Finite Group Databasebeta

← C67×#16452 #30695703

Subgroups — C67×#16452 #30695703

Order 17152.

1310 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×#393×C67C211yesmaximal, characteristic
2C2×#387×C67C211yesmaximal, characteristic, complemented
3C67×#1446C211yesmaximal, characteristic, complemented
4C67×#1446C211yesmaximal, characteristic, complemented
5C67×#1445C211yesmaximal, characteristic, complemented
6C67×#1443C211yesmaximal, characteristic, complemented
7C67×#1443C211yesmaximal, characteristic, complemented
8C67×#1442C211yesmaximal, characteristic, complemented
9C67×#1440C211yesmaximal, characteristic
10C67×#1440C211yesmaximal, characteristic
11C67×#1440C211yesmaximal, characteristic
12C67×#1439C211yesmaximal, characteristic
13C67×#1439C211yesmaximal, characteristic
14C67×#1437C211yesmaximal, characteristic
15C67×#1434C211yesmaximal, characteristic, complemented
16C23×Q8×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×C22⋊C4×C67C2211yescharacteristic
26C22×C42×C67C2211yescharacteristic
27#393×C67—24no—
28#387×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
54C22×Q8×C67—22no—
55C22×Q8×C67—22no—
56C22×Q8×C67—22no—
57C22×Q8×C67—41no—
58C22×Q8×C67—41no—
59C22×Q8×C67—41no—
60C22×Q8×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—22no—
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—41no—
93C2×C22⋊C4×C67—41no—
94C2×C22⋊C4×C67—41no—
95C2×C22⋊C4×C67—41no—
96C2×C22⋊C4×C67—41no—
97C2×C22⋊C4×C67—41no—
98C2×C22⋊C4×C67—41no—
99C2×C22⋊C4×C67—41no—
100C2×C22⋊C4×C67—41no—
101C2×C22⋊C4×C67—41no—
102C2×C42×C67—22no—
103C2×C42×C67—22no—
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—41no—
115#95×C67—41no—
116#95×C67—41no—
117#95×C67—41no—
118#95×C67—41no—
119#95×C67—41no—
120#95×C67—41no—
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×C67D414yes—
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×C67—21no—
142C24×C67—21no—
143C24×C67#4112yes—
144C24×C67C2411yescharacteristic
145C2×Q8×C67—44no—
146C2×Q8×C67—44no—
147C2×Q8×C67—44no—
148C2×Q8×C67—44no—
149C2×Q8×C67—44no—
150C2×Q8×C67—44no—
151C2×Q8×C67—44no—
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—21no—
235C22×C4×C67—21no—
236C22×C4×C67—21no—
237C22×C4×C67—21no—
238C22×C4×C67—21no—
239C22×C4×C67—21no—
240C22×C4×C67—21no—
241C22×C4×C67—21no—
242C22×C4×C67C2×D412yes—
243C22×C4×C67C2×D412yes—
244C22×C4×C67C2×D412yes—
245C22×C4×C67#4112yes—
246C22×C4×C67#4112yes—
247C22×C4×C67#4112yes—
248C22×C4×C67#4112yes—
249C22×C4×C67#4112yes—
250C4⋊C4×C67—28no—
251C4⋊C4×C67—44no—
252C22⋊C4×C67—44no—
253C22⋊C4×C67—44no—
254C22⋊C4×C67—44no—
255C22⋊C4×C67—44no—
256C22⋊C4×C67—44no—
257C22⋊C4×C67—44no—
258C22⋊C4×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—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—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×C67C22×D411yescharacteristic
296C23×C67C2×#4111yescharacteristic
297C23×C67C2×#4111yescharacteristic
298C23×C67C2×#4111yescharacteristic
299C23×C67C2×#4111yescharacteristic
300C23×C67C2×#4111yescharacteristic
301C23×C67C2×#4111yescharacteristic
302C23×C67H(5,𝔽2)11yescharacteristic
303C23×C67H(5,𝔽2)11yescharacteristic
304C23×C67H(5,𝔽2)11yescharacteristic
305C23×C67H(5,𝔽2)11yescharacteristic
306C23×C67H(5,𝔽2)11yescharacteristic
307C23×C672−1+411yescharacteristic
308C23×C672−1+411yescharacteristic
309C23×C672−1+411yescharacteristic
310Q8×C67—416no—
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—41no—
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—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—41no—
409C22×C67—42no—
410C22×C67—42no—
411C22×C67—42no—
412C22×C67—42no—
413C22×C67—42no—
414C22×C67—42no—
415C22×C67—42no—
416C22×C67—81no—
417C22×C67—81no—
418C22×C67—81no—
419C22×C67—81no—
420C22×C67—81no—
421C22×C67—81no—
422C22×C67—81no—
423C22×C67—81no—
424C22×C67#52511yescharacteristic
425C22×C67#52911yescharacteristic
426C22×C67#52911yescharacteristic
427C22×C67#53511yescharacteristic
428C22×C67#53611yescharacteristic
429C22×C67#53811yescharacteristic
430C22×C67#53811yescharacteristic
431C22×C67#53811yescharacteristic
432C22×C67#53811yescharacteristic
433C22×C67#53911yescharacteristic
434C22×C67#53911yescharacteristic
435C22×C67#54111yescharacteristic
436C22×C67#54211yescharacteristic
437C22×C67#54211yescharacteristic
438C22×C67#54211yescharacteristic
439C22×C67#54211yescharacteristic
440C22×C67#54211yescharacteristic
441C22×C67#54211yescharacteristic
442C22×C67#54211yescharacteristic
443C22×C67#54611yescharacteristic
444C22×C67#54611yescharacteristic
445C22×C67#54611yescharacteristic
446C22×C67#54811yescharacteristic
447C22×C67#55111yescharacteristic
448C22×C67#55111yescharacteristic
449C22×C67#55111yescharacteristic
450C22×C67#55211yescharacteristic
451C22×C67#55211yescharacteristic
452C22×C67#55511yescharacteristic
453C22×C67#55611yescharacteristic
454C22×C67#55911yescharacteristic
455C22×C67#56011yescharacteristic
456C22×C67#56211yescharacteristic
457C22×C67#56211yescharacteristic
458C22×C67#56311yescharacteristic
459C4×C67—42no—
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#16452C6711yesmaximal, characteristic, direct product factor, Sylow
474C2×C67—82no—
475C2×C67#245911yescharacteristic
476C2×C67#247711yescharacteristic
477C2×C67#252711yescharacteristic
478C2×C67#263211yescharacteristic
479C2×C67#265011yescharacteristic
480C2×C67#265311yescharacteristic
481C2×C67#268511yescharacteristic
482C2×C67#269011yescharacteristic
483C2×C67#269611yescharacteristic
484C2×C67#270011yescharacteristic
485C2×C67#273711yescharacteristic
486C2×C67#275111yescharacteristic
487C2×C67#275411yescharacteristic
488C2×C67#277511yescharacteristic
489C2×C67#283011yescharacteristic
490C2×#393C2×C6711yescharacteristic
491C2×#387C2×C6711yescharacteristic, complemented
492#1446C2×C6711yescharacteristic, complemented
493#1446C2×C6711yescharacteristic, complemented
494#1445C2×C6711yescharacteristic, complemented
495#1443C2×C6711yescharacteristic, complemented
496#1443C2×C6711yescharacteristic, complemented
497#1442C2×C6711yescharacteristic, complemented
498#1440C2×C6711yescharacteristic
499#1440C2×C6711yescharacteristic
500#1440C2×C6711yescharacteristic
501#1439C2×C6711yescharacteristic
502#1439C2×C6711yescharacteristic
503#1437C2×C6711yescharacteristic
504#1434C2×C6711yescharacteristic, complemented
505C67#1645211yescharacteristic, direct product factor, Sylow
506C23×Q8C22×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×C22⋊C4C22×C6711yescharacteristic
516C22×C42C22×C6711yescharacteristic
517#393—24no—
518#387—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
544C22×Q8—22no—
545C22×Q8—22no—
546C22×Q8—22no—
547C22×Q8—41no—
548C22×Q8—41no—
549C22×Q8—41no—
550C22×Q8—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—22no—
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—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—41no—
592C2×C42—22no—
593C2×C42—22no—
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—41no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95—41no—
609#95—41no—
610#95—41no—
611#95—41no—
612#95—41no—
613#95—41no—
614#95—41no—
615#95—41no—
616#95—41no—
617#95—41no—
618#95D4×C6714yes—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24#41×C6712yes—
634C24C24×C6711yescharacteristic
635C2×Q8—44no—
636C2×Q8—44no—
637C2×Q8—44no—
638C2×Q8—44no—
639C2×Q8—44no—
640C2×Q8—44no—
641C2×Q8—44no—
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—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4C2×D4×C6712yes—
733C22×C4C2×D4×C6712yes—
734C22×C4C2×D4×C6712yes—
735C22×C4#41×C6712yes—
736C22×C4#41×C6712yes—
737C22×C4#41×C6712yes—
738C22×C4#41×C6712yes—
739C22×C4#41×C6712yes—
740C4⋊C4—28no—
741C4⋊C4—44no—
742C22⋊C4—44no—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—44no—
749C42—44no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
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—41no—
785C23C22×D4×C6711yescharacteristic
786C23C2×#41×C6711yescharacteristic
787C23C2×#41×C6711yescharacteristic
788C23C2×#41×C6711yescharacteristic
789C23C2×#41×C6711yescharacteristic
790C23C2×#41×C6711yescharacteristic
791C23C2×#41×C6711yescharacteristic
792C23H(5,𝔽2)×C6711yescharacteristic
793C23H(5,𝔽2)×C6711yescharacteristic
794C23H(5,𝔽2)×C6711yescharacteristic
795C23H(5,𝔽2)×C6711yescharacteristic
796C23H(5,𝔽2)×C6711yescharacteristic
797C232−1+4×C6711yescharacteristic
798C232−1+4×C6711yescharacteristic
799C232−1+4×C6711yescharacteristic
800Q8—416no—
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—41no—
826C2×C4—41no—
827C2×C4—41no—
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—41no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22#525×C6711yescharacteristic
915C22#529×C6711yescharacteristic
916C22#529×C6711yescharacteristic
917C22#535×C6711yescharacteristic
918C22#536×C6711yescharacteristic
919C22#538×C6711yescharacteristic
920C22#538×C6711yescharacteristic
921C22#538×C6711yescharacteristic
922C22#538×C6711yescharacteristic
923C22#539×C6711yescharacteristic
924C22#539×C6711yescharacteristic
925C22#541×C6711yescharacteristic
926C22#542×C6711yescharacteristic
927C22#542×C6711yescharacteristic
928C22#542×C6711yescharacteristic
929C22#542×C6711yescharacteristic
930C22#542×C6711yescharacteristic
931C22#542×C6711yescharacteristic
932C22#542×C6711yescharacteristic
933C22#546×C6711yescharacteristic
934C22#546×C6711yescharacteristic
935C22#546×C6711yescharacteristic
936C22#548×C6711yescharacteristic
937C22#551×C6711yescharacteristic
938C22#551×C6711yescharacteristic
939C22#551×C6711yescharacteristic
940C22#552×C6711yescharacteristic
941C22#552×C6711yescharacteristic
942C22#555×C6711yescharacteristic
943C22#556×C6711yescharacteristic
944C22#559×C6711yescharacteristic
945C22#560×C6711yescharacteristic
946C22#562×C6711yescharacteristic
947C22#562×C6711yescharacteristic
948C22#563×C6711yescharacteristic
949C4—42no—
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—82no—
964C2C67×#245911yescharacteristic
965C2C67×#247711yescharacteristic
966C2C67×#252711yescharacteristic
967C2C67×#263211yescharacteristic
968C2C67×#265011yescharacteristic
969C2C67×#265311yescharacteristic
970C2C67×#268511yescharacteristic
971C2C67×#269011yescharacteristic
972C2C67×#269611yescharacteristic
973C2C67×#270011yescharacteristic
974C2C67×#273711yescharacteristic
975C2C67×#275111yescharacteristic
976C2C67×#275411yescharacteristic
977C2C67×#277511yescharacteristic
978C2C67×#283011yescharacteristic
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
2. C2×#387×C67C2semidirect
3. C67×#1446C2semidirect
4. C67×#1446C2semidirect
5. C67×#1445C2semidirect
6. C67×#1443C2semidirect
7. C67×#1443C2semidirect
8. C67×#1442C2semidirect
15. C67×#1434C2semidirect
473. #16452C67direct (N × H)
491. C2×#387C2×C67semidirect
492. #1446C2×C67semidirect
493. #1446C2×C67semidirect
494. #1445C2×C67semidirect
495. #1443C2×C67semidirect
496. #1443C2×C67semidirect
497. #1442C2×C67semidirect
504. #1434C2×C67semidirect
505. C67#16452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#393×C672
C2×#387×C672
C67×#14462
C67×#14452
C67×#14432
C67×#14422
C67×#14402
C67×#14392
C67×#14372
C67×#14342
#1645267