Finite Group Databasebeta

← C137×#24218 #46873604

Subgroups — C137×#24218 #46873604

Order 35072.

1612 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C137C211yesmaximal, characteristic, complemented
2C2×#463×C137C211yesmaximal, characteristic, complemented
3C2×#459×C137C211yesmaximal, characteristic, complemented
4C2×#449×C137C211yesmaximal, characteristic, complemented
5C2×#447×C137C211yesmaximal, characteristic, complemented
6#2324×C137C211yesmaximal, characteristic, complemented
7#2042×C137C211yesmaximal, characteristic, complemented
8#2041×C137C211yesmaximal, characteristic, complemented
9#2012×C137C211yesmaximal, characteristic, complemented
10#2011×C137C211yesmaximal, characteristic, complemented
11#1983×C137C211yesmaximal, characteristic, complemented
12#1982×C137C211yesmaximal, characteristic, complemented
13#1798×C137C211yesmaximal, characteristic, complemented
14#1788×C137C211yesmaximal, characteristic, complemented
15#1786×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C22×SD16×C137C2211yescharacteristic, complemented
19C22×D8×C137C2211yescharacteristic
20C22×D8×C137C2211yescharacteristic
21C22×D8×C137C2211yescharacteristic, complemented
22#535×C137—24no—
23#535×C137—24no—
24C2×#127×C137C2211yescharacteristic
25C2×#127×C137C2211yescharacteristic
26C2×#124×C137C2211yescharacteristic
27C2×#124×C137C2211yescharacteristic
28C2×#121×C137—21no—
29C2×#121×C137—21no—
30C2×#121×C137C2211yescharacteristic
31C2×#120×C137—21no—
32C2×#120×C137—21no—
33C2×C4×D4×C137C2211yescharacteristic, complemented
34C2×#117×C137C2211yescharacteristic
35#463×C137—24no—
36#459×C137—24no—
37#449×C137—24no—
38#447×C137—24no—
39C2×C4⋊C8×C137C2211yescharacteristic, complemented
40C2×C4⋊C8×C137C2211yescharacteristic, complemented
41C2×#103×C137C2211yescharacteristic, complemented
42C2×#103×C137C2211yescharacteristic, complemented
43C2×#103×C137C2211yescharacteristic, complemented
44C2×#102×C137C2211yescharacteristic
45C2×#102×C137C2211yescharacteristic
46C2×#102×C137C2211yescharacteristic
47C2×#102×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic
49C2×#102×C137C2211yescharacteristic
50C2×#102×C137C2211yescharacteristic, complemented
51C2×#102×C137C2211yescharacteristic, complemented
52C2×#102×C137C2211yescharacteristic, complemented
53C2×C22⋊C8×C137C2211yescharacteristic
54C2×C22⋊C8×C137C2211yescharacteristic
55#390×C137—21no—
56#390×C137C2211yescharacteristic, complemented
57#389×C137C2211yescharacteristic, complemented
58#388×C137—21no—
59#386×C137—21no—
60#385×C137—21no—
61#380×C137C2211yescharacteristic
62C4×C4⋊C4×C137C2211yescharacteristic, complemented
63#336×C137C2211yescharacteristic, complemented
64#336×C137C2211yescharacteristic, complemented
65C25×C137—21no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—22no—
69C2×#41×C137—22no—
70C2×#41×C137—41no—
71C2×#41×C137—41no—
72C22×Q8×C137C2311yescharacteristic
73C22×D4×C137—21no—
74C22×D4×C137—21no—
75C22×D4×C137—22no—
76C22×D4×C137—22no—
77C22×D4×C137—21no—
78C22×D4×C137—21no—
79C22×D4×C137—21no—
80C22×D4×C137—21no—
81C22×D4×C137—21no—
82C22×D4×C137—22no—
83C22×D4×C137—22no—
84C22×D4×C137—41no—
85C22×D4×C137—41no—
86C22×D4×C137C2311yescharacteristic
87C22×D4×C137C2311yescharacteristic
88C22×D4×C137C2311yescharacteristic
89C22×D4×C137C2311yescharacteristic
90C23×C4×C137—21no—
91C23×C4×C137—21no—
92C23×C4×C137C2311yescharacteristic
93C2×SD16×C137—22no—
94C2×SD16×C137—22no—
95C2×SD16×C137—41no—
96C2×D8×C137—22no—
97C2×D8×C137—22no—
98C2×D8×C137—22no—
99C2×D8×C137—22no—
100C2×D8×C137—22no—
101C2×D8×C137—22no—
102C2×D8×C137—41no—
103C2×D8×C137—41no—
104C2×D8×C137—41no—
105C22×C8×C137C2311yescharacteristic
106C22×C8×C137C2311yescharacteristic
107C22×C8×C137C2311yescharacteristic
108C22×C8×C137C2311yescharacteristic
109#127×C137—22no—
110#127×C137—22no—
111#127×C137—22no—
112#127×C137D414yescomplemented
113#124×C137—22no—
114#124×C137—22no—
115#124×C137—22no—
116#124×C137D414yescomplemented
117#121×C137—28no—
118#121×C137—28no—
119#121×C137—22no—
120#121×C137D414yescomplemented
121#120×C137—28no—
122#120×C137—28no—
123C4×D4×C137—22no—
124C4×D4×C137—22no—
125#117×C137—22no—
126#117×C137—22no—
127C2×C4⋊C4×C137—21no—
128C2×C4⋊C4×C137D411yescharacteristic
129C2×C4⋊C4×C137D411yescharacteristic
130C2×C4⋊C4×C137C2311yescharacteristic
131C2×C4⋊C4×C137C2311yescharacteristic
132C2×C4⋊C4×C137C2311yescharacteristic
133C2×C22⋊C4×C137—21no—
134C2×C22⋊C4×C137—21no—
135C2×C22⋊C4×C137—21no—
136C2×C22⋊C4×C137—21no—
137C2×C22⋊C4×C137—21no—
138C2×C22⋊C4×C137—21no—
139C2×C22⋊C4×C137—21no—
140C2×C22⋊C4×C137—21no—
141C2×C22⋊C4×C137—21no—
142C2×C22⋊C4×C137D411yescharacteristic
143C2×C22⋊C4×C137D411yescharacteristic
144C2×C42×C137—21no—
145C2×C42×C137C2311yescharacteristic
146C2×C42×C137C2311yescharacteristic
147C4⋊C8×C137—22no—
148C4⋊C8×C137—22no—
149#103×C137—22no—
150#103×C137—22no—
151#103×C137—41no—
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—41no—
159#102×C137—41no—
160#102×C137—41no—
161C22⋊C8×C137—22no—
162C22⋊C8×C137—22no—
163#95×C137—21no—
164#95×C137—21no—
165#95×C137—21no—
166C24×C137—24no—
167C24×C137—21no—
168C24×C137—21no—
169C24×C137—21no—
170C24×C137—21no—
171C24×C137—42no—
172C24×C137—42no—
173C24×C137—81no—
174C24×C137—81no—
175C24×C137—81no—
176C24×C137—81no—
177C24×C137C2×D411yescharacteristic
178#41×C137—44no—
179#41×C137—44no—
180#41×C137—44no—
181#41×C137—44no—
182C2×Q8×C137—21no—
183C2×Q8×C137—21no—
184C2×Q8×C137—21no—
185C2×Q8×C137—21no—
186C2×Q8×C137—21no—
187C2×Q8×C137C2×D412yes—
188C2×D4×C137—24no—
189C2×D4×C137—24no—
190C2×D4×C137—24no—
191C2×D4×C137—24no—
192C2×D4×C137—24no—
193C2×D4×C137—24no—
194C2×D4×C137—24no—
195C2×D4×C137—21no—
196C2×D4×C137—21no—
197C2×D4×C137—21no—
198C2×D4×C137—21no—
199C2×D4×C137—21no—
200C2×D4×C137—21no—
201C2×D4×C137—21no—
202C2×D4×C137—21no—
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—44no—
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—81no—
224C2×D4×C137—81no—
225C2×D4×C137—81no—
226C2×D4×C137—81no—
227C2×D4×C137—81no—
228C2×D4×C137—81no—
229C2×D4×C137—81no—
230C2×D4×C137—81no—
231C2×D4×C137—81no—
232C2×D4×C137—81no—
233C2×D4×C137C2×D412yes—
234C2×D4×C137C2×D412yes—
235C2×D4×C137C2×D412yes—
236C2×D4×C137C2×D412yes—
237C22×C4×C137—21no—
238C22×C4×C137—21no—
239C22×C4×C137—21no—
240C22×C4×C137—21no—
241C22×C4×C137—24no—
242C22×C4×C137—21no—
243C22×C4×C137—21no—
244C22×C4×C137—21no—
245C22×C4×C137—21no—
246C22×C4×C137—42no—
247C22×C4×C137—42no—
248C22×C4×C137—42no—
249C22×C4×C137—81no—
250C22×C4×C137—81no—
251C22×C4×C137C2×D411yescharacteristic
252C22×C4×C137C2×D411yescharacteristic
253C22×C4×C137C2×D411yescharacteristic
254C22×C4×C137C2×D411yescharacteristic
255C22×C4×C137C2×D411yescharacteristic
256C22×C4×C137C2×D412yes—
257C22×C4×C137#4112yes—
258C22×C4×C137C2411yescharacteristic
259SD16×C137—44no—
260D8×C137—44no—
261D8×C137—44no—
262D8×C137—44no—
263C2×C8×C137—21no—
264C2×C8×C137—21no—
265C2×C8×C137—21no—
266C2×C8×C137—21no—
267C2×C8×C137—21no—
268C2×C8×C137—21no—
269C2×C8×C137—21no—
270C2×C8×C137—21no—
271C2×C8×C137—21no—
272C2×C8×C137—21no—
273C2×C8×C137—21no—
274C2×C8×C137—21no—
275C4⋊C4×C137—22no—
276C4⋊C4×C137—22no—
277C4⋊C4×C137—21no—
278C4⋊C4×C137—21no—
279C4⋊C4×C137—21no—
280C4⋊C4×C137—21no—
281C4⋊C4×C137—21no—
282C4⋊C4×C137—81no—
283C4⋊C4×C137C2×D412yes—
284C22⋊C4×C137—24no—
285C22⋊C4×C137—24no—
286C22⋊C4×C137—24no—
287C22⋊C4×C137—24no—
288C22⋊C4×C137—22no—
289C22⋊C4×C137—22no—
290C22⋊C4×C137—24no—
291C22⋊C4×C137—42no—
292C22⋊C4×C137—81no—
293C22⋊C4×C137—81no—
294C22⋊C4×C137—81no—
295C42×C137—21no—
296C42×C137—21no—
297C42×C137—81no—
298C42×C137C2×D412yes—
299C42×C137C2×D412yes—
300C23×C137—21no—
301C23×C137—21no—
302C23×C137—21no—
303C23×C137—21no—
304C23×C137—21no—
305C23×C137—21no—
306C23×C137—22no—
307C23×C137—22no—
308C23×C137—22no—
309C23×C137—22no—
310C23×C137—48no—
311C23×C137—41no—
312C23×C137—41no—
313C23×C137—41no—
314C23×C137—41no—
315C23×C137—41no—
316C23×C137—41no—
317C23×C137—41no—
318C23×C137—41no—
319C23×C137—41no—
320C23×C137—41no—
321C23×C137—41no—
322C23×C137—41no—
323C23×C137—41no—
324C23×C137—41no—
325C23×C137—41no—
326C23×C137—41no—
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—84no—
336C23×C137—84no—
337C23×C137—84no—
338C23×C137—84no—
339C23×C137—84no—
340C23×C137—84no—
341C23×C137#12112yes—
342C23×C137C22×D411yescharacteristic
343Q8×C137—22no—
344Q8×C137—22no—
345Q8×C137—41no—
346Q8×C137—41no—
347D4×C137—22no—
348D4×C137—22no—
349D4×C137—22no—
350D4×C137—22no—
351D4×C137—22no—
352D4×C137—22no—
353D4×C137—22no—
354D4×C137—22no—
355D4×C137—48no—
356D4×C137—48no—
357D4×C137—41no—
358D4×C137—41no—
359D4×C137—41no—
360D4×C137—41no—
361D4×C137—41no—
362D4×C137—41no—
363D4×C137—41no—
364D4×C137—41no—
365D4×C137—84no—
366D4×C137—84no—
367D4×C137—84no—
368D4×C137—84no—
369D4×C137—84no—
370C2×C4×C137—21no—
371C2×C4×C137—21no—
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—21no—
382C2×C4×C137—22no—
383C2×C4×C137—22no—
384C2×C4×C137—21no—
385C2×C4×C137—21no—
386C2×C4×C137—21no—
387C2×C4×C137—21no—
388C2×C4×C137—48no—
389C2×C4×C137—41no—
390C2×C4×C137—41no—
391C2×C4×C137—41no—
392C2×C4×C137—41no—
393C2×C4×C137—41no—
394C2×C4×C137—41no—
395C2×C4×C137—41no—
396C2×C4×C137—41no—
397C2×C4×C137—41no—
398C2×C4×C137—41no—
399C2×C4×C137—84no—
400C2×C4×C137#12012yes—
401C2×C4×C137#12012yes—
402C2×C4×C137#12112yes—
403C2×C4×C137C22×D411yescharacteristic
404C2×C4×C137C22×D411yescharacteristic
405C2×C4×C137C22×D411yescharacteristic
406C2×C4×C137C2×#4111yescharacteristic
407C2×C4×C137H(5,𝔽2)11yescharacteristic
408C2×C4×C137H(5,𝔽2)11yescharacteristic
409C8×C137—41no—
410C8×C137—41no—
411C8×C137—41no—
412C8×C137—41no—
413C22×C137—22no—
414C22×C137—22no—
415C22×C137—22no—
416C22×C137—41no—
417C22×C137—41no—
418C22×C137—41no—
419C22×C137—41no—
420C22×C137—42no—
421C22×C137—42no—
422C22×C137—42no—
423C22×C137—42no—
424C22×C137—42no—
425C22×C137—42no—
426C22×C137—42no—
427C22×C137—42no—
428C22×C137—42no—
429C22×C137—42no—
430C22×C137—42no—
431C22×C137—42no—
432C22×C137—816no—
433C22×C137—81no—
434C22×C137—81no—
435C22×C137—81no—
436C22×C137—81no—
437C22×C137—81no—
438C22×C137—81no—
439C22×C137—81no—
440C22×C137—81no—
441C22×C137—81no—
442C22×C137—81no—
443C22×C137—81no—
444C22×C137—81no—
445C22×C137—81no—
446C22×C137—81no—
447C22×C137—81no—
448C22×C137—81no—
449C22×C137C2×#12011yescharacteristic
450C22×C137C2×#12111yescharacteristic
451C22×C137#53511yescharacteristic
452C22×C137#57611yescharacteristic
453C22×C137#57611yescharacteristic
454C22×C137#57611yescharacteristic
455C22×C137#57711yescharacteristic
456C4×C137—22no—
457C4×C137—22no—
458C4×C137—22no—
459C4×C137—42no—
460C4×C137—41no—
461C4×C137—41no—
462C4×C137—42no—
463C4×C137—81no—
464C4×C137—81no—
465C4×C137D4211yescharacteristic
466C4×C137D4211yescharacteristic
467C4×C137#54611yescharacteristic
468C4×C137#54611yescharacteristic
469C2×C137—42no—
470C2×C137—82no—
471C2×C137—82no—
472C2×C137—82no—
473C2×C137—82no—
474C2×C137#240811yescharacteristic
475C2×C137#300811yescharacteristic
476C2×C137#301211yescharacteristic
477C2×C137#304111yescharacteristic
478C2×C137#304511yescharacteristic
479C2×C137#322011yescharacteristic
480C2×C137#322411yescharacteristic
481#24218C13711yesmaximal, characteristic, direct product factor, Sylow
482C137#2421811yescharacteristic, direct product factor, Sylow
483C2×#535C2×C13711yescharacteristic, complemented
484C2×#463C2×C13711yescharacteristic, complemented
485C2×#459C2×C13711yescharacteristic, complemented
486C2×#449C2×C13711yescharacteristic, complemented
487C2×#447C2×C13711yescharacteristic, complemented
488#2324C2×C13711yescharacteristic, complemented
489#2042C2×C13711yescharacteristic, complemented
490#2041C2×C13711yescharacteristic, complemented
491#2012C2×C13711yescharacteristic, complemented
492#2011C2×C13711yescharacteristic, complemented
493#1983C2×C13711yescharacteristic, complemented
494#1982C2×C13711yescharacteristic, complemented
495#1798C2×C13711yescharacteristic, complemented
496#1788C2×C13711yescharacteristic, complemented
497#1786C2×C13711yescharacteristic, complemented
498C22×#41C22×C13711yescharacteristic
499C23×D4C22×C13711yescharacteristic
500C22×SD16C22×C13711yescharacteristic, complemented
501C22×D8C22×C13711yescharacteristic
502C22×D8C22×C13711yescharacteristic
503C22×D8C22×C13711yescharacteristic, complemented
504#535—24no—
505#535—24no—
506C2×#127C22×C13711yescharacteristic
507C2×#127C22×C13711yescharacteristic
508C2×#124C22×C13711yescharacteristic
509C2×#124C22×C13711yescharacteristic
510C2×#121—21no—
511C2×#121—21no—
512C2×#121C22×C13711yescharacteristic
513C2×#120—21no—
514C2×#120—21no—
515C2×C4×D4C22×C13711yescharacteristic, complemented
516C2×#117C22×C13711yescharacteristic
517#463—24no—
518#459—24no—
519#449—24no—
520#447—24no—
521C2×C4⋊C8C22×C13711yescharacteristic, complemented
522C2×C4⋊C8C22×C13711yescharacteristic, complemented
523C2×#103C22×C13711yescharacteristic, complemented
524C2×#103C22×C13711yescharacteristic, complemented
525C2×#103C22×C13711yescharacteristic, complemented
526C2×#102C22×C13711yescharacteristic
527C2×#102C22×C13711yescharacteristic
528C2×#102C22×C13711yescharacteristic
529C2×#102C22×C13711yescharacteristic
530C2×#102C22×C13711yescharacteristic
531C2×#102C22×C13711yescharacteristic
532C2×#102C22×C13711yescharacteristic, complemented
533C2×#102C22×C13711yescharacteristic, complemented
534C2×#102C22×C13711yescharacteristic, complemented
535C2×C22⋊C8C22×C13711yescharacteristic
536C2×C22⋊C8C22×C13711yescharacteristic
537#390—21no—
538#390C22×C13711yescharacteristic, complemented
539#389C22×C13711yescharacteristic, complemented
540#388—21no—
541#386—21no—
542#385—21no—
543#380C22×C13711yescharacteristic
544C4×C4⋊C4C22×C13711yescharacteristic, complemented
545#336C22×C13711yescharacteristic, complemented
546#336C22×C13711yescharacteristic, complemented
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C23×C13711yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—22no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4C23×C13711yescharacteristic
569C22×D4C23×C13711yescharacteristic
570C22×D4C23×C13711yescharacteristic
571C22×D4C23×C13711yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C13711yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—41no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C22×C8C23×C13711yescharacteristic
588C22×C8C23×C13711yescharacteristic
589C22×C8C23×C13711yescharacteristic
590C22×C8C23×C13711yescharacteristic
591#127—22no—
592#127—22no—
593#127—22no—
594#127D4×C13714yescomplemented
595#124—22no—
596#124—22no—
597#124—22no—
598#124D4×C13714yescomplemented
599#121—28no—
600#121—28no—
601#121—22no—
602#121D4×C13714yescomplemented
603#120—28no—
604#120—28no—
605C4×D4—22no—
606C4×D4—22no—
607#117—22no—
608#117—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4D4×C13711yescharacteristic
611C2×C4⋊C4D4×C13711yescharacteristic
612C2×C4⋊C4C23×C13711yescharacteristic
613C2×C4⋊C4C23×C13711yescharacteristic
614C2×C4⋊C4C23×C13711yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4D4×C13711yescharacteristic
625C2×C22⋊C4D4×C13711yescharacteristic
626C2×C42—21no—
627C2×C42C23×C13711yescharacteristic
628C2×C42C23×C13711yescharacteristic
629C4⋊C8—22no—
630C4⋊C8—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641#102—41no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—42no—
654C24—42no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24—81no—
659C24C2×D4×C13711yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8C2×D4×C13712yes—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4C2×D4×C13712yes—
716C2×D4C2×D4×C13712yes—
717C2×D4C2×D4×C13712yes—
718C2×D4C2×D4×C13712yes—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4C2×D4×C13711yescharacteristic
734C22×C4C2×D4×C13711yescharacteristic
735C22×C4C2×D4×C13711yescharacteristic
736C22×C4C2×D4×C13711yescharacteristic
737C22×C4C2×D4×C13711yescharacteristic
738C22×C4C2×D4×C13712yes—
739C22×C4#41×C13712yes—
740C22×C4C24×C13711yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744D8—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—81no—
765C4⋊C4C2×D4×C13712yes—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—24no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C42—21no—
778C42—21no—
779C42—81no—
780C42C2×D4×C13712yes—
781C42C2×D4×C13712yes—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—48no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23#121×C13712yes—
824C23C22×D4×C13711yescharacteristic
825Q8—22no—
826Q8—22no—
827Q8—41no—
828Q8—41no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—48no—
838D4—48no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4—84no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—48no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—84no—
882C2×C4#120×C13712yes—
883C2×C4#120×C13712yes—
884C2×C4#121×C13712yes—
885C2×C4C22×D4×C13711yescharacteristic
886C2×C4C22×D4×C13711yescharacteristic
887C2×C4C22×D4×C13711yescharacteristic
888C2×C4C2×#41×C13711yescharacteristic
889C2×C4H(5,𝔽2)×C13711yescharacteristic
890C2×C4H(5,𝔽2)×C13711yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—816no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C13711yescharacteristic
932C22C2×#121×C13711yescharacteristic
933C22#535×C13711yescharacteristic
934C22#576×C13711yescharacteristic
935C22#576×C13711yescharacteristic
936C22#576×C13711yescharacteristic
937C22#577×C13711yescharacteristic
938C4—22no—
939C4—22no—
940C4—22no—
941C4—42no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—81no—
946C4—81no—
947C4D42×C13711yescharacteristic
948C4D42×C13711yescharacteristic
949C4#546×C13711yescharacteristic
950C4#546×C13711yescharacteristic
951C2—42no—
952C2—82no—
953C2—82no—
954C2—82no—
955C2—82no—
956C2#2408×C13711yescharacteristic
957C2#3008×C13711yescharacteristic
958C2#3012×C13711yescharacteristic
959C2#3041×C13711yescharacteristic
960C2#3045×C13711yescharacteristic
961C2#3220×C13711yescharacteristic
962C2#3224×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×#117×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#535×C137C2semidirect
2. C2×#463×C137C2semidirect
3. C2×#459×C137C2semidirect
4. C2×#449×C137C2semidirect
5. C2×#447×C137C2semidirect
6. #2324×C137C2semidirect
7. #2042×C137C2semidirect
8. #2041×C137C2semidirect
9. #2012×C137C2semidirect
10. #2011×C137C2semidirect
11. #1983×C137C2semidirect
12. #1982×C137C2semidirect
13. #1798×C137C2semidirect
14. #1788×C137C2semidirect
15. #1786×C137C2semidirect
18. C22×SD16×C137C22semidirect
21. C22×D8×C137C22semidirect
33. C2×C4×D4×C137C22semidirect
39. C2×C4⋊C8×C137C22semidirect
40. C2×C4⋊C8×C137C22semidirect
41. C2×#103×C137C22semidirect
42. C2×#103×C137C22semidirect
43. C2×#103×C137C22semidirect
50. C2×#102×C137C22semidirect
51. C2×#102×C137C22semidirect
52. C2×#102×C137C22semidirect
56. #390×C137C22semidirect
57. #389×C137C22semidirect
62. C4×C4⋊C4×C137C22semidirect
63. #336×C137C22semidirect
64. #336×C137C22semidirect
112. #127×C137D4semidirect
116. #124×C137D4semidirect
120. #121×C137D4semidirect
481. #24218C137direct (N × H)
482. C137#24218direct (N × H)
483. C2×#535C2×C137semidirect
484. C2×#463C2×C137semidirect
485. C2×#459C2×C137semidirect
486. C2×#449C2×C137semidirect
487. C2×#447C2×C137semidirect
488. #2324C2×C137semidirect
489. #2042C2×C137semidirect
490. #2041C2×C137semidirect
491. #2012C2×C137semidirect
492. #2011C2×C137semidirect
493. #1983C2×C137semidirect
494. #1982C2×C137semidirect
495. #1798C2×C137semidirect
496. #1788C2×C137semidirect
497. #1786C2×C137semidirect
500. C22×SD16C22×C137semidirect
503. C22×D8C22×C137semidirect
515. C2×C4×D4C22×C137semidirect
521. C2×C4⋊C8C22×C137semidirect
522. C2×C4⋊C8C22×C137semidirect
523. C2×#103C22×C137semidirect
524. C2×#103C22×C137semidirect
525. C2×#103C22×C137semidirect
532. C2×#102C22×C137semidirect
533. C2×#102C22×C137semidirect
534. C2×#102C22×C137semidirect
538. #390C22×C137semidirect
539. #389C22×C137semidirect
544. C4×C4⋊C4C22×C137semidirect
545. #336C22×C137semidirect
546. #336C22×C137semidirect
594. #127D4×C137semidirect
598. #124D4×C137semidirect
602. #121D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1372
C2×#463×C1372
C2×#459×C1372
C2×#449×C1372
C2×#447×C1372
#2324×C1372
#2042×C1372
#2041×C1372
#2012×C1372
#2011×C1372
#1983×C1372
#1982×C1372
#1798×C1372
#1788×C1372
#1786×C1372
#24218137