Finite Group Databasebeta

← C137×#14730 #46864116

Subgroups — C137×#14730 #46864116

Order 35072.

2578 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C137C211yesmaximal, characteristic, complemented
2C2×#394×C137C211yesmaximal, characteristic, complemented
3C2×#392×C137C211yesmaximal, characteristic
4C2×#386×C137C211yesmaximal, characteristic, complemented
5C2×#386×C137C211yesmaximal, characteristic, complemented
6C2×#381×C137C211yesmaximal, characteristic, complemented
7#1442×C137C211yesmaximal, characteristic, complemented
8#1440×C137C211yesmaximal, characteristic, complemented
9#1439×C137C211yesmaximal, characteristic, complemented
10#1439×C137C211yesmaximal, characteristic, complemented
11#1438×C137C211yesmaximal, characteristic, complemented
12#1438×C137C211yesmaximal, characteristic, complemented
13#1437×C137C211yesmaximal, characteristic, complemented
14#1436×C137C211yesmaximal, characteristic, complemented
15C22⋊#95×C137C211yesmaximal, characteristic, complemented
16C23×D4×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C23×D4×C137C2211yescharacteristic
19C24×C4×C137C2211yescharacteristic
20C24×C4×C137C2211yescharacteristic
21C2×C4×D4×C137—24no—
22C2×C4×D4×C137—24no—
23C2×C4×D4×C137—24no—
24C22×C4⋊C4×C137C2211yescharacteristic
25C22×C4⋊C4×C137C2211yescharacteristic
26C22×C22⋊C4×C137C2211yescharacteristic
27C22×C22⋊C4×C137C2211yescharacteristic
28C22×C22⋊C4×C137C2211yescharacteristic
29C22×C22⋊C4×C137C2211yescharacteristic
30C22×C22⋊C4×C137C2211yescharacteristic
31C22×C22⋊C4×C137C2211yescharacteristic
32C22×C22⋊C4×C137C2211yescharacteristic
33C22×C22⋊C4×C137C2211yescharacteristic
34C22×C22⋊C4×C137C2211yescharacteristic
35C22×C22⋊C4×C137C2211yescharacteristic
36C22×C22⋊C4×C137C2211yescharacteristic
37C22×C22⋊C4×C137C2211yescharacteristic
38C22×C22⋊C4×C137C2211yescharacteristic
39C22×C42×C137C2211yescharacteristic
40#394×C137—24no—
41#392×C137—24no—
42#386×C137—24no—
43#386×C137—24no—
44#381×C137—24no—
45C2×#95×C137C2211yescharacteristic
46C2×#95×C137C2211yescharacteristic
47C2×#95×C137C2211yescharacteristic
48C2×#95×C137C2211yescharacteristic
49C2×#95×C137C2211yescharacteristic
50C2×#95×C137C2211yescharacteristic
51C2×#95×C137C2211yescharacteristic
52C2×#95×C137C2211yescharacteristic
53C2×#95×C137C2211yescharacteristic
54C2×#95×C137C2211yescharacteristic
55C2×#95×C137C2211yescharacteristic
56C2×#95×C137C2211yescharacteristic
57C2×#95×C137C2211yescharacteristic
58C2×#95×C137C2211yescharacteristic
59C25×C137C2311yescharacteristic
60C25×C137C2311yescharacteristic
61C25×C137C2311yescharacteristic
62C22×D4×C137—22no—
63C22×D4×C137—22no—
64C22×D4×C137—22no—
65C22×D4×C137—22no—
66C22×D4×C137—22no—
67C22×D4×C137—22no—
68C22×D4×C137—22no—
69C22×D4×C137—22no—
70C22×D4×C137—22no—
71C22×D4×C137—22no—
72C22×D4×C137—22no—
73C22×D4×C137—22no—
74C22×D4×C137—22no—
75C22×D4×C137—22no—
76C22×D4×C137—22no—
77C22×D4×C137—22no—
78C22×D4×C137—41no—
79C22×D4×C137—41no—
80C22×D4×C137—41no—
81C22×D4×C137—41no—
82C22×D4×C137D414yes—
83C23×C4×C137—22no—
84C23×C4×C137—22no—
85C23×C4×C137—22no—
86C23×C4×C137—22no—
87C23×C4×C137—22no—
88C23×C4×C137—22no—
89C23×C4×C137—22no—
90C23×C4×C137—22no—
91C23×C4×C137—22no—
92C23×C4×C137—41no—
93C23×C4×C137—41no—
94C23×C4×C137—41no—
95C23×C4×C137—41no—
96C23×C4×C137D414yescomplemented
97C23×C4×C137C2311yescharacteristic
98C23×C4×C137C2311yescharacteristic
99C23×C4×C137C2311yescharacteristic
100C23×C4×C137C2311yescharacteristic
101C23×C4×C137C2311yescharacteristic
102C23×C4×C137C2311yescharacteristic
103C23×C4×C137C2311yescharacteristic
104C23×C4×C137C2311yescharacteristic
105C23×C4×C137C2311yescharacteristic
106C23×C4×C137C2311yescharacteristic
107C23×C4×C137C2311yescharacteristic
108C23×C4×C137C2311yescharacteristic
109C4×D4×C137—232no—
110C2×C4⋊C4×C137—22no—
111C2×C4⋊C4×C137—22no—
112C2×C4⋊C4×C137—22no—
113C2×C4⋊C4×C137—22no—
114C2×C4⋊C4×C137—22no—
115C2×C4⋊C4×C137—41no—
116C2×C22⋊C4×C137—22no—
117C2×C22⋊C4×C137—22no—
118C2×C22⋊C4×C137—22no—
119C2×C22⋊C4×C137—22no—
120C2×C22⋊C4×C137—22no—
121C2×C22⋊C4×C137—22no—
122C2×C22⋊C4×C137—22no—
123C2×C22⋊C4×C137—22no—
124C2×C22⋊C4×C137—22no—
125C2×C22⋊C4×C137—22no—
126C2×C22⋊C4×C137—22no—
127C2×C22⋊C4×C137—22no—
128C2×C22⋊C4×C137—22no—
129C2×C22⋊C4×C137—22no—
130C2×C22⋊C4×C137—22no—
131C2×C22⋊C4×C137—22no—
132C2×C22⋊C4×C137—22no—
133C2×C22⋊C4×C137—22no—
134C2×C22⋊C4×C137—22no—
135C2×C22⋊C4×C137—22no—
136C2×C22⋊C4×C137—22no—
137C2×C22⋊C4×C137—22no—
138C2×C22⋊C4×C137—22no—
139C2×C22⋊C4×C137—22no—
140C2×C22⋊C4×C137—22no—
141C2×C22⋊C4×C137—22no—
142C2×C22⋊C4×C137—41no—
143C2×C22⋊C4×C137—41no—
144C2×C22⋊C4×C137—41no—
145C2×C22⋊C4×C137—41no—
146C2×C22⋊C4×C137—41no—
147C2×C22⋊C4×C137—41no—
148C2×C22⋊C4×C137—41no—
149C2×C22⋊C4×C137—41no—
150C2×C22⋊C4×C137—41no—
151C2×C22⋊C4×C137—41no—
152C2×C22⋊C4×C137—41no—
153C2×C22⋊C4×C137—41no—
154C2×C22⋊C4×C137D414yescomplemented
155C2×C42×C137—22no—
156C2×C42×C137—22no—
157C2×C42×C137—22no—
158#95×C137—22no—
159#95×C137—22no—
160#95×C137—22no—
161#95×C137—22no—
162#95×C137—22no—
163#95×C137—22no—
164#95×C137—22no—
165#95×C137—22no—
166#95×C137—22no—
167#95×C137—22no—
168#95×C137—41no—
169#95×C137—41no—
170#95×C137—41no—
171#95×C137D414yescomplemented
172C24×C137—21no—
173C24×C137—21no—
174C24×C137—21no—
175C24×C137—21no—
176C24×C137—21no—
177C24×C137—21no—
178C24×C137—21no—
179C24×C137—21no—
180C24×C137—21no—
181C24×C137—21no—
182C24×C137—21no—
183C24×C137—21no—
184C24×C137—21no—
185C24×C137—21no—
186C24×C137—21no—
187C24×C137—21no—
188C24×C137—21no—
189C24×C137—21no—
190C24×C137—21no—
191C24×C137—21no—
192C24×C137—21no—
193C24×C137—21no—
194C24×C137—21no—
195C24×C137—21no—
196C24×C137—21no—
197C24×C137—21no—
198C24×C137—21no—
199C24×C137—21no—
200C24×C137—21no—
201C24×C137—21no—
202C24×C137—21no—
203C24×C137—21no—
204C24×C137—21no—
205C24×C137—21no—
206C24×C137—21no—
207C24×C137—21no—
208C24×C137—21no—
209C24×C137—21no—
210C24×C137C2×D412yes—
211C24×C137C2×D412yes—
212C24×C137C2×D412yes—
213C24×C137C2×D412yes—
214C24×C137#4112yes—
215C24×C137#4112yes—
216C24×C137#4112yes—
217C24×C137C2411yescharacteristic
218C2×D4×C137—28no—
219C2×D4×C137—28no—
220C2×D4×C137—28no—
221C2×D4×C137—28no—
222C2×D4×C137—28no—
223C2×D4×C137—28no—
224C2×D4×C137—28no—
225C2×D4×C137—28no—
226C2×D4×C137—28no—
227C2×D4×C137—44no—
228C2×D4×C137—44no—
229C2×D4×C137—44no—
230C2×D4×C137—44no—
231C2×D4×C137—44no—
232C2×D4×C137—44no—
233C2×D4×C137—44no—
234C2×D4×C137—44no—
235C2×D4×C137—44no—
236C2×D4×C137—44no—
237C2×D4×C137—44no—
238C2×D4×C137—44no—
239C22×C4×C137—21no—
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—28no—
248C22×C4×C137—28no—
249C22×C4×C137—21no—
250C22×C4×C137—21no—
251C22×C4×C137—21no—
252C22×C4×C137—21no—
253C22×C4×C137—21no—
254C22×C4×C137—21no—
255C22×C4×C137—21no—
256C22×C4×C137—21no—
257C22×C4×C137—21no—
258C22×C4×C137—21no—
259C22×C4×C137—21no—
260C22×C4×C137—21no—
261C22×C4×C137—21no—
262C22×C4×C137—21no—
263C22×C4×C137—21no—
264C22×C4×C137—21no—
265C22×C4×C137—21no—
266C22×C4×C137—21no—
267C22×C4×C137—21no—
268C22×C4×C137—21no—
269C22×C4×C137—21no—
270C22×C4×C137—21no—
271C22×C4×C137—21no—
272C22×C4×C137—21no—
273C22×C4×C137—21no—
274C22×C4×C137—21no—
275C22×C4×C137—21no—
276C22×C4×C137—21no—
277C22×C4×C137—21no—
278C22×C4×C137—21no—
279C22×C4×C137—21no—
280C22×C4×C137—21no—
281C22×C4×C137—21no—
282C22×C4×C137—21no—
283C22×C4×C137—21no—
284C22×C4×C137—21no—
285C22×C4×C137—28no—
286C22×C4×C137—21no—
287C22×C4×C137—21no—
288C22×C4×C137—21no—
289C22×C4×C137—21no—
290C22×C4×C137—21no—
291C22×C4×C137—21no—
292C22×C4×C137—21no—
293C22×C4×C137—21no—
294C22×C4×C137—21no—
295C22×C4×C137—21no—
296C22×C4×C137—21no—
297C22×C4×C137—21no—
298C22×C4×C137—21no—
299C22×C4×C137—21no—
300C22×C4×C137—21no—
301C22×C4×C137—21no—
302C22×C4×C137—21no—
303C22×C4×C137—21no—
304C22×C4×C137—21no—
305C22×C4×C137—21no—
306C22×C4×C137—21no—
307C22×C4×C137—21no—
308C22×C4×C137—21no—
309C22×C4×C137—21no—
310C22×C4×C137—21no—
311C22×C4×C137—21no—
312C22×C4×C137—21no—
313C22×C4×C137—21no—
314C22×C4×C137—44no—
315C22×C4×C137—44no—
316C22×C4×C137—44no—
317C22×C4×C137—44no—
318C22×C4×C137—44no—
319C22×C4×C137—44no—
320C22×C4×C137—44no—
321C22×C4×C137—44no—
322C22×C4×C137—44no—
323C22×C4×C137—44no—
324C22×C4×C137—44no—
325C22×C4×C137C2×D412yes—
326C22×C4×C137C2×D412yes—
327C22×C4×C137C2×D412yes—
328C22×C4×C137C2×D412yes—
329C22×C4×C137C2×D412yes—
330C22×C4×C137C2×D412yes—
331C22×C4×C137C2×D412yes—
332C22×C4×C137C2×D412yes—
333C22×C4×C137#4112yes—
334C22×C4×C137#4112yes—
335C22×C4×C137#4112yes—
336C22×C4×C137#4112yes—
337C4⋊C4×C137—28no—
338C4⋊C4×C137—44no—
339C22⋊C4×C137—28no—
340C22⋊C4×C137—28no—
341C22⋊C4×C137—44no—
342C22⋊C4×C137—44no—
343C22⋊C4×C137—44no—
344C22⋊C4×C137—44no—
345C22⋊C4×C137—44no—
346C22⋊C4×C137—44no—
347C22⋊C4×C137—44no—
348C22⋊C4×C137—44no—
349C22⋊C4×C137—44no—
350C22⋊C4×C137—44no—
351C22⋊C4×C137—44no—
352C42×C137—28no—
353C23×C137—22no—
354C23×C137—22no—
355C23×C137—22no—
356C23×C137—22no—
357C23×C137—22no—
358C23×C137—22no—
359C23×C137—22no—
360C23×C137—22no—
361C23×C137—22no—
362C23×C137—22no—
363C23×C137—22no—
364C23×C137—22no—
365C23×C137—22no—
366C23×C137—22no—
367C23×C137—22no—
368C23×C137—22no—
369C23×C137—22no—
370C23×C137—22no—
371C23×C137—22no—
372C23×C137—22no—
373C23×C137—22no—
374C23×C137—22no—
375C23×C137—22no—
376C23×C137—22no—
377C23×C137—22no—
378C23×C137—22no—
379C23×C137—22no—
380C23×C137—22no—
381C23×C137—22no—
382C23×C137—22no—
383C23×C137—22no—
384C23×C137—22no—
385C23×C137—22no—
386C23×C137—22no—
387C23×C137—22no—
388C23×C137—22no—
389C23×C137—22no—
390C23×C137—22no—
391C23×C137—22no—
392C23×C137—22no—
393C23×C137—22no—
394C23×C137—22no—
395C23×C137—22no—
396C23×C137—41no—
397C23×C137—41no—
398C23×C137—41no—
399C23×C137—41no—
400C23×C137—41no—
401C23×C137—41no—
402C23×C137—41no—
403C23×C137—41no—
404C23×C137—41no—
405C23×C137—41no—
406C23×C137—41no—
407C23×C137—41no—
408C23×C137—41no—
409C23×C137—41no—
410C23×C137—41no—
411C23×C137—41no—
412C23×C137—41no—
413C23×C137—41no—
414C23×C137—41no—
415C23×C137—41no—
416C23×C137—41no—
417C23×C137—41no—
418C23×C137—41no—
419C23×C137—41no—
420C23×C137—41no—
421C23×C137—41no—
422C23×C137—41no—
423C23×C137—41no—
424C23×C137—41no—
425C23×C137—41no—
426C23×C137—41no—
427C23×C137—41no—
428C23×C137—41no—
429C23×C137—41no—
430C23×C137—41no—
431C23×C137—41no—
432C23×C137—41no—
433C23×C137—41no—
434C23×C137—41no—
435C23×C137—41no—
436C23×C137—41no—
437C23×C137—41no—
438C23×C137—41no—
439C23×C137—41no—
440C23×C137—41no—
441C23×C137—41no—
442C23×C137—41no—
443C23×C137—41no—
444C23×C137—41no—
445C23×C137—41no—
446C23×C137—41no—
447C23×C137—41no—
448C23×C137—41no—
449C23×C137—41no—
450C23×C137—41no—
451C23×C137—41no—
452C23×C137—41no—
453C23×C137—41no—
454C23×C137—41no—
455C23×C137—41no—
456C23×C137#12014yes—
457C23×C137#12314yes—
458C23×C137C22×D411yescharacteristic
459C23×C137C22×D411yescharacteristic
460C23×C137C22×D411yescharacteristic
461C23×C137C22×D411yescharacteristic
462C23×C137C2×#4111yescharacteristic
463C23×C137C2×#4111yescharacteristic
464C23×C137C2×#4111yescharacteristic
465C23×C137C2×#4111yescharacteristic
466C23×C137C2×#4111yescharacteristic
467C23×C137C2×#4111yescharacteristic
468C23×C137C2×#4111yescharacteristic
469C23×C137H(5,𝔽2)11yescharacteristic
470C23×C137H(5,𝔽2)11yescharacteristic
471C23×C137H(5,𝔽2)11yescharacteristic
472C23×C137H(5,𝔽2)11yescharacteristic
473D4×C137—232no—
474D4×C137—416no—
475D4×C137—416no—
476C2×C4×C137—22no—
477C2×C4×C137—22no—
478C2×C4×C137—22no—
479C2×C4×C137—22no—
480C2×C4×C137—22no—
481C2×C4×C137—22no—
482C2×C4×C137—22no—
483C2×C4×C137—22no—
484C2×C4×C137—22no—
485C2×C4×C137—22no—
486C2×C4×C137—22no—
487C2×C4×C137—22no—
488C2×C4×C137—22no—
489C2×C4×C137—22no—
490C2×C4×C137—22no—
491C2×C4×C137—22no—
492C2×C4×C137—22no—
493C2×C4×C137—22no—
494C2×C4×C137—22no—
495C2×C4×C137—22no—
496C2×C4×C137—22no—
497C2×C4×C137—22no—
498C2×C4×C137—22no—
499C2×C4×C137—22no—
500C2×C4×C137—22no—
501C2×C4×C137—22no—
502C2×C4×C137—22no—
503C2×C4×C137—22no—
504C2×C4×C137—22no—
505C2×C4×C137—22no—
506C2×C4×C137—416no—
507C2×C4×C137—416no—
508C2×C4×C137—41no—
509C2×C4×C137—41no—
510C2×C4×C137—41no—
511C2×C4×C137—41no—
512C2×C4×C137—41no—
513C2×C4×C137—41no—
514C2×C4×C137—41no—
515C2×C4×C137—41no—
516C2×C4×C137—41no—
517C2×C4×C137—41no—
518C2×C4×C137—41no—
519C2×C4×C137—41no—
520C2×C4×C137—41no—
521C2×C4×C137—41no—
522C2×C4×C137—41no—
523C2×C4×C137—41no—
524C2×C4×C137—41no—
525C2×C4×C137—41no—
526C2×C4×C137—41no—
527C2×C4×C137—41no—
528C2×C4×C137—41no—
529C2×C4×C137—41no—
530C2×C4×C137—41no—
531C2×C4×C137—41no—
532C2×C4×C137—41no—
533C2×C4×C137—41no—
534C2×C4×C137—41no—
535C2×C4×C137—41no—
536C2×C4×C137—41no—
537C2×C4×C137—41no—
538C2×C4×C137—41no—
539C2×C4×C137—41no—
540C2×C4×C137—41no—
541C2×C4×C137—41no—
542C2×C4×C137—41no—
543C2×C4×C137—41no—
544C2×C4×C137—41no—
545C2×C4×C137—41no—
546C2×C4×C137—41no—
547C2×C4×C137—41no—
548C2×C4×C137—41no—
549C2×C4×C137—41no—
550C2×C4×C137—41no—
551C2×C4×C137—41no—
552C2×C4×C137—41no—
553C2×C4×C137—41no—
554C2×C4×C137—41no—
555C2×C4×C137—41no—
556C2×C4×C137—41no—
557C2×C4×C137—41no—
558C2×C4×C137—41no—
559C2×C4×C137—41no—
560C2×C4×C137#12114yes—
561C2×C4×C137#12314yes—
562C22×C137—24no—
563C22×C137—24no—
564C22×C137—24no—
565C22×C137—24no—
566C22×C137—24no—
567C22×C137—24no—
568C22×C137—42no—
569C22×C137—42no—
570C22×C137—42no—
571C22×C137—42no—
572C22×C137—42no—
573C22×C137—42no—
574C22×C137—42no—
575C22×C137—42no—
576C22×C137—42no—
577C22×C137—42no—
578C22×C137—42no—
579C22×C137—42no—
580C22×C137—42no—
581C22×C137—42no—
582C22×C137—42no—
583C22×C137—42no—
584C22×C137—42no—
585C22×C137—42no—
586C22×C137—42no—
587C22×C137—42no—
588C22×C137—42no—
589C22×C137—42no—
590C22×C137—42no—
591C22×C137—42no—
592C22×C137—42no—
593C22×C137—42no—
594C22×C137—42no—
595C22×C137—42no—
596C22×C137—42no—
597C22×C137—42no—
598C22×C137—42no—
599C22×C137—81no—
600C22×C137—81no—
601C22×C137—81no—
602C22×C137—81no—
603C22×C137—81no—
604C22×C137—81no—
605C22×C137—81no—
606C22×C137—81no—
607C22×C137C2×#12011yescharacteristic
608C22×C137C2×#12111yescharacteristic
609C22×C137C2×#12311yescharacteristic
610C22×C137C2×#12311yescharacteristic
611C22×C137#52511yescharacteristic
612C22×C137#52511yescharacteristic
613C22×C137#52511yescharacteristic
614C22×C137#52511yescharacteristic
615C22×C137#52511yescharacteristic
616C22×C137#52511yescharacteristic
617C22×C137#52911yescharacteristic
618C22×C137#52911yescharacteristic
619C22×C137#53211yescharacteristic
620C22×C137#53411yescharacteristic
621C22×C137#53511yescharacteristic
622C22×C137#53811yescharacteristic
623C22×C137#53811yescharacteristic
624C22×C137#54011yescharacteristic
625C22×C137#54011yescharacteristic
626C22×C137D4211yescharacteristic
627C22×C137D4211yescharacteristic
628C22×C137#54611yescharacteristic
629C22×C137#54611yescharacteristic
630C22×C137#54611yescharacteristic
631C22×C137#54611yescharacteristic
632C22×C137#54611yescharacteristic
633C22×C137#54611yescharacteristic
634C22×C137#54611yescharacteristic
635C22×C137#55011yescharacteristic
636C22×C137#55111yescharacteristic
637C22×C137#55311yescharacteristic
638C22×C137#55311yescharacteristic
639C22×C137#55311yescharacteristic
640C22×C137#55511yescharacteristic
641C22×C137#55911yescharacteristic
642C4×C137—24no—
643C4×C137—24no—
644C4×C137—42no—
645C4×C137—42no—
646C4×C137—42no—
647C4×C137—42no—
648C4×C137—42no—
649C4×C137—42no—
650C4×C137—81no—
651C4×C137—81no—
652C4×C137—81no—
653C4×C137—81no—
654C2×C137—44no—
655C2×C137—44no—
656C2×C137—82no—
657C2×C137#239211yescharacteristic
658C2×C137#240411yescharacteristic
659C2×C137#241011yescharacteristic
660C2×C137#241411yescharacteristic
661C2×C137#241811yescharacteristic
662C2×C137#242011yescharacteristic
663C2×C137#244411yescharacteristic
664C2×C137#244511yescharacteristic
665C2×C137#245611yescharacteristic
666C2×C137#245711yescharacteristic
667C2×C137#245911yescharacteristic
668C2×C137#246411yescharacteristic
669C2×C137#260011yescharacteristic
670C2×C137#263511yescharacteristic
671C2×C137#284911yescharacteristic
672#14730C13711yesmaximal, characteristic, direct product factor, Sylow
673C137#1473011yescharacteristic, direct product factor, Sylow
674C22×C4×D4C2×C13711yescharacteristic, complemented
675C2×#394C2×C13711yescharacteristic, complemented
676C2×#392C2×C13711yescharacteristic
677C2×#386C2×C13711yescharacteristic, complemented
678C2×#386C2×C13711yescharacteristic, complemented
679C2×#381C2×C13711yescharacteristic, complemented
680#1442C2×C13711yescharacteristic, complemented
681#1440C2×C13711yescharacteristic, complemented
682#1439C2×C13711yescharacteristic, complemented
683#1439C2×C13711yescharacteristic, complemented
684#1438C2×C13711yescharacteristic, complemented
685#1438C2×C13711yescharacteristic, complemented
686#1437C2×C13711yescharacteristic, complemented
687#1436C2×C13711yescharacteristic, complemented
688C22⋊#95C2×C13711yescharacteristic, complemented
689C23×D4C22×C13711yescharacteristic
690C23×D4C22×C13711yescharacteristic
691C23×D4C22×C13711yescharacteristic
692C24×C4C22×C13711yescharacteristic
693C24×C4C22×C13711yescharacteristic
694C2×C4×D4—24no—
695C2×C4×D4—24no—
696C2×C4×D4—24no—
697C22×C4⋊C4C22×C13711yescharacteristic
698C22×C4⋊C4C22×C13711yescharacteristic
699C22×C22⋊C4C22×C13711yescharacteristic
700C22×C22⋊C4C22×C13711yescharacteristic
701C22×C22⋊C4C22×C13711yescharacteristic
702C22×C22⋊C4C22×C13711yescharacteristic
703C22×C22⋊C4C22×C13711yescharacteristic
704C22×C22⋊C4C22×C13711yescharacteristic
705C22×C22⋊C4C22×C13711yescharacteristic
706C22×C22⋊C4C22×C13711yescharacteristic
707C22×C22⋊C4C22×C13711yescharacteristic
708C22×C22⋊C4C22×C13711yescharacteristic
709C22×C22⋊C4C22×C13711yescharacteristic
710C22×C22⋊C4C22×C13711yescharacteristic
711C22×C22⋊C4C22×C13711yescharacteristic
712C22×C42C22×C13711yescharacteristic
713#394—24no—
714#392—24no—
715#386—24no—
716#386—24no—
717#381—24no—
718C2×#95C22×C13711yescharacteristic
719C2×#95C22×C13711yescharacteristic
720C2×#95C22×C13711yescharacteristic
721C2×#95C22×C13711yescharacteristic
722C2×#95C22×C13711yescharacteristic
723C2×#95C22×C13711yescharacteristic
724C2×#95C22×C13711yescharacteristic
725C2×#95C22×C13711yescharacteristic
726C2×#95C22×C13711yescharacteristic
727C2×#95C22×C13711yescharacteristic
728C2×#95C22×C13711yescharacteristic
729C2×#95C22×C13711yescharacteristic
730C2×#95C22×C13711yescharacteristic
731C2×#95C22×C13711yescharacteristic
732C25C23×C13711yescharacteristic
733C25C23×C13711yescharacteristic
734C25C23×C13711yescharacteristic
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—41no—
752C22×D4—41no—
753C22×D4—41no—
754C22×D4—41no—
755C22×D4D4×C13714yes—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—22no—
760C23×C4—22no—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4—41no—
769C23×C4D4×C13714yescomplemented
770C23×C4C23×C13711yescharacteristic
771C23×C4C23×C13711yescharacteristic
772C23×C4C23×C13711yescharacteristic
773C23×C4C23×C13711yescharacteristic
774C23×C4C23×C13711yescharacteristic
775C23×C4C23×C13711yescharacteristic
776C23×C4C23×C13711yescharacteristic
777C23×C4C23×C13711yescharacteristic
778C23×C4C23×C13711yescharacteristic
779C23×C4C23×C13711yescharacteristic
780C23×C4C23×C13711yescharacteristic
781C23×C4C23×C13711yescharacteristic
782C4×D4—232no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—22no—
788C2×C4⋊C4—41no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4D4×C13714yescomplemented
828C2×C42—22no—
829C2×C42—22no—
830C2×C42—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—41no—
842#95—41no—
843#95—41no—
844#95D4×C13714yescomplemented
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24C2×D4×C13712yes—
884C24C2×D4×C13712yes—
885C24C2×D4×C13712yes—
886C24C2×D4×C13712yes—
887C24#41×C13712yes—
888C24#41×C13712yes—
889C24#41×C13712yes—
890C24C24×C13711yescharacteristic
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—28no—
897C2×D4—28no—
898C2×D4—28no—
899C2×D4—28no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—28no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4C2×D4×C13712yes—
999C22×C4C2×D4×C13712yes—
1000C22×C4C2×D4×C13712yes—
1001C22×C4C2×D4×C13712yes—
1002C22×C4C2×D4×C13712yes—
1003C22×C4C2×D4×C13712yes—
1004C22×C4C2×D4×C13712yes—
1005C22×C4C2×D4×C13712yes—
1006C22×C4#41×C13712yes—
1007C22×C4#41×C13712yes—
1008C22×C4#41×C13712yes—
1009C22×C4#41×C13712yes—
1010C4⋊C4—28no—
1011C4⋊C4—44no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—44no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C42—28no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23#120×C13714yes—
1130C23#123×C13714yes—
1131C23C22×D4×C13711yescharacteristic
1132C23C22×D4×C13711yescharacteristic
1133C23C22×D4×C13711yescharacteristic
1134C23C22×D4×C13711yescharacteristic
1135C23C2×#41×C13711yescharacteristic
1136C23C2×#41×C13711yescharacteristic
1137C23C2×#41×C13711yescharacteristic
1138C23C2×#41×C13711yescharacteristic
1139C23C2×#41×C13711yescharacteristic
1140C23C2×#41×C13711yescharacteristic
1141C23C2×#41×C13711yescharacteristic
1142C23H(5,𝔽2)×C13711yescharacteristic
1143C23H(5,𝔽2)×C13711yescharacteristic
1144C23H(5,𝔽2)×C13711yescharacteristic
1145C23H(5,𝔽2)×C13711yescharacteristic
1146D4—232no—
1147D4—416no—
1148D4—416no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—416no—
1180C2×C4—416no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4#121×C13714yes—
1234C2×C4#123×C13714yes—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22C2×#120×C13711yescharacteristic
1281C22C2×#121×C13711yescharacteristic
1282C22C2×#123×C13711yescharacteristic
1283C22C2×#123×C13711yescharacteristic
1284C22#525×C13711yescharacteristic
1285C22#525×C13711yescharacteristic
1286C22#525×C13711yescharacteristic
1287C22#525×C13711yescharacteristic
1288C22#525×C13711yescharacteristic
1289C22#525×C13711yescharacteristic
1290C22#529×C13711yescharacteristic
1291C22#529×C13711yescharacteristic
1292C22#532×C13711yescharacteristic
1293C22#534×C13711yescharacteristic
1294C22#535×C13711yescharacteristic
1295C22#538×C13711yescharacteristic
1296C22#538×C13711yescharacteristic
1297C22#540×C13711yescharacteristic
1298C22#540×C13711yescharacteristic
1299C22D42×C13711yescharacteristic
1300C22D42×C13711yescharacteristic
1301C22#546×C13711yescharacteristic
1302C22#546×C13711yescharacteristic
1303C22#546×C13711yescharacteristic
1304C22#546×C13711yescharacteristic
1305C22#546×C13711yescharacteristic
1306C22#546×C13711yescharacteristic
1307C22#546×C13711yescharacteristic
1308C22#550×C13711yescharacteristic
1309C22#551×C13711yescharacteristic
1310C22#553×C13711yescharacteristic
1311C22#553×C13711yescharacteristic
1312C22#553×C13711yescharacteristic
1313C22#555×C13711yescharacteristic
1314C22#559×C13711yescharacteristic
1315C4—24no—
1316C4—24no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C2—44no—
1328C2—44no—
1329C2—82no—
1330C2#2392×C13711yescharacteristic
1331C2#2404×C13711yescharacteristic
1332C2#2410×C13711yescharacteristic
1333C2#2414×C13711yescharacteristic
1334C2#2418×C13711yescharacteristic
1335C2#2420×C13711yescharacteristic
1336C2#2444×C13711yescharacteristic
1337C2#2445×C13711yescharacteristic
1338C2#2456×C13711yescharacteristic
1339C2#2457×C13711yescharacteristic
1340C2#2459×C13711yescharacteristic
1341C2#2464×C13711yescharacteristic
1342C2#2600×C13711yescharacteristic
1343C2#2635×C13711yescharacteristic
1344C2#2849×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutator, Frattini, cosocleC24C24×C137
prime radicalC2×#392×C137C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C4×D4×C137C2semidirect
2. C2×#394×C137C2semidirect
4. C2×#386×C137C2semidirect
5. C2×#386×C137C2semidirect
6. C2×#381×C137C2semidirect
7. #1442×C137C2semidirect
8. #1440×C137C2semidirect
9. #1439×C137C2semidirect
10. #1439×C137C2semidirect
11. #1438×C137C2semidirect
12. #1438×C137C2semidirect
13. #1437×C137C2semidirect
14. #1436×C137C2semidirect
15. C22⋊#95×C137C2semidirect
96. C23×C4×C137D4semidirect
154. C2×C22⋊C4×C137D4semidirect
171. #95×C137D4semidirect
672. #14730C137direct (N × H)
673. C137#14730direct (N × H)
674. C22×C4×D4C2×C137semidirect
675. C2×#394C2×C137semidirect
677. C2×#386C2×C137semidirect
678. C2×#386C2×C137semidirect
679. C2×#381C2×C137semidirect
680. #1442C2×C137semidirect
681. #1440C2×C137semidirect
682. #1439C2×C137semidirect
683. #1439C2×C137semidirect
684. #1438C2×C137semidirect
685. #1438C2×C137semidirect
686. #1437C2×C137semidirect
687. #1436C2×C137semidirect
688. C22⋊#95C2×C137semidirect
769. C23×C4D4×C137semidirect
827. C2×C22⋊C4D4×C137semidirect
844. #95D4×C137semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C1372
C2×#394×C1372
C2×#392×C1372
C2×#386×C1372
C2×#381×C1372
#1442×C1372
#1440×C1372
#1439×C1372
#1438×C1372
#1437×C1372
#1436×C1372
C22⋊#95×C1372
#14730137