Finite Group Databasebeta

← C67×#21557 #30700808

Subgroups — C67×#21557 #30700808

Order 17152.

906 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#471×C67C211yesmaximal, characteristic
2C4×#137×C67C211yesmaximal, characteristic, complemented
3C4×AGL(1,ℤ/8)×C67C211yesmaximal, characteristic
4C2×#440×C67C211yesmaximal, characteristic, complemented
5C67×#2875C211yesmaximal, characteristic, complemented
6C67×#1977C211yesmaximal, characteristic, complemented
7C67×#1952C211yesmaximal, characteristic, complemented
8C67×#1931C211yesmaximal, characteristic, complemented
9C67×#1930C211yesmaximal, characteristic, complemented
10C67×#1908C211yesmaximal, characteristic, complemented
11C67×#1907C211yesmaximal, characteristic
12C67×#1816C211yesmaximal, characteristic, complemented
13C67×#1778C211yesmaximal, characteristic, complemented
14C4×#101×C67C211yesmaximal, characteristic, complemented
15C4×#100×C67C211yesmaximal, characteristic, complemented
16C2×#137×C67C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C67C2211yescharacteristic
18C22×SD16×C67C2211yescharacteristic
19C2×#131×C67C2211yescharacteristic
20C2×#131×C67C2211yescharacteristic
21C4×#41×C67C2211yescharacteristic
22C2×C4×Q8×C67C2211yescharacteristic
23C2×C4×D4×C67C2211yescharacteristic
24#471×C67C418yescomplemented
25#442×C67—21no—
26#441×C67—21no—
27#440×C67—21no—
28#440×C67—21no—
29#440×C67—21no—
30#440×C67—21no—
31#440×C67—21no—
32#440×C67—21no—
33C4×Q16×C67—21no—
34C4×SD16×C67—21no—
35C4×SD16×C67—21no—
36C4×D8×C67—21no—
37C2×#108×C67C2211yescharacteristic
38C2×#108×C67C2211yescharacteristic
39#428×C67C2211yescharacteristic
40#428×C67C2211yescharacteristic
41C2×#107×C67C2211yescharacteristic
42#419×C67C2211yescharacteristic
43#418×C67C2211yescharacteristic
44#417×C67C2211yescharacteristic
45#417×C67C2211yescharacteristic
46C2×#103×C67C2211yescharacteristic
47C2×#102×C67C2211yescharacteristic
48C2×#101×C67C2211yescharacteristic
49C2×#101×C67C2211yescharacteristic
50C2×#100×C67C2211yescharacteristic
51C2×#100×C67C2211yescharacteristic
52#405×C67—21no—
53#405×C67—21no—
54#405×C67C2211yescharacteristic
55#405×C67C2211yescharacteristic
56C4×M16×C67—21no—
57C4×M16×C67C2211yescharacteristic
58C4×M16×C67C2211yescharacteristic
59C4×M16×C67C2211yescharacteristic
60C2×#97×C67—21no—
61C2×#97×C67C2211yescharacteristic
62#343×C67C2211yescharacteristic
63#343×C67C2211yescharacteristic
64#343×C67C2211yescharacteristic
65#343×C67C2211yescharacteristic
66#341×C67C2211yescharacteristic
67#341×C67C2211yescharacteristic
68C2×#41×C67C2311yescharacteristic
69C22×Q8×C67C2311yescharacteristic
70C22×D4×C67C2311yescharacteristic
71C23×C4×C67—21no—
72#137×C67—22no—
73#137×C67C2×C414yescomplemented
74AGL(1,ℤ/8)×C67—22no—
75AGL(1,ℤ/8)×C67C2×C414yes—
76C2×Q16×C67—21no—
77C2×SD16×C67—21no—
78C2×SD16×C67—21no—
79C2×SD16×C67—21no—
80C2×SD16×C67—21no—
81C2×SD16×C67—22no—
82C2×SD16×C67C2×C414yescomplemented
83C2×D8×C67—21no—
84#131×C67—22no—
85#131×C67—22no—
86#131×C67—22no—
87#131×C67C2×C414yescomplemented
88C2×M16×C67—21no—
89C2×M16×C67—21no—
90C2×M16×C67C2311yescharacteristic
91C2×M16×C67C2311yescharacteristic
92C2×M16×C67C2311yescharacteristic
93C2×M16×C67C2311yescharacteristic
94C2×M16×C67C2311yescharacteristic
95C2×M16×C67C2311yescharacteristic
96C22×C8×C67—21no—
97C22×C8×C67—21no—
98C22×C8×C67C2311yescharacteristic
99C22×C8×C67C2311yescharacteristic
100C4×Q8×C67—21no—
101C4×Q8×C67—21no—
102C4×Q8×C67—21no—
103C4×Q8×C67—21no—
104C4×Q8×C67D411yescharacteristic
105C4×Q8×C67D411yescharacteristic
106C4×D4×C67—21no—
107C4×D4×C67—21no—
108C4×D4×C67—21no—
109C4×D4×C67—21no—
110C4×D4×C67—21no—
111C4×D4×C67—21no—
112C4×D4×C67D411yescharacteristic
113C4×D4×C67D411yescharacteristic
114#117×C67—21no—
115#117×C67C2311yescharacteristic
116C2×C4⋊C4×C67—21no—
117C2×C4⋊C4×C67C2311yescharacteristic
118C2×C4⋊C4×C67C2311yescharacteristic
119C2×C22⋊C4×C67—21no—
120C2×C42×C67—21no—
121C2×C42×C67—21no—
122C2×C42×C67C2311yescharacteristic
123#108×C67—22no—
124#108×C67C2×C414yescomplemented
125#107×C67—21no—
126#107×C67—21no—
127#107×C67—21no—
128#107×C67—21no—
129#106×C67—21no—
130#106×C67—21no—
131#103×C67—21no—
132#103×C67—21no—
133#103×C67—21no—
134#103×C67—21no—
135#103×C67—21no—
136#103×C67—21no—
137#102×C67—21no—
138#102×C67—21no—
139#102×C67—21no—
140#102×C67—21no—
141#102×C67—21no—
142#102×C67—21no—
143#101×C67—22no—
144#101×C67C2×C414yescomplemented
145#100×C67—22no—
146#100×C67C2×C414yescomplemented
147#97×C67—21no—
148#97×C67—21no—
149#97×C67—21no—
150#97×C67—21no—
151#97×C67—21no—
152#97×C67D411yescharacteristic
153#97×C67D411yescharacteristic
154#97×C67D411yescharacteristic
155#97×C67D411yescharacteristic
156C4×C8×C67—21no—
157C4×C8×C67—21no—
158C4×C8×C67—21no—
159C4×C8×C67—21no—
160C4×C8×C67—21no—
161C24×C67—21no—
162#41×C67—21no—
163#41×C67—21no—
164#41×C67C22×C412yes—
165#41×C67#4112yes—
166C2×Q8×C67—21no—
167C2×Q8×C67—21no—
168C2×Q8×C67—21no—
169C2×Q8×C67—21no—
170C2×Q8×C67—21no—
171C2×Q8×C67C22×C412yes—
172C2×Q8×C67C2×D411yescharacteristic
173C2×D4×C67—21no—
174C2×D4×C67—21no—
175C2×D4×C67—21no—
176C2×D4×C67—21no—
177C2×D4×C67—21no—
178C2×D4×C67—21no—
179C2×D4×C67C22×C412yes—
180C2×D4×C67C2×D411yescharacteristic
181C22×C4×C67—21no—
182C22×C4×C67—21no—
183C22×C4×C67—21no—
184C22×C4×C67—21no—
185C22×C4×C67—21no—
186C22×C4×C67—21no—
187C22×C4×C67—41no—
188C22×C4×C67—41no—
189C22×C4×C67—82no—
190C22×C4×C67#4111yescharacteristic
191C22×C4×C67#4111yescharacteristic
192C22×C4×C67C2411yescharacteristic
193Q16×C67—24no—
194SD16×C67—24no—
195SD16×C67—24no—
196SD16×C67—24no—
197SD16×C67—24no—
198D8×C67—24no—
199M16×C67—24no—
200M16×C67—21no—
201M16×C67—21no—
202M16×C67—21no—
203M16×C67—21no—
204M16×C67—24no—
205M16×C67—21no—
206M16×C67—21no—
207M16×C67—21no—
208M16×C67—21no—
209M16×C67C22×C412yes—
210M16×C67C22×C412yes—
211M16×C67C22×C412yes—
212M16×C67#4112yes—
213C2×C8×C67—24no—
214C2×C8×C67—21no—
215C2×C8×C67—21no—
216C2×C8×C67—21no—
217C2×C8×C67—21no—
218C2×C8×C67—21no—
219C2×C8×C67—21no—
220C2×C8×C67—24no—
221C2×C8×C67—21no—
222C2×C8×C67—21no—
223C2×C8×C67C22×C412yes—
224C2×C8×C67C2×D411yescharacteristic
225C2×C8×C67C2×D411yescharacteristic
226C2×C8×C67C2×D411yescharacteristic
227C2×C8×C67C2×D411yescharacteristic
228C2×C8×C67#4112yes—
229C4⋊C4×C67—21no—
230C4⋊C4×C67—21no—
231C4⋊C4×C67—21no—
232C4⋊C4×C67—21no—
233C4⋊C4×C67—21no—
234C4⋊C4×C67—21no—
235C4⋊C4×C67—41no—
236C4⋊C4×C67—41no—
237C4⋊C4×C67C2×D411yescharacteristic
238C4⋊C4×C67C2×D411yescharacteristic
239C22⋊C4×C67—21no—
240C22⋊C4×C67—21no—
241C22⋊C4×C67—21no—
242C22⋊C4×C67—41no—
243C22⋊C4×C67—41no—
244C42×C67—21no—
245C42×C67—21no—
246C42×C67—21no—
247C42×C67—41no—
248C42×C67—41no—
249C42×C67C2×D411yescharacteristic
250C42×C67C2×D411yescharacteristic
251C42×C67C2×D411yescharacteristic
252C42×C67C2×D411yescharacteristic
253C23×C67—21no—
254C23×C67—22no—
255C23×C67—41no—
256C23×C67—41no—
257C23×C67—81no—
258C23×C67—81no—
259C23×C67C2×#4111yescharacteristic
260Q8×C67—21no—
261Q8×C67—22no—
262Q8×C67—22no—
263Q8×C67—41no—
264Q8×C67—41no—
265Q8×C67C4×D412yes—
266D4×C67—22no—
267D4×C67—22no—
268D4×C67—22no—
269D4×C67—22no—
270D4×C67—21no—
271D4×C67—41no—
272D4×C67—41no—
273D4×C67C4×D412yes—
274C2×C4×C67—21no—
275C2×C4×C67—22no—
276C2×C4×C67—22no—
277C2×C4×C67—22no—
278C2×C4×C67—21no—
279C2×C4×C67—21no—
280C2×C4×C67—41no—
281C2×C4×C67—41no—
282C2×C4×C67—41no—
283C2×C4×C67—41no—
284C2×C4×C67—41no—
285C2×C4×C67—41no—
286C2×C4×C67—81no—
287C2×C4×C67—81no—
288C2×C4×C67—82no—
289C2×C4×C67—82no—
290C2×C4×C67—81no—
291C2×C4×C67—81no—
292C2×C4×C67#12111yescharacteristic
293C2×C4×C67#12111yescharacteristic
294C2×C4×C67#12111yescharacteristic
295C2×C4×C67#12111yescharacteristic
296C2×C4×C67C23×C411yescharacteristic
297C2×C4×C67C22×D411yescharacteristic
298C2×C4×C67C22×D411yescharacteristic
299C2×C4×C67C2×#4111yescharacteristic
300C2×C4×C67C2×#4111yescharacteristic
301C2×C4×C67C2×#4111yescharacteristic
302C8×C67—22no—
303C8×C67—22no—
304C8×C67—22no—
305C8×C67—21no—
306C8×C67—22no—
307C8×C67—21no—
308C8×C67—41no—
309C8×C67—41no—
310C8×C67C4×D412yes—
311C8×C67C4×D412yes—
312C22×C67—21no—
313C22×C67—21no—
314C22×C67—22no—
315C22×C67—41no—
316C22×C67—41no—
317C22×C67—42no—
318C22×C67—82no—
319C22×C67—82no—
320C22×C67—81no—
321C22×C67—81no—
322C22×C67C4×#4111yescharacteristic
323C22×C67C2×#12111yescharacteristic
324C22×C67#52911yescharacteristic
325C4×C67—22no—
326C4×C67—21no—
327C4×C67—21no—
328C4×C67—21no—
329C4×C67—21no—
330C4×C67—42no—
331C4×C67—41no—
332C4×C67—41no—
333C4×C67—81no—
334C4×C67—81no—
335C4×C67C2×C4×D411yescharacteristic
336C4×C67C2×C4×D411yescharacteristic
337C4×C67#52511yescharacteristic
338C4×C67#53211yescharacteristic
339#21557C6711yesmaximal, characteristic, direct product factor, Sylow
340C2×C67—21no—
341C2×C67—21no—
342C2×C67—42no—
343C2×C67—82no—
344C2×C67C4×#12111yescharacteristic
345C2×C67#306811yescharacteristic
346C2×C67#306911yescharacteristic
347C2×#471C2×C6711yescharacteristic
348C4×#137C2×C6711yescharacteristic, complemented
349C4×AGL(1,ℤ/8)C2×C6711yescharacteristic
350C2×#440C2×C6711yescharacteristic, complemented
351#2875C2×C6711yescharacteristic, complemented
352#1977C2×C6711yescharacteristic, complemented
353#1952C2×C6711yescharacteristic, complemented
354#1931C2×C6711yescharacteristic, complemented
355#1930C2×C6711yescharacteristic, complemented
356#1908C2×C6711yescharacteristic, complemented
357#1907C2×C6711yescharacteristic
358#1816C2×C6711yescharacteristic, complemented
359#1778C2×C6711yescharacteristic, complemented
360C4×#101C2×C6711yescharacteristic, complemented
361C4×#100C2×C6711yescharacteristic, complemented
362C67#2155711yescharacteristic, direct product factor, Sylow
363C2×#137C22×C6711yescharacteristic
364C2×AGL(1,ℤ/8)C22×C6711yescharacteristic
365C22×SD16C22×C6711yescharacteristic
366C2×#131C22×C6711yescharacteristic
367C2×#131C22×C6711yescharacteristic
368C4×#41C22×C6711yescharacteristic
369C2×C4×Q8C22×C6711yescharacteristic
370C2×C4×D4C22×C6711yescharacteristic
371#471C4×C6718yescomplemented
372#442—21no—
373#441—21no—
374#440—21no—
375#440—21no—
376#440—21no—
377#440—21no—
378#440—21no—
379#440—21no—
380C4×Q16—21no—
381C4×SD16—21no—
382C4×SD16—21no—
383C4×D8—21no—
384C2×#108C22×C6711yescharacteristic
385C2×#108C22×C6711yescharacteristic
386#428C22×C6711yescharacteristic
387#428C22×C6711yescharacteristic
388C2×#107C22×C6711yescharacteristic
389#419C22×C6711yescharacteristic
390#418C22×C6711yescharacteristic
391#417C22×C6711yescharacteristic
392#417C22×C6711yescharacteristic
393C2×#103C22×C6711yescharacteristic
394C2×#102C22×C6711yescharacteristic
395C2×#101C22×C6711yescharacteristic
396C2×#101C22×C6711yescharacteristic
397C2×#100C22×C6711yescharacteristic
398C2×#100C22×C6711yescharacteristic
399#405—21no—
400#405—21no—
401#405C22×C6711yescharacteristic
402#405C22×C6711yescharacteristic
403C4×M16—21no—
404C4×M16C22×C6711yescharacteristic
405C4×M16C22×C6711yescharacteristic
406C4×M16C22×C6711yescharacteristic
407C2×#97—21no—
408C2×#97C22×C6711yescharacteristic
409#343C22×C6711yescharacteristic
410#343C22×C6711yescharacteristic
411#343C22×C6711yescharacteristic
412#343C22×C6711yescharacteristic
413#341C22×C6711yescharacteristic
414#341C22×C6711yescharacteristic
415C2×#41C23×C6711yescharacteristic
416C22×Q8C23×C6711yescharacteristic
417C22×D4C23×C6711yescharacteristic
418C23×C4—21no—
419#137—22no—
420#137C2×C4×C6714yescomplemented
421AGL(1,ℤ/8)—22no—
422AGL(1,ℤ/8)C2×C4×C6714yes—
423C2×Q16—21no—
424C2×SD16—21no—
425C2×SD16—21no—
426C2×SD16—21no—
427C2×SD16—21no—
428C2×SD16—22no—
429C2×SD16C2×C4×C6714yescomplemented
430C2×D8—21no—
431#131—22no—
432#131—22no—
433#131—22no—
434#131C2×C4×C6714yescomplemented
435C2×M16—21no—
436C2×M16—21no—
437C2×M16C23×C6711yescharacteristic
438C2×M16C23×C6711yescharacteristic
439C2×M16C23×C6711yescharacteristic
440C2×M16C23×C6711yescharacteristic
441C2×M16C23×C6711yescharacteristic
442C2×M16C23×C6711yescharacteristic
443C22×C8—21no—
444C22×C8—21no—
445C22×C8C23×C6711yescharacteristic
446C22×C8C23×C6711yescharacteristic
447C4×Q8—21no—
448C4×Q8—21no—
449C4×Q8—21no—
450C4×Q8—21no—
451C4×Q8D4×C6711yescharacteristic
452C4×Q8D4×C6711yescharacteristic
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4—21no—
458C4×D4—21no—
459C4×D4D4×C6711yescharacteristic
460C4×D4D4×C6711yescharacteristic
461#117—21no—
462#117C23×C6711yescharacteristic
463C2×C4⋊C4—21no—
464C2×C4⋊C4C23×C6711yescharacteristic
465C2×C4⋊C4C23×C6711yescharacteristic
466C2×C22⋊C4—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42C23×C6711yescharacteristic
470#108—22no—
471#108C2×C4×C6714yescomplemented
472#107—21no—
473#107—21no—
474#107—21no—
475#107—21no—
476#106—21no—
477#106—21no—
478#103—21no—
479#103—21no—
480#103—21no—
481#103—21no—
482#103—21no—
483#103—21no—
484#102—21no—
485#102—21no—
486#102—21no—
487#102—21no—
488#102—21no—
489#102—21no—
490#101—22no—
491#101C2×C4×C6714yescomplemented
492#100—22no—
493#100C2×C4×C6714yescomplemented
494#97—21no—
495#97—21no—
496#97—21no—
497#97—21no—
498#97—21no—
499#97D4×C6711yescharacteristic
500#97D4×C6711yescharacteristic
501#97D4×C6711yescharacteristic
502#97D4×C6711yescharacteristic
503C4×C8—21no—
504C4×C8—21no—
505C4×C8—21no—
506C4×C8—21no—
507C4×C8—21no—
508C24—21no—
509#41—21no—
510#41—21no—
511#41C22×C4×C6712yes—
512#41#41×C6712yes—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8C22×C4×C6712yes—
519C2×Q8C2×D4×C6711yescharacteristic
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4C22×C4×C6712yes—
527C2×D4C2×D4×C6711yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—82no—
537C22×C4#41×C6711yescharacteristic
538C22×C4#41×C6711yescharacteristic
539C22×C4C24×C6711yescharacteristic
540Q16—24no—
541SD16—24no—
542SD16—24no—
543SD16—24no—
544SD16—24no—
545D8—24no—
546M16—24no—
547M16—21no—
548M16—21no—
549M16—21no—
550M16—21no—
551M16—24no—
552M16—21no—
553M16—21no—
554M16—21no—
555M16—21no—
556M16C22×C4×C6712yes—
557M16C22×C4×C6712yes—
558M16C22×C4×C6712yes—
559M16#41×C6712yes—
560C2×C8—24no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—24no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8C22×C4×C6712yes—
571C2×C8C2×D4×C6711yescharacteristic
572C2×C8C2×D4×C6711yescharacteristic
573C2×C8C2×D4×C6711yescharacteristic
574C2×C8C2×D4×C6711yescharacteristic
575C2×C8#41×C6712yes—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4C2×D4×C6711yescharacteristic
585C4⋊C4C2×D4×C6711yescharacteristic
586C22⋊C4—21no—
587C22⋊C4—21no—
588C22⋊C4—21no—
589C22⋊C4—41no—
590C22⋊C4—41no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—41no—
595C42—41no—
596C42C2×D4×C6711yescharacteristic
597C42C2×D4×C6711yescharacteristic
598C42C2×D4×C6711yescharacteristic
599C42C2×D4×C6711yescharacteristic
600C23—21no—
601C23—22no—
602C23—41no—
603C23—41no—
604C23—81no—
605C23—81no—
606C23C2×#41×C6711yescharacteristic
607Q8—21no—
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8C4×D4×C6712yes—
613D4—22no—
614D4—22no—
615D4—22no—
616D4—22no—
617D4—21no—
618D4—41no—
619D4—41no—
620D4C4×D4×C6712yes—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—82no—
636C2×C4—82no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4#121×C6711yescharacteristic
640C2×C4#121×C6711yescharacteristic
641C2×C4#121×C6711yescharacteristic
642C2×C4#121×C6711yescharacteristic
643C2×C4C23×C4×C6711yescharacteristic
644C2×C4C22×D4×C6711yescharacteristic
645C2×C4C22×D4×C6711yescharacteristic
646C2×C4C2×#41×C6711yescharacteristic
647C2×C4C2×#41×C6711yescharacteristic
648C2×C4C2×#41×C6711yescharacteristic
649C8—22no—
650C8—22no—
651C8—22no—
652C8—21no—
653C8—22no—
654C8—21no—
655C8—41no—
656C8—41no—
657C8C4×D4×C6712yes—
658C8C4×D4×C6712yes—
659C22—21no—
660C22—21no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—82no—
666C22—82no—
667C22—81no—
668C22—81no—
669C22C4×#41×C6711yescharacteristic
670C22C2×#121×C6711yescharacteristic
671C22#529×C6711yescharacteristic
672C4—22no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—42no—
678C4—41no—
679C4—41no—
680C4—81no—
681C4—81no—
682C4C2×C4×D4×C6711yescharacteristic
683C4C2×C4×D4×C6711yescharacteristic
684C4#525×C6711yescharacteristic
685C4#532×C6711yescharacteristic
686C2—21no—
687C2—21no—
688C2—42no—
689C2—82no—
690C2C4×#121×C6711yescharacteristic
691C2C67×#306811yescharacteristic
692C2C67×#306911yescharacteristic
subgroupG/H
center, socleC22×C67C2×#121
commutatorC2×C4C23×C4×C67
Frattini, cosocleC22×C4C24×C67
prime radicalC2×AGL(1,ℤ/8)×C67C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#137×C67C2semidirect
4. C2×#440×C67C2semidirect
5. C67×#2875C2semidirect
6. C67×#1977C2semidirect
7. C67×#1952C2semidirect
8. C67×#1931C2semidirect
9. C67×#1930C2semidirect
10. C67×#1908C2semidirect
12. C67×#1816C2semidirect
13. C67×#1778C2semidirect
14. C4×#101×C67C2semidirect
15. C4×#100×C67C2semidirect
24. #471×C67C4semidirect
73. #137×C67C2×C4semidirect
82. C2×SD16×C67C2×C4semidirect
87. #131×C67C2×C4semidirect
124. #108×C67C2×C4semidirect
144. #101×C67C2×C4semidirect
146. #100×C67C2×C4semidirect
339. #21557C67direct (N × H)
348. C4×#137C2×C67semidirect
350. C2×#440C2×C67semidirect
351. #2875C2×C67semidirect
352. #1977C2×C67semidirect
353. #1952C2×C67semidirect
354. #1931C2×C67semidirect
355. #1930C2×C67semidirect
356. #1908C2×C67semidirect
358. #1816C2×C67semidirect
359. #1778C2×C67semidirect
360. C4×#101C2×C67semidirect
361. C4×#100C2×C67semidirect
362. C67#21557direct (N × H)
371. #471C4×C67semidirect
420. #137C2×C4×C67semidirect
429. C2×SD16C2×C4×C67semidirect
434. #131C2×C4×C67semidirect
471. #108C2×C4×C67semidirect
491. #101C2×C4×C67semidirect
493. #100C2×C4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#471×C672
C4×#137×C672
C4×AGL(1,ℤ/8)×C672
C2×#440×C672
C67×#28752
C67×#19772
C67×#19522
C67×#19312
C67×#19302
C67×#19082
C67×#19072
C67×#18162
C67×#17782
C4×#101×C672
C4×#100×C672
#2155767