Finite Group Databasebeta

← C137×#23857 #46873243

Subgroups — C137×#23857 #46873243

Order 35072.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C137C211yesmaximal, characteristic, complemented
2C2×#550×C137C211yesmaximal, characteristic, complemented
3C2×#452×C137C211yesmaximal, characteristic, complemented
4C2×#449×C137C211yesmaximal, characteristic, complemented
5C2×#449×C137C211yesmaximal, characteristic, complemented
6#2407×C137C211yesmaximal, characteristic, complemented
7#2014×C137C211yesmaximal, characteristic, complemented
8#2011×C137C211yesmaximal, characteristic, complemented
9#2000×C137C211yesmaximal, characteristic, complemented
10#1999×C137C211yesmaximal, characteristic, complemented
11#1893×C137C211yesmaximal, characteristic, complemented
12#1880×C137C211yesmaximal, characteristic, complemented
13#1878×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×SD16×C137C2211yescharacteristic
24C22×SD16×C137C2211yescharacteristic
25C22×SD16×C137C2211yescharacteristic
26C22×D8×C137C2211yescharacteristic
27C22×D8×C137C2211yescharacteristic
28C23×C8×C137C2211yescharacteristic
29#550×C137—24no—
30#550×C137—24no—
31C2×#127×C137—21no—
32C2×#127×C137C2211yescharacteristic
33C2×C22⋊Q8×C137C2211yescharacteristic
34C2×#121×C137—21no—
35C2×#121×C137—21no—
36C2×#121×C137C2211yescharacteristic
37C2×#121×C137C2211yescharacteristic
38C2×#121×C137C2211yescharacteristic
39C2×C4×Q8×C137C2211yescharacteristic
40C2×C4×D4×C137—21no—
41C2×C4×D4×C137C2211yescharacteristic
42#452×C137—24no—
43#449×C137—24no—
44#449×C137—24no—
45C2×#103×C137C2211yescharacteristic
46C2×#103×C137C2211yescharacteristic
47C2×#103×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic
49C2×#102×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×D4×C137—21no—
88C22×D4×C137—21no—
89C22×D4×C137—21no—
90C22×D4×C137—21no—
91C22×D4×C137—21no—
92C22×D4×C137—21no—
93C22×D4×C137—21no—
94C22×D4×C137—21no—
95C22×D4×C137D411yescharacteristic
96C22×D4×C137C2311yescharacteristic
97C22×D4×C137C2311yescharacteristic
98C22×D4×C137C2311yescharacteristic
99C23×C4×C137—21no—
100C23×C4×C137—21no—
101C23×C4×C137—21no—
102C23×C4×C137C2311yescharacteristic
103C23×C4×C137C2311yescharacteristic
104#135×C137—232no—
105C2×Q16×C137—22no—
106C2×Q16×C137—22no—
107C2×Q16×C137D414yescomplemented
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×C137—22no—
120C2×D8×C137—22no—
121C2×D8×C137—22no—
122C2×D8×C137—41no—
123C22×C8×C137—22no—
124C22×C8×C137—22no—
125C22×C8×C137—22no—
126C22×C8×C137C2311yescharacteristic
127C22×C8×C137C2311yescharacteristic
128C22×C8×C137C2311yescharacteristic
129C22×C8×C137C2311yescharacteristic
130#127×C137—28no—
131#127×C137—22no—
132#127×C137—22no—
133C22⋊Q8×C137—22no—
134C22⋊Q8×C137—41no—
135#121×C137—28no—
136#121×C137—28no—
137#121×C137—22no—
138#121×C137—22no—
139#121×C137—22no—
140#121×C137—22no—
141#121×C137—41no—
142#121×C137D414yescomplemented
143C4×Q8×C137—22no—
144C4×Q8×C137—22no—
145C4×D4×C137—28no—
146C4×D4×C137—22no—
147C4×D4×C137—22no—
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×C137D411yescharacteristic
162C2×C22⋊C4×C137D411yescharacteristic
163C2×C42×C137—21no—
164C2×C42×C137C2311yescharacteristic
165#103×C137—22no—
166#103×C137—22no—
167#103×C137—22no—
168#102×C137—22no—
169#102×C137—22no—
170#102×C137—22no—
171#102×C137—41no—
172#102×C137—41no—
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×C137—21no—
182C24×C137C2×D411yescharacteristic
183C24×C137C2×D411yescharacteristic
184#41×C137—28no—
185#41×C137—28no—
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—
195#41×C137—44no—
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×C137C2×D412yes—
205C2×Q8×C137C2×D412yes—
206C2×Q8×C137C2×D412yes—
207C2×Q8×C137C2×D412yes—
208C2×D4×C137—24no—
209C2×D4×C137—24no—
210C2×D4×C137—22no—
211C2×D4×C137—24no—
212C2×D4×C137—24no—
213C2×D4×C137—24no—
214C2×D4×C137—24no—
215C2×D4×C137—22no—
216C2×D4×C137—21no—
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—21no—
226C2×D4×C137—21no—
227C2×D4×C137—21no—
228C2×D4×C137—21no—
229C2×D4×C137—21no—
230C2×D4×C137—21no—
231C2×D4×C137—41no—
232C2×D4×C137—42no—
233C2×D4×C137—42no—
234C2×D4×C137—42no—
235C2×D4×C137—42no—
236C2×D4×C137—42no—
237C2×D4×C137—42no—
238C2×D4×C137—42no—
239C2×D4×C137—42no—
240C2×D4×C137—42no—
241C2×D4×C137—42no—
242C2×D4×C137—42no—
243C2×D4×C137—81no—
244C2×D4×C137—81no—
245C2×D4×C137—81no—
246C2×D4×C137—81no—
247C2×D4×C137—81no—
248C2×D4×C137—81no—
249C2×D4×C137—81no—
250C2×D4×C137C2×D412yes—
251C2×D4×C137C2×D412yes—
252C2×D4×C137C2×D412yes—
253C22×C4×C137—21no—
254C22×C4×C137—21no—
255C22×C4×C137—21no—
256C22×C4×C137—21no—
257C22×C4×C137—21no—
258C22×C4×C137—24no—
259C22×C4×C137—21no—
260C22×C4×C137—21no—
261C22×C4×C137—24no—
262C22×C4×C137—21no—
263C22×C4×C137—21no—
264C22×C4×C137—21no—
265C22×C4×C137—21no—
266C22×C4×C137—21no—
267C22×C4×C137—21no—
268C22×C4×C137—21no—
269C22×C4×C137—21no—
270C22×C4×C137—42no—
271C22×C4×C137—42no—
272C22×C4×C137—42no—
273C22×C4×C137—42no—
274C22×C4×C137—42no—
275C22×C4×C137—42no—
276C22×C4×C137—42no—
277C22×C4×C137C2×D411yescharacteristic
278C22×C4×C137C2×D411yescharacteristic
279C22×C4×C137C2×D411yescharacteristic
280C22×C4×C137C2×D412yes—
281C22×C4×C137C2×D412yes—
282C22×C4×C137C2×D411yescharacteristic
283C22×C4×C137C2411yescharacteristic
284Q16×C137—28no—
285SD16×C137—28no—
286SD16×C137—28no—
287SD16×C137—44no—
288D8×C137—28no—
289D8×C137—44no—
290C2×C8×C137—28no—
291C2×C8×C137—21no—
292C2×C8×C137—21no—
293C2×C8×C137—21no—
294C2×C8×C137—21no—
295C2×C8×C137—21no—
296C2×C8×C137—21no—
297C2×C8×C137—21no—
298C2×C8×C137—21no—
299C2×C8×C137—21no—
300C2×C8×C137—21no—
301C2×C8×C137C2×D412yes—
302C2×C8×C137C2×D412yes—
303C4⋊C4×C137—24no—
304C4⋊C4×C137—22no—
305C4⋊C4×C137—21no—
306C4⋊C4×C137—21no—
307C4⋊C4×C137—21no—
308C4⋊C4×C137—21no—
309C4⋊C4×C137—21no—
310C4⋊C4×C137—42no—
311C4⋊C4×C137C2×D412yes—
312C22⋊C4×C137—24no—
313C22⋊C4×C137—22no—
314C22⋊C4×C137—24no—
315C22⋊C4×C137—22no—
316C22⋊C4×C137—42no—
317C22⋊C4×C137—42no—
318C22⋊C4×C137—42no—
319C22⋊C4×C137—81no—
320C22⋊C4×C137—81no—
321C42×C137—24no—
322C42×C137—21no—
323C42×C137—21no—
324C23×C137—21no—
325C23×C137—21no—
326C23×C137—21no—
327C23×C137—21no—
328C23×C137—21no—
329C23×C137—21no—
330C23×C137—21no—
331C23×C137—22no—
332C23×C137—22no—
333C23×C137—21no—
334C23×C137—22no—
335C23×C137—21no—
336C23×C137—21no—
337C23×C137—21no—
338C23×C137—21no—
339C23×C137—21no—
340C23×C137—41no—
341C23×C137—41no—
342C23×C137—41no—
343C23×C137—41no—
344C23×C137—41no—
345C23×C137—41no—
346C23×C137—41no—
347C23×C137—41no—
348C23×C137—41no—
349C23×C137—41no—
350C23×C137—41no—
351C23×C137—41no—
352C23×C137—41no—
353C23×C137—41no—
354C23×C137—41no—
355C23×C137—41no—
356C23×C137—41no—
357C23×C137—41no—
358C23×C137#12012yes—
359C23×C137C22×D411yescharacteristic
360Q8×C137—22no—
361Q8×C137—22no—
362Q8×C137—22no—
363Q8×C137—22no—
364Q8×C137—22no—
365Q8×C137—41no—
366Q8×C137—41no—
367Q8×C137#12014yes—
368D4×C137—22no—
369D4×C137—22no—
370D4×C137—22no—
371D4×C137—22no—
372D4×C137—22no—
373D4×C137—22no—
374D4×C137—44no—
375D4×C137—48no—
376D4×C137—48no—
377D4×C137—48no—
378D4×C137—48no—
379D4×C137—41no—
380D4×C137—41no—
381D4×C137—41no—
382D4×C137—41no—
383D4×C137—41no—
384D4×C137—41no—
385D4×C137—84no—
386D4×C137—84no—
387D4×C137—84no—
388D4×C137—84no—
389C2×C4×C137—21no—
390C2×C4×C137—22no—
391C2×C4×C137—21no—
392C2×C4×C137—21no—
393C2×C4×C137—22no—
394C2×C4×C137—22no—
395C2×C4×C137—21no—
396C2×C4×C137—22no—
397C2×C4×C137—22no—
398C2×C4×C137—22no—
399C2×C4×C137—22no—
400C2×C4×C137—21no—
401C2×C4×C137—22no—
402C2×C4×C137—21no—
403C2×C4×C137—21no—
404C2×C4×C137—22no—
405C2×C4×C137—21no—
406C2×C4×C137—21no—
407C2×C4×C137—21no—
408C2×C4×C137—48no—
409C2×C4×C137—48no—
410C2×C4×C137—48no—
411C2×C4×C137—41no—
412C2×C4×C137—41no—
413C2×C4×C137—41no—
414C2×C4×C137—41no—
415C2×C4×C137—41no—
416C2×C4×C137—41no—
417C2×C4×C137—41no—
418C2×C4×C137—41no—
419C2×C4×C137—41no—
420C2×C4×C137—41no—
421C2×C4×C137—41no—
422C2×C4×C137—41no—
423C2×C4×C137—41no—
424C2×C4×C137—41no—
425C2×C4×C137#12012yes—
426C2×C4×C137#13512yescomplemented
427C2×C4×C137C22×D411yescharacteristic
428C2×C4×C137C22×D411yescharacteristic
429C2×C4×C137C22×D411yescharacteristic
430C2×C4×C137C22×D411yescharacteristic
431C2×C4×C137H(5,𝔽2)11yescharacteristic
432C2×C4×C137H(5,𝔽2)11yescharacteristic
433C8×C137—22no—
434C8×C137—22no—
435C8×C137—41no—
436C8×C137—41no—
437C22×C137—22no—
438C22×C137—22no—
439C22×C137—22no—
440C22×C137—41no—
441C22×C137—41no—
442C22×C137—41no—
443C22×C137—41no—
444C22×C137—42no—
445C22×C137—42no—
446C22×C137—42no—
447C22×C137—41no—
448C22×C137—41no—
449C22×C137—42no—
450C22×C137—42no—
451C22×C137—41no—
452C22×C137—42no—
453C22×C137—42no—
454C22×C137—41no—
455C22×C137—42no—
456C22×C137—41no—
457C22×C137—41no—
458C22×C137—42no—
459C22×C137—41no—
460C22×C137—81no—
461C22×C137—81no—
462C22×C137—81no—
463C22×C137—81no—
464C22×C137—81no—
465C22×C137—81no—
466C22×C137—81no—
467C22×C137—81no—
468C22×C137—81no—
469C22×C137—81no—
470C22×C137—81no—
471C22×C137—81no—
472C22×C137C2×#12011yescharacteristic
473C22×C137D4211yescharacteristic
474C22×C137D4211yescharacteristic
475C22×C137C2×#13511yescharacteristic
476C22×C137#57511yescharacteristic
477C22×C137#57611yescharacteristic
478C22×C137#57711yescharacteristic
479C4×C137—22no—
480C4×C137—24no—
481C4×C137—22no—
482C4×C137—41no—
483C4×C137—42no—
484C4×C137—41no—
485C4×C137—42no—
486C4×C137—81no—
487C4×C137—81no—
488C4×C137C2×#12011yescharacteristic
489C4×C137#53411yescharacteristic
490C4×C137D4211yescharacteristic
491C4×C137D4211yescharacteristic
492C2×C137—42no—
493C2×C137—81no—
494C2×C137—82no—
495C2×C137—82no—
496C2×C137—82no—
497C2×C137#240311yescharacteristic
498C2×C137#300211yescharacteristic
499C2×C137#301211yescharacteristic
500C2×C137#326811yescharacteristic
501C2×C137#327111yescharacteristic
502C2×C137#328411yescharacteristic
503C2×C137#328711yescharacteristic
504#23857C13711yesmaximal, characteristic, direct product factor, Sylow
505C137#2385711yescharacteristic, direct product factor, Sylow
506C22×#135C2×C13711yescharacteristic, complemented
507C2×#550C2×C13711yescharacteristic, complemented
508C2×#452C2×C13711yescharacteristic, complemented
509C2×#449C2×C13711yescharacteristic, complemented
510C2×#449C2×C13711yescharacteristic, complemented
511#2407C2×C13711yescharacteristic, complemented
512#2014C2×C13711yescharacteristic, complemented
513#2011C2×C13711yescharacteristic, complemented
514#2000C2×C13711yescharacteristic, complemented
515#1999C2×C13711yescharacteristic, complemented
516#1893C2×C13711yescharacteristic, complemented
517#1880C2×C13711yescharacteristic, complemented
518#1878C2×C13711yescharacteristic, complemented
519#1869C2×C13711yescharacteristic, complemented
520#1788C2×C13711yescharacteristic, complemented
521C22×#41C22×C13711yescharacteristic
522C22×#41C22×C13711yescharacteristic
523C22×#41C22×C13711yescharacteristic
524C2×#135—24no—
525C2×#135—24no—
526C2×#135—24no—
527C22×Q16C22×C13711yescharacteristic
528C22×SD16C22×C13711yescharacteristic
529C22×SD16C22×C13711yescharacteristic
530C22×SD16C22×C13711yescharacteristic
531C22×D8C22×C13711yescharacteristic
532C22×D8C22×C13711yescharacteristic
533C23×C8C22×C13711yescharacteristic
534#550—24no—
535#550—24no—
536C2×#127—21no—
537C2×#127C22×C13711yescharacteristic
538C2×C22⋊Q8C22×C13711yescharacteristic
539C2×#121—21no—
540C2×#121—21no—
541C2×#121C22×C13711yescharacteristic
542C2×#121C22×C13711yescharacteristic
543C2×#121C22×C13711yescharacteristic
544C2×C4×Q8C22×C13711yescharacteristic
545C2×C4×D4—21no—
546C2×C4×D4C22×C13711yescharacteristic
547#452—24no—
548#449—24no—
549#449—24no—
550C2×#103C22×C13711yescharacteristic
551C2×#103C22×C13711yescharacteristic
552C2×#103C22×C13711yescharacteristic
553C2×#102C22×C13711yescharacteristic
554C2×#102C22×C13711yescharacteristic
555C2×#102C22×C13711yescharacteristic
556C2×#102C22×C13711yescharacteristic
557C2×#102C22×C13711yescharacteristic
558C2×C22⋊C8C22×C13711yescharacteristic
559C2×C22⋊C8C22×C13711yescharacteristic
560C2×C22⋊C8C22×C13711yescharacteristic
561#394—21no—
562#392—21no—
563#391C22×C13711yescharacteristic
564#390C22×C13711yescharacteristic
565#386—21no—
566#385—21no—
567#380C22×C13711yescharacteristic
568#340C22×C13711yescharacteristic
569#340C22×C13711yescharacteristic
570#336C22×C13711yescharacteristic
571#336C22×C13711yescharacteristic
572C2×#41—22no—
573C2×#41—22no—
574C2×#41—22no—
575C2×#41—22no—
576C2×#41—22no—
577C2×#41—22no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—41no—
584C2×#41—41no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C13714yescomplemented
590C22×Q8C23×C13711yescharacteristic
591C22×Q8C23×C13711yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4D4×C13711yescharacteristic
601C22×D4C23×C13711yescharacteristic
602C22×D4C23×C13711yescharacteristic
603C22×D4C23×C13711yescharacteristic
604C23×C4—21no—
605C23×C4—21no—
606C23×C4—21no—
607C23×C4C23×C13711yescharacteristic
608C23×C4C23×C13711yescharacteristic
609#135—232no—
610C2×Q16—22no—
611C2×Q16—22no—
612C2×Q16D4×C13714yescomplemented
613C2×SD16—22no—
614C2×SD16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—41no—
621C2×SD16D4×C13714yescomplemented
622C2×D8—22no—
623C2×D8—22no—
624C2×D8—22no—
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—41no—
628C22×C8—22no—
629C22×C8—22no—
630C22×C8—22no—
631C22×C8C23×C13711yescharacteristic
632C22×C8C23×C13711yescharacteristic
633C22×C8C23×C13711yescharacteristic
634C22×C8C23×C13711yescharacteristic
635#127—28no—
636#127—22no—
637#127—22no—
638C22⋊Q8—22no—
639C22⋊Q8—41no—
640#121—28no—
641#121—28no—
642#121—22no—
643#121—22no—
644#121—22no—
645#121—22no—
646#121—41no—
647#121D4×C13714yescomplemented
648C4×Q8—22no—
649C4×Q8—22no—
650C4×D4—28no—
651C4×D4—22no—
652C4×D4—22no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4D4×C13711yescharacteristic
656C2×C4⋊C4C23×C13711yescharacteristic
657C2×C4⋊C4C23×C13711yescharacteristic
658C2×C4⋊C4C23×C13711yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4D4×C13711yescharacteristic
667C2×C22⋊C4D4×C13711yescharacteristic
668C2×C42—21no—
669C2×C42C23×C13711yescharacteristic
670#103—22no—
671#103—22no—
672#103—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—41no—
677#102—41no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680C22⋊C8—22no—
681#95—21no—
682#95—21no—
683#95—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×D4×C13711yescharacteristic
688C24C2×D4×C13711yescharacteristic
689#41—28no—
690#41—28no—
691#41—44no—
692#41—44no—
693#41—44no—
694#41—44no—
695#41—44no—
696#41—44no—
697#41—44no—
698#41—44no—
699#41—44no—
700#41—44no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8C2×D4×C13712yes—
710C2×Q8C2×D4×C13712yes—
711C2×Q8C2×D4×C13712yes—
712C2×Q8C2×D4×C13712yes—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4C2×D4×C13712yes—
756C2×D4C2×D4×C13712yes—
757C2×D4C2×D4×C13712yes—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—24no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4C2×D4×C13711yescharacteristic
783C22×C4C2×D4×C13711yescharacteristic
784C22×C4C2×D4×C13711yescharacteristic
785C22×C4C2×D4×C13712yes—
786C22×C4C2×D4×C13712yes—
787C22×C4C2×D4×C13711yescharacteristic
788C22×C4C24×C13711yescharacteristic
789Q16—28no—
790SD16—28no—
791SD16—28no—
792SD16—44no—
793D8—28no—
794D8—44no—
795C2×C8—28no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8C2×D4×C13712yes—
807C2×C8C2×D4×C13712yes—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—42no—
816C4⋊C4C2×D4×C13712yes—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—22no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—42no—
824C22⋊C4—81no—
825C22⋊C4—81no—
826C42—24no—
827C42—21no—
828C42—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—21no—
839C23—22no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23#120×C13712yes—
864C23C22×D4×C13711yescharacteristic
865Q8—22no—
866Q8—22no—
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—41no—
871Q8—41no—
872Q8#120×C13714yes—
873D4—22no—
874D4—22no—
875D4—22no—
876D4—22no—
877D4—22no—
878D4—22no—
879D4—44no—
880D4—48no—
881D4—48no—
882D4—48no—
883D4—48no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—84no—
891D4—84no—
892D4—84no—
893D4—84no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—48no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4#120×C13712yes—
931C2×C4#135×C13712yescomplemented
932C2×C4C22×D4×C13711yescharacteristic
933C2×C4C22×D4×C13711yescharacteristic
934C2×C4C22×D4×C13711yescharacteristic
935C2×C4C22×D4×C13711yescharacteristic
936C2×C4H(5,𝔽2)×C13711yescharacteristic
937C2×C4H(5,𝔽2)×C13711yescharacteristic
938C8—22no—
939C8—22no—
940C8—41no—
941C8—41no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—41no—
953C22—41no—
954C22—42no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22C2×#120×C13711yescharacteristic
978C22D42×C13711yescharacteristic
979C22D42×C13711yescharacteristic
980C22C2×#135×C13711yescharacteristic
981C22#575×C13711yescharacteristic
982C22#576×C13711yescharacteristic
983C22#577×C13711yescharacteristic
984C4—22no—
985C4—24no—
986C4—22no—
987C4—41no—
988C4—42no—
989C4—41no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4C2×#120×C13711yescharacteristic
994C4#534×C13711yescharacteristic
995C4D42×C13711yescharacteristic
996C4D42×C13711yescharacteristic
997C2—42no—
998C2—81no—
999C2—82no—
1000C2—82no—
1001C2—82no—
1002C2#2403×C13711yescharacteristic
1003C2#3002×C13711yescharacteristic
1004C2#3012×C13711yescharacteristic
1005C2#3268×C13711yescharacteristic
1006C2#3271×C13711yescharacteristic
1007C2#3284×C13711yescharacteristic
1008C2#3287×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×#550×C137C2semidirect
3. C2×#452×C137C2semidirect
4. C2×#449×C137C2semidirect
5. C2×#449×C137C2semidirect
6. #2407×C137C2semidirect
7. #2014×C137C2semidirect
8. #2011×C137C2semidirect
9. #2000×C137C2semidirect
10. #1999×C137C2semidirect
11. #1893×C137C2semidirect
12. #1880×C137C2semidirect
13. #1878×C137C2semidirect
14. #1869×C137C2semidirect
15. #1788×C137C2semidirect
84. C2×#41×C137D4semidirect
107. C2×Q16×C137D4semidirect
116. C2×SD16×C137D4semidirect
142. #121×C137D4semidirect
426. C2×C4×C137#135semidirect
504. #23857C137direct (N × H)
505. C137#23857direct (N × H)
506. C22×#135C2×C137semidirect
507. C2×#550C2×C137semidirect
508. C2×#452C2×C137semidirect
509. C2×#449C2×C137semidirect
510. C2×#449C2×C137semidirect
511. #2407C2×C137semidirect
512. #2014C2×C137semidirect
513. #2011C2×C137semidirect
514. #2000C2×C137semidirect
515. #1999C2×C137semidirect
516. #1893C2×C137semidirect
517. #1880C2×C137semidirect
518. #1878C2×C137semidirect
519. #1869C2×C137semidirect
520. #1788C2×C137semidirect
589. C2×#41D4×C137semidirect
612. C2×Q16D4×C137semidirect
621. C2×SD16D4×C137semidirect
647. #121D4×C137semidirect
931. 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×#550×C1372
C2×#452×C1372
C2×#449×C1372
#2407×C1372
#2014×C1372
#2011×C1372
#2000×C1372
#1999×C1372
#1893×C1372
#1880×C1372
#1878×C1372
#1869×C1372
#1788×C1372
#23857137