Finite Group Databasebeta

← C137×#15501 #46864887

Subgroups — C137×#15501 #46864887

Order 35072.

2154 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C137C211yesmaximal, characteristic, complemented
2C2×#394×C137C211yesmaximal, characteristic, complemented
3C2×#392×C137C211yesmaximal, characteristic
4C2×#390×C137C211yesmaximal, characteristic, complemented
5C2×#386×C137C211yesmaximal, characteristic, complemented
6C2×#386×C137C211yesmaximal, characteristic, complemented
7#1441×C137C211yesmaximal, characteristic, complemented
8#1440×C137C211yesmaximal, characteristic, complemented
9#1440×C137C211yesmaximal, characteristic, complemented
10#1439×C137C211yesmaximal, characteristic, complemented
11#1438×C137C211yesmaximal, characteristic, complemented
12#1438×C137C211yesmaximal, characteristic, complemented
13#1437×C137C211yesmaximal, characteristic, complemented
14#1434×C137C211yesmaximal, characteristic, complemented
15C22⋊#95×C137C211yesmaximal, characteristic, complemented
16C23×D4×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C23×D4×C137C2211yescharacteristic
19C24×C4×C137C2211yescharacteristic
20C22×C4⋊C4×C137C2211yescharacteristic
21C22×C4⋊C4×C137C2211yescharacteristic
22C22×C22⋊C4×C137C2211yescharacteristic
23C22×C22⋊C4×C137C2211yescharacteristic
24C22×C22⋊C4×C137C2211yescharacteristic
25C22×C22⋊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×C42×C137C2211yescharacteristic
37#397×C137—24no—
38#394×C137—24no—
39#392×C137—24no—
40#390×C137—24no—
41#386×C137—24no—
42#386×C137—24no—
43C2×#95×C137C2211yescharacteristic
44C2×#95×C137C2211yescharacteristic
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
57C25×C137C2311yescharacteristic
58C25×C137C2311yescharacteristic
59C25×C137C2311yescharacteristic
60C22×D4×C137—22no—
61C22×D4×C137—22no—
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—41no—
73C22×D4×C137—41no—
74C22×D4×C137—41no—
75C22×D4×C137—41no—
76C22×D4×C137—41no—
77C22×D4×C137—41no—
78C22×D4×C137—41no—
79C22×D4×C137—41no—
80C22×D4×C137D414yes—
81C23×C4×C137—22no—
82C23×C4×C137—22no—
83C23×C4×C137—22no—
84C23×C4×C137—41no—
85C23×C4×C137—41no—
86C23×C4×C137—41no—
87C23×C4×C137—41no—
88C23×C4×C137C2311yescharacteristic
89C23×C4×C137C2311yescharacteristic
90C23×C4×C137C2311yescharacteristic
91C23×C4×C137C2311yescharacteristic
92C23×C4×C137C2311yescharacteristic
93C23×C4×C137C2311yescharacteristic
94C23×C4×C137C2311yescharacteristic
95C23×C4×C137C2311yescharacteristic
96C23×C4×C137C2311yescharacteristic
97C23×C4×C137C2311yescharacteristic
98C23×C4×C137C2311yescharacteristic
99C23×C4×C137C2311yescharacteristic
100C2×C4⋊C4×C137—22no—
101C2×C4⋊C4×C137—22no—
102C2×C4⋊C4×C137—22no—
103C2×C4⋊C4×C137—22no—
104C2×C4⋊C4×C137—41no—
105C2×C4⋊C4×C137—41no—
106C2×C22⋊C4×C137—22no—
107C2×C22⋊C4×C137—22no—
108C2×C22⋊C4×C137—22no—
109C2×C22⋊C4×C137—22no—
110C2×C22⋊C4×C137—22no—
111C2×C22⋊C4×C137—22no—
112C2×C22⋊C4×C137—22no—
113C2×C22⋊C4×C137—22no—
114C2×C22⋊C4×C137—22no—
115C2×C22⋊C4×C137—22no—
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—41no—
132C2×C22⋊C4×C137—41no—
133C2×C22⋊C4×C137—41no—
134C2×C22⋊C4×C137—41no—
135C2×C22⋊C4×C137—41no—
136C2×C22⋊C4×C137—41no—
137C2×C22⋊C4×C137—41no—
138C2×C22⋊C4×C137—41no—
139C2×C22⋊C4×C137—41no—
140C2×C22⋊C4×C137—41no—
141C2×C22⋊C4×C137—41no—
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×C137D414yescomplemented
148C2×C42×C137—22no—
149C2×C42×C137—22no—
150C2×C42×C137—41no—
151#95×C137—22no—
152#95×C137—22no—
153#95×C137—22no—
154#95×C137—22no—
155#95×C137—22no—
156#95×C137—22no—
157#95×C137—22no—
158#95×C137—22no—
159#95×C137—41no—
160#95×C137—41no—
161#95×C137—41no—
162#95×C137—41no—
163#95×C137—41no—
164#95×C137D414yescomplemented
165C24×C137—21no—
166C24×C137—21no—
167C24×C137—21no—
168C24×C137—21no—
169C24×C137—21no—
170C24×C137—21no—
171C24×C137—21no—
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×C137C2×D412yes—
206C24×C137C2×D412yes—
207C24×C137C2×D412yes—
208C24×C137#4112yes—
209C24×C137#4112yes—
210C24×C137C2411yescharacteristic
211C2×D4×C137—28no—
212C2×D4×C137—28no—
213C2×D4×C137—28no—
214C2×D4×C137—44no—
215C2×D4×C137—44no—
216C2×D4×C137—44no—
217C2×D4×C137—44no—
218C2×D4×C137—44no—
219C2×D4×C137—44no—
220C2×D4×C137—44no—
221C2×D4×C137—44no—
222C2×D4×C137—44no—
223C2×D4×C137—44no—
224C2×D4×C137—44no—
225C2×D4×C137—44no—
226C2×D4×C137—44no—
227C2×D4×C137—44no—
228C2×D4×C137—44no—
229C2×D4×C137—44no—
230C2×D4×C137—44no—
231C2×D4×C137—44no—
232C22×C4×C137—21no—
233C22×C4×C137—21no—
234C22×C4×C137—21no—
235C22×C4×C137—21no—
236C22×C4×C137—21no—
237C22×C4×C137—21no—
238C22×C4×C137—21no—
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—21no—
248C22×C4×C137—21no—
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—21no—
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—44no—
307C22×C4×C137—44no—
308C22×C4×C137—44no—
309C22×C4×C137—44no—
310C22×C4×C137—44no—
311C22×C4×C137—44no—
312C22×C4×C137—44no—
313C22×C4×C137C2×D412yes—
314C22×C4×C137C2×D412yes—
315C22×C4×C137C2×D412yes—
316C22×C4×C137C2×D412yes—
317C22×C4×C137C2×D412yes—
318C22×C4×C137C2×D412yes—
319C22×C4×C137#4112yes—
320C22×C4×C137#4112yes—
321C22×C4×C137#4112yes—
322C22×C4×C137#4112yes—
323C4⋊C4×C137—44no—
324C4⋊C4×C137—44no—
325C22⋊C4×C137—44no—
326C22⋊C4×C137—44no—
327C22⋊C4×C137—44no—
328C22⋊C4×C137—44no—
329C22⋊C4×C137—44no—
330C22⋊C4×C137—44no—
331C22⋊C4×C137—44no—
332C22⋊C4×C137—44no—
333C22⋊C4×C137—44no—
334C22⋊C4×C137—44no—
335C22⋊C4×C137—44no—
336C22⋊C4×C137—44no—
337C22⋊C4×C137—44no—
338C22⋊C4×C137—44no—
339C42×C137—44no—
340C23×C137—22no—
341C23×C137—22no—
342C23×C137—22no—
343C23×C137—22no—
344C23×C137—22no—
345C23×C137—22no—
346C23×C137—22no—
347C23×C137—22no—
348C23×C137—22no—
349C23×C137—22no—
350C23×C137—22no—
351C23×C137—22no—
352C23×C137—22no—
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—41no—
373C23×C137—41no—
374C23×C137—41no—
375C23×C137—41no—
376C23×C137—41no—
377C23×C137—41no—
378C23×C137—41no—
379C23×C137—41no—
380C23×C137—41no—
381C23×C137—41no—
382C23×C137—41no—
383C23×C137—41no—
384C23×C137—41no—
385C23×C137—41no—
386C23×C137—41no—
387C23×C137—41no—
388C23×C137—41no—
389C23×C137—41no—
390C23×C137—41no—
391C23×C137—41no—
392C23×C137—41no—
393C23×C137—41no—
394C23×C137—41no—
395C23×C137—41no—
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#12114yes—
445C23×C137C22×D411yescharacteristic
446C23×C137C22×D411yescharacteristic
447C23×C137C22×D411yescharacteristic
448C23×C137C2×#4111yescharacteristic
449C23×C137C2×#4111yescharacteristic
450C23×C137C2×#4111yescharacteristic
451C23×C137C2×#4111yescharacteristic
452C23×C137C2×#4111yescharacteristic
453C23×C137C2×#4111yescharacteristic
454C23×C137H(5,𝔽2)11yescharacteristic
455C23×C137H(5,𝔽2)11yescharacteristic
456C23×C137H(5,𝔽2)11yescharacteristic
457C23×C137H(5,𝔽2)11yescharacteristic
458C23×C137H(5,𝔽2)11yescharacteristic
459C23×C137H(5,𝔽2)11yescharacteristic
460D4×C137—416no—
461D4×C137—416no—
462D4×C137—416no—
463C2×C4×C137—22no—
464C2×C4×C137—22no—
465C2×C4×C137—22no—
466C2×C4×C137—22no—
467C2×C4×C137—22no—
468C2×C4×C137—22no—
469C2×C4×C137—22no—
470C2×C4×C137—22no—
471C2×C4×C137—22no—
472C2×C4×C137—22no—
473C2×C4×C137—22no—
474C2×C4×C137—22no—
475C2×C4×C137—22no—
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—416no—
491C2×C4×C137—41no—
492C2×C4×C137—41no—
493C2×C4×C137—41no—
494C2×C4×C137—41no—
495C2×C4×C137—41no—
496C2×C4×C137—41no—
497C2×C4×C137—41no—
498C2×C4×C137—41no—
499C2×C4×C137—41no—
500C2×C4×C137—41no—
501C2×C4×C137—41no—
502C2×C4×C137—41no—
503C2×C4×C137—41no—
504C2×C4×C137—41no—
505C2×C4×C137—41no—
506C2×C4×C137—41no—
507C2×C4×C137—41no—
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#12314yes—
548C22×C137—24no—
549C22×C137—24no—
550C22×C137—24no—
551C22×C137—42no—
552C22×C137—42no—
553C22×C137—42no—
554C22×C137—42no—
555C22×C137—42no—
556C22×C137—42no—
557C22×C137—42no—
558C22×C137—42no—
559C22×C137—42no—
560C22×C137—42no—
561C22×C137—42no—
562C22×C137—42no—
563C22×C137—42no—
564C22×C137—42no—
565C22×C137—42no—
566C22×C137—42no—
567C22×C137—42no—
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—81no—
578C22×C137—81no—
579C22×C137—81no—
580C22×C137—81no—
581C22×C137—81no—
582C22×C137—81no—
583C22×C137—81no—
584C22×C137—81no—
585C22×C137—81no—
586C22×C137—81no—
587C22×C137—81no—
588C22×C137—81no—
589C22×C137—81no—
590C22×C137—81no—
591C22×C137—81no—
592C22×C137—81no—
593C22×C137C2×#12111yescharacteristic
594C22×C137C2×#12311yescharacteristic
595C22×C137#52511yescharacteristic
596C22×C137#52911yescharacteristic
597C22×C137#53211yescharacteristic
598C22×C137#53211yescharacteristic
599C22×C137#53411yescharacteristic
600C22×C137#53411yescharacteristic
601C22×C137#53511yescharacteristic
602C22×C137#53811yescharacteristic
603C22×C137#53811yescharacteristic
604C22×C137#53811yescharacteristic
605C22×C137#53811yescharacteristic
606C22×C137#54011yescharacteristic
607C22×C137#54011yescharacteristic
608C22×C137D4211yescharacteristic
609C22×C137D4211yescharacteristic
610C22×C137#54611yescharacteristic
611C22×C137#54611yescharacteristic
612C22×C137#54611yescharacteristic
613C22×C137#54611yescharacteristic
614C22×C137#54611yescharacteristic
615C22×C137#54611yescharacteristic
616C22×C137#54611yescharacteristic
617C22×C137#55011yescharacteristic
618C22×C137#55111yescharacteristic
619C22×C137#55111yescharacteristic
620C22×C137#55111yescharacteristic
621C22×C137#55311yescharacteristic
622C22×C137#55311yescharacteristic
623C22×C137#55311yescharacteristic
624C22×C137#55511yescharacteristic
625C22×C137#55911yescharacteristic
626C22×C137#56011yescharacteristic
627C22×C137#56011yescharacteristic
628C4×C137—24no—
629C4×C137—42no—
630C4×C137—42no—
631C4×C137—42no—
632C4×C137—42no—
633C4×C137—42no—
634C4×C137—42no—
635C4×C137—42no—
636C4×C137—81no—
637C4×C137—81no—
638C4×C137—81no—
639C4×C137—81no—
640C2×C137—44no—
641C2×C137—82no—
642C2×C137—82no—
643C2×C137#241211yescharacteristic
644C2×C137#242011yescharacteristic
645C2×C137#242411yescharacteristic
646C2×C137#244511yescharacteristic
647C2×C137#246711yescharacteristic
648C2×C137#254311yescharacteristic
649C2×C137#255511yescharacteristic
650C2×C137#255711yescharacteristic
651C2×C137#260311yescharacteristic
652C2×C137#267311yescharacteristic
653C2×C137#267811yescharacteristic
654C2×C137#268811yescharacteristic
655C2×C137#269711yescharacteristic
656C2×C137#275611yescharacteristic
657C2×C137#279711yescharacteristic
658#15501C13711yesmaximal, characteristic, direct product factor, Sylow
659C137#1550111yescharacteristic, direct product factor, Sylow
660C2×#397C2×C13711yescharacteristic, complemented
661C2×#394C2×C13711yescharacteristic, complemented
662C2×#392C2×C13711yescharacteristic
663C2×#390C2×C13711yescharacteristic, complemented
664C2×#386C2×C13711yescharacteristic, complemented
665C2×#386C2×C13711yescharacteristic, complemented
666#1441C2×C13711yescharacteristic, complemented
667#1440C2×C13711yescharacteristic, complemented
668#1440C2×C13711yescharacteristic, complemented
669#1439C2×C13711yescharacteristic, complemented
670#1438C2×C13711yescharacteristic, complemented
671#1438C2×C13711yescharacteristic, complemented
672#1437C2×C13711yescharacteristic, complemented
673#1434C2×C13711yescharacteristic, complemented
674C22⋊#95C2×C13711yescharacteristic, complemented
675C23×D4C22×C13711yescharacteristic
676C23×D4C22×C13711yescharacteristic
677C23×D4C22×C13711yescharacteristic
678C24×C4C22×C13711yescharacteristic
679C22×C4⋊C4C22×C13711yescharacteristic
680C22×C4⋊C4C22×C13711yescharacteristic
681C22×C22⋊C4C22×C13711yescharacteristic
682C22×C22⋊C4C22×C13711yescharacteristic
683C22×C22⋊C4C22×C13711yescharacteristic
684C22×C22⋊C4C22×C13711yescharacteristic
685C22×C22⋊C4C22×C13711yescharacteristic
686C22×C22⋊C4C22×C13711yescharacteristic
687C22×C22⋊C4C22×C13711yescharacteristic
688C22×C22⋊C4C22×C13711yescharacteristic
689C22×C22⋊C4C22×C13711yescharacteristic
690C22×C22⋊C4C22×C13711yescharacteristic
691C22×C22⋊C4C22×C13711yescharacteristic
692C22×C22⋊C4C22×C13711yescharacteristic
693C22×C22⋊C4C22×C13711yescharacteristic
694C22×C22⋊C4C22×C13711yescharacteristic
695C22×C42C22×C13711yescharacteristic
696#397—24no—
697#394—24no—
698#392—24no—
699#390—24no—
700#386—24no—
701#386—24no—
702C2×#95C22×C13711yescharacteristic
703C2×#95C22×C13711yescharacteristic
704C2×#95C22×C13711yescharacteristic
705C2×#95C22×C13711yescharacteristic
706C2×#95C22×C13711yescharacteristic
707C2×#95C22×C13711yescharacteristic
708C2×#95C22×C13711yescharacteristic
709C2×#95C22×C13711yescharacteristic
710C2×#95C22×C13711yescharacteristic
711C2×#95C22×C13711yescharacteristic
712C2×#95C22×C13711yescharacteristic
713C2×#95C22×C13711yescharacteristic
714C2×#95C22×C13711yescharacteristic
715C2×#95C22×C13711yescharacteristic
716C25C23×C13711yescharacteristic
717C25C23×C13711yescharacteristic
718C25C23×C13711yescharacteristic
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4—41no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4D4×C13714yes—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—22no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4—41no—
747C23×C4C23×C13711yescharacteristic
748C23×C4C23×C13711yescharacteristic
749C23×C4C23×C13711yescharacteristic
750C23×C4C23×C13711yescharacteristic
751C23×C4C23×C13711yescharacteristic
752C23×C4C23×C13711yescharacteristic
753C23×C4C23×C13711yescharacteristic
754C23×C4C23×C13711yescharacteristic
755C23×C4C23×C13711yescharacteristic
756C23×C4C23×C13711yescharacteristic
757C23×C4C23×C13711yescharacteristic
758C23×C4C23×C13711yescharacteristic
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794C2×C22⋊C4—41no—
795C2×C22⋊C4—41no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4D4×C13714yescomplemented
807C2×C42—22no—
808C2×C42—22no—
809C2×C42—41no—
810#95—22no—
811#95—22no—
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—41no—
819#95—41no—
820#95—41no—
821#95—41no—
822#95—41no—
823#95D4×C13714yescomplemented
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
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—
864C24C2×D4×C13712yes—
865C24C2×D4×C13712yes—
866C24C2×D4×C13712yes—
867C24#41×C13712yes—
868C24#41×C13712yes—
869C24C24×C13711yescharacteristic
870C2×D4—28no—
871C2×D4—28no—
872C2×D4—28no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
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—21no—
921C22×C4—21no—
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—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—44no—
966C22×C4—44no—
967C22×C4—44no—
968C22×C4—44no—
969C22×C4—44no—
970C22×C4—44no—
971C22×C4—44no—
972C22×C4C2×D4×C13712yes—
973C22×C4C2×D4×C13712yes—
974C22×C4C2×D4×C13712yes—
975C22×C4C2×D4×C13712yes—
976C22×C4C2×D4×C13712yes—
977C22×C4C2×D4×C13712yes—
978C22×C4#41×C13712yes—
979C22×C4#41×C13712yes—
980C22×C4#41×C13712yes—
981C22×C4#41×C13712yes—
982C4⋊C4—44no—
983C4⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
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—
998C42—44no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
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#121×C13714yes—
1104C23C22×D4×C13711yescharacteristic
1105C23C22×D4×C13711yescharacteristic
1106C23C22×D4×C13711yescharacteristic
1107C23C2×#41×C13711yescharacteristic
1108C23C2×#41×C13711yescharacteristic
1109C23C2×#41×C13711yescharacteristic
1110C23C2×#41×C13711yescharacteristic
1111C23C2×#41×C13711yescharacteristic
1112C23C2×#41×C13711yescharacteristic
1113C23H(5,𝔽2)×C13711yescharacteristic
1114C23H(5,𝔽2)×C13711yescharacteristic
1115C23H(5,𝔽2)×C13711yescharacteristic
1116C23H(5,𝔽2)×C13711yescharacteristic
1117C23H(5,𝔽2)×C13711yescharacteristic
1118C23H(5,𝔽2)×C13711yescharacteristic
1119D4—416no—
1120D4—416no—
1121D4—416no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—416no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
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#123×C13714yes—
1207C22—24no—
1208C22—24no—
1209C22—24no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22C2×#121×C13711yescharacteristic
1253C22C2×#123×C13711yescharacteristic
1254C22#525×C13711yescharacteristic
1255C22#529×C13711yescharacteristic
1256C22#532×C13711yescharacteristic
1257C22#532×C13711yescharacteristic
1258C22#534×C13711yescharacteristic
1259C22#534×C13711yescharacteristic
1260C22#535×C13711yescharacteristic
1261C22#538×C13711yescharacteristic
1262C22#538×C13711yescharacteristic
1263C22#538×C13711yescharacteristic
1264C22#538×C13711yescharacteristic
1265C22#540×C13711yescharacteristic
1266C22#540×C13711yescharacteristic
1267C22D42×C13711yescharacteristic
1268C22D42×C13711yescharacteristic
1269C22#546×C13711yescharacteristic
1270C22#546×C13711yescharacteristic
1271C22#546×C13711yescharacteristic
1272C22#546×C13711yescharacteristic
1273C22#546×C13711yescharacteristic
1274C22#546×C13711yescharacteristic
1275C22#546×C13711yescharacteristic
1276C22#550×C13711yescharacteristic
1277C22#551×C13711yescharacteristic
1278C22#551×C13711yescharacteristic
1279C22#551×C13711yescharacteristic
1280C22#553×C13711yescharacteristic
1281C22#553×C13711yescharacteristic
1282C22#553×C13711yescharacteristic
1283C22#555×C13711yescharacteristic
1284C22#559×C13711yescharacteristic
1285C22#560×C13711yescharacteristic
1286C22#560×C13711yescharacteristic
1287C4—24no—
1288C4—42no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C2—44no—
1300C2—82no—
1301C2—82no—
1302C2#2412×C13711yescharacteristic
1303C2#2420×C13711yescharacteristic
1304C2#2424×C13711yescharacteristic
1305C2#2445×C13711yescharacteristic
1306C2#2467×C13711yescharacteristic
1307C2#2543×C13711yescharacteristic
1308C2#2555×C13711yescharacteristic
1309C2#2557×C13711yescharacteristic
1310C2#2603×C13711yescharacteristic
1311C2#2673×C13711yescharacteristic
1312C2#2678×C13711yescharacteristic
1313C2#2688×C13711yescharacteristic
1314C2#2697×C13711yescharacteristic
1315C2#2756×C13711yescharacteristic
1316C2#2797×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. C2×#397×C137C2semidirect
2. C2×#394×C137C2semidirect
4. C2×#390×C137C2semidirect
5. C2×#386×C137C2semidirect
6. C2×#386×C137C2semidirect
7. #1441×C137C2semidirect
8. #1440×C137C2semidirect
9. #1440×C137C2semidirect
10. #1439×C137C2semidirect
11. #1438×C137C2semidirect
12. #1438×C137C2semidirect
13. #1437×C137C2semidirect
14. #1434×C137C2semidirect
15. C22⋊#95×C137C2semidirect
147. C2×C22⋊C4×C137D4semidirect
164. #95×C137D4semidirect
658. #15501C137direct (N × H)
659. C137#15501direct (N × H)
660. C2×#397C2×C137semidirect
661. C2×#394C2×C137semidirect
663. C2×#390C2×C137semidirect
664. C2×#386C2×C137semidirect
665. C2×#386C2×C137semidirect
666. #1441C2×C137semidirect
667. #1440C2×C137semidirect
668. #1440C2×C137semidirect
669. #1439C2×C137semidirect
670. #1438C2×C137semidirect
671. #1438C2×C137semidirect
672. #1437C2×C137semidirect
673. #1434C2×C137semidirect
674. C22⋊#95C2×C137semidirect
806. C2×C22⋊C4D4×C137semidirect
823. #95D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#397×C1372
C2×#394×C1372
C2×#392×C1372
C2×#390×C1372
C2×#386×C1372
#1441×C1372
#1440×C1372
#1439×C1372
#1438×C1372
#1437×C1372
#1434×C1372
C22⋊#95×C1372
#15501137