Finite Group Databasebeta

← C67×#24909 #30704160

Subgroups — C67×#24909 #30704160

Order 17152.

1198 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C67C211yesmaximal, characteristic
2C2×#442×C67C211yesmaximal, characteristic, complemented
3C67×#2420C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
5C67×#2092C211yesmaximal, characteristic, complemented
6C67×#2077C211yesmaximal, characteristic, complemented
7C67×#2054C211yesmaximal, characteristic, complemented
8C67×#2033C211yesmaximal, characteristic, complemented
9C67×#1936C211yesmaximal, characteristic, complemented
10C67×#1924C211yesmaximal, characteristic, complemented
11C67×#1879C211yesmaximal, characteristic, complemented
12C67×#1879C211yesmaximal, characteristic, complemented
13C67×#1862C211yesmaximal, characteristic, complemented
14C67×#1804C211yesmaximal, characteristic, complemented
15C67×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C67C2211yescharacteristic
17C22×D8×C67C2211yescharacteristic
18C22×D8×C67C2211yescharacteristic
19C2×#121×C67C2211yescharacteristic
20C2×C4×D4×C67C2211yescharacteristic
21C2×C4×D4×C67C2211yescharacteristic
22C2×C4×D4×C67C2211yescharacteristic, complemented
23C22×C22⋊C4×C67—21no—
24#447×C67—24no—
25#442×C67—24no—
26C2×#107×C67C2211yescharacteristic, complemented
27C2×#106×C67C2211yescharacteristic, complemented
28C2×C4⋊C8×C67C2211yescharacteristic, complemented
29C2×#102×C67C2211yescharacteristic
30C2×#102×C67C2211yescharacteristic
31C2×#102×C67C2211yescharacteristic
32C2×#102×C67C2211yescharacteristic
33C2×#102×C67C2211yescharacteristic
34C2×#102×C67C2211yescharacteristic
35C2×#102×C67C2211yescharacteristic, complemented
36C2×#102×C67C2211yescharacteristic, complemented
37C2×C22⋊C8×C67C2211yescharacteristic
38C2×C22⋊C8×C67C2211yescharacteristic
39C2×#97×C67C2211yescharacteristic, complemented
40#397×C67—21no—
41#394×C67—21no—
42#390×C67C2211yescharacteristic
43#390×C67C2211yescharacteristic
44#390×C67C2211yescharacteristic, complemented
45#389×C67C2211yescharacteristic, complemented
46#386×C67—21no—
47#386×C67—21no—
48#386×C67—21no—
49#382×C67C2211yescharacteristic, complemented
50#381×C67—21no—
51#380×C67C2211yescharacteristic
52#380×C67C2211yescharacteristic
53#379×C67—21no—
54C4×C22⋊C4×C67C2211yescharacteristic
55#340×C67C2211yescharacteristic, complemented
56#340×C67C2211yescharacteristic, complemented
57#340×C67C2211yescharacteristic, complemented
58#340×C67C2211yescharacteristic, complemented
59#336×C67C2211yescharacteristic, complemented
60#336×C67C2211yescharacteristic, complemented
61C25×C67—21no—
62C22×D4×C67—22no—
63C22×D4×C67—22no—
64C22×D4×C67—22no—
65C22×D4×C67—22no—
66C22×D4×C67—21no—
67C22×D4×C67—21no—
68C22×D4×C67—41no—
69C22×D4×C67—41no—
70C22×D4×C67C2311yescharacteristic
71C22×D4×C67C2311yescharacteristic
72C22×D4×C67C2311yescharacteristic
73C23×C4×C67—21no—
74C23×C4×C67—21no—
75C23×C4×C67—21no—
76C23×C4×C67C2311yescharacteristic
77C2×D8×C67—22no—
78C2×D8×C67—22no—
79C2×D8×C67—22no—
80C2×D8×C67—22no—
81C2×D8×C67—41no—
82C2×D8×C67D414yes—
83C22×C8×C67C2311yescharacteristic
84C22×C8×C67C2311yescharacteristic
85C22×C8×C67C2311yescharacteristic
86C22×C8×C67C2311yescharacteristic
87#121×C67—22no—
88#121×C67—41no—
89C4×D4×C67—22no—
90C4×D4×C67—22no—
91C4×D4×C67—22no—
92C4×D4×C67—41no—
93C4×D4×C67—41no—
94C4×D4×C67—41no—
95C2×C4⋊C4×C67—21no—
96C2×C4⋊C4×C67C2311yescharacteristic
97C2×C4⋊C4×C67C2311yescharacteristic
98C2×C4⋊C4×C67C2311yescharacteristic
99C2×C4⋊C4×C67C2311yescharacteristic
100C2×C4⋊C4×C67C2311yescharacteristic
101C2×C22⋊C4×C67—21no—
102C2×C22⋊C4×C67—21no—
103C2×C22⋊C4×C67—21no—
104C2×C22⋊C4×C67—21no—
105C2×C22⋊C4×C67—21no—
106C2×C22⋊C4×C67—21no—
107C2×C22⋊C4×C67—21no—
108C2×C22⋊C4×C67—21no—
109C2×C22⋊C4×C67—21no—
110C2×C22⋊C4×C67—21no—
111C2×C22⋊C4×C67—21no—
112C2×C22⋊C4×C67—21no—
113C2×C22⋊C4×C67—44no—
114C2×C22⋊C4×C67D411yescharacteristic
115C2×C22⋊C4×C67D411yescharacteristic
116C2×C42×C67C2311yescharacteristic
117C2×C42×C67C2311yescharacteristic
118#107×C67—41no—
119#106×C67—22no—
120C4⋊C8×C67—41no—
121#102×C67—22no—
122#102×C67—22no—
123#102×C67—22no—
124#102×C67—22no—
125#102×C67—22no—
126#102×C67—22no—
127#102×C67—41no—
128#102×C67—41no—
129C22⋊C8×C67—22no—
130C22⋊C8×C67—41no—
131#97×C67—22no—
132#95×C67—21no—
133#95×C67—21no—
134#95×C67—21no—
135#95×C67—21no—
136#95×C67—21no—
137#95×C67D411yescharacteristic
138#95×C67D411yescharacteristic
139C24×C67—21no—
140C24×C67—24no—
141C24×C67—21no—
142C24×C67—21no—
143C24×C67—42no—
144C24×C67—42no—
145C24×C67—42no—
146C24×C67—42no—
147C24×C67—81no—
148C24×C67—81no—
149C24×C67C2×D411yescharacteristic
150C2×D4×C67—24no—
151C2×D4×C67—21no—
152C2×D4×C67—21no—
153C2×D4×C67—21no—
154C2×D4×C67—21no—
155C2×D4×C67—21no—
156C2×D4×C67—21no—
157C2×D4×C67—21no—
158C2×D4×C67—21no—
159C2×D4×C67—21no—
160C2×D4×C67—21no—
161C2×D4×C67—21no—
162C2×D4×C67—21no—
163C2×D4×C67—21no—
164C2×D4×C67—42no—
165C2×D4×C67—42no—
166C2×D4×C67—44no—
167C2×D4×C67—44no—
168C2×D4×C67—44no—
169C2×D4×C67—44no—
170C2×D4×C67—42no—
171C2×D4×C67—42no—
172C2×D4×C67—81no—
173C2×D4×C67C2×D412yes—
174C2×D4×C67C2×D412yes—
175C2×D4×C67#4112yes—
176C2×D4×C67#4112yes—
177C2×D4×C67#4112yes—
178C22×C4×C67—21no—
179C22×C4×C67—21no—
180C22×C4×C67—21no—
181C22×C4×C67—21no—
182C22×C4×C67—21no—
183C22×C4×C67—21no—
184C22×C4×C67—21no—
185C22×C4×C67—21no—
186C22×C4×C67—21no—
187C22×C4×C67—21no—
188C22×C4×C67—21no—
189C22×C4×C67—42no—
190C22×C4×C67—42no—
191C22×C4×C67—42no—
192C22×C4×C67—42no—
193C22×C4×C67—42no—
194C22×C4×C67—42no—
195C22×C4×C67—81no—
196C22×C4×C67—81no—
197C22×C4×C67—81no—
198C22×C4×C67C2×D411yescharacteristic
199C22×C4×C67C2×D411yescharacteristic
200C22×C4×C67C2×D411yescharacteristic
201C22×C4×C67C2×D411yescharacteristic
202C22×C4×C67C2×D411yescharacteristic
203C22×C4×C67C2411yescharacteristic
204D8×C67—28no—
205D8×C67—44no—
206C2×C8×C67—21no—
207C2×C8×C67—21no—
208C2×C8×C67—21no—
209C2×C8×C67—21no—
210C2×C8×C67—21no—
211C2×C8×C67—21no—
212C2×C8×C67—21no—
213C2×C8×C67—21no—
214C2×C8×C67—21no—
215C2×C8×C67—21no—
216C2×C8×C67—21no—
217C2×C8×C67C2×D412yes—
218C4⋊C4×C67—21no—
219C4⋊C4×C67—21no—
220C4⋊C4×C67—21no—
221C4⋊C4×C67—21no—
222C4⋊C4×C67—21no—
223C4⋊C4×C67—21no—
224C4⋊C4×C67—21no—
225C4⋊C4×C67—21no—
226C4⋊C4×C67—21no—
227C4⋊C4×C67—21no—
228C4⋊C4×C67—81no—
229C22⋊C4×C67—22no—
230C22⋊C4×C67—41no—
231C22⋊C4×C67—42no—
232C22⋊C4×C67—42no—
233C22⋊C4×C67—42no—
234C22⋊C4×C67—42no—
235C22⋊C4×C67—42no—
236C22⋊C4×C67—42no—
237C22⋊C4×C67—42no—
238C22⋊C4×C67—81no—
239C22⋊C4×C67—81no—
240C22⋊C4×C67—81no—
241C22⋊C4×C67—81no—
242C22⋊C4×C67—81no—
243C42×C67—21no—
244C42×C67—21no—
245C42×C67—21no—
246C42×C67—21no—
247C23×C67—21no—
248C23×C67—22no—
249C23×C67—22no—
250C23×C67—21no—
251C23×C67—22no—
252C23×C67—21no—
253C23×C67—21no—
254C23×C67—21no—
255C23×C67—21no—
256C23×C67—22no—
257C23×C67—22no—
258C23×C67—48no—
259C23×C67—48no—
260C23×C67—41no—
261C23×C67—41no—
262C23×C67—41no—
263C23×C67—41no—
264C23×C67—41no—
265C23×C67—41no—
266C23×C67—41no—
267C23×C67—41no—
268C23×C67—41no—
269C23×C67—41no—
270C23×C67—41no—
271C23×C67—41no—
272C23×C67—41no—
273C23×C67—41no—
274C23×C67—41no—
275C23×C67—41no—
276C23×C67—84no—
277C23×C67—84no—
278C23×C67—84no—
279C23×C67—84no—
280C23×C67—84no—
281C23×C67AGL(1,ℤ/8)12yes—
282C23×C67C22×D411yescharacteristic
283D4×C67—22no—
284D4×C67—22no—
285D4×C67—22no—
286D4×C67—22no—
287D4×C67—22no—
288D4×C67—22no—
289D4×C67—22no—
290D4×C67—48no—
291D4×C67—41no—
292D4×C67—41no—
293D4×C67—41no—
294D4×C67—41no—
295D4×C67—84no—
296D4×C67#12314yes—
297C2×C4×C67—21no—
298C2×C4×C67—21no—
299C2×C4×C67—21no—
300C2×C4×C67—21no—
301C2×C4×C67—21no—
302C2×C4×C67—21no—
303C2×C4×C67—21no—
304C2×C4×C67—21no—
305C2×C4×C67—21no—
306C2×C4×C67—21no—
307C2×C4×C67—21no—
308C2×C4×C67—21no—
309C2×C4×C67—21no—
310C2×C4×C67—21no—
311C2×C4×C67—21no—
312C2×C4×C67—41no—
313C2×C4×C67—41no—
314C2×C4×C67—41no—
315C2×C4×C67—41no—
316C2×C4×C67—41no—
317C2×C4×C67—41no—
318C2×C4×C67—41no—
319C2×C4×C67—41no—
320C2×C4×C67—41no—
321C2×C4×C67—41no—
322C2×C4×C67—41no—
323C2×C4×C67—41no—
324C2×C4×C67—41no—
325C2×C4×C67—41no—
326C2×C4×C67—41no—
327C2×C4×C67—41no—
328C2×C4×C67—41no—
329C2×C4×C67—41no—
330C2×C4×C67—41no—
331C2×C4×C67—84no—
332C2×C4×C67—84no—
333C2×C4×C67—84no—
334C2×C4×C67C22×D411yescharacteristic
335C2×C4×C67C2×#4111yescharacteristic
336C2×C4×C67C2×#4111yescharacteristic
337C2×C4×C67C2×#4111yescharacteristic
338C2×C4×C67H(5,𝔽2)11yescharacteristic
339C2×C4×C67H(5,𝔽2)11yescharacteristic
340C8×C67—22no—
341C8×C67—41no—
342C8×C67—41no—
343C8×C67—41no—
344C22×C67—22no—
345C22×C67—24no—
346C22×C67—22no—
347C22×C67—22no—
348C22×C67—42no—
349C22×C67—41no—
350C22×C67—42no—
351C22×C67—41no—
352C22×C67—42no—
353C22×C67—41no—
354C22×C67—42no—
355C22×C67—42no—
356C22×C67—41no—
357C22×C67—42no—
358C22×C67—42no—
359C22×C67—42no—
360C22×C67—42no—
361C22×C67—42no—
362C22×C67—42no—
363C22×C67—42no—
364C22×C67—816no—
365C22×C67—81no—
366C22×C67—81no—
367C22×C67—81no—
368C22×C67—81no—
369C22×C67—81no—
370C22×C67—81no—
371C22×C67—81no—
372C22×C67—81no—
373C22×C67#52511yescharacteristic
374C22×C67D4211yescharacteristic
375C22×C67#54611yescharacteristic
376C22×C67C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C67#57511yescharacteristic
378C22×C67#57611yescharacteristic
379C22×C67#57611yescharacteristic
380C4×C67—41no—
381C4×C67—41no—
382C4×C67—41no—
383C4×C67—41no—
384C4×C67—41no—
385C4×C67—81no—
386C4×C67—81no—
387C4×C67—81no—
388C4×C67—81no—
389C4×C67—81no—
390C4×C67C2×#12311yescharacteristic
391C4×C67#53811yescharacteristic
392C4×C67#54611yescharacteristic
393C4×C67#55111yescharacteristic
394#24909C6711yesmaximal, characteristic, direct product factor, Sylow
395C2×C67—42no—
396C2×C67—44no—
397C2×C67—82no—
398C2×C67—82no—
399C2×C67#241811yescharacteristic
400C2×C67#311411yescharacteristic
401C2×C67#312211yescharacteristic
402C2×C67#326411yescharacteristic
403C2×C67#327311yescharacteristic
404C2×C67#331811yescharacteristic
405C2×C67#331911yescharacteristic
406C2×#447C2×C6711yescharacteristic
407C2×#442C2×C6711yescharacteristic, complemented
408#2420C2×C6711yescharacteristic, complemented
409D4×C22⋊C4C2×C6711yescharacteristic, complemented
410#2092C2×C6711yescharacteristic, complemented
411#2077C2×C6711yescharacteristic, complemented
412#2054C2×C6711yescharacteristic, complemented
413#2033C2×C6711yescharacteristic, complemented
414#1936C2×C6711yescharacteristic, complemented
415#1924C2×C6711yescharacteristic, complemented
416#1879C2×C6711yescharacteristic, complemented
417#1879C2×C6711yescharacteristic, complemented
418#1862C2×C6711yescharacteristic, complemented
419#1804C2×C6711yescharacteristic, complemented
420#1786C2×C6711yescharacteristic, complemented
421C67#2490911yescharacteristic, direct product factor, Sylow
422C23×D4C22×C6711yescharacteristic
423C22×D8C22×C6711yescharacteristic
424C22×D8C22×C6711yescharacteristic
425C2×#121C22×C6711yescharacteristic
426C2×C4×D4C22×C6711yescharacteristic
427C2×C4×D4C22×C6711yescharacteristic
428C2×C4×D4C22×C6711yescharacteristic, complemented
429C22×C22⋊C4—21no—
430#447—24no—
431#442—24no—
432C2×#107C22×C6711yescharacteristic, complemented
433C2×#106C22×C6711yescharacteristic, complemented
434C2×C4⋊C8C22×C6711yescharacteristic, complemented
435C2×#102C22×C6711yescharacteristic
436C2×#102C22×C6711yescharacteristic
437C2×#102C22×C6711yescharacteristic
438C2×#102C22×C6711yescharacteristic
439C2×#102C22×C6711yescharacteristic
440C2×#102C22×C6711yescharacteristic
441C2×#102C22×C6711yescharacteristic, complemented
442C2×#102C22×C6711yescharacteristic, complemented
443C2×C22⋊C8C22×C6711yescharacteristic
444C2×C22⋊C8C22×C6711yescharacteristic
445C2×#97C22×C6711yescharacteristic, complemented
446#397—21no—
447#394—21no—
448#390C22×C6711yescharacteristic
449#390C22×C6711yescharacteristic
450#390C22×C6711yescharacteristic, complemented
451#389C22×C6711yescharacteristic, complemented
452#386—21no—
453#386—21no—
454#386—21no—
455#382C22×C6711yescharacteristic, complemented
456#381—21no—
457#380C22×C6711yescharacteristic
458#380C22×C6711yescharacteristic
459#379—21no—
460C4×C22⋊C4C22×C6711yescharacteristic
461#340C22×C6711yescharacteristic, complemented
462#340C22×C6711yescharacteristic, complemented
463#340C22×C6711yescharacteristic, complemented
464#340C22×C6711yescharacteristic, complemented
465#336C22×C6711yescharacteristic, complemented
466#336C22×C6711yescharacteristic, complemented
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C23×C6711yescharacteristic
477C22×D4C23×C6711yescharacteristic
478C22×D4C23×C6711yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C6711yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8D4×C6714yes—
489C22×C8C23×C6711yescharacteristic
490C22×C8C23×C6711yescharacteristic
491C22×C8C23×C6711yescharacteristic
492C22×C8C23×C6711yescharacteristic
493#121—22no—
494#121—41no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—41no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4C23×C6711yescharacteristic
503C2×C4⋊C4C23×C6711yescharacteristic
504C2×C4⋊C4C23×C6711yescharacteristic
505C2×C4⋊C4C23×C6711yescharacteristic
506C2×C4⋊C4C23×C6711yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—44no—
520C2×C22⋊C4D4×C6711yescharacteristic
521C2×C22⋊C4D4×C6711yescharacteristic
522C2×C42C23×C6711yescharacteristic
523C2×C42C23×C6711yescharacteristic
524#107—41no—
525#106—22no—
526C4⋊C8—41no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535C22⋊C8—22no—
536C22⋊C8—41no—
537#97—22no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95D4×C6711yescharacteristic
544#95D4×C6711yescharacteristic
545C24—21no—
546C24—24no—
547C24—21no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C6711yescharacteristic
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4C2×D4×C6712yes—
580C2×D4C2×D4×C6712yes—
581C2×D4#41×C6712yes—
582C2×D4#41×C6712yes—
583C2×D4#41×C6712yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4C2×D4×C6711yescharacteristic
605C22×C4C2×D4×C6711yescharacteristic
606C22×C4C2×D4×C6711yescharacteristic
607C22×C4C2×D4×C6711yescharacteristic
608C22×C4C2×D4×C6711yescharacteristic
609C22×C4C24×C6711yescharacteristic
610D8—28no—
611D8—44no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8C2×D4×C6712yes—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—81no—
635C22⋊C4—22no—
636C22⋊C4—41no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C23—21no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—22no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23AGL(1,ℤ/8)×C6712yes—
688C23C22×D4×C6711yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4#123×C6714yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—84no—
740C2×C4C22×D4×C6711yescharacteristic
741C2×C4C2×#41×C6711yescharacteristic
742C2×C4C2×#41×C6711yescharacteristic
743C2×C4C2×#41×C6711yescharacteristic
744C2×C4H(5,𝔽2)×C6711yescharacteristic
745C2×C4H(5,𝔽2)×C6711yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—24no—
753C22—22no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22#525×C6711yescharacteristic
780C22D42×C6711yescharacteristic
781C22#546×C6711yescharacteristic
782C22C2×AGL(1,ℤ/8)×C6711yescharacteristic
783C22#575×C6711yescharacteristic
784C22#576×C6711yescharacteristic
785C22#576×C6711yescharacteristic
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×#123×C6711yescharacteristic
797C4#538×C6711yescharacteristic
798C4#546×C6711yescharacteristic
799C4#551×C6711yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—82no—
804C2C67×#241811yescharacteristic
805C2C67×#311411yescharacteristic
806C2C67×#312211yescharacteristic
807C2C67×#326411yescharacteristic
808C2C67×#327311yescharacteristic
809C2C67×#331811yescharacteristic
810C2C67×#331911yescharacteristic
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
2. C2×#442×C67C2semidirect
3. C67×#2420C2semidirect
4. D4×C22⋊C4×C67C2semidirect
5. C67×#2092C2semidirect
6. C67×#2077C2semidirect
7. C67×#2054C2semidirect
8. C67×#2033C2semidirect
9. C67×#1936C2semidirect
10. C67×#1924C2semidirect
11. C67×#1879C2semidirect
12. C67×#1879C2semidirect
13. C67×#1862C2semidirect
14. C67×#1804C2semidirect
15. C67×#1786C2semidirect
22. C2×C4×D4×C67C22semidirect
26. C2×#107×C67C22semidirect
27. C2×#106×C67C22semidirect
28. C2×C4⋊C8×C67C22semidirect
35. C2×#102×C67C22semidirect
36. C2×#102×C67C22semidirect
39. C2×#97×C67C22semidirect
44. #390×C67C22semidirect
45. #389×C67C22semidirect
49. #382×C67C22semidirect
55. #340×C67C22semidirect
56. #340×C67C22semidirect
57. #340×C67C22semidirect
58. #340×C67C22semidirect
59. #336×C67C22semidirect
60. #336×C67C22semidirect
394. #24909C67direct (N × H)
407. C2×#442C2×C67semidirect
408. #2420C2×C67semidirect
409. D4×C22⋊C4C2×C67semidirect
410. #2092C2×C67semidirect
411. #2077C2×C67semidirect
412. #2054C2×C67semidirect
413. #2033C2×C67semidirect
414. #1936C2×C67semidirect
415. #1924C2×C67semidirect
416. #1879C2×C67semidirect
417. #1879C2×C67semidirect
418. #1862C2×C67semidirect
419. #1804C2×C67semidirect
420. #1786C2×C67semidirect
421. C67#24909direct (N × H)
428. C2×C4×D4C22×C67semidirect
432. C2×#107C22×C67semidirect
433. C2×#106C22×C67semidirect
434. C2×C4⋊C8C22×C67semidirect
441. C2×#102C22×C67semidirect
442. C2×#102C22×C67semidirect
445. C2×#97C22×C67semidirect
450. #390C22×C67semidirect
451. #389C22×C67semidirect
455. #382C22×C67semidirect
461. #340C22×C67semidirect
462. #340C22×C67semidirect
463. #340C22×C67semidirect
464. #340C22×C67semidirect
465. #336C22×C67semidirect
466. #336C22×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C672
C2×#442×C672
C67×#24202
D4×C22⋊C4×C672
C67×#20922
C67×#20772
C67×#20542
C67×#20332
C67×#19362
C67×#19242
C67×#18792
C67×#18622
C67×#18042
C67×#17862
#2490967