Finite Group Databasebeta

← C137×#24220 #46873606

Subgroups — C137×#24220 #46873606

Order 35072.

1556 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C137C211yesmaximal, characteristic
2C2×#464×C137C211yesmaximal, characteristic, complemented
3C2×#460×C137C211yesmaximal, characteristic, complemented
4C2×#452×C137C211yesmaximal, characteristic, complemented
5C2×#450×C137C211yesmaximal, characteristic, complemented
6#2323×C137C211yesmaximal, characteristic, complemented
7#2042×C137C211yesmaximal, characteristic, complemented
8#2041×C137C211yesmaximal, characteristic, complemented
9#2015×C137C211yesmaximal, characteristic, complemented
10#2014×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×Q16×C137C2211yescharacteristic, complemented
19C22×SD16×C137C2211yescharacteristic
20C22×SD16×C137C2211yescharacteristic
21C22×SD16×C137C2211yescharacteristic, complemented
22#535×C137—24no—
23#535×C137—24no—
24C2×#127×C137C2211yescharacteristic
25C2×#127×C137C2211yescharacteristic
26C2×#124×C137C2211yescharacteristic
27C2×#124×C137C2211yescharacteristic
28C2×C22⋊Q8×C137C2211yescharacteristic
29C2×#121×C137—21no—
30C2×#121×C137—21no—
31C2×#120×C137—21no—
32C2×#120×C137—21no—
33C2×C4×Q8×C137C2211yescharacteristic, complemented
34C2×#117×C137C2211yescharacteristic
35#464×C137—24no—
36#460×C137—24no—
37#452×C137—24no—
38#450×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#391×C137C2211yescharacteristic, complemented
56#389×C137—21no—
57#389×C137C2211yescharacteristic, complemented
58#388×C137—21no—
59#388×C137—21no—
60#387×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×Q8×C137C2311yescharacteristic
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
89C23×C4×C137—21no—
90C23×C4×C137C2311yescharacteristic
91C2×Q16×C137—22no—
92C2×Q16×C137—22no—
93C2×Q16×C137—41no—
94C2×SD16×C137—22no—
95C2×SD16×C137—22no—
96C2×SD16×C137—22no—
97C2×SD16×C137—22no—
98C2×SD16×C137—22no—
99C2×SD16×C137—22no—
100C2×SD16×C137—41no—
101C2×SD16×C137—41no—
102C2×SD16×C137—41no—
103C22×C8×C137C2311yescharacteristic
104C22×C8×C137C2311yescharacteristic
105C22×C8×C137C2311yescharacteristic
106C22×C8×C137C2311yescharacteristic
107#127×C137—22no—
108#127×C137—22no—
109#127×C137—22no—
110#127×C137D414yes—
111#124×C137—22no—
112#124×C137—22no—
113#124×C137—22no—
114#124×C137D414yes—
115C22⋊Q8×C137—22no—
116C22⋊Q8×C137D414yescomplemented
117#121×C137—28no—
118#121×C137—28no—
119#120×C137—28no—
120#120×C137—28no—
121C4×Q8×C137—22no—
122C4×Q8×C137—22no—
123#117×C137—22no—
124#117×C137—22no—
125C2×C4⋊C4×C137—21no—
126C2×C4⋊C4×C137—21no—
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×C137D411yescharacteristic
140C2×C22⋊C4×C137D411yescharacteristic
141C2×C42×C137—21no—
142C2×C42×C137—21no—
143C2×C42×C137C2311yescharacteristic
144C2×C42×C137C2311yescharacteristic
145C4⋊C8×C137—22no—
146C4⋊C8×C137—22no—
147#103×C137—22no—
148#103×C137—22no—
149#103×C137—41no—
150#102×C137—22no—
151#102×C137—22no—
152#102×C137—22no—
153#102×C137—22no—
154#102×C137—22no—
155#102×C137—22no—
156#102×C137—41no—
157#102×C137—41no—
158#102×C137—41no—
159C22⋊C8×C137—22no—
160C22⋊C8×C137—22no—
161#95×C137—21no—
162#95×C137—21no—
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—42no—
171C24×C137—42no—
172C24×C137—81no—
173C24×C137—81no—
174C24×C137—81no—
175C24×C137—81no—
176C24×C137C2×D411yescharacteristic
177#41×C137—44no—
178#41×C137—44no—
179#41×C137—44no—
180#41×C137—44no—
181C2×Q8×C137—21no—
182C2×Q8×C137—21no—
183C2×Q8×C137—21no—
184C2×Q8×C137—21no—
185C2×Q8×C137—21no—
186C2×Q8×C137—21no—
187C2×Q8×C137—21no—
188C2×Q8×C137—21no—
189C2×Q8×C137—21no—
190C2×Q8×C137—21no—
191C2×Q8×C137C2×D412yes—
192C2×Q8×C137C2×D412yes—
193C2×D4×C137—24no—
194C2×D4×C137—24no—
195C2×D4×C137—24no—
196C2×D4×C137—24no—
197C2×D4×C137—24no—
198C2×D4×C137—24no—
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—44no—
215C2×D4×C137—44no—
216C2×D4×C137—44no—
217C2×D4×C137—44no—
218C2×D4×C137—42no—
219C2×D4×C137—42no—
220C2×D4×C137—42no—
221C2×D4×C137—42no—
222C2×D4×C137—81no—
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×C137C2×D412yes—
231C2×D4×C137C2×D412yes—
232C2×D4×C137C2×D412yes—
233C22×C4×C137—21no—
234C22×C4×C137—21no—
235C22×C4×C137—21no—
236C22×C4×C137—21no—
237C22×C4×C137—24no—
238C22×C4×C137—21no—
239C22×C4×C137—21no—
240C22×C4×C137—21no—
241C22×C4×C137—21no—
242C22×C4×C137—21no—
243C22×C4×C137—42no—
244C22×C4×C137—42no—
245C22×C4×C137C2×D411yescharacteristic
246C22×C4×C137C2×D411yescharacteristic
247C22×C4×C137C2×D411yescharacteristic
248C22×C4×C137C2×D411yescharacteristic
249C22×C4×C137C2×D411yescharacteristic
250C22×C4×C137C2×D412yes—
251C22×C4×C137#4112yes—
252C22×C4×C137C2411yescharacteristic
253Q16×C137—44no—
254SD16×C137—44no—
255SD16×C137—44no—
256SD16×C137—44no—
257C2×C8×C137—21no—
258C2×C8×C137—21no—
259C2×C8×C137—21no—
260C2×C8×C137—21no—
261C2×C8×C137—21no—
262C2×C8×C137—21no—
263C2×C8×C137—21no—
264C2×C8×C137—21no—
265C2×C8×C137—21no—
266C2×C8×C137—21no—
267C2×C8×C137—21no—
268C2×C8×C137—21no—
269C4⋊C4×C137—22no—
270C4⋊C4×C137—22no—
271C4⋊C4×C137—24no—
272C4⋊C4×C137—21no—
273C4⋊C4×C137—21no—
274C4⋊C4×C137—21no—
275C4⋊C4×C137—21no—
276C4⋊C4×C137—21no—
277C4⋊C4×C137—42no—
278C4⋊C4×C137—81no—
279C4⋊C4×C137C2×D412yes—
280C22⋊C4×C137—24no—
281C22⋊C4×C137—24no—
282C22⋊C4×C137—24no—
283C22⋊C4×C137—24no—
284C22⋊C4×C137—24no—
285C22⋊C4×C137—22no—
286C22⋊C4×C137—22no—
287C22⋊C4×C137—81no—
288C42×C137—21no—
289C42×C137—21no—
290C42×C137—42no—
291C42×C137—81no—
292C42×C137C2×D412yes—
293C42×C137C2×D412yes—
294C23×C137—21no—
295C23×C137—21no—
296C23×C137—21no—
297C23×C137—21no—
298C23×C137—21no—
299C23×C137—21no—
300C23×C137—22no—
301C23×C137—22no—
302C23×C137—22no—
303C23×C137—48no—
304C23×C137—41no—
305C23×C137—41no—
306C23×C137—41no—
307C23×C137—41no—
308C23×C137—41no—
309C23×C137—41no—
310C23×C137—41no—
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—84no—
323C23×C137—84no—
324C23×C137—84no—
325C23×C137—84no—
326C23×C137—84no—
327C23×C137—84no—
328C23×C137#12112yes—
329C23×C137C22×D411yescharacteristic
330Q8×C137—22no—
331Q8×C137—22no—
332Q8×C137—22no—
333Q8×C137—22no—
334Q8×C137—41no—
335Q8×C137—41no—
336Q8×C137—41no—
337Q8×C137—41no—
338D4×C137—22no—
339D4×C137—22no—
340D4×C137—22no—
341D4×C137—22no—
342D4×C137—22no—
343D4×C137—22no—
344D4×C137—48no—
345D4×C137—48no—
346D4×C137—41no—
347D4×C137—41no—
348D4×C137—41no—
349D4×C137—41no—
350D4×C137—41no—
351D4×C137—41no—
352D4×C137—84no—
353D4×C137—84no—
354D4×C137—84no—
355D4×C137—84no—
356C2×C4×C137—21no—
357C2×C4×C137—21no—
358C2×C4×C137—21no—
359C2×C4×C137—21no—
360C2×C4×C137—21no—
361C2×C4×C137—21no—
362C2×C4×C137—22no—
363C2×C4×C137—22no—
364C2×C4×C137—22no—
365C2×C4×C137—22no—
366C2×C4×C137—21no—
367C2×C4×C137—21no—
368C2×C4×C137—22no—
369C2×C4×C137—22no—
370C2×C4×C137—22no—
371C2×C4×C137—21no—
372C2×C4×C137—21no—
373C2×C4×C137—21no—
374C2×C4×C137—21no—
375C2×C4×C137—48no—
376C2×C4×C137—41no—
377C2×C4×C137—41no—
378C2×C4×C137—41no—
379C2×C4×C137—41no—
380C2×C4×C137—41no—
381C2×C4×C137—41no—
382C2×C4×C137—41no—
383C2×C4×C137—41no—
384C2×C4×C137—41no—
385C2×C4×C137—41no—
386C2×C4×C137—41no—
387C2×C4×C137—41no—
388C2×C4×C137#12012yes—
389C2×C4×C137#12012yes—
390C2×C4×C137#12112yes—
391C2×C4×C137C22×D411yescharacteristic
392C2×C4×C137C22×D411yescharacteristic
393C2×C4×C137C22×D411yescharacteristic
394C2×C4×C137C2×#4111yescharacteristic
395C2×C4×C137H(5,𝔽2)11yescharacteristic
396C2×C4×C137H(5,𝔽2)11yescharacteristic
397C8×C137—41no—
398C8×C137—41no—
399C8×C137—41no—
400C8×C137—41no—
401C22×C137—22no—
402C22×C137—22no—
403C22×C137—22no—
404C22×C137—41no—
405C22×C137—41no—
406C22×C137—41no—
407C22×C137—41no—
408C22×C137—42no—
409C22×C137—42no—
410C22×C137—42no—
411C22×C137—42no—
412C22×C137—42no—
413C22×C137—42no—
414C22×C137—42no—
415C22×C137—42no—
416C22×C137—42no—
417C22×C137—816no—
418C22×C137—81no—
419C22×C137—81no—
420C22×C137—81no—
421C22×C137—81no—
422C22×C137—81no—
423C22×C137—81no—
424C22×C137—81no—
425C22×C137—81no—
426C22×C137—81no—
427C22×C137—81no—
428C22×C137—81no—
429C22×C137—81no—
430C22×C137C2×#12011yescharacteristic
431C22×C137C2×#12111yescharacteristic
432C22×C137#53511yescharacteristic
433C22×C137#57611yescharacteristic
434C22×C137#57711yescharacteristic
435C22×C137#57711yescharacteristic
436C22×C137#57711yescharacteristic
437C4×C137—22no—
438C4×C137—22no—
439C4×C137—22no—
440C4×C137—42no—
441C4×C137—42no—
442C4×C137—41no—
443C4×C137—41no—
444C4×C137—42no—
445C4×C137—81no—
446C4×C137—81no—
447C4×C137D4211yescharacteristic
448C4×C137D4211yescharacteristic
449C4×C137#54611yescharacteristic
450C4×C137#54611yescharacteristic
451C2×C137—42no—
452C2×C137—82no—
453C2×C137—82no—
454C2×C137—82no—
455C2×C137#240811yescharacteristic
456C2×C137#300911yescharacteristic
457C2×C137#301211yescharacteristic
458C2×C137#304311yescharacteristic
459C2×C137#304511yescharacteristic
460C2×C137#322211yescharacteristic
461C2×C137#322411yescharacteristic
462#24220C13711yesmaximal, characteristic, direct product factor, Sylow
463C137#2422011yescharacteristic, direct product factor, Sylow
464C2×#535C2×C13711yescharacteristic
465C2×#464C2×C13711yescharacteristic, complemented
466C2×#460C2×C13711yescharacteristic, complemented
467C2×#452C2×C13711yescharacteristic, complemented
468C2×#450C2×C13711yescharacteristic, complemented
469#2323C2×C13711yescharacteristic, complemented
470#2042C2×C13711yescharacteristic, complemented
471#2041C2×C13711yescharacteristic, complemented
472#2015C2×C13711yescharacteristic, complemented
473#2014C2×C13711yescharacteristic, complemented
474#1983C2×C13711yescharacteristic, complemented
475#1982C2×C13711yescharacteristic, complemented
476#1798C2×C13711yescharacteristic, complemented
477#1788C2×C13711yescharacteristic, complemented
478#1786C2×C13711yescharacteristic, complemented
479C22×#41C22×C13711yescharacteristic
480C23×D4C22×C13711yescharacteristic
481C22×Q16C22×C13711yescharacteristic, complemented
482C22×SD16C22×C13711yescharacteristic
483C22×SD16C22×C13711yescharacteristic
484C22×SD16C22×C13711yescharacteristic, complemented
485#535—24no—
486#535—24no—
487C2×#127C22×C13711yescharacteristic
488C2×#127C22×C13711yescharacteristic
489C2×#124C22×C13711yescharacteristic
490C2×#124C22×C13711yescharacteristic
491C2×C22⋊Q8C22×C13711yescharacteristic
492C2×#121—21no—
493C2×#121—21no—
494C2×#120—21no—
495C2×#120—21no—
496C2×C4×Q8C22×C13711yescharacteristic, complemented
497C2×#117C22×C13711yescharacteristic
498#464—24no—
499#460—24no—
500#452—24no—
501#450—24no—
502C2×C4⋊C8C22×C13711yescharacteristic, complemented
503C2×C4⋊C8C22×C13711yescharacteristic, complemented
504C2×#103C22×C13711yescharacteristic, complemented
505C2×#103C22×C13711yescharacteristic, complemented
506C2×#103C22×C13711yescharacteristic, complemented
507C2×#102C22×C13711yescharacteristic
508C2×#102C22×C13711yescharacteristic
509C2×#102C22×C13711yescharacteristic
510C2×#102C22×C13711yescharacteristic
511C2×#102C22×C13711yescharacteristic
512C2×#102C22×C13711yescharacteristic
513C2×#102C22×C13711yescharacteristic, complemented
514C2×#102C22×C13711yescharacteristic, complemented
515C2×#102C22×C13711yescharacteristic, complemented
516C2×C22⋊C8C22×C13711yescharacteristic
517C2×C22⋊C8C22×C13711yescharacteristic
518#391C22×C13711yescharacteristic, complemented
519#389—21no—
520#389C22×C13711yescharacteristic, complemented
521#388—21no—
522#388—21no—
523#387—21no—
524#380C22×C13711yescharacteristic
525C4×C4⋊C4C22×C13711yescharacteristic, complemented
526#336C22×C13711yescharacteristic, complemented
527#336C22×C13711yescharacteristic, complemented
528C25—21no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—41no—
534C2×#41—41no—
535C22×Q8C23×C13711yescharacteristic
536C22×Q8C23×C13711yescharacteristic
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—41no—
548C22×D4—41no—
549C22×D4C23×C13711yescharacteristic
550C22×D4C23×C13711yescharacteristic
551C22×D4C23×C13711yescharacteristic
552C23×C4—21no—
553C23×C4C23×C13711yescharacteristic
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—41no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C22×C8C23×C13711yescharacteristic
567C22×C8C23×C13711yescharacteristic
568C22×C8C23×C13711yescharacteristic
569C22×C8C23×C13711yescharacteristic
570#127—22no—
571#127—22no—
572#127—22no—
573#127D4×C13714yes—
574#124—22no—
575#124—22no—
576#124—22no—
577#124D4×C13714yes—
578C22⋊Q8—22no—
579C22⋊Q8D4×C13714yescomplemented
580#121—28no—
581#121—28no—
582#120—28no—
583#120—28no—
584C4×Q8—22no—
585C4×Q8—22no—
586#117—22no—
587#117—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4D4×C13711yescharacteristic
592C2×C4⋊C4D4×C13711yescharacteristic
593C2×C4⋊C4C23×C13711yescharacteristic
594C2×C4⋊C4C23×C13711yescharacteristic
595C2×C4⋊C4C23×C13711yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4D4×C13711yescharacteristic
603C2×C22⋊C4D4×C13711yescharacteristic
604C2×C42—21no—
605C2×C42—21no—
606C2×C42C23×C13711yescharacteristic
607C2×C42C23×C13711yescharacteristic
608C4⋊C8—22no—
609C4⋊C8—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—22no—
619#102—41no—
620#102—41no—
621#102—41no—
622C22⋊C8—22no—
623C22⋊C8—22no—
624#95—21no—
625#95—21no—
626#95—21no—
627#95—21no—
628#95—21no—
629C24—24no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—81no—
636C24—81no—
637C24—81no—
638C24—81no—
639C24C2×D4×C13711yescharacteristic
640#41—44no—
641#41—44no—
642#41—44no—
643#41—44no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8C2×D4×C13712yes—
655C2×Q8C2×D4×C13712yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—81no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4—81no—
690C2×D4—81no—
691C2×D4—81no—
692C2×D4—81no—
693C2×D4C2×D4×C13712yes—
694C2×D4C2×D4×C13712yes—
695C2×D4C2×D4×C13712yes—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—24no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4C2×D4×C13711yescharacteristic
709C22×C4C2×D4×C13711yescharacteristic
710C22×C4C2×D4×C13711yescharacteristic
711C22×C4C2×D4×C13711yescharacteristic
712C22×C4C2×D4×C13711yescharacteristic
713C22×C4C2×D4×C13712yes—
714C22×C4#41×C13712yes—
715C22×C4C24×C13711yescharacteristic
716Q16—44no—
717SD16—44no—
718SD16—44no—
719SD16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—42no—
741C4⋊C4—81no—
742C4⋊C4C2×D4×C13712yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—81no—
751C42—21no—
752C42—21no—
753C42—42no—
754C42—81no—
755C42C2×D4×C13712yes—
756C42C2×D4×C13712yes—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—48no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#121×C13712yes—
792C23C22×D4×C13711yescharacteristic
793Q8—22no—
794Q8—22no—
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—84no—
816D4—84no—
817D4—84no—
818D4—84no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—48no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4#120×C13712yes—
852C2×C4#120×C13712yes—
853C2×C4#121×C13712yes—
854C2×C4C22×D4×C13711yescharacteristic
855C2×C4C22×D4×C13711yescharacteristic
856C2×C4C22×D4×C13711yescharacteristic
857C2×C4C2×#41×C13711yescharacteristic
858C2×C4H(5,𝔽2)×C13711yescharacteristic
859C2×C4H(5,𝔽2)×C13711yescharacteristic
860C8—41no—
861C8—41no—
862C8—41no—
863C8—41no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—816no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22C2×#120×C13711yescharacteristic
894C22C2×#121×C13711yescharacteristic
895C22#535×C13711yescharacteristic
896C22#576×C13711yescharacteristic
897C22#577×C13711yescharacteristic
898C22#577×C13711yescharacteristic
899C22#577×C13711yescharacteristic
900C4—22no—
901C4—22no—
902C4—22no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—41no—
907C4—41no—
908C4—81no—
909C4—81no—
910C4D42×C13711yescharacteristic
911C4D42×C13711yescharacteristic
912C4#546×C13711yescharacteristic
913C4#546×C13711yescharacteristic
914C2—42no—
915C2—82no—
916C2—82no—
917C2—82no—
918C2#2408×C13711yescharacteristic
919C2#3009×C13711yescharacteristic
920C2#3012×C13711yescharacteristic
921C2#3043×C13711yescharacteristic
922C2#3045×C13711yescharacteristic
923C2#3222×C13711yescharacteristic
924C2#3224×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC2×#535×C137C2
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
2. C2×#464×C137C2semidirect
3. C2×#460×C137C2semidirect
4. C2×#452×C137C2semidirect
5. C2×#450×C137C2semidirect
6. #2323×C137C2semidirect
7. #2042×C137C2semidirect
8. #2041×C137C2semidirect
9. #2015×C137C2semidirect
10. #2014×C137C2semidirect
11. #1983×C137C2semidirect
12. #1982×C137C2semidirect
13. #1798×C137C2semidirect
14. #1788×C137C2semidirect
15. #1786×C137C2semidirect
18. C22×Q16×C137C22semidirect
21. C22×SD16×C137C22semidirect
33. C2×C4×Q8×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
55. #391×C137C22semidirect
57. #389×C137C22semidirect
62. C4×C4⋊C4×C137C22semidirect
63. #336×C137C22semidirect
64. #336×C137C22semidirect
116. C22⋊Q8×C137D4semidirect
462. #24220C137direct (N × H)
463. C137#24220direct (N × H)
465. C2×#464C2×C137semidirect
466. C2×#460C2×C137semidirect
467. C2×#452C2×C137semidirect
468. C2×#450C2×C137semidirect
469. #2323C2×C137semidirect
470. #2042C2×C137semidirect
471. #2041C2×C137semidirect
472. #2015C2×C137semidirect
473. #2014C2×C137semidirect
474. #1983C2×C137semidirect
475. #1982C2×C137semidirect
476. #1798C2×C137semidirect
477. #1788C2×C137semidirect
478. #1786C2×C137semidirect
481. C22×Q16C22×C137semidirect
484. C22×SD16C22×C137semidirect
496. C2×C4×Q8C22×C137semidirect
502. C2×C4⋊C8C22×C137semidirect
503. C2×C4⋊C8C22×C137semidirect
504. C2×#103C22×C137semidirect
505. C2×#103C22×C137semidirect
506. C2×#103C22×C137semidirect
513. C2×#102C22×C137semidirect
514. C2×#102C22×C137semidirect
515. C2×#102C22×C137semidirect
518. #391C22×C137semidirect
520. #389C22×C137semidirect
525. C4×C4⋊C4C22×C137semidirect
526. #336C22×C137semidirect
527. #336C22×C137semidirect
579. C22⋊Q8D4×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×#464×C1372
C2×#460×C1372
C2×#452×C1372
C2×#450×C1372
#2323×C1372
#2042×C1372
#2041×C1372
#2015×C1372
#2014×C1372
#1983×C1372
#1982×C1372
#1798×C1372
#1788×C1372
#1786×C1372
#24220137