Finite Group Databasebeta

← C137×#14722 #46864108

Subgroups — C137×#14722 #46864108

Order 35072.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#121×C137C211yesmaximal, characteristic, complemented
2C22×C4×D4×C137C211yesmaximal, characteristic, complemented
3C2×#394×C137C211yesmaximal, characteristic, complemented
4C2×#392×C137C211yesmaximal, characteristic, complemented
5C2×#392×C137C212yesmaximal, complemented
6C2×#386×C137C212yesmaximal, complemented
7#1441×C137C211yesmaximal, characteristic, complemented
8#1439×C137C211yesmaximal, characteristic, complemented
9#1438×C137C212yesmaximal, complemented
10#1437×C137C212yesmaximal, complemented
11C22⋊#95×C137C211yesmaximal, characteristic, complemented
12C23×D4×C137C2211yescharacteristic
13C23×D4×C137C2212yes—
14C23×D4×C137C2211yescharacteristic
15C23×D4×C137C2212yes—
16C24×C4×C137C2211yescharacteristic
17C24×C4×C137C2211yescharacteristic
18C2×#121×C137—24no—
19C2×#121×C137—28no—
20C2×C4×D4×C137—24no—
21C2×C4×D4×C137—24no—
22C2×C4×D4×C137—24no—
23C22×C4⋊C4×C137C2211yescharacteristic
24C22×C4⋊C4×C137C2211yescharacteristic
25C22×C22⋊C4×C137C2212yes—
26C22×C22⋊C4×C137C2211yescharacteristic
27C22×C22⋊C4×C137C2212yes—
28C22×C22⋊C4×C137C2212yes—
29C22×C22⋊C4×C137C2212yes—
30C22×C22⋊C4×C137C2212yes—
31C22×C22⋊C4×C137C2212yes—
32C22×C22⋊C4×C137C2211yescharacteristic
33C22×C42×C137C2211yescharacteristic
34#394×C137—24no—
35#392×C137—28no—
36#392×C137—24no—
37#386×C137—28no—
38C2×#95×C137C2212yes—
39C2×#95×C137C2212yes—
40C2×#95×C137C2211yescharacteristic
41C2×#95×C137C2212yes—
42C2×#95×C137C2211yescharacteristic
43C2×#95×C137C2212yes—
44C25×C137C2312yes—
45C25×C137C2311yescharacteristic
46C25×C137C2311yescharacteristic
47C22×D4×C137—22no—
48C22×D4×C137—22no—
49C22×D4×C137—22no—
50C22×D4×C137—22no—
51C22×D4×C137—24no—
52C22×D4×C137—24no—
53C22×D4×C137—24no—
54C22×D4×C137—24no—
55C22×D4×C137—24no—
56C22×D4×C137—24no—
57C22×D4×C137—24no—
58C22×D4×C137—24no—
59C22×D4×C137—24no—
60C22×D4×C137—22no—
61C22×D4×C137—24no—
62C22×D4×C137—22no—
63C22×D4×C137—22no—
64C22×D4×C137—22no—
65C22×D4×C137—22no—
66C22×D4×C137—24no—
67C22×D4×C137—42no—
68C22×D4×C137—42no—
69C22×D4×C137—42no—
70C22×D4×C137—42no—
71C22×D4×C137—42no—
72C22×D4×C137D414yescomplemented
73C23×C4×C137—22no—
74C23×C4×C137—22no—
75C23×C4×C137—22no—
76C23×C4×C137—22no—
77C23×C4×C137—22no—
78C23×C4×C137—24no—
79C23×C4×C137—24no—
80C23×C4×C137—42no—
81C23×C4×C137—42no—
82C23×C4×C137D414yescomplemented
83C23×C4×C137C2312yes—
84C23×C4×C137C2312yes—
85C23×C4×C137C2311yescharacteristic
86C23×C4×C137C2311yescharacteristic
87C23×C4×C137C2312yes—
88C23×C4×C137C2311yescharacteristic
89C23×C4×C137C2311yescharacteristic
90C23×C4×C137C2311yescharacteristic
91#121×C137—232no—
92C4×D4×C137—232no—
93C2×C4⋊C4×C137—22no—
94C2×C4⋊C4×C137—22no—
95C2×C4⋊C4×C137—24no—
96C2×C4⋊C4×C137—22no—
97C2×C4⋊C4×C137D414yescomplemented
98C2×C22⋊C4×C137—22no—
99C2×C22⋊C4×C137—22no—
100C2×C22⋊C4×C137—22no—
101C2×C22⋊C4×C137—22no—
102C2×C22⋊C4×C137—22no—
103C2×C22⋊C4×C137—24no—
104C2×C22⋊C4×C137—24no—
105C2×C22⋊C4×C137—24no—
106C2×C22⋊C4×C137—24no—
107C2×C22⋊C4×C137—24no—
108C2×C22⋊C4×C137—24no—
109C2×C22⋊C4×C137—24no—
110C2×C22⋊C4×C137—24no—
111C2×C22⋊C4×C137—24no—
112C2×C22⋊C4×C137—24no—
113C2×C22⋊C4×C137—24no—
114C2×C22⋊C4×C137—24no—
115C2×C22⋊C4×C137—24no—
116C2×C22⋊C4×C137—42no—
117C2×C22⋊C4×C137—42no—
118C2×C22⋊C4×C137—42no—
119C2×C22⋊C4×C137—42no—
120C2×C22⋊C4×C137D418yescomplemented
121C2×C22⋊C4×C137D414yescomplemented
122C2×C42×C137—22no—
123C2×C42×C137—22no—
124C2×C42×C137—22no—
125#95×C137—24no—
126#95×C137—24no—
127#95×C137—22no—
128#95×C137—24no—
129#95×C137—22no—
130#95×C137—42no—
131C24×C137—21no—
132C24×C137—21no—
133C24×C137—21no—
134C24×C137—21no—
135C24×C137—22no—
136C24×C137—22no—
137C24×C137—22no—
138C24×C137—21no—
139C24×C137—21no—
140C24×C137—21no—
141C24×C137—21no—
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—22no—
155C24×C137—22no—
156C24×C137—22no—
157C24×C137—22no—
158C24×C137—22no—
159C24×C137—22no—
160C24×C137—22no—
161C24×C137C2×D414yes—
162C24×C137C2×D412yes—
163C24×C137C2×D412yes—
164C24×C137C2×D412yes—
165C24×C137C2×D412yes—
166C24×C137#4112yes—
167C24×C137#4112yes—
168C24×C137C2411yescharacteristic
169C2×D4×C137—28no—
170C2×D4×C137—28no—
171C2×D4×C137—28no—
172C2×D4×C137—28no—
173C2×D4×C137—28no—
174C2×D4×C137—28no—
175C2×D4×C137—28no—
176C2×D4×C137—216no—
177C2×D4×C137—216no—
178C2×D4×C137—28no—
179C2×D4×C137—48no—
180C2×D4×C137—48no—
181C2×D4×C137—48no—
182C2×D4×C137—48no—
183C2×D4×C137—48no—
184C2×D4×C137—48no—
185C2×D4×C137—44no—
186C2×D4×C137—48no—
187C2×D4×C137—48no—
188C2×D4×C137—48no—
189C2×D4×C137—48no—
190C2×D4×C137—48no—
191C2×D4×C137—48no—
192C2×D4×C137—48no—
193C2×D4×C137—48no—
194C2×D4×C137—44no—
195C22×C4×C137—21no—
196C22×C4×C137—21no—
197C22×C4×C137—21no—
198C22×C4×C137—21no—
199C22×C4×C137—22no—
200C22×C4×C137—21no—
201C22×C4×C137—21no—
202C22×C4×C137—22no—
203C22×C4×C137—22no—
204C22×C4×C137—28no—
205C22×C4×C137—22no—
206C22×C4×C137—22no—
207C22×C4×C137—22no—
208C22×C4×C137—22no—
209C22×C4×C137—22no—
210C22×C4×C137—21no—
211C22×C4×C137—21no—
212C22×C4×C137—21no—
213C22×C4×C137—21no—
214C22×C4×C137—22no—
215C22×C4×C137—22no—
216C22×C4×C137—22no—
217C22×C4×C137—22no—
218C22×C4×C137—22no—
219C22×C4×C137—22no—
220C22×C4×C137—22no—
221C22×C4×C137—22no—
222C22×C4×C137—22no—
223C22×C4×C137—22no—
224C22×C4×C137—22no—
225C22×C4×C137—28no—
226C22×C4×C137—28no—
227C22×C4×C137—22no—
228C22×C4×C137—22no—
229C22×C4×C137—22no—
230C22×C4×C137—22no—
231C22×C4×C137—22no—
232C22×C4×C137—22no—
233C22×C4×C137—22no—
234C22×C4×C137—44no—
235C22×C4×C137—48no—
236C22×C4×C137—48no—
237C22×C4×C137—48no—
238C22×C4×C137—48no—
239C22×C4×C137—44no—
240C22×C4×C137—44no—
241C22×C4×C137C2×D414yes—
242C22×C4×C137C2×D412yes—
243C22×C4×C137C2×D412yes—
244C22×C4×C137C2×D414yes—
245C22×C4×C137C2×D412yes—
246C22×C4×C137C2×D412yes—
247C22×C4×C137C2×D412yes—
248C22×C4×C137C2×D412yes—
249C22×C4×C137C2×D412yes—
250C22×C4×C137C2×D412yes—
251C22×C4×C137#4114yes—
252C22×C4×C137#4112yes—
253C4⋊C4×C137—28no—
254C4⋊C4×C137—28no—
255C22⋊C4×C137—28no—
256C22⋊C4×C137—28no—
257C22⋊C4×C137—216no—
258C22⋊C4×C137—48no—
259C22⋊C4×C137—48no—
260C22⋊C4×C137—48no—
261C22⋊C4×C137—48no—
262C22⋊C4×C137—48no—
263C42×C137—28no—
264C23×C137—22no—
265C23×C137—22no—
266C23×C137—22no—
267C23×C137—22no—
268C23×C137—22no—
269C23×C137—22no—
270C23×C137—22no—
271C23×C137—22no—
272C23×C137—22no—
273C23×C137—22no—
274C23×C137—22no—
275C23×C137—22no—
276C23×C137—22no—
277C23×C137—24no—
278C23×C137—22no—
279C23×C137—22no—
280C23×C137—22no—
281C23×C137—24no—
282C23×C137—24no—
283C23×C137—24no—
284C23×C137—24no—
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—24no—
295C23×C137—24no—
296C23×C137—24no—
297C23×C137—41no—
298C23×C137—42no—
299C23×C137—42no—
300C23×C137—42no—
301C23×C137—41no—
302C23×C137—41no—
303C23×C137—41no—
304C23×C137—42no—
305C23×C137—42no—
306C23×C137—42no—
307C23×C137—42no—
308C23×C137—42no—
309C23×C137—42no—
310C23×C137—42no—
311C23×C137—42no—
312C23×C137—42no—
313C23×C137—42no—
314C23×C137—42no—
315C23×C137—42no—
316C23×C137—42no—
317C23×C137—42no—
318C23×C137—42no—
319C23×C137—42no—
320C23×C137—42no—
321C23×C137—42no—
322C23×C137—42no—
323C23×C137—42no—
324C23×C137—42no—
325C23×C137—42no—
326C23×C137—42no—
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#12114yes—
344C23×C137#12114yescomplemented
345C23×C137C22×D411yescharacteristic
346C23×C137C22×D411yescharacteristic
347C23×C137C22×D411yescharacteristic
348C23×C137C22×D412yes—
349C23×C137C22×D411yescharacteristic
350C23×C137C2×#4111yescharacteristic
351C23×C137C2×#4111yescharacteristic
352C23×C137C2×#4111yescharacteristic
353C23×C137C2×#4112yes—
354C23×C137H(5,𝔽2)12yes—
355C23×C137H(5,𝔽2)12yes—
356D4×C137—232no—
357D4×C137—416no—
358D4×C137—432no—
359D4×C137—432no—
360C2×C4×C137—22no—
361C2×C4×C137—22no—
362C2×C4×C137—22no—
363C2×C4×C137—22no—
364C2×C4×C137—22no—
365C2×C4×C137—22no—
366C2×C4×C137—22no—
367C2×C4×C137—22no—
368C2×C4×C137—22no—
369C2×C4×C137—22no—
370C2×C4×C137—24no—
371C2×C4×C137—24no—
372C2×C4×C137—24no—
373C2×C4×C137—24no—
374C2×C4×C137—22no—
375C2×C4×C137—22no—
376C2×C4×C137—24no—
377C2×C4×C137—24no—
378C2×C4×C137—24no—
379C2×C4×C137—24no—
380C2×C4×C137—24no—
381C2×C4×C137—24no—
382C2×C4×C137—24no—
383C2×C4×C137—24no—
384C2×C4×C137—416no—
385C2×C4×C137—416no—
386C2×C4×C137—41no—
387C2×C4×C137—42no—
388C2×C4×C137—42no—
389C2×C4×C137—41no—
390C2×C4×C137—41no—
391C2×C4×C137—41no—
392C2×C4×C137—42no—
393C2×C4×C137—42no—
394C2×C4×C137—42no—
395C2×C4×C137—42no—
396C2×C4×C137—42no—
397C2×C4×C137—42no—
398C2×C4×C137—42no—
399C2×C4×C137—42no—
400C2×C4×C137—42no—
401C2×C4×C137—42no—
402C2×C4×C137—42no—
403C2×C4×C137—42no—
404C2×C4×C137—42no—
405C2×C4×C137—42no—
406C2×C4×C137—42no—
407C2×C4×C137#12014yes—
408C2×C4×C137#12014yes—
409C2×C4×C137#12114yescomplemented
410C22×C137—24no—
411C22×C137—24no—
412C22×C137—24no—
413C22×C137—28no—
414C22×C137—24no—
415C22×C137—42no—
416C22×C137—42no—
417C22×C137—42no—
418C22×C137—42no—
419C22×C137—42no—
420C22×C137—42no—
421C22×C137—42no—
422C22×C137—44no—
423C22×C137—44no—
424C22×C137—44no—
425C22×C137—42no—
426C22×C137—42no—
427C22×C137—44no—
428C22×C137—44no—
429C22×C137—44no—
430C22×C137—44no—
431C22×C137—42no—
432C22×C137—44no—
433C22×C137—44no—
434C22×C137—44no—
435C22×C137—44no—
436C22×C137—44no—
437C22×C137—44no—
438C22×C137—44no—
439C22×C137—82no—
440C22×C137—82no—
441C22×C137—82no—
442C22×C137—82no—
443C22×C137—82no—
444C22×C137—82no—
445C22×C137—82no—
446C22×C137—82no—
447C22×C137C2×#12011yescharacteristic
448C22×C137C2×#12011yescharacteristic
449C22×C137C2×#12111yescharacteristic
450C22×C137C2×#12111yescharacteristic
451C22×C137C2×#12111yescharacteristic
452C22×C137#52511yescharacteristic
453C22×C137#52511yescharacteristic
454C22×C137#52511yescharacteristic
455C22×C137#52512yes—
456C22×C137#53212yes—
457C22×C137#53211yescharacteristic
458C22×C137#53411yescharacteristic
459C22×C137#53511yescharacteristic
460C22×C137#53812yes—
461C22×C137#54012yes—
462C22×C137D4212yes—
463C22×C137D4212yes—
464C22×C137D4212yes—
465C22×C137#54612yes—
466C22×C137#54612yes—
467C22×C137#54612yes—
468C22×C137#55012yes—
469C22×C137#55312yes—
470C4×C137—24no—
471C4×C137—24no—
472C4×C137—24no—
473C4×C137—42no—
474C4×C137—44no—
475C4×C137—44no—
476C4×C137—42no—
477C4×C137—82no—
478C2×C137—44no—
479C2×C137—44no—
480C2×C137—84no—
481C2×C137#238811yescharacteristic
482C2×C137#240311yescharacteristic
483C2×C137#240811yescharacteristic
484C2×C137#242412yes—
485C2×C137#242812yes—
486C2×C137#243111yescharacteristic
487C2×C137#245612yes—
488C2×C137#246412yes—
489C2×C137#254311yescharacteristic
490C2×C137#263511yescharacteristic
491C2×C137#284711yescharacteristic
492#14722C13711yesmaximal, characteristic, direct product factor, Sylow
493C137#1472211yescharacteristic, direct product factor, Sylow
494C22×#121C2×C13711yescharacteristic, complemented
495C22×C4×D4C2×C13711yescharacteristic, complemented
496C2×#394C2×C13711yescharacteristic, complemented
497C2×#392C2×C13712yescomplemented
498C2×#392C2×C13711yescharacteristic, complemented
499C2×#386C2×C13712yescomplemented
500#1441C2×C13711yescharacteristic, complemented
501#1439C2×C13711yescharacteristic, complemented
502#1438C2×C13712yescomplemented
503#1437C2×C13712yescomplemented
504C22⋊#95C2×C13711yescharacteristic, complemented
505C23×D4C22×C13711yescharacteristic
506C23×D4C22×C13712yes—
507C23×D4C22×C13711yescharacteristic
508C23×D4C22×C13712yes—
509C24×C4C22×C13711yescharacteristic
510C24×C4C22×C13711yescharacteristic
511C2×#121—24no—
512C2×#121—28no—
513C2×C4×D4—24no—
514C2×C4×D4—24no—
515C2×C4×D4—24no—
516C22×C4⋊C4C22×C13711yescharacteristic
517C22×C4⋊C4C22×C13711yescharacteristic
518C22×C22⋊C4C22×C13712yes—
519C22×C22⋊C4C22×C13711yescharacteristic
520C22×C22⋊C4C22×C13712yes—
521C22×C22⋊C4C22×C13712yes—
522C22×C22⋊C4C22×C13712yes—
523C22×C22⋊C4C22×C13712yes—
524C22×C22⋊C4C22×C13711yescharacteristic
525C22×C22⋊C4C22×C13712yes—
526C22×C42C22×C13711yescharacteristic
527#394—24no—
528#392—28no—
529#392—24no—
530#386—28no—
531C2×#95C22×C13711yescharacteristic
532C2×#95C22×C13712yes—
533C2×#95C22×C13711yescharacteristic
534C2×#95C22×C13712yes—
535C2×#95C22×C13712yes—
536C2×#95C22×C13712yes—
537C25C23×C13712yes—
538C25C23×C13711yescharacteristic
539C25C23×C13711yescharacteristic
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—24no—
546C22×D4—24no—
547C22×D4—24no—
548C22×D4—24no—
549C22×D4—24no—
550C22×D4—24no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—22no—
554C22×D4—24no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—24no—
560C22×D4—42no—
561C22×D4—42no—
562C22×D4—42no—
563C22×D4—42no—
564C22×D4—42no—
565C22×D4D4×C13714yescomplemented
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—24no—
572C23×C4—24no—
573C23×C4—42no—
574C23×C4—42no—
575C23×C4D4×C13714yescomplemented
576C23×C4C23×C13712yes—
577C23×C4C23×C13711yescharacteristic
578C23×C4C23×C13711yescharacteristic
579C23×C4C23×C13712yes—
580C23×C4C23×C13712yes—
581C23×C4C23×C13711yescharacteristic
582C23×C4C23×C13711yescharacteristic
583C23×C4C23×C13711yescharacteristic
584#121—232no—
585C4×D4—232no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—24no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4D4×C13714yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—24no—
598C2×C22⋊C4—24no—
599C2×C22⋊C4—24no—
600C2×C22⋊C4—24no—
601C2×C22⋊C4—24no—
602C2×C22⋊C4—24no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—24no—
605C2×C22⋊C4—24no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4—42no—
612C2×C22⋊C4—42no—
613C2×C22⋊C4D4×C13714yescomplemented
614C2×C22⋊C4D4×C13718yescomplemented
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618#95—24no—
619#95—24no—
620#95—22no—
621#95—24no—
622#95—22no—
623#95—42no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24C2×D4×C13714yes—
655C24C2×D4×C13712yes—
656C24C2×D4×C13712yes—
657C24C2×D4×C13712yes—
658C24C2×D4×C13712yes—
659C24#41×C13712yes—
660C24#41×C13712yes—
661C24C24×C13711yescharacteristic
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—28no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—44no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—44no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—28no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4C2×D4×C13714yes—
735C22×C4C2×D4×C13712yes—
736C22×C4C2×D4×C13712yes—
737C22×C4C2×D4×C13714yes—
738C22×C4C2×D4×C13712yes—
739C22×C4C2×D4×C13712yes—
740C22×C4C2×D4×C13712yes—
741C22×C4C2×D4×C13712yes—
742C22×C4C2×D4×C13712yes—
743C22×C4C2×D4×C13712yes—
744C22×C4#41×C13714yes—
745C22×C4#41×C13712yes—
746C4⋊C4—28no—
747C4⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—28no—
750C22⋊C4—216no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C22⋊C4—48no—
756C42—28no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—41no—
793C23—42no—
794C23—42no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23#121×C13714yes—
837C23#121×C13714yescomplemented
838C23C22×D4×C13711yescharacteristic
839C23C22×D4×C13711yescharacteristic
840C23C22×D4×C13711yescharacteristic
841C23C22×D4×C13712yes—
842C23C22×D4×C13711yescharacteristic
843C23C2×#41×C13711yescharacteristic
844C23C2×#41×C13711yescharacteristic
845C23C2×#41×C13711yescharacteristic
846C23C2×#41×C13712yes—
847C23H(5,𝔽2)×C13712yes—
848C23H(5,𝔽2)×C13712yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4#120×C13714yes—
901C2×C4#120×C13714yes—
902C2×C4#121×C13714yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—28no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—42no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×#120×C13711yescharacteristic
941C22C2×#120×C13711yescharacteristic
942C22C2×#121×C13711yescharacteristic
943C22C2×#121×C13711yescharacteristic
944C22C2×#121×C13711yescharacteristic
945C22#525×C13711yescharacteristic
946C22#525×C13711yescharacteristic
947C22#525×C13711yescharacteristic
948C22#525×C13712yes—
949C22#532×C13711yescharacteristic
950C22#532×C13712yes—
951C22#534×C13711yescharacteristic
952C22#535×C13711yescharacteristic
953C22#538×C13712yes—
954C22#540×C13712yes—
955C22D42×C13712yes—
956C22D42×C13712yes—
957C22D42×C13712yes—
958C22#546×C13712yes—
959C22#546×C13712yes—
960C22#546×C13712yes—
961C22#550×C13712yes—
962C22#553×C13712yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2#2388×C13711yescharacteristic
975C2#2403×C13711yescharacteristic
976C2#2408×C13711yescharacteristic
977C2#2424×C13712yes—
978C2#2428×C13712yes—
979C2#2431×C13711yescharacteristic
980C2#2456×C13712yes—
981C2#2464×C13712yes—
982C2#2543×C13711yescharacteristic
983C2#2635×C13711yescharacteristic
984C2#2847×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutator, Frattini, cosocleC24C24×C137
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#121×C137C2semidirect
2. C22×C4×D4×C137C2semidirect
3. C2×#394×C137C2semidirect
4. C2×#392×C137C2semidirect
5. C2×#392×C137C2semidirect
6. C2×#386×C137C2semidirect
7. #1441×C137C2semidirect
8. #1439×C137C2semidirect
9. #1438×C137C2semidirect
10. #1437×C137C2semidirect
11. C22⋊#95×C137C2semidirect
72. C22×D4×C137D4semidirect
82. C23×C4×C137D4semidirect
97. C2×C4⋊C4×C137D4semidirect
120. C2×C22⋊C4×C137D4semidirect
121. C2×C22⋊C4×C137D4semidirect
344. C23×C137#121semidirect
409. C2×C4×C137#121semidirect
492. #14722C137direct (N × H)
493. C137#14722direct (N × H)
494. C22×#121C2×C137semidirect
495. C22×C4×D4C2×C137semidirect
496. C2×#394C2×C137semidirect
497. C2×#392C2×C137semidirect
498. C2×#392C2×C137semidirect
499. C2×#386C2×C137semidirect
500. #1441C2×C137semidirect
501. #1439C2×C137semidirect
502. #1438C2×C137semidirect
503. #1437C2×C137semidirect
504. C22⋊#95C2×C137semidirect
565. C22×D4D4×C137semidirect
575. C23×C4D4×C137semidirect
590. C2×C4⋊C4D4×C137semidirect
613. C2×C22⋊C4D4×C137semidirect
614. C2×C22⋊C4D4×C137semidirect
837. C23#121×C137semidirect
902. C2×C4#121×C137semidirect

Maximal subgroups

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

subgroupindex
C22×#121×C1372
C22×C4×D4×C1372
C2×#394×C1372
C2×#392×C1372
C2×#386×C1372
#1441×C1372
#1439×C1372
#1438×C1372
#1437×C1372
C22⋊#95×C1372
#14722137