Finite Group Databasebeta

← C137×#22780 #46872166

Subgroups — C137×#22780 #46872166

Order 35072.

942 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#442×C137C211yesmaximal, characteristic
2#2354×C137C211yesmaximal, characteristic, complemented
3#2349×C137C211yesmaximal, characteristic, complemented
4#1936×C137C211yesmaximal, characteristic, complemented
5#1934×C137C211yesmaximal, characteristic, complemented
6#1920×C137C211yesmaximal, characteristic, complemented
7#1919×C137C211yesmaximal, characteristic, complemented
8#1879×C137C211yesmaximal, characteristic
9#1879×C137C211yesmaximal, characteristic
10#1836×C137C211yesmaximal, characteristic, complemented
11#1804×C137C211yesmaximal, characteristic, complemented
12#1802×C137C211yesmaximal, characteristic, complemented
13#1771×C137C211yesmaximal, characteristic, complemented
14#1762×C137C211yesmaximal, characteristic, complemented
15C4×#102×C137C211yesmaximal, characteristic, complemented
16C22×D8×C137C2211yescharacteristic
17C2×C4×D4×C137C2211yescharacteristic
18C2×C4×D4×C137C2211yescharacteristic
19C2×C4×D4×C137C2211yescharacteristic
20C2×C4×D4×C137C2211yescharacteristic
21C2×#117×C137—21no—
22#442×C137C418yescomplemented
23C2×#106×C137C2211yescharacteristic
24C2×C4⋊C8×C137C2211yescharacteristic
25C2×#102×C137C2211yescharacteristic
26C2×#102×C137C2211yescharacteristic
27C2×#102×C137C2211yescharacteristic
28C2×#102×C137C2211yescharacteristic
29C2×#102×C137C2211yescharacteristic
30C2×#102×C137C2211yescharacteristic
31C2×#97×C137C2211yescharacteristic
32C2×#97×C137C2211yescharacteristic
33C2×C4×C8×C137C2211yescharacteristic
34#390×C137C2211yescharacteristic
35#390×C137C2211yescharacteristic
36#389×C137C2211yescharacteristic
37#389×C137C2211yescharacteristic
38#388×C137—21no—
39#388×C137—21no—
40#385×C137—21no—
41#385×C137—21no—
42#384×C137C2211yescharacteristic
43#382×C137C2211yescharacteristic
44#380×C137—21no—
45#380×C137—21no—
46C4×C4⋊C4×C137C2211yescharacteristic
47C4×C4⋊C4×C137C2211yescharacteristic
48C4×C4⋊C4×C137C2211yescharacteristic
49C2×#95×C137—21no—
50#340×C137C2211yescharacteristic
51#340×C137C2211yescharacteristic
52#340×C137C2211yescharacteristic
53#340×C137C2211yescharacteristic
54#340×C137C2211yescharacteristic
55#340×C137C2211yescharacteristic
56#340×C137C2211yescharacteristic
57#340×C137C2211yescharacteristic
58#336×C137C2211yescharacteristic
59#336×C137C2211yescharacteristic
60C22×D4×C137C2311yescharacteristic
61C22×D4×C137C2311yescharacteristic
62C23×C4×C137—21no—
63C23×C4×C137—21no—
64C23×C4×C137—21no—
65C23×C4×C137—21no—
66C2×D8×C137—22no—
67C2×D8×C137—22no—
68C2×D8×C137C2×C414yes—
69C22×C8×C137C2311yescharacteristic
70C22×C8×C137C2311yescharacteristic
71C22×C8×C137C2311yescharacteristic
72C22×C8×C137C2311yescharacteristic
73C4×D4×C137—22no—
74C4×D4×C137—22no—
75C4×D4×C137—22no—
76C4×D4×C137—22no—
77C4×D4×C137—41no—
78C4×D4×C137—41no—
79C4×D4×C137C2×C414yes—
80C4×D4×C137C2×C414yescomplemented
81#117×C137—44no—
82C2×C4⋊C4×C137—21no—
83C2×C4⋊C4×C137—21no—
84C2×C4⋊C4×C137—21no—
85C2×C4⋊C4×C137—21no—
86C2×C4⋊C4×C137D411yescharacteristic
87C2×C4⋊C4×C137D411yescharacteristic
88C2×C4⋊C4×C137C2311yescharacteristic
89C2×C4⋊C4×C137C2311yescharacteristic
90C2×C4⋊C4×C137C2311yescharacteristic
91C2×C4⋊C4×C137C2311yescharacteristic
92C2×C4⋊C4×C137C2311yescharacteristic
93C2×C4⋊C4×C137C2311yescharacteristic
94C2×C22⋊C4×C137—21no—
95C2×C22⋊C4×C137—21no—
96C2×C22⋊C4×C137—21no—
97C2×C22⋊C4×C137—21no—
98C2×C22⋊C4×C137—21no—
99C2×C22⋊C4×C137—21no—
100C2×C22⋊C4×C137—21no—
101C2×C22⋊C4×C137—21no—
102C2×C42×C137—21no—
103C2×C42×C137—21no—
104C2×C42×C137C2311yescharacteristic
105C2×C42×C137C2311yescharacteristic
106C2×C42×C137C2311yescharacteristic
107#106×C137C2×C414yescomplemented
108C4⋊C8×C137—22no—
109#102×C137—22no—
110#102×C137—22no—
111#102×C137—41no—
112#102×C137—41no—
113#102×C137C2×C414yes—
114#102×C137C2×C414yescomplemented
115#97×C137—41no—
116#97×C137C2×C414yescomplemented
117C4×C8×C137—41no—
118#95×C137—21no—
119#95×C137—21no—
120#95×C137—21no—
121#95×C137—21no—
122#95×C137—21no—
123#95×C137—21no—
124#95×C137D411yescharacteristic
125#95×C137D411yescharacteristic
126C24×C137—21no—
127C24×C137—21no—
128C2×D4×C137—21no—
129C2×D4×C137—21no—
130C2×D4×C137—21no—
131C2×D4×C137—21no—
132C2×D4×C137—21no—
133C2×D4×C137—21no—
134C2×D4×C137—21no—
135C2×D4×C137—21no—
136C2×D4×C137C22×C412yes—
137C2×D4×C137C22×C412yes—
138C2×D4×C137#4112yes—
139C2×D4×C137#4112yes—
140C22×C4×C137—21no—
141C22×C4×C137—21no—
142C22×C4×C137—24no—
143C22×C4×C137—24no—
144C22×C4×C137—21no—
145C22×C4×C137—21no—
146C22×C4×C137—21no—
147C22×C4×C137—21no—
148C22×C4×C137—42no—
149C22×C4×C137—42no—
150C22×C4×C137—42no—
151C22×C4×C137—42no—
152C22×C4×C137—42no—
153C22×C4×C137—42no—
154C22×C4×C137—81no—
155C22×C4×C137—81no—
156C22×C4×C137—81no—
157C22×C4×C137—81no—
158C22×C4×C137C2×D411yescharacteristic
159C22×C4×C137C2×D411yescharacteristic
160C22×C4×C137C2×D411yescharacteristic
161C22×C4×C137C2×D411yescharacteristic
162C22×C4×C137C2×D411yescharacteristic
163C22×C4×C137C2×D411yescharacteristic
164C22×C4×C137C2411yescharacteristic
165D8×C137—28no—
166C2×C8×C137—21no—
167C2×C8×C137—21no—
168C2×C8×C137—21no—
169C2×C8×C137—21no—
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×C137C22×C412yes—
177C2×C8×C137C22×C412yes—
178C4⋊C4×C137—22no—
179C4⋊C4×C137—21no—
180C4⋊C4×C137—21no—
181C4⋊C4×C137—21no—
182C4⋊C4×C137—21no—
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—41no—
190C4⋊C4×C137—42no—
191C4⋊C4×C137—81no—
192C4⋊C4×C137—81no—
193C4⋊C4×C137—81no—
194C4⋊C4×C137C22×C412yes—
195C4⋊C4×C137C22×C412yes—
196C22⋊C4×C137—24no—
197C22⋊C4×C137—24no—
198C22⋊C4×C137—42no—
199C22⋊C4×C137—42no—
200C22⋊C4×C137—42no—
201C22⋊C4×C137—42no—
202C22⋊C4×C137—81no—
203C22⋊C4×C137—81no—
204C42×C137—21no—
205C42×C137—21no—
206C42×C137—21no—
207C42×C137—21no—
208C42×C137—42no—
209C42×C137—42no—
210C42×C137C22×C412yes—
211C42×C137#4112yes—
212C23×C137—22no—
213C23×C137—22no—
214C23×C137—22no—
215C23×C137—22no—
216C23×C137—41no—
217C23×C137—41no—
218C23×C137—41no—
219C23×C137—41no—
220C23×C137—41no—
221C23×C137—41no—
222C23×C137—41no—
223C23×C137—41no—
224C23×C137—41no—
225C23×C137—41no—
226C23×C137C22×D411yescharacteristic
227D4×C137—22no—
228D4×C137—22no—
229D4×C137—22no—
230D4×C137—22no—
231D4×C137—22no—
232D4×C137—41no—
233D4×C137—41no—
234D4×C137#11714yescomplemented
235C2×C4×C137—21no—
236C2×C4×C137—21no—
237C2×C4×C137—21no—
238C2×C4×C137—21no—
239C2×C4×C137—21no—
240C2×C4×C137—21no—
241C2×C4×C137—22no—
242C2×C4×C137—22no—
243C2×C4×C137—21no—
244C2×C4×C137—21no—
245C2×C4×C137—21no—
246C2×C4×C137—21no—
247C2×C4×C137—21no—
248C2×C4×C137—21no—
249C2×C4×C137—21no—
250C2×C4×C137—21no—
251C2×C4×C137—21no—
252C2×C4×C137—48no—
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—84no—
270C2×C4×C137—84no—
271C2×C4×C137—84no—
272C2×C4×C137C4×D412yes—
273C2×C4×C137C4×D412yes—
274C2×C4×C137AGL(1,ℤ/8)12yes—
275C2×C4×C137C23×C411yescharacteristic
276C2×C4×C137C2×#4111yescharacteristic
277C2×C4×C137C2×#4111yescharacteristic
278C2×C4×C137C2×#4111yescharacteristic
279C2×C4×C137H(5,𝔽2)11yescharacteristic
280C2×C4×C1372−1+411yescharacteristic
281C8×C137—22no—
282C8×C137—22no—
283C8×C137—41no—
284C8×C137—41no—
285C22×C137—24no—
286C22×C137—42no—
287C22×C137—42no—
288C22×C137—42no—
289C22×C137—42no—
290C22×C137—42no—
291C22×C137—42no—
292C22×C137—42no—
293C22×C137—42no—
294C22×C137—42no—
295C22×C137—81no—
296C22×C137—81no—
297C22×C137—81no—
298C22×C137—81no—
299C22×C137C2×C4×D411yescharacteristic
300C22×C137#54611yescharacteristic
301C22×C137#54811yescharacteristic
302C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
303C22×C137#57511yescharacteristic
304C22×C137#57611yescharacteristic
305C22×C137#57711yescharacteristic
306C4×C137—22no—
307C4×C137—22no—
308C4×C137—22no—
309C4×C137—42no—
310C4×C137—42no—
311C4×C137—41no—
312C4×C137—41no—
313C4×C137—41no—
314C4×C137—81no—
315C4×C137—81no—
316C4×C137—81no—
317C4×C137—81no—
318C4×C137C2×#11711yescharacteristic
319C4×C137#52011yescharacteristic
320C4×C137#55211yescharacteristic
321C4×C137#55311yescharacteristic
322C2×C137—44no—
323C2×C137—82no—
324C2×C137#235211yescharacteristic
325C2×C137C4×AGL(1,ℤ/8)11yescharacteristic
326C2×C137#294611yescharacteristic
327C2×C137#330611yescharacteristic
328C2×C137#331911yescharacteristic
329C2×C137#336611yescharacteristic
330C2×C137#337611yescharacteristic
331#22780C13711yesmaximal, characteristic, direct product factor, Sylow
332C137#2278011yescharacteristic, direct product factor, Sylow
333C2×#442C2×C13711yescharacteristic
334#2354C2×C13711yescharacteristic, complemented
335#2349C2×C13711yescharacteristic, complemented
336#1936C2×C13711yescharacteristic, complemented
337#1934C2×C13711yescharacteristic, complemented
338#1920C2×C13711yescharacteristic, complemented
339#1919C2×C13711yescharacteristic, complemented
340#1879C2×C13711yescharacteristic
341#1879C2×C13711yescharacteristic
342#1836C2×C13711yescharacteristic, complemented
343#1804C2×C13711yescharacteristic, complemented
344#1802C2×C13711yescharacteristic, complemented
345#1771C2×C13711yescharacteristic, complemented
346#1762C2×C13711yescharacteristic, complemented
347C4×#102C2×C13711yescharacteristic, complemented
348C22×D8C22×C13711yescharacteristic
349C2×C4×D4C22×C13711yescharacteristic
350C2×C4×D4C22×C13711yescharacteristic
351C2×C4×D4C22×C13711yescharacteristic
352C2×C4×D4C22×C13711yescharacteristic
353C2×#117—21no—
354#442C4×C13718yescomplemented
355C2×#106C22×C13711yescharacteristic
356C2×C4⋊C8C22×C13711yescharacteristic
357C2×#102C22×C13711yescharacteristic
358C2×#102C22×C13711yescharacteristic
359C2×#102C22×C13711yescharacteristic
360C2×#102C22×C13711yescharacteristic
361C2×#102C22×C13711yescharacteristic
362C2×#102C22×C13711yescharacteristic
363C2×#97C22×C13711yescharacteristic
364C2×#97C22×C13711yescharacteristic
365C2×C4×C8C22×C13711yescharacteristic
366#390C22×C13711yescharacteristic
367#390C22×C13711yescharacteristic
368#389C22×C13711yescharacteristic
369#389C22×C13711yescharacteristic
370#388—21no—
371#388—21no—
372#385—21no—
373#385—21no—
374#384C22×C13711yescharacteristic
375#382C22×C13711yescharacteristic
376#380—21no—
377#380—21no—
378C4×C4⋊C4C22×C13711yescharacteristic
379C4×C4⋊C4C22×C13711yescharacteristic
380C4×C4⋊C4C22×C13711yescharacteristic
381C2×#95—21no—
382#340C22×C13711yescharacteristic
383#340C22×C13711yescharacteristic
384#340C22×C13711yescharacteristic
385#340C22×C13711yescharacteristic
386#340C22×C13711yescharacteristic
387#340C22×C13711yescharacteristic
388#340C22×C13711yescharacteristic
389#340C22×C13711yescharacteristic
390#336C22×C13711yescharacteristic
391#336C22×C13711yescharacteristic
392C22×D4C23×C13711yescharacteristic
393C22×D4C23×C13711yescharacteristic
394C23×C4—21no—
395C23×C4—21no—
396C23×C4—21no—
397C23×C4—21no—
398C2×D8—22no—
399C2×D8—22no—
400C2×D8C2×C4×C13714yes—
401C22×C8C23×C13711yescharacteristic
402C22×C8C23×C13711yescharacteristic
403C22×C8C23×C13711yescharacteristic
404C22×C8C23×C13711yescharacteristic
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—41no—
410C4×D4—41no—
411C4×D4C2×C4×C13714yes—
412C4×D4C2×C4×C13714yescomplemented
413#117—44no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4D4×C13711yescharacteristic
419C2×C4⋊C4D4×C13711yescharacteristic
420C2×C4⋊C4C23×C13711yescharacteristic
421C2×C4⋊C4C23×C13711yescharacteristic
422C2×C4⋊C4C23×C13711yescharacteristic
423C2×C4⋊C4C23×C13711yescharacteristic
424C2×C4⋊C4C23×C13711yescharacteristic
425C2×C4⋊C4C23×C13711yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42C23×C13711yescharacteristic
437C2×C42C23×C13711yescharacteristic
438C2×C42C23×C13711yescharacteristic
439#106C2×C4×C13714yescomplemented
440C4⋊C8—22no—
441#102—22no—
442#102—22no—
443#102—41no—
444#102—41no—
445#102C2×C4×C13714yes—
446#102C2×C4×C13714yescomplemented
447#97—41no—
448#97C2×C4×C13714yescomplemented
449C4×C8—41no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95D4×C13711yescharacteristic
457#95D4×C13711yescharacteristic
458C24—21no—
459C24—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4C22×C4×C13712yes—
469C2×D4C22×C4×C13712yes—
470C2×D4#41×C13712yes—
471C2×D4#41×C13712yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4C2×D4×C13711yescharacteristic
491C22×C4C2×D4×C13711yescharacteristic
492C22×C4C2×D4×C13711yescharacteristic
493C22×C4C2×D4×C13711yescharacteristic
494C22×C4C2×D4×C13711yescharacteristic
495C22×C4C2×D4×C13711yescharacteristic
496C22×C4C24×C13711yescharacteristic
497D8—28no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8C22×C4×C13712yes—
509C2×C8C22×C4×C13712yes—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—41no—
522C4⋊C4—42no—
523C4⋊C4—81no—
524C4⋊C4—81no—
525C4⋊C4—81no—
526C4⋊C4C22×C4×C13712yes—
527C4⋊C4C22×C4×C13712yes—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—42no—
531C22⋊C4—42no—
532C22⋊C4—42no—
533C22⋊C4—42no—
534C22⋊C4—81no—
535C22⋊C4—81no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—42no—
541C42—42no—
542C42C22×C4×C13712yes—
543C42#41×C13712yes—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23C22×D4×C13711yescharacteristic
559D4—22no—
560D4—22no—
561D4—22no—
562D4—22no—
563D4—22no—
564D4—41no—
565D4—41no—
566D4#117×C13714yescomplemented
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—48no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
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—84no—
602C2×C4—84no—
603C2×C4—84no—
604C2×C4C4×D4×C13712yes—
605C2×C4C4×D4×C13712yes—
606C2×C4AGL(1,ℤ/8)×C13712yes—
607C2×C4C23×C4×C13711yescharacteristic
608C2×C4C2×#41×C13711yescharacteristic
609C2×C4C2×#41×C13711yescharacteristic
610C2×C4C2×#41×C13711yescharacteristic
611C2×C4H(5,𝔽2)×C13711yescharacteristic
612C2×C42−1+4×C13711yescharacteristic
613C8—22no—
614C8—22no—
615C8—41no—
616C8—41no—
617C22—24no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22C2×C4×D4×C13711yescharacteristic
632C22#546×C13711yescharacteristic
633C22#548×C13711yescharacteristic
634C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
635C22#575×C13711yescharacteristic
636C22#576×C13711yescharacteristic
637C22#577×C13711yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—42no—
645C4—42no—
646C4—81no—
647C4—81no—
648C4—81no—
649C4—81no—
650C4C2×#117×C13711yescharacteristic
651C4#520×C13711yescharacteristic
652C4#552×C13711yescharacteristic
653C4#553×C13711yescharacteristic
654C2—44no—
655C2—82no—
656C2#2352×C13711yescharacteristic
657C2C4×AGL(1,ℤ/8)×C13711yescharacteristic
658C2#2946×C13711yescharacteristic
659C2#3306×C13711yescharacteristic
660C2#3319×C13711yescharacteristic
661C2#3366×C13711yescharacteristic
662C2#3376×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutatorC2×C4C23×C4×C137
Frattini, cosocleC22×C4C24×C137
prime radicalC22×D8×C137C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C4×C4⋊C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2354×C137C2semidirect
3. #2349×C137C2semidirect
4. #1936×C137C2semidirect
5. #1934×C137C2semidirect
6. #1920×C137C2semidirect
7. #1919×C137C2semidirect
10. #1836×C137C2semidirect
11. #1804×C137C2semidirect
12. #1802×C137C2semidirect
13. #1771×C137C2semidirect
14. #1762×C137C2semidirect
15. C4×#102×C137C2semidirect
22. #442×C137C4semidirect
80. C4×D4×C137C2×C4semidirect
107. #106×C137C2×C4semidirect
114. #102×C137C2×C4semidirect
116. #97×C137C2×C4semidirect
234. D4×C137#117semidirect
331. #22780C137direct (N × H)
332. C137#22780direct (N × H)
334. #2354C2×C137semidirect
335. #2349C2×C137semidirect
336. #1936C2×C137semidirect
337. #1934C2×C137semidirect
338. #1920C2×C137semidirect
339. #1919C2×C137semidirect
342. #1836C2×C137semidirect
343. #1804C2×C137semidirect
344. #1802C2×C137semidirect
345. #1771C2×C137semidirect
346. #1762C2×C137semidirect
347. C4×#102C2×C137semidirect
354. #442C4×C137semidirect
412. C4×D4C2×C4×C137semidirect
439. #106C2×C4×C137semidirect
446. #102C2×C4×C137semidirect
448. #97C2×C4×C137semidirect
566. D4#117×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#442×C1372
#2354×C1372
#2349×C1372
#1936×C1372
#1934×C1372
#1920×C1372
#1919×C1372
#1879×C1372
#1836×C1372
#1804×C1372
#1802×C1372
#1771×C1372
#1762×C1372
C4×#102×C1372
#22780137