Finite Group Databasebeta

← C67×#14828 #30694079

Subgroups — C67×#14828 #30694079

Order 17152.

1434 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#397×C67C211yesmaximal, characteristic
2C2×C4×C22⋊C4×C67C211yesmaximal, characteristic
3C67×#1443C211yesmaximal, characteristic, complemented
4C67×#1443C211yesmaximal, characteristic, complemented
5C67×#1443C211yesmaximal, characteristic, complemented
6C67×#1441C211yesmaximal, characteristic, complemented
7C67×#1440C211yesmaximal, characteristic
8C67×#1440C211yesmaximal, characteristic
9C67×#1439C211yesmaximal, characteristic
10C67×#1436C211yesmaximal, characteristic, complemented
11C67×#1436C211yesmaximal, characteristic, complemented
12C67×#1434C211yesmaximal, characteristic, complemented
13C67×#1434C211yesmaximal, characteristic, complemented
14C67×C22⋊#95C211yesmaximal, characteristic
15C67×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C67C2211yescharacteristic
17C22×C4⋊C4×C67C2211yescharacteristic
18C22×C4⋊C4×C67C2211yescharacteristic
19C22×C22⋊C4×C67C2211yescharacteristic
20C22×C22⋊C4×C67C2211yescharacteristic
21C22×C22⋊C4×C67C2211yescharacteristic
22C22×C22⋊C4×C67C2211yescharacteristic
23C22×C22⋊C4×C67C2211yescharacteristic
24C22×C22⋊C4×C67C2211yescharacteristic
25C22×C42×C67C2211yescharacteristic
26C22×C42×C67C2211yescharacteristic
27#397×C67—24no—
28C4×C22⋊C4×C67—24no—
29C2×#95×C67C2211yescharacteristic
30C2×#95×C67C2211yescharacteristic
31C2×#95×C67C2211yescharacteristic
32C2×#95×C67C2211yescharacteristic
33C2×#95×C67C2211yescharacteristic
34C2×#95×C67C2211yescharacteristic
35C2×#95×C67C2211yescharacteristic
36C2×#95×C67C2211yescharacteristic
37C2×#95×C67C2211yescharacteristic
38C2×#95×C67C2211yescharacteristic
39C2×#95×C67C2211yescharacteristic
40C2×#95×C67C2211yescharacteristic
41C2×#95×C67C2211yescharacteristic
42C2×#95×C67C2211yescharacteristic
43C2×#95×C67C2211yescharacteristic
44C2×#95×C67C2211yescharacteristic
45C2×#95×C67C2211yescharacteristic
46C2×#95×C67C2211yescharacteristic
47C2×#95×C67C2211yescharacteristic
48C2×#95×C67C2211yescharacteristic
49C2×#95×C67C2211yescharacteristic
50C2×#95×C67C2211yescharacteristic
51C2×#95×C67C2211yescharacteristic
52C2×#95×C67C2211yescharacteristic
53C25×C67C2311yescharacteristic
54C23×C4×C67—22no—
55C23×C4×C67—22no—
56C23×C4×C67—22no—
57C23×C4×C67—22no—
58C23×C4×C67—22no—
59C23×C4×C67—41no—
60C23×C4×C67—41no—
61C23×C4×C67C2311yescharacteristic
62C23×C4×C67C2311yescharacteristic
63C23×C4×C67C2311yescharacteristic
64C23×C4×C67C2311yescharacteristic
65C23×C4×C67C2311yescharacteristic
66C23×C4×C67C2311yescharacteristic
67C23×C4×C67C2311yescharacteristic
68C23×C4×C67C2311yescharacteristic
69C23×C4×C67C2311yescharacteristic
70C23×C4×C67C2311yescharacteristic
71C23×C4×C67C2311yescharacteristic
72C23×C4×C67C2311yescharacteristic
73C23×C4×C67C2311yescharacteristic
74C23×C4×C67C2311yescharacteristic
75C2×C4⋊C4×C67—22no—
76C2×C4⋊C4×C67—22no—
77C2×C4⋊C4×C67—22no—
78C2×C4⋊C4×C67—22no—
79C2×C4⋊C4×C67—41no—
80C2×C4⋊C4×C67—41no—
81C2×C22⋊C4×C67—22no—
82C2×C22⋊C4×C67—22no—
83C2×C22⋊C4×C67—22no—
84C2×C22⋊C4×C67—22no—
85C2×C22⋊C4×C67—22no—
86C2×C22⋊C4×C67—22no—
87C2×C22⋊C4×C67—22no—
88C2×C22⋊C4×C67—22no—
89C2×C22⋊C4×C67—22no—
90C2×C22⋊C4×C67—22no—
91C2×C22⋊C4×C67—22no—
92C2×C22⋊C4×C67—22no—
93C2×C22⋊C4×C67—22no—
94C2×C22⋊C4×C67—41no—
95C2×C22⋊C4×C67—41no—
96C2×C22⋊C4×C67—41no—
97C2×C22⋊C4×C67—41no—
98C2×C22⋊C4×C67D414yes—
99C2×C42×C67—22no—
100C2×C42×C67—22no—
101C2×C42×C67—22no—
102C2×C42×C67—22no—
103C2×C42×C67—41no—
104C2×C42×C67—41no—
105#95×C67—22no—
106#95×C67—22no—
107#95×C67—22no—
108#95×C67—22no—
109#95×C67—22no—
110#95×C67—22no—
111#95×C67—22no—
112#95×C67—22no—
113#95×C67—22no—
114#95×C67—22no—
115#95×C67—22no—
116#95×C67—22no—
117#95×C67—22no—
118#95×C67—22no—
119#95×C67—22no—
120#95×C67—22no—
121#95×C67—41no—
122#95×C67—41no—
123#95×C67—41no—
124#95×C67—41no—
125#95×C67—41no—
126#95×C67—41no—
127#95×C67—41no—
128#95×C67—41no—
129C24×C67—21no—
130C24×C67—21no—
131C24×C67—21no—
132C24×C67—21no—
133C24×C67—21no—
134C24×C67—21no—
135C24×C67—21no—
136C24×C67—21no—
137C24×C67—21no—
138C24×C67—21no—
139C24×C67—21no—
140C24×C67—21no—
141C24×C67C2×D412yes—
142C24×C67#4112yes—
143C24×C67#4112yes—
144C24×C67C2411yescharacteristic
145C22×C4×C67—21no—
146C22×C4×C67—21no—
147C22×C4×C67—21no—
148C22×C4×C67—21no—
149C22×C4×C67—28no—
150C22×C4×C67—21no—
151C22×C4×C67—21no—
152C22×C4×C67—21no—
153C22×C4×C67—21no—
154C22×C4×C67—21no—
155C22×C4×C67—21no—
156C22×C4×C67—21no—
157C22×C4×C67—21no—
158C22×C4×C67—21no—
159C22×C4×C67—21no—
160C22×C4×C67—21no—
161C22×C4×C67—21no—
162C22×C4×C67—21no—
163C22×C4×C67—21no—
164C22×C4×C67—21no—
165C22×C4×C67—21no—
166C22×C4×C67—21no—
167C22×C4×C67—21no—
168C22×C4×C67—21no—
169C22×C4×C67—21no—
170C22×C4×C67—21no—
171C22×C4×C67—21no—
172C22×C4×C67—21no—
173C22×C4×C67—21no—
174C22×C4×C67—21no—
175C22×C4×C67—21no—
176C22×C4×C67—21no—
177C22×C4×C67—21no—
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—21no—
190C22×C4×C67—21no—
191C22×C4×C67—21no—
192C22×C4×C67—21no—
193C22×C4×C67—21no—
194C22×C4×C67—21no—
195C22×C4×C67—21no—
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—21no—
208C22×C4×C67—21no—
209C22×C4×C67—21no—
210C22×C4×C67—21no—
211C22×C4×C67—21no—
212C22×C4×C67—21no—
213C22×C4×C67—21no—
214C22×C4×C67—21no—
215C22×C4×C67—21no—
216C22×C4×C67—21no—
217C22×C4×C67—21no—
218C22×C4×C67—21no—
219C22×C4×C67—21no—
220C22×C4×C67—21no—
221C22×C4×C67—21no—
222C22×C4×C67—21no—
223C22×C4×C67—21no—
224C22×C4×C67—21no—
225C22×C4×C67—21no—
226C22×C4×C67—21no—
227C22×C4×C67—21no—
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—44no—
235C22×C4×C67—44no—
236C22×C4×C67—44no—
237C22×C4×C67—44no—
238C22×C4×C67—44no—
239C22×C4×C67—44no—
240C22×C4×C67C2×D412yes—
241C22×C4×C67C2×D412yes—
242C22×C4×C67#4112yes—
243C22×C4×C67#4112yes—
244C22×C4×C67#4112yes—
245C22×C4×C67#4112yes—
246C22×C4×C67#4112yes—
247C22×C4×C67#4112yes—
248C22×C4×C67#4112yes—
249C22×C4×C67#4112yes—
250C4⋊C4×C67—44no—
251C4⋊C4×C67—44no—
252C22⋊C4×C67—28no—
253C22⋊C4×C67—28no—
254C22⋊C4×C67—44no—
255C22⋊C4×C67—44no—
256C22⋊C4×C67—44no—
257C22⋊C4×C67—44no—
258C42×C67—44no—
259C42×C67—44no—
260C23×C67—22no—
261C23×C67—22no—
262C23×C67—22no—
263C23×C67—22no—
264C23×C67—22no—
265C23×C67—22no—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67—22no—
278C23×C67—41no—
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#12314yes—
295C23×C67C22×D411yescharacteristic
296C23×C67C2×#4111yescharacteristic
297C23×C67C2×#4111yescharacteristic
298C23×C67C2×#4111yescharacteristic
299C23×C67C2×#4111yescharacteristic
300C23×C67C2×#4111yescharacteristic
301C23×C67C2×#4111yescharacteristic
302C23×C67C2×#4111yescharacteristic
303C23×C67C2×#4111yescharacteristic
304C23×C67C2×#4111yescharacteristic
305C23×C67C2×#4111yescharacteristic
306C23×C67H(5,𝔽2)11yescharacteristic
307C23×C67H(5,𝔽2)11yescharacteristic
308C23×C67H(5,𝔽2)11yescharacteristic
309C23×C672−1+411yescharacteristic
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—22no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—22no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—22no—
321C2×C4×C67—22no—
322C2×C4×C67—22no—
323C2×C4×C67—22no—
324C2×C4×C67—22no—
325C2×C4×C67—22no—
326C2×C4×C67—22no—
327C2×C4×C67—22no—
328C2×C4×C67—22no—
329C2×C4×C67—22no—
330C2×C4×C67—22no—
331C2×C4×C67—22no—
332C2×C4×C67—22no—
333C2×C4×C67—22no—
334C2×C4×C67—22no—
335C2×C4×C67—22no—
336C2×C4×C67—22no—
337C2×C4×C67—416no—
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—41no—
355C2×C4×C67—41no—
356C2×C4×C67—41no—
357C2×C4×C67—41no—
358C2×C4×C67—41no—
359C2×C4×C67—41no—
360C2×C4×C67—41no—
361C2×C4×C67—41no—
362C2×C4×C67—41no—
363C2×C4×C67—41no—
364C2×C4×C67—41no—
365C2×C4×C67—41no—
366C2×C4×C67—41no—
367C2×C4×C67—41no—
368C2×C4×C67—41no—
369C2×C4×C67—41no—
370C2×C4×C67—41no—
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—41no—
390C2×C4×C67—41no—
391C2×C4×C67—41no—
392C2×C4×C67—41no—
393C2×C4×C67—41no—
394C2×C4×C67—41no—
395C2×C4×C67—41no—
396C2×C4×C67—41no—
397C2×C4×C67—41no—
398C2×C4×C67—41no—
399C2×C4×C67—41no—
400C2×C4×C67—41no—
401C2×C4×C67—41no—
402C2×C4×C67—41no—
403C2×C4×C67—41no—
404C2×C4×C67—41no—
405C2×C4×C67—41no—
406C2×C4×C67—41no—
407C2×C4×C67—41no—
408C2×C4×C67#12614yes—
409C22×C67—24no—
410C22×C67—24no—
411C22×C67—24no—
412C22×C67—42no—
413C22×C67—42no—
414C22×C67—42no—
415C22×C67—42no—
416C22×C67—42no—
417C22×C67—42no—
418C22×C67—42no—
419C22×C67—42no—
420C22×C67—42no—
421C22×C67—42no—
422C22×C67—42no—
423C22×C67—42no—
424C22×C67C2×#12311yescharacteristic
425C22×C67#52511yescharacteristic
426C22×C67#52511yescharacteristic
427C22×C67C2×#12611yescharacteristic
428C22×C67#52911yescharacteristic
429C22×C67#52911yescharacteristic
430C22×C67#52911yescharacteristic
431C22×C67#52911yescharacteristic
432C22×C67#52911yescharacteristic
433C22×C67#52911yescharacteristic
434C22×C67#52911yescharacteristic
435C22×C67#52911yescharacteristic
436C22×C67#52911yescharacteristic
437C22×C67#53811yescharacteristic
438C22×C67#53811yescharacteristic
439C22×C67#53911yescharacteristic
440C22×C67#53911yescharacteristic
441C22×C67#54011yescharacteristic
442C22×C67#54211yescharacteristic
443C22×C67#54611yescharacteristic
444C22×C67#54611yescharacteristic
445C22×C67#54611yescharacteristic
446C22×C67#54711yescharacteristic
447C22×C67#55111yescharacteristic
448C22×C67#55111yescharacteristic
449C22×C67#55111yescharacteristic
450C22×C67#55111yescharacteristic
451C22×C67#55211yescharacteristic
452C22×C67#55311yescharacteristic
453C22×C67#55311yescharacteristic
454C22×C67#55311yescharacteristic
455C22×C67#55311yescharacteristic
456C22×C67#55511yescharacteristic
457C22×C67#55611yescharacteristic
458C22×C67#55611yescharacteristic
459C4×C67—24no—
460C4×C67—42no—
461C4×C67—42no—
462C4×C67—42no—
463C4×C67—42no—
464C4×C67—42no—
465C4×C67—42no—
466C4×C67—42no—
467C4×C67—81no—
468C4×C67—81no—
469C4×C67—81no—
470C4×C67—81no—
471C4×C67—81no—
472C4×C67—81no—
473#14828C6711yesmaximal, characteristic, direct product factor, Sylow
474C2×C67—44no—
475C2×C67#240111yescharacteristic
476C2×C67#241911yescharacteristic
477C2×C67#244411yescharacteristic
478C2×C67#245711yescharacteristic
479C2×C67#246611yescharacteristic
480C2×C67#247411yescharacteristic
481C2×C67#248011yescharacteristic
482C2×C67#249411yescharacteristic
483C2×C67#251811yescharacteristic
484C2×C67#252311yescharacteristic
485C2×C67#253111yescharacteristic
486C2×C67#257711yescharacteristic
487C2×C67#257811yescharacteristic
488C2×C67#264911yescharacteristic
489C2×C67#285311yescharacteristic
490C2×#397C2×C6711yescharacteristic
491C2×C4×C22⋊C4C2×C6711yescharacteristic
492#1443C2×C6711yescharacteristic, complemented
493#1443C2×C6711yescharacteristic, complemented
494#1443C2×C6711yescharacteristic, complemented
495#1441C2×C6711yescharacteristic, complemented
496#1440C2×C6711yescharacteristic
497#1440C2×C6711yescharacteristic
498#1439C2×C6711yescharacteristic
499#1436C2×C6711yescharacteristic, complemented
500#1436C2×C6711yescharacteristic, complemented
501#1434C2×C6711yescharacteristic, complemented
502#1434C2×C6711yescharacteristic, complemented
503C22⋊#95C2×C6711yescharacteristic
504C22⋊#95C2×C6711yescharacteristic
505C67#1482811yescharacteristic, direct product factor, Sylow
506C24×C4C22×C6711yescharacteristic
507C22×C4⋊C4C22×C6711yescharacteristic
508C22×C4⋊C4C22×C6711yescharacteristic
509C22×C22⋊C4C22×C6711yescharacteristic
510C22×C22⋊C4C22×C6711yescharacteristic
511C22×C22⋊C4C22×C6711yescharacteristic
512C22×C22⋊C4C22×C6711yescharacteristic
513C22×C22⋊C4C22×C6711yescharacteristic
514C22×C22⋊C4C22×C6711yescharacteristic
515C22×C42C22×C6711yescharacteristic
516C22×C42C22×C6711yescharacteristic
517#397—24no—
518C4×C22⋊C4—24no—
519C2×#95C22×C6711yescharacteristic
520C2×#95C22×C6711yescharacteristic
521C2×#95C22×C6711yescharacteristic
522C2×#95C22×C6711yescharacteristic
523C2×#95C22×C6711yescharacteristic
524C2×#95C22×C6711yescharacteristic
525C2×#95C22×C6711yescharacteristic
526C2×#95C22×C6711yescharacteristic
527C2×#95C22×C6711yescharacteristic
528C2×#95C22×C6711yescharacteristic
529C2×#95C22×C6711yescharacteristic
530C2×#95C22×C6711yescharacteristic
531C2×#95C22×C6711yescharacteristic
532C2×#95C22×C6711yescharacteristic
533C2×#95C22×C6711yescharacteristic
534C2×#95C22×C6711yescharacteristic
535C2×#95C22×C6711yescharacteristic
536C2×#95C22×C6711yescharacteristic
537C2×#95C22×C6711yescharacteristic
538C2×#95C22×C6711yescharacteristic
539C2×#95C22×C6711yescharacteristic
540C2×#95C22×C6711yescharacteristic
541C2×#95C22×C6711yescharacteristic
542C2×#95C22×C6711yescharacteristic
543C25C23×C6711yescharacteristic
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—41no—
550C23×C4—41no—
551C23×C4C23×C6711yescharacteristic
552C23×C4C23×C6711yescharacteristic
553C23×C4C23×C6711yescharacteristic
554C23×C4C23×C6711yescharacteristic
555C23×C4C23×C6711yescharacteristic
556C23×C4C23×C6711yescharacteristic
557C23×C4C23×C6711yescharacteristic
558C23×C4C23×C6711yescharacteristic
559C23×C4C23×C6711yescharacteristic
560C23×C4C23×C6711yescharacteristic
561C23×C4C23×C6711yescharacteristic
562C23×C4C23×C6711yescharacteristic
563C23×C4C23×C6711yescharacteristic
564C23×C4C23×C6711yescharacteristic
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—41no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4D4×C6714yes—
589C2×C42—22no—
590C2×C42—22no—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—41no—
594C2×C42—41no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—41no—
612#95—41no—
613#95—41no—
614#95—41no—
615#95—41no—
616#95—41no—
617#95—41no—
618#95—41no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24C2×D4×C6712yes—
632C24#41×C6712yes—
633C24#41×C6712yes—
634C24C24×C6711yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—28no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
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—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4C2×D4×C6712yes—
731C22×C4C2×D4×C6712yes—
732C22×C4#41×C6712yes—
733C22×C4#41×C6712yes—
734C22×C4#41×C6712yes—
735C22×C4#41×C6712yes—
736C22×C4#41×C6712yes—
737C22×C4#41×C6712yes—
738C22×C4#41×C6712yes—
739C22×C4#41×C6712yes—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C22⋊C4—28no—
743C22⋊C4—28no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C42—44no—
749C42—44no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23#123×C6714yes—
785C23C22×D4×C6711yescharacteristic
786C23C2×#41×C6711yescharacteristic
787C23C2×#41×C6711yescharacteristic
788C23C2×#41×C6711yescharacteristic
789C23C2×#41×C6711yescharacteristic
790C23C2×#41×C6711yescharacteristic
791C23C2×#41×C6711yescharacteristic
792C23C2×#41×C6711yescharacteristic
793C23C2×#41×C6711yescharacteristic
794C23C2×#41×C6711yescharacteristic
795C23C2×#41×C6711yescharacteristic
796C23H(5,𝔽2)×C6711yescharacteristic
797C23H(5,𝔽2)×C6711yescharacteristic
798C23H(5,𝔽2)×C6711yescharacteristic
799C232−1+4×C6711yescharacteristic
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—416no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
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—41no—
861C2×C4—41no—
862C2×C4—41no—
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—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4#126×C6714yes—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22C2×#123×C6711yescharacteristic
915C22#525×C6711yescharacteristic
916C22#525×C6711yescharacteristic
917C22C2×#126×C6711yescharacteristic
918C22#529×C6711yescharacteristic
919C22#529×C6711yescharacteristic
920C22#529×C6711yescharacteristic
921C22#529×C6711yescharacteristic
922C22#529×C6711yescharacteristic
923C22#529×C6711yescharacteristic
924C22#529×C6711yescharacteristic
925C22#529×C6711yescharacteristic
926C22#529×C6711yescharacteristic
927C22#538×C6711yescharacteristic
928C22#538×C6711yescharacteristic
929C22#539×C6711yescharacteristic
930C22#539×C6711yescharacteristic
931C22#540×C6711yescharacteristic
932C22#542×C6711yescharacteristic
933C22#546×C6711yescharacteristic
934C22#546×C6711yescharacteristic
935C22#546×C6711yescharacteristic
936C22#547×C6711yescharacteristic
937C22#551×C6711yescharacteristic
938C22#551×C6711yescharacteristic
939C22#551×C6711yescharacteristic
940C22#551×C6711yescharacteristic
941C22#552×C6711yescharacteristic
942C22#553×C6711yescharacteristic
943C22#553×C6711yescharacteristic
944C22#553×C6711yescharacteristic
945C22#553×C6711yescharacteristic
946C22#555×C6711yescharacteristic
947C22#556×C6711yescharacteristic
948C22#556×C6711yescharacteristic
949C4—24no—
950C4—42no—
951C4—42no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—81no—
958C4—81no—
959C4—81no—
960C4—81no—
961C4—81no—
962C4—81no—
963C2—44no—
964C2C67×#240111yescharacteristic
965C2C67×#241911yescharacteristic
966C2C67×#244411yescharacteristic
967C2C67×#245711yescharacteristic
968C2C67×#246611yescharacteristic
969C2C67×#247411yescharacteristic
970C2C67×#248011yescharacteristic
971C2C67×#249411yescharacteristic
972C2C67×#251811yescharacteristic
973C2C67×#252311yescharacteristic
974C2C67×#253111yescharacteristic
975C2C67×#257711yescharacteristic
976C2C67×#257811yescharacteristic
977C2C67×#264911yescharacteristic
978C2C67×#285311yescharacteristic
subgroupG/H
center, socleC24×C67C24
commutator, Frattini, cosocleC24C24×C67
prime radicalC25×C67C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C67 ◁ G

Complements

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

NH ≅ G/Ntype
3. C67×#1443C2semidirect
4. C67×#1443C2semidirect
5. C67×#1443C2semidirect
6. C67×#1441C2semidirect
10. C67×#1436C2semidirect
11. C67×#1436C2semidirect
12. C67×#1434C2semidirect
13. C67×#1434C2semidirect
473. #14828C67direct (N × H)
492. #1443C2×C67semidirect
493. #1443C2×C67semidirect
494. #1443C2×C67semidirect
495. #1441C2×C67semidirect
499. #1436C2×C67semidirect
500. #1436C2×C67semidirect
501. #1434C2×C67semidirect
502. #1434C2×C67semidirect
505. C67#14828direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#397×C672
C2×C4×C22⋊C4×C672
C67×#14432
C67×#14412
C67×#14402
C67×#14392
C67×#14362
C67×#14342
C67×C22⋊#952
#1482867