Finite Group Databasebeta

← C137×#14761 #46864147

Subgroups — C137×#14761 #46864147

Order 35072.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C137C211yesmaximal, characteristic
2C2×#394×C137C211yesmaximal, characteristic
3C2×#389×C137C211yesmaximal, characteristic, complemented
4C2×#388×C137C211yesmaximal, characteristic, complemented
5C2×#385×C137C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C137C211yesmaximal, characteristic, complemented
7#1444×C137C211yesmaximal, characteristic, complemented
8#1442×C137C211yesmaximal, characteristic, complemented
9#1440×C137C211yesmaximal, characteristic, complemented
10#1439×C137C211yesmaximal, characteristic, complemented
11#1439×C137C211yesmaximal, characteristic, complemented
12#1439×C137C211yesmaximal, characteristic, complemented
13#1438×C137C211yesmaximal, characteristic
14#1437×C137C211yesmaximal, characteristic, complemented
15#1436×C137C211yesmaximal, characteristic, complemented
16C23×D4×C137C2211yescharacteristic
17C24×C4×C137C2211yescharacteristic
18C2×#123×C137—24no—
19C2×#123×C137—24no—
20C2×#123×C137—24no—
21C22×C4⋊C4×C137C2211yescharacteristic
22C22×C4⋊C4×C137C2211yescharacteristic
23C22×C4⋊C4×C137C2211yescharacteristic
24C22×C4⋊C4×C137C2211yescharacteristic
25C22×C4⋊C4×C137C2211yescharacteristic
26C22×C4⋊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×C42×C137C2211yescharacteristic
39C22×C42×C137C2211yescharacteristic
40#394×C137—24no—
41#389×C137—24no—
42#388×C137—24no—
43#385×C137—24no—
44C4×C22⋊C4×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
61C22×D4×C137—22no—
62C22×D4×C137—22no—
63C22×D4×C137—22no—
64C22×D4×C137—22no—
65C22×D4×C137—22no—
66C22×D4×C137—41no—
67C22×D4×C137—41no—
68C23×C4×C137—22no—
69C23×C4×C137—22no—
70C23×C4×C137—22no—
71C23×C4×C137—22no—
72C23×C4×C137—41no—
73C23×C4×C137—41no—
74C23×C4×C137D414yes—
75C23×C4×C137C2311yescharacteristic
76C23×C4×C137C2311yescharacteristic
77C23×C4×C137C2311yescharacteristic
78C23×C4×C137C2311yescharacteristic
79C23×C4×C137C2311yescharacteristic
80C23×C4×C137C2311yescharacteristic
81C23×C4×C137C2311yescharacteristic
82C23×C4×C137C2311yescharacteristic
83C23×C4×C137C2311yescharacteristic
84C23×C4×C137C2311yescharacteristic
85C23×C4×C137C2311yescharacteristic
86C23×C4×C137C2311yescharacteristic
87C23×C4×C137C2311yescharacteristic
88#123×C137—232no—
89C2×C4⋊C4×C137—22no—
90C2×C4⋊C4×C137—22no—
91C2×C4⋊C4×C137—22no—
92C2×C4⋊C4×C137—22no—
93C2×C4⋊C4×C137—22no—
94C2×C4⋊C4×C137—22no—
95C2×C4⋊C4×C137—22no—
96C2×C4⋊C4×C137—22no—
97C2×C4⋊C4×C137—22no—
98C2×C4⋊C4×C137—22no—
99C2×C4⋊C4×C137—22no—
100C2×C4⋊C4×C137—22no—
101C2×C4⋊C4×C137—22no—
102C2×C4⋊C4×C137—22no—
103C2×C4⋊C4×C137—41no—
104C2×C4⋊C4×C137—41no—
105C2×C4⋊C4×C137—41no—
106C2×C4⋊C4×C137D414yes—
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—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—41no—
137C2×C22⋊C4×C137—41no—
138C2×C22⋊C4×C137D414yes—
139C2×C22⋊C4×C137D414yes—
140C2×C42×C137—22no—
141C2×C42×C137—22no—
142C2×C42×C137—22no—
143C2×C42×C137—22no—
144C2×C42×C137—41no—
145C2×C42×C137—41no—
146#95×C137—22no—
147#95×C137—22no—
148#95×C137—22no—
149#95×C137—22no—
150#95×C137—22no—
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—
160C24×C137—21no—
161C24×C137—21no—
162C24×C137—21no—
163C24×C137—21no—
164C24×C137—21no—
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×C137C2×D412yes—
187C24×C137C2×D412yes—
188C24×C137C2×D412yes—
189C24×C137#4112yes—
190C24×C137C2411yescharacteristic
191C2×D4×C137—28no—
192C2×D4×C137—44no—
193C2×D4×C137—44no—
194C2×D4×C137—44no—
195C2×D4×C137—44no—
196C2×D4×C137—44no—
197C2×D4×C137—44no—
198C22×C4×C137—21no—
199C22×C4×C137—21no—
200C22×C4×C137—21no—
201C22×C4×C137—21no—
202C22×C4×C137—21no—
203C22×C4×C137—21no—
204C22×C4×C137—21no—
205C22×C4×C137—21no—
206C22×C4×C137—28no—
207C22×C4×C137—21no—
208C22×C4×C137—21no—
209C22×C4×C137—21no—
210C22×C4×C137—21no—
211C22×C4×C137—21no—
212C22×C4×C137—21no—
213C22×C4×C137—21no—
214C22×C4×C137—21no—
215C22×C4×C137—21no—
216C22×C4×C137—21no—
217C22×C4×C137—21no—
218C22×C4×C137—21no—
219C22×C4×C137—21no—
220C22×C4×C137—21no—
221C22×C4×C137—21no—
222C22×C4×C137—21no—
223C22×C4×C137—21no—
224C22×C4×C137—21no—
225C22×C4×C137—21no—
226C22×C4×C137—21no—
227C22×C4×C137—21no—
228C22×C4×C137—21no—
229C22×C4×C137—21no—
230C22×C4×C137—21no—
231C22×C4×C137—21no—
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—28no—
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—44no—
277C22×C4×C137—44no—
278C22×C4×C137—44no—
279C22×C4×C137—44no—
280C22×C4×C137—44no—
281C22×C4×C137C2×D412yes—
282C22×C4×C137C2×D412yes—
283C22×C4×C137C2×D412yes—
284C22×C4×C137C2×D412yes—
285C22×C4×C137C2×D412yes—
286C22×C4×C137C2×D412yes—
287C22×C4×C137C2×D412yes—
288C22×C4×C137C2×D412yes—
289C22×C4×C137C2×D412yes—
290C22×C4×C137#4112yes—
291C22×C4×C137#4112yes—
292C22×C4×C137#4112yes—
293C22×C4×C137#4112yes—
294C22×C4×C137#4112yes—
295C22×C4×C137#4112yes—
296C4⋊C4×C137—28no—
297C4⋊C4×C137—28no—
298C4⋊C4×C137—28no—
299C4⋊C4×C137—44no—
300C4⋊C4×C137—44no—
301C4⋊C4×C137—44no—
302C22⋊C4×C137—28no—
303C22⋊C4×C137—28no—
304C22⋊C4×C137—28no—
305C22⋊C4×C137—28no—
306C22⋊C4×C137—28no—
307C22⋊C4×C137—28no—
308C22⋊C4×C137—28no—
309C22⋊C4×C137—44no—
310C22⋊C4×C137—44no—
311C22⋊C4×C137—44no—
312C22⋊C4×C137—44no—
313C42×C137—44no—
314C42×C137—44no—
315C23×C137—22no—
316C23×C137—22no—
317C23×C137—22no—
318C23×C137—22no—
319C23×C137—22no—
320C23×C137—22no—
321C23×C137—22no—
322C23×C137—22no—
323C23×C137—22no—
324C23×C137—22no—
325C23×C137—22no—
326C23×C137—22no—
327C23×C137—22no—
328C23×C137—22no—
329C23×C137—22no—
330C23×C137—22no—
331C23×C137—22no—
332C23×C137—22no—
333C23×C137—22no—
334C23×C137—22no—
335C23×C137—22no—
336C23×C137—22no—
337C23×C137—22no—
338C23×C137—22no—
339C23×C137—22no—
340C23×C137—41no—
341C23×C137—41no—
342C23×C137—41no—
343C23×C137—41no—
344C23×C137—41no—
345C23×C137—41no—
346C23×C137—41no—
347C23×C137—41no—
348C23×C137—41no—
349C23×C137—41no—
350C23×C137—41no—
351C23×C137—41no—
352C23×C137—41no—
353C23×C137—41no—
354C23×C137—41no—
355C23×C137—41no—
356C23×C137—41no—
357C23×C137—41no—
358C23×C137—41no—
359C23×C137—41no—
360C23×C137—41no—
361C23×C137—41no—
362C23×C137—41no—
363C23×C137—41no—
364C23×C137—41no—
365C23×C137—41no—
366C23×C137—41no—
367C23×C137—41no—
368C23×C137—41no—
369C23×C137—41no—
370C23×C137—41no—
371C23×C137—41no—
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#12114yes—
385C23×C137C22×D411yescharacteristic
386C23×C137C22×D411yescharacteristic
387C23×C137C22×D411yescharacteristic
388C23×C137C22×D411yescharacteristic
389C23×C137C2×#4111yescharacteristic
390C23×C137C2×#4111yescharacteristic
391C23×C137C2×#4111yescharacteristic
392C23×C137C2×#4111yescharacteristic
393C23×C137C2×#4111yescharacteristic
394C23×C137C2×#4111yescharacteristic
395C23×C137C2×#4111yescharacteristic
396C23×C137H(5,𝔽2)11yescharacteristic
397C23×C137H(5,𝔽2)11yescharacteristic
398C23×C1372−1+411yescharacteristic
399C23×C1372−1+411yescharacteristic
400D4×C137—416no—
401C2×C4×C137—22no—
402C2×C4×C137—22no—
403C2×C4×C137—22no—
404C2×C4×C137—22no—
405C2×C4×C137—22no—
406C2×C4×C137—22no—
407C2×C4×C137—22no—
408C2×C4×C137—22no—
409C2×C4×C137—22no—
410C2×C4×C137—22no—
411C2×C4×C137—22no—
412C2×C4×C137—22no—
413C2×C4×C137—22no—
414C2×C4×C137—22no—
415C2×C4×C137—22no—
416C2×C4×C137—22no—
417C2×C4×C137—22no—
418C2×C4×C137—22no—
419C2×C4×C137—22no—
420C2×C4×C137—22no—
421C2×C4×C137—22no—
422C2×C4×C137—22no—
423C2×C4×C137—22no—
424C2×C4×C137—22no—
425C2×C4×C137—22no—
426C2×C4×C137—22no—
427C2×C4×C137—22no—
428C2×C4×C137—22no—
429C2×C4×C137—22no—
430C2×C4×C137—22no—
431C2×C4×C137—22no—
432C2×C4×C137—22no—
433C2×C4×C137—22no—
434C2×C4×C137—22no—
435C2×C4×C137—22no—
436C2×C4×C137—22no—
437C2×C4×C137—22no—
438C2×C4×C137—22no—
439C2×C4×C137—22no—
440C2×C4×C137—416no—
441C2×C4×C137—41no—
442C2×C4×C137—41no—
443C2×C4×C137—41no—
444C2×C4×C137—41no—
445C2×C4×C137—41no—
446C2×C4×C137—41no—
447C2×C4×C137—41no—
448C2×C4×C137—41no—
449C2×C4×C137—41no—
450C2×C4×C137—41no—
451C2×C4×C137—41no—
452C2×C4×C137—41no—
453C2×C4×C137—41no—
454C2×C4×C137—41no—
455C2×C4×C137—41no—
456C2×C4×C137—41no—
457C2×C4×C137—41no—
458C2×C4×C137—41no—
459C2×C4×C137—41no—
460C2×C4×C137—41no—
461C2×C4×C137—41no—
462C2×C4×C137—41no—
463C2×C4×C137—41no—
464C2×C4×C137—41no—
465C2×C4×C137—41no—
466C2×C4×C137—41no—
467C2×C4×C137—41no—
468C2×C4×C137—41no—
469C2×C4×C137—41no—
470C2×C4×C137—41no—
471C2×C4×C137—41no—
472C2×C4×C137—41no—
473C2×C4×C137—41no—
474C2×C4×C137—41no—
475C2×C4×C137—41no—
476C2×C4×C137—41no—
477C2×C4×C137—41no—
478C2×C4×C137—41no—
479C2×C4×C137—41no—
480C2×C4×C137—41no—
481C2×C4×C137—41no—
482C2×C4×C137—41no—
483C2×C4×C137—41no—
484C2×C4×C137—41no—
485C2×C4×C137—41no—
486C2×C4×C137—41no—
487C2×C4×C137—41no—
488C2×C4×C137—41no—
489C2×C4×C137—41no—
490C2×C4×C137—41no—
491C2×C4×C137#12014yes—
492C2×C4×C137#12314yescomplemented
493C22×C137—24no—
494C22×C137—24no—
495C22×C137—24no—
496C22×C137—42no—
497C22×C137—42no—
498C22×C137—42no—
499C22×C137—42no—
500C22×C137—42no—
501C22×C137—42no—
502C22×C137—42no—
503C22×C137—42no—
504C22×C137—42no—
505C22×C137—42no—
506C22×C137—42no—
507C22×C137—42no—
508C22×C137—42no—
509C22×C137—42no—
510C22×C137—42no—
511C22×C137—42no—
512C22×C137—42no—
513C22×C137—42no—
514C22×C137—42no—
515C22×C137—81no—
516C22×C137—81no—
517C22×C137—81no—
518C22×C137—81no—
519C22×C137—81no—
520C22×C137—81no—
521C22×C137—81no—
522C22×C137—81no—
523C22×C137C2×#12011yescharacteristic
524C22×C137C2×#12111yescharacteristic
525C22×C137C2×#12311yescharacteristic
526C22×C137#52511yescharacteristic
527C22×C137#52511yescharacteristic
528C22×C137#52511yescharacteristic
529C22×C137#52511yescharacteristic
530C22×C137#52911yescharacteristic
531C22×C137#52911yescharacteristic
532C22×C137#53211yescharacteristic
533C22×C137#53211yescharacteristic
534C22×C137#53211yescharacteristic
535C22×C137#53211yescharacteristic
536C22×C137#53411yescharacteristic
537C22×C137#53611yescharacteristic
538C22×C137#53911yescharacteristic
539C22×C137#53911yescharacteristic
540C22×C137#54211yescharacteristic
541C22×C137#54211yescharacteristic
542C22×C137D4211yescharacteristic
543C22×C137D4211yescharacteristic
544C22×C137#54611yescharacteristic
545C22×C137#54611yescharacteristic
546C22×C137#54711yescharacteristic
547C22×C137#54711yescharacteristic
548C22×C137#54711yescharacteristic
549C22×C137#54711yescharacteristic
550C22×C137#54811yescharacteristic
551C22×C137#54811yescharacteristic
552C22×C137#55111yescharacteristic
553C22×C137#55211yescharacteristic
554C22×C137#55211yescharacteristic
555C22×C137#55311yescharacteristic
556C22×C137#55311yescharacteristic
557C22×C137#55911yescharacteristic
558C4×C137—24no—
559C4×C137—24no—
560C4×C137—42no—
561C4×C137—42no—
562C4×C137—42no—
563C4×C137—42no—
564C4×C137—42no—
565C4×C137—42no—
566C4×C137—42no—
567C4×C137—42no—
568C4×C137—42no—
569C4×C137—81no—
570C4×C137—81no—
571C2×C137—44no—
572C2×C137—82no—
573C2×C137#238811yescharacteristic
574C2×C137#241011yescharacteristic
575C2×C137#241311yescharacteristic
576C2×C137#242211yescharacteristic
577C2×C137#243211yescharacteristic
578C2×C137#244311yescharacteristic
579C2×C137#245511yescharacteristic
580C2×C137#245811yescharacteristic
581C2×C137#246111yescharacteristic
582C2×C137#247011yescharacteristic
583C2×C137#255311yescharacteristic
584C2×C137#255811yescharacteristic
585C2×C137#260211yescharacteristic
586C2×C137#266311yescharacteristic
587C2×C137#285411yescharacteristic
588#14761C13711yesmaximal, characteristic, direct product factor, Sylow
589C137#1476111yescharacteristic, direct product factor, Sylow
590C22×#123C2×C13711yescharacteristic
591C2×#394C2×C13711yescharacteristic
592C2×#389C2×C13711yescharacteristic, complemented
593C2×#388C2×C13711yescharacteristic, complemented
594C2×#385C2×C13711yescharacteristic, complemented
595C2×C4×C22⋊C4C2×C13711yescharacteristic, complemented
596#1444C2×C13711yescharacteristic, complemented
597#1442C2×C13711yescharacteristic, complemented
598#1440C2×C13711yescharacteristic, complemented
599#1439C2×C13711yescharacteristic, complemented
600#1439C2×C13711yescharacteristic, complemented
601#1439C2×C13711yescharacteristic, complemented
602#1438C2×C13711yescharacteristic
603#1437C2×C13711yescharacteristic, complemented
604#1436C2×C13711yescharacteristic, complemented
605C23×D4C22×C13711yescharacteristic
606C24×C4C22×C13711yescharacteristic
607C2×#123—24no—
608C2×#123—24no—
609C2×#123—24no—
610C22×C4⋊C4C22×C13711yescharacteristic
611C22×C4⋊C4C22×C13711yescharacteristic
612C22×C4⋊C4C22×C13711yescharacteristic
613C22×C4⋊C4C22×C13711yescharacteristic
614C22×C4⋊C4C22×C13711yescharacteristic
615C22×C4⋊C4C22×C13711yescharacteristic
616C22×C22⋊C4C22×C13711yescharacteristic
617C22×C22⋊C4C22×C13711yescharacteristic
618C22×C22⋊C4C22×C13711yescharacteristic
619C22×C22⋊C4C22×C13711yescharacteristic
620C22×C22⋊C4C22×C13711yescharacteristic
621C22×C22⋊C4C22×C13711yescharacteristic
622C22×C22⋊C4C22×C13711yescharacteristic
623C22×C22⋊C4C22×C13711yescharacteristic
624C22×C22⋊C4C22×C13711yescharacteristic
625C22×C22⋊C4C22×C13711yescharacteristic
626C22×C22⋊C4C22×C13711yescharacteristic
627C22×C42C22×C13711yescharacteristic
628C22×C42C22×C13711yescharacteristic
629#394—24no—
630#389—24no—
631#388—24no—
632#385—24no—
633C4×C22⋊C4—24no—
634C2×#95C22×C13711yescharacteristic
635C2×#95C22×C13711yescharacteristic
636C2×#95C22×C13711yescharacteristic
637C2×#95C22×C13711yescharacteristic
638C2×#95C22×C13711yescharacteristic
639C2×#95C22×C13711yescharacteristic
640C2×#95C22×C13711yescharacteristic
641C2×#95C22×C13711yescharacteristic
642C2×#95C22×C13711yescharacteristic
643C2×#95C22×C13711yescharacteristic
644C2×#95C22×C13711yescharacteristic
645C2×#95C22×C13711yescharacteristic
646C2×#95C22×C13711yescharacteristic
647C2×#95C22×C13711yescharacteristic
648C25C23×C13711yescharacteristic
649C25C23×C13711yescharacteristic
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—22no—
655C22×D4—41no—
656C22×D4—41no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—41no—
662C23×C4—41no—
663C23×C4D4×C13714yes—
664C23×C4C23×C13711yescharacteristic
665C23×C4C23×C13711yescharacteristic
666C23×C4C23×C13711yescharacteristic
667C23×C4C23×C13711yescharacteristic
668C23×C4C23×C13711yescharacteristic
669C23×C4C23×C13711yescharacteristic
670C23×C4C23×C13711yescharacteristic
671C23×C4C23×C13711yescharacteristic
672C23×C4C23×C13711yescharacteristic
673C23×C4C23×C13711yescharacteristic
674C23×C4C23×C13711yescharacteristic
675C23×C4C23×C13711yescharacteristic
676C23×C4C23×C13711yescharacteristic
677#123—232no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4D4×C13714yes—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4D4×C13714yes—
728C2×C22⋊C4D4×C13714yes—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732C2×C42—22no—
733C2×C42—41no—
734C2×C42—41no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—22no—
744#95—22no—
745#95—22no—
746#95—22no—
747#95—22no—
748#95—41no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24C2×D4×C13712yes—
776C24C2×D4×C13712yes—
777C24C2×D4×C13712yes—
778C24#41×C13712yes—
779C24C24×C13711yescharacteristic
780C2×D4—28no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—28no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—28no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4C2×D4×C13712yes—
871C22×C4C2×D4×C13712yes—
872C22×C4C2×D4×C13712yes—
873C22×C4C2×D4×C13712yes—
874C22×C4C2×D4×C13712yes—
875C22×C4C2×D4×C13712yes—
876C22×C4C2×D4×C13712yes—
877C22×C4C2×D4×C13712yes—
878C22×C4C2×D4×C13712yes—
879C22×C4#41×C13712yes—
880C22×C4#41×C13712yes—
881C22×C4#41×C13712yes—
882C22×C4#41×C13712yes—
883C22×C4#41×C13712yes—
884C22×C4#41×C13712yes—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—44no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—28no—
894C22⋊C4—28no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—28no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C42—44no—
903C42—44no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23#121×C13714yes—
974C23C22×D4×C13711yescharacteristic
975C23C22×D4×C13711yescharacteristic
976C23C22×D4×C13711yescharacteristic
977C23C22×D4×C13711yescharacteristic
978C23C2×#41×C13711yescharacteristic
979C23C2×#41×C13711yescharacteristic
980C23C2×#41×C13711yescharacteristic
981C23C2×#41×C13711yescharacteristic
982C23C2×#41×C13711yescharacteristic
983C23C2×#41×C13711yescharacteristic
984C23C2×#41×C13711yescharacteristic
985C23H(5,𝔽2)×C13711yescharacteristic
986C23H(5,𝔽2)×C13711yescharacteristic
987C232−1+4×C13711yescharacteristic
988C232−1+4×C13711yescharacteristic
989D4—416no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—416no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4#120×C13714yes—
1081C2×C4#123×C13714yescomplemented
1082C22—24no—
1083C22—24no—
1084C22—24no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22C2×#120×C13711yescharacteristic
1113C22C2×#121×C13711yescharacteristic
1114C22C2×#123×C13711yescharacteristic
1115C22#525×C13711yescharacteristic
1116C22#525×C13711yescharacteristic
1117C22#525×C13711yescharacteristic
1118C22#525×C13711yescharacteristic
1119C22#529×C13711yescharacteristic
1120C22#529×C13711yescharacteristic
1121C22#532×C13711yescharacteristic
1122C22#532×C13711yescharacteristic
1123C22#532×C13711yescharacteristic
1124C22#532×C13711yescharacteristic
1125C22#534×C13711yescharacteristic
1126C22#536×C13711yescharacteristic
1127C22#539×C13711yescharacteristic
1128C22#539×C13711yescharacteristic
1129C22#542×C13711yescharacteristic
1130C22#542×C13711yescharacteristic
1131C22D42×C13711yescharacteristic
1132C22D42×C13711yescharacteristic
1133C22#546×C13711yescharacteristic
1134C22#546×C13711yescharacteristic
1135C22#547×C13711yescharacteristic
1136C22#547×C13711yescharacteristic
1137C22#547×C13711yescharacteristic
1138C22#547×C13711yescharacteristic
1139C22#548×C13711yescharacteristic
1140C22#548×C13711yescharacteristic
1141C22#551×C13711yescharacteristic
1142C22#552×C13711yescharacteristic
1143C22#552×C13711yescharacteristic
1144C22#553×C13711yescharacteristic
1145C22#553×C13711yescharacteristic
1146C22#559×C13711yescharacteristic
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—81no—
1159C4—81no—
1160C2—44no—
1161C2—82no—
1162C2#2388×C13711yescharacteristic
1163C2#2410×C13711yescharacteristic
1164C2#2413×C13711yescharacteristic
1165C2#2422×C13711yescharacteristic
1166C2#2432×C13711yescharacteristic
1167C2#2443×C13711yescharacteristic
1168C2#2455×C13711yescharacteristic
1169C2#2458×C13711yescharacteristic
1170C2#2461×C13711yescharacteristic
1171C2#2470×C13711yescharacteristic
1172C2#2553×C13711yescharacteristic
1173C2#2558×C13711yescharacteristic
1174C2#2602×C13711yescharacteristic
1175C2#2663×C13711yescharacteristic
1176C2#2854×C13711yescharacteristic
subgroupG/H
center, socleC24×C137C24
commutator, Frattini, cosocleC24C24×C137
prime radicalC23×D4×C137C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#389×C137C2semidirect
4. C2×#388×C137C2semidirect
5. C2×#385×C137C2semidirect
6. C2×C4×C22⋊C4×C137C2semidirect
7. #1444×C137C2semidirect
8. #1442×C137C2semidirect
9. #1440×C137C2semidirect
10. #1439×C137C2semidirect
11. #1439×C137C2semidirect
12. #1439×C137C2semidirect
14. #1437×C137C2semidirect
15. #1436×C137C2semidirect
492. C2×C4×C137#123semidirect
588. #14761C137direct (N × H)
589. C137#14761direct (N × H)
592. C2×#389C2×C137semidirect
593. C2×#388C2×C137semidirect
594. C2×#385C2×C137semidirect
595. C2×C4×C22⋊C4C2×C137semidirect
596. #1444C2×C137semidirect
597. #1442C2×C137semidirect
598. #1440C2×C137semidirect
599. #1439C2×C137semidirect
600. #1439C2×C137semidirect
601. #1439C2×C137semidirect
603. #1437C2×C137semidirect
604. #1436C2×C137semidirect
1081. C2×C4#123×C137semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1372
C2×#394×C1372
C2×#389×C1372
C2×#388×C1372
C2×#385×C1372
C2×C4×C22⋊C4×C1372
#1444×C1372
#1442×C1372
#1440×C1372
#1439×C1372
#1438×C1372
#1437×C1372
#1436×C1372
#14761137