Finite Group Databasebeta

← C137×#26216 #46875602

Subgroups — C137×#26216 #46875602

Order 35072.

840 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2415×C137C211yesmaximal, characteristic
2D4×C4⋊C4×C137C211yesmaximal, characteristic
3#2100×C137C211yesmaximal, characteristic, complemented
4#2075×C137C211yesmaximal, characteristic, complemented
5#2072×C137C211yesmaximal, characteristic, complemented
6#2035×C137C211yesmaximal, characteristic, complemented
7#1928×C137C211yesmaximal, characteristic, complemented
8#1919×C137C211yesmaximal, characteristic, complemented
9#1894×C137C211yesmaximal, characteristic, complemented
10#1872×C137C211yesmaximal, characteristic, complemented
11#1872×C137C211yesmaximal, characteristic, complemented
12#1870×C137C211yesmaximal, characteristic
13#1854×C137C211yesmaximal, characteristic, complemented
14#1823×C137C211yesmaximal, characteristic, complemented
15#1736×C137C211yesmaximal, characteristic, complemented
16C22×M16×C137C2211yescharacteristic
17C2×C22⋊Q8×C137C2211yescharacteristic
18C2×C22⋊Q8×C137C2211yescharacteristic
19C2×C4×D4×C137—21no—
20C2×C4×D4×C137C2211yescharacteristic
21C2×#117×C137C2211yescharacteristic
22C22×C4⋊C4×C137C2211yescharacteristic
23C22×C4⋊C4×C137C2211yescharacteristic
24C2×#107×C137C2211yescharacteristic
25C2×#106×C137C2211yescharacteristic
26C2×#103×C137C2211yescharacteristic
27C2×#103×C137C2211yescharacteristic
28C2×#103×C137C2211yescharacteristic
29C2×#103×C137C2211yescharacteristic
30C2×C22⋊C8×C137C2211yescharacteristic
31C2×C22⋊C8×C137C2211yescharacteristic
32C2×C22⋊C8×C137C2211yescharacteristic
33#397×C137—21no—
34#394×C137—21no—
35#391×C137C2211yescharacteristic
36#389×C137—21no—
37#389×C137—21no—
38#389×C137C2211yescharacteristic
39#388×C137—21no—
40#385×C137—21no—
41#385×C137—21no—
42#384×C137C2211yescharacteristic
43#380×C137C2211yescharacteristic
44#380×C137C2211yescharacteristic
45#380×C137C2211yescharacteristic
46C4×C4⋊C4×C137C2211yescharacteristic
47#340×C137C2211yescharacteristic
48#340×C137C2211yescharacteristic
49#340×C137C2211yescharacteristic
50#340×C137C2211yescharacteristic
51#340×C137C2211yescharacteristic
52#340×C137C2211yescharacteristic
53#340×C137C2211yescharacteristic
54#340×C137C2211yescharacteristic
55#340×C137C2211yescharacteristic
56#340×C137C2211yescharacteristic
57#336×C137C2211yescharacteristic
58#336×C137C2211yescharacteristic
59C22×Q8×C137C2311yescharacteristic
60C22×D4×C137D411yescharacteristic
61C23×C4×C137—21no—
62C23×C4×C137—21no—
63C23×C4×C137C2311yescharacteristic
64C23×C4×C137C2311yescharacteristic
65C2×M16×C137—22no—
66C2×M16×C137—41no—
67C2×M16×C137—41no—
68C22×C8×C137C2311yescharacteristic
69C22×C8×C137C2311yescharacteristic
70C22×C8×C137C2311yescharacteristic
71C22×C8×C137C2311yescharacteristic
72C22⋊Q8×C137—22no—
73C22⋊Q8×C137—22no—
74C22⋊Q8×C137—22no—
75C22⋊Q8×C137—41no—
76C4×D4×C137—22no—
77C4×D4×C137—22no—
78C4×D4×C137—44no—
79#117×C137—22no—
80#117×C137—41no—
81C2×C4⋊C4×C137—22no—
82C2×C4⋊C4×C137—22no—
83C2×C4⋊C4×C137—21no—
84C2×C4⋊C4×C137—21no—
85C2×C4⋊C4×C137—21no—
86C2×C4⋊C4×C137—21no—
87C2×C4⋊C4×C137—21no—
88C2×C4⋊C4×C137—21no—
89C2×C4⋊C4×C137—21no—
90C2×C4⋊C4×C137—41no—
91C2×C4⋊C4×C137—41no—
92C2×C4⋊C4×C137D411yescharacteristic
93C2×C4⋊C4×C137C2311yescharacteristic
94C2×C4⋊C4×C137C2311yescharacteristic
95C2×C4⋊C4×C137C2311yescharacteristic
96C2×C4⋊C4×C137C2311yescharacteristic
97C2×C4⋊C4×C137C2311yescharacteristic
98C2×C4⋊C4×C137C2311yescharacteristic
99C2×C4⋊C4×C137C2311yescharacteristic
100C2×C22⋊C4×C137—21no—
101C2×C22⋊C4×C137—21no—
102C2×C22⋊C4×C137—21no—
103C2×C22⋊C4×C137—21no—
104C2×C22⋊C4×C137—21no—
105C2×C22⋊C4×C137—21no—
106C2×C22⋊C4×C137D411yescharacteristic
107C2×C22⋊C4×C137D411yescharacteristic
108C2×C42×C137—21no—
109C2×C42×C137—21no—
110C2×C42×C137C2311yescharacteristic
111#107×C137—41no—
112#106×C137—22no—
113#103×C137—22no—
114#103×C137—41no—
115#103×C137—41no—
116#103×C137—41no—
117C22⋊C8×C137—22no—
118C22⋊C8×C137—41no—
119C22⋊C8×C137—41no—
120#95×C137—21no—
121#95×C137—21no—
122#95×C137—21no—
123#95×C137—21no—
124#95×C137—21no—
125#95×C137—21no—
126#95×C137—21no—
127C24×C137C2×D411yescharacteristic
128C24×C137C2×D411yescharacteristic
129C2×Q8×C137—21no—
130C2×Q8×C137—21no—
131C2×Q8×C137—21no—
132C2×Q8×C137—21no—
133C2×Q8×C137—21no—
134C2×Q8×C137—21no—
135C2×D4×C137—22no—
136C2×D4×C137—22no—
137C2×D4×C137—22no—
138C22×C4×C137—21no—
139C22×C4×C137—21no—
140C22×C4×C137—21no—
141C22×C4×C137—21no—
142C22×C4×C137—21no—
143C22×C4×C137—21no—
144C22×C4×C137—21no—
145C22×C4×C137—21no—
146C22×C4×C137—21no—
147C22×C4×C137—21no—
148C22×C4×C137—21no—
149C22×C4×C137—21no—
150C22×C4×C137—21no—
151C22×C4×C137—21no—
152C22×C4×C137—21no—
153C22×C4×C137—21no—
154C22×C4×C137—21no—
155C22×C4×C137—21no—
156C22×C4×C137—42no—
157C22×C4×C137—42no—
158C22×C4×C137—42no—
159C22×C4×C137—42no—
160C22×C4×C137—81no—
161C22×C4×C137—81no—
162C22×C4×C137C2×D411yescharacteristic
163C22×C4×C137C2×D411yescharacteristic
164C22×C4×C137C2×D411yescharacteristic
165C22×C4×C137C2×D411yescharacteristic
166C22×C4×C137#4112yes—
167C22×C4×C137#4112yes—
168C22×C4×C137C2411yescharacteristic
169M16×C137—44no—
170C2×C8×C137—21no—
171C2×C8×C137—21no—
172C2×C8×C137—21no—
173C2×C8×C137—21no—
174C2×C8×C137—21no—
175C2×C8×C137—21no—
176C2×C8×C137—21no—
177C2×C8×C137—21no—
178C2×C8×C137—21no—
179C2×C8×C137—21no—
180C2×C8×C137—21no—
181C2×C8×C137—21no—
182C4⋊C4×C137—22no—
183C4⋊C4×C137—21no—
184C4⋊C4×C137—21no—
185C4⋊C4×C137—21no—
186C4⋊C4×C137—21no—
187C4⋊C4×C137—21no—
188C4⋊C4×C137—21no—
189C4⋊C4×C137—21no—
190C4⋊C4×C137—21no—
191C4⋊C4×C137—21no—
192C4⋊C4×C137—21no—
193C4⋊C4×C137—21no—
194C4⋊C4×C137—21no—
195C4⋊C4×C137—42no—
196C4⋊C4×C137—42no—
197C4⋊C4×C137—42no—
198C4⋊C4×C137—42no—
199C4⋊C4×C137—42no—
200C4⋊C4×C137—42no—
201C4⋊C4×C137—81no—
202C4⋊C4×C137#4112yes—
203C4⋊C4×C137#4112yes—
204C22⋊C4×C137—22no—
205C22⋊C4×C137—22no—
206C22⋊C4×C137—42no—
207C22⋊C4×C137—42no—
208C22⋊C4×C137—42no—
209C22⋊C4×C137—42no—
210C22⋊C4×C137—42no—
211C22⋊C4×C137—42no—
212C42×C137—21no—
213C42×C137—21no—
214C42×C137—42no—
215C42×C137—42no—
216C23×C137—21no—
217C23×C137—21no—
218C23×C137—21no—
219C23×C137—21no—
220C23×C137—21no—
221C23×C137—21no—
222C23×C137—21no—
223C23×C137—21no—
224C23×C137—21no—
225C23×C137—21no—
226C23×C137—21no—
227C23×C137—21no—
228C23×C137#12312yes—
229C23×C137AGL(1,ℤ/8)12yes—
230C23×C137C22×D411yescharacteristic
231Q8×C137—41no—
232Q8×C137—41no—
233Q8×C137—41no—
234Q8×C137—41no—
235D4×C137—28no—
236C2×C4×C137—21no—
237C2×C4×C137—21no—
238C2×C4×C137—21no—
239C2×C4×C137—21no—
240C2×C4×C137—22no—
241C2×C4×C137—22no—
242C2×C4×C137—22no—
243C2×C4×C137—22no—
244C2×C4×C137—21no—
245C2×C4×C137—21no—
246C2×C4×C137—22no—
247C2×C4×C137—22no—
248C2×C4×C137—21no—
249C2×C4×C137—21no—
250C2×C4×C137—21no—
251C2×C4×C137—21no—
252C2×C4×C137—41no—
253C2×C4×C137—41no—
254C2×C4×C137—41no—
255C2×C4×C137—41no—
256C2×C4×C137—41no—
257C2×C4×C137—41no—
258C2×C4×C137—41no—
259C2×C4×C137—41no—
260C2×C4×C137—41no—
261C2×C4×C137—41no—
262C2×C4×C137—41no—
263C2×C4×C137—41no—
264C2×C4×C137—41no—
265C2×C4×C137—41no—
266C2×C4×C137—41no—
267C2×C4×C137—41no—
268C2×C4×C137—41no—
269C2×C4×C137—41no—
270C2×C4×C137—41no—
271C2×C4×C137—41no—
272C2×C4×C137—41no—
273C2×C4×C137—41no—
274C2×C4×C137—41no—
275C2×C4×C137—41no—
276C2×C4×C137—41no—
277C2×C4×C137—41no—
278C2×C4×C137—84no—
279C2×C4×C137—84no—
280C2×C4×C137#12312yes—
281C2×C4×C137#13712yes—
282C2×C4×C137C2×#4111yescharacteristic
283C2×C4×C137C2×#4111yescharacteristic
284C2×C4×C137C2×#4111yescharacteristic
285C2×C4×C137C2×#4111yescharacteristic
286C2×C4×C137H(5,𝔽2)11yescharacteristic
287C2×C4×C137H(5,𝔽2)11yescharacteristic
288C8×C137—41no—
289C8×C137—41no—
290C8×C137—41no—
291C8×C137—41no—
292C22×C137—22no—
293C22×C137—22no—
294C22×C137—22no—
295C22×C137—22no—
296C22×C137—22no—
297C22×C137—22no—
298C22×C137—41no—
299C22×C137—41no—
300C22×C137—41no—
301C22×C137—41no—
302C22×C137—41no—
303C22×C137—41no—
304C22×C137—41no—
305C22×C137—41no—
306C22×C137C2×#12311yescharacteristic
307C22×C137#54611yescharacteristic
308C22×C137#54611yescharacteristic
309C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
310C22×C137C2×#13711yescharacteristic
311C22×C137#57711yescharacteristic
312C22×C137#57811yescharacteristic
313C4×C137—22no—
314C4×C137—22no—
315C4×C137—42no—
316C4×C137—41no—
317C4×C137—41no—
318C4×C137—42no—
319C4×C137—81no—
320C4×C137—81no—
321C4×C137—81no—
322C4×C137—81no—
323C4×C137—81no—
324C4×C137—81no—
325C4×C137#52911yescharacteristic
326C4×C137#53811yescharacteristic
327C4×C137#55311yescharacteristic
328C4×C137#55311yescharacteristic
329C2×C137—42no—
330C2×C137—42no—
331C2×C137#244411yescharacteristic
332C2×C137#309211yescharacteristic
333C2×C137#309711yescharacteristic
334C2×C137#330811yescharacteristic
335C2×C137#331011yescharacteristic
336C2×C137#332811yescharacteristic
337C2×C137#333111yescharacteristic
338#26216C13711yesmaximal, characteristic, direct product factor, Sylow
339C137#2621611yescharacteristic, direct product factor, Sylow
340#2415C2×C13711yescharacteristic
341D4×C4⋊C4C2×C13711yescharacteristic
342#2100C2×C13711yescharacteristic, complemented
343#2075C2×C13711yescharacteristic, complemented
344#2072C2×C13711yescharacteristic, complemented
345#2035C2×C13711yescharacteristic, complemented
346#1928C2×C13711yescharacteristic, complemented
347#1919C2×C13711yescharacteristic, complemented
348#1894C2×C13711yescharacteristic, complemented
349#1872C2×C13711yescharacteristic, complemented
350#1872C2×C13711yescharacteristic, complemented
351#1870C2×C13711yescharacteristic
352#1854C2×C13711yescharacteristic, complemented
353#1823C2×C13711yescharacteristic, complemented
354#1736C2×C13711yescharacteristic, complemented
355C22×M16C22×C13711yescharacteristic
356C2×C22⋊Q8C22×C13711yescharacteristic
357C2×C22⋊Q8C22×C13711yescharacteristic
358C2×C4×D4—21no—
359C2×C4×D4C22×C13711yescharacteristic
360C2×#117C22×C13711yescharacteristic
361C22×C4⋊C4C22×C13711yescharacteristic
362C22×C4⋊C4C22×C13711yescharacteristic
363C2×#107C22×C13711yescharacteristic
364C2×#106C22×C13711yescharacteristic
365C2×#103C22×C13711yescharacteristic
366C2×#103C22×C13711yescharacteristic
367C2×#103C22×C13711yescharacteristic
368C2×#103C22×C13711yescharacteristic
369C2×C22⋊C8C22×C13711yescharacteristic
370C2×C22⋊C8C22×C13711yescharacteristic
371C2×C22⋊C8C22×C13711yescharacteristic
372#397—21no—
373#394—21no—
374#391C22×C13711yescharacteristic
375#389—21no—
376#389—21no—
377#389C22×C13711yescharacteristic
378#388—21no—
379#385—21no—
380#385—21no—
381#384C22×C13711yescharacteristic
382#380C22×C13711yescharacteristic
383#380C22×C13711yescharacteristic
384#380C22×C13711yescharacteristic
385C4×C4⋊C4C22×C13711yescharacteristic
386#340C22×C13711yescharacteristic
387#340C22×C13711yescharacteristic
388#340C22×C13711yescharacteristic
389#340C22×C13711yescharacteristic
390#340C22×C13711yescharacteristic
391#340C22×C13711yescharacteristic
392#340C22×C13711yescharacteristic
393#340C22×C13711yescharacteristic
394#340C22×C13711yescharacteristic
395#340C22×C13711yescharacteristic
396#336C22×C13711yescharacteristic
397#336C22×C13711yescharacteristic
398C22×Q8C23×C13711yescharacteristic
399C22×D4D4×C13711yescharacteristic
400C23×C4—21no—
401C23×C4—21no—
402C23×C4C23×C13711yescharacteristic
403C23×C4C23×C13711yescharacteristic
404C2×M16—22no—
405C2×M16—41no—
406C2×M16—41no—
407C22×C8C23×C13711yescharacteristic
408C22×C8C23×C13711yescharacteristic
409C22×C8C23×C13711yescharacteristic
410C22×C8C23×C13711yescharacteristic
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—41no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—44no—
418#117—22no—
419#117—41no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—41no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4D4×C13711yescharacteristic
432C2×C4⋊C4C23×C13711yescharacteristic
433C2×C4⋊C4C23×C13711yescharacteristic
434C2×C4⋊C4C23×C13711yescharacteristic
435C2×C4⋊C4C23×C13711yescharacteristic
436C2×C4⋊C4C23×C13711yescharacteristic
437C2×C4⋊C4C23×C13711yescharacteristic
438C2×C4⋊C4C23×C13711yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4D4×C13711yescharacteristic
446C2×C22⋊C4D4×C13711yescharacteristic
447C2×C42—21no—
448C2×C42—21no—
449C2×C42C23×C13711yescharacteristic
450#107—41no—
451#106—22no—
452#103—22no—
453#103—41no—
454#103—41no—
455#103—41no—
456C22⋊C8—22no—
457C22⋊C8—41no—
458C22⋊C8—41no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466C24C2×D4×C13711yescharacteristic
467C24C2×D4×C13711yescharacteristic
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4C2×D4×C13711yescharacteristic
502C22×C4C2×D4×C13711yescharacteristic
503C22×C4C2×D4×C13711yescharacteristic
504C22×C4C2×D4×C13711yescharacteristic
505C22×C4#41×C13712yes—
506C22×C4#41×C13712yes—
507C22×C4C24×C13711yescharacteristic
508M16—44no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—81no—
541C4⋊C4#41×C13712yes—
542C4⋊C4#41×C13712yes—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—42no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23#123×C13712yes—
568C23AGL(1,ℤ/8)×C13712yes—
569C23C22×D4×C13711yescharacteristic
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—41no—
574D4—28no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—84no—
618C2×C4—84no—
619C2×C4#123×C13712yes—
620C2×C4#137×C13712yes—
621C2×C4C2×#41×C13711yescharacteristic
622C2×C4C2×#41×C13711yescharacteristic
623C2×C4C2×#41×C13711yescharacteristic
624C2×C4C2×#41×C13711yescharacteristic
625C2×C4H(5,𝔽2)×C13711yescharacteristic
626C2×C4H(5,𝔽2)×C13711yescharacteristic
627C8—41no—
628C8—41no—
629C8—41no—
630C8—41no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22C2×#123×C13711yescharacteristic
646C22#546×C13711yescharacteristic
647C22#546×C13711yescharacteristic
648C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
649C22C2×#137×C13711yescharacteristic
650C22#577×C13711yescharacteristic
651C22#578×C13711yescharacteristic
652C4—22no—
653C4—22no—
654C4—42no—
655C4—42no—
656C4—41no—
657C4—41no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4#529×C13711yescharacteristic
665C4#538×C13711yescharacteristic
666C4#553×C13711yescharacteristic
667C4#553×C13711yescharacteristic
668C2—42no—
669C2—42no—
670C2#2444×C13711yescharacteristic
671C2#3092×C13711yescharacteristic
672C2#3097×C13711yescharacteristic
673C2#3308×C13711yescharacteristic
674C2#3310×C13711yescharacteristic
675C2#3328×C13711yescharacteristic
676C2#3331×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC22×D4×C137D4
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
3. #2100×C137C2semidirect
4. #2075×C137C2semidirect
5. #2072×C137C2semidirect
6. #2035×C137C2semidirect
7. #1928×C137C2semidirect
8. #1919×C137C2semidirect
9. #1894×C137C2semidirect
10. #1872×C137C2semidirect
11. #1872×C137C2semidirect
13. #1854×C137C2semidirect
14. #1823×C137C2semidirect
15. #1736×C137C2semidirect
338. #26216C137direct (N × H)
339. C137#26216direct (N × H)
342. #2100C2×C137semidirect
343. #2075C2×C137semidirect
344. #2072C2×C137semidirect
345. #2035C2×C137semidirect
346. #1928C2×C137semidirect
347. #1919C2×C137semidirect
348. #1894C2×C137semidirect
349. #1872C2×C137semidirect
350. #1872C2×C137semidirect
352. #1854C2×C137semidirect
353. #1823C2×C137semidirect
354. #1736C2×C137semidirect

Maximal subgroups

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

subgroupindex
#2415×C1372
D4×C4⋊C4×C1372
#2100×C1372
#2075×C1372
#2072×C1372
#2035×C1372
#1928×C1372
#1919×C1372
#1894×C1372
#1872×C1372
#1870×C1372
#1854×C1372
#1823×C1372
#1736×C1372
#26216137