Finite Group Databasebeta

← C67×#25172 #30704423

Subgroups — C67×#25172 #30704423

Order 17152.

1310 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C67C211yesmaximal, characteristic, complemented
2C2×#450×C67C211yesmaximal, characteristic, complemented
3C2×#447×C67C211yesmaximal, characteristic
4C2×#442×C67C211yesmaximal, characteristic, complemented
5C67×#2427C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
7C67×#2065C211yesmaximal, characteristic, complemented
8C67×#2035C211yesmaximal, characteristic, complemented
9C67×#2033C211yesmaximal, characteristic, complemented
10C67×#2012C211yesmaximal, characteristic, complemented
11C67×#1973C211yesmaximal, characteristic, complemented
12C67×#1924C211yesmaximal, characteristic, complemented
13C67×#1879C211yesmaximal, characteristic, complemented
14C67×#1877C211yesmaximal, characteristic, complemented
15C67×#1862C211yesmaximal, characteristic, complemented
16C23×D4×C67C2211yescharacteristic
17C22×SD16×C67C2211yescharacteristic
18C22×SD16×C67C2211yescharacteristic
19C22×D8×C67C2211yescharacteristic
20C22×D8×C67C2211yescharacteristic
21C2×#124×C67C2211yescharacteristic, complemented
22C2×C22⋊Q8×C67C2211yescharacteristic
23C2×#121×C67C2211yescharacteristic
24C2×C4×D4×C67C2211yescharacteristic
25C2×C4×D4×C67C2211yescharacteristic
26C2×C4×D4×C67C2211yescharacteristic, complemented
27C22×C22⋊C4×C67—21no—
28#463×C67—24no—
29#450×C67—24no—
30#447×C67—24no—
31#442×C67—24no—
32C2×#107×C67C2211yescharacteristic, complemented
33C2×#106×C67C2211yescharacteristic, complemented
34C2×C4⋊C8×C67C2211yescharacteristic, complemented
35C2×#103×C67C2211yescharacteristic, complemented
36C2×#103×C67C2211yescharacteristic, complemented
37C2×#102×C67C2211yescharacteristic
38C2×#102×C67C2211yescharacteristic
39C2×#102×C67C2211yescharacteristic
40C2×#102×C67C2211yescharacteristic
41C2×#102×C67C2211yescharacteristic, complemented
42C2×#102×C67C2211yescharacteristic, complemented
43C2×C22⋊C8×C67C2211yescharacteristic
44C2×C22⋊C8×C67C2211yescharacteristic
45C2×#97×C67C2211yescharacteristic, complemented
46#397×C67—21no—
47#394×C67—21no—
48#391×C67C2211yescharacteristic, complemented
49#390×C67C2211yescharacteristic
50#390×C67C2211yescharacteristic
51#389×C67C2211yescharacteristic, complemented
52#386×C67—21no—
53#386×C67—21no—
54#386×C67—21no—
55#380×C67—21no—
56#380×C67C2211yescharacteristic
57#379×C67—21no—
58C4×C22⋊C4×C67C2211yescharacteristic
59#340×C67C2211yescharacteristic, complemented
60#340×C67C2211yescharacteristic, complemented
61#336×C67C2211yescharacteristic, complemented
62#336×C67C2211yescharacteristic, complemented
63C25×C67—21no—
64C22×Q8×C67C2311yescharacteristic
65C22×D4×C67—22no—
66C22×D4×C67—22no—
67C22×D4×C67—22no—
68C22×D4×C67—22no—
69C22×D4×C67—21no—
70C22×D4×C67—21no—
71C22×D4×C67—41no—
72C22×D4×C67—41no—
73C22×D4×C67C2311yescharacteristic
74C22×D4×C67C2311yescharacteristic
75C22×D4×C67C2311yescharacteristic
76C23×C4×C67—21no—
77C23×C4×C67—21no—
78C23×C4×C67—21no—
79C23×C4×C67C2311yescharacteristic
80C2×SD16×C67—22no—
81C2×SD16×C67—22no—
82C2×SD16×C67—22no—
83C2×SD16×C67—22no—
84C2×SD16×C67—22no—
85C2×SD16×C67—41no—
86C2×D8×C67—22no—
87C2×D8×C67—22no—
88C2×D8×C67—22no—
89C2×D8×C67—22no—
90C2×D8×C67—41no—
91C2×D8×C67D414yes—
92C22×C8×C67C2311yescharacteristic
93C22×C8×C67C2311yescharacteristic
94C22×C8×C67C2311yescharacteristic
95C22×C8×C67C2311yescharacteristic
96#124×C67—22no—
97#124×C67—41no—
98C22⋊Q8×C67—22no—
99C22⋊Q8×C67—41no—
100#121×C67—22no—
101#121×C67—41no—
102C4×D4×C67—22no—
103C4×D4×C67—22no—
104C4×D4×C67—22no—
105C4×D4×C67—41no—
106C4×D4×C67—41no—
107C4×D4×C67—41no—
108C2×C4⋊C4×C67—21no—
109C2×C4⋊C4×C67—21no—
110C2×C4⋊C4×C67C2311yescharacteristic
111C2×C4⋊C4×C67C2311yescharacteristic
112C2×C4⋊C4×C67C2311yescharacteristic
113C2×C4⋊C4×C67C2311yescharacteristic
114C2×C22⋊C4×C67—21no—
115C2×C22⋊C4×C67—21no—
116C2×C22⋊C4×C67—21no—
117C2×C22⋊C4×C67—21no—
118C2×C22⋊C4×C67—21no—
119C2×C22⋊C4×C67—21no—
120C2×C22⋊C4×C67—21no—
121C2×C22⋊C4×C67—21no—
122C2×C22⋊C4×C67—21no—
123C2×C22⋊C4×C67—21no—
124C2×C22⋊C4×C67—21no—
125C2×C22⋊C4×C67—21no—
126C2×C22⋊C4×C67—44no—
127C2×C22⋊C4×C67D411yescharacteristic
128C2×C22⋊C4×C67D411yescharacteristic
129C2×C42×C67C2311yescharacteristic
130C2×C42×C67C2311yescharacteristic
131#107×C67—41no—
132#106×C67—22no—
133C4⋊C8×C67—22no—
134#103×C67—22no—
135#103×C67—41no—
136#102×C67—22no—
137#102×C67—22no—
138#102×C67—22no—
139#102×C67—22no—
140#102×C67—22no—
141#102×C67D414yescomplemented
142C22⋊C8×C67—22no—
143C22⋊C8×C67—22no—
144#97×C67—22no—
145#95×C67—21no—
146#95×C67—21no—
147#95×C67—21no—
148#95×C67—21no—
149#95×C67D411yescharacteristic
150#95×C67D411yescharacteristic
151C24×C67—21no—
152C24×C67—24no—
153C24×C67—21no—
154C24×C67—21no—
155C24×C67—42no—
156C24×C67—42no—
157C24×C67—42no—
158C24×C67—42no—
159C24×C67—81no—
160C24×C67—81no—
161C24×C67C2×D411yescharacteristic
162C2×Q8×C67—21no—
163C2×Q8×C67—21no—
164C2×Q8×C67—21no—
165C2×Q8×C67—21no—
166C2×Q8×C67—21no—
167C2×Q8×C67—21no—
168C2×D4×C67—24no—
169C2×D4×C67—21no—
170C2×D4×C67—21no—
171C2×D4×C67—21no—
172C2×D4×C67—21no—
173C2×D4×C67—21no—
174C2×D4×C67—21no—
175C2×D4×C67—21no—
176C2×D4×C67—21no—
177C2×D4×C67—21no—
178C2×D4×C67—21no—
179C2×D4×C67—21no—
180C2×D4×C67—21no—
181C2×D4×C67—21no—
182C2×D4×C67—42no—
183C2×D4×C67—42no—
184C2×D4×C67—44no—
185C2×D4×C67—44no—
186C2×D4×C67—44no—
187C2×D4×C67—44no—
188C2×D4×C67—42no—
189C2×D4×C67—42no—
190C2×D4×C67—81no—
191C2×D4×C67C2×D412yes—
192C2×D4×C67C2×D412yes—
193C2×D4×C67C2×D412yes—
194C2×D4×C67#4112yes—
195C2×D4×C67#4112yes—
196C22×C4×C67—21no—
197C22×C4×C67—21no—
198C22×C4×C67—21no—
199C22×C4×C67—21no—
200C22×C4×C67—21no—
201C22×C4×C67—21no—
202C22×C4×C67—21no—
203C22×C4×C67—21no—
204C22×C4×C67—21no—
205C22×C4×C67—21no—
206C22×C4×C67—21no—
207C22×C4×C67—42no—
208C22×C4×C67—42no—
209C22×C4×C67—42no—
210C22×C4×C67—42no—
211C22×C4×C67—42no—
212C22×C4×C67—42no—
213C22×C4×C67—81no—
214C22×C4×C67—81no—
215C22×C4×C67—81no—
216C22×C4×C67C2×D411yescharacteristic
217C22×C4×C67C2×D411yescharacteristic
218C22×C4×C67C2×D411yescharacteristic
219C22×C4×C67C2×D411yescharacteristic
220C22×C4×C67C2×D411yescharacteristic
221C22×C4×C67C2411yescharacteristic
222SD16×C67—44no—
223SD16×C67—44no—
224D8×C67—28no—
225D8×C67—44no—
226C2×C8×C67—21no—
227C2×C8×C67—21no—
228C2×C8×C67—21no—
229C2×C8×C67—21no—
230C2×C8×C67—21no—
231C2×C8×C67—21no—
232C2×C8×C67—21no—
233C2×C8×C67—21no—
234C2×C8×C67—21no—
235C2×C8×C67—21no—
236C2×C8×C67C2×D412yes—
237C2×C8×C67C2×D412yes—
238C4⋊C4×C67—21no—
239C4⋊C4×C67—21no—
240C4⋊C4×C67—21no—
241C4⋊C4×C67—21no—
242C4⋊C4×C67—21no—
243C4⋊C4×C67—21no—
244C4⋊C4×C67—21no—
245C4⋊C4×C67—42no—
246C4⋊C4×C67—81no—
247C4⋊C4×C67C2×D412yes—
248C22⋊C4×C67—22no—
249C22⋊C4×C67—41no—
250C22⋊C4×C67—42no—
251C22⋊C4×C67—42no—
252C22⋊C4×C67—42no—
253C22⋊C4×C67—42no—
254C22⋊C4×C67—42no—
255C22⋊C4×C67—42no—
256C22⋊C4×C67—42no—
257C22⋊C4×C67—42no—
258C22⋊C4×C67—42no—
259C22⋊C4×C67—42no—
260C22⋊C4×C67—81no—
261C22⋊C4×C67—81no—
262C42×C67—21no—
263C42×C67—21no—
264C42×C67—21no—
265C42×C67—21no—
266C23×C67—21no—
267C23×C67—22no—
268C23×C67—21no—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—21no—
272C23×C67—21no—
273C23×C67—21no—
274C23×C67—21no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67—48no—
278C23×C67—48no—
279C23×C67—41no—
280C23×C67—41no—
281C23×C67—41no—
282C23×C67—41no—
283C23×C67—41no—
284C23×C67—41no—
285C23×C67—41no—
286C23×C67—41no—
287C23×C67—41no—
288C23×C67—41no—
289C23×C67—41no—
290C23×C67—41no—
291C23×C67—41no—
292C23×C67—41no—
293C23×C67—41no—
294C23×C67—41no—
295C23×C67—84no—
296C23×C67—84no—
297C23×C67—84no—
298C23×C67—84no—
299C23×C67—84no—
300C23×C67AGL(1,ℤ/8)12yes—
301C23×C67C22×D411yescharacteristic
302Q8×C67—41no—
303Q8×C67—41no—
304Q8×C67—41no—
305Q8×C67—41no—
306D4×C67—22no—
307D4×C67—22no—
308D4×C67—22no—
309D4×C67—22no—
310D4×C67—22no—
311D4×C67—22no—
312D4×C67—22no—
313D4×C67—48no—
314D4×C67—41no—
315D4×C67—41no—
316D4×C67—41no—
317D4×C67—41no—
318D4×C67—84no—
319D4×C67#12114yes—
320C2×C4×C67—21no—
321C2×C4×C67—21no—
322C2×C4×C67—21no—
323C2×C4×C67—21no—
324C2×C4×C67—21no—
325C2×C4×C67—22no—
326C2×C4×C67—21no—
327C2×C4×C67—21no—
328C2×C4×C67—21no—
329C2×C4×C67—21no—
330C2×C4×C67—21no—
331C2×C4×C67—21no—
332C2×C4×C67—21no—
333C2×C4×C67—21no—
334C2×C4×C67—21no—
335C2×C4×C67—21no—
336C2×C4×C67—41no—
337C2×C4×C67—41no—
338C2×C4×C67—41no—
339C2×C4×C67—41no—
340C2×C4×C67—41no—
341C2×C4×C67—41no—
342C2×C4×C67—41no—
343C2×C4×C67—41no—
344C2×C4×C67—41no—
345C2×C4×C67—41no—
346C2×C4×C67—41no—
347C2×C4×C67—41no—
348C2×C4×C67—41no—
349C2×C4×C67—41no—
350C2×C4×C67—41no—
351C2×C4×C67—41no—
352C2×C4×C67—41no—
353C2×C4×C67—41no—
354C2×C4×C67—84no—
355C2×C4×C67—84no—
356C2×C4×C67—84no—
357C2×C4×C67C22×D411yescharacteristic
358C2×C4×C67C22×D411yescharacteristic
359C2×C4×C67C2×#4111yescharacteristic
360C2×C4×C67C2×#4111yescharacteristic
361C2×C4×C67H(5,𝔽2)11yescharacteristic
362C2×C4×C67H(5,𝔽2)11yescharacteristic
363C8×C67—22no—
364C8×C67—22no—
365C8×C67—41no—
366C8×C67—41no—
367C22×C67—22no—
368C22×C67—24no—
369C22×C67—22no—
370C22×C67—22no—
371C22×C67—42no—
372C22×C67—41no—
373C22×C67—42no—
374C22×C67—41no—
375C22×C67—42no—
376C22×C67—42no—
377C22×C67—41no—
378C22×C67—42no—
379C22×C67—41no—
380C22×C67—42no—
381C22×C67—42no—
382C22×C67—42no—
383C22×C67—42no—
384C22×C67—42no—
385C22×C67—42no—
386C22×C67—42no—
387C22×C67—816no—
388C22×C67—81no—
389C22×C67—81no—
390C22×C67—81no—
391C22×C67—81no—
392C22×C67—81no—
393C22×C67—81no—
394C22×C67—81no—
395C22×C67—81no—
396C22×C67#52511yescharacteristic
397C22×C67D4211yescharacteristic
398C22×C67D4211yescharacteristic
399C22×C67C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C67#57511yescharacteristic
401C22×C67#57611yescharacteristic
402C22×C67#57711yescharacteristic
403C4×C67—41no—
404C4×C67—41no—
405C4×C67—41no—
406C4×C67—41no—
407C4×C67—41no—
408C4×C67—42no—
409C4×C67—81no—
410C4×C67—81no—
411C4×C67—81no—
412C4×C67—81no—
413C4×C67C2×#12111yescharacteristic
414C4×C67#53811yescharacteristic
415C4×C67#54611yescharacteristic
416C4×C67#54611yescharacteristic
417#25172C6711yesmaximal, characteristic, direct product factor, Sylow
418C2×C67—42no—
419C2×C67—44no—
420C2×C67—82no—
421C2×C67—82no—
422C2×C67#242411yescharacteristic
423C2×C67#311411yescharacteristic
424C2×C67#311811yescharacteristic
425C2×C67#326411yescharacteristic
426C2×C67#326511yescharacteristic
427C2×C67#326711yescharacteristic
428C2×C67#327311yescharacteristic
429C2×#463C2×C6711yescharacteristic, complemented
430C2×#450C2×C6711yescharacteristic, complemented
431C2×#447C2×C6711yescharacteristic
432C2×#442C2×C6711yescharacteristic, complemented
433#2427C2×C6711yescharacteristic, complemented
434D4×C22⋊C4C2×C6711yescharacteristic, complemented
435#2065C2×C6711yescharacteristic, complemented
436#2035C2×C6711yescharacteristic, complemented
437#2033C2×C6711yescharacteristic, complemented
438#2012C2×C6711yescharacteristic, complemented
439#1973C2×C6711yescharacteristic, complemented
440#1924C2×C6711yescharacteristic, complemented
441#1879C2×C6711yescharacteristic, complemented
442#1877C2×C6711yescharacteristic, complemented
443#1862C2×C6711yescharacteristic, complemented
444C67#2517211yescharacteristic, direct product factor, Sylow
445C23×D4C22×C6711yescharacteristic
446C22×SD16C22×C6711yescharacteristic
447C22×SD16C22×C6711yescharacteristic
448C22×D8C22×C6711yescharacteristic
449C22×D8C22×C6711yescharacteristic
450C2×#124C22×C6711yescharacteristic, complemented
451C2×C22⋊Q8C22×C6711yescharacteristic
452C2×#121C22×C6711yescharacteristic
453C2×C4×D4C22×C6711yescharacteristic
454C2×C4×D4C22×C6711yescharacteristic
455C2×C4×D4C22×C6711yescharacteristic, complemented
456C22×C22⋊C4—21no—
457#463—24no—
458#450—24no—
459#447—24no—
460#442—24no—
461C2×#107C22×C6711yescharacteristic, complemented
462C2×#106C22×C6711yescharacteristic, complemented
463C2×C4⋊C8C22×C6711yescharacteristic, complemented
464C2×#103C22×C6711yescharacteristic, complemented
465C2×#103C22×C6711yescharacteristic, complemented
466C2×#102C22×C6711yescharacteristic
467C2×#102C22×C6711yescharacteristic
468C2×#102C22×C6711yescharacteristic
469C2×#102C22×C6711yescharacteristic
470C2×#102C22×C6711yescharacteristic, complemented
471C2×#102C22×C6711yescharacteristic, complemented
472C2×C22⋊C8C22×C6711yescharacteristic
473C2×C22⋊C8C22×C6711yescharacteristic
474C2×#97C22×C6711yescharacteristic, complemented
475#397—21no—
476#394—21no—
477#391C22×C6711yescharacteristic, complemented
478#390C22×C6711yescharacteristic
479#390C22×C6711yescharacteristic
480#389C22×C6711yescharacteristic, complemented
481#386—21no—
482#386—21no—
483#386—21no—
484#380—21no—
485#380C22×C6711yescharacteristic
486#379—21no—
487C4×C22⋊C4C22×C6711yescharacteristic
488#340C22×C6711yescharacteristic, complemented
489#340C22×C6711yescharacteristic, complemented
490#336C22×C6711yescharacteristic, complemented
491#336C22×C6711yescharacteristic, complemented
492C25—21no—
493C22×Q8C23×C6711yescharacteristic
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C23×C6711yescharacteristic
503C22×D4C23×C6711yescharacteristic
504C22×D4C23×C6711yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C23×C6711yescharacteristic
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—41no—
520C2×D8D4×C6714yes—
521C22×C8C23×C6711yescharacteristic
522C22×C8C23×C6711yescharacteristic
523C22×C8C23×C6711yescharacteristic
524C22×C8C23×C6711yescharacteristic
525#124—22no—
526#124—41no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529#121—22no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4C23×C6711yescharacteristic
540C2×C4⋊C4C23×C6711yescharacteristic
541C2×C4⋊C4C23×C6711yescharacteristic
542C2×C4⋊C4C23×C6711yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C6711yescharacteristic
557C2×C22⋊C4D4×C6711yescharacteristic
558C2×C42C23×C6711yescharacteristic
559C2×C42C23×C6711yescharacteristic
560#107—41no—
561#106—22no—
562C4⋊C8—22no—
563#103—22no—
564#103—41no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102D4×C6714yescomplemented
571C22⋊C8—22no—
572C22⋊C8—22no—
573#97—22no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95D4×C6711yescharacteristic
579#95D4×C6711yescharacteristic
580C24—21no—
581C24—24no—
582C24—21no—
583C24—21no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C6711yescharacteristic
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×D4—24no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C6712yes—
621C2×D4C2×D4×C6712yes—
622C2×D4C2×D4×C6712yes—
623C2×D4#41×C6712yes—
624C2×D4#41×C6712yes—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4C2×D4×C6711yescharacteristic
646C22×C4C2×D4×C6711yescharacteristic
647C22×C4C2×D4×C6711yescharacteristic
648C22×C4C2×D4×C6711yescharacteristic
649C22×C4C2×D4×C6711yescharacteristic
650C22×C4C24×C6711yescharacteristic
651SD16—44no—
652SD16—44no—
653D8—28no—
654D8—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8C2×D4×C6712yes—
666C2×C8C2×D4×C6712yes—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—42no—
675C4⋊C4—81no—
676C4⋊C4C2×D4×C6712yes—
677C22⋊C4—22no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—81no—
690C22⋊C4—81no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—48no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23AGL(1,ℤ/8)×C6712yes—
730C23C22×D4×C6711yescharacteristic
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—48no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4#121×C6714yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4C22×D4×C6711yescharacteristic
787C2×C4C22×D4×C6711yescharacteristic
788C2×C4C2×#41×C6711yescharacteristic
789C2×C4C2×#41×C6711yescharacteristic
790C2×C4H(5,𝔽2)×C6711yescharacteristic
791C2×C4H(5,𝔽2)×C6711yescharacteristic
792C8—22no—
793C8—22no—
794C8—41no—
795C8—41no—
796C22—22no—
797C22—22no—
798C22—24no—
799C22—22no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—816no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22#525×C6711yescharacteristic
826C22D42×C6711yescharacteristic
827C22D42×C6711yescharacteristic
828C22C2×AGL(1,ℤ/8)×C6711yescharacteristic
829C22#575×C6711yescharacteristic
830C22#576×C6711yescharacteristic
831C22#577×C6711yescharacteristic
832C4—41no—
833C4—41no—
834C4—41no—
835C4—42no—
836C4—41no—
837C4—41no—
838C4—81no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4C2×#121×C6711yescharacteristic
843C4#538×C6711yescharacteristic
844C4#546×C6711yescharacteristic
845C4#546×C6711yescharacteristic
846C2—42no—
847C2—44no—
848C2—82no—
849C2—82no—
850C2C67×#242411yescharacteristic
851C2C67×#311411yescharacteristic
852C2C67×#311811yescharacteristic
853C2C67×#326411yescharacteristic
854C2C67×#326511yescharacteristic
855C2C67×#326711yescharacteristic
856C2C67×#327311yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC2×#447×C67C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C4×C22⋊C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#463×C67C2semidirect
2. C2×#450×C67C2semidirect
4. C2×#442×C67C2semidirect
5. C67×#2427C2semidirect
6. D4×C22⋊C4×C67C2semidirect
7. C67×#2065C2semidirect
8. C67×#2035C2semidirect
9. C67×#2033C2semidirect
10. C67×#2012C2semidirect
11. C67×#1973C2semidirect
12. C67×#1924C2semidirect
13. C67×#1879C2semidirect
14. C67×#1877C2semidirect
15. C67×#1862C2semidirect
21. C2×#124×C67C22semidirect
26. C2×C4×D4×C67C22semidirect
32. C2×#107×C67C22semidirect
33. C2×#106×C67C22semidirect
34. C2×C4⋊C8×C67C22semidirect
35. C2×#103×C67C22semidirect
36. C2×#103×C67C22semidirect
41. C2×#102×C67C22semidirect
42. C2×#102×C67C22semidirect
45. C2×#97×C67C22semidirect
48. #391×C67C22semidirect
51. #389×C67C22semidirect
59. #340×C67C22semidirect
60. #340×C67C22semidirect
61. #336×C67C22semidirect
62. #336×C67C22semidirect
141. #102×C67D4semidirect
417. #25172C67direct (N × H)
429. C2×#463C2×C67semidirect
430. C2×#450C2×C67semidirect
432. C2×#442C2×C67semidirect
433. #2427C2×C67semidirect
434. D4×C22⋊C4C2×C67semidirect
435. #2065C2×C67semidirect
436. #2035C2×C67semidirect
437. #2033C2×C67semidirect
438. #2012C2×C67semidirect
439. #1973C2×C67semidirect
440. #1924C2×C67semidirect
441. #1879C2×C67semidirect
442. #1877C2×C67semidirect
443. #1862C2×C67semidirect
444. C67#25172direct (N × H)
450. C2×#124C22×C67semidirect
455. C2×C4×D4C22×C67semidirect
461. C2×#107C22×C67semidirect
462. C2×#106C22×C67semidirect
463. C2×C4⋊C8C22×C67semidirect
464. C2×#103C22×C67semidirect
465. C2×#103C22×C67semidirect
470. C2×#102C22×C67semidirect
471. C2×#102C22×C67semidirect
474. C2×#97C22×C67semidirect
477. #391C22×C67semidirect
480. #389C22×C67semidirect
488. #340C22×C67semidirect
489. #340C22×C67semidirect
490. #336C22×C67semidirect
491. #336C22×C67semidirect
570. #102D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C672
C2×#450×C672
C2×#447×C672
C2×#442×C672
C67×#24272
D4×C22⋊C4×C672
C67×#20652
C67×#20352
C67×#20332
C67×#20122
C67×#19732
C67×#19242
C67×#18792
C67×#18772
C67×#18622
#2517267