Finite Group Databasebeta

← C137×#24438 #46873824

Subgroups — C137×#24438 #46873824

Order 35072.

1498 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C137C211yesmaximal, characteristic, complemented
2C2×#465×C137C211yesmaximal, characteristic, complemented
3C2×#449×C137C211yesmaximal, characteristic, complemented
4C2×#449×C137C211yesmaximal, characteristic, complemented
5C2×#416×C137C211yesmaximal, characteristic, complemented
6#2414×C137C211yesmaximal, characteristic, complemented
7#2043×C137C211yesmaximal, characteristic, complemented
8#2035×C137C211yesmaximal, characteristic, complemented
9#2013×C137C211yesmaximal, characteristic, complemented
10#2000×C137C211yesmaximal, characteristic, complemented
11#1879×C137C211yesmaximal, characteristic, complemented
12#1873×C137C211yesmaximal, characteristic, complemented
13#1869×C137C211yesmaximal, characteristic, complemented
14#1864×C137C211yesmaximal, characteristic, complemented
15#1788×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C22×#41×C137C2211yescharacteristic
18C22×SD16×C137C2211yescharacteristic
19C22×SD16×C137C2211yescharacteristic
20C22×D8×C137C2211yescharacteristic
21C23×C8×C137C2211yescharacteristic
22#547×C137—24no—
23#547×C137—24no—
24C2×C4⋊Q8×C137C2211yescharacteristic
25C2×#123×C137—21no—
26C2×#123×C137—21no—
27C2×C22⋊Q8×C137C2211yescharacteristic
28C2×C22⋊Q8×C137C2211yescharacteristic
29C2×#121×C137—21no—
30C2×#121×C137C2211yescharacteristic
31C2×#121×C137C2211yescharacteristic
32C2×C4×D4×C137C2211yescharacteristic
33C2×C4×D4×C137C2211yescharacteristic
34C2×#117×C137C2211yescharacteristic
35C22×C4⋊C4×C137—21no—
36#465×C137—24no—
37#449×C137—24no—
38#449×C137—24no—
39C2×#106×C137C2211yescharacteristic
40#416×C137—24no—
41C2×#103×C137C2211yescharacteristic
42C2×#103×C137C2211yescharacteristic
43C2×#103×C137C2211yescharacteristic
44C2×#103×C137C2211yescharacteristic
45C2×#103×C137C2211yescharacteristic
46C2×#103×C137C2211yescharacteristic
47C2×#102×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic
49C2×#102×C137C2211yescharacteristic
50C2×#102×C137C2211yescharacteristic
51C2×C22⋊C8×C137C2211yescharacteristic
52C2×C22⋊C8×C137C2211yescharacteristic
53C2×C22⋊C8×C137C2211yescharacteristic
54#394×C137—21no—
55#392×C137—21no—
56#390×C137—21no—
57#390×C137C2211yescharacteristic
58#389×C137C2211yescharacteristic
59#388×C137—21no—
60#380×C137C2211yescharacteristic
61#340×C137C2211yescharacteristic
62#340×C137C2211yescharacteristic
63#336×C137C2211yescharacteristic
64#336×C137C2211yescharacteristic
65C2×#41×C137—22no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—22no—
69C2×#41×C137—22no—
70C2×#41×C137—22no—
71C2×#41×C137—22no—
72C2×#41×C137—41no—
73C2×#41×C137—41no—
74C2×#41×C137—41no—
75C2×#41×C137—41no—
76C2×#41×C137D414yescomplemented
77C22×Q8×C137C2311yescharacteristic
78C22×Q8×C137C2311yescharacteristic
79C22×D4×C137—21no—
80C22×D4×C137—21no—
81C22×D4×C137—21no—
82C22×D4×C137—21no—
83C22×D4×C137D411yescharacteristic
84C22×D4×C137C2311yescharacteristic
85C22×D4×C137C2311yescharacteristic
86C23×C4×C137—21no—
87C23×C4×C137—21no—
88C23×C4×C137—21no—
89C23×C4×C137C2311yescharacteristic
90C23×C4×C137C2311yescharacteristic
91C2×SD16×C137—22no—
92C2×SD16×C137—22no—
93C2×SD16×C137—22no—
94C2×SD16×C137—41no—
95C2×SD16×C137—41no—
96C2×SD16×C137—41no—
97C2×D8×C137—22no—
98C2×D8×C137—22no—
99C2×D8×C137—22no—
100C22×C8×C137—22no—
101C22×C8×C137—22no—
102C22×C8×C137—41no—
103C22×C8×C137C2311yescharacteristic
104C22×C8×C137C2311yescharacteristic
105C22×C8×C137C2311yescharacteristic
106C22×C8×C137C2311yescharacteristic
107C4⋊Q8×C137—22no—
108C4⋊Q8×C137—22no—
109#123×C137—28no—
110#123×C137—28no—
111C22⋊Q8×C137—22no—
112C22⋊Q8×C137—22no—
113C22⋊Q8×C137—22no—
114C22⋊Q8×C137D414yescomplemented
115#121×C137—28no—
116#121×C137—22no—
117#121×C137—22no—
118#121×C137—22no—
119#121×C137—41no—
120C4×D4×C137—22no—
121C4×D4×C137—22no—
122C4×D4×C137—22no—
123C4×D4×C137—22no—
124#117×C137—22no—
125#117×C137—41no—
126C2×C4⋊C4×C137—28no—
127C2×C4⋊C4×C137—21no—
128C2×C4⋊C4×C137—21no—
129C2×C4⋊C4×C137—21no—
130C2×C4⋊C4×C137—21no—
131C2×C4⋊C4×C137—21no—
132C2×C4⋊C4×C137D411yescharacteristic
133C2×C4⋊C4×C137C2311yescharacteristic
134C2×C4⋊C4×C137C2311yescharacteristic
135C2×C4⋊C4×C137C2311yescharacteristic
136C2×C4⋊C4×C137C2311yescharacteristic
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×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#106×C137—22no—
151#103×C137—22no—
152#103×C137—22no—
153#103×C137—22no—
154#103×C137—22no—
155#103×C137—22no—
156#103×C137—41no—
157#102×C137—22no—
158#102×C137—22no—
159#102×C137—22no—
160#102×C137D414yescomplemented
161C22⋊C8×C137—22no—
162C22⋊C8×C137—22no—
163C22⋊C8×C137—41no—
164#95×C137—21no—
165#95×C137—21no—
166C24×C137—21no—
167C24×C137—21no—
168C24×C137C2×D411yescharacteristic
169C24×C137C2×D411yescharacteristic
170#41×C137—28no—
171#41×C137—44no—
172#41×C137—44no—
173#41×C137—44no—
174#41×C137—44no—
175#41×C137—44no—
176#41×C137—44no—
177#41×C137—44no—
178C2×Q8×C137—21no—
179C2×Q8×C137—21no—
180C2×Q8×C137—21no—
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×C137C2×D412yes—
189C2×Q8×C137C2×D412yes—
190C2×D4×C137—24no—
191C2×D4×C137—22no—
192C2×D4×C137—24no—
193C2×D4×C137—22no—
194C2×D4×C137—21no—
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—41no—
204C2×D4×C137—42no—
205C2×D4×C137—42no—
206C2×D4×C137—42no—
207C2×D4×C137—42no—
208C2×D4×C137—42no—
209C2×D4×C137—42no—
210C2×D4×C137—42no—
211C2×D4×C137—81no—
212C2×D4×C137—81no—
213C2×D4×C137—81no—
214C2×D4×C137C2×D412yes—
215C2×D4×C137C2×D412yes—
216C2×D4×C137#4112yes—
217C22×C4×C137—21no—
218C22×C4×C137—21no—
219C22×C4×C137—21no—
220C22×C4×C137—21no—
221C22×C4×C137—24no—
222C22×C4×C137—24no—
223C22×C4×C137—21no—
224C22×C4×C137—21no—
225C22×C4×C137—21no—
226C22×C4×C137—21no—
227C22×C4×C137—24no—
228C22×C4×C137—21no—
229C22×C4×C137—21no—
230C22×C4×C137—21no—
231C22×C4×C137—21no—
232C22×C4×C137—21no—
233C22×C4×C137—21no—
234C22×C4×C137—21no—
235C22×C4×C137—21no—
236C22×C4×C137—42no—
237C22×C4×C137—42no—
238C22×C4×C137—42no—
239C22×C4×C137—42no—
240C22×C4×C137—42no—
241C22×C4×C137—42no—
242C22×C4×C137C2×D411yescharacteristic
243C22×C4×C137C2×D411yescharacteristic
244C22×C4×C137C2×D411yescharacteristic
245C22×C4×C137C2×D412yes—
246C22×C4×C137C2×D412yes—
247C22×C4×C137C2×D411yescharacteristic
248C22×C4×C137C2411yescharacteristic
249SD16×C137—44no—
250SD16×C137—44no—
251D8×C137—44no—
252C2×C8×C137—21no—
253C2×C8×C137—21no—
254C2×C8×C137—21no—
255C2×C8×C137—21no—
256C2×C8×C137—21no—
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—44no—
264C2×C8×C137C2×D412yes—
265C4⋊C4×C137—24no—
266C4⋊C4×C137—24no—
267C4⋊C4×C137—24no—
268C4⋊C4×C137—22no—
269C4⋊C4×C137—24no—
270C4⋊C4×C137—21no—
271C4⋊C4×C137—21no—
272C4⋊C4×C137—21no—
273C4⋊C4×C137—21no—
274C4⋊C4×C137—21no—
275C4⋊C4×C137—21no—
276C4⋊C4×C137—81no—
277C4⋊C4×C137C2×D412yes—
278C4⋊C4×C137C2×D412yes—
279C22⋊C4×C137—24no—
280C22⋊C4×C137—24no—
281C22⋊C4×C137—24no—
282C22⋊C4×C137—22no—
283C22⋊C4×C137—22no—
284C22⋊C4×C137—42no—
285C22⋊C4×C137—42no—
286C22⋊C4×C137—42no—
287C22⋊C4×C137—42no—
288C22⋊C4×C137—81no—
289C22⋊C4×C137—81no—
290C42×C137—21no—
291C42×C137—21no—
292C42×C137—42no—
293C23×C137—22no—
294C23×C137—21no—
295C23×C137—22no—
296C23×C137—21no—
297C23×C137—22no—
298C23×C137—21no—
299C23×C137—21no—
300C23×C137—21no—
301C23×C137—21no—
302C23×C137—21no—
303C23×C137—21no—
304C23×C137—21no—
305C23×C137—21no—
306C23×C137—21no—
307C23×C137—21no—
308C23×C137—21no—
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#12012yes—
321C23×C137C22×D411yescharacteristic
322Q8×C137—22no—
323Q8×C137—22no—
324Q8×C137—22no—
325Q8×C137—22no—
326Q8×C137—41no—
327Q8×C137—41no—
328Q8×C137—41no—
329Q8×C137—41no—
330D4×C137—22no—
331D4×C137—22no—
332D4×C137—22no—
333D4×C137—44no—
334D4×C137—48no—
335D4×C137—48no—
336D4×C137—41no—
337D4×C137—41no—
338D4×C137—41no—
339D4×C137—41no—
340D4×C137—84no—
341D4×C137—84no—
342D4×C137#12114yes—
343C2×C4×C137—21no—
344C2×C4×C137—21no—
345C2×C4×C137—21no—
346C2×C4×C137—21no—
347C2×C4×C137—22no—
348C2×C4×C137—22no—
349C2×C4×C137—22no—
350C2×C4×C137—22no—
351C2×C4×C137—21no—
352C2×C4×C137—22no—
353C2×C4×C137—21no—
354C2×C4×C137—22no—
355C2×C4×C137—22no—
356C2×C4×C137—22no—
357C2×C4×C137—21no—
358C2×C4×C137—21no—
359C2×C4×C137—21no—
360C2×C4×C137—21no—
361C2×C4×C137—48no—
362C2×C4×C137—48no—
363C2×C4×C137—48no—
364C2×C4×C137—41no—
365C2×C4×C137—41no—
366C2×C4×C137—41no—
367C2×C4×C137—41no—
368C2×C4×C137—41no—
369C2×C4×C137—41no—
370C2×C4×C137—41no—
371C2×C4×C137—41no—
372C2×C4×C137—41no—
373C2×C4×C137—41no—
374C2×C4×C137—41no—
375C2×C4×C137—41no—
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#12012yes—
383C2×C4×C137#13512yes—
384C2×C4×C137C22×D411yescharacteristic
385C2×C4×C137C22×D411yescharacteristic
386C2×C4×C137C22×D411yescharacteristic
387C2×C4×C137C2×#4111yescharacteristic
388C2×C4×C137H(5,𝔽2)11yescharacteristic
389C2×C4×C137H(5,𝔽2)11yescharacteristic
390C8×C137—22no—
391C8×C137—41no—
392C8×C137—41no—
393C8×C137—41no—
394C22×C137—22no—
395C22×C137—24no—
396C22×C137—22no—
397C22×C137—22no—
398C22×C137—42no—
399C22×C137—42no—
400C22×C137—41no—
401C22×C137—42no—
402C22×C137—41no—
403C22×C137—42no—
404C22×C137—41no—
405C22×C137—42no—
406C22×C137—41no—
407C22×C137—42no—
408C22×C137—41no—
409C22×C137—41no—
410C22×C137—41no—
411C22×C137—41no—
412C22×C137—41no—
413C22×C137—41no—
414C22×C137—41no—
415C22×C137—81no—
416C22×C137—81no—
417C22×C137—81no—
418C22×C137—81no—
419C22×C137—81no—
420C22×C137—81no—
421C22×C137—81no—
422C22×C137C2×#12011yescharacteristic
423C22×C137D4211yescharacteristic
424C22×C137#54611yescharacteristic
425C22×C137C2×#13511yescharacteristic
426C22×C137#57511yescharacteristic
427C22×C137#57711yescharacteristic
428C22×C137#57711yescharacteristic
429C4×C137—22no—
430C4×C137—22no—
431C4×C137—41no—
432C4×C137—42no—
433C4×C137—42no—
434C4×C137—42no—
435C4×C137—41no—
436C4×C137—42no—
437C4×C137—81no—
438C4×C137—81no—
439C4×C137C2×#12111yescharacteristic
440C4×C137#53411yescharacteristic
441C4×C137D4211yescharacteristic
442C4×C137#54611yescharacteristic
443C2×C137—42no—
444C2×C137—44no—
445C2×C137—81no—
446C2×C137—161no—
447C2×C137#241011yescharacteristic
448C2×C137#300211yescharacteristic
449C2×C137#301011yescharacteristic
450C2×C137#326711yescharacteristic
451C2×C137#328411yescharacteristic
452C2×C137#330311yescharacteristic
453C2×C137#330711yescharacteristic
454#24438C13711yesmaximal, characteristic, direct product factor, Sylow
455C137#2443811yescharacteristic, direct product factor, Sylow
456C2×#547C2×C13711yescharacteristic, complemented
457C2×#465C2×C13711yescharacteristic, complemented
458C2×#449C2×C13711yescharacteristic, complemented
459C2×#449C2×C13711yescharacteristic, complemented
460C2×#416C2×C13711yescharacteristic, complemented
461#2414C2×C13711yescharacteristic, complemented
462#2043C2×C13711yescharacteristic, complemented
463#2035C2×C13711yescharacteristic, complemented
464#2013C2×C13711yescharacteristic, complemented
465#2000C2×C13711yescharacteristic, complemented
466#1879C2×C13711yescharacteristic, complemented
467#1873C2×C13711yescharacteristic, complemented
468#1869C2×C13711yescharacteristic, complemented
469#1864C2×C13711yescharacteristic, complemented
470#1788C2×C13711yescharacteristic, complemented
471C22×#41C22×C13711yescharacteristic
472C22×#41C22×C13711yescharacteristic
473C22×SD16C22×C13711yescharacteristic
474C22×SD16C22×C13711yescharacteristic
475C22×D8C22×C13711yescharacteristic
476C23×C8C22×C13711yescharacteristic
477#547—24no—
478#547—24no—
479C2×C4⋊Q8C22×C13711yescharacteristic
480C2×#123—21no—
481C2×#123—21no—
482C2×C22⋊Q8C22×C13711yescharacteristic
483C2×C22⋊Q8C22×C13711yescharacteristic
484C2×#121—21no—
485C2×#121C22×C13711yescharacteristic
486C2×#121C22×C13711yescharacteristic
487C2×C4×D4C22×C13711yescharacteristic
488C2×C4×D4C22×C13711yescharacteristic
489C2×#117C22×C13711yescharacteristic
490C22×C4⋊C4—21no—
491#465—24no—
492#449—24no—
493#449—24no—
494C2×#106C22×C13711yescharacteristic
495#416—24no—
496C2×#103C22×C13711yescharacteristic
497C2×#103C22×C13711yescharacteristic
498C2×#103C22×C13711yescharacteristic
499C2×#103C22×C13711yescharacteristic
500C2×#103C22×C13711yescharacteristic
501C2×#103C22×C13711yescharacteristic
502C2×#102C22×C13711yescharacteristic
503C2×#102C22×C13711yescharacteristic
504C2×#102C22×C13711yescharacteristic
505C2×#102C22×C13711yescharacteristic
506C2×C22⋊C8C22×C13711yescharacteristic
507C2×C22⋊C8C22×C13711yescharacteristic
508C2×C22⋊C8C22×C13711yescharacteristic
509#394—21no—
510#392—21no—
511#390—21no—
512#390C22×C13711yescharacteristic
513#389C22×C13711yescharacteristic
514#388—21no—
515#380C22×C13711yescharacteristic
516#340C22×C13711yescharacteristic
517#340C22×C13711yescharacteristic
518#336C22×C13711yescharacteristic
519#336C22×C13711yescharacteristic
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41D4×C13714yescomplemented
532C22×Q8C23×C13711yescharacteristic
533C22×Q8C23×C13711yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4D4×C13711yescharacteristic
539C22×D4C23×C13711yescharacteristic
540C22×D4C23×C13711yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C23×C13711yescharacteristic
545C23×C4C23×C13711yescharacteristic
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8C23×C13711yescharacteristic
559C22×C8C23×C13711yescharacteristic
560C22×C8C23×C13711yescharacteristic
561C22×C8C23×C13711yescharacteristic
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564#123—28no—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8D4×C13714yescomplemented
570#121—28no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—41no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579#117—22no—
580#117—41no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4D4×C13711yescharacteristic
588C2×C4⋊C4C23×C13711yescharacteristic
589C2×C4⋊C4C23×C13711yescharacteristic
590C2×C4⋊C4C23×C13711yescharacteristic
591C2×C4⋊C4C23×C13711yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C13711yescharacteristic
602C2×C22⋊C4D4×C13711yescharacteristic
603C2×C42—21no—
604C2×C42C23×C13711yescharacteristic
605#106—22no—
606#103—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—41no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102D4×C13714yescomplemented
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—41no—
619#95—21no—
620#95—21no—
621C24—21no—
622C24—21no—
623C24C2×D4×C13711yescharacteristic
624C24C2×D4×C13711yescharacteristic
625#41—28no—
626#41—44no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C13712yes—
644C2×Q8C2×D4×C13712yes—
645C2×D4—24no—
646C2×D4—22no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—41no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—81no—
667C2×D4—81no—
668C2×D4—81no—
669C2×D4C2×D4×C13712yes—
670C2×D4C2×D4×C13712yes—
671C2×D4#41×C13712yes—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4C2×D4×C13711yescharacteristic
698C22×C4C2×D4×C13711yescharacteristic
699C22×C4C2×D4×C13711yescharacteristic
700C22×C4C2×D4×C13712yes—
701C22×C4C2×D4×C13712yes—
702C22×C4C2×D4×C13711yescharacteristic
703C22×C4C24×C13711yescharacteristic
704SD16—44no—
705SD16—44no—
706D8—44no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—44no—
719C2×C8C2×D4×C13712yes—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—24no—
723C4⋊C4—22no—
724C4⋊C4—24no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—81no—
732C4⋊C4C2×D4×C13712yes—
733C4⋊C4C2×D4×C13712yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—81no—
744C22⋊C4—81no—
745C42—21no—
746C42—21no—
747C42—42no—
748C23—22no—
749C23—21no—
750C23—22no—
751C23—21no—
752C23—22no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23#120×C13712yes—
776C23C22×D4×C13711yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—48no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4#121×C13714yes—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—48no—
817C2×C4—48no—
818C2×C4—48no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4#120×C13712yes—
838C2×C4#135×C13712yes—
839C2×C4C22×D4×C13711yescharacteristic
840C2×C4C22×D4×C13711yescharacteristic
841C2×C4C22×D4×C13711yescharacteristic
842C2×C4C2×#41×C13711yescharacteristic
843C2×C4H(5,𝔽2)×C13711yescharacteristic
844C2×C4H(5,𝔽2)×C13711yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—24no—
851C22—22no—
852C22—22no—
853C22—41no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—41no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#120×C13711yescharacteristic
878C22D42×C13711yescharacteristic
879C22#546×C13711yescharacteristic
880C22C2×#135×C13711yescharacteristic
881C22#575×C13711yescharacteristic
882C22#577×C13711yescharacteristic
883C22#577×C13711yescharacteristic
884C4—22no—
885C4—22no—
886C4—41no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—41no—
891C4—42no—
892C4—81no—
893C4—81no—
894C4C2×#121×C13711yescharacteristic
895C4#534×C13711yescharacteristic
896C4D42×C13711yescharacteristic
897C4#546×C13711yescharacteristic
898C2—42no—
899C2—44no—
900C2—81no—
901C2—161no—
902C2#2410×C13711yescharacteristic
903C2#3002×C13711yescharacteristic
904C2#3010×C13711yescharacteristic
905C2#3267×C13711yescharacteristic
906C2#3284×C13711yescharacteristic
907C2#3303×C13711yescharacteristic
908C2#3307×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. C2×#547×C137C2semidirect
2. C2×#465×C137C2semidirect
3. C2×#449×C137C2semidirect
4. C2×#449×C137C2semidirect
5. C2×#416×C137C2semidirect
6. #2414×C137C2semidirect
7. #2043×C137C2semidirect
8. #2035×C137C2semidirect
9. #2013×C137C2semidirect
10. #2000×C137C2semidirect
11. #1879×C137C2semidirect
12. #1873×C137C2semidirect
13. #1869×C137C2semidirect
14. #1864×C137C2semidirect
15. #1788×C137C2semidirect
76. C2×#41×C137D4semidirect
114. C22⋊Q8×C137D4semidirect
160. #102×C137D4semidirect
454. #24438C137direct (N × H)
455. C137#24438direct (N × H)
456. C2×#547C2×C137semidirect
457. C2×#465C2×C137semidirect
458. C2×#449C2×C137semidirect
459. C2×#449C2×C137semidirect
460. C2×#416C2×C137semidirect
461. #2414C2×C137semidirect
462. #2043C2×C137semidirect
463. #2035C2×C137semidirect
464. #2013C2×C137semidirect
465. #2000C2×C137semidirect
466. #1879C2×C137semidirect
467. #1873C2×C137semidirect
468. #1869C2×C137semidirect
469. #1864C2×C137semidirect
470. #1788C2×C137semidirect
531. C2×#41D4×C137semidirect
569. C22⋊Q8D4×C137semidirect
615. #102D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1372
C2×#465×C1372
C2×#449×C1372
C2×#416×C1372
#2414×C1372
#2043×C1372
#2035×C1372
#2013×C1372
#2000×C1372
#1879×C1372
#1873×C1372
#1869×C1372
#1864×C1372
#1788×C1372
#24438137