Finite Group Databasebeta

← C137×#24450 #46873836

Subgroups — C137×#24450 #46873836

Order 35072.

1620 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C137C211yesmaximal, characteristic, complemented
2C2×#468×C137C211yesmaximal, characteristic, complemented
3C2×#449×C137C211yesmaximal, characteristic, complemented
4C2×#447×C137C211yesmaximal, characteristic, complemented
5C2×#418×C137C211yesmaximal, characteristic, complemented
6#2414×C137C211yesmaximal, characteristic, complemented
7#2042×C137C211yesmaximal, characteristic, complemented
8#2033×C137C211yesmaximal, characteristic, complemented
9#2012×C137C211yesmaximal, characteristic, complemented
10#1999×C137C211yesmaximal, characteristic, complemented
11#1879×C137C211yesmaximal, characteristic, complemented
12#1873×C137C211yesmaximal, characteristic, complemented
13#1870×C137C211yesmaximal, characteristic, complemented
14#1862×C137C211yesmaximal, characteristic, complemented
15#1788×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C22×SD16×C137C2211yescharacteristic, complemented
19C22×D8×C137C2211yescharacteristic
20C22×D8×C137C2211yescharacteristic
21C22×M16×C137C2211yescharacteristic
22#546×C137—24no—
23#546×C137—24no—
24C2×#124×C137C2211yescharacteristic
25C2×#123×C137—21no—
26C2×C22⋊Q8×C137C2211yescharacteristic
27C2×#121×C137—21no—
28C2×#121×C137C2211yescharacteristic
29C2×#121×C137C2211yescharacteristic
30C2×#121×C137C2211yescharacteristic, complemented
31C2×#120×C137—21no—
32C2×C4×D4×C137C2211yescharacteristic
33C2×C4×D4×C137C2211yescharacteristic
34C2×#117×C137C2211yescharacteristic
35C22×C22⋊C4×C137—21no—
36#468×C137—24no—
37#449×C137—24no—
38#447×C137—24no—
39C2×#107×C137C2211yescharacteristic, complemented
40#418×C137—24no—
41C2×#103×C137C2211yescharacteristic, complemented
42C2×#103×C137C2211yescharacteristic, complemented
43C2×#103×C137C2211yescharacteristic, complemented
44C2×#102×C137C2211yescharacteristic
45C2×#102×C137C2211yescharacteristic
46C2×#102×C137C2211yescharacteristic
47C2×#102×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic
49C2×#102×C137C2211yescharacteristic
50C2×#102×C137C2211yescharacteristic, complemented
51C2×C22⋊C8×C137C2211yescharacteristic
52C2×C22⋊C8×C137C2211yescharacteristic, complemented
53C2×C22⋊C8×C137C2211yescharacteristic, complemented
54#394×C137—21no—
55#392×C137—21no—
56#390×C137—21no—
57#390×C137C2211yescharacteristic, complemented
58#389×C137C2211yescharacteristic, complemented
59#388×C137—21no—
60#380×C137C2211yescharacteristic, complemented
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—22no—
70C2×#41×C137—41no—
71C2×#41×C137—41no—
72C22×Q8×C137C2311yescharacteristic
73C22×D4×C137—22no—
74C22×D4×C137—22no—
75C22×D4×C137—21no—
76C22×D4×C137—21no—
77C22×D4×C137—21no—
78C22×D4×C137—21no—
79C22×D4×C137—21no—
80C22×D4×C137—22no—
81C22×D4×C137—41no—
82C22×D4×C137—41no—
83C22×D4×C137D411yescharacteristic
84C22×D4×C137D414yescomplemented
85C22×D4×C137C2311yescharacteristic
86C22×D4×C137C2311yescharacteristic
87C22×D4×C137C2311yescharacteristic
88C23×C4×C137—21no—
89C23×C4×C137—21no—
90C23×C4×C137C2311yescharacteristic
91C23×C4×C137C2311yescharacteristic
92C2×SD16×C137—22no—
93C2×SD16×C137—22no—
94C2×SD16×C137—41no—
95C2×D8×C137—22no—
96C2×D8×C137—22no—
97C2×D8×C137—22no—
98C2×D8×C137—22no—
99C2×D8×C137—41no—
100C2×D8×C137—41no—
101C2×M16×C137—22no—
102C2×M16×C137—22no—
103C2×M16×C137—41no—
104C22×C8×C137C2311yescharacteristic
105C22×C8×C137C2311yescharacteristic
106C22×C8×C137C2311yescharacteristic
107C22×C8×C137C2311yescharacteristic
108#124×C137—22no—
109#124×C137—22no—
110#123×C137—28no—
111C22⋊Q8×C137—22no—
112C22⋊Q8×C137D414yescomplemented
113#121×C137—28no—
114#121×C137—22no—
115#121×C137—22no—
116#121×C137—22no—
117#121×C137—22no—
118#121×C137—22no—
119#121×C137—41no—
120#120×C137—28no—
121C4×D4×C137—22no—
122C4×D4×C137—22no—
123C4×D4×C137—22no—
124C4×D4×C137—22no—
125#117×C137—22no—
126#117×C137—41no—
127C2×C4⋊C4×C137—21no—
128C2×C4⋊C4×C137—21no—
129C2×C4⋊C4×C137D411yescharacteristic
130C2×C4⋊C4×C137C2311yescharacteristic
131C2×C4⋊C4×C137C2311yescharacteristic
132C2×C4⋊C4×C137C2311yescharacteristic
133C2×C4⋊C4×C137C2311yescharacteristic
134C2×C22⋊C4×C137—28no—
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×C137—21no—
144C2×C22⋊C4×C137—21no—
145C2×C22⋊C4×C137—21no—
146C2×C22⋊C4×C137D411yescharacteristic
147C2×C22⋊C4×C137D411yescharacteristic
148C2×C42×C137—21no—
149C2×C42×C137C2311yescharacteristic
150#107×C137—22no—
151#103×C137—22no—
152#103×C137—22no—
153#103×C137—41no—
154#102×C137—22no—
155#102×C137—22no—
156#102×C137—22no—
157#102×C137—22no—
158#102×C137—22no—
159#102×C137—22no—
160#102×C137D414yescomplemented
161C22⋊C8×C137—22no—
162C22⋊C8×C137—22no—
163C22⋊C8×C137—41no—
164#95×C137—21no—
165#95×C137—21no—
166C24×C137—21no—
167C24×C137—21no—
168C24×C137—24no—
169C24×C137—21no—
170C24×C137—42no—
171C24×C137—42no—
172C24×C137—42no—
173C24×C137—42no—
174C24×C137—81no—
175C24×C137—81no—
176C24×C137C2×D411yescharacteristic
177C24×C137C2×D411yescharacteristic
178#41×C137—44no—
179#41×C137—44no—
180#41×C137—44no—
181#41×C137—44no—
182C2×Q8×C137—21no—
183C2×Q8×C137—21no—
184C2×Q8×C137—21no—
185C2×Q8×C137—21no—
186C2×Q8×C137—21no—
187C2×Q8×C137C2×D412yes—
188C2×D4×C137—28no—
189C2×D4×C137—24no—
190C2×D4×C137—22no—
191C2×D4×C137—24no—
192C2×D4×C137—24no—
193C2×D4×C137—21no—
194C2×D4×C137—21no—
195C2×D4×C137—21no—
196C2×D4×C137—21no—
197C2×D4×C137—21no—
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—21no—
207C2×D4×C137—44no—
208C2×D4×C137—44no—
209C2×D4×C137—44no—
210C2×D4×C137—41no—
211C2×D4×C137—41no—
212C2×D4×C137—42no—
213C2×D4×C137—42no—
214C2×D4×C137—42no—
215C2×D4×C137—42no—
216C2×D4×C137—42no—
217C2×D4×C137—42no—
218C2×D4×C137—42no—
219C2×D4×C137—81no—
220C2×D4×C137—81no—
221C2×D4×C137—81no—
222C2×D4×C137—81no—
223C2×D4×C137—81no—
224C2×D4×C137C2×D412yes—
225C2×D4×C137C2×D412yes—
226C2×D4×C137C2×D412yes—
227C2×D4×C137#4112yes—
228C22×C4×C137—21no—
229C22×C4×C137—21no—
230C22×C4×C137—21no—
231C22×C4×C137—21no—
232C22×C4×C137—24no—
233C22×C4×C137—21no—
234C22×C4×C137—21no—
235C22×C4×C137—21no—
236C22×C4×C137—24no—
237C22×C4×C137—21no—
238C22×C4×C137—21no—
239C22×C4×C137—21no—
240C22×C4×C137—21no—
241C22×C4×C137—21no—
242C22×C4×C137—21no—
243C22×C4×C137—21no—
244C22×C4×C137—21no—
245C22×C4×C137—42no—
246C22×C4×C137—42no—
247C22×C4×C137—81no—
248C22×C4×C137—81no—
249C22×C4×C137C2×D411yescharacteristic
250C22×C4×C137C2×D411yescharacteristic
251C22×C4×C137C2×D411yescharacteristic
252C22×C4×C137C2×D411yescharacteristic
253C22×C4×C137C2×D412yes—
254C22×C4×C137C2×D412yes—
255C22×C4×C137C2411yescharacteristic
256SD16×C137—44no—
257D8×C137—44no—
258D8×C137—44no—
259M16×C137—44no—
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×C137—21no—
269C2×C8×C137—21no—
270C2×C8×C137—21no—
271C2×C8×C137C2×D412yes—
272C4⋊C4×C137—24no—
273C4⋊C4×C137—22no—
274C4⋊C4×C137—21no—
275C4⋊C4×C137—21no—
276C4⋊C4×C137—21no—
277C4⋊C4×C137—21no—
278C4⋊C4×C137—21no—
279C4⋊C4×C137—21no—
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—24no—
289C22⋊C4×C137—22no—
290C22⋊C4×C137—42no—
291C22⋊C4×C137—42no—
292C22⋊C4×C137—42no—
293C22⋊C4×C137—42no—
294C22⋊C4×C137—81no—
295C22⋊C4×C137—81no—
296C42×C137—21no—
297C42×C137—21no—
298C42×C137—42no—
299C23×C137—22no—
300C23×C137—21no—
301C23×C137—22no—
302C23×C137—21no—
303C23×C137—22no—
304C23×C137—21no—
305C23×C137—21no—
306C23×C137—21no—
307C23×C137—21no—
308C23×C137—22no—
309C23×C137—21no—
310C23×C137—21no—
311C23×C137—21no—
312C23×C137—21no—
313C23×C137—21no—
314C23×C137—21no—
315C23×C137—21no—
316C23×C137—48no—
317C23×C137—48no—
318C23×C137—41no—
319C23×C137—41no—
320C23×C137—41no—
321C23×C137—41no—
322C23×C137—41no—
323C23×C137—41no—
324C23×C137—41no—
325C23×C137—41no—
326C23×C137—41no—
327C23×C137—41no—
328C23×C137—41no—
329C23×C137—41no—
330C23×C137—41no—
331C23×C137—41no—
332C23×C137—41no—
333C23×C137—41no—
334C23×C137—41no—
335C23×C137—84no—
336C23×C137—84no—
337C23×C137—84no—
338C23×C137—84no—
339C23×C137—84no—
340C23×C137#12012yes—
341C23×C137C22×D411yescharacteristic
342Q8×C137—22no—
343Q8×C137—22no—
344Q8×C137—41no—
345Q8×C137—41no—
346D4×C137—22no—
347D4×C137—22no—
348D4×C137—22no—
349D4×C137—22no—
350D4×C137—22no—
351D4×C137—48no—
352D4×C137—44no—
353D4×C137—48no—
354D4×C137—41no—
355D4×C137—41no—
356D4×C137—41no—
357D4×C137—41no—
358D4×C137—41no—
359D4×C137—41no—
360D4×C137—84no—
361D4×C137—84no—
362D4×C137—84no—
363D4×C137#12114yes—
364C2×C4×C137—21no—
365C2×C4×C137—21no—
366C2×C4×C137—22no—
367C2×C4×C137—22no—
368C2×C4×C137—22no—
369C2×C4×C137—22no—
370C2×C4×C137—21no—
371C2×C4×C137—21no—
372C2×C4×C137—22no—
373C2×C4×C137—21no—
374C2×C4×C137—22no—
375C2×C4×C137—22no—
376C2×C4×C137—21no—
377C2×C4×C137—21no—
378C2×C4×C137—21no—
379C2×C4×C137—21no—
380C2×C4×C137—21no—
381C2×C4×C137—21no—
382C2×C4×C137—48no—
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—41no—
390C2×C4×C137—41no—
391C2×C4×C137—41no—
392C2×C4×C137—41no—
393C2×C4×C137—41no—
394C2×C4×C137—41no—
395C2×C4×C137—41no—
396C2×C4×C137—41no—
397C2×C4×C137—41no—
398C2×C4×C137—41no—
399C2×C4×C137—84no—
400C2×C4×C137#12012yes—
401C2×C4×C137C22×D411yescharacteristic
402C2×C4×C137C22×D411yescharacteristic
403C2×C4×C137C22×D411yescharacteristic
404C2×C4×C137C2×#4111yescharacteristic
405C2×C4×C137H(5,𝔽2)11yescharacteristic
406C2×C4×C137H(5,𝔽2)11yescharacteristic
407C8×C137—22no—
408C8×C137—41no—
409C8×C137—41no—
410C8×C137—41no—
411C22×C137—22no—
412C22×C137—24no—
413C22×C137—22no—
414C22×C137—22no—
415C22×C137—42no—
416C22×C137—42no—
417C22×C137—41no—
418C22×C137—42no—
419C22×C137—41no—
420C22×C137—42no—
421C22×C137—41no—
422C22×C137—42no—
423C22×C137—41no—
424C22×C137—42no—
425C22×C137—41no—
426C22×C137—42no—
427C22×C137—41no—
428C22×C137—42no—
429C22×C137—41no—
430C22×C137—42no—
431C22×C137—41no—
432C22×C137—41no—
433C22×C137—41no—
434C22×C137—41no—
435C22×C137—816no—
436C22×C137—81no—
437C22×C137—81no—
438C22×C137—81no—
439C22×C137—81no—
440C22×C137—81no—
441C22×C137—81no—
442C22×C137—81no—
443C22×C137—81no—
444C22×C137—81no—
445C22×C137—81no—
446C22×C137—81no—
447C22×C137C2×#12011yescharacteristic
448C22×C137D4211yescharacteristic
449C22×C137#54611yescharacteristic
450C22×C137#57511yescharacteristic
451C22×C137#57511yescharacteristic
452C22×C137#57611yescharacteristic
453C22×C137#57611yescharacteristic
454C4×C137—22no—
455C4×C137—41no—
456C4×C137—42no—
457C4×C137—41no—
458C4×C137—41no—
459C4×C137—42no—
460C4×C137—42no—
461C4×C137—81no—
462C4×C137—81no—
463C4×C137C2×#12111yescharacteristic
464C4×C137#53411yescharacteristic
465C4×C137D4211yescharacteristic
466C4×C137#54611yescharacteristic
467C2×C137—42no—
468C2×C137—44no—
469C2×C137—81no—
470C2×C137—82no—
471C2×C137—161no—
472C2×C137#241011yescharacteristic
473C2×C137#300511yescharacteristic
474C2×C137#300811yescharacteristic
475C2×C137#326811yescharacteristic
476C2×C137#327311yescharacteristic
477C2×C137#331911yescharacteristic
478C2×C137#332211yescharacteristic
479#24450C13711yesmaximal, characteristic, direct product factor, Sylow
480C137#2445011yescharacteristic, direct product factor, Sylow
481C2×#546C2×C13711yescharacteristic, complemented
482C2×#468C2×C13711yescharacteristic, complemented
483C2×#449C2×C13711yescharacteristic, complemented
484C2×#447C2×C13711yescharacteristic, complemented
485C2×#418C2×C13711yescharacteristic, complemented
486#2414C2×C13711yescharacteristic, complemented
487#2042C2×C13711yescharacteristic, complemented
488#2033C2×C13711yescharacteristic, complemented
489#2012C2×C13711yescharacteristic, complemented
490#1999C2×C13711yescharacteristic, complemented
491#1879C2×C13711yescharacteristic, complemented
492#1873C2×C13711yescharacteristic, complemented
493#1870C2×C13711yescharacteristic, complemented
494#1862C2×C13711yescharacteristic, complemented
495#1788C2×C13711yescharacteristic, complemented
496C22×#41C22×C13711yescharacteristic
497C23×D4C22×C13711yescharacteristic
498C22×SD16C22×C13711yescharacteristic, complemented
499C22×D8C22×C13711yescharacteristic
500C22×D8C22×C13711yescharacteristic
501C22×M16C22×C13711yescharacteristic
502#546—24no—
503#546—24no—
504C2×#124C22×C13711yescharacteristic
505C2×#123—21no—
506C2×C22⋊Q8C22×C13711yescharacteristic
507C2×#121—21no—
508C2×#121C22×C13711yescharacteristic
509C2×#121C22×C13711yescharacteristic
510C2×#121C22×C13711yescharacteristic, complemented
511C2×#120—21no—
512C2×C4×D4C22×C13711yescharacteristic
513C2×C4×D4C22×C13711yescharacteristic
514C2×#117C22×C13711yescharacteristic
515C22×C22⋊C4—21no—
516#468—24no—
517#449—24no—
518#447—24no—
519C2×#107C22×C13711yescharacteristic, complemented
520#418—24no—
521C2×#103C22×C13711yescharacteristic, complemented
522C2×#103C22×C13711yescharacteristic, complemented
523C2×#103C22×C13711yescharacteristic, complemented
524C2×#102C22×C13711yescharacteristic
525C2×#102C22×C13711yescharacteristic
526C2×#102C22×C13711yescharacteristic
527C2×#102C22×C13711yescharacteristic
528C2×#102C22×C13711yescharacteristic
529C2×#102C22×C13711yescharacteristic
530C2×#102C22×C13711yescharacteristic, complemented
531C2×C22⋊C8C22×C13711yescharacteristic
532C2×C22⋊C8C22×C13711yescharacteristic, complemented
533C2×C22⋊C8C22×C13711yescharacteristic, complemented
534#394—21no—
535#392—21no—
536#390—21no—
537#390C22×C13711yescharacteristic, complemented
538#389C22×C13711yescharacteristic, complemented
539#388—21no—
540#380C22×C13711yescharacteristic, complemented
541#340C22×C13711yescharacteristic, complemented
542#340C22×C13711yescharacteristic, complemented
543#336C22×C13711yescharacteristic, complemented
544#336C22×C13711yescharacteristic, complemented
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C22×Q8C23×C13711yescharacteristic
553C22×D4—22no—
554C22×D4—22no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4D4×C13711yescharacteristic
564C22×D4D4×C13714yescomplemented
565C22×D4C23×C13711yescharacteristic
566C22×D4C23×C13711yescharacteristic
567C22×D4C23×C13711yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C23×C13711yescharacteristic
571C23×C4C23×C13711yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—41no—
580C2×D8—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8C23×C13711yescharacteristic
585C22×C8C23×C13711yescharacteristic
586C22×C8C23×C13711yescharacteristic
587C22×C8C23×C13711yescharacteristic
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C13714yescomplemented
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—22no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4D4×C13711yescharacteristic
610C2×C4⋊C4C23×C13711yescharacteristic
611C2×C4⋊C4C23×C13711yescharacteristic
612C2×C4⋊C4C23×C13711yescharacteristic
613C2×C4⋊C4C23×C13711yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C13711yescharacteristic
627C2×C22⋊C4D4×C13711yescharacteristic
628C2×C42—21no—
629C2×C42C23×C13711yescharacteristic
630#107—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102D4×C13714yescomplemented
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—21no—
648C24—24no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C13711yescharacteristic
657C24C2×D4×C13711yescharacteristic
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C13712yes—
668C2×D4—28no—
669C2×D4—24no—
670C2×D4—22no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—44no—
690C2×D4—41no—
691C2×D4—41no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4C2×D4×C13712yes—
705C2×D4C2×D4×C13712yes—
706C2×D4C2×D4×C13712yes—
707C2×D4#41×C13712yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C13711yescharacteristic
730C22×C4C2×D4×C13711yescharacteristic
731C22×C4C2×D4×C13711yescharacteristic
732C22×C4C2×D4×C13711yescharacteristic
733C22×C4C2×D4×C13712yes—
734C22×C4C2×D4×C13712yes—
735C22×C4C24×C13711yescharacteristic
736SD16—44no—
737D8—44no—
738D8—44no—
739M16—44no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8C2×D4×C13712yes—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—81no—
761C4⋊C4C2×D4×C13712yes—
762C4⋊C4C2×D4×C13712yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—24no—
769C22⋊C4—22no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—42no—
779C23—22no—
780C23—21no—
781C23—22no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—48no—
797C23—48no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23#120×C13712yes—
821C23C22×D4×C13711yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—48no—
832D4—48no—
833D4—44no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4#121×C13714yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4#120×C13712yes—
881C2×C4C22×D4×C13711yescharacteristic
882C2×C4C22×D4×C13711yescharacteristic
883C2×C4C22×D4×C13711yescharacteristic
884C2×C4C2×#41×C13711yescharacteristic
885C2×C4H(5,𝔽2)×C13711yescharacteristic
886C2×C4H(5,𝔽2)×C13711yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—42no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—41no—
914C22—41no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C13711yescharacteristic
928C22D42×C13711yescharacteristic
929C22#546×C13711yescharacteristic
930C22#575×C13711yescharacteristic
931C22#575×C13711yescharacteristic
932C22#576×C13711yescharacteristic
933C22#576×C13711yescharacteristic
934C4—22no—
935C4—41no—
936C4—42no—
937C4—41no—
938C4—41no—
939C4—42no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×#121×C13711yescharacteristic
944C4#534×C13711yescharacteristic
945C4D42×C13711yescharacteristic
946C4#546×C13711yescharacteristic
947C2—42no—
948C2—44no—
949C2—81no—
950C2—82no—
951C2—161no—
952C2#2410×C13711yescharacteristic
953C2#3005×C13711yescharacteristic
954C2#3008×C13711yescharacteristic
955C2#3268×C13711yescharacteristic
956C2#3273×C13711yescharacteristic
957C2#3319×C13711yescharacteristic
958C2#3322×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
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
1. C2×#546×C137C2semidirect
2. C2×#468×C137C2semidirect
3. C2×#449×C137C2semidirect
4. C2×#447×C137C2semidirect
5. C2×#418×C137C2semidirect
6. #2414×C137C2semidirect
7. #2042×C137C2semidirect
8. #2033×C137C2semidirect
9. #2012×C137C2semidirect
10. #1999×C137C2semidirect
11. #1879×C137C2semidirect
12. #1873×C137C2semidirect
13. #1870×C137C2semidirect
14. #1862×C137C2semidirect
15. #1788×C137C2semidirect
18. C22×SD16×C137C22semidirect
30. C2×#121×C137C22semidirect
39. C2×#107×C137C22semidirect
41. C2×#103×C137C22semidirect
42. C2×#103×C137C22semidirect
43. C2×#103×C137C22semidirect
50. C2×#102×C137C22semidirect
52. C2×C22⋊C8×C137C22semidirect
53. C2×C22⋊C8×C137C22semidirect
57. #390×C137C22semidirect
58. #389×C137C22semidirect
60. #380×C137C22semidirect
61. #340×C137C22semidirect
62. #340×C137C22semidirect
63. #336×C137C22semidirect
64. #336×C137C22semidirect
84. C22×D4×C137D4semidirect
112. C22⋊Q8×C137D4semidirect
160. #102×C137D4semidirect
479. #24450C137direct (N × H)
480. C137#24450direct (N × H)
481. C2×#546C2×C137semidirect
482. C2×#468C2×C137semidirect
483. C2×#449C2×C137semidirect
484. C2×#447C2×C137semidirect
485. C2×#418C2×C137semidirect
486. #2414C2×C137semidirect
487. #2042C2×C137semidirect
488. #2033C2×C137semidirect
489. #2012C2×C137semidirect
490. #1999C2×C137semidirect
491. #1879C2×C137semidirect
492. #1873C2×C137semidirect
493. #1870C2×C137semidirect
494. #1862C2×C137semidirect
495. #1788C2×C137semidirect
498. C22×SD16C22×C137semidirect
510. C2×#121C22×C137semidirect
519. C2×#107C22×C137semidirect
521. C2×#103C22×C137semidirect
522. C2×#103C22×C137semidirect
523. C2×#103C22×C137semidirect
530. C2×#102C22×C137semidirect
532. C2×C22⋊C8C22×C137semidirect
533. C2×C22⋊C8C22×C137semidirect
537. #390C22×C137semidirect
538. #389C22×C137semidirect
540. #380C22×C137semidirect
541. #340C22×C137semidirect
542. #340C22×C137semidirect
543. #336C22×C137semidirect
544. #336C22×C137semidirect
564. C22×D4D4×C137semidirect
592. C22⋊Q8D4×C137semidirect
640. #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×#449×C1372
C2×#447×C1372
C2×#418×C1372
#2414×C1372
#2042×C1372
#2033×C1372
#2012×C1372
#1999×C1372
#1879×C1372
#1873×C1372
#1870×C1372
#1862×C1372
#1788×C1372
#24450137