Finite Group Databasebeta

← C67×#33347 #30712598

Subgroups — C67×#33347 #30712598

Order 17152.

1236 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
1C67×#3449C211yesmaximal, characteristic
2C2×#413×C67C211yesmaximal, characteristic, complemented
3C2×#410×C67C211yesmaximal, characteristic, complemented
4C67×#2123C212yesmaximal, complemented
5C67×#2122C212yesmaximal, complemented
6C67×#2121C214yesmaximal, complemented
7C67×#2120C214yesmaximal, complemented
8C22×#41×C67C411yescharacteristic, complemented
9C22×#41×C67C2211yescharacteristic
10C22×M16×C67—21no—
11#537×C67—21no—
12#537×C67—21no—
13#536×C67—21no—
14#536×C67C411yescharacteristic, complemented
15#536×C67C2211yescharacteristic
16#535×C67—21no—
17#535×C67C411yescharacteristic, complemented
18#535×C67C2211yescharacteristic
19#534×C67C412yescomplemented
20#534×C67C2212yes—
21#532×C67—21no—
22#532×C67—21no—
23#525×C67—21no—
24#525×C67—21no—
25#525×C67C412yescomplemented
26#525×C67C2212yes—
27C2×#117×C67—21no—
28C2×#117×C67C411yescharacteristic, complemented
29#413×C67—21no—
30#413×C67—21no—
31#413×C67C2212yes—
32#413×C67C2212yes—
33C2×#101×C67—21no—
34C2×#100×C67C2212yes—
35#410×C67—21no—
36#410×C67—21no—
37#410×C67C2212yes—
38#410×C67C2212yes—
39C2×#99×C67—21no—
40C2×#99×C67C2212yes—
41#352×C67C2218yescomplemented
42AΣL(1,𝔽16)×C67C2218yescomplemented
43C2×#41×C67—21no—
44C2×#41×C67—21no—
45C2×#41×C67—21no—
46C2×#41×C67—21no—
47C2×#41×C67—41no—
48C2×#41×C67—41no—
49C2×#41×C67—41no—
50C2×#41×C67—41no—
51C2×#41×C67—41no—
52C2×#41×C67—41no—
53C2×#41×C67—41no—
54C2×#41×C67—41no—
55C2×#41×C67C2×C411yescharacteristic
56C2×#41×C67C2×C411yescharacteristic
57C2×#41×C67D411yescharacteristic
58C2×#41×C67D411yescharacteristic
59C2×#41×C67D411yescharacteristic
60C2×#41×C67D411yescharacteristic
61C2×#41×C67C2311yescharacteristic
62C2×#41×C67C2311yescharacteristic
63C22×Q8×C67C2×C411yescharacteristic, complemented
64C22×Q8×C67D411yescharacteristic
65C22×D4×C67C2×C411yescharacteristic
66C22×D4×C67C2×C412yes—
67C22×D4×C67C2×C411yescharacteristic, complemented
68C22×D4×C67D411yescharacteristic
69C22×D4×C67C2311yescharacteristic
70C23×C4×C67C2×C411yescharacteristic
71C23×C4×C67C2×C412yescomplemented
72C23×C4×C67D411yescharacteristic
73C23×C4×C67D411yescharacteristic
74C2×M16×C67—22no—
75C2×M16×C67—22no—
76C2×M16×C67—22no—
77C2×M16×C67—41no—
78C2×M16×C67—41no—
79C2×M16×C67—41no—
80C22×C8×C67—41no—
81C4⋊Q8×C67—21no—
82C4⋊Q8×C67—21no—
83#127×C67—21no—
84#127×C67—21no—
85#124×C67—21no—
86#124×C67—21no—
87#124×C67—21no—
88#124×C67—21no—
89#123×C67—22no—
90#123×C67—22no—
91#123×C67C2×C412yes—
92#123×C67C2×C412yescomplemented
93#123×C67C2×C412yescomplemented
94#123×C67C2312yes—
95C22⋊Q8×C67—22no—
96C22⋊Q8×C67—22no—
97C22⋊Q8×C67—21no—
98C22⋊Q8×C67—21no—
99C22⋊Q8×C67—21no—
100C22⋊Q8×C67—21no—
101#121×C67—22no—
102#121×C67—22no—
103#121×C67—22no—
104#121×C67—22no—
105#121×C67—22no—
106#121×C67—22no—
107#121×C67—21no—
108#121×C67—21no—
109#121×C67—21no—
110#121×C67—21no—
111#120×C67—22no—
112#120×C67—22no—
113#120×C67C2×C412yes—
114#120×C67C2×C412yescomplemented
115#120×C67C2×C412yescomplemented
116#120×C67C2312yes—
117C4×D4×C67—22no—
118C4×D4×C67—22no—
119C4×D4×C67—22no—
120C4×D4×C67—22no—
121#117×C67—21no—
122#117×C67—21no—
123#117×C67—22no—
124#117×C67—22no—
125#117×C67—41no—
126#117×C67—41no—
127#117×C67C2×C412yescomplemented
128#117×C67C2×C411yescharacteristic, complemented
129#117×C67C2×C411yescharacteristic, complemented
130C2×C4⋊C4×C67—21no—
131C2×C4⋊C4×C67—41no—
132C2×C22⋊C4×C67—22no—
133C2×C22⋊C4×C67C2×C412yes—
134C2×C42×C67—21no—
135C2×C42×C67—41no—
136#101×C67—22no—
137#101×C67—22no—
138#100×C67—22no—
139#100×C67C2314yes—
140#99×C67—22no—
141#99×C67—22no—
142#99×C67—22no—
143#99×C67C2314yes—
144C24×C67C22⋊C411yescharacteristic
145C24×C67C22×C411yescharacteristic
146C24×C67C22×C412yes—
147C24×C67C2×D411yescharacteristic
148#41×C67—41no—
149#41×C67—41no—
150#41×C67—41no—
151#41×C67—41no—
152#41×C67—41no—
153#41×C67—41no—
154#41×C67—41no—
155#41×C67—41no—
156#41×C67—41no—
157#41×C67—41no—
158#41×C67—41no—
159#41×C67—41no—
160#41×C67—41no—
161#41×C67—41no—
162#41×C67—41no—
163#41×C67—41no—
164#41×C67—42no—
165#41×C67—42no—
166#41×C67—42no—
167#41×C67—42no—
168#41×C67—42no—
169#41×C67—42no—
170#41×C67—41no—
171#41×C67—41no—
172#41×C67—41no—
173#41×C67—41no—
174C2×Q8×C67—21no—
175C2×Q8×C67—21no—
176C2×Q8×C67—41no—
177C2×Q8×C67—41no—
178C2×Q8×C67—41no—
179C2×Q8×C67—41no—
180C2×Q8×C67C22⋊C411yescharacteristic
181C2×Q8×C67C22⋊C411yescharacteristic
182C2×Q8×C67C2×D411yescharacteristic
183C2×Q8×C67C2×D411yescharacteristic
184C2×D4×C67—22no—
185C2×D4×C67—22no—
186C2×D4×C67—22no—
187C2×D4×C67—22no—
188C2×D4×C67—22no—
189C2×D4×C67—22no—
190C2×D4×C67—21no—
191C2×D4×C67—21no—
192C2×D4×C67—41no—
193C2×D4×C67—41no—
194C2×D4×C67—41no—
195C2×D4×C67—41no—
196C2×D4×C67—41no—
197C2×D4×C67—41no—
198C2×D4×C67—41no—
199C2×D4×C67—41no—
200C2×D4×C67—42no—
201C2×D4×C67—42no—
202C2×D4×C67C22⋊C411yescharacteristic
203C2×D4×C67C22⋊C411yescharacteristic
204C2×D4×C67C22⋊C411yescharacteristic
205C2×D4×C67C22⋊C411yescharacteristic
206C2×D4×C67C22×C411yescharacteristic
207C2×D4×C67C22×C411yescharacteristic
208C2×D4×C67C22×C411yescharacteristic
209C2×D4×C67C2×D411yescharacteristic
210C2×D4×C67C2×D411yescharacteristic
211C2×D4×C67C2×D411yescharacteristic
212C2×D4×C67C2×D411yescharacteristic
213C2×D4×C67C2411yescharacteristic
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—22no—
227C22×C4×C67—22no—
228C22×C4×C67—22no—
229C22×C4×C67—42no—
230C22×C4×C67—42no—
231C22×C4×C67—42no—
232C22×C4×C67C22⋊C411yescharacteristic
233C22×C4×C67C22⋊C411yescharacteristic
234C22×C4×C67C22⋊C411yescharacteristic
235C22×C4×C67C22⋊C411yescharacteristic
236C22×C4×C67C22⋊C411yescharacteristic
237C22×C4×C67C22⋊C411yescharacteristic
238C22×C4×C67C22⋊C411yescharacteristic
239C22×C4×C67C22⋊C411yescharacteristic
240C22×C4×C67C22⋊C411yescharacteristic
241C22×C4×C67C22×C411yescharacteristic
242C22×C4×C67C22×C411yescharacteristic
243C22×C4×C67C22×C412yes—
244C22×C4×C67C2×D411yescharacteristic
245C22×C4×C67C2×D411yescharacteristic
246C22×C4×C67C2×D411yescharacteristic
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2×D411yescharacteristic
249M16×C67—24no—
250M16×C67—42no—
251M16×C67—42no—
252M16×C67—42no—
253C2×C8×C67—42no—
254C2×C8×C67—42no—
255C2×C8×C67—42no—
256C4⋊C4×C67—22no—
257C4⋊C4×C67—21no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67—22no—
260C4⋊C4×C67—22no—
261C4⋊C4×C67—22no—
262C4⋊C4×C67—22no—
263C4⋊C4×C67—42no—
264C4⋊C4×C67—42no—
265C22⋊C4×C67—22no—
266C22⋊C4×C67—22no—
267C22⋊C4×C67—22no—
268C22⋊C4×C67—22no—
269C22⋊C4×C67—22no—
270C22⋊C4×C67—22no—
271C22⋊C4×C67—22no—
272C22⋊C4×C67—22no—
273C22⋊C4×C67—22no—
274C22⋊C4×C67—24no—
275C22⋊C4×C67—42no—
276C22⋊C4×C67C22×C412yes—
277C22⋊C4×C67C22×C412yes—
278C42×C67—22no—
279C42×C67—21no—
280C42×C67—21no—
281C42×C67—42no—
282C42×C67—42no—
283C23×C67—21no—
284C23×C67—21no—
285C23×C67—21no—
286C23×C67—21no—
287C23×C67—21no—
288C23×C67—21no—
289C23×C67—22no—
290C23×C67—42no—
291C23×C67—81no—
292C23×C67—81no—
293C23×C67—81no—
294C23×C67—82no—
295C23×C67C2×C22⋊C411yescharacteristic
296C23×C67C2×C22⋊C411yescharacteristic
297C23×C67C2×C22⋊C411yescharacteristic
298C23×C67C2×C22⋊C411yescharacteristic
299C23×C67C2×C22⋊C411yescharacteristic
300C23×C67C23×C411yescharacteristic
301C23×C67C22×D411yescharacteristic
302Q8×C67—41no—
303Q8×C67—41no—
304Q8×C67—41no—
305Q8×C67—41no—
306Q8×C67—42no—
307Q8×C67—41no—
308Q8×C67—41no—
309D4×C67—41no—
310D4×C67—41no—
311D4×C67—41no—
312D4×C67—41no—
313D4×C67—41no—
314D4×C67—41no—
315D4×C67—41no—
316D4×C67—41no—
317D4×C67—41no—
318D4×C67—41no—
319D4×C67—41no—
320D4×C67—41no—
321D4×C67—42no—
322D4×C67—44no—
323D4×C67—42no—
324D4×C67—42no—
325D4×C67—41no—
326D4×C67—41no—
327D4×C67—82no—
328D4×C67—82no—
329D4×C67—82no—
330D4×C67—82no—
331C2×C4×C67—21no—
332C2×C4×C67—21no—
333C2×C4×C67—21no—
334C2×C4×C67—21no—
335C2×C4×C67—21no—
336C2×C4×C67—21no—
337C2×C4×C67—21no—
338C2×C4×C67—21no—
339C2×C4×C67—21no—
340C2×C4×C67—21no—
341C2×C4×C67—21no—
342C2×C4×C67—21no—
343C2×C4×C67—21no—
344C2×C4×C67—21no—
345C2×C4×C67—21no—
346C2×C4×C67—21no—
347C2×C4×C67—21no—
348C2×C4×C67—21no—
349C2×C4×C67—21no—
350C2×C4×C67—21no—
351C2×C4×C67—21no—
352C2×C4×C67—21no—
353C2×C4×C67—21no—
354C2×C4×C67—21no—
355C2×C4×C67—21no—
356C2×C4×C67—21no—
357C2×C4×C67—21no—
358C2×C4×C67—21no—
359C2×C4×C67—21no—
360C2×C4×C67—21no—
361C2×C4×C67—22no—
362C2×C4×C67—22no—
363C2×C4×C67—22no—
364C2×C4×C67—44no—
365C2×C4×C67—42no—
366C2×C4×C67—42no—
367C2×C4×C67—42no—
368C2×C4×C67—44no—
369C2×C4×C67—82no—
370C2×C4×C67—84no—
371C2×C4×C67#9911yescharacteristic
372C2×C4×C67#9911yescharacteristic
373C2×C4×C67#9911yescharacteristic
374C2×C4×C67#9911yescharacteristic
375C2×C4×C67C2×C22⋊C411yescharacteristic
376C2×C4×C67C2×C22⋊C411yescharacteristic
377C2×C4×C67C2×C22⋊C411yescharacteristic
378C2×C4×C67C2×C22⋊C411yescharacteristic
379C2×C4×C67C2×C22⋊C411yescharacteristic
380C2×C4×C67C2×C22⋊C411yescharacteristic
381C2×C4×C67C2×C22⋊C411yescharacteristic
382C2×C4×C67C22×D411yescharacteristic
383C8×C67—44no—
384C22×C67—21no—
385C22×C67—21no—
386C22×C67—21no—
387C22×C67—21no—
388C22×C67—21no—
389C22×C67—21no—
390C22×C67—41no—
391C22×C67—41no—
392C22×C67—41no—
393C22×C67—41no—
394C22×C67—41no—
395C22×C67—41no—
396C22×C67—41no—
397C22×C67—42no—
398C22×C67—42no—
399C22×C67—42no—
400C22×C67—42no—
401C22×C67—42no—
402C22×C67—81no—
403C22×C67—81no—
404C22×C67—81no—
405C22×C67—81no—
406C22×C67—84no—
407C22×C67C2×#9911yescharacteristic
408C22×C67C2×#9911yescharacteristic
409C22×C67C22×C22⋊C411yescharacteristic
410C4×C67—21no—
411C4×C67—21no—
412C4×C67—21no—
413C4×C67—21no—
414C4×C67—21no—
415C4×C67—21no—
416C4×C67—42no—
417C4×C67—42no—
418C4×C67—42no—
419C4×C67—84no—
420C4×C67C2×#9911yescharacteristic
421C4×C67C2×#9911yescharacteristic
422C4×C67C2×#9911yescharacteristic
423C4×C67C2×#9911yescharacteristic
424#33347C6711yesmaximal, characteristic, direct product factor, Sylow
425C2×C67—21no—
426C2×C67—21no—
427C2×C67—21no—
428C2×C67—41no—
429C2×C67—41no—
430C2×C67—41no—
431C2×C67—41no—
432C2×C67—41no—
433C2×C67—41no—
434C2×C67—82no—
435C2×C67C22×#9911yescharacteristic
436#3449C2×C6711yescharacteristic
437C2×#413C2×C6711yescharacteristic, complemented
438C2×#410C2×C6711yescharacteristic, complemented
439#2123C2×C6712yescomplemented
440#2122C2×C6712yescomplemented
441#2121C2×C6714yescomplemented
442#2120C2×C6714yescomplemented
443C67#3334711yescharacteristic, direct product factor, Sylow
444C22×#41C4×C6711yescharacteristic, complemented
445C22×#41C22×C6711yescharacteristic
446C22×M16—21no—
447#537—21no—
448#537—21no—
449#536—21no—
450#536C4×C6711yescharacteristic, complemented
451#536C22×C6711yescharacteristic
452#535—21no—
453#535C4×C6711yescharacteristic, complemented
454#535C22×C6711yescharacteristic
455#534C4×C6712yescomplemented
456#534C22×C6712yes—
457#532—21no—
458#532—21no—
459#525—21no—
460#525—21no—
461#525C4×C6712yescomplemented
462#525C22×C6712yes—
463C2×#117—21no—
464C2×#117C4×C6711yescharacteristic, complemented
465#413—21no—
466#413—21no—
467#413C22×C6712yes—
468#413C22×C6712yes—
469C2×#101—21no—
470C2×#100C22×C6712yes—
471#410—21no—
472#410—21no—
473#410C22×C6712yes—
474#410C22×C6712yes—
475C2×#99—21no—
476C2×#99C22×C6712yes—
477#352C22×C6718yescomplemented
478AΣL(1,𝔽16)C22×C6718yescomplemented
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41C2×C4×C6711yescharacteristic
492C2×#41C2×C4×C6711yescharacteristic
493C2×#41D4×C6711yescharacteristic
494C2×#41D4×C6711yescharacteristic
495C2×#41D4×C6711yescharacteristic
496C2×#41D4×C6711yescharacteristic
497C2×#41C23×C6711yescharacteristic
498C2×#41C23×C6711yescharacteristic
499C22×Q8C2×C4×C6711yescharacteristic, complemented
500C22×Q8D4×C6711yescharacteristic
501C22×D4C2×C4×C6711yescharacteristic
502C22×D4C2×C4×C6712yes—
503C22×D4C2×C4×C6711yescharacteristic, complemented
504C22×D4D4×C6711yescharacteristic
505C22×D4C23×C6711yescharacteristic
506C23×C4C2×C4×C6711yescharacteristic
507C23×C4C2×C4×C6712yescomplemented
508C23×C4D4×C6711yescharacteristic
509C23×C4D4×C6711yescharacteristic
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—41no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519#127—21no—
520#127—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#123—22no—
526#123—22no—
527#123C2×C4×C6712yes—
528#123C2×C4×C6712yescomplemented
529#123C2×C4×C6712yescomplemented
530#123C23×C6712yes—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#120—22no—
548#120—22no—
549#120C2×C4×C6712yes—
550#120C2×C4×C6712yescomplemented
551#120C2×C4×C6712yescomplemented
552#120C23×C6712yes—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557#117—21no—
558#117—21no—
559#117—22no—
560#117—22no—
561#117—41no—
562#117—41no—
563#117C2×C4×C6712yescomplemented
564#117C2×C4×C6711yescharacteristic, complemented
565#117C2×C4×C6711yescharacteristic, complemented
566C2×C4⋊C4—21no—
567C2×C4⋊C4—41no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4C2×C4×C6712yes—
570C2×C42—21no—
571C2×C42—41no—
572#101—22no—
573#101—22no—
574#100—22no—
575#100C23×C6714yes—
576#99—22no—
577#99—22no—
578#99—22no—
579#99C23×C6714yes—
580C24C22⋊C4×C6711yescharacteristic
581C24C22×C4×C6711yescharacteristic
582C24C22×C4×C6712yes—
583C24C2×D4×C6711yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22⋊C4×C6711yescharacteristic
617C2×Q8C22⋊C4×C6711yescharacteristic
618C2×Q8C2×D4×C6711yescharacteristic
619C2×Q8C2×D4×C6711yescharacteristic
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4C22⋊C4×C6711yescharacteristic
639C2×D4C22⋊C4×C6711yescharacteristic
640C2×D4C22⋊C4×C6711yescharacteristic
641C2×D4C22⋊C4×C6711yescharacteristic
642C2×D4C22×C4×C6711yescharacteristic
643C2×D4C22×C4×C6711yescharacteristic
644C2×D4C22×C4×C6711yescharacteristic
645C2×D4C2×D4×C6711yescharacteristic
646C2×D4C2×D4×C6711yescharacteristic
647C2×D4C2×D4×C6711yescharacteristic
648C2×D4C2×D4×C6711yescharacteristic
649C2×D4C24×C6711yescharacteristic
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—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22⋊C4×C6711yescharacteristic
669C22×C4C22⋊C4×C6711yescharacteristic
670C22×C4C22⋊C4×C6711yescharacteristic
671C22×C4C22⋊C4×C6711yescharacteristic
672C22×C4C22⋊C4×C6711yescharacteristic
673C22×C4C22⋊C4×C6711yescharacteristic
674C22×C4C22⋊C4×C6711yescharacteristic
675C22×C4C22⋊C4×C6711yescharacteristic
676C22×C4C22⋊C4×C6711yescharacteristic
677C22×C4C22×C4×C6711yescharacteristic
678C22×C4C22×C4×C6711yescharacteristic
679C22×C4C22×C4×C6712yes—
680C22×C4C2×D4×C6711yescharacteristic
681C22×C4C2×D4×C6711yescharacteristic
682C22×C4C2×D4×C6711yescharacteristic
683C22×C4C2×D4×C6711yescharacteristic
684C22×C4C2×D4×C6711yescharacteristic
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—24no—
711C22⋊C4—42no—
712C22⋊C4C22×C4×C6712yes—
713C22⋊C4C22×C4×C6712yes—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—42no—
718C42—42no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C22⋊C4×C6711yescharacteristic
732C23C2×C22⋊C4×C6711yescharacteristic
733C23C2×C22⋊C4×C6711yescharacteristic
734C23C2×C22⋊C4×C6711yescharacteristic
735C23C2×C22⋊C4×C6711yescharacteristic
736C23C23×C4×C6711yescharacteristic
737C23C22×D4×C6711yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—82no—
806C2×C4—84no—
807C2×C4#99×C6711yescharacteristic
808C2×C4#99×C6711yescharacteristic
809C2×C4#99×C6711yescharacteristic
810C2×C4#99×C6711yescharacteristic
811C2×C4C2×C22⋊C4×C6711yescharacteristic
812C2×C4C2×C22⋊C4×C6711yescharacteristic
813C2×C4C2×C22⋊C4×C6711yescharacteristic
814C2×C4C2×C22⋊C4×C6711yescharacteristic
815C2×C4C2×C22⋊C4×C6711yescharacteristic
816C2×C4C2×C22⋊C4×C6711yescharacteristic
817C2×C4C2×C22⋊C4×C6711yescharacteristic
818C2×C4C22×D4×C6711yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×#99×C6711yescharacteristic
844C22C2×#99×C6711yescharacteristic
845C22C22×C22⋊C4×C6711yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—84no—
856C4C2×#99×C6711yescharacteristic
857C4C2×#99×C6711yescharacteristic
858C4C2×#99×C6711yescharacteristic
859C4C2×#99×C6711yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×#99×C6711yescharacteristic
subgroupG/H
centerC4×C67C2×#99
commutatorC23C23×C4×C67
Frattini, cosocleC2×D4C24×C67
socleC2×C67C22×#99
prime radicalC67×#3449C2
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C67 ◁ C22×C4×C67 ◁ C22×#41×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#413×C67C2semidirect
3. C2×#410×C67C2semidirect
4. C67×#2123C2semidirect
5. C67×#2122C2semidirect
6. C67×#2121C2semidirect
7. C67×#2120C2semidirect
8. C22×#41×C67C4semidirect
14. #536×C67C4semidirect
17. #535×C67C4semidirect
19. #534×C67C4semidirect
25. #525×C67C4semidirect
28. C2×#117×C67C4semidirect
41. #352×C67C22semidirect
42. AΣL(1,𝔽16)×C67C22semidirect
63. C22×Q8×C67C2×C4semidirect
67. C22×D4×C67C2×C4semidirect
71. C23×C4×C67C2×C4semidirect
92. #123×C67C2×C4semidirect
93. #123×C67C2×C4semidirect
114. #120×C67C2×C4semidirect
115. #120×C67C2×C4semidirect
127. #117×C67C2×C4semidirect
128. #117×C67C2×C4semidirect
129. #117×C67C2×C4semidirect
424. #33347C67direct (N × H)
437. C2×#413C2×C67semidirect
438. C2×#410C2×C67semidirect
439. #2123C2×C67semidirect
440. #2122C2×C67semidirect
441. #2121C2×C67semidirect
442. #2120C2×C67semidirect
443. C67#33347direct (N × H)
444. C22×#41C4×C67semidirect
450. #536C4×C67semidirect
453. #535C4×C67semidirect
455. #534C4×C67semidirect
461. #525C4×C67semidirect
464. C2×#117C4×C67semidirect
477. #352C22×C67semidirect
478. AΣL(1,𝔽16)C22×C67semidirect
499. C22×Q8C2×C4×C67semidirect
503. C22×D4C2×C4×C67semidirect
507. C23×C4C2×C4×C67semidirect
528. #123C2×C4×C67semidirect
529. #123C2×C4×C67semidirect
550. #120C2×C4×C67semidirect
551. #120C2×C4×C67semidirect
563. #117C2×C4×C67semidirect
564. #117C2×C4×C67semidirect
565. #117C2×C4×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#34492
C2×#413×C672
C2×#410×C672
C67×#21232
C67×#21222
C67×#21212
C67×#21202
#3334767