Finite Group Databasebeta

← C137×#14725 #46864111

Subgroups — C137×#14725 #46864111

Order 35072.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C137C211yesmaximal, characteristic
2C23×C22⋊C4×C137C211yesmaximal, characteristic, complemented
3C2×#394×C137C212yesmaximal, complemented
4C2×#386×C137C211yesmaximal, characteristic, complemented
5C2×#386×C137C211yesmaximal, characteristic, complemented
6C2×#380×C137C211yesmaximal, characteristic, complemented
7C2×#379×C137C211yesmaximal, characteristic, complemented
8#1440×C137C212yesmaximal, complemented
9#1439×C137C212yesmaximal, complemented
10#1438×C137C212yesmaximal, complemented
11C22⋊#95×C137C211yesmaximal, characteristic, complemented
12C26×C137C2211yescharacteristic
13C23×D4×C137C2211yescharacteristic
14C23×D4×C137C2212yes—
15C24×C4×C137C2211yescharacteristic
16C24×C4×C137C2211yescharacteristic
17C2×#120×C137—24no—
18C2×#120×C137—24no—
19C2×#120×C137—24no—
20C22×C4⋊C4×C137C2212yescomplemented
21C22×C22⋊C4×C137—24no—
22C22×C22⋊C4×C137—28no—
23C22×C22⋊C4×C137C2211yescharacteristic
24C22×C22⋊C4×C137C2211yescharacteristic
25C22×C22⋊C4×C137C2212yes—
26C22×C22⋊C4×C137C2212yes—
27C22×C22⋊C4×C137C2212yes—
28C22×C22⋊C4×C137C2211yescharacteristic
29C22×C22⋊C4×C137C2212yes—
30C22×C22⋊C4×C137C2212yes—
31C22×C22⋊C4×C137C2211yescharacteristic, complemented
32C22×C22⋊C4×C137C2212yescomplemented
33C22×C22⋊C4×C137C2211yescharacteristic, complemented
34#394×C137—28no—
35#386×C137—24no—
36#386×C137—24no—
37#380×C137—24no—
38#379×C137—24no—
39C2×#95×C137C2212yescomplemented
40C2×#95×C137C2211yescharacteristic, complemented
41C2×#95×C137C2212yescomplemented
42C2×#95×C137C2211yescharacteristic, complemented
43C2×#95×C137C2212yescomplemented
44C2×#95×C137C2212yescomplemented
45C25×C137—24no—
46C25×C137—22no—
47C25×C137—24no—
48C25×C137—22no—
49C25×C137—22no—
50C25×C137—22no—
51C25×C137—22no—
52C25×C137—22no—
53C25×C137—42no—
54C25×C137—42no—
55C25×C137D414yes—
56C25×C137C2311yescharacteristic
57C25×C137C2312yes—
58C25×C137C2311yescharacteristic
59C22×D4×C137—22no—
60C22×D4×C137—24no—
61C22×D4×C137—24no—
62C22×D4×C137—22no—
63C22×D4×C137—22no—
64C22×D4×C137—22no—
65C22×D4×C137—22no—
66C22×D4×C137—22no—
67C22×D4×C137—24no—
68C22×D4×C137—24no—
69C22×D4×C137—24no—
70C22×D4×C137—42no—
71C22×D4×C137—42no—
72C22×D4×C137D414yes—
73C23×C4×C137—22no—
74C23×C4×C137—22no—
75C23×C4×C137—22no—
76C23×C4×C137—24no—
77C23×C4×C137—24no—
78C23×C4×C137—22no—
79C23×C4×C137—22no—
80C23×C4×C137—42no—
81C23×C4×C137—42no—
82C23×C4×C137D414yescomplemented
83C23×C4×C137C2311yescharacteristic
84C23×C4×C137C2311yescharacteristic
85C23×C4×C137C2312yes—
86C23×C4×C137C2311yescharacteristic
87C23×C4×C137C2311yescharacteristic
88C23×C4×C137C2312yes—
89C23×C4×C137C2312yes—
90C23×C4×C137C2311yescharacteristic
91#120×C137—232no—
92C2×C4⋊C4×C137—24no—
93C2×C4⋊C4×C137—24no—
94C2×C4⋊C4×C137—42no—
95C2×C22⋊C4×C137—232no—
96C2×C22⋊C4×C137—24no—
97C2×C22⋊C4×C137—24no—
98C2×C22⋊C4×C137—22no—
99C2×C22⋊C4×C137—22no—
100C2×C22⋊C4×C137—24no—
101C2×C22⋊C4×C137—24no—
102C2×C22⋊C4×C137—24no—
103C2×C22⋊C4×C137—24no—
104C2×C22⋊C4×C137—24no—
105C2×C22⋊C4×C137—24no—
106C2×C22⋊C4×C137—24no—
107C2×C22⋊C4×C137—22no—
108C2×C22⋊C4×C137—24no—
109C2×C22⋊C4×C137—22no—
110C2×C22⋊C4×C137—22no—
111C2×C22⋊C4×C137—22no—
112C2×C22⋊C4×C137—22no—
113C2×C22⋊C4×C137—24no—
114C2×C22⋊C4×C137—24no—
115C2×C22⋊C4×C137—24no—
116C2×C22⋊C4×C137—22no—
117C2×C22⋊C4×C137—22no—
118C2×C22⋊C4×C137—22no—
119C2×C22⋊C4×C137—24no—
120C2×C22⋊C4×C137—24no—
121C2×C22⋊C4×C137—42no—
122C2×C22⋊C4×C137—42no—
123C2×C22⋊C4×C137—42no—
124C2×C22⋊C4×C137—42no—
125C2×C22⋊C4×C137D414yes—
126C2×C22⋊C4×C137D418yescomplemented
127#95×C137—24no—
128#95×C137—22no—
129#95×C137—22no—
130#95×C137—24no—
131#95×C137—24no—
132#95×C137—42no—
133C24×C137—22no—
134C24×C137—22no—
135C24×C137—22no—
136C24×C137—22no—
137C24×C137—28no—
138C24×C137—28no—
139C24×C137—216no—
140C24×C137—216no—
141C24×C137—28no—
142C24×C137—22no—
143C24×C137—22no—
144C24×C137—22no—
145C24×C137—22no—
146C24×C137—22no—
147C24×C137—22no—
148C24×C137—22no—
149C24×C137—22no—
150C24×C137—22no—
151C24×C137—22no—
152C24×C137—22no—
153C24×C137—22no—
154C24×C137—28no—
155C24×C137—28no—
156C24×C137—21no—
157C24×C137—22no—
158C24×C137—21no—
159C24×C137—21no—
160C24×C137—21no—
161C24×C137—21no—
162C24×C137—21no—
163C24×C137—22no—
164C24×C137—22no—
165C24×C137—22no—
166C24×C137—48no—
167C24×C137—48no—
168C24×C137—48no—
169C24×C137—48no—
170C24×C137—48no—
171C24×C137—48no—
172C24×C137—48no—
173C24×C137—48no—
174C24×C137—48no—
175C24×C137—44no—
176C24×C137—44no—
177C24×C137—48no—
178C24×C137—44no—
179C24×C137—44no—
180C24×C137—44no—
181C24×C137—44no—
182C24×C137C2×D412yes—
183C24×C137C2×D414yes—
184C24×C137C2×D414yes—
185C24×C137C2×D412yes—
186C24×C137C2×D412yes—
187C24×C137C2×D412yes—
188C24×C137C2×D412yes—
189C24×C137#4114yes—
190C24×C137#4112yes—
191C24×C137#4112yes—
192C24×C137#4112yes—
193C24×C137C2411yescharacteristic
194C2×D4×C137—216no—
195C2×D4×C137—28no—
196C2×D4×C137—28no—
197C2×D4×C137—28no—
198C2×D4×C137—48no—
199C2×D4×C137—48no—
200C2×D4×C137—48no—
201C2×D4×C137—48no—
202C2×D4×C137—48no—
203C2×D4×C137—48no—
204C2×D4×C137—44no—
205C2×D4×C137—44no—
206C2×D4×C137—44no—
207C2×D4×C137—44no—
208C22×C4×C137—21no—
209C22×C4×C137—21no—
210C22×C4×C137—22no—
211C22×C4×C137—28no—
212C22×C4×C137—28no—
213C22×C4×C137—21no—
214C22×C4×C137—21no—
215C22×C4×C137—22no—
216C22×C4×C137—22no—
217C22×C4×C137—22no—
218C22×C4×C137—22no—
219C22×C4×C137—22no—
220C22×C4×C137—21no—
221C22×C4×C137—21no—
222C22×C4×C137—22no—
223C22×C4×C137—22no—
224C22×C4×C137—21no—
225C22×C4×C137—22no—
226C22×C4×C137—21no—
227C22×C4×C137—21no—
228C22×C4×C137—21no—
229C22×C4×C137—22no—
230C22×C4×C137—22no—
231C22×C4×C137—22no—
232C22×C4×C137—22no—
233C22×C4×C137—22no—
234C22×C4×C137—22no—
235C22×C4×C137—28no—
236C22×C4×C137—21no—
237C22×C4×C137—22no—
238C22×C4×C137—22no—
239C22×C4×C137—21no—
240C22×C4×C137—22no—
241C22×C4×C137—22no—
242C22×C4×C137—21no—
243C22×C4×C137—21no—
244C22×C4×C137—22no—
245C22×C4×C137—21no—
246C22×C4×C137—22no—
247C22×C4×C137—21no—
248C22×C4×C137—22no—
249C22×C4×C137—22no—
250C22×C4×C137—22no—
251C22×C4×C137—22no—
252C22×C4×C137—22no—
253C22×C4×C137—44no—
254C22×C4×C137—48no—
255C22×C4×C137—48no—
256C22×C4×C137—48no—
257C22×C4×C137—48no—
258C22×C4×C137—44no—
259C22×C4×C137—44no—
260C22×C4×C137C2×D412yes—
261C22×C4×C137C2×D412yes—
262C22×C4×C137C2×D414yes—
263C22×C4×C137C2×D414yes—
264C22×C4×C137C2×D412yes—
265C22×C4×C137C2×D414yes—
266C4⋊C4×C137—48no—
267C22⋊C4×C137—216no—
268C22⋊C4×C137—216no—
269C22⋊C4×C137—28no—
270C22⋊C4×C137—216no—
271C22⋊C4×C137—48no—
272C22⋊C4×C137—44no—
273C22⋊C4×C137—48no—
274C22⋊C4×C137—44no—
275C22⋊C4×C137—48no—
276C22⋊C4×C137—44no—
277C22⋊C4×C137—44no—
278C23×C137—22no—
279C23×C137—24no—
280C23×C137—22no—
281C23×C137—24no—
282C23×C137—22no—
283C23×C137—24no—
284C23×C137—22no—
285C23×C137—24no—
286C23×C137—24no—
287C23×C137—24no—
288C23×C137—24no—
289C23×C137—24no—
290C23×C137—24no—
291C23×C137—24no—
292C23×C137—24no—
293C23×C137—24no—
294C23×C137—232no—
295C23×C137—24no—
296C23×C137—24no—
297C23×C137—24no—
298C23×C137—24no—
299C23×C137—24no—
300C23×C137—24no—
301C23×C137—24no—
302C23×C137—24no—
303C23×C137—24no—
304C23×C137—24no—
305C23×C137—24no—
306C23×C137—24no—
307C23×C137—24no—
308C23×C137—24no—
309C23×C137—24no—
310C23×C137—24no—
311C23×C137—24no—
312C23×C137—24no—
313C23×C137—22no—
314C23×C137—22no—
315C23×C137—22no—
316C23×C137—24no—
317C23×C137—24no—
318C23×C137—432no—
319C23×C137—432no—
320C23×C137—416no—
321C23×C137—416no—
322C23×C137—416no—
323C23×C137—416no—
324C23×C137—432no—
325C23×C137—432no—
326C23×C137—416no—
327C23×C137—42no—
328C23×C137—42no—
329C23×C137—42no—
330C23×C137—42no—
331C23×C137—42no—
332C23×C137—42no—
333C23×C137—42no—
334C23×C137—42no—
335C23×C137—42no—
336C23×C137—42no—
337C23×C137—42no—
338C23×C137—42no—
339C23×C137—42no—
340C23×C137—42no—
341C23×C137—42no—
342C23×C137—42no—
343C23×C137—416no—
344C23×C137—41no—
345C23×C137—41no—
346C23×C137—41no—
347C23×C137—42no—
348C23×C137—41no—
349C23×C137—42no—
350C23×C137—41no—
351C23×C137—41no—
352C23×C137—41no—
353C23×C137—42no—
354C23×C137—41no—
355C23×C137—42no—
356C23×C137—42no—
357C23×C137—42no—
358C23×C137—42no—
359C23×C137—42no—
360C23×C137—42no—
361C23×C137—42no—
362C23×C137#12014yes—
363C23×C137#12118yes—
364C23×C137#12114yes—
365C23×C137#12114yes—
366C23×C137#12114yes—
367C23×C137#12314yes—
368C23×C137#12314yes—
369C23×C137#12414yes—
370C23×C137C22×D411yescharacteristic
371C23×C137C22×D411yescharacteristic
372C23×C137C22×D411yescharacteristic
373C23×C137C22×D412yes—
374C23×C137C22×D411yescharacteristic
375C23×C137C2×#4111yescharacteristic
376C23×C137C2×#4111yescharacteristic
377C23×C137C2×#4111yescharacteristic
378C23×C137C2×#4112yes—
379C23×C137H(5,𝔽2)12yes—
380C23×C137H(5,𝔽2)12yes—
381D4×C137—432no—
382D4×C137—416no—
383C2×C4×C137—22no—
384C2×C4×C137—22no—
385C2×C4×C137—24no—
386C2×C4×C137—24no—
387C2×C4×C137—24no—
388C2×C4×C137—22no—
389C2×C4×C137—22no—
390C2×C4×C137—24no—
391C2×C4×C137—22no—
392C2×C4×C137—22no—
393C2×C4×C137—22no—
394C2×C4×C137—22no—
395C2×C4×C137—24no—
396C2×C4×C137—24no—
397C2×C4×C137—24no—
398C2×C4×C137—24no—
399C2×C4×C137—416no—
400C2×C4×C137—416no—
401C2×C4×C137—42no—
402C2×C4×C137—41no—
403C2×C4×C137—41no—
404C2×C4×C137—42no—
405C2×C4×C137—41no—
406C2×C4×C137—41no—
407C2×C4×C137—42no—
408C2×C4×C137—42no—
409C2×C4×C137—42no—
410C2×C4×C137—42no—
411C2×C4×C137—42no—
412C2×C4×C137—42no—
413C2×C4×C137—42no—
414C2×C4×C137—42no—
415C2×C4×C137—41no—
416C2×C4×C137—42no—
417C2×C4×C137—41no—
418C2×C4×C137—42no—
419C2×C4×C137—41no—
420C2×C4×C137—42no—
421C2×C4×C137—41no—
422C2×C4×C137—42no—
423C2×C4×C137—42no—
424C2×C4×C137—41no—
425C2×C4×C137—42no—
426C2×C4×C137—41no—
427C2×C4×C137—42no—
428C2×C4×C137—42no—
429C2×C4×C137—42no—
430C2×C4×C137—42no—
431C2×C4×C137—42no—
432C2×C4×C137#12014yescomplemented
433C22×C137—24no—
434C22×C137—24no—
435C22×C137—24no—
436C22×C137—24no—
437C22×C137—28no—
438C22×C137—24no—
439C22×C137—28no—
440C22×C137—28no—
441C22×C137—28no—
442C22×C137—24no—
443C22×C137—28no—
444C22×C137—28no—
445C22×C137—28no—
446C22×C137—464no—
447C22×C137—44no—
448C22×C137—44no—
449C22×C137—44no—
450C22×C137—44no—
451C22×C137—44no—
452C22×C137—44no—
453C22×C137—44no—
454C22×C137—44no—
455C22×C137—44no—
456C22×C137—44no—
457C22×C137—44no—
458C22×C137—44no—
459C22×C137—42no—
460C22×C137—42no—
461C22×C137—44no—
462C22×C137—44no—
463C22×C137—42no—
464C22×C137—81no—
465C22×C137—81no—
466C22×C137—81no—
467C22×C137—81no—
468C22×C137—82no—
469C22×C137—82no—
470C22×C137#39418yescomplemented
471C22×C137C2×#12011yescharacteristic
472C22×C137C2×#12011yescharacteristic
473C22×C137C2×#12111yescharacteristic
474C22×C137C2×#12112yes—
475C22×C137C2×#12111yescharacteristic
476C22×C137C2×#12111yescharacteristic
477C22×C137C2×#12311yescharacteristic
478C22×C137C2×#12311yescharacteristic
479C22×C137#52511yescharacteristic
480C22×C137#52512yes—
481C22×C137C2×#12411yescharacteristic
482C22×C137#53412yes—
483C22×C137#53411yescharacteristic
484C22×C137#53511yescharacteristic
485C22×C137#53812yes—
486C22×C137D4212yes—
487C22×C137D4212yes—
488C22×C137#54612yes—
489C22×C137#54612yes—
490C22×C137#54612yes—
491C22×C137#54612yes—
492C22×C137#55112yes—
493C22×C137#55112yes—
494C4×C137—24no—
495C4×C137—42no—
496C4×C137—44no—
497C4×C137—42no—
498C4×C137—44no—
499C4×C137—81no—
500C4×C137—81no—
501C4×C137—82no—
502C2×C137—28no—
503C2×C137—48no—
504C2×C137—82no—
505C2×C137C2×#39411yescharacteristic
506C2×C137#240811yescharacteristic
507C2×C137#241011yescharacteristic
508C2×C137#241012yes—
509C2×C137#241111yescharacteristic
510C2×C137#241212yes—
511C2×C137#241812yes—
512C2×C137#247212yes—
513C2×C137#253411yescharacteristic
514C2×C137#261711yescharacteristic
515C2×C137#284711yescharacteristic
516#14725C13711yesmaximal, characteristic, direct product factor, Sylow
517C137#1472511yescharacteristic, direct product factor, Sylow
518C22×#120C2×C13711yescharacteristic
519C23×C22⋊C4C2×C13711yescharacteristic, complemented
520C2×#394C2×C13712yescomplemented
521C2×#386C2×C13711yescharacteristic, complemented
522C2×#386C2×C13711yescharacteristic, complemented
523C2×#380C2×C13711yescharacteristic, complemented
524C2×#379C2×C13711yescharacteristic, complemented
525#1440C2×C13712yescomplemented
526#1439C2×C13712yescomplemented
527#1438C2×C13712yescomplemented
528C22⋊#95C2×C13711yescharacteristic, complemented
529C26C22×C13711yescharacteristic
530C23×D4C22×C13711yescharacteristic
531C23×D4C22×C13712yes—
532C24×C4C22×C13711yescharacteristic
533C24×C4C22×C13711yescharacteristic
534C2×#120—24no—
535C2×#120—24no—
536C2×#120—24no—
537C22×C4⋊C4C22×C13712yescomplemented
538C22×C22⋊C4—24no—
539C22×C22⋊C4—28no—
540C22×C22⋊C4C22×C13712yes—
541C22×C22⋊C4C22×C13712yes—
542C22×C22⋊C4C22×C13712yes—
543C22×C22⋊C4C22×C13711yescharacteristic
544C22×C22⋊C4C22×C13711yescharacteristic
545C22×C22⋊C4C22×C13711yescharacteristic
546C22×C22⋊C4C22×C13712yes—
547C22×C22⋊C4C22×C13712yes—
548C22×C22⋊C4C22×C13711yescharacteristic, complemented
549C22×C22⋊C4C22×C13712yescomplemented
550C22×C22⋊C4C22×C13711yescharacteristic, complemented
551#394—28no—
552#386—24no—
553#386—24no—
554#380—24no—
555#379—24no—
556C2×#95C22×C13712yescomplemented
557C2×#95C22×C13712yescomplemented
558C2×#95C22×C13711yescharacteristic, complemented
559C2×#95C22×C13712yescomplemented
560C2×#95C22×C13711yescharacteristic, complemented
561C2×#95C22×C13712yescomplemented
562C25—24no—
563C25—22no—
564C25—24no—
565C25—22no—
566C25—22no—
567C25—22no—
568C25—22no—
569C25—22no—
570C25—42no—
571C25—42no—
572C25D4×C13714yes—
573C25C23×C13711yescharacteristic
574C25C23×C13712yes—
575C25C23×C13711yescharacteristic
576C22×D4—24no—
577C22×D4—24no—
578C22×D4—22no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—42no—
588C22×D4—42no—
589C22×D4D4×C13714yes—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—24no—
594C23×C4—24no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—42no—
598C23×C4—42no—
599C23×C4D4×C13714yescomplemented
600C23×C4C23×C13712yes—
601C23×C4C23×C13711yescharacteristic
602C23×C4C23×C13711yescharacteristic
603C23×C4C23×C13711yescharacteristic
604C23×C4C23×C13712yes—
605C23×C4C23×C13712yes—
606C23×C4C23×C13711yescharacteristic
607C23×C4C23×C13711yescharacteristic
608#120—232no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—42no—
612C2×C22⋊C4—232no—
613C2×C22⋊C4—24no—
614C2×C22⋊C4—24no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—24no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—42no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4D4×C13714yes—
643C2×C22⋊C4D4×C13718yescomplemented
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—42no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—216no—
657C24—216no—
658C24—28no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—28no—
672C24—28no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24C2×D4×C13712yes—
700C24C2×D4×C13714yes—
701C24C2×D4×C13714yes—
702C24C2×D4×C13712yes—
703C24C2×D4×C13712yes—
704C24C2×D4×C13712yes—
705C24C2×D4×C13712yes—
706C24#41×C13714yes—
707C24#41×C13712yes—
708C24#41×C13712yes—
709C24#41×C13712yes—
710C24C24×C13711yescharacteristic
711C2×D4—216no—
712C2×D4—28no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—22no—
728C22×C4—28no—
729C22×C4—28no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—22no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—28no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—44no—
771C22×C4—48no—
772C22×C4—48no—
773C22×C4—48no—
774C22×C4—48no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C13712yes—
778C22×C4C2×D4×C13712yes—
779C22×C4C2×D4×C13714yes—
780C22×C4C2×D4×C13714yes—
781C22×C4C2×D4×C13712yes—
782C22×C4C2×D4×C13714yes—
783C4⋊C4—48no—
784C22⋊C4—216no—
785C22⋊C4—216no—
786C22⋊C4—28no—
787C22⋊C4—216no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—48no—
791C22⋊C4—44no—
792C22⋊C4—48no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C23—22no—
796C23—24no—
797C23—22no—
798C23—24no—
799C23—22no—
800C23—24no—
801C23—22no—
802C23—24no—
803C23—24no—
804C23—24no—
805C23—24no—
806C23—24no—
807C23—24no—
808C23—24no—
809C23—24no—
810C23—24no—
811C23—232no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—24no—
834C23—24no—
835C23—432no—
836C23—432no—
837C23—416no—
838C23—416no—
839C23—416no—
840C23—416no—
841C23—416no—
842C23—432no—
843C23—432no—
844C23—416no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—41no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—41no—
872C23—42no—
873C23—42no—
874C23—42no—
875C23—42no—
876C23—42no—
877C23—42no—
878C23—42no—
879C23#120×C13714yes—
880C23#121×C13718yes—
881C23#121×C13714yes—
882C23#121×C13714yes—
883C23#121×C13714yes—
884C23#123×C13714yes—
885C23#123×C13714yes—
886C23#124×C13714yes—
887C23C22×D4×C13711yescharacteristic
888C23C22×D4×C13711yescharacteristic
889C23C22×D4×C13711yescharacteristic
890C23C22×D4×C13712yes—
891C23C22×D4×C13711yescharacteristic
892C23C2×#41×C13711yescharacteristic
893C23C2×#41×C13711yescharacteristic
894C23C2×#41×C13711yescharacteristic
895C23C2×#41×C13712yes—
896C23H(5,𝔽2)×C13712yes—
897C23H(5,𝔽2)×C13712yes—
898D4—432no—
899D4—416no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—24no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—416no—
917C2×C4—416no—
918C2×C4—42no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—41no—
937C2×C4—42no—
938C2×C4—41no—
939C2×C4—42no—
940C2×C4—41no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—41no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4#120×C13714yescomplemented
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—28no—
956C22—24no—
957C22—28no—
958C22—28no—
959C22—28no—
960C22—28no—
961C22—28no—
962C22—28no—
963C22—464no—
964C22—44no—
965C22—44no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—44no—
980C22—44no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—82no—
986C22—82no—
987C22#394×C13718yescomplemented
988C22C2×#120×C13711yescharacteristic
989C22C2×#120×C13711yescharacteristic
990C22C2×#121×C13711yescharacteristic
991C22C2×#121×C13711yescharacteristic
992C22C2×#121×C13712yes—
993C22C2×#121×C13711yescharacteristic
994C22C2×#123×C13711yescharacteristic
995C22C2×#123×C13711yescharacteristic
996C22#525×C13711yescharacteristic
997C22#525×C13712yes—
998C22C2×#124×C13711yescharacteristic
999C22#534×C13711yescharacteristic
1000C22#534×C13712yes—
1001C22#535×C13711yescharacteristic
1002C22#538×C13712yes—
1003C22D42×C13712yes—
1004C22D42×C13712yes—
1005C22#546×C13712yes—
1006C22#546×C13712yes—
1007C22#546×C13712yes—
1008C22#546×C13712yes—
1009C22#551×C13712yes—
1010C22#551×C13712yes—
1011C4—24no—
1012C4—42no—
1013C4—44no—
1014C4—42no—
1015C4—44no—
1016C4—81no—
1017C4—81no—
1018C4—82no—
1019C2—28no—
1020C2—48no—
1021C2—82no—
1022C2C2×#394×C13711yescharacteristic
1023C2#2408×C13711yescharacteristic
1024C2#2410×C13711yescharacteristic
1025C2#2410×C13712yes—
1026C2#2411×C13711yescharacteristic
1027C2#2412×C13712yes—
1028C2#2418×C13712yes—
1029C2#2472×C13712yes—
1030C2#2534×C13711yescharacteristic
1031C2#2617×C13711yescharacteristic
1032C2#2847×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutator, Frattini, cosocleC24C24×C137
prime radicalC22×#120×C137C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C137C2semidirect
3. C2×#394×C137C2semidirect
4. C2×#386×C137C2semidirect
5. C2×#386×C137C2semidirect
6. C2×#380×C137C2semidirect
7. C2×#379×C137C2semidirect
8. #1440×C137C2semidirect
9. #1439×C137C2semidirect
10. #1438×C137C2semidirect
11. C22⋊#95×C137C2semidirect
20. C22×C4⋊C4×C137C22semidirect
31. C22×C22⋊C4×C137C22semidirect
32. C22×C22⋊C4×C137C22semidirect
33. C22×C22⋊C4×C137C22semidirect
39. C2×#95×C137C22semidirect
40. C2×#95×C137C22semidirect
41. C2×#95×C137C22semidirect
42. C2×#95×C137C22semidirect
43. C2×#95×C137C22semidirect
44. C2×#95×C137C22semidirect
82. C23×C4×C137D4semidirect
126. C2×C22⋊C4×C137D4semidirect
432. C2×C4×C137#120semidirect
470. C22×C137#394semidirect
516. #14725C137direct (N × H)
517. C137#14725direct (N × H)
519. C23×C22⋊C4C2×C137semidirect
520. C2×#394C2×C137semidirect
521. C2×#386C2×C137semidirect
522. C2×#386C2×C137semidirect
523. C2×#380C2×C137semidirect
524. C2×#379C2×C137semidirect
525. #1440C2×C137semidirect
526. #1439C2×C137semidirect
527. #1438C2×C137semidirect
528. C22⋊#95C2×C137semidirect
537. C22×C4⋊C4C22×C137semidirect
548. C22×C22⋊C4C22×C137semidirect
549. C22×C22⋊C4C22×C137semidirect
550. C22×C22⋊C4C22×C137semidirect
556. C2×#95C22×C137semidirect
557. C2×#95C22×C137semidirect
558. C2×#95C22×C137semidirect
559. C2×#95C22×C137semidirect
560. C2×#95C22×C137semidirect
561. C2×#95C22×C137semidirect
599. C23×C4D4×C137semidirect
643. C2×C22⋊C4D4×C137semidirect
949. C2×C4#120×C137semidirect
987. C22#394×C137semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1372
C23×C22⋊C4×C1372
C2×#394×C1372
C2×#386×C1372
C2×#380×C1372
C2×#379×C1372
#1440×C1372
#1439×C1372
#1438×C1372
C22⋊#95×C1372
#14725137