Finite Group Databasebeta

← C67×#23878 #30703129

Subgroups — C67×#23878 #30703129

Order 17152.

1814 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#575×C67C211yesmaximal, characteristic, complemented
2C67×#3488C211yesmaximal, characteristic, complemented
3C2×#455×C67C211yesmaximal, characteristic, complemented
4C2×#453×C67C211yesmaximal, characteristic, complemented
5C67×#3005C211yesmaximal, characteristic, complemented
6C67×#2431C211yesmaximal, characteristic, complemented
7C67×#2007C211yesmaximal, characteristic, complemented
8C67×#2006C211yesmaximal, characteristic, complemented
9C67×#2004C211yesmaximal, characteristic, complemented
10C67×#2002C211yesmaximal, characteristic, complemented
11C67×#1900C211yesmaximal, characteristic, complemented
12C67×#1883C211yesmaximal, characteristic, complemented
13C67×#1882C211yesmaximal, characteristic, complemented
14C67×#1871C211yesmaximal, characteristic, complemented
15C67×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C67C2211yescharacteristic
17C22×#41×C67C2211yescharacteristic
18C22×#41×C67C2211yescharacteristic, complemented
19#575×C67—24no—
20#575×C67—24no—
21C2×#137×C67—21no—
22C2×#137×C67C2211yescharacteristic
23C2×#137×C67C2211yescharacteristic, complemented
24C2×#137×C67C2211yescharacteristic, complemented
25C2×AGL(1,ℤ/8)×C67—21no—
26C2×AGL(1,ℤ/8)×C67C2211yescharacteristic
27C2×AGL(1,ℤ/8)×C67C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C67C2211yescharacteristic, complemented
29C2×#135×C67—21no—
30C2×#135×C67—21no—
31C22×M16×C67C2211yescharacteristic, complemented
32#550×C67—21no—
33#548×C67—21no—
34#546×C67—21no—
35#546×C67—22no—
36D42×C67—22no—
37D42×C67—21no—
38#537×C67—21no—
39#537×C67C2211yescharacteristic
40#535×C67—21no—
41#535×C67C2211yescharacteristic
42C2×#127×C67C2211yescharacteristic, complemented
43C2×#124×C67C2211yescharacteristic, complemented
44#525×C67—21no—
45#525×C67C2211yescharacteristic
46C2×#121×C67—21no—
47C2×#121×C67C2211yescharacteristic
48#520×C67C2211yescharacteristic
49#455×C67—24no—
50#453×C67—24no—
51#452×C67—21no—
52#452×C67—21no—
53#449×C67—21no—
54#449×C67—21no—
55C2×#104×C67C2211yescharacteristic
56C2×#104×C67C2211yescharacteristic
57C2×#104×C67C2211yescharacteristic, complemented
58C2×#104×C67C2211yescharacteristic, complemented
59C2×#104×C67C2211yescharacteristic, complemented
60C2×#104×C67C2211yescharacteristic, complemented
61#419×C67C2211yescharacteristic, complemented
62#418×C67C2211yescharacteristic, complemented
63C2×#100×C67C2211yescharacteristic, complemented
64C2×#100×C67C2211yescharacteristic, complemented
65#407×C67C2211yescharacteristic, complemented
66#392×C67—22no—
67#391×C67C2211yescharacteristic, complemented
68#390×C67C2211yescharacteristic, complemented
69#386×C67—22no—
70C4×C22⋊C4×C67C2211yescharacteristic, complemented
71#343×C67C2211yescharacteristic, complemented
72#343×C67C2211yescharacteristic, complemented
73#339×C67C2211yescharacteristic, complemented
74#339×C67C2211yescharacteristic, complemented
75H(5,𝔽2)×C67—22no—
76H(5,𝔽2)×C67—22no—
77H(5,𝔽2)×C67—41no—
78H(5,𝔽2)×C67—41no—
79C2×#41×C67—21no—
80C2×#41×C67—21no—
81C2×#41×C67—21no—
82C2×#41×C67—21no—
83C2×#41×C67—22no—
84C2×#41×C67—22no—
85C2×#41×C67—22no—
86C2×#41×C67—22no—
87C2×#41×C67—21no—
88C2×#41×C67—21no—
89C2×#41×C67—21no—
90C2×#41×C67—21no—
91C2×#41×C67—41no—
92C2×#41×C67—41no—
93C2×#41×C67—41no—
94C2×#41×C67—41no—
95C2×#41×C67D411yescharacteristic, complemented
96C2×#41×C67D411yescharacteristic, complemented
97C2×#41×C67C2311yescharacteristic
98C2×#41×C67C2311yescharacteristic
99C2×#41×C67C2311yescharacteristic
100C22×Q8×C67D411yescharacteristic, complemented
101C22×Q8×C67C2311yescharacteristic
102C22×D4×C67—21no—
103C22×D4×C67—22no—
104C22×D4×C67—22no—
105C22×D4×C67—21no—
106C22×D4×C67—21no—
107C22×D4×C67—21no—
108C22×D4×C67—22no—
109C22×D4×C67D412yes—
110C22×D4×C67D411yescharacteristic, complemented
111C22×D4×C67C2311yescharacteristic
112C22×D4×C67C2311yescharacteristic
113C23×C4×C67—21no—
114C23×C4×C67—21no—
115C23×C4×C67C2311yescharacteristic
116#137×C67—28no—
117#137×C67—22no—
118#137×C67—22no—
119#137×C67—22no—
120#137×C67—22no—
121#137×C67—41no—
122#137×C67D414yescomplemented
123AGL(1,ℤ/8)×C67—28no—
124AGL(1,ℤ/8)×C67—22no—
125AGL(1,ℤ/8)×C67—22no—
126AGL(1,ℤ/8)×C67—22no—
127AGL(1,ℤ/8)×C67—22no—
128AGL(1,ℤ/8)×C67—41no—
129AGL(1,ℤ/8)×C67D414yescomplemented
130#135×C67—28no—
131#135×C67—28no—
132C2×Q16×C67—21no—
133C2×Q16×C67—21no—
134C2×Q16×C67—21no—
135C2×SD16×C67—21no—
136C2×SD16×C67—21no—
137C2×SD16×C67—21no—
138C2×SD16×C67—21no—
139C2×SD16×C67—21no—
140C2×SD16×C67—21no—
141C2×D8×C67—21no—
142C2×D8×C67—21no—
143C2×D8×C67—21no—
144C2×M16×C67—21no—
145C2×M16×C67—22no—
146C2×M16×C67—22no—
147C2×M16×C67C2311yescharacteristic
148C2×M16×C67C2311yescharacteristic
149C2×M16×C67C2311yescharacteristic
150C2×M16×C67C2311yescharacteristic
151C22×C8×C67—21no—
152#127×C67—22no—
153#127×C67—21no—
154#127×C67—22no—
155#127×C67—41no—
156#124×C67—22no—
157#124×C67—21no—
158#124×C67—22no—
159#124×C67—41no—
160#123×C67—22no—
161#123×C67—21no—
162C22⋊Q8×C67—22no—
163C22⋊Q8×C67—21no—
164C22⋊Q8×C67—21no—
165C22⋊Q8×C67D411yescharacteristic, complemented
166C22⋊Q8×C67D411yescharacteristic, complemented
167#121×C67—22no—
168#121×C67—22no—
169#121×C67—22no—
170#121×C67—22no—
171#121×C67—22no—
172#121×C67—21no—
173#121×C67—21no—
174#121×C67—21no—
175#121×C67—21no—
176#121×C67—21no—
177#121×C67—21no—
178#121×C67—22no—
179#121×C67—21no—
180#121×C67—21no—
181#121×C67D411yescharacteristic, complemented
182#121×C67D411yescharacteristic, complemented
183#120×C67—22no—
184#120×C67—22no—
185#120×C67—22no—
186#120×C67—21no—
187#120×C67—22no—
188C4×Q8×C67—21no—
189C4×D4×C67—22no—
190C4×D4×C67—22no—
191C4×D4×C67—21no—
192C4×D4×C67—22no—
193C4×D4×C67—21no—
194C4×D4×C67—21no—
195#117×C67—21no—
196#117×C67C2311yescharacteristic
197C2×C4⋊C4×C67—21no—
198C2×C4⋊C4×C67C2311yescharacteristic
199C2×C22⋊C4×C67—22no—
200C2×C22⋊C4×C67—22no—
201C2×C22⋊C4×C67—21no—
202C2×C22⋊C4×C67—22no—
203C2×C22⋊C4×C67D412yes—
204C2×C42×C67C2311yescharacteristic
205C2×C42×C67C2311yescharacteristic
206#104×C67—22no—
207#104×C67—22no—
208#104×C67—22no—
209#104×C67—22no—
210#104×C67—41no—
211#104×C67—41no—
212#103×C67—21no—
213#103×C67—21no—
214#102×C67—21no—
215#102×C67—21no—
216#100×C67—22no—
217#100×C67—22no—
218C22⋊C8×C67—21no—
219C22⋊C8×C67—21no—
220#95×C67—21no—
221#95×C67—22no—
222C24×C67—22no—
223C24×C67—21no—
224C24×C67—21no—
225C24×C67C2×D412yes—
226C24×C67C2×D411yescharacteristic
227#41×C67—21no—
228#41×C67—21no—
229#41×C67—24no—
230#41×C67—24no—
231#41×C67—22no—
232#41×C67—22no—
233#41×C67—21no—
234#41×C67—21no—
235#41×C67—21no—
236#41×C67—21no—
237#41×C67—21no—
238#41×C67—21no—
239#41×C67—21no—
240#41×C67—21no—
241#41×C67—42no—
242#41×C67—42no—
243#41×C67—41no—
244#41×C67—41no—
245#41×C67—42no—
246#41×C67—42no—
247#41×C67—42no—
248#41×C67—42no—
249#41×C67—42no—
250#41×C67—42no—
251#41×C67—42no—
252#41×C67—42no—
253#41×C67—42no—
254#41×C67—42no—
255#41×C67—42no—
256#41×C67—42no—
257#41×C67C2×D412yes—
258#41×C67C2×D412yes—
259C2×Q8×C67—21no—
260C2×Q8×C67—21no—
261C2×Q8×C67—22no—
262C2×Q8×C67—21no—
263C2×Q8×C67—21no—
264C2×Q8×C67—21no—
265C2×Q8×C67—21no—
266C2×Q8×C67—41no—
267C2×Q8×C67C2×D411yescharacteristic
268C2×Q8×C67C2×D411yescharacteristic
269C2×Q8×C67C2×D411yescharacteristic
270C2×Q8×C67C2×D412yescomplemented
271C2×D4×C67—21no—
272C2×D4×C67—22no—
273C2×D4×C67—22no—
274C2×D4×C67—22no—
275C2×D4×C67—22no—
276C2×D4×C67—21no—
277C2×D4×C67—21no—
278C2×D4×C67—21no—
279C2×D4×C67—21no—
280C2×D4×C67—21no—
281C2×D4×C67—22no—
282C2×D4×C67—22no—
283C2×D4×C67—22no—
284C2×D4×C67—21no—
285C2×D4×C67—22no—
286C2×D4×C67—21no—
287C2×D4×C67—21no—
288C2×D4×C67—21no—
289C2×D4×C67—21no—
290C2×D4×C67—21no—
291C2×D4×C67—21no—
292C2×D4×C67—21no—
293C2×D4×C67—21no—
294C2×D4×C67—21no—
295C2×D4×C67—21no—
296C2×D4×C67—21no—
297C2×D4×C67—21no—
298C2×D4×C67—41no—
299C2×D4×C67—42no—
300C2×D4×C67—42no—
301C2×D4×C67—42no—
302C2×D4×C67—44no—
303C2×D4×C67—42no—
304C2×D4×C67—42no—
305C2×D4×C67—44no—
306C2×D4×C67—44no—
307C2×D4×C67—42no—
308C2×D4×C67—42no—
309C2×D4×C67—41no—
310C2×D4×C67—41no—
311C2×D4×C67—42no—
312C2×D4×C67—44no—
313C2×D4×C67—82no—
314C2×D4×C67—82no—
315C2×D4×C67—84no—
316C2×D4×C67C2×D411yescharacteristic
317C2×D4×C67C2×D411yescharacteristic
318C2×D4×C67C2×D411yescharacteristic
319C2×D4×C67C2×D412yescomplemented
320C22×C4×C67—21no—
321C22×C4×C67—21no—
322C22×C4×C67—21no—
323C22×C4×C67—21no—
324C22×C4×C67—21no—
325C22×C4×C67—22no—
326C22×C4×C67—21no—
327C22×C4×C67—21no—
328C22×C4×C67—21no—
329C22×C4×C67—22no—
330C22×C4×C67—21no—
331C22×C4×C67—21no—
332C22×C4×C67—21no—
333C22×C4×C67—21no—
334C22×C4×C67—21no—
335C22×C4×C67—42no—
336C22×C4×C67—42no—
337C22×C4×C67—42no—
338C22×C4×C67—42no—
339C22×C4×C67—41no—
340C22×C4×C67—41no—
341C22×C4×C67C2×D411yescharacteristic
342C22×C4×C67C2×D411yescharacteristic
343C22×C4×C67C2×D411yescharacteristic
344C22×C4×C67C2×D411yescharacteristic
345C22×C4×C67C2×D411yescharacteristic
346C22×C4×C67C2×D412yes—
347C22×C4×C67C2411yescharacteristic
348Q16×C67—24no—
349Q16×C67—24no—
350Q16×C67—42no—
351SD16×C67—24no—
352SD16×C67—24no—
353SD16×C67—24no—
354SD16×C67—24no—
355SD16×C67—42no—
356SD16×C67—42no—
357D8×C67—24no—
358D8×C67—24no—
359D8×C67—42no—
360M16×C67—24no—
361M16×C67—21no—
362M16×C67—21no—
363M16×C67—21no—
364M16×C67—21no—
365M16×C67—21no—
366M16×C67—21no—
367M16×C67C2×D412yescomplemented
368M16×C67C2×D412yescomplemented
369C2×C8×C67—24no—
370C2×C8×C67—21no—
371C2×C8×C67—21no—
372C2×C8×C67—21no—
373C2×C8×C67—21no—
374C4⋊C4×C67—22no—
375C4⋊C4×C67—22no—
376C4⋊C4×C67—21no—
377C4⋊C4×C67—21no—
378C4⋊C4×C67—21no—
379C4⋊C4×C67—21no—
380C4⋊C4×C67C2×D411yescharacteristic
381C4⋊C4×C67C2×D411yescharacteristic
382C22⋊C4×C67—22no—
383C22⋊C4×C67—22no—
384C22⋊C4×C67—22no—
385C22⋊C4×C67—22no—
386C22⋊C4×C67—22no—
387C22⋊C4×C67—21no—
388C22⋊C4×C67—21no—
389C22⋊C4×C67—21no—
390C22⋊C4×C67—21no—
391C22⋊C4×C67—22no—
392C22⋊C4×C67—22no—
393C22⋊C4×C67—21no—
394C22⋊C4×C67—44no—
395C22⋊C4×C67—42no—
396C22⋊C4×C67—82no—
397C42×C67—22no—
398C42×C67—21no—
399C42×C67—21no—
400C42×C67—21no—
401C42×C67—21no—
402C42×C67—21no—
403C23×C67—21no—
404C23×C67—21no—
405C23×C67—21no—
406C23×C67—22no—
407C23×C67—21no—
408C23×C67—21no—
409C23×C67—22no—
410C23×C67—22no—
411C23×C67—22no—
412C23×C67—41no—
413C23×C67—41no—
414C23×C67—42no—
415C23×C67—42no—
416C23×C67—42no—
417C23×C67—42no—
418C23×C67—44no—
419C23×C67—42no—
420C23×C67—42no—
421C23×C67—41no—
422C23×C67—41no—
423C23×C67—81no—
424C23×C67—82no—
425C23×C67—82no—
426C23×C67#12011yescharacteristic
427C23×C67#12011yescharacteristic
428C23×C67C22×D411yescharacteristic
429Q8×C67—21no—
430Q8×C67—21no—
431Q8×C67—22no—
432Q8×C67—21no—
433Q8×C67—21no—
434Q8×C67—22no—
435Q8×C67—21no—
436Q8×C67—42no—
437Q8×C67—41no—
438Q8×C67—41no—
439Q8×C67#12012yes—
440D4×C67—22no—
441D4×C67—22no—
442D4×C67—21no—
443D4×C67—22no—
444D4×C67—21no—
445D4×C67—21no—
446D4×C67—21no—
447D4×C67—22no—
448D4×C67—21no—
449D4×C67—42no—
450D4×C67—42no—
451D4×C67—44no—
452D4×C67—42no—
453D4×C67—44no—
454D4×C67—44no—
455D4×C67—42no—
456D4×C67—44no—
457D4×C67—44no—
458D4×C67—41no—
459D4×C67—41no—
460D4×C67—41no—
461D4×C67—41no—
462D4×C67—41no—
463D4×C67—41no—
464D4×C67—41no—
465D4×C67—41no—
466D4×C67—41no—
467D4×C67—41no—
468D4×C67—81no—
469D4×C67—82no—
470D4×C67—82no—
471D4×C67—82no—
472D4×C67—82no—
473D4×C67—88no—
474D4×C67#12012yes—
475C2×C4×C67—21no—
476C2×C4×C67—21no—
477C2×C4×C67—21no—
478C2×C4×C67—21no—
479C2×C4×C67—21no—
480C2×C4×C67—21no—
481C2×C4×C67—21no—
482C2×C4×C67—21no—
483C2×C4×C67—21no—
484C2×C4×C67—21no—
485C2×C4×C67—21no—
486C2×C4×C67—22no—
487C2×C4×C67—22no—
488C2×C4×C67—22no—
489C2×C4×C67—21no—
490C2×C4×C67—22no—
491C2×C4×C67—21no—
492C2×C4×C67—21no—
493C2×C4×C67—21no—
494C2×C4×C67—22no—
495C2×C4×C67—42no—
496C2×C4×C67—42no—
497C2×C4×C67—42no—
498C2×C4×C67—44no—
499C2×C4×C67—44no—
500C2×C4×C67—44no—
501C2×C4×C67—41no—
502C2×C4×C67—41no—
503C2×C4×C67—41no—
504C2×C4×C67—41no—
505C2×C4×C67—41no—
506C2×C4×C67—41no—
507C2×C4×C67—41no—
508C2×C4×C67—41no—
509C2×C4×C67—42no—
510C2×C4×C67—41no—
511C2×C4×C67—41no—
512C2×C4×C67—41no—
513C2×C4×C67—82no—
514C2×C4×C67#12011yescharacteristic
515C2×C4×C67#12011yescharacteristic
516C2×C4×C67C22×D411yescharacteristic
517C2×C4×C67C22×D411yescharacteristic
518C2×C4×C67C22×D411yescharacteristic
519C2×C4×C67C22×D411yescharacteristic
520C2×C4×C67H(5,𝔽2)11yescharacteristic
521C2×C4×C67H(5,𝔽2)11yescharacteristic
522C8×C67—22no—
523C8×C67—22no—
524C8×C67—41no—
525C8×C67—41no—
526C22×C67—21no—
527C22×C67—21no—
528C22×C67—21no—
529C22×C67—21no—
530C22×C67—22no—
531C22×C67—21no—
532C22×C67—21no—
533C22×C67—21no—
534C22×C67—21no—
535C22×C67—44no—
536C22×C67—41no—
537C22×C67—41no—
538C22×C67—41no—
539C22×C67—42no—
540C22×C67—41no—
541C22×C67—42no—
542C22×C67—41no—
543C22×C67—42no—
544C22×C67—41no—
545C22×C67—42no—
546C22×C67—41no—
547C22×C67—41no—
548C22×C67—81no—
549C22×C67—81no—
550C22×C67—82no—
551C22×C67—82no—
552C22×C67—82no—
553C22×C67—84no—
554C22×C67—81no—
555C22×C67—81no—
556C22×C67—164no—
557C22×C67C2×#12011yescharacteristic
558C22×C67D4211yescharacteristic
559C22×C67D4211yescharacteristic
560C4×C67—21no—
561C4×C67—21no—
562C4×C67—22no—
563C4×C67—42no—
564C4×C67—41no—
565C4×C67—41no—
566C4×C67—42no—
567C4×C67—41no—
568C4×C67—42no—
569C4×C67—41no—
570C4×C67—81no—
571C4×C67C2×#12011yescharacteristic
572C4×C67#53411yescharacteristic
573C4×C67D4211yescharacteristic
574C4×C67D4211yescharacteristic
575#23878C6711yesmaximal, characteristic, direct product factor, Sylow
576C2×C67—21no—
577C2×C67—21no—
578C2×C67—41no—
579C2×C67—41no—
580C2×C67—42no—
581C2×C67—82no—
582C2×C67—81no—
583C2×C67—82no—
584C2×C67—81no—
585C2×C67#240311yescharacteristic
586C2×C67#301811yescharacteristic
587C2×C67#301911yescharacteristic
588C2×#575C2×C6711yescharacteristic, complemented
589#3488C2×C6711yescharacteristic, complemented
590C2×#455C2×C6711yescharacteristic, complemented
591C2×#453C2×C6711yescharacteristic, complemented
592#3005C2×C6711yescharacteristic, complemented
593#2431C2×C6711yescharacteristic, complemented
594#2007C2×C6711yescharacteristic, complemented
595#2006C2×C6711yescharacteristic, complemented
596#2004C2×C6711yescharacteristic, complemented
597#2002C2×C6711yescharacteristic, complemented
598#1900C2×C6711yescharacteristic, complemented
599#1883C2×C6711yescharacteristic, complemented
600#1882C2×C6711yescharacteristic, complemented
601#1871C2×C6711yescharacteristic, complemented
602#1789C2×C6711yescharacteristic, complemented
603C67#2387811yescharacteristic, direct product factor, Sylow
604C2×H(5,𝔽2)C22×C6711yescharacteristic
605C22×#41C22×C6711yescharacteristic
606C22×#41C22×C6711yescharacteristic, complemented
607#575—24no—
608#575—24no—
609C2×#137—21no—
610C2×#137C22×C6711yescharacteristic
611C2×#137C22×C6711yescharacteristic, complemented
612C2×#137C22×C6711yescharacteristic, complemented
613C2×AGL(1,ℤ/8)—21no—
614C2×AGL(1,ℤ/8)C22×C6711yescharacteristic
615C2×AGL(1,ℤ/8)C22×C6711yescharacteristic, complemented
616C2×AGL(1,ℤ/8)C22×C6711yescharacteristic, complemented
617C2×#135—21no—
618C2×#135—21no—
619C22×M16C22×C6711yescharacteristic, complemented
620#550—21no—
621#548—21no—
622#546—21no—
623#546—22no—
624D42—22no—
625D42—21no—
626#537—21no—
627#537C22×C6711yescharacteristic
628#535—21no—
629#535C22×C6711yescharacteristic
630C2×#127C22×C6711yescharacteristic, complemented
631C2×#124C22×C6711yescharacteristic, complemented
632#525—21no—
633#525C22×C6711yescharacteristic
634C2×#121—21no—
635C2×#121C22×C6711yescharacteristic
636#520C22×C6711yescharacteristic
637#455—24no—
638#453—24no—
639#452—21no—
640#452—21no—
641#449—21no—
642#449—21no—
643C2×#104C22×C6711yescharacteristic
644C2×#104C22×C6711yescharacteristic
645C2×#104C22×C6711yescharacteristic, complemented
646C2×#104C22×C6711yescharacteristic, complemented
647C2×#104C22×C6711yescharacteristic, complemented
648C2×#104C22×C6711yescharacteristic, complemented
649#419C22×C6711yescharacteristic, complemented
650#418C22×C6711yescharacteristic, complemented
651C2×#100C22×C6711yescharacteristic, complemented
652C2×#100C22×C6711yescharacteristic, complemented
653#407C22×C6711yescharacteristic, complemented
654#392—22no—
655#391C22×C6711yescharacteristic, complemented
656#390C22×C6711yescharacteristic, complemented
657#386—22no—
658C4×C22⋊C4C22×C6711yescharacteristic, complemented
659#343C22×C6711yescharacteristic, complemented
660#343C22×C6711yescharacteristic, complemented
661#339C22×C6711yescharacteristic, complemented
662#339C22×C6711yescharacteristic, complemented
663H(5,𝔽2)—22no—
664H(5,𝔽2)—22no—
665H(5,𝔽2)—41no—
666H(5,𝔽2)—41no—
667C2×#41—21no—
668C2×#41—21no—
669C2×#41—21no—
670C2×#41—21no—
671C2×#41—22no—
672C2×#41—22no—
673C2×#41—22no—
674C2×#41—22no—
675C2×#41—21no—
676C2×#41—21no—
677C2×#41—21no—
678C2×#41—21no—
679C2×#41—41no—
680C2×#41—41no—
681C2×#41—41no—
682C2×#41—41no—
683C2×#41D4×C6711yescharacteristic, complemented
684C2×#41D4×C6711yescharacteristic, complemented
685C2×#41C23×C6711yescharacteristic
686C2×#41C23×C6711yescharacteristic
687C2×#41C23×C6711yescharacteristic
688C22×Q8D4×C6711yescharacteristic, complemented
689C22×Q8C23×C6711yescharacteristic
690C22×D4—21no—
691C22×D4—22no—
692C22×D4—22no—
693C22×D4—21no—
694C22×D4—21no—
695C22×D4—21no—
696C22×D4—22no—
697C22×D4D4×C6712yes—
698C22×D4D4×C6711yescharacteristic, complemented
699C22×D4C23×C6711yescharacteristic
700C22×D4C23×C6711yescharacteristic
701C23×C4—21no—
702C23×C4—21no—
703C23×C4C23×C6711yescharacteristic
704#137—28no—
705#137—22no—
706#137—22no—
707#137—22no—
708#137—22no—
709#137—41no—
710#137D4×C6714yescomplemented
711AGL(1,ℤ/8)—28no—
712AGL(1,ℤ/8)—22no—
713AGL(1,ℤ/8)—22no—
714AGL(1,ℤ/8)—22no—
715AGL(1,ℤ/8)—22no—
716AGL(1,ℤ/8)—41no—
717AGL(1,ℤ/8)D4×C6714yescomplemented
718#135—28no—
719#135—28no—
720C2×Q16—21no—
721C2×Q16—21no—
722C2×Q16—21no—
723C2×SD16—21no—
724C2×SD16—21no—
725C2×SD16—21no—
726C2×SD16—21no—
727C2×SD16—21no—
728C2×SD16—21no—
729C2×D8—21no—
730C2×D8—21no—
731C2×D8—21no—
732C2×M16—21no—
733C2×M16—22no—
734C2×M16—22no—
735C2×M16C23×C6711yescharacteristic
736C2×M16C23×C6711yescharacteristic
737C2×M16C23×C6711yescharacteristic
738C2×M16C23×C6711yescharacteristic
739C22×C8—21no—
740#127—22no—
741#127—21no—
742#127—22no—
743#127—41no—
744#124—22no—
745#124—21no—
746#124—22no—
747#124—41no—
748#123—22no—
749#123—21no—
750C22⋊Q8—22no—
751C22⋊Q8—21no—
752C22⋊Q8—21no—
753C22⋊Q8D4×C6711yescharacteristic, complemented
754C22⋊Q8D4×C6711yescharacteristic, complemented
755#121—22no—
756#121—22no—
757#121—22no—
758#121—22no—
759#121—22no—
760#121—21no—
761#121—21no—
762#121—21no—
763#121—21no—
764#121—21no—
765#121—21no—
766#121—22no—
767#121—21no—
768#121—21no—
769#121D4×C6711yescharacteristic, complemented
770#121D4×C6711yescharacteristic, complemented
771#120—22no—
772#120—22no—
773#120—22no—
774#120—21no—
775#120—22no—
776C4×Q8—21no—
777C4×D4—22no—
778C4×D4—22no—
779C4×D4—21no—
780C4×D4—22no—
781C4×D4—21no—
782C4×D4—21no—
783#117—21no—
784#117C23×C6711yescharacteristic
785C2×C4⋊C4—21no—
786C2×C4⋊C4C23×C6711yescharacteristic
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—21no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4D4×C6712yes—
792C2×C42C23×C6711yescharacteristic
793C2×C42C23×C6711yescharacteristic
794#104—22no—
795#104—22no—
796#104—22no—
797#104—22no—
798#104—41no—
799#104—41no—
800#103—21no—
801#103—21no—
802#102—21no—
803#102—21no—
804#100—22no—
805#100—22no—
806C22⋊C8—21no—
807C22⋊C8—21no—
808#95—21no—
809#95—22no—
810C24—22no—
811C24—21no—
812C24—21no—
813C24C2×D4×C6712yes—
814C24C2×D4×C6711yescharacteristic
815#41—21no—
816#41—21no—
817#41—24no—
818#41—24no—
819#41—22no—
820#41—22no—
821#41—21no—
822#41—21no—
823#41—21no—
824#41—21no—
825#41—21no—
826#41—21no—
827#41—21no—
828#41—21no—
829#41—42no—
830#41—42no—
831#41—41no—
832#41—41no—
833#41—42no—
834#41—42no—
835#41—42no—
836#41—42no—
837#41—42no—
838#41—42no—
839#41—42no—
840#41—42no—
841#41—42no—
842#41—42no—
843#41—42no—
844#41—42no—
845#41C2×D4×C6712yes—
846#41C2×D4×C6712yes—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—22no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—41no—
855C2×Q8C2×D4×C6711yescharacteristic
856C2×Q8C2×D4×C6711yescharacteristic
857C2×Q8C2×D4×C6711yescharacteristic
858C2×Q8C2×D4×C6712yescomplemented
859C2×D4—21no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—22no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—22no—
870C2×D4—22no—
871C2×D4—22no—
872C2×D4—21no—
873C2×D4—22no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—44no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—84no—
904C2×D4C2×D4×C6711yescharacteristic
905C2×D4C2×D4×C6711yescharacteristic
906C2×D4C2×D4×C6711yescharacteristic
907C2×D4C2×D4×C6712yescomplemented
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4C2×D4×C6711yescharacteristic
930C22×C4C2×D4×C6711yescharacteristic
931C22×C4C2×D4×C6711yescharacteristic
932C22×C4C2×D4×C6711yescharacteristic
933C22×C4C2×D4×C6711yescharacteristic
934C22×C4C2×D4×C6712yes—
935C22×C4C24×C6711yescharacteristic
936Q16—24no—
937Q16—24no—
938Q16—42no—
939SD16—24no—
940SD16—24no—
941SD16—24no—
942SD16—24no—
943SD16—42no—
944SD16—42no—
945D8—24no—
946D8—24no—
947D8—42no—
948M16—24no—
949M16—21no—
950M16—21no—
951M16—21no—
952M16—21no—
953M16—21no—
954M16—21no—
955M16C2×D4×C6712yescomplemented
956M16C2×D4×C6712yescomplemented
957C2×C8—24no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4C2×D4×C6711yescharacteristic
969C4⋊C4C2×D4×C6711yescharacteristic
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—21no—
976C22⋊C4—21no—
977C22⋊C4—21no—
978C22⋊C4—21no—
979C22⋊C4—22no—
980C22⋊C4—22no—
981C22⋊C4—21no—
982C22⋊C4—44no—
983C22⋊C4—42no—
984C22⋊C4—82no—
985C42—22no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—21no—
996C23—21no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—44no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—81no—
1012C23—82no—
1013C23—82no—
1014C23#120×C6711yescharacteristic
1015C23#120×C6711yescharacteristic
1016C23C22×D4×C6711yescharacteristic
1017Q8—21no—
1018Q8—21no—
1019Q8—22no—
1020Q8—21no—
1021Q8—21no—
1022Q8—22no—
1023Q8—21no—
1024Q8—42no—
1025Q8—41no—
1026Q8—41no—
1027Q8#120×C6712yes—
1028D4—22no—
1029D4—22no—
1030D4—21no—
1031D4—22no—
1032D4—21no—
1033D4—21no—
1034D4—21no—
1035D4—22no—
1036D4—21no—
1037D4—42no—
1038D4—42no—
1039D4—44no—
1040D4—42no—
1041D4—44no—
1042D4—44no—
1043D4—42no—
1044D4—44no—
1045D4—44no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—82no—
1057D4—81no—
1058D4—82no—
1059D4—82no—
1060D4—82no—
1061D4—88no—
1062D4#120×C6712yes—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—42no—
1084C2×C4—42no—
1085C2×C4—42no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—42no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—82no—
1102C2×C4#120×C6711yescharacteristic
1103C2×C4#120×C6711yescharacteristic
1104C2×C4C22×D4×C6711yescharacteristic
1105C2×C4C22×D4×C6711yescharacteristic
1106C2×C4C22×D4×C6711yescharacteristic
1107C2×C4C22×D4×C6711yescharacteristic
1108C2×C4H(5,𝔽2)×C6711yescharacteristic
1109C2×C4H(5,𝔽2)×C6711yescharacteristic
1110C8—22no—
1111C8—22no—
1112C8—41no—
1113C8—41no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—22no—
1123C22—44no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—42no—
1134C22—41no—
1135C22—42no—
1136C22—81no—
1137C22—81no—
1138C22—82no—
1139C22—82no—
1140C22—82no—
1141C22—84no—
1142C22—81no—
1143C22—81no—
1144C22—164no—
1145C22C2×#120×C6711yescharacteristic
1146C22D42×C6711yescharacteristic
1147C22D42×C6711yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—42no—
1152C4—41no—
1153C4—42no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—42no—
1158C4—81no—
1159C4C2×#120×C6711yescharacteristic
1160C4#534×C6711yescharacteristic
1161C4D42×C6711yescharacteristic
1162C4D42×C6711yescharacteristic
1163C2—21no—
1164C2—21no—
1165C2—41no—
1166C2—41no—
1167C2—42no—
1168C2—82no—
1169C2—81no—
1170C2—82no—
1171C2—81no—
1172C2C67×#240311yescharacteristic
1173C2C67×#301811yescharacteristic
1174C2C67×#301911yescharacteristic
subgroupG/H
center, socleC22×C67C2×#120
commutator, Frattini, cosocleC22×C4C24×C67
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#575×C67C2semidirect
2. C67×#3488C2semidirect
3. C2×#455×C67C2semidirect
4. C2×#453×C67C2semidirect
5. C67×#3005C2semidirect
6. C67×#2431C2semidirect
7. C67×#2007C2semidirect
8. C67×#2006C2semidirect
9. C67×#2004C2semidirect
10. C67×#2002C2semidirect
11. C67×#1900C2semidirect
12. C67×#1883C2semidirect
13. C67×#1882C2semidirect
14. C67×#1871C2semidirect
15. C67×#1789C2semidirect
18. C22×#41×C67C22semidirect
23. C2×#137×C67C22semidirect
24. C2×#137×C67C22semidirect
27. C2×AGL(1,ℤ/8)×C67C22semidirect
28. C2×AGL(1,ℤ/8)×C67C22semidirect
31. C22×M16×C67C22semidirect
42. C2×#127×C67C22semidirect
43. C2×#124×C67C22semidirect
57. C2×#104×C67C22semidirect
58. C2×#104×C67C22semidirect
59. C2×#104×C67C22semidirect
60. C2×#104×C67C22semidirect
61. #419×C67C22semidirect
62. #418×C67C22semidirect
63. C2×#100×C67C22semidirect
64. C2×#100×C67C22semidirect
65. #407×C67C22semidirect
67. #391×C67C22semidirect
68. #390×C67C22semidirect
70. C4×C22⋊C4×C67C22semidirect
71. #343×C67C22semidirect
72. #343×C67C22semidirect
73. #339×C67C22semidirect
74. #339×C67C22semidirect
95. C2×#41×C67D4semidirect
96. C2×#41×C67D4semidirect
100. C22×Q8×C67D4semidirect
110. C22×D4×C67D4semidirect
122. #137×C67D4semidirect
129. AGL(1,ℤ/8)×C67D4semidirect
165. C22⋊Q8×C67D4semidirect
166. C22⋊Q8×C67D4semidirect
181. #121×C67D4semidirect
182. #121×C67D4semidirect
270. C2×Q8×C67C2×D4semidirect
319. C2×D4×C67C2×D4semidirect
367. M16×C67C2×D4semidirect
368. M16×C67C2×D4semidirect
575. #23878C67direct (N × H)
588. C2×#575C2×C67semidirect
589. #3488C2×C67semidirect
590. C2×#455C2×C67semidirect
591. C2×#453C2×C67semidirect
592. #3005C2×C67semidirect
593. #2431C2×C67semidirect
594. #2007C2×C67semidirect
595. #2006C2×C67semidirect
596. #2004C2×C67semidirect
597. #2002C2×C67semidirect
598. #1900C2×C67semidirect
599. #1883C2×C67semidirect
600. #1882C2×C67semidirect
601. #1871C2×C67semidirect
602. #1789C2×C67semidirect
603. C67#23878direct (N × H)
606. C22×#41C22×C67semidirect
611. C2×#137C22×C67semidirect
612. C2×#137C22×C67semidirect
615. C2×AGL(1,ℤ/8)C22×C67semidirect
616. C2×AGL(1,ℤ/8)C22×C67semidirect
619. C22×M16C22×C67semidirect
630. C2×#127C22×C67semidirect
631. C2×#124C22×C67semidirect
645. C2×#104C22×C67semidirect
646. C2×#104C22×C67semidirect
647. C2×#104C22×C67semidirect
648. C2×#104C22×C67semidirect
649. #419C22×C67semidirect
650. #418C22×C67semidirect
651. C2×#100C22×C67semidirect
652. C2×#100C22×C67semidirect
653. #407C22×C67semidirect
655. #391C22×C67semidirect
656. #390C22×C67semidirect
658. C4×C22⋊C4C22×C67semidirect
659. #343C22×C67semidirect
660. #343C22×C67semidirect
661. #339C22×C67semidirect
662. #339C22×C67semidirect
683. C2×#41D4×C67semidirect
684. C2×#41D4×C67semidirect
688. C22×Q8D4×C67semidirect
698. C22×D4D4×C67semidirect
710. #137D4×C67semidirect
717. AGL(1,ℤ/8)D4×C67semidirect
753. C22⋊Q8D4×C67semidirect
754. C22⋊Q8D4×C67semidirect
769. #121D4×C67semidirect
770. #121D4×C67semidirect
858. C2×Q8C2×D4×C67semidirect
907. C2×D4C2×D4×C67semidirect
955. M16C2×D4×C67semidirect
956. M16C2×D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#575×C672
C67×#34882
C2×#455×C672
C2×#453×C672
C67×#30052
C67×#24312
C67×#20072
C67×#20062
C67×#20042
C67×#20022
C67×#19002
C67×#18832
C67×#18822
C67×#18712
C67×#17892
#2387867