Finite Group Databasebeta

← C137×#23853 #46873239

Subgroups — C137×#23853 #46873239

Order 35072.

1800 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C137C211yesmaximal, characteristic, complemented
2C2×#547×C137C211yesmaximal, characteristic, complemented
3C2×#452×C137C211yesmaximal, characteristic, complemented
4C2×#452×C137C211yesmaximal, characteristic, complemented
5C2×#449×C137C211yesmaximal, characteristic, complemented
6#2407×C137C211yesmaximal, characteristic, complemented
7#2016×C137C211yesmaximal, characteristic, complemented
8#2013×C137C211yesmaximal, characteristic, complemented
9#2001×C137C211yesmaximal, characteristic, complemented
10#2000×C137C211yesmaximal, characteristic, complemented
11#1892×C137C211yesmaximal, characteristic, complemented
12#1879×C137C211yesmaximal, characteristic, complemented
13#1877×C137C211yesmaximal, characteristic, complemented
14#1869×C137C211yesmaximal, characteristic, complemented
15#1788×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C22×#41×C137C2211yescharacteristic
18C22×#41×C137C2211yescharacteristic
19C2×#135×C137—24no—
20C2×#135×C137—24no—
21C2×#135×C137—24no—
22C22×Q16×C137C2211yescharacteristic
23C22×Q16×C137C2211yescharacteristic
24C22×SD16×C137C2211yescharacteristic
25C22×SD16×C137C2211yescharacteristic
26C22×SD16×C137C2211yescharacteristic
27C22×D8×C137C2211yescharacteristic
28C23×C8×C137C2211yescharacteristic
29#547×C137—24no—
30#547×C137—24no—
31C2×C4⋊Q8×C137C2211yescharacteristic
32C2×#123×C137—21no—
33C2×#123×C137—21no—
34C2×C22⋊Q8×C137C2211yescharacteristic
35C2×C22⋊Q8×C137C2211yescharacteristic
36C2×C22⋊Q8×C137C2211yescharacteristic
37C2×#121×C137—21no—
38C2×#121×C137C2211yescharacteristic
39C2×C4×D4×C137C2211yescharacteristic
40C2×C4×D4×C137C2211yescharacteristic
41C22×C4⋊C4×C137—21no—
42#452×C137—24no—
43#452×C137—24no—
44#449×C137—24no—
45C2×#103×C137C2211yescharacteristic
46C2×#103×C137C2211yescharacteristic
47C2×#103×C137C2211yescharacteristic
48C2×#103×C137C2211yescharacteristic
49C2×#103×C137C2211yescharacteristic
50C2×#102×C137C2211yescharacteristic
51C2×#102×C137C2211yescharacteristic
52C2×#102×C137C2211yescharacteristic
53C2×C22⋊C8×C137C2211yescharacteristic
54C2×C22⋊C8×C137C2211yescharacteristic
55C2×C22⋊C8×C137C2211yescharacteristic
56#394×C137—21no—
57#392×C137—21no—
58#391×C137C2211yescharacteristic
59#390×C137C2211yescharacteristic
60#386×C137—21no—
61#385×C137—21no—
62#380×C137C2211yescharacteristic
63#340×C137C2211yescharacteristic
64#340×C137C2211yescharacteristic
65#336×C137C2211yescharacteristic
66#336×C137C2211yescharacteristic
67C2×#41×C137—22no—
68C2×#41×C137—22no—
69C2×#41×C137—22no—
70C2×#41×C137—22no—
71C2×#41×C137—22no—
72C2×#41×C137—22no—
73C2×#41×C137—22no—
74C2×#41×C137—22no—
75C2×#41×C137—22no—
76C2×#41×C137—22no—
77C2×#41×C137—22no—
78C2×#41×C137—41no—
79C2×#41×C137—41no—
80C2×#41×C137—41no—
81C2×#41×C137—41no—
82C2×#41×C137—41no—
83C2×#41×C137—41no—
84C2×#41×C137D414yescomplemented
85C22×Q8×C137C2311yescharacteristic
86C22×Q8×C137C2311yescharacteristic
87C22×Q8×C137C2311yescharacteristic
88C22×D4×C137—21no—
89C22×D4×C137—21no—
90C22×D4×C137—21no—
91C22×D4×C137—21no—
92C22×D4×C137D411yescharacteristic
93C22×D4×C137C2311yescharacteristic
94C22×D4×C137C2311yescharacteristic
95C23×C4×C137—21no—
96C23×C4×C137—21no—
97C23×C4×C137—21no—
98C23×C4×C137—21no—
99C23×C4×C137C2311yescharacteristic
100C23×C4×C137C2311yescharacteristic
101#135×C137—232no—
102C2×Q16×C137—22no—
103C2×Q16×C137—22no—
104C2×Q16×C137—22no—
105C2×Q16×C137—22no—
106C2×Q16×C137—22no—
107C2×Q16×C137—41no—
108C2×SD16×C137—22no—
109C2×SD16×C137—22no—
110C2×SD16×C137—22no—
111C2×SD16×C137—22no—
112C2×SD16×C137—22no—
113C2×SD16×C137—22no—
114C2×SD16×C137—22no—
115C2×SD16×C137—41no—
116C2×SD16×C137D414yescomplemented
117C2×D8×C137—22no—
118C2×D8×C137—22no—
119C2×D8×C137D414yescomplemented
120C22×C8×C137—22no—
121C22×C8×C137—22no—
122C22×C8×C137—22no—
123C22×C8×C137C2311yescharacteristic
124C22×C8×C137C2311yescharacteristic
125C22×C8×C137C2311yescharacteristic
126C22×C8×C137C2311yescharacteristic
127C4⋊Q8×C137—22no—
128C4⋊Q8×C137—22no—
129#123×C137—28no—
130#123×C137—28no—
131C22⋊Q8×C137—22no—
132C22⋊Q8×C137—22no—
133C22⋊Q8×C137—22no—
134C22⋊Q8×C137—22no—
135C22⋊Q8×C137—41no—
136C22⋊Q8×C137D414yescomplemented
137#121×C137—28no—
138#121×C137—22no—
139#121×C137—41no—
140C4×D4×C137—22no—
141C4×D4×C137—22no—
142C4×D4×C137—22no—
143C4×D4×C137—22no—
144C2×C4⋊C4×C137—28no—
145C2×C4⋊C4×C137—21no—
146C2×C4⋊C4×C137—21no—
147C2×C4⋊C4×C137—21no—
148C2×C4⋊C4×C137—21no—
149C2×C4⋊C4×C137—21no—
150C2×C4⋊C4×C137D411yescharacteristic
151C2×C4⋊C4×C137C2311yescharacteristic
152C2×C4⋊C4×C137C2311yescharacteristic
153C2×C4⋊C4×C137C2311yescharacteristic
154C2×C22⋊C4×C137—21no—
155C2×C22⋊C4×C137—21no—
156C2×C22⋊C4×C137—21no—
157C2×C22⋊C4×C137—21no—
158C2×C22⋊C4×C137—21no—
159C2×C22⋊C4×C137—21no—
160C2×C22⋊C4×C137—21no—
161C2×C22⋊C4×C137—21no—
162C2×C22⋊C4×C137D411yescharacteristic
163C2×C22⋊C4×C137D411yescharacteristic
164C2×C42×C137C2311yescharacteristic
165#103×C137—22no—
166#103×C137—22no—
167#103×C137—22no—
168#103×C137—41no—
169#103×C137—41no—
170#102×C137—22no—
171#102×C137—22no—
172#102×C137—22no—
173C22⋊C8×C137—22no—
174C22⋊C8×C137—22no—
175C22⋊C8×C137—22no—
176#95×C137—21no—
177#95×C137—21no—
178#95×C137—21no—
179C24×C137—21no—
180C24×C137—21no—
181C24×C137C2×D411yescharacteristic
182C24×C137C2×D411yescharacteristic
183#41×C137—28no—
184#41×C137—28no—
185#41×C137—44no—
186#41×C137—44no—
187#41×C137—44no—
188#41×C137—44no—
189#41×C137—44no—
190#41×C137—44no—
191#41×C137—44no—
192#41×C137—44no—
193#41×C137—44no—
194#41×C137—44no—
195C2×Q8×C137—21no—
196C2×Q8×C137—21no—
197C2×Q8×C137—21no—
198C2×Q8×C137—21no—
199C2×Q8×C137—21no—
200C2×Q8×C137—21no—
201C2×Q8×C137—21no—
202C2×Q8×C137—21no—
203C2×Q8×C137—21no—
204C2×Q8×C137—21no—
205C2×Q8×C137—21no—
206C2×Q8×C137—21no—
207C2×Q8×C137—21no—
208C2×Q8×C137—21no—
209C2×Q8×C137—21no—
210C2×Q8×C137C2×D412yes—
211C2×Q8×C137C2×D412yes—
212C2×Q8×C137C2×D412yes—
213C2×D4×C137—24no—
214C2×D4×C137—22no—
215C2×D4×C137—24no—
216C2×D4×C137—22no—
217C2×D4×C137—21no—
218C2×D4×C137—21no—
219C2×D4×C137—21no—
220C2×D4×C137—21no—
221C2×D4×C137—21no—
222C2×D4×C137—21no—
223C2×D4×C137—21no—
224C2×D4×C137—21no—
225C2×D4×C137—41no—
226C2×D4×C137—42no—
227C2×D4×C137—42no—
228C2×D4×C137—42no—
229C2×D4×C137—42no—
230C2×D4×C137—42no—
231C2×D4×C137—42no—
232C2×D4×C137—42no—
233C2×D4×C137—42no—
234C2×D4×C137—42no—
235C2×D4×C137—81no—
236C2×D4×C137C2×D412yes—
237C2×D4×C137C2×D412yes—
238C2×D4×C137C2×D412yes—
239C2×D4×C137C2×D412yes—
240C22×C4×C137—21no—
241C22×C4×C137—21no—
242C22×C4×C137—21no—
243C22×C4×C137—21no—
244C22×C4×C137—24no—
245C22×C4×C137—24no—
246C22×C4×C137—21no—
247C22×C4×C137—21no—
248C22×C4×C137—21no—
249C22×C4×C137—21no—
250C22×C4×C137—24no—
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—42no—
260C22×C4×C137—42no—
261C22×C4×C137—42no—
262C22×C4×C137—42no—
263C22×C4×C137—42no—
264C22×C4×C137—42no—
265C22×C4×C137—42no—
266C22×C4×C137—42no—
267C22×C4×C137—42no—
268C22×C4×C137C2×D411yescharacteristic
269C22×C4×C137C2×D411yescharacteristic
270C22×C4×C137C2×D411yescharacteristic
271C22×C4×C137C2×D412yes—
272C22×C4×C137C2×D412yes—
273C22×C4×C137C2×D411yescharacteristic
274C22×C4×C137C2411yescharacteristic
275Q16×C137—28no—
276Q16×C137—44no—
277SD16×C137—28no—
278SD16×C137—28no—
279SD16×C137—44no—
280D8×C137—28no—
281C2×C8×C137—28no—
282C2×C8×C137—21no—
283C2×C8×C137—21no—
284C2×C8×C137—21no—
285C2×C8×C137—21no—
286C2×C8×C137—21no—
287C2×C8×C137—21no—
288C2×C8×C137—21no—
289C2×C8×C137—21no—
290C2×C8×C137—21no—
291C2×C8×C137—21no—
292C2×C8×C137C2×D412yes—
293C2×C8×C137C2×D412yes—
294C4⋊C4×C137—24no—
295C4⋊C4×C137—24no—
296C4⋊C4×C137—24no—
297C4⋊C4×C137—22no—
298C4⋊C4×C137—24no—
299C4⋊C4×C137—21no—
300C4⋊C4×C137—21no—
301C4⋊C4×C137—21no—
302C4⋊C4×C137—21no—
303C4⋊C4×C137—21no—
304C4⋊C4×C137—42no—
305C4⋊C4×C137C2×D412yes—
306C22⋊C4×C137—24no—
307C22⋊C4×C137—24no—
308C22⋊C4×C137—24no—
309C22⋊C4×C137—22no—
310C22⋊C4×C137—22no—
311C22⋊C4×C137—42no—
312C22⋊C4×C137—42no—
313C22⋊C4×C137—42no—
314C22⋊C4×C137—81no—
315C22⋊C4×C137—81no—
316C42×C137—21no—
317C42×C137—21no—
318C23×C137—22no—
319C23×C137—21no—
320C23×C137—21no—
321C23×C137—22no—
322C23×C137—22no—
323C23×C137—21no—
324C23×C137—21no—
325C23×C137—21no—
326C23×C137—21no—
327C23×C137—21no—
328C23×C137—21no—
329C23×C137—22no—
330C23×C137—21no—
331C23×C137—21no—
332C23×C137—21no—
333C23×C137—21no—
334C23×C137—21no—
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—41no—
344C23×C137—41no—
345C23×C137#12012yes—
346C23×C137C22×D411yescharacteristic
347Q8×C137—22no—
348Q8×C137—22no—
349Q8×C137—22no—
350Q8×C137—22no—
351Q8×C137—22no—
352Q8×C137—22no—
353Q8×C137—41no—
354Q8×C137—41no—
355Q8×C137—41no—
356Q8×C137—41no—
357Q8×C137—41no—
358Q8×C137—41no—
359D4×C137—22no—
360D4×C137—22no—
361D4×C137—22no—
362D4×C137—22no—
363D4×C137—22no—
364D4×C137—44no—
365D4×C137—48no—
366D4×C137—48no—
367D4×C137—48no—
368D4×C137—41no—
369D4×C137—41no—
370D4×C137—84no—
371D4×C137#12014yes—
372C2×C4×C137—21no—
373C2×C4×C137—21no—
374C2×C4×C137—21no—
375C2×C4×C137—21no—
376C2×C4×C137—22no—
377C2×C4×C137—22no—
378C2×C4×C137—22no—
379C2×C4×C137—22no—
380C2×C4×C137—21no—
381C2×C4×C137—22no—
382C2×C4×C137—21no—
383C2×C4×C137—22no—
384C2×C4×C137—22no—
385C2×C4×C137—21no—
386C2×C4×C137—22no—
387C2×C4×C137—21no—
388C2×C4×C137—21no—
389C2×C4×C137—21no—
390C2×C4×C137—48no—
391C2×C4×C137—48no—
392C2×C4×C137—48no—
393C2×C4×C137—48no—
394C2×C4×C137—41no—
395C2×C4×C137—41no—
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#12012yes—
413C2×C4×C137#13512yescomplemented
414C2×C4×C137C22×D411yescharacteristic
415C2×C4×C137C22×D411yescharacteristic
416C2×C4×C137C22×D411yescharacteristic
417C2×C4×C137C22×D411yescharacteristic
418C2×C4×C137H(5,𝔽2)11yescharacteristic
419C2×C4×C137H(5,𝔽2)11yescharacteristic
420C8×C137—22no—
421C8×C137—22no—
422C8×C137—41no—
423C8×C137—41no—
424C22×C137—22no—
425C22×C137—24no—
426C22×C137—22no—
427C22×C137—22no—
428C22×C137—42no—
429C22×C137—41no—
430C22×C137—42no—
431C22×C137—42no—
432C22×C137—41no—
433C22×C137—42no—
434C22×C137—41no—
435C22×C137—42no—
436C22×C137—41no—
437C22×C137—42no—
438C22×C137—42no—
439C22×C137—41no—
440C22×C137—41no—
441C22×C137—41no—
442C22×C137—42no—
443C22×C137—41no—
444C22×C137—41no—
445C22×C137—41no—
446C22×C137—42no—
447C22×C137—41no—
448C22×C137—81no—
449C22×C137—81no—
450C22×C137—81no—
451C22×C137—81no—
452C22×C137C2×#12011yescharacteristic
453C22×C137D4211yescharacteristic
454C22×C137D4211yescharacteristic
455C22×C137C2×#13511yescharacteristic
456C22×C137#57511yescharacteristic
457C22×C137#57711yescharacteristic
458C22×C137#57811yescharacteristic
459C4×C137—22no—
460C4×C137—22no—
461C4×C137—41no—
462C4×C137—42no—
463C4×C137—42no—
464C4×C137—42no—
465C4×C137—42no—
466C4×C137—41no—
467C4×C137—81no—
468C4×C137—81no—
469C4×C137C2×#12011yescharacteristic
470C4×C137#53411yescharacteristic
471C4×C137D4211yescharacteristic
472C4×C137D4211yescharacteristic
473C2×C137—42no—
474C2×C137—44no—
475C2×C137—81no—
476C2×C137—82no—
477C2×C137#240311yescharacteristic
478C2×C137#300211yescharacteristic
479C2×C137#301311yescharacteristic
480C2×C137#326711yescharacteristic
481C2×C137#326911yescharacteristic
482C2×C137#328311yescharacteristic
483C2×C137#328411yescharacteristic
484#23853C13711yesmaximal, characteristic, direct product factor, Sylow
485C137#2385311yescharacteristic, direct product factor, Sylow
486C22×#135C2×C13711yescharacteristic, complemented
487C2×#547C2×C13711yescharacteristic, complemented
488C2×#452C2×C13711yescharacteristic, complemented
489C2×#452C2×C13711yescharacteristic, complemented
490C2×#449C2×C13711yescharacteristic, complemented
491#2407C2×C13711yescharacteristic, complemented
492#2016C2×C13711yescharacteristic, complemented
493#2013C2×C13711yescharacteristic, complemented
494#2001C2×C13711yescharacteristic, complemented
495#2000C2×C13711yescharacteristic, complemented
496#1892C2×C13711yescharacteristic, complemented
497#1879C2×C13711yescharacteristic, complemented
498#1877C2×C13711yescharacteristic, complemented
499#1869C2×C13711yescharacteristic, complemented
500#1788C2×C13711yescharacteristic, complemented
501C22×#41C22×C13711yescharacteristic
502C22×#41C22×C13711yescharacteristic
503C22×#41C22×C13711yescharacteristic
504C2×#135—24no—
505C2×#135—24no—
506C2×#135—24no—
507C22×Q16C22×C13711yescharacteristic
508C22×Q16C22×C13711yescharacteristic
509C22×SD16C22×C13711yescharacteristic
510C22×SD16C22×C13711yescharacteristic
511C22×SD16C22×C13711yescharacteristic
512C22×D8C22×C13711yescharacteristic
513C23×C8C22×C13711yescharacteristic
514#547—24no—
515#547—24no—
516C2×C4⋊Q8C22×C13711yescharacteristic
517C2×#123—21no—
518C2×#123—21no—
519C2×C22⋊Q8C22×C13711yescharacteristic
520C2×C22⋊Q8C22×C13711yescharacteristic
521C2×C22⋊Q8C22×C13711yescharacteristic
522C2×#121—21no—
523C2×#121C22×C13711yescharacteristic
524C2×C4×D4C22×C13711yescharacteristic
525C2×C4×D4C22×C13711yescharacteristic
526C22×C4⋊C4—21no—
527#452—24no—
528#452—24no—
529#449—24no—
530C2×#103C22×C13711yescharacteristic
531C2×#103C22×C13711yescharacteristic
532C2×#103C22×C13711yescharacteristic
533C2×#103C22×C13711yescharacteristic
534C2×#103C22×C13711yescharacteristic
535C2×#102C22×C13711yescharacteristic
536C2×#102C22×C13711yescharacteristic
537C2×#102C22×C13711yescharacteristic
538C2×C22⋊C8C22×C13711yescharacteristic
539C2×C22⋊C8C22×C13711yescharacteristic
540C2×C22⋊C8C22×C13711yescharacteristic
541#394—21no—
542#392—21no—
543#391C22×C13711yescharacteristic
544#390C22×C13711yescharacteristic
545#386—21no—
546#385—21no—
547#380C22×C13711yescharacteristic
548#340C22×C13711yescharacteristic
549#340C22×C13711yescharacteristic
550#336C22×C13711yescharacteristic
551#336C22×C13711yescharacteristic
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—22no—
556C2×#41—22no—
557C2×#41—22no—
558C2×#41—22no—
559C2×#41—22no—
560C2×#41—22no—
561C2×#41—22no—
562C2×#41—22no—
563C2×#41—41no—
564C2×#41—41no—
565C2×#41—41no—
566C2×#41—41no—
567C2×#41—41no—
568C2×#41—41no—
569C2×#41D4×C13714yescomplemented
570C22×Q8C23×C13711yescharacteristic
571C22×Q8C23×C13711yescharacteristic
572C22×Q8C23×C13711yescharacteristic
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4D4×C13711yescharacteristic
578C22×D4C23×C13711yescharacteristic
579C22×D4C23×C13711yescharacteristic
580C23×C4—21no—
581C23×C4—21no—
582C23×C4—21no—
583C23×C4—21no—
584C23×C4C23×C13711yescharacteristic
585C23×C4C23×C13711yescharacteristic
586#135—232no—
587C2×Q16—22no—
588C2×Q16—22no—
589C2×Q16—22no—
590C2×Q16—22no—
591C2×Q16—22no—
592C2×Q16—41no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—41no—
601C2×SD16D4×C13714yescomplemented
602C2×D8—22no—
603C2×D8—22no—
604C2×D8D4×C13714yescomplemented
605C22×C8—22no—
606C22×C8—22no—
607C22×C8—22no—
608C22×C8C23×C13711yescharacteristic
609C22×C8C23×C13711yescharacteristic
610C22×C8C23×C13711yescharacteristic
611C22×C8C23×C13711yescharacteristic
612C4⋊Q8—22no—
613C4⋊Q8—22no—
614#123—28no—
615#123—28no—
616C22⋊Q8—22no—
617C22⋊Q8—22no—
618C22⋊Q8—22no—
619C22⋊Q8—22no—
620C22⋊Q8—41no—
621C22⋊Q8D4×C13714yescomplemented
622#121—28no—
623#121—22no—
624#121—41no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—22no—
629C2×C4⋊C4—28no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4D4×C13711yescharacteristic
636C2×C4⋊C4C23×C13711yescharacteristic
637C2×C4⋊C4C23×C13711yescharacteristic
638C2×C4⋊C4C23×C13711yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4D4×C13711yescharacteristic
648C2×C22⋊C4D4×C13711yescharacteristic
649C2×C42C23×C13711yescharacteristic
650#103—22no—
651#103—22no—
652#103—22no—
653#103—41no—
654#103—41no—
655#102—22no—
656#102—22no—
657#102—22no—
658C22⋊C8—22no—
659C22⋊C8—22no—
660C22⋊C8—22no—
661#95—21no—
662#95—21no—
663#95—21no—
664C24—21no—
665C24—21no—
666C24C2×D4×C13711yescharacteristic
667C24C2×D4×C13711yescharacteristic
668#41—28no—
669#41—28no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674#41—44no—
675#41—44no—
676#41—44no—
677#41—44no—
678#41—44no—
679#41—44no—
680C2×Q8—21no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8C2×D4×C13712yes—
696C2×Q8C2×D4×C13712yes—
697C2×Q8C2×D4×C13712yes—
698C2×D4—24no—
699C2×D4—22no—
700C2×D4—24no—
701C2×D4—22no—
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—41no—
711C2×D4—42no—
712C2×D4—42no—
713C2×D4—42no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—81no—
721C2×D4C2×D4×C13712yes—
722C2×D4C2×D4×C13712yes—
723C2×D4C2×D4×C13712yes—
724C2×D4C2×D4×C13712yes—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—24no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—42no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—42no—
748C22×C4—42no—
749C22×C4—42no—
750C22×C4—42no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4C2×D4×C13711yescharacteristic
754C22×C4C2×D4×C13711yescharacteristic
755C22×C4C2×D4×C13711yescharacteristic
756C22×C4C2×D4×C13712yes—
757C22×C4C2×D4×C13712yes—
758C22×C4C2×D4×C13711yescharacteristic
759C22×C4C24×C13711yescharacteristic
760Q16—28no—
761Q16—44no—
762SD16—28no—
763SD16—28no—
764SD16—44no—
765D8—28no—
766C2×C8—28no—
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×C8—21no—
777C2×C8C2×D4×C13712yes—
778C2×C8C2×D4×C13712yes—
779C4⋊C4—24no—
780C4⋊C4—24no—
781C4⋊C4—24no—
782C4⋊C4—22no—
783C4⋊C4—24no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—42no—
790C4⋊C4C2×D4×C13712yes—
791C22⋊C4—24no—
792C22⋊C4—24no—
793C22⋊C4—24no—
794C22⋊C4—22no—
795C22⋊C4—22no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C22⋊C4—42no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C42—21no—
802C42—21no—
803C23—22no—
804C23—21no—
805C23—21no—
806C23—22no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—22no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23#120×C13712yes—
831C23C22×D4×C13711yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—22no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844D4—22no—
845D4—22no—
846D4—22no—
847D4—22no—
848D4—22no—
849D4—44no—
850D4—48no—
851D4—48no—
852D4—48no—
853D4—41no—
854D4—41no—
855D4—84no—
856D4#120×C13714yes—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—21no—
866C2×C4—22no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—21no—
871C2×C4—22no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—48no—
876C2×C4—48no—
877C2×C4—48no—
878C2×C4—48no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4#120×C13712yes—
898C2×C4#135×C13712yescomplemented
899C2×C4C22×D4×C13711yescharacteristic
900C2×C4C22×D4×C13711yescharacteristic
901C2×C4C22×D4×C13711yescharacteristic
902C2×C4C22×D4×C13711yescharacteristic
903C2×C4H(5,𝔽2)×C13711yescharacteristic
904C2×C4H(5,𝔽2)×C13711yescharacteristic
905C8—22no—
906C8—22no—
907C8—41no—
908C8—41no—
909C22—22no—
910C22—24no—
911C22—22no—
912C22—22no—
913C22—42no—
914C22—41no—
915C22—42no—
916C22—42no—
917C22—41no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—41no—
922C22—42no—
923C22—42no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—42no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—42no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22C2×#120×C13711yescharacteristic
938C22D42×C13711yescharacteristic
939C22D42×C13711yescharacteristic
940C22C2×#135×C13711yescharacteristic
941C22#575×C13711yescharacteristic
942C22#577×C13711yescharacteristic
943C22#578×C13711yescharacteristic
944C4—22no—
945C4—22no—
946C4—41no—
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—41no—
952C4—81no—
953C4—81no—
954C4C2×#120×C13711yescharacteristic
955C4#534×C13711yescharacteristic
956C4D42×C13711yescharacteristic
957C4D42×C13711yescharacteristic
958C2—42no—
959C2—44no—
960C2—81no—
961C2—82no—
962C2#2403×C13711yescharacteristic
963C2#3002×C13711yescharacteristic
964C2#3013×C13711yescharacteristic
965C2#3267×C13711yescharacteristic
966C2#3269×C13711yescharacteristic
967C2#3283×C13711yescharacteristic
968C2#3284×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
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
1. C22×#135×C137C2semidirect
2. C2×#547×C137C2semidirect
3. C2×#452×C137C2semidirect
4. C2×#452×C137C2semidirect
5. C2×#449×C137C2semidirect
6. #2407×C137C2semidirect
7. #2016×C137C2semidirect
8. #2013×C137C2semidirect
9. #2001×C137C2semidirect
10. #2000×C137C2semidirect
11. #1892×C137C2semidirect
12. #1879×C137C2semidirect
13. #1877×C137C2semidirect
14. #1869×C137C2semidirect
15. #1788×C137C2semidirect
84. C2×#41×C137D4semidirect
116. C2×SD16×C137D4semidirect
119. C2×D8×C137D4semidirect
136. C22⋊Q8×C137D4semidirect
413. C2×C4×C137#135semidirect
484. #23853C137direct (N × H)
485. C137#23853direct (N × H)
486. C22×#135C2×C137semidirect
487. C2×#547C2×C137semidirect
488. C2×#452C2×C137semidirect
489. C2×#452C2×C137semidirect
490. C2×#449C2×C137semidirect
491. #2407C2×C137semidirect
492. #2016C2×C137semidirect
493. #2013C2×C137semidirect
494. #2001C2×C137semidirect
495. #2000C2×C137semidirect
496. #1892C2×C137semidirect
497. #1879C2×C137semidirect
498. #1877C2×C137semidirect
499. #1869C2×C137semidirect
500. #1788C2×C137semidirect
569. C2×#41D4×C137semidirect
601. C2×SD16D4×C137semidirect
604. C2×D8D4×C137semidirect
621. C22⋊Q8D4×C137semidirect
898. C2×C4#135×C137semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1372
C2×#547×C1372
C2×#452×C1372
C2×#449×C1372
#2407×C1372
#2016×C1372
#2013×C1372
#2001×C1372
#2000×C1372
#1892×C1372
#1879×C1372
#1877×C1372
#1869×C1372
#1788×C1372
#23853137