Finite Group Databasebeta

← C67×#25890 #30705141

Subgroups — C67×#25890 #30705141

Order 17152.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C67C211yesmaximal, characteristic
2C2×#488×C67C211yesmaximal, characteristic, complemented
3C2×#478×C67C211yesmaximal, characteristic, complemented
4C67×#2562C211yesmaximal, characteristic, complemented
5C67×#2036C211yesmaximal, characteristic, complemented
6C67×#2035C211yesmaximal, characteristic, complemented
7C67×#2034C211yesmaximal, characteristic, complemented
8C67×#2033C211yesmaximal, characteristic, complemented
9C67×#1983C211yesmaximal, characteristic, complemented
10C67×#1954C211yesmaximal, characteristic, complemented
11C67×#1788C211yesmaximal, characteristic, complemented
12C67×#1788C211yesmaximal, characteristic, complemented
13C67×#1786C211yesmaximal, characteristic, complemented
14C67×#1786C211yesmaximal, characteristic, complemented
15C4×#102×C67C211yesmaximal, characteristic, complemented
16C22×#41×C67C2211yescharacteristic
17C23×D4×C67C2211yescharacteristic
18#546×C67—24no—
19#546×C67—24no—
20C2×#125×C67C2211yescharacteristic, complemented
21C2×#124×C67C2211yescharacteristic
22C2×#123×C67—21no—
23C2×C22⋊Q8×C67C2211yescharacteristic
24C2×#121×C67—21no—
25C2×#121×C67C2211yescharacteristic
26C2×#120×C67—21no—
27C2×C4×D4×C67C2211yescharacteristic
28C2×C4×D4×C67C2211yescharacteristic
29C22×C22⋊C4×C67—21no—
30#488×C67—24no—
31#478×C67—24no—
32C2×#107×C67C2211yescharacteristic, complemented
33C2×#106×C67C2211yescharacteristic, complemented
34C2×C4⋊C8×C67C2211yescharacteristic, complemented
35C2×#103×C67C2211yescharacteristic, complemented
36C2×#103×C67C2211yescharacteristic, complemented
37C2×#103×C67C2211yescharacteristic, complemented
38C2×#103×C67C2211yescharacteristic, complemented
39C2×#102×C67C2211yescharacteristic
40C2×#102×C67C2211yescharacteristic
41C2×#102×C67C2211yescharacteristic
42C2×#102×C67C2211yescharacteristic
43C2×#102×C67C2211yescharacteristic
44C2×#102×C67C2211yescharacteristic
45C2×#102×C67C2211yescharacteristic
46C2×#102×C67C2211yescharacteristic
47C2×C22⋊C8×C67C2211yescharacteristic
48C2×C22⋊C8×C67C2211yescharacteristic
49C2×C22⋊C8×C67C2211yescharacteristic, complemented
50C2×C22⋊C8×C67C2211yescharacteristic, complemented
51C2×C4×C8×C67C2211yescharacteristic, complemented
52#400×C67—21no—
53#394×C67—21no—
54#388×C67—21no—
55#388×C67—21no—
56#380×C67C2211yescharacteristic
57#380×C67C2211yescharacteristic
58#380×C67C2211yescharacteristic, complemented
59#380×C67C2211yescharacteristic, complemented
60C4×C4⋊C4×C67C2211yescharacteristic, complemented
61#340×C67C2211yescharacteristic, complemented
62#340×C67C2211yescharacteristic, complemented
63C25×C67—21no—
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—22no—
74C22×D4×C67—22no—
75C22×D4×C67—22no—
76C22×D4×C67—22no—
77C22×D4×C67—21no—
78C22×D4×C67—41no—
79C22×D4×C67—41no—
80C22×D4×C67D411yescharacteristic
81C22×D4×C67C2311yescharacteristic
82C22×D4×C67C2311yescharacteristic
83C23×C4×C67—21no—
84C23×C4×C67—21no—
85C23×C4×C67C2311yescharacteristic
86C23×C4×C67C2311yescharacteristic
87C22×C8×C67C2311yescharacteristic
88C22×C8×C67C2311yescharacteristic
89C22×C8×C67C2311yescharacteristic
90C22×C8×C67C2311yescharacteristic
91#125×C67—22no—
92#125×C67—22no—
93#124×C67—22no—
94#124×C67D414yes—
95#123×C67—28no—
96C22⋊Q8×C67—22no—
97C22⋊Q8×C67—22no—
98#121×C67—28no—
99#121×C67—22no—
100#121×C67—22no—
101#120×C67—28no—
102C4×D4×C67—22no—
103C4×D4×C67—22no—
104C4×D4×C67—22no—
105C4×D4×C67D414yes—
106C2×C4⋊C4×C67—21no—
107C2×C4⋊C4×C67—21no—
108C2×C4⋊C4×C67—21no—
109C2×C4⋊C4×C67D411yescharacteristic
110C2×C4⋊C4×C67C2311yescharacteristic
111C2×C4⋊C4×C67C2311yescharacteristic
112C2×C4⋊C4×C67C2311yescharacteristic
113C2×C4⋊C4×C67C2311yescharacteristic
114C2×C4⋊C4×C67C2311yescharacteristic
115C2×C22⋊C4×C67—28no—
116C2×C22⋊C4×C67—21no—
117C2×C22⋊C4×C67—21no—
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×C67D411yescharacteristic
126C2×C22⋊C4×C67D411yescharacteristic
127C2×C42×C67—21no—
128C2×C42×C67C2311yescharacteristic
129#107×C67—22no—
130#106×C67—22no—
131C4⋊C8×C67—22no—
132#103×C67—22no—
133#103×C67—22no—
134#103×C67—41no—
135#103×C67—41no—
136#102×C67—22no—
137#102×C67—22no—
138#102×C67—22no—
139#102×C67—22no—
140#102×C67—22no—
141#102×C67—22no—
142#102×C67—41no—
143#102×C67—41no—
144C22⋊C8×C67—41no—
145C22⋊C8×C67—41no—
146C22⋊C8×C67—41no—
147C22⋊C8×C67—41no—
148C4×C8×C67—22no—
149#95×C67—21no—
150#95×C67—21no—
151#95×C67—21no—
152#95×C67—21no—
153#95×C67—21no—
154C24×C67—21no—
155C24×C67—24no—
156C24×C67—21no—
157C24×C67—42no—
158C24×C67—42no—
159C24×C67—42no—
160C24×C67—42no—
161C24×C67—81no—
162C24×C67—81no—
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—22no—
178C2×D4×C67—24no—
179C2×D4×C67—22no—
180C2×D4×C67—21no—
181C2×D4×C67—21no—
182C2×D4×C67—21no—
183C2×D4×C67—21no—
184C2×D4×C67—21no—
185C2×D4×C67—21no—
186C2×D4×C67—21no—
187C2×D4×C67—21no—
188C2×D4×C67—41no—
189C2×D4×C67—42no—
190C2×D4×C67—42no—
191C2×D4×C67—44no—
192C2×D4×C67—44no—
193C2×D4×C67—44no—
194C2×D4×C67—42no—
195C2×D4×C67—42no—
196C2×D4×C67—44no—
197C2×D4×C67—81no—
198C2×D4×C67—81no—
199C2×D4×C67C2×D412yes—
200C2×D4×C67C2×D412yes—
201C2×D4×C67#4112yes—
202C2×D4×C67#4112yes—
203C22×C4×C67—24no—
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—24no—
219C22×C4×C67—21no—
220C22×C4×C67—21no—
221C22×C4×C67—21no—
222C22×C4×C67—21no—
223C22×C4×C67—42no—
224C22×C4×C67—42no—
225C22×C4×C67—81no—
226C22×C4×C67—81no—
227C22×C4×C67C2×D411yescharacteristic
228C22×C4×C67C2×D411yescharacteristic
229C22×C4×C67C2×D411yescharacteristic
230C22×C4×C67C2×D411yescharacteristic
231C22×C4×C67C2411yescharacteristic
232C2×C8×C67—21no—
233C2×C8×C67—21no—
234C2×C8×C67—21no—
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—
244C4⋊C4×C67—24no—
245C4⋊C4×C67—22no—
246C4⋊C4×C67—21no—
247C4⋊C4×C67—21no—
248C4⋊C4×C67—21no—
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—42no—
256C4⋊C4×C67—42no—
257C4⋊C4×C67C2×D412yes—
258C22⋊C4×C67—24no—
259C22⋊C4×C67—24no—
260C22⋊C4×C67—22no—
261C22⋊C4×C67—24no—
262C22⋊C4×C67—24no—
263C22⋊C4×C67—24no—
264C22⋊C4×C67—22no—
265C22⋊C4×C67—42no—
266C22⋊C4×C67—42no—
267C22⋊C4×C67—81no—
268C22⋊C4×C67—81no—
269C42×C67—81no—
270C42×C67C2×D412yes—
271C42×C67C2×D412yes—
272C23×C67—21no—
273C23×C67—22no—
274C23×C67—21no—
275C23×C67—21no—
276C23×C67—22no—
277C23×C67—22no—
278C23×C67—21no—
279C23×C67—21no—
280C23×C67—21no—
281C23×C67—22no—
282C23×C67—21no—
283C23×C67—21no—
284C23×C67—21no—
285C23×C67—21no—
286C23×C67—21no—
287C23×C67—21no—
288C23×C67—21no—
289C23×C67—48no—
290C23×C67—48no—
291C23×C67—41no—
292C23×C67—41no—
293C23×C67—41no—
294C23×C67—41no—
295C23×C67—41no—
296C23×C67—41no—
297C23×C67—41no—
298C23×C67—41no—
299C23×C67—41no—
300C23×C67—41no—
301C23×C67—84no—
302C23×C67—84no—
303C23×C67—84no—
304C23×C67—84no—
305C23×C67—84no—
306C23×C67#13512yes—
307C23×C67C22×D411yescharacteristic
308Q8×C67—22no—
309Q8×C67—22no—
310Q8×C67—41no—
311Q8×C67—41no—
312D4×C67—22no—
313D4×C67—22no—
314D4×C67—22no—
315D4×C67—22no—
316D4×C67—22no—
317D4×C67—44no—
318D4×C67—48no—
319D4×C67—48no—
320D4×C67—41no—
321D4×C67—41no—
322D4×C67—84no—
323D4×C67#12414yes—
324C2×C4×C67—21no—
325C2×C4×C67—21no—
326C2×C4×C67—21no—
327C2×C4×C67—21no—
328C2×C4×C67—22no—
329C2×C4×C67—21no—
330C2×C4×C67—22no—
331C2×C4×C67—21no—
332C2×C4×C67—21no—
333C2×C4×C67—21no—
334C2×C4×C67—21no—
335C2×C4×C67—21no—
336C2×C4×C67—48no—
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—84no—
362C2×C4×C67#12012yes—
363C2×C4×C67#12012yes—
364C2×C4×C67C22×D411yescharacteristic
365C2×C4×C67C22×D411yescharacteristic
366C2×C4×C67C2×#4111yescharacteristic
367C2×C4×C67C2×#4111yescharacteristic
368C2×C4×C67H(5,𝔽2)11yescharacteristic
369C2×C4×C67H(5,𝔽2)11yescharacteristic
370C8×C67—41no—
371C8×C67—41no—
372C8×C67—41no—
373C8×C67—41no—
374C22×C67—24no—
375C22×C67—22no—
376C22×C67—22no—
377C22×C67—22no—
378C22×C67—41no—
379C22×C67—42no—
380C22×C67—42no—
381C22×C67—41no—
382C22×C67—42no—
383C22×C67—42no—
384C22×C67—41no—
385C22×C67—42no—
386C22×C67—41no—
387C22×C67—42no—
388C22×C67—41no—
389C22×C67—42no—
390C22×C67—41no—
391C22×C67—42no—
392C22×C67—41no—
393C22×C67—42no—
394C22×C67—41no—
395C22×C67—41no—
396C22×C67—41no—
397C22×C67—41no—
398C22×C67—816no—
399C22×C67—81no—
400C22×C67—81no—
401C22×C67—81no—
402C22×C67—81no—
403C22×C67C2×#12011yescharacteristic
404C22×C67#54611yescharacteristic
405C22×C67#54611yescharacteristic
406C22×C67C2×#13511yescharacteristic
407C22×C67#57511yescharacteristic
408C22×C67#57611yescharacteristic
409C22×C67#57711yescharacteristic
410C4×C67—22no—
411C4×C67—22no—
412C4×C67—41no—
413C4×C67—41no—
414C4×C67—42no—
415C4×C67—42no—
416C4×C67—81no—
417C4×C67—81no—
418C4×C67—81no—
419C4×C67—81no—
420C4×C67C2×#12411yescharacteristic
421C4×C67#53511yescharacteristic
422C4×C67#54611yescharacteristic
423C4×C67#54611yescharacteristic
424#25890C6711yesmaximal, characteristic, direct product factor, Sylow
425C2×C67—42no—
426C2×C67—44no—
427C2×C67—81no—
428C2×C67—82no—
429C2×C67#243511yescharacteristic
430C2×C67#300211yescharacteristic
431C2×C67#301211yescharacteristic
432C2×C67#329611yescharacteristic
433C2×C67#329711yescharacteristic
434C2×C67#332211yescharacteristic
435C2×C67#332311yescharacteristic
436C2×#546C2×C6711yescharacteristic
437C2×#488C2×C6711yescharacteristic, complemented
438C2×#478C2×C6711yescharacteristic, complemented
439#2562C2×C6711yescharacteristic, complemented
440#2036C2×C6711yescharacteristic, complemented
441#2035C2×C6711yescharacteristic, complemented
442#2034C2×C6711yescharacteristic, complemented
443#2033C2×C6711yescharacteristic, complemented
444#1983C2×C6711yescharacteristic, complemented
445#1954C2×C6711yescharacteristic, complemented
446#1788C2×C6711yescharacteristic, complemented
447#1788C2×C6711yescharacteristic, complemented
448#1786C2×C6711yescharacteristic, complemented
449#1786C2×C6711yescharacteristic, complemented
450C4×#102C2×C6711yescharacteristic, complemented
451C67#2589011yescharacteristic, direct product factor, Sylow
452C22×#41C22×C6711yescharacteristic
453C23×D4C22×C6711yescharacteristic
454#546—24no—
455#546—24no—
456C2×#125C22×C6711yescharacteristic, complemented
457C2×#124C22×C6711yescharacteristic
458C2×#123—21no—
459C2×C22⋊Q8C22×C6711yescharacteristic
460C2×#121—21no—
461C2×#121C22×C6711yescharacteristic
462C2×#120—21no—
463C2×C4×D4C22×C6711yescharacteristic
464C2×C4×D4C22×C6711yescharacteristic
465C22×C22⋊C4—21no—
466#488—24no—
467#478—24no—
468C2×#107C22×C6711yescharacteristic, complemented
469C2×#106C22×C6711yescharacteristic, complemented
470C2×C4⋊C8C22×C6711yescharacteristic, complemented
471C2×#103C22×C6711yescharacteristic, complemented
472C2×#103C22×C6711yescharacteristic, complemented
473C2×#103C22×C6711yescharacteristic, complemented
474C2×#103C22×C6711yescharacteristic, complemented
475C2×#102C22×C6711yescharacteristic
476C2×#102C22×C6711yescharacteristic
477C2×#102C22×C6711yescharacteristic
478C2×#102C22×C6711yescharacteristic
479C2×#102C22×C6711yescharacteristic
480C2×#102C22×C6711yescharacteristic
481C2×#102C22×C6711yescharacteristic
482C2×#102C22×C6711yescharacteristic
483C2×C22⋊C8C22×C6711yescharacteristic
484C2×C22⋊C8C22×C6711yescharacteristic
485C2×C22⋊C8C22×C6711yescharacteristic, complemented
486C2×C22⋊C8C22×C6711yescharacteristic, complemented
487C2×C4×C8C22×C6711yescharacteristic, complemented
488#400—21no—
489#394—21no—
490#388—21no—
491#388—21no—
492#380C22×C6711yescharacteristic
493#380C22×C6711yescharacteristic
494#380C22×C6711yescharacteristic, complemented
495#380C22×C6711yescharacteristic, complemented
496C4×C4⋊C4C22×C6711yescharacteristic, complemented
497#340C22×C6711yescharacteristic, complemented
498#340C22×C6711yescharacteristic, complemented
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C23×C6711yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C6711yescharacteristic
517C22×D4C23×C6711yescharacteristic
518C22×D4C23×C6711yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C6711yescharacteristic
522C23×C4C23×C6711yescharacteristic
523C22×C8C23×C6711yescharacteristic
524C22×C8C23×C6711yescharacteristic
525C22×C8C23×C6711yescharacteristic
526C22×C8C23×C6711yescharacteristic
527#125—22no—
528#125—22no—
529#124—22no—
530#124D4×C6714yes—
531#123—28no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534#121—28no—
535#121—22no—
536#121—22no—
537#120—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4D4×C6714yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4D4×C6711yescharacteristic
546C2×C4⋊C4C23×C6711yescharacteristic
547C2×C4⋊C4C23×C6711yescharacteristic
548C2×C4⋊C4C23×C6711yescharacteristic
549C2×C4⋊C4C23×C6711yescharacteristic
550C2×C4⋊C4C23×C6711yescharacteristic
551C2×C22⋊C4—28no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4D4×C6711yescharacteristic
562C2×C22⋊C4D4×C6711yescharacteristic
563C2×C42—21no—
564C2×C42C23×C6711yescharacteristic
565#107—22no—
566#106—22no—
567C4⋊C8—22no—
568#103—22no—
569#103—22no—
570#103—41no—
571#103—41no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580C22⋊C8—41no—
581C22⋊C8—41no—
582C22⋊C8—41no—
583C22⋊C8—41no—
584C4×C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590C24—21no—
591C24—24no—
592C24—21no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×D4×C6711yescharacteristic
600C24C2×D4×C6711yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×D4×C6712yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C6712yes—
636C2×D4C2×D4×C6712yes—
637C2×D4#41×C6712yes—
638C2×D4#41×C6712yes—
639C22×C4—24no—
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—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4C2×D4×C6711yescharacteristic
664C22×C4C2×D4×C6711yescharacteristic
665C22×C4C2×D4×C6711yescharacteristic
666C22×C4C2×D4×C6711yescharacteristic
667C22×C4C24×C6711yescharacteristic
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4C2×D4×C6712yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C42—81no—
706C42C2×D4×C6712yes—
707C42C2×D4×C6712yes—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23#135×C6712yes—
743C23C22×D4×C6711yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—44no—
754D4—48no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4#124×C6714yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
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—84no—
798C2×C4#120×C6712yes—
799C2×C4#120×C6712yes—
800C2×C4C22×D4×C6711yescharacteristic
801C2×C4C22×D4×C6711yescharacteristic
802C2×C4C2×#41×C6711yescharacteristic
803C2×C4C2×#41×C6711yescharacteristic
804C2×C4H(5,𝔽2)×C6711yescharacteristic
805C2×C4H(5,𝔽2)×C6711yescharacteristic
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—24no—
813C22—22no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—816no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#120×C6711yescharacteristic
840C22#546×C6711yescharacteristic
841C22#546×C6711yescharacteristic
842C22C2×#135×C6711yescharacteristic
843C22#575×C6711yescharacteristic
844C22#576×C6711yescharacteristic
845C22#577×C6711yescharacteristic
846C4—22no—
847C4—22no—
848C4—42no—
849C4—41no—
850C4—41no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C2×#124×C6711yescharacteristic
857C4#535×C6711yescharacteristic
858C4#546×C6711yescharacteristic
859C4#546×C6711yescharacteristic
860C2—42no—
861C2—44no—
862C2—81no—
863C2—82no—
864C2C67×#243511yescharacteristic
865C2C67×#300211yescharacteristic
866C2C67×#301211yescharacteristic
867C2C67×#329611yescharacteristic
868C2C67×#329711yescharacteristic
869C2C67×#332211yescharacteristic
870C2C67×#332311yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC2×#546×C67C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×C4×D4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#488×C67C2semidirect
3. C2×#478×C67C2semidirect
4. C67×#2562C2semidirect
5. C67×#2036C2semidirect
6. C67×#2035C2semidirect
7. C67×#2034C2semidirect
8. C67×#2033C2semidirect
9. C67×#1983C2semidirect
10. C67×#1954C2semidirect
11. C67×#1788C2semidirect
12. C67×#1788C2semidirect
13. C67×#1786C2semidirect
14. C67×#1786C2semidirect
15. C4×#102×C67C2semidirect
20. C2×#125×C67C22semidirect
32. C2×#107×C67C22semidirect
33. C2×#106×C67C22semidirect
34. C2×C4⋊C8×C67C22semidirect
35. C2×#103×C67C22semidirect
36. C2×#103×C67C22semidirect
37. C2×#103×C67C22semidirect
38. C2×#103×C67C22semidirect
49. C2×C22⋊C8×C67C22semidirect
50. C2×C22⋊C8×C67C22semidirect
51. C2×C4×C8×C67C22semidirect
58. #380×C67C22semidirect
59. #380×C67C22semidirect
60. C4×C4⋊C4×C67C22semidirect
61. #340×C67C22semidirect
62. #340×C67C22semidirect
424. #25890C67direct (N × H)
437. C2×#488C2×C67semidirect
438. C2×#478C2×C67semidirect
439. #2562C2×C67semidirect
440. #2036C2×C67semidirect
441. #2035C2×C67semidirect
442. #2034C2×C67semidirect
443. #2033C2×C67semidirect
444. #1983C2×C67semidirect
445. #1954C2×C67semidirect
446. #1788C2×C67semidirect
447. #1788C2×C67semidirect
448. #1786C2×C67semidirect
449. #1786C2×C67semidirect
450. C4×#102C2×C67semidirect
451. C67#25890direct (N × H)
456. C2×#125C22×C67semidirect
468. C2×#107C22×C67semidirect
469. C2×#106C22×C67semidirect
470. C2×C4⋊C8C22×C67semidirect
471. C2×#103C22×C67semidirect
472. C2×#103C22×C67semidirect
473. C2×#103C22×C67semidirect
474. C2×#103C22×C67semidirect
485. C2×C22⋊C8C22×C67semidirect
486. C2×C22⋊C8C22×C67semidirect
487. C2×C4×C8C22×C67semidirect
494. #380C22×C67semidirect
495. #380C22×C67semidirect
496. C4×C4⋊C4C22×C67semidirect
497. #340C22×C67semidirect
498. #340C22×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C672
C2×#488×C672
C2×#478×C672
C67×#25622
C67×#20362
C67×#20352
C67×#20342
C67×#20332
C67×#19832
C67×#19542
C67×#17882
C67×#17862
C4×#102×C672
#2589067