137—42no—
95#123×C137D414yescomplemented
96C22⋊Q8×C137—22no—
97#121×C137—28no—
98#121×C137—28no—
99#121×C137—22no—
100#121×C137—24no—
101#121×C137—24no—
102#121×C137—24no—
103#120×C137—28no—
104#120×C137—24no—
105#120×C137—22no—
106#120×C137—22no—
107#120×C137—22no—
108#120×C137—22no—
109#120×C137—24no—
110#120×C137—22no—
111#120×C137—22no—
112#120×C137—22no—
113#120×C137—22no—
114#120×C137—24no—
115#120×C137—42no—
116#120×C137D414yescomplemented
117C4×D4×C137—24no—
118C4×D4×C137—24no—
119#117×C137—21no—
120C2×C4⋊C4×C137—21no—
121C2×C4⋊C4×C137—21no—
122C2×C4⋊C4×C137—22no—
123C2×C22⋊C4×C137—22no—
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—22no—
131C2×C22⋊C4×C137—22no—
132C2×C22⋊C4×C137—22no—
133C2×C22⋊C4×C137—22no—
134C2×C22⋊C4×C137—24no—
135C2×C22⋊C4×C137—24no—
136C2×C22⋊C4×C137D414yescomplemented
137C2×C22⋊C4×C137C2312yes—
138C2×C22⋊C4×C137C2312yes—
139C2×C22⋊C4×C137C2312yes—
140C2×C22⋊C4×C137C2311yescharacteristic
141C2×C22⋊C4×C137C2311yescharacteristic
142#99×C137—22no—
143#99×C137—22no—
144#99×C137—24no—
145#99×C137—24no—
146#99×C137—42no—
147#95×C137—24no—
148C24×C137—21no—
149C24×C137—21no—
150C24×C137—22no—
151C24×C137—21no—
152C24×C137—22no—
153C24×C137—21no—
154C24×C137—22no—
155C24×C137—22no—
156C24×C137—21no—
157C24×C137—22no—
158C24×C137—41no—
159C24×C137—82no—
160C24×C137—82no—
161C24×C137—82no—
162C24×C137C2×D411yescharacteristic
163C24×C137C2×D412yes—
164C24×C137C2×D411yescharacteristic
165C24×C137C2×D414yes—
166C24×C137C2×D411yescharacteristic
167C24×C137C2×D411yescharacteristic
168C24×C137C2×D412yescomplemented
169C24×C137C2411yescharacteristic
170#41×C137—44no—
171#41×C137—44no—
172#41×C137—42no—
173#41×C137—42no—
174C2×Q8×C137—21no—
175C2×D4×C137—22no—
176C2×D4×C137—22no—
177C2×D4×C137—22no—
178C2×D4×C137—24no—
179C2×D4×C137—24no—
180C2×D4×C137—21no—
181C2×D4×C137—24no—
182C2×D4×C137—22no—
183C2×D4×C137—22no—
184C2×D4×C137—22no—
185C2×D4×C137—22no—
186C2×D4×C137—22no—
187C2×D4×C137—22no—
188C2×D4×C137—22no—
189C2×D4×C137—21no—
190C2×D4×C137—21no—
191C2×D4×C137—22no—
192C2×D4×C137—22no—
193C2×D4×C137—22no—
194C2×D4×C137—22no—
195C2×D4×C137—24no—
196C2×D4×C137—24no—
197C2×D4×C137—24no—
198C2×D4×C137—24no—
199C2×D4×C137—22no—
200C2×D4×C137—41no—
201C2×D4×C137—41no—
202C2×D4×C137—48no—
203C2×D4×C137—48no—
204C2×D4×C137—48no—
205C2×D4×C137—44no—
206C2×D4×C137—44no—
207C2×D4×C137—48no—
208C2×D4×C137—42no—
209C2×D4×C137—42no—
210C2×D4×C137—42no—
211C2×D4×C137—42no—
212C2×D4×C137—42no—
213C2×D4×C137—42no—
214C2×D4×C137—44no—
215C2×D4×C137—84no—
216C2×D4×C137—82no—
217C2×D4×C137—82no—
218C2×D4×C137—84no—
219C2×D4×C137—84no—
220C2×D4×C137C2×D412yes—
221C2×D4×C137C2×D412yes—
222C22×C4×C137—21no—
223C22×C4×C137—22no—
224C22×C4×C137—22no—
225C22×C4×C137—22no—
226C22×C4×C137—21no—
227C22×C4×C137—21no—
228C22×C4×C137—21no—
229C22×C4×C137—21no—
230C22×C4×C137—22no—
231C22×C4×C137—22no—
232C22×C4×C137—24no—
233C22×C4×C137—22no—
234C22×C4×C137—22no—
235C22×C4×C137—22no—
236C22×C4×C137—41no—
237C22×C4×C137—82no—
238C22×C4×C137C2×D412yes—
239C22×C4×C137C2×D411yescharacteristic
240C22×C4×C137C2×D411yescharacteristic
241C22×C4×C137C2×D414yes—
242C22×C4×C137C2×D412yescomplemented
243C4⋊C4×C137—24no—
244C4⋊C4×C137—22no—
245C4⋊C4×C137—24no—
246C4⋊C4×C137—24no—
247C4⋊C4×C137—44no—
248C22⋊C4×C137—24no—
249C22⋊C4×C137—22no—
250C22⋊C4×C137—24no—
251C22⋊C4×C137—24no—
252C22⋊C4×C137—24no—
253C22⋊C4×C137—24no—
254C22⋊C4×C137—24no—
255C22⋊C4×C137—24no—
256C22⋊C4×C137—24no—
257C22⋊C4×C137—21no—
258C22⋊C4×C137—21no—
259C22⋊C4×C137—22no—
260C22⋊C4×C137—22no—
261C22⋊C4×C137—24no—
262C22⋊C4×C137—22no—
263C22⋊C4×C137—22no—
264C22⋊C4×C137—22no—
265C22⋊C4×C137—22no—
266C22⋊C4×C137—44no—
267C22⋊C4×C137—44no—
268C22⋊C4×C137—84no—
269C22⋊C4×C137—84no—
270C22⋊C4×C137C2×D412yescomplemented
271C22⋊C4×C137C2×D412yescomplemented
272C42×C137—22no—
273C23×C137—21no—
274C23×C137—21no—
275C23×C137—21no—
276C23×C137—21no—
277C23×C137—21no—
278C23×C137—21no—
279C23×C137—24no—
280C23×C137—24no—
281C23×C137—21no—
282C23×C137—22no—
283C23×C137—21no—
284C23×C137—22no—
285C23×C137—24no—
286C23×C137—21no—
287C23×C137—22no—
288C23×C137—22no—
289C23×C137—42no—
290C23×C137—42no—
291C23×C137—42no—
292C23×C137—44no—
293C23×C137—44no—
294C23×C137—44no—
295C23×C137—42no—
296C23×C137—42no—
297C23×C137—44no—
298C23×C137—44no—
299C23×C137—42no—
300C23×C137—42no—
301C23×C137—44no—
302C23×C137—42no—
303C23×C137—44no—
304C23×C137—41no—
305C23×C137—41no—
306C23×C137—42no—
307C23×C137—82no—
308C23×C137—82no—
309C23×C137—82no—
310C23×C137—82no—
311C23×C137—82no—
312C23×C137—84no—
313C23×C137—84no—
314C23×C137—84no—
315C23×C137—82no—
316C23×C137—84no—
317C23×C137#12012yes—
318C23×C137#12012yes—
319C23×C137#12012yes—
320C23×C137C22×D411yescharacteristic
321C23×C137C22×D412yes—
322C23×C137C22×D411yescharacteristic
323C23×C137C22×D411yescharacteristic
324C23×C137H(5,𝔽2)12yes—
325Q8×C137—42no—
326D4×C137—24no—
327D4×C137—24no—
328D4×C137—44no—
329D4×C137—42no—
330D4×C137—44no—
331D4×C137—48no—
332D4×C137—48no—
333D4×C137—44no—
334D4×C137—48no—
335D4×C137—42no—
336D4×C137—42no—
337D4×C137—42no—
338D4×C137—42no—
339D4×C137—42no—
340D4×C137—42no—
341D4×C137—84no—
342D4×C137—84no—
343D4×C137—84no—
344D4×C137—84no—
345D4×C137—88no—
346C2×C4×C137—21no—
347C2×C4×C137—21no—
348C2×C4×C137—22no—
349C2×C4×C137—22no—
350C2×C4×C137—21no—
351C2×C4×C137—22no—
352C2×C4×C137—24no—
353C2×C4×C137—22no—
354C2×C4×C137—21no—
355C2×C4×C137—21no—
356C2×C4×C137—22no—
357C2×C4×C137—24no—
358C2×C4×C137—22no—
359C2×C4×C137—44no—
360C2×C4×C137—44no—
361C2×C4×C137—42no—
362C2×C4×C137—42no—
363C2×C4×C137—42no—
364C2×C4×C137—41no—
365C2×C4×C137—41no—
366C2×C4×C137—42no—
367C2×C4×C137—44no—
368C2×C4×C137—44no—
369C2×C4×C137—44no—
370C2×C4×C137—42no—
371C2×C4×C137—42no—
372C2×C4×C137—84no—
373C2×C4×C137—82no—
374C2×C4×C137#12012yes—
375C22×C137—24no—
376C22×C137—22no—
377C22×C137—22no—
378C22×C137—22no—
379C22×C137—22no—
380C22×C137—22no—
381C22×C137—24no—
382C22×C137—22no—
383C22×C137—41no—
384C22×C137—41no—
385C22×C137—42no—
386C22×C137—42no—
387C22×C137—42no—
388C22×C137—42no—
389C22×C137—42no—
390C22×C137—42no—
391C22×C137—42no—
392C22×C137—42no—
393C22×C137—42no—
394C22×C137—44no—
395C22×C137—44no—
396C22×C137—42no—
397C22×C137—42no—
398C22×C137—42no—
399C22×C137—41no—
400C22×C137—44no—
401C22×C137—42no—
402C22×C137—84no—
403C22×C137—84no—
404C22×C137—81no—
405C22×C137—82no—
406C22×C137—82no—
407C22×C137—81no—
408C22×C137—84no—
409C22×C137—82no—
410C22×C137—88no—
411C22×C137—82no—
412C22×C137—162no—
413C22×C137C2×#12011yescharacteristic
414C22×C137C2×#12011yescharacteristic
415C22×C137#53411yescharacteristic
416C22×C137D4212yes—
417C22×C137D4212yes—
418C4×C137—22no—
419C4×C137—42no—
420C4×C137—42no—
421C4×C137—41no—
422C4×C137—42no—
423C4×C137—42no—
424C4×C137—44no—
425C4×C137—82no—
426C4×C137—82no—
427C2×C137—21no—
428C2×C137—22no—
429C2×C137—22no—
430C2×C137—21no—
431C2×C137—42no—
432C2×C137—42no—
433C2×C137—42no—
434C2×C137—82no—
435C2×C137—81no—
436C2×C137—82no—
437C2×C137#240311yescharacteristic
438C2×C137#302612yes—
439#23903C13711yesmaximal, characteristic, direct product factor, Sylow
440C137#2390311yescharacteristic, direct product factor, Sylow
441#3484C2×C13711yescharacteristic, complemented
442C2×#534C2×C13711yescharacteristic, complemented
443C2×#458C2×C13711yescharacteristic, complemented
444C2×B(4,𝔽2)C2×C13711yescharacteristic, complemented
445#2613C2×C13712yescomplemented
446#2022C2×C13712yescomplemented
447#2021C2×C13712yescomplemented
448#1898C2×C13712yescomplemented
449#1890C2×C13711yescharacteristic, complemented
450#1889C2×C13711yescharacteristic, complemented
451#1781C2×C13711yescharacteristic, complemented
452C2×H(5,𝔽2)C22×C13711yescharacteristic
453C23×D4C22×C13711yescharacteristic
454C23×D4C22×C13711yescharacteristic, complemented
455#546—24no—
456D42—24no—
457#535—21no—
458#534—21no—
459#534—24no—
460#534—24no—
461#534C22×C13712yes—
462#525—21no—
463C2×#123—21no—
464C2×#123C22×C13711yescharacteristic
465C2×#123C22×C13711yescharacteristic, complemented
466C2×#123C22×C13712yescomplemented
467C2×#121—21no—
468C2×#121—21no—
469C2×#120—21no—
470C2×#120—21no—
471C2×#120C22×C13711yescharacteristic
472C2×#120C22×C13712yes—
473C2×#120C22×C13711yescharacteristic, complemented
474C2×#120C22×C13712yescomplemented
475#518C22×C13711yescharacteristic
476C22×C22⋊C4C22×C13711yescharacteristic, complemented
477#458—24no—
478B(4,𝔽2)—24no—
479C2×#99C22×C13711yescharacteristic
480C2×#99C22×C13711yescharacteristic
481C2×#99C22×C13712yescomplemented
482C2×#99C22×C13712yescomplemented
483C2×#99C22×C13712yescomplemented
484#394—24no—
485#392—24no—
486#381C22×C13712yescomplemented
487#379C22×C13712yescomplemented
488#379C22×C13712yescomplemented
489#342C22×C13712yescomplemented
490#342C22×C13712yescomplemented
491C25D4×C13711yescharacteristic, complemented
492C25C23×C13711yescharacteristic
493C25C23×C13711yescharacteristic
494H(5,𝔽2)—22no—
495H(5,𝔽2)—22no—
496H(5,𝔽2)—42no—
497C2×#41—21no—
498C2×#41—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—22no—
503C22×D4—24no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—24no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—42no—
514C22×D4—42no—
515C22×D4D4×C13711yescharacteristic, complemented
516C22×D4D4×C13711yescharacteristic, complemented
517C22×D4D4×C13714yescomplemented
518C22×D4C23×C13712yes—
519C22×D4C23×C13711yescharacteristic
520C22×D4C23×C13711yescharacteristic
521C23×C4—21no—
522C23×C4D4×C13711yescharacteristic, complemented
523C23×C4C23×C13711yescharacteristic
524#127—22no—
525#124—22no—
526#123—28no—
527#123—22no—
528#123—22no—
529#123—22no—
530#123—22no—
531#123—22no—
532#123—22no—
533#123—24no—
534#123—42no—
535#123D4×C13714yescomplemented
536C22⋊Q8—22no—
537#121—28no—
538#121—28no—
539#121—22no—
540#121—24no—
541#121—24no—
542#121—24no—
543#120—28no—
544#120—24no—
545#120—22no—
546#120—22no—
547#120—22no—
548#120—22no—
549#120—24no—
550#120—22no—
551#120—22no—
552#120—22no—
553#120—22no—
554#120—24no—
555#120—42no—
556#120D4×C13714yescomplemented
557C4×D4—24no—
558C4×D4—24no—
559#117—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4D4×C13714yescomplemented
577C2×C22⋊C4C23×C13712yes—
578C2×C22⋊C4C23×C13712yes—
579C2×C22⋊C4C23×C13712yes—
580C2×C22⋊C4C23×C13711yescharacteristic
581C2×C22⋊C4C23×C13711yescharacteristic
582#99—22no—
583#99—22no—
584#99—24no—
585#99—24no—
586#99—42no—
587#95—24no—
588C24—21no—
589C24—21no—
590C24—22no—
591C24—21no—
592C24—22no—
593C24—21no—
594C24—22no—
595C24—22no—
596C24—21no—
597C24—22no—
598C24—41no—
599C24—82no—
600C24—82no—
601C24—82no—
602C24C2×D4×C13711yescharacteristic
603C24C2×D4×C13712yes—
604C24C2×D4×C13711yescharacteristic
605C24C2×D4×C13714yes—
606C24C2×D4×C13711yescharacteristic
607C24C2×D4×C13711yescharacteristic
608C24C2×D4×C13712yescomplemented
609C24C24×C13711yescharacteristic
610#41—44no—
611#41—44no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—21no—
621C2×D4—24no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—24no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—22no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—48no—
643C2×D4—48no—
644C2×D4—48no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—48no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—44no—
655C2×D4—84no—
656C2×D4—82no—
657C2×D4—82no—
658C2×D4—84no—
659C2×D4—84no—
660C2×D4C2×D4×C13712yes—
661C2×D4C2×D4×C13712yes—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—24no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—41no—
677C22×C4—82no—
678C22×C4C2×D4×C13712yes—
679C22×C4C2×D4×C13711yescharacteristic
680C22×C4C2×D4×C13711yescharacteristic
681C22×C4C2×D4×C13714yes—
682C22×C4C2×D4×C13712yescomplemented
683C4⋊C4—24no—
684C4⋊C4—22no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—44no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—24no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—21no—
698C22⋊C4—21no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—44no—
707C22⋊C4—44no—
708C22⋊C4—84no—
709C22⋊C4—84no—
710C22⋊C4C2×D4×C13712yescomplemented
711C22⋊C4C2×D4×C13712yescomplemented
712C42—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—24no—
720C23—24no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—21no—
727C23—22no—
728C23—22no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—42no—
736C23—42no—
737C23—44no—
738C23—44no—
739C23—42no—
740C23—42no—
741C23—44no—
742C23—42no—
743C23—44no—
744C23—41no—
745C23—41no—
746C23—42no—
747C23—82no—
748C23—82no—
749C23—82no—
750C23—82no—
751C23—82no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—82no—
756C23—84no—
757C23#120×C13712yes—
758C23#120×C13712yes—
759C23#120×C13712yes—
760C23C22×D4×C13711yescharacteristic
761C23C22×D4×C13712yes—
762C23C22×D4×C13711yescharacteristic
763C23C22×D4×C13711yescharacteristic
764C23H(5,𝔽2)×C13712yes—
765Q8—42no—
766D4—24no—
767D4—24no—
768D4—44no—
769D4—42no—
770D4—44no—
771D4—48no—
772D4—48no—
773D4—44no—
774D4—48no—
775D4—42no—
776D4—42no—
777D4—42no—
778D4—42no—
779D4—42no—
780D4—42no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785D4—88no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—84no—
813C2×C4—82no—
814C2×C4#120×C13712yes—
815C22—24no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—24no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—44no—
841C22—42no—
842C22—84no—
843C22—84no—
844C22—81no—
845C22—82no—
846C22—81no—
847C22—82no—
848C22—84no—
849C22—82no—
850C22—88no—
851C22—82no—
852C22—162no—
853C22C2×#120×C13711yescharacteristic
854C22C2×#120×C13711yescharacteristic
855C22#534×C13711yescharacteristic
856C22D42×C13712yes—
857C22D42×C13712yes—
858C4—22no—
859C4—42no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—42no—
864C4—44no—
865C4—82no—
866C4—82no—
867C2—21no—
868C2—22no—
869C2—22no—
870C2—21no—
871C2—42no—
872C2—42no—
873C2—42no—
874C2—82no—
875C2—81no—
876C2—82no—
877C2#2403×C13711yescharacteristic
878C2#3026×C13712yes—
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC24C24×C137
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C25×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3484×C137C2semidirect
2. C2×#534×C137C2semidirect
3. C2×#458×C137C2semidirect
4. C2×B(4,𝔽2)×C137C2semidirect
5. #2613×C137C2semidirect
6. #2022×C137C2semidirect
7. #2021×C137C2semidirect
8. #1898×C137C2semidirect
9. #1890×C137C2semidirect
10. #1889×C137C2semidirect
11. #1781×C137C2semidirect
14. C23×D4×C137C22semidirect
25. C2×#123×C137C22semidirect
26. C2×#123×C137C22semidirect
33. C2×#120×C137C22semidirect
34. C2×#120×C137C22semidirect
36. C22×C22⋊C4×C137C22semidirect
41. C2×#99×C137C22semidirect
42. C2×#99×C137C22semidirect
43. C2×#99×C137C22semidirect
46. #381×C137C22semidirect
47. #379×C137C22semidirect
48. #379×C137C22semidirect
49. #342×C137C22semidirect
50. #342×C137C22semidirect
51. C25×C137D4semidirect
75. C22×D4×C137D4semidirect
76. C22×D4×C137D4semidirect
77. C22×D4×C137D4semidirect
82. C23×C4×C137D4semidirect
95. #123×C137D4semidirect
116. #120×C137D4semidirect
136. C2×C22⋊C4×C137D4semidirect
168. C24×C137C2×D4semidirect
242. C22×C4×C137C2×D4semidirect
270. C22⋊C4×C137C2×D4semidirect
271. C22⋊C4×C137C2×D4semidirect
439. #23903C137direct (N × H)
440. C137#23903direct (N × H)
441. #3484C2×C137semidirect
442. C2×#534C2×C137semidirect
443. C2×#458C2×C137semidirect
444. C2×B(4,𝔽2)C2×C137semidirect
445. #2613C2×C137semidirect
446. #2022C2×C137semidirect
447. #2021C2×C137semidirect
448. #1898C2×C137semidirect
449. #1890C2×C137semidirect
450. #1889C2×C137semidirect
451. #1781C2×C137semidirect
454. C23×D4C22×C137semidirect
465. C2×#123C22×C137semidirect
466. C2×#123C22×C137semidirect
473. C2×#120C22×C137semidirect
474. C2×#120C22×C137semidirect
476. C22×C22⋊C4C22×C137semidirect
481. C2×#99C22×C137semidirect
482. C2×#99C22×C137semidirect
483. C2×#99C22×C137semidirect
486. #381C22×C137semidirect
487. #379C22×C137semidirect
488. #379C22×C137semidirect
489. #342C22×C137semidirect
490. #342C22×C137semidirect
491. C25D4×C137semidirect
515. C22×D4D4×C137semidirect
516. C22×D4D4×C137semidirect
517. C22×D4D4×C137semidirect
522. C23×C4D4×C137semidirect
535. #123D4×C137semidirect
556. #120D4×C137semidirect
576. C2×C22⋊C4D4×C137semidirect
608. C24C2×D4×C137semidirect
682. C22×C4C2×D4×C137semidirect
710. C22⋊C4C2×D4×C137semidirect
711. C22⋊C4C2×D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3484×C1372
C2×#534×C1372
C2×#458×C1372
C2×B(4,𝔽2)×C1372
#2613×C1372
#2022×C1372
#2021×C1372
#1898×C1372
#1890×C1372
#1889×C1372
#1781×C1372
#23903137