Finite Group Databasebeta

← C67×#24008 #30703259

Subgroups — C67×#24008 #30703259

Order 17152.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C67C211yesmaximal, characteristic
2C2×#485×C67C211yesmaximal, characteristic, complemented
3C2×#482×C67C211yesmaximal, characteristic, complemented
4C67×#2280C211yesmaximal, characteristic, complemented
5C67×#2036C211yesmaximal, characteristic, complemented
6C67×#2035C211yesmaximal, characteristic, complemented
7C67×#2034C211yesmaximal, characteristic, complemented
8C67×#2033C211yesmaximal, characteristic, complemented
9C67×#1875C211yesmaximal, characteristic, complemented
10C67×#1873C211yesmaximal, characteristic, complemented
11C67×#1854C211yesmaximal, characteristic, complemented
12C67×#1854C211yesmaximal, characteristic, complemented
13C67×#1788C211yesmaximal, characteristic, complemented
14C67×#1788C211yesmaximal, characteristic, complemented
15C67×#1779C211yesmaximal, characteristic, complemented
16C22×#41×C67C2211yescharacteristic
17C24×C4×C67C2211yescharacteristic
18#525×C67—24no—
19#525×C67—24no—
20C2×#123×C67—21no—
21C2×C22⋊Q8×C67C2211yescharacteristic
22C2×C22⋊Q8×C67C2211yescharacteristic
23C2×#121×C67C2211yescharacteristic
24C2×#121×C67C2211yescharacteristic
25C2×#120×C67—21no—
26C2×C4×D4×C67—21no—
27C2×C4×D4×C67—21no—
28C2×#117×C67C2211yescharacteristic
29C2×#117×C67C2211yescharacteristic
30C2×#117×C67C2211yescharacteristic
31#485×C67—24no—
32#482×C67—24no—
33C2×#107×C67C2211yescharacteristic, complemented
34C2×#107×C67C2211yescharacteristic, complemented
35C2×#106×C67C2211yescharacteristic, complemented
36C2×#106×C67C2211yescharacteristic, complemented
37C2×#103×C67C2211yescharacteristic, complemented
38C2×#103×C67C2211yescharacteristic, complemented
39C2×#103×C67C2211yescharacteristic, complemented
40C2×#103×C67C2211yescharacteristic, complemented
41C2×#102×C67C2211yescharacteristic, complemented
42C2×#102×C67C2211yescharacteristic, complemented
43C2×#102×C67C2211yescharacteristic, complemented
44C2×#102×C67C2211yescharacteristic, complemented
45C2×C22⋊C8×C67C2211yescharacteristic
46C2×C22⋊C8×C67C2211yescharacteristic
47C2×C22⋊C8×C67C2211yescharacteristic
48C2×C22⋊C8×C67C2211yescharacteristic
49C2×C22⋊C8×C67C2211yescharacteristic
50C2×C22⋊C8×C67C2211yescharacteristic
51#381×C67—21no—
52#380×C67C2211yescharacteristic
53#380×C67C2211yescharacteristic
54#380×C67C2211yescharacteristic
55#380×C67C2211yescharacteristic
56#379×C67—21no—
57C4×C22⋊C4×C67—21no—
58C4×C22⋊C4×C67—21no—
59#340×C67C2211yescharacteristic, complemented
60#340×C67C2211yescharacteristic, complemented
61#340×C67C2211yescharacteristic, complemented
62#340×C67C2211yescharacteristic, complemented
63C25×C67D411yescharacteristic
64C2×#41×C67—22no—
65C2×#41×C67—22no—
66C2×#41×C67—22no—
67C2×#41×C67—22no—
68C2×#41×C67—41no—
69C2×#41×C67—41no—
70C22×Q8×C67C2311yescharacteristic
71C22×D4×C67—21no—
72C22×D4×C67—21no—
73C22×D4×C67—21no—
74C22×D4×C67C2311yescharacteristic
75C23×C4×C67—21no—
76C23×C4×C67—22no—
77C23×C4×C67—22no—
78C23×C4×C67—22no—
79C23×C4×C67—22no—
80C23×C4×C67—41no—
81C23×C4×C67—41no—
82C23×C4×C67D411yescharacteristic
83C23×C4×C67D411yescharacteristic
84C23×C4×C67D411yescharacteristic
85C23×C4×C67C2311yescharacteristic
86C23×C4×C67C2311yescharacteristic
87C23×C4×C67C2311yescharacteristic
88C22×C8×C67C2311yescharacteristic
89C22×C8×C67C2311yescharacteristic
90C22×C8×C67C2311yescharacteristic
91C22×C8×C67C2311yescharacteristic
92#123×C67—28no—
93C22⋊Q8×C67—22no—
94C22⋊Q8×C67—22no—
95C22⋊Q8×C67—22no—
96C22⋊Q8×C67D414yes—
97#121×C67—22no—
98#121×C67—22no—
99#121×C67—22no—
100#121×C67D414yes—
101#120×C67—28no—
102C4×D4×C67—28no—
103C4×D4×C67—28no—
104#117×C67—22no—
105#117×C67—22no—
106#117×C67—22no—
107#117×C67—22no—
108#117×C67—41no—
109#117×C67—41no—
110C2×C4⋊C4×C67—21no—
111C2×C4⋊C4×C67—21no—
112C2×C4⋊C4×C67C2311yescharacteristic
113C2×C4⋊C4×C67C2311yescharacteristic
114C2×C4⋊C4×C67C2311yescharacteristic
115C2×C4⋊C4×C67C2311yescharacteristic
116C2×C4⋊C4×C67C2311yescharacteristic
117C2×C4⋊C4×C67C2311yescharacteristic
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—21no—
127C2×C22⋊C4×C67—21no—
128C2×C22⋊C4×C67—21no—
129C2×C42×C67—21no—
130C2×C42×C67—21no—
131C2×C42×C67—21no—
132#107×C67—22no—
133#107×C67—22no—
134#106×C67—22no—
135#106×C67—22no—
136#103×C67—22no—
137#103×C67—22no—
138#103×C67—41no—
139#103×C67—41no—
140#102×C67—22no—
141#102×C67—22no—
142#102×C67—41no—
143#102×C67—41no—
144C22⋊C8×C67—22no—
145C22⋊C8×C67—22no—
146C22⋊C8×C67—22no—
147C22⋊C8×C67—22no—
148C22⋊C8×C67—41no—
149C22⋊C8×C67—41no—
150#95×C67—21no—
151#95×C67—21no—
152#95×C67—21no—
153#95×C67—21no—
154C24×C67—22no—
155C24×C67—22no—
156C24×C67—22no—
157C24×C67—21no—
158C24×C67—41no—
159C24×C67—41no—
160C24×C67—41no—
161C24×C67—41no—
162C24×C67C2×D411yescharacteristic
163C24×C67C2×D411yescharacteristic
164C24×C67C2×D411yescharacteristic
165#41×C67—44no—
166#41×C67—44no—
167#41×C67—44no—
168#41×C67—44no—
169C2×Q8×C67—21no—
170C2×Q8×C67—21no—
171C2×Q8×C67—21no—
172C2×Q8×C67—21no—
173C2×Q8×C67—21no—
174C2×Q8×C67C2×D412yes—
175C2×D4×C67—24no—
176C2×D4×C67—24no—
177C2×D4×C67—24no—
178C2×D4×C67—21no—
179C2×D4×C67—21no—
180C2×D4×C67—21no—
181C2×D4×C67—21no—
182C2×D4×C67—21no—
183C2×D4×C67—42no—
184C2×D4×C67—42no—
185C2×D4×C67—42no—
186C2×D4×C67—42no—
187C2×D4×C67—42no—
188C2×D4×C67—42no—
189C2×D4×C67C2×D412yes—
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—24no—
199C22×C4×C67—22no—
200C22×C4×C67—22no—
201C22×C4×C67—21no—
202C22×C4×C67—21no—
203C22×C4×C67—21no—
204C22×C4×C67—22no—
205C22×C4×C67—22no—
206C22×C4×C67—22no—
207C22×C4×C67—22no—
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—41no—
219C22×C4×C67—41no—
220C22×C4×C67—41no—
221C22×C4×C67—44no—
222C22×C4×C67—44no—
223C22×C4×C67—44no—
224C22×C4×C67—44no—
225C22×C4×C67—42no—
226C22×C4×C67—42no—
227C22×C4×C67C2×D411yescharacteristic
228C22×C4×C67C2×D411yescharacteristic
229C22×C4×C67C2×D412yes—
230C22×C4×C67C2×D412yes—
231C22×C4×C67C2×D411yescharacteristic
232C22×C4×C67#4112yes—
233C22×C4×C67#4112yes—
234C22×C4×C67C2411yescharacteristic
235C2×C8×C67—21no—
236C2×C8×C67—21no—
237C2×C8×C67—21no—
238C2×C8×C67—21no—
239C2×C8×C67—21no—
240C2×C8×C67—21no—
241C2×C8×C67—21no—
242C2×C8×C67—21no—
243C2×C8×C67—21no—
244C2×C8×C67—21no—
245C2×C8×C67—21no—
246C2×C8×C67—21no—
247C4⋊C4×C67—24no—
248C4⋊C4×C67—24no—
249C4⋊C4×C67—21no—
250C4⋊C4×C67—21no—
251C4⋊C4×C67—21no—
252C4⋊C4×C67—21no—
253C4⋊C4×C67—21no—
254C4⋊C4×C67—21no—
255C4⋊C4×C67—21no—
256C4⋊C4×C67—21no—
257C4⋊C4×C67—21no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67C2×D412yes—
260C4⋊C4×C67C2×D412yes—
261C22⋊C4×C67—24no—
262C22⋊C4×C67—24no—
263C22⋊C4×C67—24no—
264C22⋊C4×C67—24no—
265C22⋊C4×C67—24no—
266C22⋊C4×C67—42no—
267C22⋊C4×C67—42no—
268C22⋊C4×C67—42no—
269C22⋊C4×C67—42no—
270C22⋊C4×C67—42no—
271C22⋊C4×C67—42no—
272C42×C67—24no—
273C42×C67—42no—
274C42×C67—42no—
275C23×C67—21no—
276C23×C67—21no—
277C23×C67—21no—
278C23×C67—21no—
279C23×C67—21no—
280C23×C67—21no—
281C23×C67—21no—
282C23×C67—21no—
283C23×C67—21no—
284C23×C67—21no—
285C23×C67—21no—
286C23×C67—21no—
287C23×C67—21no—
288C23×C67—21no—
289C23×C67—21no—
290C23×C67—21no—
291C23×C67—21no—
292C23×C67—21no—
293C23×C67—22no—
294C23×C67—44no—
295C23×C67—44no—
296C23×C67—44no—
297C23×C67—44no—
298C23×C67—44no—
299C23×C67—44no—
300C23×C67—44no—
301C23×C67—41no—
302C23×C67—41no—
303C23×C67—41no—
304C23×C67—41no—
305C23×C67—41no—
306C23×C67—41no—
307C23×C67#12012yes—
308C23×C67#12312yes—
309C23×C67#13512yes—
310C23×C67C22×D411yescharacteristic
311Q8×C67—22no—
312Q8×C67—22no—
313Q8×C67—41no—
314Q8×C67—41no—
315D4×C67—22no—
316D4×C67—22no—
317D4×C67—48no—
318D4×C67—48no—
319D4×C67—48no—
320D4×C67—41no—
321D4×C67—41no—
322C2×C4×C67—21no—
323C2×C4×C67—21no—
324C2×C4×C67—21no—
325C2×C4×C67—21no—
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—21no—
337C2×C4×C67—22no—
338C2×C4×C67—21no—
339C2×C4×C67—21no—
340C2×C4×C67—44no—
341C2×C4×C67—44no—
342C2×C4×C67—44no—
343C2×C4×C67—48no—
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#12012yes—
367C2×C4×C67#12312yes—
368C2×C4×C67C22×D411yescharacteristic
369C2×C4×C67C22×D411yescharacteristic
370C2×C4×C67C2×#4111yescharacteristic
371C2×C4×C67C2×#4111yescharacteristic
372C2×C4×C67H(5,𝔽2)11yescharacteristic
373C2×C4×C67H(5,𝔽2)11yescharacteristic
374C8×C67—41no—
375C8×C67—41no—
376C8×C67—41no—
377C8×C67—41no—
378C22×C67—22no—
379C22×C67—22no—
380C22×C67—22no—
381C22×C67—22no—
382C22×C67—22no—
383C22×C67—22no—
384C22×C67—22no—
385C22×C67—22no—
386C22×C67—22no—
387C22×C67—416no—
388C22×C67—41no—
389C22×C67—41no—
390C22×C67—41no—
391C22×C67—41no—
392C22×C67—41no—
393C22×C67—41no—
394C22×C67—41no—
395C22×C67—41no—
396C22×C67—41no—
397C22×C67—41no—
398C22×C67—41no—
399C22×C67—41no—
400C22×C67—42no—
401C22×C67—42no—
402C22×C67—42no—
403C22×C67—81no—
404C22×C67—81no—
405C22×C67—81no—
406C22×C67—81no—
407C22×C67C2×#12011yescharacteristic
408C22×C67C2×#12311yescharacteristic
409C22×C67#53411yescharacteristic
410C22×C67C2×#13511yescharacteristic
411C22×C67#57511yescharacteristic
412C22×C67#57511yescharacteristic
413C22×C67#57511yescharacteristic
414C4×C67—22no—
415C4×C67—22no—
416C4×C67—41no—
417C4×C67—42no—
418C4×C67—42no—
419C4×C67—42no—
420C4×C67—81no—
421C4×C67—81no—
422C4×C67—81no—
423C4×C67—81no—
424C4×C67#54611yescharacteristic
425C4×C67#54611yescharacteristic
426C4×C67#54611yescharacteristic
427C4×C67#54611yescharacteristic
428#24008C6711yesmaximal, characteristic, direct product factor, Sylow
429C2×C67—42no—
430C2×C67—42no—
431C2×C67—42no—
432C2×C67—82no—
433C2×C67#240511yescharacteristic
434C2×C67#300211yescharacteristic
435C2×C67#300511yescharacteristic
436C2×C67#309111yescharacteristic
437C2×C67#309311yescharacteristic
438C2×C67#319111yescharacteristic
439C2×C67#319711yescharacteristic
440C2×#525C2×C6711yescharacteristic
441C2×#485C2×C6711yescharacteristic, complemented
442C2×#482C2×C6711yescharacteristic, complemented
443#2280C2×C6711yescharacteristic, complemented
444#2036C2×C6711yescharacteristic, complemented
445#2035C2×C6711yescharacteristic, complemented
446#2034C2×C6711yescharacteristic, complemented
447#2033C2×C6711yescharacteristic, complemented
448#1875C2×C6711yescharacteristic, complemented
449#1873C2×C6711yescharacteristic, complemented
450#1854C2×C6711yescharacteristic, complemented
451#1854C2×C6711yescharacteristic, complemented
452#1788C2×C6711yescharacteristic, complemented
453#1788C2×C6711yescharacteristic, complemented
454#1779C2×C6711yescharacteristic, complemented
455C67#2400811yescharacteristic, direct product factor, Sylow
456C22×#41C22×C6711yescharacteristic
457C24×C4C22×C6711yescharacteristic
458#525—24no—
459#525—24no—
460C2×#123—21no—
461C2×C22⋊Q8C22×C6711yescharacteristic
462C2×C22⋊Q8C22×C6711yescharacteristic
463C2×#121C22×C6711yescharacteristic
464C2×#121C22×C6711yescharacteristic
465C2×#120—21no—
466C2×C4×D4—21no—
467C2×C4×D4—21no—
468C2×#117C22×C6711yescharacteristic
469C2×#117C22×C6711yescharacteristic
470C2×#117C22×C6711yescharacteristic
471#485—24no—
472#482—24no—
473C2×#107C22×C6711yescharacteristic, complemented
474C2×#107C22×C6711yescharacteristic, complemented
475C2×#106C22×C6711yescharacteristic, complemented
476C2×#106C22×C6711yescharacteristic, complemented
477C2×#103C22×C6711yescharacteristic, complemented
478C2×#103C22×C6711yescharacteristic, complemented
479C2×#103C22×C6711yescharacteristic, complemented
480C2×#103C22×C6711yescharacteristic, complemented
481C2×#102C22×C6711yescharacteristic, complemented
482C2×#102C22×C6711yescharacteristic, complemented
483C2×#102C22×C6711yescharacteristic, complemented
484C2×#102C22×C6711yescharacteristic, complemented
485C2×C22⋊C8C22×C6711yescharacteristic
486C2×C22⋊C8C22×C6711yescharacteristic
487C2×C22⋊C8C22×C6711yescharacteristic
488C2×C22⋊C8C22×C6711yescharacteristic
489C2×C22⋊C8C22×C6711yescharacteristic
490C2×C22⋊C8C22×C6711yescharacteristic
491#381—21no—
492#380C22×C6711yescharacteristic
493#380C22×C6711yescharacteristic
494#380C22×C6711yescharacteristic
495#380C22×C6711yescharacteristic
496#379—21no—
497C4×C22⋊C4—21no—
498C4×C22⋊C4—21no—
499#340C22×C6711yescharacteristic, complemented
500#340C22×C6711yescharacteristic, complemented
501#340C22×C6711yescharacteristic, complemented
502#340C22×C6711yescharacteristic, complemented
503C25D4×C6711yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C23×C6711yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4C23×C6711yescharacteristic
515C23×C4—21no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—22no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4D4×C6711yescharacteristic
523C23×C4D4×C6711yescharacteristic
524C23×C4D4×C6711yescharacteristic
525C23×C4C23×C6711yescharacteristic
526C23×C4C23×C6711yescharacteristic
527C23×C4C23×C6711yescharacteristic
528C22×C8C23×C6711yescharacteristic
529C22×C8C23×C6711yescharacteristic
530C22×C8C23×C6711yescharacteristic
531C22×C8C23×C6711yescharacteristic
532#123—28no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8D4×C6714yes—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C6714yes—
541#120—28no—
542C4×D4—28no—
543C4×D4—28no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—41no—
549#117—41no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4C23×C6711yescharacteristic
553C2×C4⋊C4C23×C6711yescharacteristic
554C2×C4⋊C4C23×C6711yescharacteristic
555C2×C4⋊C4C23×C6711yescharacteristic
556C2×C4⋊C4C23×C6711yescharacteristic
557C2×C4⋊C4C23×C6711yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—21no—
572#107—22no—
573#107—22no—
574#106—22no—
575#106—22no—
576#103—22no—
577#103—22no—
578#103—41no—
579#103—41no—
580#102—22no—
581#102—22no—
582#102—41no—
583#102—41no—
584C22⋊C8—22no—
585C22⋊C8—22no—
586C22⋊C8—22no—
587C22⋊C8—22no—
588C22⋊C8—41no—
589C22⋊C8—41no—
590#95—21no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—41no—
602C24C2×D4×C6711yescharacteristic
603C24C2×D4×C6711yescharacteristic
604C24C2×D4×C6711yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×D4×C6712yes—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4C2×D4×C6712yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
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—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C6711yescharacteristic
668C22×C4C2×D4×C6711yescharacteristic
669C22×C4C2×D4×C6712yes—
670C22×C4C2×D4×C6712yes—
671C22×C4C2×D4×C6711yescharacteristic
672C22×C4#41×C6712yes—
673C22×C4#41×C6712yes—
674C22×C4C24×C6711yescharacteristic
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4C2×D4×C6712yes—
700C4⋊C4C2×D4×C6712yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C42—24no—
713C42—42no—
714C42—42no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23#120×C6712yes—
748C23#123×C6712yes—
749C23#135×C6712yes—
750C23C22×D4×C6711yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—48no—
759D4—48no—
760D4—41no—
761D4—41no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4#120×C6712yes—
807C2×C4#123×C6712yes—
808C2×C4C22×D4×C6711yescharacteristic
809C2×C4C22×D4×C6711yescharacteristic
810C2×C4C2×#41×C6711yescharacteristic
811C2×C4C2×#41×C6711yescharacteristic
812C2×C4H(5,𝔽2)×C6711yescharacteristic
813C2×C4H(5,𝔽2)×C6711yescharacteristic
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22C2×#120×C6711yescharacteristic
848C22C2×#123×C6711yescharacteristic
849C22#534×C6711yescharacteristic
850C22C2×#135×C6711yescharacteristic
851C22#575×C6711yescharacteristic
852C22#575×C6711yescharacteristic
853C22#575×C6711yescharacteristic
854C4—22no—
855C4—22no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4#546×C6711yescharacteristic
865C4#546×C6711yescharacteristic
866C4#546×C6711yescharacteristic
867C4#546×C6711yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—82no—
872C2C67×#240511yescharacteristic
873C2C67×#300211yescharacteristic
874C2C67×#300511yescharacteristic
875C2C67×#309111yescharacteristic
876C2C67×#309311yescharacteristic
877C2C67×#319111yescharacteristic
878C2C67×#319711yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC2×#525×C67C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C24×C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C67C2semidirect
3. C2×#482×C67C2semidirect
4. C67×#2280C2semidirect
5. C67×#2036C2semidirect
6. C67×#2035C2semidirect
7. C67×#2034C2semidirect
8. C67×#2033C2semidirect
9. C67×#1875C2semidirect
10. C67×#1873C2semidirect
11. C67×#1854C2semidirect
12. C67×#1854C2semidirect
13. C67×#1788C2semidirect
14. C67×#1788C2semidirect
15. C67×#1779C2semidirect
33. C2×#107×C67C22semidirect
34. C2×#107×C67C22semidirect
35. C2×#106×C67C22semidirect
36. C2×#106×C67C22semidirect
37. C2×#103×C67C22semidirect
38. C2×#103×C67C22semidirect
39. C2×#103×C67C22semidirect
40. C2×#103×C67C22semidirect
41. C2×#102×C67C22semidirect
42. C2×#102×C67C22semidirect
43. C2×#102×C67C22semidirect
44. C2×#102×C67C22semidirect
59. #340×C67C22semidirect
60. #340×C67C22semidirect
61. #340×C67C22semidirect
62. #340×C67C22semidirect
428. #24008C67direct (N × H)
441. C2×#485C2×C67semidirect
442. C2×#482C2×C67semidirect
443. #2280C2×C67semidirect
444. #2036C2×C67semidirect
445. #2035C2×C67semidirect
446. #2034C2×C67semidirect
447. #2033C2×C67semidirect
448. #1875C2×C67semidirect
449. #1873C2×C67semidirect
450. #1854C2×C67semidirect
451. #1854C2×C67semidirect
452. #1788C2×C67semidirect
453. #1788C2×C67semidirect
454. #1779C2×C67semidirect
455. C67#24008direct (N × H)
473. C2×#107C22×C67semidirect
474. C2×#107C22×C67semidirect
475. C2×#106C22×C67semidirect
476. C2×#106C22×C67semidirect
477. C2×#103C22×C67semidirect
478. C2×#103C22×C67semidirect
479. C2×#103C22×C67semidirect
480. C2×#103C22×C67semidirect
481. C2×#102C22×C67semidirect
482. C2×#102C22×C67semidirect
483. C2×#102C22×C67semidirect
484. C2×#102C22×C67semidirect
499. #340C22×C67semidirect
500. #340C22×C67semidirect
501. #340C22×C67semidirect
502. #340C22×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C672
C2×#485×C672
C2×#482×C672
C67×#22802
C67×#20362
C67×#20352
C67×#20342
C67×#20332
C67×#18752
C67×#18732
C67×#18542
C67×#17882
C67×#17792
#2400867