Finite Group Databasebeta

← C67×#24043 #30703294

Subgroups — C67×#24043 #30703294

Order 17152.

1328 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C67C211yesmaximal, characteristic
2C2×#485×C67C211yesmaximal, characteristic, complemented
3C2×#416×C67C211yesmaximal, characteristic, complemented
4C67×#2485C211yesmaximal, characteristic, complemented
5C67×#2043C211yesmaximal, characteristic, complemented
6C67×#2043C211yesmaximal, characteristic, complemented
7C67×#2036C211yesmaximal, characteristic, complemented
8C67×#2035C211yesmaximal, characteristic, complemented
9C67×#1892C211yesmaximal, characteristic, complemented
10C67×#1869C211yesmaximal, characteristic, complemented
11C67×#1864C211yesmaximal, characteristic, complemented
12C67×#1862C211yesmaximal, characteristic, complemented
13C67×#1788C211yesmaximal, characteristic, complemented
14C67×#1788C211yesmaximal, characteristic, complemented
15C67×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C67C2211yescharacteristic
17C22×#41×C67C2211yescharacteristic
18C23×C8×C67C2211yescharacteristic
19#547×C67—24no—
20#547×C67—24no—
21C2×C4⋊Q8×C67C2211yescharacteristic
22C2×#123×C67—21no—
23C2×#123×C67—21no—
24C2×C22⋊Q8×C67C2211yescharacteristic
25C2×C22⋊Q8×C67C2211yescharacteristic
26C2×#121×C67—21no—
27C2×C4×D4×C67C2211yescharacteristic
28C2×C4×D4×C67C2211yescharacteristic
29C2×#117×C67C2211yescharacteristic
30C22×C4⋊C4×C67—21no—
31#485×C67—24no—
32C2×#107×C67C2211yescharacteristic
33C2×#106×C67C2211yescharacteristic
34#416×C67—24no—
35C2×#103×C67C2211yescharacteristic
36C2×#103×C67C2211yescharacteristic
37C2×#103×C67C2211yescharacteristic
38C2×#103×C67C2211yescharacteristic
39C2×#103×C67C2211yescharacteristic
40C2×#103×C67C2211yescharacteristic
41C2×#103×C67C2211yescharacteristic
42C2×#103×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
50#397×C67—21no—
51#394×C67—21no—
52#389×C67C2211yescharacteristic
53#389×C67C2211yescharacteristic
54#388×C67—21no—
55#387×C67—21no—
56#380×C67C2211yescharacteristic
57#380×C67C2211yescharacteristic
58#380×C67C2211yescharacteristic
59#340×C67C2211yescharacteristic
60#340×C67C2211yescharacteristic
61#336×C67C2211yescharacteristic
62#336×C67C2211yescharacteristic
63C2×#41×C67—22no—
64C2×#41×C67—22no—
65C2×#41×C67—22no—
66C2×#41×C67—22no—
67C2×#41×C67—22no—
68C2×#41×C67—22no—
69C2×#41×C67—22no—
70C2×#41×C67—41no—
71C2×#41×C67—41no—
72C2×#41×C67—41no—
73C2×#41×C67—41no—
74C2×#41×C67D414yes—
75C22×Q8×C67C2311yescharacteristic
76C22×Q8×C67C2311yescharacteristic
77C22×D4×C67—21no—
78C22×D4×C67—21no—
79C22×D4×C67D411yescharacteristic
80C22×D4×C67C2311yescharacteristic
81C23×C4×C67—21no—
82C23×C4×C67—21no—
83C23×C4×C67—21no—
84C23×C4×C67C2311yescharacteristic
85C23×C4×C67C2311yescharacteristic
86C22×C8×C67—22no—
87C22×C8×C67—41no—
88C22×C8×C67—41no—
89C22×C8×C67C2311yescharacteristic
90C22×C8×C67C2311yescharacteristic
91C22×C8×C67C2311yescharacteristic
92C22×C8×C67C2311yescharacteristic
93C4⋊Q8×C67—22no—
94C4⋊Q8×C67—22no—
95#123×C67—28no—
96#123×C67—28no—
97C22⋊Q8×C67—22no—
98C22⋊Q8×C67—22no—
99C22⋊Q8×C67—22no—
100C22⋊Q8×C67D414yes—
101#121×C67—28no—
102C4×D4×C67—22no—
103C4×D4×C67—22no—
104C4×D4×C67—22no—
105C4×D4×C67—22no—
106#117×C67—22no—
107#117×C67—22no—
108C2×C4⋊C4×C67—28no—
109C2×C4⋊C4×C67—21no—
110C2×C4⋊C4×C67—21no—
111C2×C4⋊C4×C67—21no—
112C2×C4⋊C4×C67—21no—
113C2×C4⋊C4×C67—21no—
114C2×C4⋊C4×C67—21no—
115C2×C4⋊C4×C67D411yescharacteristic
116C2×C4⋊C4×C67C2311yescharacteristic
117C2×C4⋊C4×C67C2311yescharacteristic
118C2×C4⋊C4×C67C2311yescharacteristic
119C2×C4⋊C4×C67C2311yescharacteristic
120C2×C4⋊C4×C67C2311yescharacteristic
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×C67D411yescharacteristic
129C2×C22⋊C4×C67D411yescharacteristic
130C2×C42×C67—21no—
131C2×C42×C67C2311yescharacteristic
132#107×C67—22no—
133#106×C67—22no—
134#103×C67—22no—
135#103×C67—22no—
136#103×C67—22no—
137#103×C67—22no—
138#103×C67—41no—
139#103×C67—41no—
140#103×C67—41no—
141#103×C67—41no—
142#102×C67—22no—
143#102×C67—22no—
144#102×C67—22no—
145#102×C67—22no—
146C22⋊C8×C67—22no—
147C22⋊C8×C67—41no—
148C22⋊C8×C67—41no—
149#95×C67—21no—
150#95×C67—21no—
151#95×C67—21no—
152#95×C67—21no—
153#95×C67—21no—
154C24×C67—21no—
155C24×C67C2×D411yescharacteristic
156C24×C67C2×D411yescharacteristic
157#41×C67—28no—
158#41×C67—44no—
159#41×C67—44no—
160#41×C67—44no—
161#41×C67—44no—
162#41×C67—44no—
163#41×C67—44no—
164#41×C67—44no—
165C2×Q8×C67—21no—
166C2×Q8×C67—21no—
167C2×Q8×C67—21no—
168C2×Q8×C67—21no—
169C2×Q8×C67—21no—
170C2×Q8×C67—21no—
171C2×Q8×C67—21no—
172C2×Q8×C67—21no—
173C2×Q8×C67—21no—
174C2×Q8×C67—21no—
175C2×Q8×C67C2×D412yes—
176C2×Q8×C67C2×D412yes—
177C2×D4×C67—24no—
178C2×D4×C67—22no—
179C2×D4×C67—24no—
180C2×D4×C67—22no—
181C2×D4×C67—21no—
182C2×D4×C67—21no—
183C2×D4×C67—21no—
184C2×D4×C67—41no—
185C2×D4×C67—42no—
186C2×D4×C67—42no—
187C2×D4×C67—42no—
188C2×D4×C67—42no—
189C2×D4×C67C2×D412yes—
190C2×D4×C67#4112yes—
191C2×D4×C67#4112yes—
192C22×C4×C67—21no—
193C22×C4×C67—21no—
194C22×C4×C67—21no—
195C22×C4×C67—21no—
196C22×C4×C67—24no—
197C22×C4×C67—24no—
198C22×C4×C67—21no—
199C22×C4×C67—21no—
200C22×C4×C67—21no—
201C22×C4×C67—24no—
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—42no—
213C22×C4×C67—42no—
214C22×C4×C67—42no—
215C22×C4×C67—42no—
216C22×C4×C67—42no—
217C22×C4×C67—42no—
218C22×C4×C67C2×D411yescharacteristic
219C22×C4×C67C2×D411yescharacteristic
220C22×C4×C67C2×D411yescharacteristic
221C22×C4×C67C2×D412yes—
222C22×C4×C67C2×D412yes—
223C22×C4×C67C2×D411yescharacteristic
224C22×C4×C67C2411yescharacteristic
225C2×C8×C67—21no—
226C2×C8×C67—21no—
227C2×C8×C67—21no—
228C2×C8×C67—21no—
229C2×C8×C67—21no—
230C2×C8×C67—21no—
231C2×C8×C67—21no—
232C2×C8×C67—21no—
233C2×C8×C67—21no—
234C2×C8×C67—21no—
235C2×C8×C67—21no—
236C2×C8×C67—21no—
237C2×C8×C67—44no—
238C4⋊C4×C67—24no—
239C4⋊C4×C67—24no—
240C4⋊C4×C67—24no—
241C4⋊C4×C67—22no—
242C4⋊C4×C67—24no—
243C4⋊C4×C67—21no—
244C4⋊C4×C67—21no—
245C4⋊C4×C67—21no—
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—42no—
253C4⋊C4×C67—81no—
254C4⋊C4×C67C2×D412yes—
255C22⋊C4×C67—24no—
256C22⋊C4×C67—24no—
257C22⋊C4×C67—24no—
258C22⋊C4×C67—22no—
259C22⋊C4×C67—22no—
260C22⋊C4×C67—42no—
261C22⋊C4×C67—42no—
262C22⋊C4×C67—81no—
263C22⋊C4×C67—81no—
264C42×C67—21no—
265C42×C67—21no—
266C42×C67—42no—
267C23×C67—22no—
268C23×C67—21no—
269C23×C67—21no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—21no—
273C23×C67—21no—
274C23×C67—21no—
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—41no—
284C23×C67—41no—
285C23×C67—41no—
286C23×C67—41no—
287C23×C67#12012yes—
288C23×C67C22×D411yescharacteristic
289Q8×C67—22no—
290Q8×C67—22no—
291Q8×C67—22no—
292Q8×C67—22no—
293Q8×C67—41no—
294Q8×C67—41no—
295Q8×C67—41no—
296Q8×C67—41no—
297D4×C67—22no—
298D4×C67—22no—
299D4×C67—22no—
300D4×C67—44no—
301D4×C67—48no—
302D4×C67—48no—
303D4×C67#12314yes—
304C2×C4×C67—21no—
305C2×C4×C67—21no—
306C2×C4×C67—21no—
307C2×C4×C67—21no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—21no—
313C2×C4×C67—22no—
314C2×C4×C67—21no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—21no—
318C2×C4×C67—21no—
319C2×C4×C67—21no—
320C2×C4×C67—21no—
321C2×C4×C67—48no—
322C2×C4×C67—48no—
323C2×C4×C67—48no—
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—41no—
334C2×C4×C67—41no—
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#12012yes—
347C2×C4×C67#13512yes—
348C2×C4×C67C22×D411yescharacteristic
349C2×C4×C67C22×D411yescharacteristic
350C2×C4×C67C2×#4111yescharacteristic
351C2×C4×C67C2×#4111yescharacteristic
352C2×C4×C67H(5,𝔽2)11yescharacteristic
353C2×C4×C67H(5,𝔽2)11yescharacteristic
354C8×C67—41no—
355C8×C67—41no—
356C8×C67—41no—
357C8×C67—41no—
358C22×C67—22no—
359C22×C67—24no—
360C22×C67—22no—
361C22×C67—22no—
362C22×C67—42no—
363C22×C67—42no—
364C22×C67—41no—
365C22×C67—42no—
366C22×C67—41no—
367C22×C67—42no—
368C22×C67—41no—
369C22×C67—42no—
370C22×C67—41no—
371C22×C67—42no—
372C22×C67—41no—
373C22×C67—41no—
374C22×C67—41no—
375C22×C67—41no—
376C22×C67—41no—
377C22×C67—41no—
378C22×C67—41no—
379C22×C67C2×#12011yescharacteristic
380C22×C67#54611yescharacteristic
381C22×C67#54611yescharacteristic
382C22×C67C2×#13511yescharacteristic
383C22×C67#57511yescharacteristic
384C22×C67#57711yescharacteristic
385C22×C67#57811yescharacteristic
386C4×C67—22no—
387C4×C67—22no—
388C4×C67—41no—
389C4×C67—42no—
390C4×C67—42no—
391C4×C67—42no—
392C4×C67—41no—
393C4×C67—81no—
394C4×C67—81no—
395C4×C67—81no—
396C4×C67—81no—
397C4×C67C2×#12311yescharacteristic
398C4×C67#53411yescharacteristic
399C4×C67#54611yescharacteristic
400C4×C67#54611yescharacteristic
401#24043C6711yesmaximal, characteristic, direct product factor, Sylow
402C2×C67—42no—
403C2×C67—44no—
404C2×C67—81no—
405C2×C67#240511yescharacteristic
406C2×C67#300211yescharacteristic
407C2×C67#301311yescharacteristic
408C2×C67#330211yescharacteristic
409C2×C67#330311yescharacteristic
410C2×C67#330711yescharacteristic
411C2×C67#331511yescharacteristic
412C2×#547C2×C6711yescharacteristic
413C2×#485C2×C6711yescharacteristic, complemented
414C2×#416C2×C6711yescharacteristic, complemented
415#2485C2×C6711yescharacteristic, complemented
416#2043C2×C6711yescharacteristic, complemented
417#2043C2×C6711yescharacteristic, complemented
418#2036C2×C6711yescharacteristic, complemented
419#2035C2×C6711yescharacteristic, complemented
420#1892C2×C6711yescharacteristic, complemented
421#1869C2×C6711yescharacteristic, complemented
422#1864C2×C6711yescharacteristic, complemented
423#1862C2×C6711yescharacteristic, complemented
424#1788C2×C6711yescharacteristic, complemented
425#1788C2×C6711yescharacteristic, complemented
426#1788C2×C6711yescharacteristic, complemented
427C67#2404311yescharacteristic, direct product factor, Sylow
428C22×#41C22×C6711yescharacteristic
429C22×#41C22×C6711yescharacteristic
430C23×C8C22×C6711yescharacteristic
431#547—24no—
432#547—24no—
433C2×C4⋊Q8C22×C6711yescharacteristic
434C2×#123—21no—
435C2×#123—21no—
436C2×C22⋊Q8C22×C6711yescharacteristic
437C2×C22⋊Q8C22×C6711yescharacteristic
438C2×#121—21no—
439C2×C4×D4C22×C6711yescharacteristic
440C2×C4×D4C22×C6711yescharacteristic
441C2×#117C22×C6711yescharacteristic
442C22×C4⋊C4—21no—
443#485—24no—
444C2×#107C22×C6711yescharacteristic
445C2×#106C22×C6711yescharacteristic
446#416—24no—
447C2×#103C22×C6711yescharacteristic
448C2×#103C22×C6711yescharacteristic
449C2×#103C22×C6711yescharacteristic
450C2×#103C22×C6711yescharacteristic
451C2×#103C22×C6711yescharacteristic
452C2×#103C22×C6711yescharacteristic
453C2×#103C22×C6711yescharacteristic
454C2×#103C22×C6711yescharacteristic
455C2×#102C22×C6711yescharacteristic
456C2×#102C22×C6711yescharacteristic
457C2×#102C22×C6711yescharacteristic
458C2×#102C22×C6711yescharacteristic
459C2×C22⋊C8C22×C6711yescharacteristic
460C2×C22⋊C8C22×C6711yescharacteristic
461C2×C22⋊C8C22×C6711yescharacteristic
462#397—21no—
463#394—21no—
464#389C22×C6711yescharacteristic
465#389C22×C6711yescharacteristic
466#388—21no—
467#387—21no—
468#380C22×C6711yescharacteristic
469#380C22×C6711yescharacteristic
470#380C22×C6711yescharacteristic
471#340C22×C6711yescharacteristic
472#340C22×C6711yescharacteristic
473#336C22×C6711yescharacteristic
474#336C22×C6711yescharacteristic
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—22no—
479C2×#41—22no—
480C2×#41—22no—
481C2×#41—22no—
482C2×#41—41no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41D4×C6714yes—
487C22×Q8C23×C6711yescharacteristic
488C22×Q8C23×C6711yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4D4×C6711yescharacteristic
492C22×D4C23×C6711yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C23×C6711yescharacteristic
497C23×C4C23×C6711yescharacteristic
498C22×C8—22no—
499C22×C8—41no—
500C22×C8—41no—
501C22×C8C23×C6711yescharacteristic
502C22×C8C23×C6711yescharacteristic
503C22×C8C23×C6711yescharacteristic
504C22×C8C23×C6711yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8—22no—
507#123—28no—
508#123—28no—
509C22⋊Q8—22no—
510C22⋊Q8—22no—
511C22⋊Q8—22no—
512C22⋊Q8D4×C6714yes—
513#121—28no—
514C4×D4—22no—
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—22no—
518#117—22no—
519#117—22no—
520C2×C4⋊C4—28no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4D4×C6711yescharacteristic
528C2×C4⋊C4C23×C6711yescharacteristic
529C2×C4⋊C4C23×C6711yescharacteristic
530C2×C4⋊C4C23×C6711yescharacteristic
531C2×C4⋊C4C23×C6711yescharacteristic
532C2×C4⋊C4C23×C6711yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4D4×C6711yescharacteristic
541C2×C22⋊C4D4×C6711yescharacteristic
542C2×C42—21no—
543C2×C42C23×C6711yescharacteristic
544#107—22no—
545#106—22no—
546#103—22no—
547#103—22no—
548#103—22no—
549#103—22no—
550#103—41no—
551#103—41no—
552#103—41no—
553#103—41no—
554#102—22no—
555#102—22no—
556#102—22no—
557#102—22no—
558C22⋊C8—22no—
559C22⋊C8—41no—
560C22⋊C8—41no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—21no—
566C24—21no—
567C24C2×D4×C6711yescharacteristic
568C24C2×D4×C6711yescharacteristic
569#41—28no—
570#41—44no—
571#41—44no—
572#41—44no—
573#41—44no—
574#41—44no—
575#41—44no—
576#41—44no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8C2×D4×C6712yes—
588C2×Q8C2×D4×C6712yes—
589C2×D4—24no—
590C2×D4—22no—
591C2×D4—24no—
592C2×D4—22no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—41no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4C2×D4×C6712yes—
602C2×D4#41×C6712yes—
603C2×D4#41×C6712yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4C2×D4×C6711yescharacteristic
631C22×C4C2×D4×C6711yescharacteristic
632C22×C4C2×D4×C6711yescharacteristic
633C22×C4C2×D4×C6712yes—
634C22×C4C2×D4×C6712yes—
635C22×C4C2×D4×C6711yescharacteristic
636C22×C4C24×C6711yescharacteristic
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—44no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—22no—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—42no—
665C4⋊C4—81no—
666C4⋊C4C2×D4×C6712yes—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C22⋊C4—81no—
676C42—21no—
677C42—21no—
678C42—42no—
679C23—22no—
680C23—21no—
681C23—21no—
682C23—22no—
683C23—22no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23#120×C6712yes—
700C23C22×D4×C6711yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—44no—
713D4—48no—
714D4—48no—
715D4#123×C6714yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—48no—
734C2×C4—48no—
735C2×C4—48no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4#120×C6712yes—
759C2×C4#135×C6712yes—
760C2×C4C22×D4×C6711yescharacteristic
761C2×C4C22×D4×C6711yescharacteristic
762C2×C4C2×#41×C6711yescharacteristic
763C2×C4C2×#41×C6711yescharacteristic
764C2×C4H(5,𝔽2)×C6711yescharacteristic
765C2×C4H(5,𝔽2)×C6711yescharacteristic
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C22—22no—
771C22—22no—
772C22—24no—
773C22—22no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22C2×#120×C6711yescharacteristic
792C22#546×C6711yescharacteristic
793C22#546×C6711yescharacteristic
794C22C2×#135×C6711yescharacteristic
795C22#575×C6711yescharacteristic
796C22#577×C6711yescharacteristic
797C22#578×C6711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—41no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4C2×#123×C6711yescharacteristic
810C4#534×C6711yescharacteristic
811C4#546×C6711yescharacteristic
812C4#546×C6711yescharacteristic
813C2—42no—
814C2—44no—
815C2—81no—
816C2C67×#240511yescharacteristic
817C2C67×#300211yescharacteristic
818C2C67×#301311yescharacteristic
819C2C67×#330211yescharacteristic
820C2C67×#330311yescharacteristic
821C2C67×#330711yescharacteristic
822C2C67×#331511yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC2×#547×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×#485×C67C2semidirect
3. C2×#416×C67C2semidirect
4. C67×#2485C2semidirect
5. C67×#2043C2semidirect
6. C67×#2043C2semidirect
7. C67×#2036C2semidirect
8. C67×#2035C2semidirect
9. C67×#1892C2semidirect
10. C67×#1869C2semidirect
11. C67×#1864C2semidirect
12. C67×#1862C2semidirect
13. C67×#1788C2semidirect
14. C67×#1788C2semidirect
15. C67×#1788C2semidirect
401. #24043C67direct (N × H)
413. C2×#485C2×C67semidirect
414. C2×#416C2×C67semidirect
415. #2485C2×C67semidirect
416. #2043C2×C67semidirect
417. #2043C2×C67semidirect
418. #2036C2×C67semidirect
419. #2035C2×C67semidirect
420. #1892C2×C67semidirect
421. #1869C2×C67semidirect
422. #1864C2×C67semidirect
423. #1862C2×C67semidirect
424. #1788C2×C67semidirect
425. #1788C2×C67semidirect
426. #1788C2×C67semidirect
427. C67#24043direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#547×C672
C2×#485×C672
C2×#416×C672
C67×#24852
C67×#20432
C67×#20362
C67×#20352
C67×#18922
C67×#18692
C67×#18642
C67×#18622
C67×#17882
#2404367