Finite Group Databasebeta

← C137×#26350 #46875736

Subgroups — C137×#26350 #46875736

Order 35072.

922 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#478×C137C211yesmaximal, characteristic, complemented
2C22×#107×C137C211yesmaximal, characteristic, complemented
3#2442×C137C211yesmaximal, characteristic, complemented
4#2361×C137C211yesmaximal, characteristic
5#2092×C137C211yesmaximal, characteristic, complemented
6#2087×C137C211yesmaximal, characteristic, complemented
7#2067×C137C211yesmaximal, characteristic, complemented
8#2059×C137C211yesmaximal, characteristic, complemented
9#1949×C137C211yesmaximal, characteristic, complemented
10#1921×C137C211yesmaximal, characteristic, complemented
11#1893×C137C211yesmaximal, characteristic
12#1874×C137C211yesmaximal, characteristic
13#1862×C137C211yesmaximal, characteristic, complemented
14#1853×C137C211yesmaximal, characteristic, complemented
15#1850×C137C211yesmaximal, characteristic, complemented
16C23×C8×C137C2211yescharacteristic
17C2×#125×C137C2211yescharacteristic
18C2×#121×C137C2211yescharacteristic
19C2×C4×D4×C137—21no—
20C2×C4×D4×C137C2211yescharacteristic
21C22×C4⋊C4×C137C2211yescharacteristic
22C22×C4⋊C4×C137C2211yescharacteristic
23#478×C137—24no—
24C2×#107×C137—24no—
25C2×#107×C137C2211yescharacteristic
26C2×#107×C137C2211yescharacteristic
27C2×#107×C137C2211yescharacteristic
28C2×#107×C137C2211yescharacteristic
29C2×#106×C137C2211yescharacteristic
30C2×#106×C137C2211yescharacteristic
31C2×C4⋊C8×C137C2211yescharacteristic
32C2×C4⋊C8×C137C2211yescharacteristic
33C2×#102×C137C2211yescharacteristic
34C2×#102×C137C2211yescharacteristic
35C2×#102×C137C2211yescharacteristic
36C2×#102×C137C2211yescharacteristic
37C2×C22⋊C8×C137C2211yescharacteristic
38#400×C137—21no—
39#398×C137—21no—
40#390×C137C2211yescharacteristic
41#389×C137C2211yescharacteristic
42#389×C137C2211yescharacteristic
43#389×C137C2211yescharacteristic
44#388×C137—21no—
45#386×C137—21no—
46#385×C137—21no—
47#385×C137—21no—
48#382×C137C2211yescharacteristic
49#380×C137—21no—
50#380×C137C2211yescharacteristic
51C4×C4⋊C4×C137C2211yescharacteristic
52C4×C22⋊C4×C137C2211yescharacteristic
53#340×C137C2211yescharacteristic
54#340×C137C2211yescharacteristic
55#340×C137C2211yescharacteristic
56#340×C137C2211yescharacteristic
57#340×C137C2211yescharacteristic
58#340×C137C2211yescharacteristic
59#336×C137C2211yescharacteristic
60#336×C137C2211yescharacteristic
61C22×D4×C137—21no—
62C22×D4×C137C2311yescharacteristic
63C23×C4×C137—21no—
64C23×C4×C137—21no—
65C23×C4×C137—21no—
66C23×C4×C137C2311yescharacteristic
67C22×C8×C137—22no—
68C22×C8×C137—22no—
69C22×C8×C137—22no—
70C22×C8×C137C2311yescharacteristic
71C22×C8×C137C2311yescharacteristic
72C22×C8×C137C2311yescharacteristic
73C22×C8×C137C2311yescharacteristic
74#125×C137—22no—
75#125×C137—41no—
76#121×C137—22no—
77#121×C137Q814yes—
78C4×D4×C137—22no—
79C4×D4×C137—41no—
80C4×D4×C137—44no—
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×C137C2311yescharacteristic
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×C22⋊C4×C137—21no—
100C2×C22⋊C4×C137—21no—
101C2×C22⋊C4×C137—21no—
102C2×C22⋊C4×C137—21no—
103C2×C22⋊C4×C137—21no—
104C2×C22⋊C4×C137D411yescharacteristic
105C2×C22⋊C4×C137D411yescharacteristic
106C2×C42×C137—21no—
107C2×C42×C137C2311yescharacteristic
108C2×C42×C137C2311yescharacteristic
109#107×C137—22no—
110#107×C137—22no—
111#107×C137—22no—
112#107×C137D414yescomplemented
113#106×C137—22no—
114#106×C137—41no—
115C4⋊C8×C137—22no—
116C4⋊C8×C137—22no—
117#102×C137—22no—
118#102×C137—22no—
119#102×C137—22no—
120#102×C137—41no—
121C22⋊C8×C137—22no—
122#95×C137—21no—
123#95×C137—21no—
124#95×C137—21no—
125#95×C137—21no—
126#95×C137—21no—
127#95×C137—21no—
128#95×C137—21no—
129#95×C137D411yescharacteristic
130#95×C137D411yescharacteristic
131C24×C137—21no—
132C24×C137C2×D411yescharacteristic
133C2×D4×C137—24no—
134C2×D4×C137—21no—
135C2×D4×C137—21no—
136C2×D4×C137—21no—
137C2×D4×C137—21no—
138C2×D4×C137—21no—
139C2×D4×C137—42no—
140C2×D4×C137—42no—
141C2×D4×C137C2×Q812yes—
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—42no—
154C22×C4×C137—42no—
155C22×C4×C137—42no—
156C22×C4×C137—42no—
157C22×C4×C137—42no—
158C22×C4×C137—42no—
159C22×C4×C137—81no—
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×C137C2×D411yescharacteristic
167C22×C4×C137C2×Q812yes—
168C22×C4×C137#4112yes—
169C22×C4×C137C2411yescharacteristic
170C2×C8×C137—28no—
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×C137C2×D412yes—
182C2×C8×C137#4112yes—
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—42no—
195C4⋊C4×C137—42no—
196C4⋊C4×C137—42no—
197C4⋊C4×C137—42no—
198C4⋊C4×C137—42no—
199C4⋊C4×C137—81no—
200C4⋊C4×C137—81no—
201C4⋊C4×C137C2×D412yes—
202C4⋊C4×C137C2×D412yes—
203C4⋊C4×C137C2×Q812yes—
204C22⋊C4×C137—22no—
205C22⋊C4×C137—22no—
206C22⋊C4×C137—24no—
207C22⋊C4×C137—42no—
208C22⋊C4×C137—42no—
209C22⋊C4×C137—42no—
210C22⋊C4×C137—81no—
211C42×C137—21no—
212C42×C137—21no—
213C42×C137—21no—
214C42×C137—21no—
215C42×C137—42no—
216C23×C137—21no—
217C23×C137—21no—
218C23×C137—21no—
219C23×C137—21no—
220C23×C137—22no—
221C23×C137—41no—
222C23×C137—41no—
223C23×C137—41no—
224C23×C137—41no—
225C23×C137—41no—
226C23×C137—41no—
227C23×C137C22⋊Q812yes—
228C23×C137#13512yes—
229C23×C137AGL(1,ℤ/8)12yes—
230C23×C137C22×D411yescharacteristic
231D4×C137—22no—
232D4×C137—22no—
233D4×C137—48no—
234D4×C137—41no—
235D4×C137—41no—
236C2×C4×C137—21no—
237C2×C4×C137—21no—
238C2×C4×C137—22no—
239C2×C4×C137—22no—
240C2×C4×C137—22no—
241C2×C4×C137—22no—
242C2×C4×C137—22no—
243C2×C4×C137—21no—
244C2×C4×C137—21no—
245C2×C4×C137—22no—
246C2×C4×C137—22no—
247C2×C4×C137—21no—
248C2×C4×C137—21no—
249C2×C4×C137—21no—
250C2×C4×C137—21no—
251C2×C4×C137—21no—
252C2×C4×C137—21no—
253C2×C4×C137—21no—
254C2×C4×C137—21no—
255C2×C4×C137—21no—
256C2×C4×C137—21no—
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—84no—
276C2×C4×C137—84no—
277C2×C4×C137—84no—
278C2×C4×C137C22⋊Q812yes—
279C2×C4×C137C22×D411yescharacteristic
280C2×C4×C137C22×Q811yescharacteristic
281C2×C4×C137C2×#4111yescharacteristic
282C2×C4×C137C2×#4111yescharacteristic
283C2×C4×C137H(5,𝔽2)11yescharacteristic
284C2×C4×C1372−1+411yescharacteristic
285C8×C137—22no—
286C8×C137—22no—
287C8×C137—41no—
288C8×C137—41no—
289C22×C137—22no—
290C22×C137—22no—
291C22×C137—22no—
292C22×C137—22no—
293C22×C137—22no—
294C22×C137—22no—
295C22×C137—42no—
296C22×C137—42no—
297C22×C137—42no—
298C22×C137—81no—
299C22×C137—81no—
300C22×C137—81no—
301C22×C137—81no—
302C22×C137#47814yescomplemented
303C22×C137C2×C22⋊Q811yescharacteristic
304C22×C137D4211yescharacteristic
305C22×C137#54711yescharacteristic
306C22×C137C2×#13511yescharacteristic
307C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
308C22×C137#57611yescharacteristic
309C22×C137#57811yescharacteristic
310C4×C137—22no—
311C4×C137—42no—
312C4×C137—41no—
313C4×C137—41no—
314C4×C137—41no—
315C4×C137—42no—
316C4×C137—42no—
317C4×C137—41no—
318C4×C137—81no—
319C4×C137—81no—
320C4×C137—81no—
321C4×C137—81no—
322C4×C137#52511yescharacteristic
323C4×C137#53911yescharacteristic
324C4×C137D4×Q811yescharacteristic
325C4×C137#55411yescharacteristic
326C2×C137—24no—
327C2×C137—82no—
328C2×C137#244911yescharacteristic
329C2×C137C2×#47811yescharacteristic
330C2×C137#308311yescharacteristic
331C2×C137#326411yescharacteristic
332C2×C137#328511yescharacteristic
333C2×C137#333911yescharacteristic
334C2×C137#334311yescharacteristic
335#26350C13711yesmaximal, characteristic, direct product factor, Sylow
336C137#2635011yescharacteristic, direct product factor, Sylow
337C2×#478C2×C13711yescharacteristic, complemented
338C22×#107C2×C13711yescharacteristic, complemented
339#2442C2×C13711yescharacteristic, complemented
340#2361C2×C13711yescharacteristic
341#2092C2×C13711yescharacteristic, complemented
342#2087C2×C13711yescharacteristic, complemented
343#2067C2×C13711yescharacteristic, complemented
344#2059C2×C13711yescharacteristic, complemented
345#1949C2×C13711yescharacteristic, complemented
346#1921C2×C13711yescharacteristic, complemented
347#1893C2×C13711yescharacteristic
348#1874C2×C13711yescharacteristic
349#1862C2×C13711yescharacteristic, complemented
350#1853C2×C13711yescharacteristic, complemented
351#1850C2×C13711yescharacteristic, complemented
352C23×C8C22×C13711yescharacteristic
353C2×#125C22×C13711yescharacteristic
354C2×#121C22×C13711yescharacteristic
355C2×C4×D4—21no—
356C2×C4×D4C22×C13711yescharacteristic
357C22×C4⋊C4C22×C13711yescharacteristic
358C22×C4⋊C4C22×C13711yescharacteristic
359#478—24no—
360C2×#107—24no—
361C2×#107C22×C13711yescharacteristic
362C2×#107C22×C13711yescharacteristic
363C2×#107C22×C13711yescharacteristic
364C2×#107C22×C13711yescharacteristic
365C2×#106C22×C13711yescharacteristic
366C2×#106C22×C13711yescharacteristic
367C2×C4⋊C8C22×C13711yescharacteristic
368C2×C4⋊C8C22×C13711yescharacteristic
369C2×#102C22×C13711yescharacteristic
370C2×#102C22×C13711yescharacteristic
371C2×#102C22×C13711yescharacteristic
372C2×#102C22×C13711yescharacteristic
373C2×C22⋊C8C22×C13711yescharacteristic
374#400—21no—
375#398—21no—
376#390C22×C13711yescharacteristic
377#389C22×C13711yescharacteristic
378#389C22×C13711yescharacteristic
379#389C22×C13711yescharacteristic
380#388—21no—
381#386—21no—
382#385—21no—
383#385—21no—
384#382C22×C13711yescharacteristic
385#380—21no—
386#380C22×C13711yescharacteristic
387C4×C4⋊C4C22×C13711yescharacteristic
388C4×C22⋊C4C22×C13711yescharacteristic
389#340C22×C13711yescharacteristic
390#340C22×C13711yescharacteristic
391#340C22×C13711yescharacteristic
392#340C22×C13711yescharacteristic
393#340C22×C13711yescharacteristic
394#340C22×C13711yescharacteristic
395#336C22×C13711yescharacteristic
396#336C22×C13711yescharacteristic
397C22×D4—21no—
398C22×D4C23×C13711yescharacteristic
399C23×C4—21no—
400C23×C4—21no—
401C23×C4—21no—
402C23×C4C23×C13711yescharacteristic
403C22×C8—22no—
404C22×C8—22no—
405C22×C8—22no—
406C22×C8C23×C13711yescharacteristic
407C22×C8C23×C13711yescharacteristic
408C22×C8C23×C13711yescharacteristic
409C22×C8C23×C13711yescharacteristic
410#125—22no—
411#125—41no—
412#121—22no—
413#121Q8×C13714yes—
414C4×D4—22no—
415C4×D4—41no—
416C4×D4—44no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—41no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4C23×C13711yescharacteristic
429C2×C4⋊C4C23×C13711yescharacteristic
430C2×C4⋊C4C23×C13711yescharacteristic
431C2×C4⋊C4C23×C13711yescharacteristic
432C2×C4⋊C4C23×C13711yescharacteristic
433C2×C4⋊C4C23×C13711yescharacteristic
434C2×C4⋊C4C23×C13711yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4D4×C13711yescharacteristic
441C2×C22⋊C4D4×C13711yescharacteristic
442C2×C42—21no—
443C2×C42C23×C13711yescharacteristic
444C2×C42C23×C13711yescharacteristic
445#107—22no—
446#107—22no—
447#107—22no—
448#107D4×C13714yescomplemented
449#106—22no—
450#106—41no—
451C4⋊C8—22no—
452C4⋊C8—22no—
453#102—22no—
454#102—22no—
455#102—22no—
456#102—41no—
457C22⋊C8—22no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95D4×C13711yescharacteristic
466#95D4×C13711yescharacteristic
467C24—21no—
468C24C2×D4×C13711yescharacteristic
469C2×D4—24no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4C2×Q8×C13712yes—
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—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—81no—
496C22×C4—81no—
497C22×C4—81no—
498C22×C4C2×D4×C13711yescharacteristic
499C22×C4C2×D4×C13711yescharacteristic
500C22×C4C2×D4×C13711yescharacteristic
501C22×C4C2×D4×C13711yescharacteristic
502C22×C4C2×D4×C13711yescharacteristic
503C22×C4C2×Q8×C13712yes—
504C22×C4#41×C13712yes—
505C22×C4C24×C13711yescharacteristic
506C2×C8—28no—
507C2×C8—21no—
508C2×C8—21no—
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×C8C2×D4×C13712yes—
518C2×C8#41×C13712yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
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—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—81no—
536C4⋊C4—81no—
537C4⋊C4C2×D4×C13712yes—
538C4⋊C4C2×D4×C13712yes—
539C4⋊C4C2×Q8×C13712yes—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—24no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—81no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—42no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C22⋊Q8×C13712yes—
564C23#135×C13712yes—
565C23AGL(1,ℤ/8)×C13712yes—
566C23C22×D4×C13711yescharacteristic
567D4—22no—
568D4—22no—
569D4—48no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
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—84no—
612C2×C4—84no—
613C2×C4—84no—
614C2×C4C22⋊Q8×C13712yes—
615C2×C4C22×D4×C13711yescharacteristic
616C2×C4C22×Q8×C13711yescharacteristic
617C2×C4C2×#41×C13711yescharacteristic
618C2×C4C2×#41×C13711yescharacteristic
619C2×C4H(5,𝔽2)×C13711yescharacteristic
620C2×C42−1+4×C13711yescharacteristic
621C8—22no—
622C8—22no—
623C8—41no—
624C8—41no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22#478×C13714yescomplemented
639C22C2×C22⋊Q8×C13711yescharacteristic
640C22D42×C13711yescharacteristic
641C22#547×C13711yescharacteristic
642C22C2×#135×C13711yescharacteristic
643C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
644C22#576×C13711yescharacteristic
645C22#578×C13711yescharacteristic
646C4—22no—
647C4—42no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4#525×C13711yescharacteristic
659C4#539×C13711yescharacteristic
660C4D4×Q8×C13711yescharacteristic
661C4#554×C13711yescharacteristic
662C2—24no—
663C2—82no—
664C2#2449×C13711yescharacteristic
665C2C2×#478×C13711yescharacteristic
666C2#3083×C13711yescharacteristic
667C2#3264×C13711yescharacteristic
668C2#3285×C13711yescharacteristic
669C2#3339×C13711yescharacteristic
670C2#3343×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC2×#121×C137C22
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×#478×C137C2semidirect
2. C22×#107×C137C2semidirect
3. #2442×C137C2semidirect
5. #2092×C137C2semidirect
6. #2087×C137C2semidirect
7. #2067×C137C2semidirect
8. #2059×C137C2semidirect
9. #1949×C137C2semidirect
10. #1921×C137C2semidirect
13. #1862×C137C2semidirect
14. #1853×C137C2semidirect
15. #1850×C137C2semidirect
112. #107×C137D4semidirect
302. C22×C137#478semidirect
335. #26350C137direct (N × H)
336. C137#26350direct (N × H)
337. C2×#478C2×C137semidirect
338. C22×#107C2×C137semidirect
339. #2442C2×C137semidirect
341. #2092C2×C137semidirect
342. #2087C2×C137semidirect
343. #2067C2×C137semidirect
344. #2059C2×C137semidirect
345. #1949C2×C137semidirect
346. #1921C2×C137semidirect
349. #1862C2×C137semidirect
350. #1853C2×C137semidirect
351. #1850C2×C137semidirect
448. #107D4×C137semidirect
638. C22#478×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#478×C1372
C22×#107×C1372
#2442×C1372
#2361×C1372
#2092×C1372
#2087×C1372
#2067×C1372
#2059×C1372
#1949×C1372
#1921×C1372
#1893×C1372
#1874×C1372
#1862×C1372
#1853×C1372
#1850×C1372
#26350137