Finite Group Databasebeta

← C137×#24452 #46873838

Subgroups — C137×#24452 #46873838

Order 35072.

1592 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C137C211yesmaximal, characteristic
2C2×#468×C137C211yesmaximal, characteristic, complemented
3C2×#452×C137C211yesmaximal, characteristic, complemented
4C2×#450×C137C211yesmaximal, characteristic, complemented
5C2×#417×C137C211yesmaximal, characteristic, complemented
6#2417×C137C211yesmaximal, characteristic, complemented
7#2042×C137C211yesmaximal, characteristic, complemented
8#2036×C137C211yesmaximal, characteristic, complemented
9#2015×C137C211yesmaximal, characteristic, complemented
10#2001×C137C211yesmaximal, characteristic, complemented
11#1877×C137C211yesmaximal, characteristic, complemented
12#1874×C137C211yesmaximal, characteristic, complemented
13#1870×C137C211yesmaximal, characteristic, complemented
14#1862×C137C211yesmaximal, characteristic, complemented
15#1786×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C22×Q16×C137C2211yescharacteristic, complemented
19C22×SD16×C137C2211yescharacteristic
20C22×SD16×C137C2211yescharacteristic
21C22×M16×C137C2211yescharacteristic, complemented
22#546×C137—24no—
23#546×C137—24no—
24C2×#124×C137C2211yescharacteristic
25C2×#123×C137—21no—
26C2×C22⋊Q8×C137C2211yescharacteristic
27C2×C22⋊Q8×C137C2211yescharacteristic
28C2×C22⋊Q8×C137C2211yescharacteristic, complemented
29C2×#121×C137—21no—
30C2×#121×C137C2211yescharacteristic
31C2×#120×C137—21no—
32C2×C4×D4×C137C2211yescharacteristic
33C2×C4×D4×C137C2211yescharacteristic
34C22×C4⋊C4×C137C2211yescharacteristic, complemented
35C22×C22⋊C4×C137—21no—
36#468×C137—24no—
37#452×C137—24no—
38#450×C137—24no—
39C2×#107×C137C2211yescharacteristic, complemented
40#417×C137—24no—
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
54#398×C137—21no—
55#396×C137—21no—
56#391×C137C2211yescharacteristic, complemented
57#389×C137C2211yescharacteristic, complemented
58#386×C137—21no—
59#380×C137—21no—
60#380×C137C2211yescharacteristic
61#340×C137C2211yescharacteristic, complemented
62#340×C137C2211yescharacteristic, complemented
63#336×C137C2211yescharacteristic, complemented
64#336×C137C2211yescharacteristic, complemented
65C25×C137—21no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—22no—
69C2×#41×C137—41no—
70C2×#41×C137—41no—
71C2×#41×C137D414yes—
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×C137—21no—
89C23×C4×C137C2311yescharacteristic
90C23×C4×C137C2311yescharacteristic
91C2×Q16×C137—22no—
92C2×Q16×C137—41no—
93C2×Q16×C137—41no—
94C2×SD16×C137—22no—
95C2×SD16×C137—22no—
96C2×SD16×C137—22no—
97C2×SD16×C137—22no—
98C2×SD16×C137—22no—
99C2×SD16×C137—41no—
100C2×M16×C137—22no—
101C2×M16×C137—22no—
102C2×M16×C137—41no—
103C22×C8×C137C2311yescharacteristic
104C22×C8×C137C2311yescharacteristic
105C22×C8×C137C2311yescharacteristic
106C22×C8×C137C2311yescharacteristic
107#124×C137—22no—
108#124×C137—22no—
109#123×C137—28no—
110C22⋊Q8×C137—22no—
111C22⋊Q8×C137—22no—
112C22⋊Q8×C137—22no—
113C22⋊Q8×C137—22no—
114C22⋊Q8×C137—22no—
115C22⋊Q8×C137—41no—
116#121×C137—28no—
117#121×C137—22no—
118#121×C137D414yes—
119#120×C137—28no—
120C4×D4×C137—22no—
121C4×D4×C137—22no—
122C4×D4×C137—22no—
123C4×D4×C137—22no—
124C2×C4⋊C4×C137—21no—
125C2×C4⋊C4×C137—22no—
126C2×C4⋊C4×C137—21no—
127C2×C4⋊C4×C137—21no—
128C2×C4⋊C4×C137—21no—
129C2×C4⋊C4×C137—21no—
130C2×C4⋊C4×C137—41no—
131C2×C4⋊C4×C137D411yescharacteristic
132C2×C4⋊C4×C137C2311yescharacteristic
133C2×C4⋊C4×C137C2311yescharacteristic
134C2×C4⋊C4×C137C2311yescharacteristic
135C2×C4⋊C4×C137C2311yescharacteristic
136C2×C22⋊C4×C137—28no—
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×C137—21no—
144C2×C22⋊C4×C137—21no—
145C2×C22⋊C4×C137D411yescharacteristic
146C2×C22⋊C4×C137D411yescharacteristic
147C2×C42×C137C2311yescharacteristic
148#107×C137—22no—
149#103×C137—22no—
150#103×C137—22no—
151#103×C137—22no—
152#103×C137—22no—
153#102×C137—22no—
154#102×C137—22no—
155#102×C137—22no—
156#102×C137—22no—
157#102×C137—41no—
158#102×C137D414yescomplemented
159C22⋊C8×C137—22no—
160C22⋊C8×C137—22no—
161C22⋊C8×C137—41no—
162#95×C137—21no—
163#95×C137—21no—
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—28no—
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×C137—21no—
192C2×Q8×C137C2×D412yes—
193C2×D4×C137—24no—
194C2×D4×C137—22no—
195C2×D4×C137—24no—
196C2×D4×C137—22no—
197C2×D4×C137—24no—
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—21no—
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—24no—
229C22×C4×C137—24no—
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—21no—
238C22×C4×C137—21no—
239C22×C4×C137—42no—
240C22×C4×C137—42no—
241C22×C4×C137—42no—
242C22×C4×C137—42no—
243C22×C4×C137—81no—
244C22×C4×C137—81no—
245C22×C4×C137—81no—
246C22×C4×C137C2×D411yescharacteristic
247C22×C4×C137C2×D411yescharacteristic
248C22×C4×C137C2×D411yescharacteristic
249C22×C4×C137C2×D411yescharacteristic
250C22×C4×C137C2×D412yes—
251C22×C4×C137C2×D412yes—
252C22×C4×C137C2411yescharacteristic
253Q16×C137—44no—
254SD16×C137—44no—
255SD16×C137—44no—
256M16×C137—44no—
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×C137—21no—
265C2×C8×C137—21no—
266C2×C8×C137—21no—
267C2×C8×C137—21no—
268C2×C8×C137C2×D412yes—
269C4⋊C4×C137—24no—
270C4⋊C4×C137—22no—
271C4⋊C4×C137—21no—
272C4⋊C4×C137—21no—
273C4⋊C4×C137—21no—
274C4⋊C4×C137—21no—
275C4⋊C4×C137—21no—
276C4⋊C4×C137—21no—
277C4⋊C4×C137—42no—
278C4⋊C4×C137—42no—
279C4⋊C4×C137—42no—
280C4⋊C4×C137—81no—
281C4⋊C4×C137C2×D412yes—
282C4⋊C4×C137C2×D412yes—
283C22⋊C4×C137—24no—
284C22⋊C4×C137—24no—
285C22⋊C4×C137—24no—
286C22⋊C4×C137—24no—
287C22⋊C4×C137—22no—
288C22⋊C4×C137—22no—
289C22⋊C4×C137—24no—
290C22⋊C4×C137—42no—
291C22⋊C4×C137—42no—
292C22⋊C4×C137—81no—
293C42×C137—21no—
294C42×C137—21no—
295C23×C137—21no—
296C23×C137—22no—
297C23×C137—21no—
298C23×C137—21no—
299C23×C137—22no—
300C23×C137—21no—
301C23×C137—21no—
302C23×C137—22no—
303C23×C137—21no—
304C23×C137—21no—
305C23×C137—21no—
306C23×C137—21no—
307C23×C137—21no—
308C23×C137—21no—
309C23×C137—21no—
310C23×C137—22no—
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#12012yes—
329C23×C137#13712yes—
330C23×C137C22×D411yescharacteristic
331Q8×C137—22no—
332Q8×C137—22no—
333Q8×C137—41no—
334Q8×C137—41no—
335Q8×C137—41no—
336Q8×C137—41no—
337Q8×C137—41no—
338Q8×C137—41no—
339D4×C137—22no—
340D4×C137—22no—
341D4×C137—22no—
342D4×C137—22no—
343D4×C137—22no—
344D4×C137—44no—
345D4×C137—48no—
346D4×C137—48no—
347D4×C137—41no—
348D4×C137—41no—
349D4×C137—84no—
350D4×C137#12114yes—
351C2×C4×C137—21no—
352C2×C4×C137—21no—
353C2×C4×C137—22no—
354C2×C4×C137—22no—
355C2×C4×C137—22no—
356C2×C4×C137—22no—
357C2×C4×C137—21no—
358C2×C4×C137—21no—
359C2×C4×C137—22no—
360C2×C4×C137—22no—
361C2×C4×C137—21no—
362C2×C4×C137—22no—
363C2×C4×C137—21no—
364C2×C4×C137—21no—
365C2×C4×C137—21no—
366C2×C4×C137—21no—
367C2×C4×C137—21no—
368C2×C4×C137—21no—
369C2×C4×C137—48no—
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—41no—
388C2×C4×C137—41no—
389C2×C4×C137—84no—
390C2×C4×C137—84no—
391C2×C4×C137#12012yes—
392C2×C4×C137C22×D411yescharacteristic
393C2×C4×C137C22×D411yescharacteristic
394C2×C4×C137C22×D411yescharacteristic
395C2×C4×C137C2×#4111yescharacteristic
396C2×C4×C137H(5,𝔽2)11yescharacteristic
397C2×C4×C137H(5,𝔽2)11yescharacteristic
398C8×C137—22no—
399C8×C137—41no—
400C8×C137—41no—
401C8×C137—41no—
402C22×C137—22no—
403C22×C137—24no—
404C22×C137—22no—
405C22×C137—22no—
406C22×C137—22no—
407C22×C137—22no—
408C22×C137—22no—
409C22×C137—41no—
410C22×C137—42no—
411C22×C137—41no—
412C22×C137—42no—
413C22×C137—42no—
414C22×C137—41no—
415C22×C137—41no—
416C22×C137—41no—
417C22×C137—42no—
418C22×C137—41no—
419C22×C137—42no—
420C22×C137—41no—
421C22×C137—41no—
422C22×C137—42no—
423C22×C137—42no—
424C22×C137—42no—
425C22×C137—42no—
426C22×C137—816no—
427C22×C137—81no—
428C22×C137—81no—
429C22×C137—81no—
430C22×C137—81no—
431C22×C137C2×#12011yescharacteristic
432C22×C137D4211yescharacteristic
433C22×C137#54611yescharacteristic
434C22×C137C2×#13711yescharacteristic
435C22×C137#57511yescharacteristic
436C22×C137#57611yescharacteristic
437C22×C137#57711yescharacteristic
438C4×C137—22no—
439C4×C137—41no—
440C4×C137—42no—
441C4×C137—41no—
442C4×C137—41no—
443C4×C137—42no—
444C4×C137—42no—
445C4×C137—81no—
446C4×C137—81no—
447C4×C137—81no—
448C4×C137C2×#12111yescharacteristic
449C4×C137#53411yescharacteristic
450C4×C137D4211yescharacteristic
451C4×C137#54611yescharacteristic
452C2×C137—42no—
453C2×C137—42no—
454C2×C137—44no—
455C2×C137—82no—
456C2×C137#241011yescharacteristic
457C2×C137#300711yescharacteristic
458C2×C137#301211yescharacteristic
459C2×C137#326611yescharacteristic
460C2×C137#327311yescharacteristic
461C2×C137#331411yescharacteristic
462C2×C137#332311yescharacteristic
463#24452C13711yesmaximal, characteristic, direct product factor, Sylow
464C137#2445211yescharacteristic, direct product factor, Sylow
465C2×#546C2×C13711yescharacteristic
466C2×#468C2×C13711yescharacteristic, complemented
467C2×#452C2×C13711yescharacteristic, complemented
468C2×#450C2×C13711yescharacteristic, complemented
469C2×#417C2×C13711yescharacteristic, complemented
470#2417C2×C13711yescharacteristic, complemented
471#2042C2×C13711yescharacteristic, complemented
472#2036C2×C13711yescharacteristic, complemented
473#2015C2×C13711yescharacteristic, complemented
474#2001C2×C13711yescharacteristic, complemented
475#1877C2×C13711yescharacteristic, complemented
476#1874C2×C13711yescharacteristic, complemented
477#1870C2×C13711yescharacteristic, complemented
478#1862C2×C13711yescharacteristic, complemented
479#1786C2×C13711yescharacteristic, complemented
480C22×#41C22×C13711yescharacteristic
481C23×D4C22×C13711yescharacteristic
482C22×Q16C22×C13711yescharacteristic, complemented
483C22×SD16C22×C13711yescharacteristic
484C22×SD16C22×C13711yescharacteristic
485C22×M16C22×C13711yescharacteristic, complemented
486#546—24no—
487#546—24no—
488C2×#124C22×C13711yescharacteristic
489C2×#123—21no—
490C2×C22⋊Q8C22×C13711yescharacteristic
491C2×C22⋊Q8C22×C13711yescharacteristic
492C2×C22⋊Q8C22×C13711yescharacteristic, complemented
493C2×#121—21no—
494C2×#121C22×C13711yescharacteristic
495C2×#120—21no—
496C2×C4×D4C22×C13711yescharacteristic
497C2×C4×D4C22×C13711yescharacteristic
498C22×C4⋊C4C22×C13711yescharacteristic, complemented
499C22×C22⋊C4—21no—
500#468—24no—
501#452—24no—
502#450—24no—
503C2×#107C22×C13711yescharacteristic, complemented
504#417—24no—
505C2×#103C22×C13711yescharacteristic, complemented
506C2×#103C22×C13711yescharacteristic, complemented
507C2×#103C22×C13711yescharacteristic, complemented
508C2×#103C22×C13711yescharacteristic, complemented
509C2×#102C22×C13711yescharacteristic
510C2×#102C22×C13711yescharacteristic
511C2×#102C22×C13711yescharacteristic
512C2×#102C22×C13711yescharacteristic
513C2×#102C22×C13711yescharacteristic
514C2×#102C22×C13711yescharacteristic
515C2×C22⋊C8C22×C13711yescharacteristic
516C2×C22⋊C8C22×C13711yescharacteristic
517C2×C22⋊C8C22×C13711yescharacteristic, complemented
518#398—21no—
519#396—21no—
520#391C22×C13711yescharacteristic, complemented
521#389C22×C13711yescharacteristic, complemented
522#386—21no—
523#380—21no—
524#380C22×C13711yescharacteristic
525#340C22×C13711yescharacteristic, complemented
526#340C22×C13711yescharacteristic, complemented
527#336C22×C13711yescharacteristic, complemented
528#336C22×C13711yescharacteristic, complemented
529C25—21no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C13714yes—
536C22×Q8C23×C13711yescharacteristic
537C22×Q8C23×C13711yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—21no—
545C22×D4—41no—
546C22×D4—41no—
547C22×D4D4×C13711yescharacteristic
548C22×D4C23×C13711yescharacteristic
549C22×D4C23×C13711yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C23×C13711yescharacteristic
554C23×C4C23×C13711yescharacteristic
555C2×Q16—22no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C22×C8C23×C13711yescharacteristic
568C22×C8C23×C13711yescharacteristic
569C22×C8C23×C13711yescharacteristic
570C22×C8C23×C13711yescharacteristic
571#124—22no—
572#124—22no—
573#123—28no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—41no—
580#121—28no—
581#121—22no—
582#121D4×C13714yes—
583#120—28no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4D4×C13711yescharacteristic
596C2×C4⋊C4C23×C13711yescharacteristic
597C2×C4⋊C4C23×C13711yescharacteristic
598C2×C4⋊C4C23×C13711yescharacteristic
599C2×C4⋊C4C23×C13711yescharacteristic
600C2×C22⋊C4—28no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4D4×C13711yescharacteristic
610C2×C22⋊C4D4×C13711yescharacteristic
611C2×C42C23×C13711yescharacteristic
612#107—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#103—22no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621#102—41no—
622#102D4×C13714yescomplemented
623C22⋊C8—22no—
624C22⋊C8—22no—
625C22⋊C8—41no—
626#95—21no—
627#95—21no—
628#95—21no—
629#95—21no—
630C24—21no—
631C24—24no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24C2×D4×C13711yescharacteristic
640C24C2×D4×C13711yescharacteristic
641#41—28no—
642#41—44no—
643#41—44no—
644#41—44no—
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×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8C2×D4×C13712yes—
657C2×D4—24no—
658C2×D4—22no—
659C2×D4—24no—
660C2×D4—22no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—41no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—44no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4C2×D4×C13712yes—
682C2×D4C2×D4×C13712yes—
683C2×D4C2×D4×C13712yes—
684C2×D4#41×C13712yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—81no—
708C22×C4—81no—
709C22×C4—81no—
710C22×C4C2×D4×C13711yescharacteristic
711C22×C4C2×D4×C13711yescharacteristic
712C22×C4C2×D4×C13711yescharacteristic
713C22×C4C2×D4×C13711yescharacteristic
714C22×C4C2×D4×C13712yes—
715C22×C4C2×D4×C13712yes—
716C22×C4C24×C13711yescharacteristic
717Q16—44no—
718SD16—44no—
719SD16—44no—
720M16—44no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C2×C8C2×D4×C13712yes—
733C4⋊C4—24no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—81no—
745C4⋊C4C2×D4×C13712yes—
746C4⋊C4C2×D4×C13712yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—24no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—81no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—22no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—21no—
765C23—21no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—48no—
776C23—48no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23—84no—
792C23#120×C13712yes—
793C23#137×C13712yes—
794C23C22×D4×C13711yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—44no—
809D4—48no—
810D4—48no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4#121×C13714yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—48no—
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—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—84no—
854C2×C4—84no—
855C2×C4#120×C13712yes—
856C2×C4C22×D4×C13711yescharacteristic
857C2×C4C22×D4×C13711yescharacteristic
858C2×C4C22×D4×C13711yescharacteristic
859C2×C4C2×#41×C13711yescharacteristic
860C2×C4H(5,𝔽2)×C13711yescharacteristic
861C2×C4H(5,𝔽2)×C13711yescharacteristic
862C8—22no—
863C8—41no—
864C8—41no—
865C8—41no—
866C22—22no—
867C22—22no—
868C22—24no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—41no—
877C22—42no—
878C22—41no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—816no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22—81no—
895C22C2×#120×C13711yescharacteristic
896C22D42×C13711yescharacteristic
897C22#546×C13711yescharacteristic
898C22C2×#137×C13711yescharacteristic
899C22#575×C13711yescharacteristic
900C22#576×C13711yescharacteristic
901C22#577×C13711yescharacteristic
902C4—22no—
903C4—41no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—42no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4C2×#121×C13711yescharacteristic
913C4#534×C13711yescharacteristic
914C4D42×C13711yescharacteristic
915C4#546×C13711yescharacteristic
916C2—42no—
917C2—42no—
918C2—44no—
919C2—82no—
920C2#2410×C13711yescharacteristic
921C2#3007×C13711yescharacteristic
922C2#3012×C13711yescharacteristic
923C2#3266×C13711yescharacteristic
924C2#3273×C13711yescharacteristic
925C2#3314×C13711yescharacteristic
926C2#3323×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×#468×C137C2semidirect
3. C2×#452×C137C2semidirect
4. C2×#450×C137C2semidirect
5. C2×#417×C137C2semidirect
6. #2417×C137C2semidirect
7. #2042×C137C2semidirect
8. #2036×C137C2semidirect
9. #2015×C137C2semidirect
10. #2001×C137C2semidirect
11. #1877×C137C2semidirect
12. #1874×C137C2semidirect
13. #1870×C137C2semidirect
14. #1862×C137C2semidirect
15. #1786×C137C2semidirect
18. C22×Q16×C137C22semidirect
21. C22×M16×C137C22semidirect
28. C2×C22⋊Q8×C137C22semidirect
34. C22×C4⋊C4×C137C22semidirect
39. C2×#107×C137C22semidirect
41. C2×#103×C137C22semidirect
42. C2×#103×C137C22semidirect
43. C2×#103×C137C22semidirect
44. C2×#103×C137C22semidirect
53. C2×C22⋊C8×C137C22semidirect
56. #391×C137C22semidirect
57. #389×C137C22semidirect
61. #340×C137C22semidirect
62. #340×C137C22semidirect
63. #336×C137C22semidirect
64. #336×C137C22semidirect
158. #102×C137D4semidirect
463. #24452C137direct (N × H)
464. C137#24452direct (N × H)
466. C2×#468C2×C137semidirect
467. C2×#452C2×C137semidirect
468. C2×#450C2×C137semidirect
469. C2×#417C2×C137semidirect
470. #2417C2×C137semidirect
471. #2042C2×C137semidirect
472. #2036C2×C137semidirect
473. #2015C2×C137semidirect
474. #2001C2×C137semidirect
475. #1877C2×C137semidirect
476. #1874C2×C137semidirect
477. #1870C2×C137semidirect
478. #1862C2×C137semidirect
479. #1786C2×C137semidirect
482. C22×Q16C22×C137semidirect
485. C22×M16C22×C137semidirect
492. C2×C22⋊Q8C22×C137semidirect
498. C22×C4⋊C4C22×C137semidirect
503. C2×#107C22×C137semidirect
505. C2×#103C22×C137semidirect
506. C2×#103C22×C137semidirect
507. C2×#103C22×C137semidirect
508. C2×#103C22×C137semidirect
517. C2×C22⋊C8C22×C137semidirect
520. #391C22×C137semidirect
521. #389C22×C137semidirect
525. #340C22×C137semidirect
526. #340C22×C137semidirect
527. #336C22×C137semidirect
528. #336C22×C137semidirect
622. #102D4×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×#468×C1372
C2×#452×C1372
C2×#450×C1372
C2×#417×C1372
#2417×C1372
#2042×C1372
#2036×C1372
#2015×C1372
#2001×C1372
#1877×C1372
#1874×C1372
#1870×C1372
#1862×C1372
#1786×C1372
#24452137