Finite Group Databasebeta

← C67×#24913 #30704164

Subgroups — C67×#24913 #30704164

Order 17152.

1226 conjugacy classes of subgroups.

The subgroup lattice has 818 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×#2422C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
5C67×#2094C211yesmaximal, characteristic, complemented
6C67×#2077C211yesmaximal, characteristic, complemented
7C67×#2054C211yesmaximal, characteristic, complemented
8C67×#2034C211yesmaximal, characteristic, complemented
9C67×#1936C211yesmaximal, characteristic, complemented
10C67×#1924C211yesmaximal, characteristic, complemented
11C67×#1879C211yesmaximal, characteristic, complemented
12C67×#1879C211yesmaximal, characteristic, complemented
13C67×#1864C211yesmaximal, characteristic, complemented
14C67×#1802C211yesmaximal, characteristic, complemented
15C67×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C67C2211yescharacteristic
17C22×D8×C67C2211yescharacteristic
18C22×D8×C67C2211yescharacteristic
19C2×#123×C67—21no—
20C2×#121×C67C2211yescharacteristic
21C2×C4×D4×C67C2211yescharacteristic
22C2×C4×D4×C67C2211yescharacteristic
23C2×C4×D4×C67C2211yescharacteristic, complemented
24C22×C22⋊C4×C67—21no—
25#447×C67—24no—
26#442×C67—24no—
27C2×#106×C67C2211yescharacteristic, complemented
28C2×#106×C67C2211yescharacteristic, complemented
29C2×C4⋊C8×C67C2211yescharacteristic, complemented
30C2×#102×C67C2211yescharacteristic
31C2×#102×C67C2211yescharacteristic
32C2×#102×C67C2211yescharacteristic
33C2×#102×C67C2211yescharacteristic
34C2×#102×C67C2211yescharacteristic
35C2×#102×C67C2211yescharacteristic
36C2×#102×C67C2211yescharacteristic, complemented
37C2×#102×C67C2211yescharacteristic, complemented
38C2×C22⋊C8×C67C2211yescharacteristic
39C2×C22⋊C8×C67C2211yescharacteristic
40C2×#97×C67C2211yescharacteristic, complemented
41#397×C67—21no—
42#394×C67—21no—
43#390×C67C2211yescharacteristic
44#390×C67C2211yescharacteristic
45#390×C67C2211yescharacteristic, complemented
46#389×C67C2211yescharacteristic, complemented
47#386×C67—21no—
48#386×C67—21no—
49#385×C67—21no—
50#384×C67C2211yescharacteristic, complemented
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#123×C67—44no—
88#121×C67—22no—
89#121×C67—41no—
90C4×D4×C67—22no—
91C4×D4×C67—22no—
92C4×D4×C67—22no—
93C4×D4×C67—41no—
94C4×D4×C67—41no—
95C4×D4×C67—41no—
96C2×C4⋊C4×C67—21no—
97C2×C4⋊C4×C67—21no—
98C2×C4⋊C4×C67—21no—
99C2×C4⋊C4×C67C2311yescharacteristic
100C2×C4⋊C4×C67C2311yescharacteristic
101C2×C4⋊C4×C67C2311yescharacteristic
102C2×C4⋊C4×C67C2311yescharacteristic
103C2×C4⋊C4×C67C2311yescharacteristic
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—21no—
114C2×C22⋊C4×C67—21no—
115C2×C22⋊C4×C67—21no—
116C2×C22⋊C4×C67—44no—
117C2×C22⋊C4×C67D411yescharacteristic
118C2×C22⋊C4×C67D411yescharacteristic
119C2×C42×C67C2311yescharacteristic
120C2×C42×C67C2311yescharacteristic
121#106×C67—22no—
122#106×C67—41no—
123C4⋊C8×C67—41no—
124#102×C67—22no—
125#102×C67—22no—
126#102×C67—22no—
127#102×C67—22no—
128#102×C67—22no—
129#102×C67—22no—
130#102×C67—41no—
131#102×C67—41no—
132C22⋊C8×C67—22no—
133C22⋊C8×C67—41no—
134#97×C67—22no—
135#95×C67—21no—
136#95×C67—21no—
137#95×C67—21no—
138#95×C67D411yescharacteristic
139#95×C67D411yescharacteristic
140C24×C67—21no—
141C24×C67—24no—
142C24×C67—21no—
143C24×C67—21no—
144C24×C67—42no—
145C24×C67—42no—
146C24×C67—42no—
147C24×C67—42no—
148C24×C67—81no—
149C24×C67—81no—
150C24×C67C2×D411yescharacteristic
151C2×D4×C67—24no—
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—21no—
165C2×D4×C67—42no—
166C2×D4×C67—42no—
167C2×D4×C67—44no—
168C2×D4×C67—44no—
169C2×D4×C67—44no—
170C2×D4×C67—44no—
171C2×D4×C67—42no—
172C2×D4×C67—42no—
173C2×D4×C67—81no—
174C2×D4×C67C2×D412yes—
175C2×D4×C67C2×D412yes—
176C2×D4×C67#4112yes—
177C2×D4×C67#4112yes—
178C2×D4×C67#4112yes—
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—21no—
190C22×C4×C67—42no—
191C22×C4×C67—42no—
192C22×C4×C67—42no—
193C22×C4×C67—42no—
194C22×C4×C67—42no—
195C22×C4×C67—42no—
196C22×C4×C67—81no—
197C22×C4×C67—81no—
198C22×C4×C67—81no—
199C22×C4×C67C2×D411yescharacteristic
200C22×C4×C67C2×D411yescharacteristic
201C22×C4×C67C2×D411yescharacteristic
202C22×C4×C67C2×D411yescharacteristic
203C22×C4×C67C2×D411yescharacteristic
204C22×C4×C67C2411yescharacteristic
205D8×C67—28no—
206D8×C67—44no—
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×C67—21no—
218C2×C8×C67C2×D412yes—
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—21no—
229C4⋊C4×C67—42no—
230C4⋊C4×C67—42no—
231C4⋊C4×C67—81no—
232C22⋊C4×C67—22no—
233C22⋊C4×C67—22no—
234C22⋊C4×C67—42no—
235C22⋊C4×C67—42no—
236C22⋊C4×C67—42no—
237C22⋊C4×C67—42no—
238C22⋊C4×C67—42no—
239C22⋊C4×C67—42no—
240C22⋊C4×C67—42no—
241C22⋊C4×C67—42no—
242C22⋊C4×C67—42no—
243C22⋊C4×C67—42no—
244C22⋊C4×C67—81no—
245C22⋊C4×C67—81no—
246C42×C67—21no—
247C42×C67—21no—
248C42×C67—21no—
249C42×C67—21no—
250C23×C67—21no—
251C23×C67—22no—
252C23×C67—22no—
253C23×C67—21no—
254C23×C67—22no—
255C23×C67—21no—
256C23×C67—21no—
257C23×C67—21no—
258C23×C67—21no—
259C23×C67—22no—
260C23×C67—22no—
261C23×C67—48no—
262C23×C67—48no—
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—41no—
277C23×C67—41no—
278C23×C67—41no—
279C23×C67—84no—
280C23×C67—84no—
281C23×C67—84no—
282C23×C67—84no—
283C23×C67—84no—
284C23×C67AGL(1,ℤ/8)12yes—
285C23×C67C22×D411yescharacteristic
286D4×C67—22no—
287D4×C67—22no—
288D4×C67—22no—
289D4×C67—22no—
290D4×C67—22no—
291D4×C67—22no—
292D4×C67—22no—
293D4×C67—48no—
294D4×C67—41no—
295D4×C67—41no—
296D4×C67—41no—
297D4×C67—41no—
298D4×C67—84no—
299D4×C67#12314yescomplemented
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—21no—
313C2×C4×C67—21no—
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—41no—
332C2×C4×C67—41no—
333C2×C4×C67—84no—
334C2×C4×C67—84no—
335C2×C4×C67—84no—
336C2×C4×C67AGL(1,ℤ/8)12yes—
337C2×C4×C67C22×D411yescharacteristic
338C2×C4×C67C2×#4111yescharacteristic
339C2×C4×C67C2×#4111yescharacteristic
340C2×C4×C67C2×#4111yescharacteristic
341C2×C4×C67H(5,𝔽2)11yescharacteristic
342C2×C4×C67H(5,𝔽2)11yescharacteristic
343C8×C67—22no—
344C8×C67—41no—
345C8×C67—41no—
346C8×C67—41no—
347C22×C67—22no—
348C22×C67—24no—
349C22×C67—22no—
350C22×C67—22no—
351C22×C67—42no—
352C22×C67—41no—
353C22×C67—42no—
354C22×C67—41no—
355C22×C67—42no—
356C22×C67—42no—
357C22×C67—41no—
358C22×C67—42no—
359C22×C67—42no—
360C22×C67—41no—
361C22×C67—42no—
362C22×C67—42no—
363C22×C67—42no—
364C22×C67—42no—
365C22×C67—42no—
366C22×C67—42no—
367C22×C67—816no—
368C22×C67—81no—
369C22×C67—81no—
370C22×C67—81no—
371C22×C67—81no—
372C22×C67—81no—
373C22×C67—81no—
374C22×C67—81no—
375C22×C67—81no—
376C22×C67#52511yescharacteristic
377C22×C67D4211yescharacteristic
378C22×C67#54611yescharacteristic
379C22×C67C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C67C2×AGL(1,ℤ/8)11yescharacteristic
381C22×C67#57611yescharacteristic
382C22×C67#57711yescharacteristic
383C4×C67—22no—
384C4×C67—41no—
385C4×C67—41no—
386C4×C67—41no—
387C4×C67—41no—
388C4×C67—81no—
389C4×C67—81no—
390C4×C67—81no—
391C4×C67—81no—
392C4×C67—81no—
393C4×C67C2×#12311yescharacteristic
394C4×C67#53811yescharacteristic
395C4×C67#54611yescharacteristic
396C4×C67#55111yescharacteristic
397#24913C6711yesmaximal, characteristic, direct product factor, Sylow
398C2×C67—42no—
399C2×C67—44no—
400C2×C67—82no—
401C2×C67—82no—
402C2×C67#241811yescharacteristic
403C2×C67#310911yescharacteristic
404C2×C67#311811yescharacteristic
405C2×C67#326411yescharacteristic
406C2×C67#327211yescharacteristic
407C2×C67#330611yescharacteristic
408C2×C67#331811yescharacteristic
409C2×#447C2×C6711yescharacteristic
410C2×#442C2×C6711yescharacteristic, complemented
411#2422C2×C6711yescharacteristic, complemented
412D4×C22⋊C4C2×C6711yescharacteristic, complemented
413#2094C2×C6711yescharacteristic, complemented
414#2077C2×C6711yescharacteristic, complemented
415#2054C2×C6711yescharacteristic, complemented
416#2034C2×C6711yescharacteristic, complemented
417#1936C2×C6711yescharacteristic, complemented
418#1924C2×C6711yescharacteristic, complemented
419#1879C2×C6711yescharacteristic, complemented
420#1879C2×C6711yescharacteristic, complemented
421#1864C2×C6711yescharacteristic, complemented
422#1802C2×C6711yescharacteristic, complemented
423#1786C2×C6711yescharacteristic, complemented
424C67#2491311yescharacteristic, direct product factor, Sylow
425C23×D4C22×C6711yescharacteristic
426C22×D8C22×C6711yescharacteristic
427C22×D8C22×C6711yescharacteristic
428C2×#123—21no—
429C2×#121C22×C6711yescharacteristic
430C2×C4×D4C22×C6711yescharacteristic
431C2×C4×D4C22×C6711yescharacteristic
432C2×C4×D4C22×C6711yescharacteristic, complemented
433C22×C22⋊C4—21no—
434#447—24no—
435#442—24no—
436C2×#106C22×C6711yescharacteristic, complemented
437C2×#106C22×C6711yescharacteristic, complemented
438C2×C4⋊C8C22×C6711yescharacteristic, complemented
439C2×#102C22×C6711yescharacteristic
440C2×#102C22×C6711yescharacteristic
441C2×#102C22×C6711yescharacteristic
442C2×#102C22×C6711yescharacteristic
443C2×#102C22×C6711yescharacteristic
444C2×#102C22×C6711yescharacteristic
445C2×#102C22×C6711yescharacteristic, complemented
446C2×#102C22×C6711yescharacteristic, complemented
447C2×C22⋊C8C22×C6711yescharacteristic
448C2×C22⋊C8C22×C6711yescharacteristic
449C2×#97C22×C6711yescharacteristic, complemented
450#397—21no—
451#394—21no—
452#390C22×C6711yescharacteristic
453#390C22×C6711yescharacteristic
454#390C22×C6711yescharacteristic, complemented
455#389C22×C6711yescharacteristic, complemented
456#386—21no—
457#386—21no—
458#385—21no—
459#384C22×C6711yescharacteristic, complemented
460#380C22×C6711yescharacteristic
461#380C22×C6711yescharacteristic
462#379—21no—
463C4×C22⋊C4C22×C6711yescharacteristic
464#340C22×C6711yescharacteristic, complemented
465#340C22×C6711yescharacteristic, complemented
466#340C22×C6711yescharacteristic, complemented
467#340C22×C6711yescharacteristic, complemented
468#336C22×C6711yescharacteristic, complemented
469#336C22×C6711yescharacteristic, complemented
470C25—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—41no—
478C22×D4—41no—
479C22×D4C23×C6711yescharacteristic
480C22×D4C23×C6711yescharacteristic
481C22×D4C23×C6711yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C6711yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—41no—
491C2×D8D4×C6714yes—
492C22×C8C23×C6711yescharacteristic
493C22×C8C23×C6711yescharacteristic
494C22×C8C23×C6711yescharacteristic
495C22×C8C23×C6711yescharacteristic
496#123—44no—
497#121—22no—
498#121—41no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—41no—
503C4×D4—41no—
504C4×D4—41no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4C23×C6711yescharacteristic
509C2×C4⋊C4C23×C6711yescharacteristic
510C2×C4⋊C4C23×C6711yescharacteristic
511C2×C4⋊C4C23×C6711yescharacteristic
512C2×C4⋊C4C23×C6711yescharacteristic
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—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—44no—
526C2×C22⋊C4D4×C6711yescharacteristic
527C2×C22⋊C4D4×C6711yescharacteristic
528C2×C42C23×C6711yescharacteristic
529C2×C42C23×C6711yescharacteristic
530#106—22no—
531#106—41no—
532C4⋊C8—41no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—22no—
539#102—41no—
540#102—41no—
541C22⋊C8—22no—
542C22⋊C8—41no—
543#97—22no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95D4×C6711yescharacteristic
548#95D4×C6711yescharacteristic
549C24—21no—
550C24—24no—
551C24—21no—
552C24—21no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—81no—
558C24—81no—
559C24C2×D4×C6711yescharacteristic
560C2×D4—24no—
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—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—44no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4C2×D4×C6712yes—
584C2×D4C2×D4×C6712yes—
585C2×D4#41×C6712yes—
586C2×D4#41×C6712yes—
587C2×D4#41×C6712yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C2×D4×C6711yescharacteristic
609C22×C4C2×D4×C6711yescharacteristic
610C22×C4C2×D4×C6711yescharacteristic
611C22×C4C2×D4×C6711yescharacteristic
612C22×C4C2×D4×C6711yescharacteristic
613C22×C4C24×C6711yescharacteristic
614D8—28no—
615D8—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8C2×D4×C6712yes—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—81no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—48no—
671C23—48no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23AGL(1,ℤ/8)×C6712yes—
694C23C22×D4×C6711yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4#123×C6714yescomplemented
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—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
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—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4AGL(1,ℤ/8)×C6712yes—
746C2×C4C22×D4×C6711yescharacteristic
747C2×C4C2×#41×C6711yescharacteristic
748C2×C4C2×#41×C6711yescharacteristic
749C2×C4C2×#41×C6711yescharacteristic
750C2×C4H(5,𝔽2)×C6711yescharacteristic
751C2×C4H(5,𝔽2)×C6711yescharacteristic
752C8—22no—
753C8—41no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—24no—
759C22—22no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—816no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22#525×C6711yescharacteristic
786C22D42×C6711yescharacteristic
787C22#546×C6711yescharacteristic
788C22C2×AGL(1,ℤ/8)×C6711yescharacteristic
789C22C2×AGL(1,ℤ/8)×C6711yescharacteristic
790C22#576×C6711yescharacteristic
791C22#577×C6711yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C2×#123×C6711yescharacteristic
803C4#538×C6711yescharacteristic
804C4#546×C6711yescharacteristic
805C4#551×C6711yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—82no—
810C2C67×#241811yescharacteristic
811C2C67×#310911yescharacteristic
812C2C67×#311811yescharacteristic
813C2C67×#326411yescharacteristic
814C2C67×#327211yescharacteristic
815C2C67×#330611yescharacteristic
816C2C67×#331811yescharacteristic
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×#2422C2semidirect
4. D4×C22⋊C4×C67C2semidirect
5. C67×#2094C2semidirect
6. C67×#2077C2semidirect
7. C67×#2054C2semidirect
8. C67×#2034C2semidirect
9. C67×#1936C2semidirect
10. C67×#1924C2semidirect
11. C67×#1879C2semidirect
12. C67×#1879C2semidirect
13. C67×#1864C2semidirect
14. C67×#1802C2semidirect
15. C67×#1786C2semidirect
23. C2×C4×D4×C67C22semidirect
27. C2×#106×C67C22semidirect
28. C2×#106×C67C22semidirect
29. C2×C4⋊C8×C67C22semidirect
36. C2×#102×C67C22semidirect
37. C2×#102×C67C22semidirect
40. C2×#97×C67C22semidirect
45. #390×C67C22semidirect
46. #389×C67C22semidirect
50. #384×C67C22semidirect
55. #340×C67C22semidirect
56. #340×C67C22semidirect
57. #340×C67C22semidirect
58. #340×C67C22semidirect
59. #336×C67C22semidirect
60. #336×C67C22semidirect
299. D4×C67#123semidirect
397. #24913C67direct (N × H)
410. C2×#442C2×C67semidirect
411. #2422C2×C67semidirect
412. D4×C22⋊C4C2×C67semidirect
413. #2094C2×C67semidirect
414. #2077C2×C67semidirect
415. #2054C2×C67semidirect
416. #2034C2×C67semidirect
417. #1936C2×C67semidirect
418. #1924C2×C67semidirect
419. #1879C2×C67semidirect
420. #1879C2×C67semidirect
421. #1864C2×C67semidirect
422. #1802C2×C67semidirect
423. #1786C2×C67semidirect
424. C67#24913direct (N × H)
432. C2×C4×D4C22×C67semidirect
436. C2×#106C22×C67semidirect
437. C2×#106C22×C67semidirect
438. C2×C4⋊C8C22×C67semidirect
445. C2×#102C22×C67semidirect
446. C2×#102C22×C67semidirect
449. C2×#97C22×C67semidirect
454. #390C22×C67semidirect
455. #389C22×C67semidirect
459. #384C22×C67semidirect
464. #340C22×C67semidirect
465. #340C22×C67semidirect
466. #340C22×C67semidirect
467. #340C22×C67semidirect
468. #336C22×C67semidirect
469. #336C22×C67semidirect
708. D4#123×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×#24222
D4×C22⋊C4×C672
C67×#20942
C67×#20772
C67×#20542
C67×#20342
C67×#19362
C67×#19242
C67×#18792
C67×#18642
C67×#18022
C67×#17862
#2491367