Finite Group Databasebeta

← C137×#24259 #46873645

Subgroups — C137×#24259 #46873645

Order 35072.

1566 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C137C211yesmaximal, characteristic
2C2×#464×C137C211yesmaximal, characteristic, complemented
3C2×#452×C137C211yesmaximal, characteristic, complemented
4C2×#450×C137C211yesmaximal, characteristic, complemented
5C2×#440×C137C211yesmaximal, characteristic, complemented
6#2538×C137C211yesmaximal, characteristic, complemented
7#2036×C137C211yesmaximal, characteristic, complemented
8#2033×C137C211yesmaximal, characteristic, complemented
9#2001×C137C211yesmaximal, characteristic, complemented
10#2000×C137C211yesmaximal, characteristic, complemented
11#1959×C137C211yesmaximal, characteristic, complemented
12#1955×C137C211yesmaximal, characteristic, complemented
13#1802×C137C211yesmaximal, characteristic, complemented
14#1788×C137C211yesmaximal, characteristic, complemented
15#1786×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C22×Q16×C137C2211yescharacteristic, complemented
19C22×SD16×C137C2211yescharacteristic
20C22×SD16×C137C2211yescharacteristic
21#546×C137—24no—
22#546×C137—24no—
23C2×#124×C137C2211yescharacteristic
24C2×#123×C137—21no—
25C2×C22⋊Q8×C137C2211yescharacteristic
26C2×C22⋊Q8×C137C2211yescharacteristic
27C2×C22⋊Q8×C137C2211yescharacteristic, complemented
28C2×#121×C137—21no—
29C2×#121×C137C2211yescharacteristic
30C2×#120×C137—21no—
31C2×C4×Q8×C137C2211yescharacteristic, complemented
32C2×C4×D4×C137C2211yescharacteristic
33C2×C4×D4×C137C2211yescharacteristic
34C22×C22⋊C4×C137—21no—
35#464×C137—24no—
36#452×C137—24no—
37#450×C137—24no—
38#440×C137—24no—
39C2×#107×C137C2211yescharacteristic, complemented
40C2×C4⋊C8×C137C2211yescharacteristic, complemented
41C2×#103×C137C2211yescharacteristic, complemented
42C2×#103×C137C2211yescharacteristic, complemented
43C2×#103×C137C2211yescharacteristic, complemented
44C2×#103×C137C2211yescharacteristic, complemented
45C2×#102×C137C2211yescharacteristic
46C2×#102×C137C2211yescharacteristic
47C2×#102×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic
49C2×#102×C137C2211yescharacteristic
50C2×#102×C137C2211yescharacteristic
51C2×C22⋊C8×C137C2211yescharacteristic
52C2×C22⋊C8×C137C2211yescharacteristic
53C2×C22⋊C8×C137C2211yescharacteristic, complemented
54C2×C22⋊C8×C137C2211yescharacteristic, complemented
55C2×#97×C137C2211yescharacteristic, complemented
56#396×C137—21no—
57#396×C137—21no—
58#390×C137—21no—
59#389×C137—21no—
60#384×C137C2211yescharacteristic, complemented
61#380×C137C2211yescharacteristic
62#380×C137C2211yescharacteristic, complemented
63#340×C137C2211yescharacteristic, complemented
64#340×C137C2211yescharacteristic, complemented
65C25×C137—21no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—22no—
69C2×#41×C137—22no—
70C2×#41×C137—41no—
71C2×#41×C137—41no—
72C22×Q8×C137C2311yescharacteristic
73C22×Q8×C137C2311yescharacteristic
74C22×D4×C137—21no—
75C22×D4×C137—21no—
76C22×D4×C137—22no—
77C22×D4×C137—22no—
78C22×D4×C137—22no—
79C22×D4×C137—22no—
80C22×D4×C137—21no—
81C22×D4×C137—41no—
82C22×D4×C137—41no—
83C22×D4×C137D411yescharacteristic
84C22×D4×C137C2311yescharacteristic
85C22×D4×C137C2311yescharacteristic
86C23×C4×C137—21no—
87C23×C4×C137—21no—
88C23×C4×C137C2311yescharacteristic
89C23×C4×C137C2311yescharacteristic
90C2×Q16×C137—22no—
91C2×Q16×C137—22no—
92C2×Q16×C137—41no—
93C2×SD16×C137—22no—
94C2×SD16×C137—22no—
95C2×SD16×C137—22no—
96C2×SD16×C137—22no—
97C2×SD16×C137—41no—
98C2×SD16×C137D414yescomplemented
99C22×C8×C137C2311yescharacteristic
100C22×C8×C137C2311yescharacteristic
101C22×C8×C137C2311yescharacteristic
102C22×C8×C137C2311yescharacteristic
103#124×C137—22no—
104#124×C137D414yes—
105#123×C137—28no—
106C22⋊Q8×C137—22no—
107C22⋊Q8×C137—22no—
108C22⋊Q8×C137—22no—
109C22⋊Q8×C137—22no—
110C22⋊Q8×C137—41no—
111C22⋊Q8×C137—41no—
112#121×C137—28no—
113#121×C137—22no—
114#121×C137—22no—
115#120×C137—28no—
116C4×Q8×C137—22no—
117C4×Q8×C137—22no—
118C4×D4×C137—22no—
119C4×D4×C137—22no—
120C4×D4×C137—22no—
121C4×D4×C137D414yes—
122C2×C4⋊C4×C137—21no—
123C2×C4⋊C4×C137—21no—
124C2×C4⋊C4×C137—21no—
125C2×C4⋊C4×C137—21no—
126C2×C4⋊C4×C137—21no—
127C2×C4⋊C4×C137—21no—
128C2×C4⋊C4×C137D411yescharacteristic
129C2×C4⋊C4×C137C2311yescharacteristic
130C2×C4⋊C4×C137C2311yescharacteristic
131C2×C4⋊C4×C137C2311yescharacteristic
132C2×C4⋊C4×C137C2311yescharacteristic
133C2×C22⋊C4×C137—28no—
134C2×C22⋊C4×C137—21no—
135C2×C22⋊C4×C137—21no—
136C2×C22⋊C4×C137—21no—
137C2×C22⋊C4×C137—21no—
138C2×C22⋊C4×C137—21no—
139C2×C22⋊C4×C137—21no—
140C2×C22⋊C4×C137—21no—
141C2×C22⋊C4×C137—21no—
142C2×C22⋊C4×C137—21no—
143C2×C22⋊C4×C137D411yescharacteristic
144C2×C22⋊C4×C137D411yescharacteristic
145C2×C42×C137—21no—
146C2×C42×C137C2311yescharacteristic
147#107×C137—22no—
148C4⋊C8×C137—22no—
149#103×C137—22no—
150#103×C137—22no—
151#103×C137—22no—
152#103×C137—41no—
153#102×C137—22no—
154#102×C137—22no—
155#102×C137—22no—
156#102×C137—22no—
157#102×C137—22no—
158#102×C137—41no—
159C22⋊C8×C137—22no—
160C22⋊C8×C137—22no—
161C22⋊C8×C137—41no—
162C22⋊C8×C137—41no—
163#97×C137—22no—
164#95×C137—21no—
165#95×C137—21no—
166C24×C137—21no—
167C24×C137—24no—
168C24×C137—21no—
169C24×C137—42no—
170C24×C137—42no—
171C24×C137—42no—
172C24×C137—42no—
173C24×C137—81no—
174C24×C137—81no—
175C24×C137C2×D411yescharacteristic
176C24×C137C2×D411yescharacteristic
177#41×C137—44no—
178#41×C137—44no—
179#41×C137—44no—
180#41×C137—44no—
181C2×Q8×C137—21no—
182C2×Q8×C137—21no—
183C2×Q8×C137—21no—
184C2×Q8×C137—21no—
185C2×Q8×C137—21no—
186C2×Q8×C137—21no—
187C2×Q8×C137—21no—
188C2×Q8×C137—21no—
189C2×Q8×C137—21no—
190C2×Q8×C137—21no—
191C2×Q8×C137C2×D412yes—
192C2×Q8×C137C2×D412yes—
193C2×D4×C137—24no—
194C2×D4×C137—24no—
195C2×D4×C137—22no—
196C2×D4×C137—24no—
197C2×D4×C137—22no—
198C2×D4×C137—21no—
199C2×D4×C137—21no—
200C2×D4×C137—21no—
201C2×D4×C137—21no—
202C2×D4×C137—21no—
203C2×D4×C137—21no—
204C2×D4×C137—21no—
205C2×D4×C137—21no—
206C2×D4×C137—41no—
207C2×D4×C137—42no—
208C2×D4×C137—42no—
209C2×D4×C137—44no—
210C2×D4×C137—44no—
211C2×D4×C137—44no—
212C2×D4×C137—42no—
213C2×D4×C137—42no—
214C2×D4×C137—44no—
215C2×D4×C137—81no—
216C2×D4×C137—81no—
217C2×D4×C137C2×D412yes—
218C2×D4×C137C2×D412yes—
219C2×D4×C137C2×D412yes—
220C2×D4×C137#4112yes—
221C22×C4×C137—24no—
222C22×C4×C137—21no—
223C22×C4×C137—21no—
224C22×C4×C137—21no—
225C22×C4×C137—21no—
226C22×C4×C137—21no—
227C22×C4×C137—21no—
228C22×C4×C137—21no—
229C22×C4×C137—21no—
230C22×C4×C137—21no—
231C22×C4×C137—21no—
232C22×C4×C137—21no—
233C22×C4×C137—21no—
234C22×C4×C137—21no—
235C22×C4×C137—21no—
236C22×C4×C137—21no—
237C22×C4×C137—24no—
238C22×C4×C137—21no—
239C22×C4×C137—21no—
240C22×C4×C137—21no—
241C22×C4×C137—42no—
242C22×C4×C137—42no—
243C22×C4×C137—81no—
244C22×C4×C137—81no—
245C22×C4×C137C2×D411yescharacteristic
246C22×C4×C137C2×D411yescharacteristic
247C22×C4×C137C2×D411yescharacteristic
248C22×C4×C137C2×D411yescharacteristic
249C22×C4×C137C2411yescharacteristic
250Q16×C137—44no—
251SD16×C137—28no—
252SD16×C137—44no—
253C2×C8×C137—21no—
254C2×C8×C137—21no—
255C2×C8×C137—21no—
256C2×C8×C137—21no—
257C2×C8×C137—21no—
258C2×C8×C137—21no—
259C2×C8×C137—21no—
260C2×C8×C137—21no—
261C2×C8×C137—21no—
262C2×C8×C137—21no—
263C2×C8×C137—21no—
264C2×C8×C137C2×D412yes—
265C4⋊C4×C137—24no—
266C4⋊C4×C137—22no—
267C4⋊C4×C137—21no—
268C4⋊C4×C137—21no—
269C4⋊C4×C137—21no—
270C4⋊C4×C137—21no—
271C4⋊C4×C137—21no—
272C4⋊C4×C137—21no—
273C4⋊C4×C137—21no—
274C4⋊C4×C137—42no—
275C4⋊C4×C137—42no—
276C4⋊C4×C137—42no—
277C4⋊C4×C137—42no—
278C4⋊C4×C137—81no—
279C4⋊C4×C137C2×D412yes—
280C22⋊C4×C137—24no—
281C22⋊C4×C137—24no—
282C22⋊C4×C137—22no—
283C22⋊C4×C137—24no—
284C22⋊C4×C137—24no—
285C22⋊C4×C137—24no—
286C22⋊C4×C137—22no—
287C22⋊C4×C137—42no—
288C22⋊C4×C137—42no—
289C22⋊C4×C137—81no—
290C22⋊C4×C137—81no—
291C42×C137—42no—
292C42×C137C2×D412yes—
293C42×C137C2×D412yes—
294C23×C137—21no—
295C23×C137—22no—
296C23×C137—21no—
297C23×C137—22no—
298C23×C137—21no—
299C23×C137—22no—
300C23×C137—21no—
301C23×C137—21no—
302C23×C137—21no—
303C23×C137—22no—
304C23×C137—21no—
305C23×C137—21no—
306C23×C137—21no—
307C23×C137—21no—
308C23×C137—21no—
309C23×C137—21no—
310C23×C137—21no—
311C23×C137—48no—
312C23×C137—48no—
313C23×C137—41no—
314C23×C137—41no—
315C23×C137—41no—
316C23×C137—41no—
317C23×C137—41no—
318C23×C137—41no—
319C23×C137—41no—
320C23×C137—41no—
321C23×C137—41no—
322C23×C137—41no—
323C23×C137—84no—
324C23×C137—84no—
325C23×C137—84no—
326C23×C137—84no—
327C23×C137—84no—
328C23×C137#13712yes—
329C23×C137C22×D411yescharacteristic
330Q8×C137—22no—
331Q8×C137—22no—
332Q8×C137—22no—
333Q8×C137—22no—
334Q8×C137—41no—
335Q8×C137—41no—
336Q8×C137—41no—
337Q8×C137—41no—
338D4×C137—22no—
339D4×C137—22no—
340D4×C137—22no—
341D4×C137—22no—
342D4×C137—22no—
343D4×C137—44no—
344D4×C137—48no—
345D4×C137—48no—
346D4×C137—41no—
347D4×C137—41no—
348D4×C137—84no—
349D4×C137#12114yes—
350C2×C4×C137—21no—
351C2×C4×C137—21no—
352C2×C4×C137—21no—
353C2×C4×C137—21no—
354C2×C4×C137—22no—
355C2×C4×C137—21no—
356C2×C4×C137—22no—
357C2×C4×C137—21no—
358C2×C4×C137—22no—
359C2×C4×C137—21no—
360C2×C4×C137—21no—
361C2×C4×C137—21no—
362C2×C4×C137—21no—
363C2×C4×C137—48no—
364C2×C4×C137—41no—
365C2×C4×C137—41no—
366C2×C4×C137—41no—
367C2×C4×C137—41no—
368C2×C4×C137—41no—
369C2×C4×C137—41no—
370C2×C4×C137—41no—
371C2×C4×C137—41no—
372C2×C4×C137—41no—
373C2×C4×C137—41no—
374C2×C4×C137—41no—
375C2×C4×C137—41no—
376C2×C4×C137—41no—
377C2×C4×C137—41no—
378C2×C4×C137—41no—
379C2×C4×C137—41no—
380C2×C4×C137—41no—
381C2×C4×C137—41no—
382C2×C4×C137—41no—
383C2×C4×C137—41no—
384C2×C4×C137—41no—
385C2×C4×C137—41no—
386C2×C4×C137—41no—
387C2×C4×C137—84no—
388C2×C4×C137#12012yes—
389C2×C4×C137#12012yes—
390C2×C4×C137C22×D411yescharacteristic
391C2×C4×C137C22×D411yescharacteristic
392C2×C4×C137C22×D411yescharacteristic
393C2×C4×C137C2×#4111yescharacteristic
394C2×C4×C137H(5,𝔽2)11yescharacteristic
395C2×C4×C137H(5,𝔽2)11yescharacteristic
396C8×C137—22no—
397C8×C137—41no—
398C8×C137—41no—
399C8×C137—41no—
400C22×C137—24no—
401C22×C137—22no—
402C22×C137—22no—
403C22×C137—22no—
404C22×C137—41no—
405C22×C137—42no—
406C22×C137—42no—
407C22×C137—42no—
408C22×C137—41no—
409C22×C137—41no—
410C22×C137—42no—
411C22×C137—41no—
412C22×C137—42no—
413C22×C137—42no—
414C22×C137—41no—
415C22×C137—42no—
416C22×C137—41no—
417C22×C137—42no—
418C22×C137—41no—
419C22×C137—41no—
420C22×C137—42no—
421C22×C137—41no—
422C22×C137—41no—
423C22×C137—41no—
424C22×C137—816no—
425C22×C137—81no—
426C22×C137—81no—
427C22×C137—81no—
428C22×C137—81no—
429C22×C137C2×#12011yescharacteristic
430C22×C137D4211yescharacteristic
431C22×C137#54611yescharacteristic
432C22×C137C2×#13711yescharacteristic
433C22×C137#57511yescharacteristic
434C22×C137#57611yescharacteristic
435C22×C137#57711yescharacteristic
436C4×C137—22no—
437C4×C137—22no—
438C4×C137—41no—
439C4×C137—41no—
440C4×C137—42no—
441C4×C137—42no—
442C4×C137—42no—
443C4×C137—81no—
444C4×C137—81no—
445C4×C137—81no—
446C4×C137C2×#12111yescharacteristic
447C4×C137#53511yescharacteristic
448C4×C137D4211yescharacteristic
449C4×C137#54611yescharacteristic
450C2×C137—42no—
451C2×C137—44no—
452C2×C137—81no—
453C2×C137—82no—
454C2×C137#240811yescharacteristic
455C2×C137#300711yescharacteristic
456C2×C137#301211yescharacteristic
457C2×C137#326611yescharacteristic
458C2×C137#326811yescharacteristic
459C2×C137#331111yescharacteristic
460C2×C137#331411yescharacteristic
461#24259C13711yesmaximal, characteristic, direct product factor, Sylow
462C137#2425911yescharacteristic, direct product factor, Sylow
463C2×#546C2×C13711yescharacteristic
464C2×#464C2×C13711yescharacteristic, complemented
465C2×#452C2×C13711yescharacteristic, complemented
466C2×#450C2×C13711yescharacteristic, complemented
467C2×#440C2×C13711yescharacteristic, complemented
468#2538C2×C13711yescharacteristic, complemented
469#2036C2×C13711yescharacteristic, complemented
470#2033C2×C13711yescharacteristic, complemented
471#2001C2×C13711yescharacteristic, complemented
472#2000C2×C13711yescharacteristic, complemented
473#1959C2×C13711yescharacteristic, complemented
474#1955C2×C13711yescharacteristic, complemented
475#1802C2×C13711yescharacteristic, complemented
476#1788C2×C13711yescharacteristic, complemented
477#1786C2×C13711yescharacteristic, complemented
478C22×#41C22×C13711yescharacteristic
479C23×D4C22×C13711yescharacteristic
480C22×Q16C22×C13711yescharacteristic, complemented
481C22×SD16C22×C13711yescharacteristic
482C22×SD16C22×C13711yescharacteristic
483#546—24no—
484#546—24no—
485C2×#124C22×C13711yescharacteristic
486C2×#123—21no—
487C2×C22⋊Q8C22×C13711yescharacteristic
488C2×C22⋊Q8C22×C13711yescharacteristic
489C2×C22⋊Q8C22×C13711yescharacteristic, complemented
490C2×#121—21no—
491C2×#121C22×C13711yescharacteristic
492C2×#120—21no—
493C2×C4×Q8C22×C13711yescharacteristic, complemented
494C2×C4×D4C22×C13711yescharacteristic
495C2×C4×D4C22×C13711yescharacteristic
496C22×C22⋊C4—21no—
497#464—24no—
498#452—24no—
499#450—24no—
500#440—24no—
501C2×#107C22×C13711yescharacteristic, complemented
502C2×C4⋊C8C22×C13711yescharacteristic, complemented
503C2×#103C22×C13711yescharacteristic, complemented
504C2×#103C22×C13711yescharacteristic, complemented
505C2×#103C22×C13711yescharacteristic, complemented
506C2×#103C22×C13711yescharacteristic, complemented
507C2×#102C22×C13711yescharacteristic
508C2×#102C22×C13711yescharacteristic
509C2×#102C22×C13711yescharacteristic
510C2×#102C22×C13711yescharacteristic
511C2×#102C22×C13711yescharacteristic
512C2×#102C22×C13711yescharacteristic
513C2×C22⋊C8C22×C13711yescharacteristic
514C2×C22⋊C8C22×C13711yescharacteristic
515C2×C22⋊C8C22×C13711yescharacteristic, complemented
516C2×C22⋊C8C22×C13711yescharacteristic, complemented
517C2×#97C22×C13711yescharacteristic, complemented
518#396—21no—
519#396—21no—
520#390—21no—
521#389—21no—
522#384C22×C13711yescharacteristic, complemented
523#380C22×C13711yescharacteristic
524#380C22×C13711yescharacteristic, complemented
525#340C22×C13711yescharacteristic, complemented
526#340C22×C13711yescharacteristic, complemented
527C25—21no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—41no—
533C2×#41—41no—
534C22×Q8C23×C13711yescharacteristic
535C22×Q8C23×C13711yescharacteristic
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—21no—
543C22×D4—41no—
544C22×D4—41no—
545C22×D4D4×C13711yescharacteristic
546C22×D4C23×C13711yescharacteristic
547C22×D4C23×C13711yescharacteristic
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C23×C13711yescharacteristic
551C23×C4C23×C13711yescharacteristic
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—41no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—41no—
560C2×SD16D4×C13714yescomplemented
561C22×C8C23×C13711yescharacteristic
562C22×C8C23×C13711yescharacteristic
563C22×C8C23×C13711yescharacteristic
564C22×C8C23×C13711yescharacteristic
565#124—22no—
566#124D4×C13714yes—
567#123—28no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574#121—28no—
575#121—22no—
576#121—22no—
577#120—28no—
578C4×Q8—22no—
579C4×Q8—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4D4×C13714yes—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4D4×C13711yescharacteristic
591C2×C4⋊C4C23×C13711yescharacteristic
592C2×C4⋊C4C23×C13711yescharacteristic
593C2×C4⋊C4C23×C13711yescharacteristic
594C2×C4⋊C4C23×C13711yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4D4×C13711yescharacteristic
606C2×C22⋊C4D4×C13711yescharacteristic
607C2×C42—21no—
608C2×C42C23×C13711yescharacteristic
609#107—22no—
610C4⋊C8—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#103—41no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—41no—
621C22⋊C8—22no—
622C22⋊C8—22no—
623C22⋊C8—41no—
624C22⋊C8—41no—
625#97—22no—
626#95—21no—
627#95—21no—
628C24—21no—
629C24—24no—
630C24—21no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—81no—
636C24—81no—
637C24C2×D4×C13711yescharacteristic
638C24C2×D4×C13711yescharacteristic
639#41—44no—
640#41—44no—
641#41—44no—
642#41—44no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8C2×D4×C13712yes—
654C2×Q8C2×D4×C13712yes—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—41no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—44no—
677C2×D4—81no—
678C2×D4—81no—
679C2×D4C2×D4×C13712yes—
680C2×D4C2×D4×C13712yes—
681C2×D4C2×D4×C13712yes—
682C2×D4#41×C13712yes—
683C22×C4—24no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—24no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—81no—
706C22×C4—81no—
707C22×C4C2×D4×C13711yescharacteristic
708C22×C4C2×D4×C13711yescharacteristic
709C22×C4C2×D4×C13711yescharacteristic
710C22×C4C2×D4×C13711yescharacteristic
711C22×C4C24×C13711yescharacteristic
712Q16—44no—
713SD16—28no—
714SD16—44no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8C2×D4×C13712yes—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—81no—
741C4⋊C4C2×D4×C13712yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—22no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—81no—
752C22⋊C4—81no—
753C42—42no—
754C42C2×D4×C13712yes—
755C42C2×D4×C13712yes—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—22no—
760C23—21no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—48no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23#137×C13712yes—
791C23C22×D4×C13711yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—22no—
795Q8—22no—
796Q8—41no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—44no—
806D4—48no—
807D4—48no—
808D4—41no—
809D4—41no—
810D4—84no—
811D4#121×C13714yes—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—84no—
850C2×C4#120×C13712yes—
851C2×C4#120×C13712yes—
852C2×C4C22×D4×C13711yescharacteristic
853C2×C4C22×D4×C13711yescharacteristic
854C2×C4C22×D4×C13711yescharacteristic
855C2×C4C2×#41×C13711yescharacteristic
856C2×C4H(5,𝔽2)×C13711yescharacteristic
857C2×C4H(5,𝔽2)×C13711yescharacteristic
858C8—22no—
859C8—41no—
860C8—41no—
861C8—41no—
862C22—22no—
863C22—24no—
864C22—22no—
865C22—22no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—41no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—816no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22C2×#120×C13711yescharacteristic
892C22D42×C13711yescharacteristic
893C22#546×C13711yescharacteristic
894C22C2×#137×C13711yescharacteristic
895C22#575×C13711yescharacteristic
896C22#576×C13711yescharacteristic
897C22#577×C13711yescharacteristic
898C4—22no—
899C4—22no—
900C4—41no—
901C4—41no—
902C4—42no—
903C4—42no—
904C4—42no—
905C4—81no—
906C4—81no—
907C4—81no—
908C4C2×#121×C13711yescharacteristic
909C4#535×C13711yescharacteristic
910C4D42×C13711yescharacteristic
911C4#546×C13711yescharacteristic
912C2—42no—
913C2—44no—
914C2—81no—
915C2—82no—
916C2#2408×C13711yescharacteristic
917C2#3007×C13711yescharacteristic
918C2#3012×C13711yescharacteristic
919C2#3266×C13711yescharacteristic
920C2#3268×C13711yescharacteristic
921C2#3311×C13711yescharacteristic
922C2#3314×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
prime radicalC2×#546×C137C2
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
2. C2×#464×C137C2semidirect
3. C2×#452×C137C2semidirect
4. C2×#450×C137C2semidirect
5. C2×#440×C137C2semidirect
6. #2538×C137C2semidirect
7. #2036×C137C2semidirect
8. #2033×C137C2semidirect
9. #2001×C137C2semidirect
10. #2000×C137C2semidirect
11. #1959×C137C2semidirect
12. #1955×C137C2semidirect
13. #1802×C137C2semidirect
14. #1788×C137C2semidirect
15. #1786×C137C2semidirect
18. C22×Q16×C137C22semidirect
27. C2×C22⋊Q8×C137C22semidirect
31. C2×C4×Q8×C137C22semidirect
39. C2×#107×C137C22semidirect
40. C2×C4⋊C8×C137C22semidirect
41. C2×#103×C137C22semidirect
42. C2×#103×C137C22semidirect
43. C2×#103×C137C22semidirect
44. C2×#103×C137C22semidirect
53. C2×C22⋊C8×C137C22semidirect
54. C2×C22⋊C8×C137C22semidirect
55. C2×#97×C137C22semidirect
60. #384×C137C22semidirect
62. #380×C137C22semidirect
63. #340×C137C22semidirect
64. #340×C137C22semidirect
98. C2×SD16×C137D4semidirect
461. #24259C137direct (N × H)
462. C137#24259direct (N × H)
464. C2×#464C2×C137semidirect
465. C2×#452C2×C137semidirect
466. C2×#450C2×C137semidirect
467. C2×#440C2×C137semidirect
468. #2538C2×C137semidirect
469. #2036C2×C137semidirect
470. #2033C2×C137semidirect
471. #2001C2×C137semidirect
472. #2000C2×C137semidirect
473. #1959C2×C137semidirect
474. #1955C2×C137semidirect
475. #1802C2×C137semidirect
476. #1788C2×C137semidirect
477. #1786C2×C137semidirect
480. C22×Q16C22×C137semidirect
489. C2×C22⋊Q8C22×C137semidirect
493. C2×C4×Q8C22×C137semidirect
501. C2×#107C22×C137semidirect
502. C2×C4⋊C8C22×C137semidirect
503. C2×#103C22×C137semidirect
504. C2×#103C22×C137semidirect
505. C2×#103C22×C137semidirect
506. C2×#103C22×C137semidirect
515. C2×C22⋊C8C22×C137semidirect
516. C2×C22⋊C8C22×C137semidirect
517. C2×#97C22×C137semidirect
522. #384C22×C137semidirect
524. #380C22×C137semidirect
525. #340C22×C137semidirect
526. #340C22×C137semidirect
560. C2×SD16D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1372
C2×#464×C1372
C2×#452×C1372
C2×#450×C1372
C2×#440×C1372
#2538×C1372
#2036×C1372
#2033×C1372
#2001×C1372
#2000×C1372
#1959×C1372
#1955×C1372
#1802×C1372
#1788×C1372
#1786×C1372
#24259137