Finite Group Databasebeta

← C137×#24031 #46873417

Subgroups — C137×#24031 #46873417

Order 35072.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3488×C137C211yesmaximal, characteristic
2#3093×C137C211yesmaximal, characteristic, complemented
3#2896×C137C211yesmaximal, characteristic, complemented
4#2500×C137C211yesmaximal, characteristic, complemented
5#2040×C137C211yesmaximal, characteristic, complemented
6#2039×C137C211yesmaximal, characteristic, complemented
7#2037×C137C211yesmaximal, characteristic, complemented
8#2037×C137C211yesmaximal, characteristic, complemented
9#1900×C137C211yesmaximal, characteristic, complemented
10#1871×C137C211yesmaximal, characteristic, complemented
11#1860×C137C211yesmaximal, characteristic, complemented
12#1859×C137C211yesmaximal, characteristic, complemented
13#1792×C137C211yesmaximal, characteristic, complemented
14#1792×C137C211yesmaximal, characteristic, complemented
15#1789×C137C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C137C2211yescharacteristic
17C22×#41×C137C2211yescharacteristic
18C22×M16×C137C2211yescharacteristic, complemented
19#550×C137—21no—
20#548×C137—21no—
21#546×C137—21no—
22#546×C137—22no—
23D42×C137—22no—
24D42×C137—21no—
25#537×C137—21no—
26#537×C137C2211yescharacteristic
27#535×C137—21no—
28#535×C137C2211yescharacteristic
29#525×C137—21no—
30#525×C137C2211yescharacteristic
31C2×#121×C137—21no—
32C2×#121×C137C2211yescharacteristic
33#520×C137C2211yescharacteristic
34C2×#117×C137C2211yescharacteristic, complemented
35#485×C137—21no—
36#485×C137—21no—
37#482×C137—21no—
38#482×C137—21no—
39#428×C137C2211yescharacteristic, complemented
40#428×C137C2211yescharacteristic, complemented
41C2×#104×C137C2211yescharacteristic
42C2×#104×C137C2211yescharacteristic
43C2×#104×C137C2211yescharacteristic, complemented
44C2×#104×C137C2211yescharacteristic, complemented
45C2×#104×C137C2211yescharacteristic, complemented
46C2×#104×C137C2211yescharacteristic, complemented
47#419×C137—21no—
48#418×C137—21no—
49#417×C137C2211yescharacteristic
50#417×C137C2211yescharacteristic
51#417×C137C2211yescharacteristic, complemented
52#417×C137C2211yescharacteristic, complemented
53#417×C137C2211yescharacteristic, complemented
54#417×C137C2211yescharacteristic, complemented
55#416×C137—21no—
56#416×C137—21no—
57C2×#100×C137C2211yescharacteristic, complemented
58C2×#100×C137C2211yescharacteristic, complemented
59#407×C137C2211yescharacteristic, complemented
60#394×C137—22no—
61#390×C137C2211yescharacteristic, complemented
62#390×C137C2211yescharacteristic, complemented
63#388×C137—22no—
64#384×C137C2211yescharacteristic, complemented
65#382×C137C2211yescharacteristic, complemented
66C4×C22⋊C4×C137C2211yescharacteristic, complemented
67#343×C137C2211yescharacteristic, complemented
68#343×C137C2211yescharacteristic, complemented
69#339×C137C2211yescharacteristic, complemented
70#339×C137C2211yescharacteristic, complemented
71H(5,𝔽2)×C137—22no—
72H(5,𝔽2)×C137—22no—
73H(5,𝔽2)×C137—41no—
74H(5,𝔽2)×C137—41no—
75C2×#41×C137—21no—
76C2×#41×C137—21no—
77C2×#41×C137—21no—
78C2×#41×C137—21no—
79C2×#41×C137—22no—
80C2×#41×C137—22no—
81C2×#41×C137—41no—
82C2×#41×C137—41no—
83C2×#41×C137D411yescharacteristic
84C2×#41×C137D411yescharacteristic
85C2×#41×C137C2311yescharacteristic
86C2×#41×C137C2311yescharacteristic
87C2×#41×C137C2311yescharacteristic
88C22×Q8×C137D411yescharacteristic
89C22×D4×C137—21no—
90C22×D4×C137—22no—
91C22×D4×C137—22no—
92C22×D4×C137—21no—
93C22×D4×C137—21no—
94C22×D4×C137D411yescharacteristic
95C22×D4×C137D412yes—
96C22×D4×C137C2311yescharacteristic
97C23×C4×C137—21no—
98C23×C4×C137C2311yescharacteristic
99C2×M16×C137—21no—
100C2×M16×C137—41no—
101C2×M16×C137—41no—
102C2×M16×C137C2311yescharacteristic
103C2×M16×C137C2311yescharacteristic
104C2×M16×C137C2311yescharacteristic
105C2×M16×C137C2311yescharacteristic
106C22×C8×C137—21no—
107#127×C137—22no—
108#127×C137—21no—
109#124×C137—22no—
110#124×C137—21no—
111#123×C137—22no—
112#123×C137—21no—
113C22⋊Q8×C137—22no—
114C22⋊Q8×C137—21no—
115C22⋊Q8×C137—21no—
116C22⋊Q8×C137D411yescharacteristic
117C22⋊Q8×C137D411yescharacteristic
118#121×C137—22no—
119#121×C137—22no—
120#121×C137—22no—
121#121×C137—22no—
122#121×C137—22no—
123#121×C137—21no—
124#121×C137—21no—
125#121×C137—21no—
126#121×C137—21no—
127#121×C137—21no—
128#121×C137—21no—
129#121×C137—22no—
130#121×C137—21no—
131#121×C137—21no—
132#121×C137D411yescharacteristic
133#121×C137D411yescharacteristic
134#120×C137—22no—
135#120×C137—22no—
136#120×C137—22no—
137#120×C137—21no—
138#120×C137—22no—
139C4×Q8×C137—21no—
140C4×D4×C137—22no—
141C4×D4×C137—22no—
142C4×D4×C137—21no—
143C4×D4×C137—22no—
144C4×D4×C137—21no—
145C4×D4×C137—21no—
146#117×C137—21no—
147#117×C137—21no—
148#117×C137—21no—
149#117×C137—21no—
150#117×C137—21no—
151#117×C137C2311yescharacteristic
152C2×C4⋊C4×C137—21no—
153C2×C4⋊C4×C137—22no—
154C2×C4⋊C4×C137C2311yescharacteristic
155C2×C4⋊C4×C137C2311yescharacteristic
156C2×C4⋊C4×C137C2311yescharacteristic
157C2×C22⋊C4×C137—22no—
158C2×C22⋊C4×C137—21no—
159C2×C22⋊C4×C137—22no—
160C2×C22⋊C4×C137—21no—
161C2×C22⋊C4×C137—22no—
162C2×C22⋊C4×C137D412yes—
163C2×C42×C137—21no—
164C2×C42×C137C2311yescharacteristic
165C2×C42×C137C2311yescharacteristic
166#107×C137—21no—
167#107×C137—21no—
168#106×C137—21no—
169#106×C137—21no—
170#104×C137—22no—
171#104×C137—22no—
172#104×C137—41no—
173#104×C137—41no—
174#104×C137—41no—
175#104×C137—41no—
176#103×C137—21no—
177#103×C137—21no—
178#103×C137—21no—
179#103×C137—21no—
180#103×C137—21no—
181#103×C137—21no—
182#102×C137—21no—
183#102×C137—21no—
184#102×C137—21no—
185#102×C137—21no—
186#102×C137—21no—
187#102×C137—21no—
188#100×C137—41no—
189#100×C137—41no—
190C22⋊C8×C137—21no—
191C22⋊C8×C137—21no—
192#95×C137—21no—
193#95×C137—22no—
194C24×C137—22no—
195C24×C137—21no—
196C24×C137C2×D412yes—
197C24×C137C2×D411yescharacteristic
198#41×C137—21no—
199#41×C137—21no—
200#41×C137—22no—
201#41×C137—22no—
202#41×C137—21no—
203#41×C137—21no—
204#41×C137—21no—
205#41×C137—21no—
206#41×C137—21no—
207#41×C137—21no—
208#41×C137—21no—
209#41×C137—21no—
210#41×C137—42no—
211#41×C137—42no—
212#41×C137—41no—
213#41×C137—41no—
214#41×C137—42no—
215#41×C137—42no—
216#41×C137—42no—
217#41×C137—42no—
218#41×C137—42no—
219#41×C137—42no—
220#41×C137#4112yes—
221#41×C137#4112yes—
222C2×Q8×C137—21no—
223C2×Q8×C137—22no—
224C2×Q8×C137—41no—
225C2×Q8×C137C2×D411yescharacteristic
226C2×Q8×C137C2×D411yescharacteristic
227C2×Q8×C137C2×D411yescharacteristic
228C2×D4×C137—21no—
229C2×D4×C137—22no—
230C2×D4×C137—22no—
231C2×D4×C137—22no—
232C2×D4×C137—22no—
233C2×D4×C137—21no—
234C2×D4×C137—21no—
235C2×D4×C137—21no—
236C2×D4×C137—21no—
237C2×D4×C137—21no—
238C2×D4×C137—22no—
239C2×D4×C137—22no—
240C2×D4×C137—22no—
241C2×D4×C137—21no—
242C2×D4×C137—22no—
243C2×D4×C137—21no—
244C2×D4×C137—21no—
245C2×D4×C137—21no—
246C2×D4×C137—21no—
247C2×D4×C137—21no—
248C2×D4×C137—21no—
249C2×D4×C137—21no—
250C2×D4×C137—41no—
251C2×D4×C137—42no—
252C2×D4×C137—42no—
253C2×D4×C137—42no—
254C2×D4×C137—42no—
255C2×D4×C137—44no—
256C2×D4×C137—44no—
257C2×D4×C137—42no—
258C2×D4×C137—42no—
259C2×D4×C137—82no—
260C2×D4×C137—84no—
261C2×D4×C137C2×D411yescharacteristic
262C2×D4×C137C2×D411yescharacteristic
263C2×D4×C137C2×D411yescharacteristic
264C22×C4×C137—21no—
265C22×C4×C137—21no—
266C22×C4×C137—21no—
267C22×C4×C137—21no—
268C22×C4×C137—21no—
269C22×C4×C137—22no—
270C22×C4×C137—21no—
271C22×C4×C137—21no—
272C22×C4×C137—22no—
273C22×C4×C137—21no—
274C22×C4×C137—21no—
275C22×C4×C137—21no—
276C22×C4×C137—21no—
277C22×C4×C137—21no—
278C22×C4×C137—21no—
279C22×C4×C137—21no—
280C22×C4×C137—42no—
281C22×C4×C137—42no—
282C22×C4×C137C2×D411yescharacteristic
283C22×C4×C137C2×D411yescharacteristic
284C22×C4×C137C2×D411yescharacteristic
285C22×C4×C137C2×D411yescharacteristic
286C22×C4×C137C2×D411yescharacteristic
287C22×C4×C137C2×D412yes—
288C22×C4×C137C2411yescharacteristic
289M16×C137—21no—
290M16×C137—21no—
291M16×C137—21no—
292M16×C137—21no—
293M16×C137—21no—
294M16×C137—21no—
295M16×C137—21no—
296M16×C137—21no—
297M16×C137—42no—
298C2×C8×C137—21no—
299C2×C8×C137—21no—
300C2×C8×C137—21no—
301C2×C8×C137—21no—
302C2×C8×C137—42no—
303C4⋊C4×C137—22no—
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—21no—
311C4⋊C4×C137—21no—
312C4⋊C4×C137—21no—
313C4⋊C4×C137—82no—
314C4⋊C4×C137C2×D411yescharacteristic
315C4⋊C4×C137C2×D411yescharacteristic
316C22⋊C4×C137—22no—
317C22⋊C4×C137—22no—
318C22⋊C4×C137—22no—
319C22⋊C4×C137—22no—
320C22⋊C4×C137—22no—
321C22⋊C4×C137—21no—
322C22⋊C4×C137—21no—
323C22⋊C4×C137—21no—
324C22⋊C4×C137—21no—
325C22⋊C4×C137—22no—
326C22⋊C4×C137—22no—
327C22⋊C4×C137—21no—
328C22⋊C4×C137—42no—
329C22⋊C4×C137—44no—
330C22⋊C4×C137—41no—
331C22⋊C4×C137—41no—
332C22⋊C4×C137—82no—
333C42×C137—22no—
334C42×C137—21no—
335C42×C137—21no—
336C42×C137—21no—
337C42×C137—21no—
338C42×C137—21no—
339C42×C137—41no—
340C42×C137—41no—
341C23×C137—21no—
342C23×C137—21no—
343C23×C137—21no—
344C23×C137—22no—
345C23×C137—21no—
346C23×C137—21no—
347C23×C137—22no—
348C23×C137—22no—
349C23×C137—41no—
350C23×C137—41no—
351C23×C137—42no—
352C23×C137—42no—
353C23×C137—44no—
354C23×C137—42no—
355C23×C137—42no—
356C23×C137—81no—
357C23×C137—82no—
358C23×C137—82no—
359C23×C137#12011yescharacteristic
360C23×C137#12011yescharacteristic
361C23×C137C22×D411yescharacteristic
362Q8×C137—21no—
363Q8×C137—21no—
364Q8×C137—21no—
365Q8×C137—21no—
366Q8×C137—21no—
367Q8×C137—42no—
368Q8×C137#12312yes—
369D4×C137—22no—
370D4×C137—22no—
371D4×C137—21no—
372D4×C137—21no—
373D4×C137—21no—
374D4×C137—21no—
375D4×C137—21no—
376D4×C137—42no—
377D4×C137—42no—
378D4×C137—44no—
379D4×C137—42no—
380D4×C137—44no—
381D4×C137—44no—
382D4×C137—42no—
383D4×C137—41no—
384D4×C137—41no—
385D4×C137—41no—
386D4×C137—41no—
387D4×C137—41no—
388D4×C137—41no—
389D4×C137—41no—
390D4×C137—41no—
391D4×C137—81no—
392D4×C137—82no—
393D4×C137—82no—
394D4×C137—82no—
395D4×C137—82no—
396D4×C137#12312yes—
397C2×C4×C137—21no—
398C2×C4×C137—21no—
399C2×C4×C137—21no—
400C2×C4×C137—21no—
401C2×C4×C137—21no—
402C2×C4×C137—21no—
403C2×C4×C137—21no—
404C2×C4×C137—21no—
405C2×C4×C137—21no—
406C2×C4×C137—21no—
407C2×C4×C137—21no—
408C2×C4×C137—22no—
409C2×C4×C137—22no—
410C2×C4×C137—22no—
411C2×C4×C137—21no—
412C2×C4×C137—22no—
413C2×C4×C137—21no—
414C2×C4×C137—21no—
415C2×C4×C137—21no—
416C2×C4×C137—42no—
417C2×C4×C137—42no—
418C2×C4×C137—42no—
419C2×C4×C137—44no—
420C2×C4×C137—41no—
421C2×C4×C137—41no—
422C2×C4×C137—41no—
423C2×C4×C137—41no—
424C2×C4×C137—41no—
425C2×C4×C137—41no—
426C2×C4×C137—42no—
427C2×C4×C137—41no—
428C2×C4×C137—42no—
429C2×C4×C137—41no—
430C2×C4×C137—42no—
431C2×C4×C137—41no—
432C2×C4×C137—41no—
433C2×C4×C137—41no—
434C2×C4×C137—82no—
435C2×C4×C137#12011yescharacteristic
436C2×C4×C137#12011yescharacteristic
437C2×C4×C137C22×D411yescharacteristic
438C2×C4×C137C22×D411yescharacteristic
439C2×C4×C137C2×#4111yescharacteristic
440C2×C4×C137C2×#4111yescharacteristic
441C2×C4×C137H(5,𝔽2)11yescharacteristic
442C2×C4×C137H(5,𝔽2)11yescharacteristic
443C8×C137—41no—
444C8×C137—41no—
445C8×C137—41no—
446C8×C137—41no—
447C22×C137—21no—
448C22×C137—21no—
449C22×C137—21no—
450C22×C137—21no—
451C22×C137—22no—
452C22×C137—21no—
453C22×C137—21no—
454C22×C137—21no—
455C22×C137—21no—
456C22×C137—41no—
457C22×C137—41no—
458C22×C137—41no—
459C22×C137—41no—
460C22×C137—42no—
461C22×C137—41no—
462C22×C137—42no—
463C22×C137—41no—
464C22×C137—42no—
465C22×C137—41no—
466C22×C137—41no—
467C22×C137—81no—
468C22×C137—81no—
469C22×C137—82no—
470C22×C137—82no—
471C22×C137—84no—
472C22×C137—164no—
473C22×C137C2×#12011yescharacteristic
474C22×C137#54611yescharacteristic
475C22×C137#54611yescharacteristic
476C4×C137—21no—
477C4×C137—21no—
478C4×C137—22no—
479C4×C137—42no—
480C4×C137—41no—
481C4×C137—41no—
482C4×C137—41no—
483C4×C137—42no—
484C4×C137—41no—
485C4×C137—81no—
486C4×C137—81no—
487C4×C137—81no—
488C4×C137C2×#12311yescharacteristic
489C4×C137#53411yescharacteristic
490C4×C137#54611yescharacteristic
491C4×C137#54611yescharacteristic
492C2×C137—21no—
493C2×C137—21no—
494C2×C137—41no—
495C2×C137—41no—
496C2×C137—42no—
497C2×C137—81no—
498C2×C137—82no—
499C2×C137—81no—
500C2×C137#240511yescharacteristic
501C2×C137#301811yescharacteristic
502C2×C137#301911yescharacteristic
503#24031C13711yesmaximal, characteristic, direct product factor, Sylow
504C137#2403111yescharacteristic, direct product factor, Sylow
505#3488C2×C13711yescharacteristic
506#3093C2×C13711yescharacteristic, complemented
507#2896C2×C13711yescharacteristic, complemented
508#2500C2×C13711yescharacteristic, complemented
509#2040C2×C13711yescharacteristic, complemented
510#2039C2×C13711yescharacteristic, complemented
511#2037C2×C13711yescharacteristic, complemented
512#2037C2×C13711yescharacteristic, complemented
513#1900C2×C13711yescharacteristic, complemented
514#1871C2×C13711yescharacteristic, complemented
515#1860C2×C13711yescharacteristic, complemented
516#1859C2×C13711yescharacteristic, complemented
517#1792C2×C13711yescharacteristic, complemented
518#1792C2×C13711yescharacteristic, complemented
519#1789C2×C13711yescharacteristic, complemented
520C2×H(5,𝔽2)C22×C13711yescharacteristic
521C22×#41C22×C13711yescharacteristic
522C22×M16C22×C13711yescharacteristic, complemented
523#550—21no—
524#548—21no—
525#546—21no—
526#546—22no—
527D42—22no—
528D42—21no—
529#537—21no—
530#537C22×C13711yescharacteristic
531#535—21no—
532#535C22×C13711yescharacteristic
533#525—21no—
534#525C22×C13711yescharacteristic
535C2×#121—21no—
536C2×#121C22×C13711yescharacteristic
537#520C22×C13711yescharacteristic
538C2×#117C22×C13711yescharacteristic, complemented
539#485—21no—
540#485—21no—
541#482—21no—
542#482—21no—
543#428C22×C13711yescharacteristic, complemented
544#428C22×C13711yescharacteristic, complemented
545C2×#104C22×C13711yescharacteristic
546C2×#104C22×C13711yescharacteristic
547C2×#104C22×C13711yescharacteristic, complemented
548C2×#104C22×C13711yescharacteristic, complemented
549C2×#104C22×C13711yescharacteristic, complemented
550C2×#104C22×C13711yescharacteristic, complemented
551#419—21no—
552#418—21no—
553#417C22×C13711yescharacteristic
554#417C22×C13711yescharacteristic
555#417C22×C13711yescharacteristic, complemented
556#417C22×C13711yescharacteristic, complemented
557#417C22×C13711yescharacteristic, complemented
558#417C22×C13711yescharacteristic, complemented
559#416—21no—
560#416—21no—
561C2×#100C22×C13711yescharacteristic, complemented
562C2×#100C22×C13711yescharacteristic, complemented
563#407C22×C13711yescharacteristic, complemented
564#394—22no—
565#390C22×C13711yescharacteristic, complemented
566#390C22×C13711yescharacteristic, complemented
567#388—22no—
568#384C22×C13711yescharacteristic, complemented
569#382C22×C13711yescharacteristic, complemented
570C4×C22⋊C4C22×C13711yescharacteristic, complemented
571#343C22×C13711yescharacteristic, complemented
572#343C22×C13711yescharacteristic, complemented
573#339C22×C13711yescharacteristic, complemented
574#339C22×C13711yescharacteristic, complemented
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C13711yescharacteristic
588C2×#41D4×C13711yescharacteristic
589C2×#41C23×C13711yescharacteristic
590C2×#41C23×C13711yescharacteristic
591C2×#41C23×C13711yescharacteristic
592C22×Q8D4×C13711yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C13711yescharacteristic
599C22×D4D4×C13712yes—
600C22×D4C23×C13711yescharacteristic
601C23×C4—21no—
602C23×C4C23×C13711yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C13711yescharacteristic
607C2×M16C23×C13711yescharacteristic
608C2×M16C23×C13711yescharacteristic
609C2×M16C23×C13711yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C13711yescharacteristic
621C22⋊Q8D4×C13711yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C13711yescharacteristic
637#121D4×C13711yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C13711yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C13711yescharacteristic
659C2×C4⋊C4C23×C13711yescharacteristic
660C2×C4⋊C4C23×C13711yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C13712yes—
667C2×C42—21no—
668C2×C42C23×C13711yescharacteristic
669C2×C42C23×C13711yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C13712yes—
701C24C2×D4×C13711yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C13712yes—
725#41#41×C13712yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C13711yescharacteristic
730C2×Q8C2×D4×C13711yescharacteristic
731C2×Q8C2×D4×C13711yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C13711yescharacteristic
766C2×D4C2×D4×C13711yescharacteristic
767C2×D4C2×D4×C13711yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C13711yescharacteristic
787C22×C4C2×D4×C13711yescharacteristic
788C22×C4C2×D4×C13711yescharacteristic
789C22×C4C2×D4×C13711yescharacteristic
790C22×C4C2×D4×C13711yescharacteristic
791C22×C4C2×D4×C13712yes—
792C22×C4C24×C13711yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C13711yescharacteristic
819C4⋊C4C2×D4×C13711yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C13711yescharacteristic
864C23#120×C13711yescharacteristic
865C23C22×D4×C13711yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C13712yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C13712yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C13711yescharacteristic
940C2×C4#120×C13711yescharacteristic
941C2×C4C22×D4×C13711yescharacteristic
942C2×C4C22×D4×C13711yescharacteristic
943C2×C4C2×#41×C13711yescharacteristic
944C2×C4C2×#41×C13711yescharacteristic
945C2×C4H(5,𝔽2)×C13711yescharacteristic
946C2×C4H(5,𝔽2)×C13711yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—22no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—42no—
965C22—41no—
966C22—42no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C13711yescharacteristic
978C22#546×C13711yescharacteristic
979C22#546×C13711yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—41no—
986C4—41no—
987C4—42no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C13711yescharacteristic
993C4#534×C13711yescharacteristic
994C4#546×C13711yescharacteristic
995C4#546×C13711yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2#2405×C13711yescharacteristic
1005C2#3018×C13711yescharacteristic
1006C2#3019×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC22×C4C24×C137
prime radical#3488×C137C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3093×C137C2semidirect
3. #2896×C137C2semidirect
4. #2500×C137C2semidirect
5. #2040×C137C2semidirect
6. #2039×C137C2semidirect
7. #2037×C137C2semidirect
8. #2037×C137C2semidirect
9. #1900×C137C2semidirect
10. #1871×C137C2semidirect
11. #1860×C137C2semidirect
12. #1859×C137C2semidirect
13. #1792×C137C2semidirect
14. #1792×C137C2semidirect
15. #1789×C137C2semidirect
18. C22×M16×C137C22semidirect
34. C2×#117×C137C22semidirect
39. #428×C137C22semidirect
40. #428×C137C22semidirect
43. C2×#104×C137C22semidirect
44. C2×#104×C137C22semidirect
45. C2×#104×C137C22semidirect
46. C2×#104×C137C22semidirect
51. #417×C137C22semidirect
52. #417×C137C22semidirect
53. #417×C137C22semidirect
54. #417×C137C22semidirect
57. C2×#100×C137C22semidirect
58. C2×#100×C137C22semidirect
59. #407×C137C22semidirect
61. #390×C137C22semidirect
62. #390×C137C22semidirect
64. #384×C137C22semidirect
65. #382×C137C22semidirect
66. C4×C22⋊C4×C137C22semidirect
67. #343×C137C22semidirect
68. #343×C137C22semidirect
69. #339×C137C22semidirect
70. #339×C137C22semidirect
503. #24031C137direct (N × H)
504. C137#24031direct (N × H)
506. #3093C2×C137semidirect
507. #2896C2×C137semidirect
508. #2500C2×C137semidirect
509. #2040C2×C137semidirect
510. #2039C2×C137semidirect
511. #2037C2×C137semidirect
512. #2037C2×C137semidirect
513. #1900C2×C137semidirect
514. #1871C2×C137semidirect
515. #1860C2×C137semidirect
516. #1859C2×C137semidirect
517. #1792C2×C137semidirect
518. #1792C2×C137semidirect
519. #1789C2×C137semidirect
522. C22×M16C22×C137semidirect
538. C2×#117C22×C137semidirect
543. #428C22×C137semidirect
544. #428C22×C137semidirect
547. C2×#104C22×C137semidirect
548. C2×#104C22×C137semidirect
549. C2×#104C22×C137semidirect
550. C2×#104C22×C137semidirect
555. #417C22×C137semidirect
556. #417C22×C137semidirect
557. #417C22×C137semidirect
558. #417C22×C137semidirect
561. C2×#100C22×C137semidirect
562. C2×#100C22×C137semidirect
563. #407C22×C137semidirect
565. #390C22×C137semidirect
566. #390C22×C137semidirect
568. #384C22×C137semidirect
569. #382C22×C137semidirect
570. C4×C22⋊C4C22×C137semidirect
571. #343C22×C137semidirect
572. #343C22×C137semidirect
573. #339C22×C137semidirect
574. #339C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3488×C1372
#3093×C1372
#2896×C1372
#2500×C1372
#2040×C1372
#2039×C1372
#2037×C1372
#1900×C1372
#1871×C1372
#1860×C1372
#1859×C1372
#1792×C1372
#1789×C1372
#24031137