Finite Group Databasebeta

← C137×#16270 #46865656

Subgroups — C137×#16270 #46865656

Order 35072.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C137C211yesmaximal, characteristic, complemented
2C2×#392×C137C211yesmaximal, characteristic
3C2×#386×C137C211yesmaximal, characteristic, complemented
4C2×#386×C137C211yesmaximal, characteristic, complemented
5#1443×C137C211yesmaximal, characteristic, complemented
6#1443×C137C211yesmaximal, characteristic, complemented
7#1440×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#1438×C137C211yesmaximal, characteristic, complemented
14#1438×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×C22⋊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
35#397×C137—24no—
36#392×C137—24no—
37#386×C137—24no—
38#386×C137—24no—
39C2×#95×C137C2211yescharacteristic
40C2×#95×C137C2211yescharacteristic
41C2×#95×C137C2211yescharacteristic
42C2×#95×C137C2211yescharacteristic
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
55C25×C137C2311yescharacteristic
56C25×C137C2311yescharacteristic
57C25×C137C2311yescharacteristic
58C22×D4×C137—22no—
59C22×D4×C137—22no—
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—41no—
69C22×D4×C137—41no—
70C22×D4×C137—41no—
71C22×D4×C137—41no—
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×C137D414yes—
79C23×C4×C137—22no—
80C23×C4×C137—22no—
81C23×C4×C137—22no—
82C23×C4×C137—41no—
83C23×C4×C137—41no—
84C23×C4×C137—41no—
85C23×C4×C137—41no—
86C23×C4×C137C2311yescharacteristic
87C23×C4×C137C2311yescharacteristic
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
98C2×C4⋊C4×C137—22no—
99C2×C4⋊C4×C137—41no—
100C2×C4⋊C4×C137—41no—
101C2×C22⋊C4×C137—22no—
102C2×C22⋊C4×C137—22no—
103C2×C22⋊C4×C137—22no—
104C2×C22⋊C4×C137—22no—
105C2×C22⋊C4×C137—22no—
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—41no—
120C2×C22⋊C4×C137—41no—
121C2×C22⋊C4×C137—41no—
122C2×C22⋊C4×C137—41no—
123C2×C22⋊C4×C137—41no—
124C2×C22⋊C4×C137—41no—
125C2×C22⋊C4×C137—41no—
126C2×C22⋊C4×C137—41no—
127C2×C22⋊C4×C137—41no—
128C2×C22⋊C4×C137—41no—
129C2×C22⋊C4×C137—41no—
130C2×C22⋊C4×C137—41no—
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—
143#95×C137—22no—
144#95×C137—22no—
145#95×C137—22no—
146#95×C137—22no—
147#95×C137—22no—
148#95×C137—22no—
149#95×C137—22no—
150#95×C137—41no—
151#95×C137—41no—
152#95×C137—41no—
153#95×C137—41no—
154#95×C137—41no—
155#95×C137—41no—
156#95×C137—41no—
157#95×C137—41no—
158#95×C137D414yescomplemented
159C24×C137—21no—
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×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×C137C2×D412yes—
200C24×C137C2×D412yes—
201C24×C137#4112yes—
202C24×C137#4112yes—
203C24×C137#4112yes—
204C24×C137C2411yescharacteristic
205C2×D4×C137—28no—
206C2×D4×C137—28no—
207C2×D4×C137—44no—
208C2×D4×C137—44no—
209C2×D4×C137—44no—
210C2×D4×C137—44no—
211C2×D4×C137—44no—
212C2×D4×C137—44no—
213C2×D4×C137—44no—
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—
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—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—44no—
305C22×C4×C137—44no—
306C22×C4×C137—44no—
307C22×C4×C137—44no—
308C22×C4×C137—44no—
309C22×C4×C137—44no—
310C22×C4×C137—44no—
311C22×C4×C137C2×D412yes—
312C22×C4×C137C2×D412yes—
313C22×C4×C137C2×D412yes—
314C22×C4×C137C2×D412yes—
315C22×C4×C137#4112yes—
316C22×C4×C137#4112yes—
317C4⋊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×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—
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—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—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—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#12314yes—
437C23×C137C22×D411yescharacteristic
438C23×C137C22×D411yescharacteristic
439C23×C137C2×#4111yescharacteristic
440C23×C137C2×#4111yescharacteristic
441C23×C137C2×#4111yescharacteristic
442C23×C137C2×#4111yescharacteristic
443C23×C137C2×#4111yescharacteristic
444C23×C137H(5,𝔽2)11yescharacteristic
445C23×C137H(5,𝔽2)11yescharacteristic
446C23×C137H(5,𝔽2)11yescharacteristic
447C23×C137H(5,𝔽2)11yescharacteristic
448C23×C137H(5,𝔽2)11yescharacteristic
449C23×C137H(5,𝔽2)11yescharacteristic
450C23×C137H(5,𝔽2)11yescharacteristic
451C23×C137H(5,𝔽2)11yescharacteristic
452D4×C137—416no—
453D4×C137—416no—
454D4×C137—416no—
455C2×C4×C137—22no—
456C2×C4×C137—22no—
457C2×C4×C137—22no—
458C2×C4×C137—22no—
459C2×C4×C137—22no—
460C2×C4×C137—22no—
461C2×C4×C137—22no—
462C2×C4×C137—22no—
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—416no—
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—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—
540C22×C137—24no—
541C22×C137—24no—
542C22×C137—24no—
543C22×C137—42no—
544C22×C137—42no—
545C22×C137—42no—
546C22×C137—42no—
547C22×C137—42no—
548C22×C137—42no—
549C22×C137—42no—
550C22×C137—42no—
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—81no—
570C22×C137—81no—
571C22×C137—81no—
572C22×C137—81no—
573C22×C137—81no—
574C22×C137—81no—
575C22×C137—81no—
576C22×C137—81no—
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×C137C2×#12311yescharacteristic
586C22×C137#52511yescharacteristic
587C22×C137#52911yescharacteristic
588C22×C137#53411yescharacteristic
589C22×C137#53411yescharacteristic
590C22×C137#53511yescharacteristic
591C22×C137#53511yescharacteristic
592C22×C137#53811yescharacteristic
593C22×C137#53811yescharacteristic
594C22×C137#53811yescharacteristic
595C22×C137#53811yescharacteristic
596C22×C137#53811yescharacteristic
597C22×C137#53811yescharacteristic
598C22×C137#53811yescharacteristic
599C22×C137#53811yescharacteristic
600C22×C137#53811yescharacteristic
601C22×C137#53811yescharacteristic
602C22×C137#54011yescharacteristic
603C22×C137#54011yescharacteristic
604C22×C137D4211yescharacteristic
605C22×C137#54611yescharacteristic
606C22×C137#54611yescharacteristic
607C22×C137#54611yescharacteristic
608C22×C137#54611yescharacteristic
609C22×C137#54611yescharacteristic
610C22×C137#55011yescharacteristic
611C22×C137#55111yescharacteristic
612C22×C137#55111yescharacteristic
613C22×C137#55311yescharacteristic
614C22×C137#55311yescharacteristic
615C22×C137#55311yescharacteristic
616C22×C137#56011yescharacteristic
617C22×C137#56011yescharacteristic
618C22×C137#56011yescharacteristic
619C22×C137#56011yescharacteristic
620C4×C137—42no—
621C4×C137—42no—
622C4×C137—42no—
623C4×C137—42no—
624C4×C137—42no—
625C4×C137—42no—
626C4×C137—81no—
627C4×C137—81no—
628C4×C137—81no—
629C4×C137—81no—
630C4×C137—81no—
631C4×C137—81no—
632C2×C137—44no—
633C2×C137—82no—
634C2×C137—82no—
635C2×C137#241811yescharacteristic
636C2×C137#244411yescharacteristic
637C2×C137#246711yescharacteristic
638C2×C137#262211yescharacteristic
639C2×C137#263111yescharacteristic
640C2×C137#264811yescharacteristic
641C2×C137#267311yescharacteristic
642C2×C137#267811yescharacteristic
643C2×C137#268811yescharacteristic
644C2×C137#269711yescharacteristic
645C2×C137#270311yescharacteristic
646C2×C137#271411yescharacteristic
647C2×C137#274911yescharacteristic
648C2×C137#277811yescharacteristic
649C2×C137#282511yescharacteristic
650#16270C13711yesmaximal, characteristic, direct product factor, Sylow
651C137#1627011yescharacteristic, direct product factor, Sylow
652C2×#397C2×C13711yescharacteristic, complemented
653C2×#392C2×C13711yescharacteristic
654C2×#386C2×C13711yescharacteristic, complemented
655C2×#386C2×C13711yescharacteristic, complemented
656#1443C2×C13711yescharacteristic, complemented
657#1443C2×C13711yescharacteristic, complemented
658#1440C2×C13711yescharacteristic, complemented
659#1440C2×C13711yescharacteristic, complemented
660#1439C2×C13711yescharacteristic, complemented
661#1439C2×C13711yescharacteristic, complemented
662#1438C2×C13711yescharacteristic, complemented
663#1438C2×C13711yescharacteristic, complemented
664#1438C2×C13711yescharacteristic, complemented
665#1438C2×C13711yescharacteristic, complemented
666C22⋊#95C2×C13711yescharacteristic, complemented
667C23×D4C22×C13711yescharacteristic
668C23×D4C22×C13711yescharacteristic
669C23×D4C22×C13711yescharacteristic
670C24×C4C22×C13711yescharacteristic
671C22×C4⋊C4C22×C13711yescharacteristic
672C22×C22⋊C4C22×C13711yescharacteristic
673C22×C22⋊C4C22×C13711yescharacteristic
674C22×C22⋊C4C22×C13711yescharacteristic
675C22×C22⋊C4C22×C13711yescharacteristic
676C22×C22⋊C4C22×C13711yescharacteristic
677C22×C22⋊C4C22×C13711yescharacteristic
678C22×C22⋊C4C22×C13711yescharacteristic
679C22×C22⋊C4C22×C13711yescharacteristic
680C22×C22⋊C4C22×C13711yescharacteristic
681C22×C22⋊C4C22×C13711yescharacteristic
682C22×C22⋊C4C22×C13711yescharacteristic
683C22×C22⋊C4C22×C13711yescharacteristic
684C22×C22⋊C4C22×C13711yescharacteristic
685C22×C22⋊C4C22×C13711yescharacteristic
686#397—24no—
687#392—24no—
688#386—24no—
689#386—24no—
690C2×#95C22×C13711yescharacteristic
691C2×#95C22×C13711yescharacteristic
692C2×#95C22×C13711yescharacteristic
693C2×#95C22×C13711yescharacteristic
694C2×#95C22×C13711yescharacteristic
695C2×#95C22×C13711yescharacteristic
696C2×#95C22×C13711yescharacteristic
697C2×#95C22×C13711yescharacteristic
698C2×#95C22×C13711yescharacteristic
699C2×#95C22×C13711yescharacteristic
700C2×#95C22×C13711yescharacteristic
701C2×#95C22×C13711yescharacteristic
702C2×#95C22×C13711yescharacteristic
703C2×#95C22×C13711yescharacteristic
704C2×#95C22×C13711yescharacteristic
705C2×#95C22×C13711yescharacteristic
706C25C23×C13711yescharacteristic
707C25C23×C13711yescharacteristic
708C25C23×C13711yescharacteristic
709C22×D4—22no—
710C22×D4—22no—
711C22×D4—22no—
712C22×D4—22no—
713C22×D4—22no—
714C22×D4—22no—
715C22×D4—22no—
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—41no—
724C22×D4—41no—
725C22×D4—41no—
726C22×D4—41no—
727C22×D4—41no—
728C22×D4—41no—
729C22×D4D4×C13714yes—
730C23×C4—22no—
731C23×C4—22no—
732C23×C4—22no—
733C23×C4—41no—
734C23×C4—41no—
735C23×C4—41no—
736C23×C4—41no—
737C23×C4C23×C13711yescharacteristic
738C23×C4C23×C13711yescharacteristic
739C23×C4C23×C13711yescharacteristic
740C23×C4C23×C13711yescharacteristic
741C23×C4C23×C13711yescharacteristic
742C23×C4C23×C13711yescharacteristic
743C23×C4C23×C13711yescharacteristic
744C23×C4C23×C13711yescharacteristic
745C23×C4C23×C13711yescharacteristic
746C23×C4C23×C13711yescharacteristic
747C23×C4C23×C13711yescharacteristic
748C23×C4C23×C13711yescharacteristic
749C2×C4⋊C4—22no—
750C2×C4⋊C4—41no—
751C2×C4⋊C4—41no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—41no—
771C2×C22⋊C4—41no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—41no—
777C2×C22⋊C4—41no—
778C2×C22⋊C4—41no—
779C2×C22⋊C4—41no—
780C2×C22⋊C4—41no—
781C2×C22⋊C4—41no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—41no—
787C2×C22⋊C4—41no—
788C2×C22⋊C4—41no—
789C2×C22⋊C4—41no—
790C2×C22⋊C4—41no—
791C2×C22⋊C4—41no—
792C2×C22⋊C4—41no—
793C2×C22⋊C4—41no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95—22no—
798#95—22no—
799#95—22no—
800#95—22no—
801#95—41no—
802#95—41no—
803#95—41no—
804#95—41no—
805#95—41no—
806#95—41no—
807#95—41no—
808#95—41no—
809#95D4×C13714yescomplemented
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—21no—
823C24—21no—
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—
850C24C2×D4×C13712yes—
851C24C2×D4×C13712yes—
852C24#41×C13712yes—
853C24#41×C13712yes—
854C24#41×C13712yes—
855C24C24×C13711yescharacteristic
856C2×D4—28no—
857C2×D4—28no—
858C2×D4—44no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—44no—
864C2×D4—44no—
865C2×D4—44no—
866C2×D4—44no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—44no—
876C2×D4—44no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
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—44no—
956C22×C4—44no—
957C22×C4—44no—
958C22×C4—44no—
959C22×C4—44no—
960C22×C4—44no—
961C22×C4—44no—
962C22×C4C2×D4×C13712yes—
963C22×C4C2×D4×C13712yes—
964C22×C4C2×D4×C13712yes—
965C22×C4C2×D4×C13712yes—
966C22×C4#41×C13712yes—
967C22×C4#41×C13712yes—
968C4⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—44no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—44no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
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—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
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#123×C13714yes—
1088C23C22×D4×C13711yescharacteristic
1089C23C22×D4×C13711yescharacteristic
1090C23C2×#41×C13711yescharacteristic
1091C23C2×#41×C13711yescharacteristic
1092C23C2×#41×C13711yescharacteristic
1093C23C2×#41×C13711yescharacteristic
1094C23C2×#41×C13711yescharacteristic
1095C23H(5,𝔽2)×C13711yescharacteristic
1096C23H(5,𝔽2)×C13711yescharacteristic
1097C23H(5,𝔽2)×C13711yescharacteristic
1098C23H(5,𝔽2)×C13711yescharacteristic
1099C23H(5,𝔽2)×C13711yescharacteristic
1100C23H(5,𝔽2)×C13711yescharacteristic
1101C23H(5,𝔽2)×C13711yescharacteristic
1102C23H(5,𝔽2)×C13711yescharacteristic
1103D4—416no—
1104D4—416no—
1105D4—416no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—416no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
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—
1191C22—24no—
1192C22—24no—
1193C22—24no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—42no—
1202C22—42no—
1203C22—42no—
1204C22—42no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22C2×#123×C13711yescharacteristic
1237C22#525×C13711yescharacteristic
1238C22#529×C13711yescharacteristic
1239C22#534×C13711yescharacteristic
1240C22#534×C13711yescharacteristic
1241C22#535×C13711yescharacteristic
1242C22#535×C13711yescharacteristic
1243C22#538×C13711yescharacteristic
1244C22#538×C13711yescharacteristic
1245C22#538×C13711yescharacteristic
1246C22#538×C13711yescharacteristic
1247C22#538×C13711yescharacteristic
1248C22#538×C13711yescharacteristic
1249C22#538×C13711yescharacteristic
1250C22#538×C13711yescharacteristic
1251C22#538×C13711yescharacteristic
1252C22#538×C13711yescharacteristic
1253C22#540×C13711yescharacteristic
1254C22#540×C13711yescharacteristic
1255C22D42×C13711yescharacteristic
1256C22#546×C13711yescharacteristic
1257C22#546×C13711yescharacteristic
1258C22#546×C13711yescharacteristic
1259C22#546×C13711yescharacteristic
1260C22#546×C13711yescharacteristic
1261C22#550×C13711yescharacteristic
1262C22#551×C13711yescharacteristic
1263C22#551×C13711yescharacteristic
1264C22#553×C13711yescharacteristic
1265C22#553×C13711yescharacteristic
1266C22#553×C13711yescharacteristic
1267C22#560×C13711yescharacteristic
1268C22#560×C13711yescharacteristic
1269C22#560×C13711yescharacteristic
1270C22#560×C13711yescharacteristic
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—42no—
1276C4—42no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C2—44no—
1284C2—82no—
1285C2—82no—
1286C2#2418×C13711yescharacteristic
1287C2#2444×C13711yescharacteristic
1288C2#2467×C13711yescharacteristic
1289C2#2622×C13711yescharacteristic
1290C2#2631×C13711yescharacteristic
1291C2#2648×C13711yescharacteristic
1292C2#2673×C13711yescharacteristic
1293C2#2678×C13711yescharacteristic
1294C2#2688×C13711yescharacteristic
1295C2#2697×C13711yescharacteristic
1296C2#2703×C13711yescharacteristic
1297C2#2714×C13711yescharacteristic
1298C2#2749×C13711yescharacteristic
1299C2#2778×C13711yescharacteristic
1300C2#2825×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
3. C2×#386×C137C2semidirect
4. C2×#386×C137C2semidirect
5. #1443×C137C2semidirect
6. #1443×C137C2semidirect
7. #1440×C137C2semidirect
8. #1440×C137C2semidirect
9. #1439×C137C2semidirect
10. #1439×C137C2semidirect
11. #1438×C137C2semidirect
12. #1438×C137C2semidirect
13. #1438×C137C2semidirect
14. #1438×C137C2semidirect
15. C22⋊#95×C137C2semidirect
158. #95×C137D4semidirect
650. #16270C137direct (N × H)
651. C137#16270direct (N × H)
652. C2×#397C2×C137semidirect
654. C2×#386C2×C137semidirect
655. C2×#386C2×C137semidirect
656. #1443C2×C137semidirect
657. #1443C2×C137semidirect
658. #1440C2×C137semidirect
659. #1440C2×C137semidirect
660. #1439C2×C137semidirect
661. #1439C2×C137semidirect
662. #1438C2×C137semidirect
663. #1438C2×C137semidirect
664. #1438C2×C137semidirect
665. #1438C2×C137semidirect
666. C22⋊#95C2×C137semidirect
809. #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×#392×C1372
C2×#386×C1372
#1443×C1372
#1440×C1372
#1439×C1372
#1438×C1372
C22⋊#95×C1372
#16270137