Finite Group Databasebeta

← C137×#24448 #46873834

Subgroups — C137×#24448 #46873834

Order 35072.

1888 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C137C211yesmaximal, characteristic
2C2×#468×C137C211yesmaximal, characteristic, complemented
3C2×#450×C137C211yesmaximal, characteristic, complemented
4C2×#450×C137C211yesmaximal, characteristic, complemented
5C2×#418×C137C211yesmaximal, characteristic, complemented
6#2415×C137C211yesmaximal, characteristic, complemented
7#2041×C137C211yesmaximal, characteristic, complemented
8#2033×C137C211yesmaximal, characteristic, complemented
9#2014×C137C211yesmaximal, characteristic, complemented
10#2000×C137C211yesmaximal, characteristic, complemented
11#1877×C137C211yesmaximal, characteristic, complemented
12#1875×C137C211yesmaximal, characteristic, complemented
13#1870×C137C211yesmaximal, characteristic, complemented
14#1862×C137C211yesmaximal, characteristic, complemented
15#1786×C137C211yesmaximal, characteristic, complemented
16C23×D4×C137—21no—
17C23×D4×C137C2211yescharacteristic
18C23×D4×C137C2211yescharacteristic
19C22×SD16×C137C2211yescharacteristic
20C22×SD16×C137C2211yescharacteristic, complemented
21C22×SD16×C137C2211yescharacteristic, complemented
22C22×M16×C137C2211yescharacteristic, complemented
23D42×C137—24no—
24D42×C137—24no—
25C2×#127×C137C2211yescharacteristic
26C2×C22⋊Q8×C137C2211yescharacteristic, complemented
27C2×C22⋊Q8×C137C2211yescharacteristic, complemented
28C2×#121×C137—21no—
29C2×#121×C137C2211yescharacteristic
30C2×#121×C137C2211yescharacteristic
31C2×#120×C137—21no—
32C2×#120×C137—21no—
33C2×C4×D4×C137C2211yescharacteristic
34C2×C4×D4×C137C2211yescharacteristic
35C2×#117×C137C2211yescharacteristic, complemented
36#468×C137—24no—
37#450×C137—24no—
38#450×C137—24no—
39C2×#107×C137C2211yescharacteristic, complemented
40#418×C137—24no—
41C2×#103×C137C2211yescharacteristic, complemented
42C2×#102×C137C2211yescharacteristic
43C2×#102×C137C2211yescharacteristic
44C2×#102×C137C2211yescharacteristic
45C2×#102×C137C2211yescharacteristic, complemented
46C2×#102×C137C2211yescharacteristic, complemented
47C2×#102×C137C2211yescharacteristic, complemented
48C2×#102×C137C2211yescharacteristic, complemented
49C2×#102×C137C2211yescharacteristic, complemented
50C2×#102×C137C2211yescharacteristic, complemented
51C2×C22⋊C8×C137C2211yescharacteristic, complemented
52C2×C22⋊C8×C137C2211yescharacteristic, complemented
53C2×C22⋊C8×C137C2211yescharacteristic, complemented
54#397×C137—21no—
55#394×C137—21no—
56#391×C137C2211yescharacteristic, complemented
57#389×C137—21no—
58#389×C137C2211yescharacteristic, complemented
59#388×C137—21no—
60#380×C137C2211yescharacteristic, complemented
61#340×C137C2211yescharacteristic, complemented
62#340×C137C2211yescharacteristic, complemented
63#336×C137C2211yescharacteristic, complemented
64#336×C137C2211yescharacteristic, complemented
65C25×C137—21no—
66C25×C137—21no—
67C22×Q8×C137C2311yescharacteristic
68C22×D4×C137—22no—
69C22×D4×C137—22no—
70C22×D4×C137—28no—
71C22×D4×C137—21no—
72C22×D4×C137—21no—
73C22×D4×C137—22no—
74C22×D4×C137—22no—
75C22×D4×C137—22no—
76C22×D4×C137—22no—
77C22×D4×C137—21no—
78C22×D4×C137—21no—
79C22×D4×C137—21no—
80C22×D4×C137—22no—
81C22×D4×C137—21no—
82C22×D4×C137—41no—
83C22×D4×C137—41no—
84C22×D4×C137—41no—
85C22×D4×C137—41no—
86C22×D4×C137—44no—
87C22×D4×C137—44no—
88C22×D4×C137D411yescharacteristic
89C22×D4×C137D414yes—
90C22×D4×C137C2311yescharacteristic
91C22×D4×C137C2311yescharacteristic
92C22×D4×C137C2311yescharacteristic
93C23×C4×C137—21no—
94C23×C4×C137C2311yescharacteristic
95C23×C4×C137C2311yescharacteristic
96C2×SD16×C137—22no—
97C2×SD16×C137—22no—
98C2×SD16×C137—22no—
99C2×SD16×C137—22no—
100C2×SD16×C137—22no—
101C2×SD16×C137—22no—
102C2×SD16×C137—41no—
103C2×SD16×C137—41no—
104C2×SD16×C137—41no—
105C2×M16×C137—22no—
106C2×M16×C137—22no—
107C2×M16×C137—41no—
108C22×C8×C137C2311yescharacteristic
109C22×C8×C137C2311yescharacteristic
110C22×C8×C137C2311yescharacteristic
111C22×C8×C137C2311yescharacteristic
112#127×C137—22no—
113#127×C137—22no—
114C22⋊Q8×C137—22no—
115C22⋊Q8×C137—22no—
116C22⋊Q8×C137—22no—
117C22⋊Q8×C137—41no—
118#121×C137—28no—
119#121×C137—22no—
120#121×C137—22no—
121#121×C137—22no—
122#121×C137D414yes—
123#120×C137—28no—
124#120×C137—28no—
125C4×D4×C137—22no—
126C4×D4×C137—22no—
127C4×D4×C137—22no—
128C4×D4×C137—22no—
129#117×C137—22no—
130#117×C137—41no—
131C2×C4⋊C4×C137—21no—
132C2×C4⋊C4×C137—21no—
133C2×C4⋊C4×C137—21no—
134C2×C4⋊C4×C137D411yescharacteristic
135C2×C4⋊C4×C137C2311yescharacteristic
136C2×C4⋊C4×C137C2311yescharacteristic
137C2×C4⋊C4×C137C2311yescharacteristic
138C2×C4⋊C4×C137C2311yescharacteristic
139C2×C22⋊C4×C137—21no—
140C2×C22⋊C4×C137—21no—
141C2×C22⋊C4×C137—21no—
142C2×C22⋊C4×C137—21no—
143C2×C22⋊C4×C137—21no—
144C2×C22⋊C4×C137—21no—
145C2×C22⋊C4×C137—21no—
146C2×C22⋊C4×C137D411yescharacteristic
147C2×C22⋊C4×C137D411yescharacteristic
148C2×C42×C137—21no—
149C2×C42×C137C2311yescharacteristic
150#107×C137—22no—
151#103×C137—22no—
152#102×C137—22no—
153#102×C137—22no—
154#102×C137—22no—
155#102×C137—22no—
156#102×C137—22no—
157#102×C137—22no—
158#102×C137—22no—
159#102×C137—41no—
160#102×C137D414yescomplemented
161C22⋊C8×C137—22no—
162C22⋊C8×C137—22no—
163C22⋊C8×C137—41no—
164#95×C137—21no—
165#95×C137—21no—
166#95×C137—21no—
167#95×C137—21no—
168C24×C137—21no—
169C24×C137—24no—
170C24×C137—21no—
171C24×C137—21no—
172C24×C137—24no—
173C24×C137—42no—
174C24×C137—42no—
175C24×C137—42no—
176C24×C137—42no—
177C24×C137—42no—
178C24×C137—42no—
179C24×C137—42no—
180C24×C137—42no—
181C24×C137—81no—
182C24×C137—81no—
183C24×C137—81no—
184C24×C137—81no—
185C24×C137C2×D411yescharacteristic
186C24×C137C2×D411yescharacteristic
187C2×Q8×C137—21no—
188C2×Q8×C137—21no—
189C2×Q8×C137—21no—
190C2×Q8×C137—21no—
191C2×Q8×C137—21no—
192C2×Q8×C137—21no—
193C2×D4×C137—22no—
194C2×D4×C137—22no—
195C2×D4×C137—28no—
196C2×D4×C137—24no—
197C2×D4×C137—24no—
198C2×D4×C137—24no—
199C2×D4×C137—24no—
200C2×D4×C137—24no—
201C2×D4×C137—24no—
202C2×D4×C137—22no—
203C2×D4×C137—21no—
204C2×D4×C137—21no—
205C2×D4×C137—21no—
206C2×D4×C137—21no—
207C2×D4×C137—21no—
208C2×D4×C137—21no—
209C2×D4×C137—21no—
210C2×D4×C137—21no—
211C2×D4×C137—21no—
212C2×D4×C137—21no—
213C2×D4×C137—21no—
214C2×D4×C137—21no—
215C2×D4×C137—21no—
216C2×D4×C137—44no—
217C2×D4×C137—44no—
218C2×D4×C137—44no—
219C2×D4×C137—42no—
220C2×D4×C137—42no—
221C2×D4×C137—42no—
222C2×D4×C137—42no—
223C2×D4×C137—42no—
224C2×D4×C137—44no—
225C2×D4×C137—44no—
226C2×D4×C137—432no—
227C2×D4×C137—44no—
228C2×D4×C137—42no—
229C2×D4×C137—42no—
230C2×D4×C137—42no—
231C2×D4×C137—42no—
232C2×D4×C137—44no—
233C2×D4×C137—42no—
234C2×D4×C137—81no—
235C2×D4×C137—81no—
236C2×D4×C137C2×D412yes—
237C2×D4×C137C2×D412yes—
238C2×D4×C137C2×D412yes—
239C2×D4×C137C2×D412yes—
240C2×D4×C137#4112yes—
241C22×C4×C137—21no—
242C22×C4×C137—21no—
243C22×C4×C137—21no—
244C22×C4×C137—21no—
245C22×C4×C137—24no—
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—42no—
258C22×C4×C137—42no—
259C22×C4×C137C2×D411yescharacteristic
260C22×C4×C137C2×D411yescharacteristic
261C22×C4×C137C2×D411yescharacteristic
262C22×C4×C137C2×D412yes—
263C22×C4×C137C2×D412yes—
264C22×C4×C137C2×D411yescharacteristic
265C22×C4×C137C2411yescharacteristic
266SD16×C137—44no—
267SD16×C137—44no—
268SD16×C137—44no—
269M16×C137—44no—
270C2×C8×C137—21no—
271C2×C8×C137—21no—
272C2×C8×C137—21no—
273C2×C8×C137—21no—
274C2×C8×C137—21no—
275C2×C8×C137—21no—
276C2×C8×C137—21no—
277C2×C8×C137—21no—
278C2×C8×C137—21no—
279C2×C8×C137—21no—
280C2×C8×C137—21no—
281C2×C8×C137C2×D412yescomplemented
282C4⋊C4×C137—22no—
283C4⋊C4×C137—21no—
284C4⋊C4×C137—21no—
285C4⋊C4×C137—21no—
286C4⋊C4×C137—21no—
287C4⋊C4×C137—21no—
288C4⋊C4×C137—21no—
289C4⋊C4×C137—42no—
290C4⋊C4×C137—42no—
291C4⋊C4×C137—42no—
292C4⋊C4×C137C2×D412yes—
293C4⋊C4×C137C2×D412yescomplemented
294C22⋊C4×C137—24no—
295C22⋊C4×C137—24no—
296C22⋊C4×C137—22no—
297C22⋊C4×C137—24no—
298C22⋊C4×C137—22no—
299C22⋊C4×C137—42no—
300C22⋊C4×C137—42no—
301C22⋊C4×C137—42no—
302C22⋊C4×C137—42no—
303C42×C137—21no—
304C42×C137—21no—
305C42×C137—42no—
306C23×C137—21no—
307C23×C137—22no—
308C23×C137—21no—
309C23×C137—21no—
310C23×C137—22no—
311C23×C137—21no—
312C23×C137—21no—
313C23×C137—22no—
314C23×C137—21no—
315C23×C137—21no—
316C23×C137—21no—
317C23×C137—21no—
318C23×C137—21no—
319C23×C137—21no—
320C23×C137—21no—
321C23×C137—22no—
322C23×C137—22no—
323C23×C137—48no—
324C23×C137—48no—
325C23×C137—48no—
326C23×C137—48no—
327C23×C137—41no—
328C23×C137—41no—
329C23×C137—41no—
330C23×C137—41no—
331C23×C137—41no—
332C23×C137—41no—
333C23×C137—41no—
334C23×C137—41no—
335C23×C137—41no—
336C23×C137—41no—
337C23×C137—41no—
338C23×C137—41no—
339C23×C137—41no—
340C23×C137—41no—
341C23×C137—41no—
342C23×C137—41no—
343C23×C137—84no—
344C23×C137—84no—
345C23×C137—84no—
346C23×C137—84no—
347C23×C137—84no—
348C23×C137—84no—
349C23×C137—84no—
350C23×C137—84no—
351C23×C137—84no—
352C23×C137—84no—
353C23×C137#12012yes—
354C23×C137AGL(1,ℤ/8)12yes—
355C23×C137C22×D411yescharacteristic
356Q8×C137—41no—
357Q8×C137—41no—
358Q8×C137—41no—
359Q8×C137—41no—
360D4×C137—28no—
361D4×C137—22no—
362D4×C137—22no—
363D4×C137—22no—
364D4×C137—22no—
365D4×C137—22no—
366D4×C137—22no—
367D4×C137—22no—
368D4×C137—48no—
369D4×C137—48no—
370D4×C137—48no—
371D4×C137—48no—
372D4×C137—48no—
373D4×C137—41no—
374D4×C137—41no—
375D4×C137—41no—
376D4×C137—41no—
377D4×C137—84no—
378D4×C137#12114yes—
379C2×C4×C137—21no—
380C2×C4×C137—21no—
381C2×C4×C137—21no—
382C2×C4×C137—21no—
383C2×C4×C137—22no—
384C2×C4×C137—22no—
385C2×C4×C137—22no—
386C2×C4×C137—22no—
387C2×C4×C137—21no—
388C2×C4×C137—21no—
389C2×C4×C137—22no—
390C2×C4×C137—22no—
391C2×C4×C137—21no—
392C2×C4×C137—21no—
393C2×C4×C137—21no—
394C2×C4×C137—21no—
395C2×C4×C137—48no—
396C2×C4×C137—41no—
397C2×C4×C137—41no—
398C2×C4×C137—41no—
399C2×C4×C137—41no—
400C2×C4×C137—41no—
401C2×C4×C137—41no—
402C2×C4×C137—41no—
403C2×C4×C137—41no—
404C2×C4×C137—41no—
405C2×C4×C137—41no—
406C2×C4×C137—41no—
407C2×C4×C137—41no—
408C2×C4×C137—41no—
409C2×C4×C137—41no—
410C2×C4×C137—41no—
411C2×C4×C137—41no—
412C2×C4×C137—41no—
413C2×C4×C137#12012yes—
414C2×C4×C137AGL(1,ℤ/8)12yes—
415C2×C4×C137C22×D411yescharacteristic
416C2×C4×C137C22×D411yescharacteristic
417C2×C4×C137C22×D411yescharacteristic
418C2×C4×C137C2×#4111yescharacteristic
419C2×C4×C137H(5,𝔽2)11yescharacteristic
420C2×C4×C137H(5,𝔽2)11yescharacteristic
421C8×C137—22no—
422C8×C137—41no—
423C8×C137—41no—
424C8×C137—41no—
425C22×C137—22no—
426C22×C137—24no—
427C22×C137—22no—
428C22×C137—22no—
429C22×C137—22no—
430C22×C137—22no—
431C22×C137—22no—
432C22×C137—41no—
433C22×C137—42no—
434C22×C137—41no—
435C22×C137—42no—
436C22×C137—41no—
437C22×C137—42no—
438C22×C137—41no—
439C22×C137—41no—
440C22×C137—42no—
441C22×C137—41no—
442C22×C137—42no—
443C22×C137—41no—
444C22×C137—41no—
445C22×C137—42no—
446C22×C137—42no—
447C22×C137—42no—
448C22×C137—42no—
449C22×C137—42no—
450C22×C137—42no—
451C22×C137—42no—
452C22×C137—816no—
453C22×C137—816no—
454C22×C137—81no—
455C22×C137—81no—
456C22×C137—81no—
457C22×C137—81no—
458C22×C137—81no—
459C22×C137—81no—
460C22×C137—81no—
461C22×C137—81no—
462C22×C137C2×#12011yescharacteristic
463C22×C137D4211yescharacteristic
464C22×C137#54611yescharacteristic
465C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
466C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
467C22×C137#57711yescharacteristic
468C22×C137#57711yescharacteristic
469C4×C137—22no—
470C4×C137—22no—
471C4×C137—41no—
472C4×C137—42no—
473C4×C137—41no—
474C4×C137—42no—
475C4×C137—81no—
476C4×C137—81no—
477C4×C137—81no—
478C4×C137C2×#12111yescharacteristic
479C4×C137#53411yescharacteristic
480C4×C137D4211yescharacteristic
481C4×C137#54611yescharacteristic
482C2×C137—42no—
483C2×C137—42no—
484C2×C137—44no—
485C2×C137—82no—
486C2×C137—82no—
487C2×C137#241011yescharacteristic
488C2×C137#300311yescharacteristic
489C2×C137#300911yescharacteristic
490C2×C137#326511yescharacteristic
491C2×C137#327211yescharacteristic
492C2×C137#331011yescharacteristic
493C2×C137#332411yescharacteristic
494#24448C13711yesmaximal, characteristic, direct product factor, Sylow
495C137#2444811yescharacteristic, direct product factor, Sylow
496C2×D42C2×C13711yescharacteristic
497C2×#468C2×C13711yescharacteristic, complemented
498C2×#450C2×C13711yescharacteristic, complemented
499C2×#450C2×C13711yescharacteristic, complemented
500C2×#418C2×C13711yescharacteristic, complemented
501#2415C2×C13711yescharacteristic, complemented
502#2041C2×C13711yescharacteristic, complemented
503#2033C2×C13711yescharacteristic, complemented
504#2014C2×C13711yescharacteristic, complemented
505#2000C2×C13711yescharacteristic, complemented
506#1877C2×C13711yescharacteristic, complemented
507#1875C2×C13711yescharacteristic, complemented
508#1870C2×C13711yescharacteristic, complemented
509#1862C2×C13711yescharacteristic, complemented
510#1786C2×C13711yescharacteristic, complemented
511C23×D4—21no—
512C23×D4C22×C13711yescharacteristic
513C23×D4C22×C13711yescharacteristic
514C22×SD16C22×C13711yescharacteristic
515C22×SD16C22×C13711yescharacteristic, complemented
516C22×SD16C22×C13711yescharacteristic, complemented
517C22×M16C22×C13711yescharacteristic, complemented
518D42—24no—
519D42—24no—
520C2×#127C22×C13711yescharacteristic
521C2×C22⋊Q8C22×C13711yescharacteristic, complemented
522C2×C22⋊Q8C22×C13711yescharacteristic, complemented
523C2×#121—21no—
524C2×#121C22×C13711yescharacteristic
525C2×#121C22×C13711yescharacteristic
526C2×#120—21no—
527C2×#120—21no—
528C2×C4×D4C22×C13711yescharacteristic
529C2×C4×D4C22×C13711yescharacteristic
530C2×#117C22×C13711yescharacteristic, complemented
531#468—24no—
532#450—24no—
533#450—24no—
534C2×#107C22×C13711yescharacteristic, complemented
535#418—24no—
536C2×#103C22×C13711yescharacteristic, complemented
537C2×#102C22×C13711yescharacteristic
538C2×#102C22×C13711yescharacteristic
539C2×#102C22×C13711yescharacteristic
540C2×#102C22×C13711yescharacteristic, complemented
541C2×#102C22×C13711yescharacteristic, complemented
542C2×#102C22×C13711yescharacteristic, complemented
543C2×#102C22×C13711yescharacteristic, complemented
544C2×#102C22×C13711yescharacteristic, complemented
545C2×#102C22×C13711yescharacteristic, complemented
546C2×C22⋊C8C22×C13711yescharacteristic, complemented
547C2×C22⋊C8C22×C13711yescharacteristic, complemented
548C2×C22⋊C8C22×C13711yescharacteristic, complemented
549#397—21no—
550#394—21no—
551#391C22×C13711yescharacteristic, complemented
552#389—21no—
553#389C22×C13711yescharacteristic, complemented
554#388—21no—
555#380C22×C13711yescharacteristic, complemented
556#340C22×C13711yescharacteristic, complemented
557#340C22×C13711yescharacteristic, complemented
558#336C22×C13711yescharacteristic, complemented
559#336C22×C13711yescharacteristic, complemented
560C25—21no—
561C25—21no—
562C22×Q8C23×C13711yescharacteristic
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—28no—
566C22×D4—21no—
567C22×D4—21no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—22no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—22no—
576C22×D4—21no—
577C22×D4—41no—
578C22×D4—41no—
579C22×D4—41no—
580C22×D4—41no—
581C22×D4—44no—
582C22×D4—44no—
583C22×D4D4×C13711yescharacteristic
584C22×D4D4×C13714yes—
585C22×D4C23×C13711yescharacteristic
586C22×D4C23×C13711yescharacteristic
587C22×D4C23×C13711yescharacteristic
588C23×C4—21no—
589C23×C4C23×C13711yescharacteristic
590C23×C4C23×C13711yescharacteristic
591C2×SD16—22no—
592C2×SD16—22no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—41no—
598C2×SD16—41no—
599C2×SD16—41no—
600C2×M16—22no—
601C2×M16—22no—
602C2×M16—41no—
603C22×C8C23×C13711yescharacteristic
604C22×C8C23×C13711yescharacteristic
605C22×C8C23×C13711yescharacteristic
606C22×C8C23×C13711yescharacteristic
607#127—22no—
608#127—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—41no—
613#121—28no—
614#121—22no—
615#121—22no—
616#121—22no—
617#121D4×C13714yes—
618#120—28no—
619#120—28no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—22no—
624#117—22no—
625#117—41no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4D4×C13711yescharacteristic
630C2×C4⋊C4C23×C13711yescharacteristic
631C2×C4⋊C4C23×C13711yescharacteristic
632C2×C4⋊C4C23×C13711yescharacteristic
633C2×C4⋊C4C23×C13711yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4D4×C13711yescharacteristic
642C2×C22⋊C4D4×C13711yescharacteristic
643C2×C42—21no—
644C2×C42C23×C13711yescharacteristic
645#107—22no—
646#103—22no—
647#102—22no—
648#102—22no—
649#102—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—41no—
655#102D4×C13714yescomplemented
656C22⋊C8—22no—
657C22⋊C8—22no—
658C22⋊C8—41no—
659#95—21no—
660#95—21no—
661#95—21no—
662#95—21no—
663C24—21no—
664C24—24no—
665C24—21no—
666C24—21no—
667C24—24no—
668C24—42no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—81no—
677C24—81no—
678C24—81no—
679C24—81no—
680C24C2×D4×C13711yescharacteristic
681C24C2×D4×C13711yescharacteristic
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—28no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—432no—
722C2×D4—44no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—44no—
728C2×D4—42no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4C2×D4×C13712yes—
732C2×D4C2×D4×C13712yes—
733C2×D4C2×D4×C13712yes—
734C2×D4C2×D4×C13712yes—
735C2×D4#41×C13712yes—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—24no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4C2×D4×C13711yescharacteristic
755C22×C4C2×D4×C13711yescharacteristic
756C22×C4C2×D4×C13711yescharacteristic
757C22×C4C2×D4×C13712yes—
758C22×C4C2×D4×C13712yes—
759C22×C4C2×D4×C13711yescharacteristic
760C22×C4C24×C13711yescharacteristic
761SD16—44no—
762SD16—44no—
763SD16—44no—
764M16—44no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8C2×D4×C13712yescomplemented
777C4⋊C4—22no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—42no—
787C4⋊C4C2×D4×C13712yes—
788C4⋊C4C2×D4×C13712yescomplemented
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—22no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—42no—
801C23—21no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—22no—
806C23—21no—
807C23—21no—
808C23—22no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—22no—
817C23—22no—
818C23—48no—
819C23—48no—
820C23—48no—
821C23—48no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—84no—
839C23—84no—
840C23—84no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23#120×C13712yes—
849C23AGL(1,ℤ/8)×C13712yes—
850C23C22×D4×C13711yescharacteristic
851Q8—41no—
852Q8—41no—
853Q8—41no—
854Q8—41no—
855D4—28no—
856D4—22no—
857D4—22no—
858D4—22no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—48no—
864D4—48no—
865D4—48no—
866D4—48no—
867D4—48no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—84no—
873D4#121×C13714yes—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—48no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4#120×C13712yes—
909C2×C4AGL(1,ℤ/8)×C13712yes—
910C2×C4C22×D4×C13711yescharacteristic
911C2×C4C22×D4×C13711yescharacteristic
912C2×C4C22×D4×C13711yescharacteristic
913C2×C4C2×#41×C13711yescharacteristic
914C2×C4H(5,𝔽2)×C13711yescharacteristic
915C2×C4H(5,𝔽2)×C13711yescharacteristic
916C8—22no—
917C8—41no—
918C8—41no—
919C8—41no—
920C22—22no—
921C22—22no—
922C22—24no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—41no—
928C22—42no—
929C22—41no—
930C22—41no—
931C22—42no—
932C22—41no—
933C22—42no—
934C22—41no—
935C22—42no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—816no—
948C22—816no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22C2×#120×C13711yescharacteristic
958C22D42×C13711yescharacteristic
959C22#546×C13711yescharacteristic
960C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
961C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
962C22#577×C13711yescharacteristic
963C22#577×C13711yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—42no—
968C4—41no—
969C4—42no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4C2×#121×C13711yescharacteristic
974C4#534×C13711yescharacteristic
975C4D42×C13711yescharacteristic
976C4#546×C13711yescharacteristic
977C2—42no—
978C2—42no—
979C2—44no—
980C2—82no—
981C2—82no—
982C2#2410×C13711yescharacteristic
983C2#3003×C13711yescharacteristic
984C2#3009×C13711yescharacteristic
985C2#3265×C13711yescharacteristic
986C2#3272×C13711yescharacteristic
987C2#3310×C13711yescharacteristic
988C2#3324×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC2×D42×C137C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C4×D4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#468×C137C2semidirect
3. C2×#450×C137C2semidirect
4. C2×#450×C137C2semidirect
5. C2×#418×C137C2semidirect
6. #2415×C137C2semidirect
7. #2041×C137C2semidirect
8. #2033×C137C2semidirect
9. #2014×C137C2semidirect
10. #2000×C137C2semidirect
11. #1877×C137C2semidirect
12. #1875×C137C2semidirect
13. #1870×C137C2semidirect
14. #1862×C137C2semidirect
15. #1786×C137C2semidirect
20. C22×SD16×C137C22semidirect
21. C22×SD16×C137C22semidirect
22. C22×M16×C137C22semidirect
26. C2×C22⋊Q8×C137C22semidirect
27. C2×C22⋊Q8×C137C22semidirect
35. C2×#117×C137C22semidirect
39. C2×#107×C137C22semidirect
41. C2×#103×C137C22semidirect
45. C2×#102×C137C22semidirect
46. C2×#102×C137C22semidirect
47. C2×#102×C137C22semidirect
48. C2×#102×C137C22semidirect
49. C2×#102×C137C22semidirect
50. C2×#102×C137C22semidirect
51. C2×C22⋊C8×C137C22semidirect
52. C2×C22⋊C8×C137C22semidirect
53. C2×C22⋊C8×C137C22semidirect
56. #391×C137C22semidirect
58. #389×C137C22semidirect
60. #380×C137C22semidirect
61. #340×C137C22semidirect
62. #340×C137C22semidirect
63. #336×C137C22semidirect
64. #336×C137C22semidirect
160. #102×C137D4semidirect
281. C2×C8×C137C2×D4semidirect
293. C4⋊C4×C137C2×D4semidirect
494. #24448C137direct (N × H)
495. C137#24448direct (N × H)
497. C2×#468C2×C137semidirect
498. C2×#450C2×C137semidirect
499. C2×#450C2×C137semidirect
500. C2×#418C2×C137semidirect
501. #2415C2×C137semidirect
502. #2041C2×C137semidirect
503. #2033C2×C137semidirect
504. #2014C2×C137semidirect
505. #2000C2×C137semidirect
506. #1877C2×C137semidirect
507. #1875C2×C137semidirect
508. #1870C2×C137semidirect
509. #1862C2×C137semidirect
510. #1786C2×C137semidirect
515. C22×SD16C22×C137semidirect
516. C22×SD16C22×C137semidirect
517. C22×M16C22×C137semidirect
521. C2×C22⋊Q8C22×C137semidirect
522. C2×C22⋊Q8C22×C137semidirect
530. C2×#117C22×C137semidirect
534. C2×#107C22×C137semidirect
536. C2×#103C22×C137semidirect
540. C2×#102C22×C137semidirect
541. C2×#102C22×C137semidirect
542. C2×#102C22×C137semidirect
543. C2×#102C22×C137semidirect
544. C2×#102C22×C137semidirect
545. C2×#102C22×C137semidirect
546. C2×C22⋊C8C22×C137semidirect
547. C2×C22⋊C8C22×C137semidirect
548. C2×C22⋊C8C22×C137semidirect
551. #391C22×C137semidirect
553. #389C22×C137semidirect
555. #380C22×C137semidirect
556. #340C22×C137semidirect
557. #340C22×C137semidirect
558. #336C22×C137semidirect
559. #336C22×C137semidirect
655. #102D4×C137semidirect
776. C2×C8C2×D4×C137semidirect
788. C4⋊C4C2×D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1372
C2×#468×C1372
C2×#450×C1372
C2×#418×C1372
#2415×C1372
#2041×C1372
#2033×C1372
#2014×C1372
#2000×C1372
#1877×C1372
#1875×C1372
#1870×C1372
#1862×C1372
#1786×C1372
#24448137