Finite Group Databasebeta

← C67×#24044 #30703295

Subgroups — C67×#24044 #30703295

Order 17152.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C67C211yesmaximal, characteristic
2C2×#482×C67C211yesmaximal, characteristic, complemented
3C2×#418×C67C211yesmaximal, characteristic, complemented
4C67×#2485C211yesmaximal, characteristic, complemented
5C67×#2041C211yesmaximal, characteristic, complemented
6C67×#2041C211yesmaximal, characteristic, complemented
7C67×#2034C211yesmaximal, characteristic, complemented
8C67×#2033C211yesmaximal, characteristic, complemented
9C67×#1895C211yesmaximal, characteristic, complemented
10C67×#1870C211yesmaximal, characteristic, complemented
11C67×#1864C211yesmaximal, characteristic, complemented
12C67×#1862C211yesmaximal, characteristic, complemented
13C67×#1786C211yesmaximal, characteristic, complemented
14C67×#1786C211yesmaximal, characteristic, complemented
15C67×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C67—21no—
17C23×D4×C67C2211yescharacteristic
18C23×D4×C67C2211yescharacteristic
19C22×M16×C67C2211yescharacteristic, complemented
20D42×C67—24no—
21D42×C67—24no—
22C2×#127×C67C2211yescharacteristic
23C2×#121×C67—21no—
24C2×#121×C67C2211yescharacteristic
25C2×#121×C67C2211yescharacteristic
26C2×#120×C67—21no—
27C2×#120×C67—21no—
28C2×C4×D4×C67C2211yescharacteristic
29C2×C4×D4×C67C2211yescharacteristic
30C2×#117×C67C2211yescharacteristic, complemented
31#482×C67—24no—
32C2×#107×C67C2211yescharacteristic, complemented
33C2×#106×C67C2211yescharacteristic, complemented
34#418×C67—24no—
35C2×#102×C67C2211yescharacteristic
36C2×#102×C67C2211yescharacteristic
37C2×#102×C67C2211yescharacteristic
38C2×#102×C67C2211yescharacteristic
39C2×#102×C67C2211yescharacteristic, complemented
40C2×#102×C67C2211yescharacteristic, complemented
41C2×#102×C67C2211yescharacteristic, complemented
42C2×#102×C67C2211yescharacteristic, complemented
43C2×#102×C67C2211yescharacteristic, complemented
44C2×#102×C67C2211yescharacteristic, complemented
45C2×#102×C67C2211yescharacteristic, complemented
46C2×#102×C67C2211yescharacteristic, complemented
47C2×C22⋊C8×C67C2211yescharacteristic, complemented
48C2×C22⋊C8×C67C2211yescharacteristic, complemented
49C2×C22⋊C8×C67C2211yescharacteristic, complemented
50#397×C67—21no—
51#394×C67—21no—
52#389×C67C2211yescharacteristic, complemented
53#389×C67C2211yescharacteristic, complemented
54#388×C67—21no—
55#387×C67—21no—
56#380×C67C2211yescharacteristic, complemented
57#380×C67C2211yescharacteristic, complemented
58#380×C67C2211yescharacteristic, complemented
59#340×C67C2211yescharacteristic, complemented
60#340×C67C2211yescharacteristic, complemented
61#336×C67C2211yescharacteristic, complemented
62#336×C67C2211yescharacteristic, complemented
63C25×C67—21no—
64C25×C67—21no—
65C22×D4×C67—22no—
66C22×D4×C67—22no—
67C22×D4×C67—28no—
68C22×D4×C67—21no—
69C22×D4×C67—21no—
70C22×D4×C67—22no—
71C22×D4×C67—22no—
72C22×D4×C67—22no—
73C22×D4×C67—22no—
74C22×D4×C67—21no—
75C22×D4×C67—21no—
76C22×D4×C67—21no—
77C22×D4×C67—22no—
78C22×D4×C67—21no—
79C22×D4×C67—41no—
80C22×D4×C67—41no—
81C22×D4×C67—41no—
82C22×D4×C67—41no—
83C22×D4×C67—44no—
84C22×D4×C67—44no—
85C22×D4×C67D411yescharacteristic
86C22×D4×C67D414yes—
87C22×D4×C67C2311yescharacteristic
88C22×D4×C67C2311yescharacteristic
89C22×D4×C67C2311yescharacteristic
90C23×C4×C67—21no—
91C23×C4×C67C2311yescharacteristic
92C23×C4×C67C2311yescharacteristic
93C2×M16×C67—22no—
94C2×M16×C67—41no—
95C2×M16×C67—41no—
96C22×C8×C67C2311yescharacteristic
97C22×C8×C67C2311yescharacteristic
98C22×C8×C67C2311yescharacteristic
99C22×C8×C67C2311yescharacteristic
100#127×C67—22no—
101#127×C67—22no—
102#121×C67—28no—
103#121×C67—22no—
104#121×C67—22no—
105#121×C67—22no—
106#121×C67D414yes—
107#120×C67—28no—
108#120×C67—28no—
109C4×D4×C67—22no—
110C4×D4×C67—22no—
111C4×D4×C67—22no—
112C4×D4×C67—22no—
113#117×C67—22no—
114#117×C67—22no—
115C2×C4⋊C4×C67—21no—
116C2×C4⋊C4×C67—21no—
117C2×C4⋊C4×C67D411yescharacteristic
118C2×C4⋊C4×C67C2311yescharacteristic
119C2×C4⋊C4×C67C2311yescharacteristic
120C2×C4⋊C4×C67C2311yescharacteristic
121C2×C4⋊C4×C67C2311yescharacteristic
122C2×C4⋊C4×C67C2311yescharacteristic
123C2×C22⋊C4×C67—21no—
124C2×C22⋊C4×C67—21no—
125C2×C22⋊C4×C67—21no—
126C2×C22⋊C4×C67—21no—
127C2×C22⋊C4×C67—21no—
128C2×C22⋊C4×C67—21no—
129C2×C22⋊C4×C67—21no—
130C2×C22⋊C4×C67D411yescharacteristic
131C2×C22⋊C4×C67D411yescharacteristic
132C2×C42×C67—21no—
133C2×C42×C67C2311yescharacteristic
134#107×C67—22no—
135#106×C67—22no—
136#102×C67—22no—
137#102×C67—22no—
138#102×C67—22no—
139#102×C67—22no—
140#102×C67—22no—
141#102×C67—22no—
142#102×C67—22no—
143#102×C67—22no—
144#102×C67—41no—
145#102×C67—41no—
146#102×C67—41no—
147#102×C67—41no—
148C22⋊C8×C67—22no—
149C22⋊C8×C67—41no—
150C22⋊C8×C67—41no—
151#95×C67—21no—
152#95×C67—21no—
153#95×C67—21no—
154#95×C67—21no—
155#95×C67—21no—
156C24×C67—21no—
157C24×C67—24no—
158C24×C67—21no—
159C24×C67—21no—
160C24×C67—24no—
161C24×C67—42no—
162C24×C67—42no—
163C24×C67—42no—
164C24×C67—42no—
165C24×C67—42no—
166C24×C67—42no—
167C24×C67—42no—
168C24×C67—42no—
169C24×C67—81no—
170C24×C67—81no—
171C24×C67—81no—
172C24×C67—81no—
173C24×C67C2×D411yescharacteristic
174C24×C67C2×D411yescharacteristic
175C2×D4×C67—22no—
176C2×D4×C67—22no—
177C2×D4×C67—28no—
178C2×D4×C67—24no—
179C2×D4×C67—24no—
180C2×D4×C67—24no—
181C2×D4×C67—24no—
182C2×D4×C67—24no—
183C2×D4×C67—24no—
184C2×D4×C67—22no—
185C2×D4×C67—21no—
186C2×D4×C67—21no—
187C2×D4×C67—21no—
188C2×D4×C67—21no—
189C2×D4×C67—21no—
190C2×D4×C67—21no—
191C2×D4×C67—21no—
192C2×D4×C67—21no—
193C2×D4×C67—21no—
194C2×D4×C67—21no—
195C2×D4×C67—21no—
196C2×D4×C67—21no—
197C2×D4×C67—21no—
198C2×D4×C67—44no—
199C2×D4×C67—44no—
200C2×D4×C67—44no—
201C2×D4×C67—42no—
202C2×D4×C67—42no—
203C2×D4×C67—42no—
204C2×D4×C67—42no—
205C2×D4×C67—42no—
206C2×D4×C67—44no—
207C2×D4×C67—44no—
208C2×D4×C67—432no—
209C2×D4×C67—44no—
210C2×D4×C67—42no—
211C2×D4×C67—42no—
212C2×D4×C67—42no—
213C2×D4×C67—42no—
214C2×D4×C67—44no—
215C2×D4×C67—42no—
216C2×D4×C67—81no—
217C2×D4×C67—81no—
218C2×D4×C67C2×D412yes—
219C2×D4×C67C2×D412yes—
220C2×D4×C67C2×D412yes—
221C2×D4×C67#4112yes—
222C2×D4×C67#4112yes—
223C22×C4×C67—21no—
224C22×C4×C67—21no—
225C22×C4×C67—21no—
226C22×C4×C67—21no—
227C22×C4×C67—24no—
228C22×C4×C67—21no—
229C22×C4×C67—21no—
230C22×C4×C67—21no—
231C22×C4×C67—21no—
232C22×C4×C67—21no—
233C22×C4×C67—21no—
234C22×C4×C67—21no—
235C22×C4×C67—21no—
236C22×C4×C67—21no—
237C22×C4×C67—21no—
238C22×C4×C67—21no—
239C22×C4×C67—42no—
240C22×C4×C67—42no—
241C22×C4×C67C2×D411yescharacteristic
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2×D411yescharacteristic
244C22×C4×C67C2×D412yes—
245C22×C4×C67C2×D412yes—
246C22×C4×C67C2×D411yescharacteristic
247C22×C4×C67C2411yescharacteristic
248M16×C67—44no—
249C2×C8×C67—21no—
250C2×C8×C67—21no—
251C2×C8×C67—21no—
252C2×C8×C67—21no—
253C2×C8×C67—21no—
254C2×C8×C67—21no—
255C2×C8×C67—21no—
256C2×C8×C67—21no—
257C2×C8×C67—21no—
258C2×C8×C67—21no—
259C2×C8×C67—21no—
260C2×C8×C67—21no—
261C4⋊C4×C67—22no—
262C4⋊C4×C67—21no—
263C4⋊C4×C67—21no—
264C4⋊C4×C67—21no—
265C4⋊C4×C67—21no—
266C4⋊C4×C67—21no—
267C4⋊C4×C67—21no—
268C4⋊C4×C67—21no—
269C4⋊C4×C67—21no—
270C4⋊C4×C67—21no—
271C4⋊C4×C67—42no—
272C4⋊C4×C67—81no—
273C4⋊C4×C67C2×D412yes—
274C22⋊C4×C67—24no—
275C22⋊C4×C67—24no—
276C22⋊C4×C67—22no—
277C22⋊C4×C67—24no—
278C22⋊C4×C67—22no—
279C22⋊C4×C67—42no—
280C22⋊C4×C67—42no—
281C22⋊C4×C67—81no—
282C22⋊C4×C67—81no—
283C42×C67—21no—
284C42×C67—21no—
285C42×C67—42no—
286C23×C67—21no—
287C23×C67—22no—
288C23×C67—21no—
289C23×C67—21no—
290C23×C67—21no—
291C23×C67—21no—
292C23×C67—22no—
293C23×C67—22no—
294C23×C67—21no—
295C23×C67—21no—
296C23×C67—21no—
297C23×C67—21no—
298C23×C67—21no—
299C23×C67—21no—
300C23×C67—21no—
301C23×C67—22no—
302C23×C67—22no—
303C23×C67—48no—
304C23×C67—48no—
305C23×C67—48no—
306C23×C67—48no—
307C23×C67—41no—
308C23×C67—41no—
309C23×C67—41no—
310C23×C67—41no—
311C23×C67—41no—
312C23×C67—41no—
313C23×C67—41no—
314C23×C67—41no—
315C23×C67—41no—
316C23×C67—41no—
317C23×C67—41no—
318C23×C67—41no—
319C23×C67—41no—
320C23×C67—41no—
321C23×C67—41no—
322C23×C67—41no—
323C23×C67—84no—
324C23×C67—84no—
325C23×C67—84no—
326C23×C67—84no—
327C23×C67—84no—
328C23×C67—84no—
329C23×C67—84no—
330C23×C67—84no—
331C23×C67—84no—
332C23×C67—84no—
333C23×C67#12012yes—
334C23×C67AGL(1,ℤ/8)12yes—
335C23×C67C22×D411yescharacteristic
336D4×C67—28no—
337D4×C67—22no—
338D4×C67—22no—
339D4×C67—22no—
340D4×C67—22no—
341D4×C67—22no—
342D4×C67—22no—
343D4×C67—22no—
344D4×C67—48no—
345D4×C67—48no—
346D4×C67—48no—
347D4×C67—48no—
348D4×C67—48no—
349D4×C67—41no—
350D4×C67—41no—
351D4×C67—41no—
352D4×C67—41no—
353D4×C67—84no—
354D4×C67#12314yes—
355C2×C4×C67—21no—
356C2×C4×C67—21no—
357C2×C4×C67—21no—
358C2×C4×C67—21no—
359C2×C4×C67—22no—
360C2×C4×C67—22no—
361C2×C4×C67—22no—
362C2×C4×C67—22no—
363C2×C4×C67—21no—
364C2×C4×C67—21no—
365C2×C4×C67—22no—
366C2×C4×C67—21no—
367C2×C4×C67—21no—
368C2×C4×C67—21no—
369C2×C4×C67—21no—
370C2×C4×C67—48no—
371C2×C4×C67—41no—
372C2×C4×C67—41no—
373C2×C4×C67—41no—
374C2×C4×C67—41no—
375C2×C4×C67—41no—
376C2×C4×C67—41no—
377C2×C4×C67—41no—
378C2×C4×C67—41no—
379C2×C4×C67—41no—
380C2×C4×C67—41no—
381C2×C4×C67—41no—
382C2×C4×C67—41no—
383C2×C4×C67—41no—
384C2×C4×C67—41no—
385C2×C4×C67—41no—
386C2×C4×C67—41no—
387C2×C4×C67—41no—
388C2×C4×C67—41no—
389C2×C4×C67#12012yes—
390C2×C4×C67AGL(1,ℤ/8)12yes—
391C2×C4×C67C22×D411yescharacteristic
392C2×C4×C67C22×D411yescharacteristic
393C2×C4×C67C2×#4111yescharacteristic
394C2×C4×C67C2×#4111yescharacteristic
395C2×C4×C67H(5,𝔽2)11yescharacteristic
396C2×C4×C67H(5,𝔽2)11yescharacteristic
397C8×C67—41no—
398C8×C67—41no—
399C8×C67—41no—
400C8×C67—41no—
401C22×C67—22no—
402C22×C67—24no—
403C22×C67—22no—
404C22×C67—22no—
405C22×C67—22no—
406C22×C67—22no—
407C22×C67—22no—
408C22×C67—41no—
409C22×C67—42no—
410C22×C67—41no—
411C22×C67—42no—
412C22×C67—41no—
413C22×C67—42no—
414C22×C67—41no—
415C22×C67—42no—
416C22×C67—41no—
417C22×C67—41no—
418C22×C67—42no—
419C22×C67—41no—
420C22×C67—41no—
421C22×C67—42no—
422C22×C67—42no—
423C22×C67—42no—
424C22×C67—42no—
425C22×C67—42no—
426C22×C67—42no—
427C22×C67—42no—
428C22×C67—816no—
429C22×C67—816no—
430C22×C67—81no—
431C22×C67—81no—
432C22×C67—81no—
433C22×C67—81no—
434C22×C67—81no—
435C22×C67—81no—
436C22×C67—81no—
437C22×C67—81no—
438C22×C67C2×#12011yescharacteristic
439C22×C67#54611yescharacteristic
440C22×C67#54611yescharacteristic
441C22×C67C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C67C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C67#57611yescharacteristic
444C22×C67#57711yescharacteristic
445C4×C67—22no—
446C4×C67—22no—
447C4×C67—41no—
448C4×C67—42no—
449C4×C67—41no—
450C4×C67—81no—
451C4×C67—81no—
452C4×C67—81no—
453C4×C67—81no—
454C4×C67C2×#12311yescharacteristic
455C4×C67#53411yescharacteristic
456C4×C67#54611yescharacteristic
457C4×C67#54611yescharacteristic
458#24044C6711yesmaximal, characteristic, direct product factor, Sylow
459C2×C67—42no—
460C2×C67—42no—
461C2×C67—44no—
462C2×C67—82no—
463C2×C67—82no—
464C2×C67#240511yescharacteristic
465C2×C67#300311yescharacteristic
466C2×C67#301211yescharacteristic
467C2×C67#331011yescharacteristic
468C2×C67#331811yescharacteristic
469C2×C67#332411yescharacteristic
470C2×C67#332511yescharacteristic
471C2×D42C2×C6711yescharacteristic
472C2×#482C2×C6711yescharacteristic, complemented
473C2×#418C2×C6711yescharacteristic, complemented
474#2485C2×C6711yescharacteristic, complemented
475#2041C2×C6711yescharacteristic, complemented
476#2041C2×C6711yescharacteristic, complemented
477#2034C2×C6711yescharacteristic, complemented
478#2033C2×C6711yescharacteristic, complemented
479#1895C2×C6711yescharacteristic, complemented
480#1870C2×C6711yescharacteristic, complemented
481#1864C2×C6711yescharacteristic, complemented
482#1862C2×C6711yescharacteristic, complemented
483#1786C2×C6711yescharacteristic, complemented
484#1786C2×C6711yescharacteristic, complemented
485#1786C2×C6711yescharacteristic, complemented
486C67#2404411yescharacteristic, direct product factor, Sylow
487C23×D4—21no—
488C23×D4C22×C6711yescharacteristic
489C23×D4C22×C6711yescharacteristic
490C22×M16C22×C6711yescharacteristic, complemented
491D42—24no—
492D42—24no—
493C2×#127C22×C6711yescharacteristic
494C2×#121—21no—
495C2×#121C22×C6711yescharacteristic
496C2×#121C22×C6711yescharacteristic
497C2×#120—21no—
498C2×#120—21no—
499C2×C4×D4C22×C6711yescharacteristic
500C2×C4×D4C22×C6711yescharacteristic
501C2×#117C22×C6711yescharacteristic, complemented
502#482—24no—
503C2×#107C22×C6711yescharacteristic, complemented
504C2×#106C22×C6711yescharacteristic, complemented
505#418—24no—
506C2×#102C22×C6711yescharacteristic
507C2×#102C22×C6711yescharacteristic
508C2×#102C22×C6711yescharacteristic
509C2×#102C22×C6711yescharacteristic
510C2×#102C22×C6711yescharacteristic, complemented
511C2×#102C22×C6711yescharacteristic, complemented
512C2×#102C22×C6711yescharacteristic, complemented
513C2×#102C22×C6711yescharacteristic, complemented
514C2×#102C22×C6711yescharacteristic, complemented
515C2×#102C22×C6711yescharacteristic, complemented
516C2×#102C22×C6711yescharacteristic, complemented
517C2×#102C22×C6711yescharacteristic, complemented
518C2×C22⋊C8C22×C6711yescharacteristic, complemented
519C2×C22⋊C8C22×C6711yescharacteristic, complemented
520C2×C22⋊C8C22×C6711yescharacteristic, complemented
521#397—21no—
522#394—21no—
523#389C22×C6711yescharacteristic, complemented
524#389C22×C6711yescharacteristic, complemented
525#388—21no—
526#387—21no—
527#380C22×C6711yescharacteristic, complemented
528#380C22×C6711yescharacteristic, complemented
529#380C22×C6711yescharacteristic, complemented
530#340C22×C6711yescharacteristic, complemented
531#340C22×C6711yescharacteristic, complemented
532#336C22×C6711yescharacteristic, complemented
533#336C22×C6711yescharacteristic, complemented
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4D4×C6711yescharacteristic
557C22×D4D4×C6714yes—
558C22×D4C23×C6711yescharacteristic
559C22×D4C23×C6711yescharacteristic
560C22×D4C23×C6711yescharacteristic
561C23×C4—21no—
562C23×C4C23×C6711yescharacteristic
563C23×C4C23×C6711yescharacteristic
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C6711yescharacteristic
568C22×C8C23×C6711yescharacteristic
569C22×C8C23×C6711yescharacteristic
570C22×C8C23×C6711yescharacteristic
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121D4×C6714yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C6711yescharacteristic
589C2×C4⋊C4C23×C6711yescharacteristic
590C2×C4⋊C4C23×C6711yescharacteristic
591C2×C4⋊C4C23×C6711yescharacteristic
592C2×C4⋊C4C23×C6711yescharacteristic
593C2×C4⋊C4C23×C6711yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C6711yescharacteristic
602C2×C22⋊C4D4×C6711yescharacteristic
603C2×C42—21no—
604C2×C42C23×C6711yescharacteristic
605#107—22no—
606#106—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C6711yescharacteristic
645C24C2×D4×C6711yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
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—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C6712yes—
690C2×D4C2×D4×C6712yes—
691C2×D4C2×D4×C6712yes—
692C2×D4#41×C6712yes—
693C2×D4#41×C6712yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C6711yescharacteristic
713C22×C4C2×D4×C6711yescharacteristic
714C22×C4C2×D4×C6711yescharacteristic
715C22×C4C2×D4×C6712yes—
716C22×C4C2×D4×C6712yes—
717C22×C4C2×D4×C6711yescharacteristic
718C22×C4C24×C6711yescharacteristic
719M16—44no—
720C2×C8—21no—
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—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C6712yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#120×C6712yes—
805C23AGL(1,ℤ/8)×C6712yes—
806C23C22×D4×C6711yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#123×C6714yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
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—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4#120×C6712yes—
861C2×C4AGL(1,ℤ/8)×C6712yes—
862C2×C4C22×D4×C6711yescharacteristic
863C2×C4C22×D4×C6711yescharacteristic
864C2×C4C2×#41×C6711yescharacteristic
865C2×C4C2×#41×C6711yescharacteristic
866C2×C4H(5,𝔽2)×C6711yescharacteristic
867C2×C4H(5,𝔽2)×C6711yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—24no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—41no—
887C22—42no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C6711yescharacteristic
910C22#546×C6711yescharacteristic
911C22#546×C6711yescharacteristic
912C22C2×AGL(1,ℤ/8)×C6711yescharacteristic
913C22C2×AGL(1,ℤ/8)×C6711yescharacteristic
914C22#576×C6711yescharacteristic
915C22#577×C6711yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—41no—
920C4—42no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×#123×C6711yescharacteristic
926C4#534×C6711yescharacteristic
927C4#546×C6711yescharacteristic
928C4#546×C6711yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2C67×#240511yescharacteristic
935C2C67×#300311yescharacteristic
936C2C67×#301211yescharacteristic
937C2C67×#331011yescharacteristic
938C2C67×#331811yescharacteristic
939C2C67×#332411yescharacteristic
940C2C67×#332511yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC2×D42×C67C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×C4×D4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#482×C67C2semidirect
3. C2×#418×C67C2semidirect
4. C67×#2485C2semidirect
5. C67×#2041C2semidirect
6. C67×#2041C2semidirect
7. C67×#2034C2semidirect
8. C67×#2033C2semidirect
9. C67×#1895C2semidirect
10. C67×#1870C2semidirect
11. C67×#1864C2semidirect
12. C67×#1862C2semidirect
13. C67×#1786C2semidirect
14. C67×#1786C2semidirect
15. C67×#1786C2semidirect
19. C22×M16×C67C22semidirect
30. C2×#117×C67C22semidirect
32. C2×#107×C67C22semidirect
33. C2×#106×C67C22semidirect
39. C2×#102×C67C22semidirect
40. C2×#102×C67C22semidirect
41. C2×#102×C67C22semidirect
42. C2×#102×C67C22semidirect
43. C2×#102×C67C22semidirect
44. C2×#102×C67C22semidirect
45. C2×#102×C67C22semidirect
46. C2×#102×C67C22semidirect
47. C2×C22⋊C8×C67C22semidirect
48. C2×C22⋊C8×C67C22semidirect
49. C2×C22⋊C8×C67C22semidirect
52. #389×C67C22semidirect
53. #389×C67C22semidirect
56. #380×C67C22semidirect
57. #380×C67C22semidirect
58. #380×C67C22semidirect
59. #340×C67C22semidirect
60. #340×C67C22semidirect
61. #336×C67C22semidirect
62. #336×C67C22semidirect
458. #24044C67direct (N × H)
472. C2×#482C2×C67semidirect
473. C2×#418C2×C67semidirect
474. #2485C2×C67semidirect
475. #2041C2×C67semidirect
476. #2041C2×C67semidirect
477. #2034C2×C67semidirect
478. #2033C2×C67semidirect
479. #1895C2×C67semidirect
480. #1870C2×C67semidirect
481. #1864C2×C67semidirect
482. #1862C2×C67semidirect
483. #1786C2×C67semidirect
484. #1786C2×C67semidirect
485. #1786C2×C67semidirect
486. C67#24044direct (N × H)
490. C22×M16C22×C67semidirect
501. C2×#117C22×C67semidirect
503. C2×#107C22×C67semidirect
504. C2×#106C22×C67semidirect
510. C2×#102C22×C67semidirect
511. C2×#102C22×C67semidirect
512. C2×#102C22×C67semidirect
513. C2×#102C22×C67semidirect
514. C2×#102C22×C67semidirect
515. C2×#102C22×C67semidirect
516. C2×#102C22×C67semidirect
517. C2×#102C22×C67semidirect
518. C2×C22⋊C8C22×C67semidirect
519. C2×C22⋊C8C22×C67semidirect
520. C2×C22⋊C8C22×C67semidirect
523. #389C22×C67semidirect
524. #389C22×C67semidirect
527. #380C22×C67semidirect
528. #380C22×C67semidirect
529. #380C22×C67semidirect
530. #340C22×C67semidirect
531. #340C22×C67semidirect
532. #336C22×C67semidirect
533. #336C22×C67semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C672
C2×#482×C672
C2×#418×C672
C67×#24852
C67×#20412
C67×#20342
C67×#20332
C67×#18952
C67×#18702
C67×#18642
C67×#18622
C67×#17862
#2404467