Finite Group Databasebeta

← C137×#25168 #46874554

Subgroups — C137×#25168 #46874554

Order 35072.

1396 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C137C211yesmaximal, characteristic, complemented
2C2×#447×C137C211yesmaximal, characteristic, complemented
3C2×#447×C137C211yesmaximal, characteristic, complemented
4C2×#442×C137C211yesmaximal, characteristic, complemented
5#2428×C137C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C137C211yesmaximal, characteristic, complemented
7#2065×C137C211yesmaximal, characteristic, complemented
8#2034×C137C211yesmaximal, characteristic, complemented
9#2034×C137C211yesmaximal, characteristic, complemented
10#2011×C137C211yesmaximal, characteristic, complemented
11#1972×C137C211yesmaximal, characteristic, complemented
12#1924×C137C211yesmaximal, characteristic, complemented
13#1879×C137C211yesmaximal, characteristic, complemented
14#1879×C137C211yesmaximal, characteristic, complemented
15#1864×C137C211yesmaximal, characteristic, complemented
16C23×D4×C137C2211yescharacteristic
17C22×D8×C137C2211yescharacteristic
18C22×D8×C137C2211yescharacteristic
19C22×D8×C137C2211yescharacteristic
20C22×D8×C137C2211yescharacteristic
21C2×#127×C137C2211yescharacteristic, complemented
22C2×#121×C137—21no—
23C2×#121×C137C2211yescharacteristic
24C2×#121×C137C2211yescharacteristic
25C2×C4×D4×C137C2211yescharacteristic
26C2×C4×D4×C137C2211yescharacteristic
27C2×C4×D4×C137C2211yescharacteristic, complemented
28C22×C22⋊C4×C137—21no—
29#459×C137—24no—
30#447×C137—24no—
31#447×C137—24no—
32#442×C137—24no—
33C2×#106×C137C2211yescharacteristic, complemented
34C2×#106×C137C2211yescharacteristic, complemented
35C2×C4⋊C8×C137C2211yescharacteristic, complemented
36C2×#102×C137C2211yescharacteristic
37C2×#102×C137C2211yescharacteristic
38C2×#102×C137C2211yescharacteristic
39C2×#102×C137C2211yescharacteristic
40C2×#102×C137C2211yescharacteristic, complemented
41C2×#102×C137C2211yescharacteristic, complemented
42C2×#102×C137C2211yescharacteristic, complemented
43C2×#102×C137C2211yescharacteristic, complemented
44C2×C22⋊C8×C137C2211yescharacteristic
45C2×C22⋊C8×C137C2211yescharacteristic
46C2×#97×C137C2211yescharacteristic, complemented
47#394×C137—21no—
48#392×C137—21no—
49#390×C137C2211yescharacteristic
50#390×C137C2211yescharacteristic
51#390×C137C2211yescharacteristic, complemented
52#389×C137C2211yescharacteristic, complemented
53#386×C137—21no—
54#386×C137—21no—
55#386×C137—21no—
56#380×C137C2211yescharacteristic
57#379×C137—21no—
58C4×C22⋊C4×C137C2211yescharacteristic
59#340×C137C2211yescharacteristic, complemented
60#340×C137C2211yescharacteristic, complemented
61#336×C137C2211yescharacteristic, complemented
62#336×C137C2211yescharacteristic, complemented
63C25×C137—21no—
64C22×D4×C137—22no—
65C22×D4×C137—22no—
66C22×D4×C137—22no—
67C22×D4×C137—22no—
68C22×D4×C137—21no—
69C22×D4×C137—21no—
70C22×D4×C137—21no—
71C22×D4×C137—21no—
72C22×D4×C137—21no—
73C22×D4×C137—41no—
74C22×D4×C137—41no—
75C22×D4×C137C2311yescharacteristic
76C22×D4×C137C2311yescharacteristic
77C22×D4×C137C2311yescharacteristic
78C22×D4×C137C2311yescharacteristic
79C23×C4×C137—21no—
80C23×C4×C137—21no—
81C23×C4×C137—21no—
82C23×C4×C137C2311yescharacteristic
83C2×D8×C137—22no—
84C2×D8×C137—22no—
85C2×D8×C137—22no—
86C2×D8×C137—22no—
87C2×D8×C137—22no—
88C2×D8×C137—22no—
89C2×D8×C137—22no—
90C2×D8×C137—22no—
91C2×D8×C137—22no—
92C2×D8×C137—41no—
93C2×D8×C137—41no—
94C2×D8×C137D414yescomplemented
95C22×C8×C137C2311yescharacteristic
96C22×C8×C137C2311yescharacteristic
97C22×C8×C137C2311yescharacteristic
98C22×C8×C137C2311yescharacteristic
99#127×C137—22no—
100#127×C137—41no—
101#121×C137—22no—
102#121×C137—22no—
103#121×C137—44no—
104#121×C137—41no—
105#121×C137—41no—
106C4×D4×C137—22no—
107C4×D4×C137—22no—
108C4×D4×C137—22no—
109C4×D4×C137—41no—
110C4×D4×C137—41no—
111C4×D4×C137—41no—
112C2×C4⋊C4×C137—21no—
113C2×C4⋊C4×C137C2311yescharacteristic
114C2×C4⋊C4×C137C2311yescharacteristic
115C2×C4⋊C4×C137C2311yescharacteristic
116C2×C4⋊C4×C137C2311yescharacteristic
117C2×C22⋊C4×C137—21no—
118C2×C22⋊C4×C137—21no—
119C2×C22⋊C4×C137—21no—
120C2×C22⋊C4×C137—21no—
121C2×C22⋊C4×C137—21no—
122C2×C22⋊C4×C137—21no—
123C2×C22⋊C4×C137—21no—
124C2×C22⋊C4×C137—21no—
125C2×C22⋊C4×C137—21no—
126C2×C22⋊C4×C137—21no—
127C2×C22⋊C4×C137—21no—
128C2×C22⋊C4×C137—21no—
129C2×C22⋊C4×C137—44no—
130C2×C22⋊C4×C137D411yescharacteristic
131C2×C22⋊C4×C137D411yescharacteristic
132C2×C42×C137C2311yescharacteristic
133C2×C42×C137C2311yescharacteristic
134#106×C137—22no—
135#106×C137—41no—
136C4⋊C8×C137—22no—
137#102×C137—22no—
138#102×C137—22no—
139#102×C137—22no—
140#102×C137—22no—
141#102×C137—22no—
142#102×C137—22no—
143#102×C137—41no—
144#102×C137D414yescomplemented
145C22⋊C8×C137—22no—
146C22⋊C8×C137—22no—
147#97×C137—22no—
148#95×C137—21no—
149#95×C137—21no—
150#95×C137D411yescharacteristic
151#95×C137D411yescharacteristic
152C24×C137—21no—
153C24×C137—24no—
154C24×C137—21no—
155C24×C137—21no—
156C24×C137—21no—
157C24×C137—42no—
158C24×C137—42no—
159C24×C137—42no—
160C24×C137—42no—
161C24×C137—81no—
162C24×C137—81no—
163C24×C137C2×D411yescharacteristic
164C2×D4×C137—24no—
165C2×D4×C137—21no—
166C2×D4×C137—21no—
167C2×D4×C137—21no—
168C2×D4×C137—21no—
169C2×D4×C137—21no—
170C2×D4×C137—21no—
171C2×D4×C137—21no—
172C2×D4×C137—21no—
173C2×D4×C137—21no—
174C2×D4×C137—21no—
175C2×D4×C137—21no—
176C2×D4×C137—21no—
177C2×D4×C137—21no—
178C2×D4×C137—21no—
179C2×D4×C137—21no—
180C2×D4×C137—21no—
181C2×D4×C137—21no—
182C2×D4×C137—21no—
183C2×D4×C137—21no—
184C2×D4×C137—42no—
185C2×D4×C137—42no—
186C2×D4×C137—42no—
187C2×D4×C137—42no—
188C2×D4×C137—42no—
189C2×D4×C137—42no—
190C2×D4×C137—44no—
191C2×D4×C137—44no—
192C2×D4×C137—44no—
193C2×D4×C137—44no—
194C2×D4×C137—42no—
195C2×D4×C137—42no—
196C2×D4×C137—42no—
197C2×D4×C137—42no—
198C2×D4×C137—81no—
199C2×D4×C137—81no—
200C2×D4×C137—81no—
201C2×D4×C137—81no—
202C2×D4×C137C2×D412yes—
203C2×D4×C137C2×D412yes—
204C2×D4×C137C2×D412yes—
205C2×D4×C137#4112yes—
206C2×D4×C137#4112yes—
207C22×C4×C137—21no—
208C22×C4×C137—21no—
209C22×C4×C137—21no—
210C22×C4×C137—21no—
211C22×C4×C137—21no—
212C22×C4×C137—21no—
213C22×C4×C137—21no—
214C22×C4×C137—21no—
215C22×C4×C137—21no—
216C22×C4×C137—21no—
217C22×C4×C137—42no—
218C22×C4×C137—42no—
219C22×C4×C137—42no—
220C22×C4×C137—42no—
221C22×C4×C137—42no—
222C22×C4×C137—42no—
223C22×C4×C137—81no—
224C22×C4×C137—81no—
225C22×C4×C137—81no—
226C22×C4×C137C2×D411yescharacteristic
227C22×C4×C137C2×D411yescharacteristic
228C22×C4×C137C2×D411yescharacteristic
229C22×C4×C137C2×D411yescharacteristic
230C22×C4×C137C2×D411yescharacteristic
231C22×C4×C137C2411yescharacteristic
232D8×C137—28no—
233D8×C137—44no—
234D8×C137—44no—
235D8×C137—44no—
236C2×C8×C137—21no—
237C2×C8×C137—21no—
238C2×C8×C137—21no—
239C2×C8×C137—21no—
240C2×C8×C137—21no—
241C2×C8×C137—21no—
242C2×C8×C137—21no—
243C2×C8×C137—21no—
244C2×C8×C137—21no—
245C2×C8×C137—21no—
246C2×C8×C137C2×D412yes—
247C2×C8×C137C2×D412yes—
248C4⋊C4×C137—21no—
249C4⋊C4×C137—21no—
250C4⋊C4×C137—21no—
251C4⋊C4×C137—21no—
252C4⋊C4×C137—21no—
253C4⋊C4×C137—21no—
254C4⋊C4×C137—21no—
255C4⋊C4×C137—42no—
256C4⋊C4×C137C2×D412yes—
257C22⋊C4×C137—22no—
258C22⋊C4×C137—22no—
259C22⋊C4×C137—42no—
260C22⋊C4×C137—42no—
261C22⋊C4×C137—42no—
262C22⋊C4×C137—42no—
263C22⋊C4×C137—42no—
264C22⋊C4×C137—42no—
265C22⋊C4×C137—42no—
266C22⋊C4×C137—42no—
267C22⋊C4×C137—42no—
268C22⋊C4×C137—81no—
269C22⋊C4×C137—81no—
270C22⋊C4×C137—81no—
271C42×C137—21no—
272C42×C137—21no—
273C42×C137—21no—
274C42×C137—21no—
275C23×C137—21no—
276C23×C137—22no—
277C23×C137—22no—
278C23×C137—22no—
279C23×C137—21no—
280C23×C137—21no—
281C23×C137—21no—
282C23×C137—21no—
283C23×C137—21no—
284C23×C137—22no—
285C23×C137—22no—
286C23×C137—48no—
287C23×C137—48no—
288C23×C137—41no—
289C23×C137—41no—
290C23×C137—41no—
291C23×C137—41no—
292C23×C137—41no—
293C23×C137—41no—
294C23×C137—41no—
295C23×C137—41no—
296C23×C137—41no—
297C23×C137—41no—
298C23×C137—41no—
299C23×C137—41no—
300C23×C137—41no—
301C23×C137—41no—
302C23×C137—41no—
303C23×C137—41no—
304C23×C137—41no—
305C23×C137—41no—
306C23×C137—41no—
307C23×C137—41no—
308C23×C137—41no—
309C23×C137—41no—
310C23×C137—41no—
311C23×C137—84no—
312C23×C137—84no—
313C23×C137—84no—
314C23×C137—84no—
315C23×C137—84no—
316C23×C137AGL(1,ℤ/8)12yes—
317C23×C137C22×D411yescharacteristic
318D4×C137—22no—
319D4×C137—22no—
320D4×C137—22no—
321D4×C137—22no—
322D4×C137—22no—
323D4×C137—22no—
324D4×C137—22no—
325D4×C137—48no—
326D4×C137—41no—
327D4×C137—41no—
328D4×C137—41no—
329D4×C137—41no—
330D4×C137—41no—
331D4×C137—41no—
332D4×C137—41no—
333D4×C137—41no—
334D4×C137—84no—
335D4×C137—84no—
336D4×C137—84no—
337D4×C137—84no—
338D4×C137#12114yescomplemented
339C2×C4×C137—21no—
340C2×C4×C137—21no—
341C2×C4×C137—21no—
342C2×C4×C137—21no—
343C2×C4×C137—21no—
344C2×C4×C137—21no—
345C2×C4×C137—22no—
346C2×C4×C137—21no—
347C2×C4×C137—21no—
348C2×C4×C137—21no—
349C2×C4×C137—21no—
350C2×C4×C137—21no—
351C2×C4×C137—21no—
352C2×C4×C137—21no—
353C2×C4×C137—21no—
354C2×C4×C137—41no—
355C2×C4×C137—41no—
356C2×C4×C137—41no—
357C2×C4×C137—41no—
358C2×C4×C137—41no—
359C2×C4×C137—41no—
360C2×C4×C137—41no—
361C2×C4×C137—41no—
362C2×C4×C137—41no—
363C2×C4×C137—41no—
364C2×C4×C137—41no—
365C2×C4×C137—41no—
366C2×C4×C137—41no—
367C2×C4×C137—41no—
368C2×C4×C137—41no—
369C2×C4×C137—84no—
370C2×C4×C137—84no—
371C2×C4×C137—84no—
372C2×C4×C137AGL(1,ℤ/8)12yes—
373C2×C4×C137C22×D411yescharacteristic
374C2×C4×C137C22×D411yescharacteristic
375C2×C4×C137C2×#4111yescharacteristic
376C2×C4×C137C2×#4111yescharacteristic
377C2×C4×C137H(5,𝔽2)11yescharacteristic
378C2×C4×C137H(5,𝔽2)11yescharacteristic
379C8×C137—22no—
380C8×C137—22no—
381C8×C137—41no—
382C8×C137—41no—
383C22×C137—22no—
384C22×C137—24no—
385C22×C137—22no—
386C22×C137—22no—
387C22×C137—42no—
388C22×C137—41no—
389C22×C137—42no—
390C22×C137—41no—
391C22×C137—42no—
392C22×C137—41no—
393C22×C137—42no—
394C22×C137—42no—
395C22×C137—42no—
396C22×C137—41no—
397C22×C137—42no—
398C22×C137—42no—
399C22×C137—42no—
400C22×C137—42no—
401C22×C137—42no—
402C22×C137—42no—
403C22×C137—816no—
404C22×C137—81no—
405C22×C137—81no—
406C22×C137—81no—
407C22×C137—81no—
408C22×C137—81no—
409C22×C137—81no—
410C22×C137—81no—
411C22×C137—81no—
412C22×C137—81no—
413C22×C137—81no—
414C22×C137—81no—
415C22×C137—81no—
416C22×C137—81no—
417C22×C137—81no—
418C22×C137—81no—
419C22×C137#52511yescharacteristic
420C22×C137D4211yescharacteristic
421C22×C137D4211yescharacteristic
422C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C137#57611yescharacteristic
425C22×C137#57611yescharacteristic
426C4×C137—22no—
427C4×C137—41no—
428C4×C137—41no—
429C4×C137—41no—
430C4×C137—42no—
431C4×C137—41no—
432C4×C137—81no—
433C4×C137—81no—
434C4×C137—81no—
435C4×C137C2×#12111yescharacteristic
436C4×C137#53811yescharacteristic
437C4×C137#54611yescharacteristic
438C4×C137#54611yescharacteristic
439C2×C137—42no—
440C2×C137—44no—
441C2×C137—82no—
442C2×C137—82no—
443C2×C137—161no—
444C2×C137#242411yescharacteristic
445C2×C137#310911yescharacteristic
446C2×C137#312211yescharacteristic
447C2×C137#326411yescharacteristic
448C2×C137#326411yescharacteristic
449C2×C137#326411yescharacteristic
450C2×C137#327411yescharacteristic
451#25168C13711yesmaximal, characteristic, direct product factor, Sylow
452C137#2516811yescharacteristic, direct product factor, Sylow
453C2×#459C2×C13711yescharacteristic, complemented
454C2×#447C2×C13711yescharacteristic, complemented
455C2×#447C2×C13711yescharacteristic, complemented
456C2×#442C2×C13711yescharacteristic, complemented
457#2428C2×C13711yescharacteristic, complemented
458D4×C22⋊C4C2×C13711yescharacteristic, complemented
459#2065C2×C13711yescharacteristic, complemented
460#2034C2×C13711yescharacteristic, complemented
461#2034C2×C13711yescharacteristic, complemented
462#2011C2×C13711yescharacteristic, complemented
463#1972C2×C13711yescharacteristic, complemented
464#1924C2×C13711yescharacteristic, complemented
465#1879C2×C13711yescharacteristic, complemented
466#1879C2×C13711yescharacteristic, complemented
467#1864C2×C13711yescharacteristic, complemented
468C23×D4C22×C13711yescharacteristic
469C22×D8C22×C13711yescharacteristic
470C22×D8C22×C13711yescharacteristic
471C22×D8C22×C13711yescharacteristic
472C22×D8C22×C13711yescharacteristic
473C2×#127C22×C13711yescharacteristic, complemented
474C2×#121—21no—
475C2×#121C22×C13711yescharacteristic
476C2×#121C22×C13711yescharacteristic
477C2×C4×D4C22×C13711yescharacteristic
478C2×C4×D4C22×C13711yescharacteristic
479C2×C4×D4C22×C13711yescharacteristic, complemented
480C22×C22⋊C4—21no—
481#459—24no—
482#447—24no—
483#447—24no—
484#442—24no—
485C2×#106C22×C13711yescharacteristic, complemented
486C2×#106C22×C13711yescharacteristic, complemented
487C2×C4⋊C8C22×C13711yescharacteristic, complemented
488C2×#102C22×C13711yescharacteristic
489C2×#102C22×C13711yescharacteristic
490C2×#102C22×C13711yescharacteristic
491C2×#102C22×C13711yescharacteristic
492C2×#102C22×C13711yescharacteristic, complemented
493C2×#102C22×C13711yescharacteristic, complemented
494C2×#102C22×C13711yescharacteristic, complemented
495C2×#102C22×C13711yescharacteristic, complemented
496C2×C22⋊C8C22×C13711yescharacteristic
497C2×C22⋊C8C22×C13711yescharacteristic
498C2×#97C22×C13711yescharacteristic, complemented
499#394—21no—
500#392—21no—
501#390C22×C13711yescharacteristic
502#390C22×C13711yescharacteristic
503#390C22×C13711yescharacteristic, complemented
504#389C22×C13711yescharacteristic, complemented
505#386—21no—
506#386—21no—
507#386—21no—
508#380C22×C13711yescharacteristic
509#379—21no—
510C4×C22⋊C4C22×C13711yescharacteristic
511#340C22×C13711yescharacteristic, complemented
512#340C22×C13711yescharacteristic, complemented
513#336C22×C13711yescharacteristic, complemented
514#336C22×C13711yescharacteristic, complemented
515C25—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C23×C13711yescharacteristic
528C22×D4C23×C13711yescharacteristic
529C22×D4C23×C13711yescharacteristic
530C22×D4C23×C13711yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C23×C13711yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8D4×C13714yescomplemented
547C22×C8C23×C13711yescharacteristic
548C22×C8C23×C13711yescharacteristic
549C22×C8C23×C13711yescharacteristic
550C22×C8C23×C13711yescharacteristic
551#127—22no—
552#127—41no—
553#121—22no—
554#121—22no—
555#121—44no—
556#121—41no—
557#121—41no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4C23×C13711yescharacteristic
566C2×C4⋊C4C23×C13711yescharacteristic
567C2×C4⋊C4C23×C13711yescharacteristic
568C2×C4⋊C4C23×C13711yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—44no—
582C2×C22⋊C4D4×C13711yescharacteristic
583C2×C22⋊C4D4×C13711yescharacteristic
584C2×C42C23×C13711yescharacteristic
585C2×C42C23×C13711yescharacteristic
586#106—22no—
587#106—41no—
588C4⋊C8—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102D4×C13714yescomplemented
597C22⋊C8—22no—
598C22⋊C8—22no—
599#97—22no—
600#95—21no—
601#95—21no—
602#95D4×C13711yescharacteristic
603#95D4×C13711yescharacteristic
604C24—21no—
605C24—24no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C13711yescharacteristic
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—44no—
643C2×D4—44no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—81no—
651C2×D4—81no—
652C2×D4—81no—
653C2×D4—81no—
654C2×D4C2×D4×C13712yes—
655C2×D4C2×D4×C13712yes—
656C2×D4C2×D4×C13712yes—
657C2×D4#41×C13712yes—
658C2×D4#41×C13712yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4—81no—
678C22×C4C2×D4×C13711yescharacteristic
679C22×C4C2×D4×C13711yescharacteristic
680C22×C4C2×D4×C13711yescharacteristic
681C22×C4C2×D4×C13711yescharacteristic
682C22×C4C2×D4×C13711yescharacteristic
683C22×C4C24×C13711yescharacteristic
684D8—28no—
685D8—44no—
686D8—44no—
687D8—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8C2×D4×C13712yes—
699C2×C8C2×D4×C13712yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4C2×D4×C13712yes—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C22⋊C4—81no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—22no—
738C23—48no—
739C23—48no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23AGL(1,ℤ/8)×C13712yes—
769C23C22×D4×C13711yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—84no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4#121×C13714yescomplemented
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—84no—
822C2×C4—84no—
823C2×C4—84no—
824C2×C4AGL(1,ℤ/8)×C13712yes—
825C2×C4C22×D4×C13711yescharacteristic
826C2×C4C22×D4×C13711yescharacteristic
827C2×C4C2×#41×C13711yescharacteristic
828C2×C4C2×#41×C13711yescharacteristic
829C2×C4H(5,𝔽2)×C13711yescharacteristic
830C2×C4H(5,𝔽2)×C13711yescharacteristic
831C8—22no—
832C8—22no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—24no—
837C22—22no—
838C22—22no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—41no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—41no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—816no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22#525×C13711yescharacteristic
872C22D42×C13711yescharacteristic
873C22D42×C13711yescharacteristic
874C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
875C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
876C22#576×C13711yescharacteristic
877C22#576×C13711yescharacteristic
878C4—22no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—42no—
883C4—41no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4C2×#121×C13711yescharacteristic
888C4#538×C13711yescharacteristic
889C4#546×C13711yescharacteristic
890C4#546×C13711yescharacteristic
891C2—42no—
892C2—44no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2#2424×C13711yescharacteristic
897C2#3109×C13711yescharacteristic
898C2#3122×C13711yescharacteristic
899C2#3264×C13711yescharacteristic
900C2#3264×C13711yescharacteristic
901C2#3264×C13711yescharacteristic
902C2#3274×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C4×C22⋊C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#459×C137C2semidirect
2. C2×#447×C137C2semidirect
3. C2×#447×C137C2semidirect
4. C2×#442×C137C2semidirect
5. #2428×C137C2semidirect
6. D4×C22⋊C4×C137C2semidirect
7. #2065×C137C2semidirect
8. #2034×C137C2semidirect
9. #2034×C137C2semidirect
10. #2011×C137C2semidirect
11. #1972×C137C2semidirect
12. #1924×C137C2semidirect
13. #1879×C137C2semidirect
14. #1879×C137C2semidirect
15. #1864×C137C2semidirect
21. C2×#127×C137C22semidirect
27. C2×C4×D4×C137C22semidirect
33. C2×#106×C137C22semidirect
34. C2×#106×C137C22semidirect
35. C2×C4⋊C8×C137C22semidirect
40. C2×#102×C137C22semidirect
41. C2×#102×C137C22semidirect
42. C2×#102×C137C22semidirect
43. C2×#102×C137C22semidirect
46. C2×#97×C137C22semidirect
51. #390×C137C22semidirect
52. #389×C137C22semidirect
59. #340×C137C22semidirect
60. #340×C137C22semidirect
61. #336×C137C22semidirect
62. #336×C137C22semidirect
94. C2×D8×C137D4semidirect
144. #102×C137D4semidirect
338. D4×C137#121semidirect
451. #25168C137direct (N × H)
452. C137#25168direct (N × H)
453. C2×#459C2×C137semidirect
454. C2×#447C2×C137semidirect
455. C2×#447C2×C137semidirect
456. C2×#442C2×C137semidirect
457. #2428C2×C137semidirect
458. D4×C22⋊C4C2×C137semidirect
459. #2065C2×C137semidirect
460. #2034C2×C137semidirect
461. #2034C2×C137semidirect
462. #2011C2×C137semidirect
463. #1972C2×C137semidirect
464. #1924C2×C137semidirect
465. #1879C2×C137semidirect
466. #1879C2×C137semidirect
467. #1864C2×C137semidirect
473. C2×#127C22×C137semidirect
479. C2×C4×D4C22×C137semidirect
485. C2×#106C22×C137semidirect
486. C2×#106C22×C137semidirect
487. C2×C4⋊C8C22×C137semidirect
492. C2×#102C22×C137semidirect
493. C2×#102C22×C137semidirect
494. C2×#102C22×C137semidirect
495. C2×#102C22×C137semidirect
498. C2×#97C22×C137semidirect
503. #390C22×C137semidirect
504. #389C22×C137semidirect
511. #340C22×C137semidirect
512. #340C22×C137semidirect
513. #336C22×C137semidirect
514. #336C22×C137semidirect
546. C2×D8D4×C137semidirect
596. #102D4×C137semidirect
790. D4#121×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1372
C2×#447×C1372
C2×#442×C1372
#2428×C1372
D4×C22⋊C4×C1372
#2065×C1372
#2034×C1372
#2011×C1372
#1972×C1372
#1924×C1372
#1879×C1372
#1864×C1372
#25168137