Finite Group Databasebeta

← C67×#24471 #30703722

Subgroups — C67×#24471 #30703722

Order 17152.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3488C211yesmaximal, characteristic
2C67×#3056C211yesmaximal, characteristic, complemented
3C2×#455×C67C211yesmaximal, characteristic, complemented
4C67×#3007C211yesmaximal, characteristic, complemented
5C2×#421×C67C211yesmaximal, characteristic, complemented
6C67×#2620C211yesmaximal, characteristic, complemented
7C67×#2039C211yesmaximal, characteristic, complemented
8C67×#2037C211yesmaximal, characteristic, complemented
9C67×#2007C211yesmaximal, characteristic, complemented
10C67×#2004C211yesmaximal, characteristic, complemented
11C67×#1900C211yesmaximal, characteristic, complemented
12C67×#1897C211yesmaximal, characteristic, complemented
13C67×#1882C211yesmaximal, characteristic, complemented
14C67×#1859C211yesmaximal, characteristic, complemented
15C67×#1792C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C67C2211yescharacteristic
17C22×#41×C67C2211yescharacteristic
18C2×#137×C67C2211yescharacteristic
19C2×#137×C67C2211yescharacteristic, complemented
20C2×#137×C67C2211yescharacteristic, complemented
21C22×M16×C67C2211yescharacteristic, complemented
22#550×C67—21no—
23#548×C67—21no—
24#546×C67—21no—
25#546×C67—22no—
26D42×C67—22no—
27D42×C67—21no—
28#537×C67—21no—
29#537×C67C2211yescharacteristic
30#535×C67—21no—
31#535×C67C2211yescharacteristic
32C2×#124×C67C2211yescharacteristic, complemented
33#525×C67—21no—
34#525×C67C2211yescharacteristic
35C2×C22⋊Q8×C67C2211yescharacteristic, complemented
36C2×#121×C67—21no—
37C2×#121×C67C2211yescharacteristic
38#520×C67C2211yescharacteristic
39C2×#117×C67C2211yescharacteristic, complemented
40#470×C67—21no—
41#468×C67—21no—
42#467×C67—21no—
43#465×C67—21no—
44#455×C67—24no—
45#452×C67—21no—
46#452×C67—21no—
47#451×C67—21no—
48#450×C67—21no—
49#428×C67C2211yescharacteristic, complemented
50#421×C67—24no—
51C2×#104×C67C2211yescharacteristic
52C2×#104×C67C2211yescharacteristic
53C2×#104×C67C2211yescharacteristic, complemented
54C2×#104×C67C2211yescharacteristic, complemented
55C2×#104×C67C2211yescharacteristic, complemented
56C2×#104×C67C2211yescharacteristic, complemented
57#419×C67C2211yescharacteristic, complemented
58#417×C67C2211yescharacteristic
59#417×C67C2211yescharacteristic, complemented
60#417×C67C2211yescharacteristic, complemented
61C2×#100×C67C2211yescharacteristic, complemented
62C2×#100×C67C2211yescharacteristic, complemented
63#407×C67C2211yescharacteristic, complemented
64#396×C67—22no—
65#394×C67—22no—
66#391×C67C2211yescharacteristic, complemented
67#390×C67C2211yescharacteristic, complemented
68#384×C67C2211yescharacteristic, complemented
69#343×C67C2211yescharacteristic, complemented
70#343×C67C2211yescharacteristic, complemented
71#339×C67C2211yescharacteristic, complemented
72#339×C67C2211yescharacteristic, complemented
73H(5,𝔽2)×C67—22no—
74H(5,𝔽2)×C67—22no—
75H(5,𝔽2)×C67—41no—
76H(5,𝔽2)×C67—41no—
77C2×#41×C67—21no—
78C2×#41×C67—21no—
79C2×#41×C67—21no—
80C2×#41×C67—21no—
81C2×#41×C67—22no—
82C2×#41×C67—22no—
83C2×#41×C67—41no—
84C2×#41×C67—41no—
85C2×#41×C67D411yescharacteristic
86C2×#41×C67D411yescharacteristic
87C2×#41×C67C2311yescharacteristic
88C2×#41×C67C2311yescharacteristic
89C2×#41×C67C2311yescharacteristic
90C22×Q8×C67D411yescharacteristic
91C22×Q8×C67C2311yescharacteristic
92C22×D4×C67—21no—
93C22×D4×C67—22no—
94C22×D4×C67—22no—
95C22×D4×C67—21no—
96C22×D4×C67—21no—
97C22×D4×C67D411yescharacteristic
98C22×D4×C67D412yes—
99C22×D4×C67C2311yescharacteristic
100C23×C4×C67—21no—
101C23×C4×C67C2311yescharacteristic
102#137×C67—22no—
103#137×C67—22no—
104#137×C67—22no—
105#137×C67—41no—
106#137×C67—41no—
107#137×C67—41no—
108C2×Q16×C67—21no—
109C2×Q16×C67—21no—
110C2×Q16×C67—21no—
111C2×SD16×C67—21no—
112C2×SD16×C67—21no—
113C2×SD16×C67—21no—
114C2×M16×C67—21no—
115C2×M16×C67—22no—
116C2×M16×C67—41no—
117C2×M16×C67C2311yescharacteristic
118C2×M16×C67C2311yescharacteristic
119C2×M16×C67C2311yescharacteristic
120C2×M16×C67C2311yescharacteristic
121C22×C8×C67—21no—
122#127×C67—22no—
123#127×C67—21no—
124#124×C67—22no—
125#124×C67—21no—
126#124×C67—22no—
127#124×C67—41no—
128#123×C67—22no—
129#123×C67—21no—
130C22⋊Q8×C67—22no—
131C22⋊Q8×C67—21no—
132C22⋊Q8×C67—21no—
133C22⋊Q8×C67—21no—
134C22⋊Q8×C67—21no—
135C22⋊Q8×C67—21no—
136C22⋊Q8×C67—21no—
137C22⋊Q8×C67D411yescharacteristic
138C22⋊Q8×C67D411yescharacteristic
139#121×C67—22no—
140#121×C67—22no—
141#121×C67—22no—
142#121×C67—22no—
143#121×C67—22no—
144#121×C67—21no—
145#121×C67—21no—
146#121×C67—21no—
147#121×C67—21no—
148#121×C67—21no—
149#121×C67—21no—
150#121×C67—22no—
151#121×C67—21no—
152#121×C67—21no—
153#121×C67D411yescharacteristic
154#121×C67D411yescharacteristic
155#120×C67—22no—
156#120×C67—22no—
157#120×C67—22no—
158#120×C67—21no—
159#120×C67—22no—
160C4×Q8×C67—21no—
161C4×D4×C67—22no—
162C4×D4×C67—22no—
163C4×D4×C67—21no—
164C4×D4×C67—22no—
165C4×D4×C67—21no—
166C4×D4×C67—21no—
167#117×C67—21no—
168#117×C67—22no—
169#117×C67—41no—
170#117×C67C2311yescharacteristic
171C2×C4⋊C4×C67—21no—
172C2×C4⋊C4×C67—21no—
173C2×C4⋊C4×C67—21no—
174C2×C4⋊C4×C67—22no—
175C2×C4⋊C4×C67C2311yescharacteristic
176C2×C4⋊C4×C67C2311yescharacteristic
177C2×C22⋊C4×C67—22no—
178C2×C22⋊C4×C67—21no—
179C2×C22⋊C4×C67—21no—
180C2×C22⋊C4×C67—22no—
181C2×C22⋊C4×C67—22no—
182C2×C22⋊C4×C67D412yes—
183C2×C42×C67C2311yescharacteristic
184C2×C42×C67C2311yescharacteristic
185#107×C67—21no—
186#106×C67—21no—
187#104×C67—22no—
188#104×C67—22no—
189#104×C67—22no—
190#104×C67—22no—
191#104×C67—41no—
192#104×C67D414yescomplemented
193#103×C67—21no—
194#103×C67—21no—
195#103×C67—21no—
196#103×C67—21no—
197#103×C67—21no—
198#102×C67—21no—
199#102×C67—21no—
200#102×C67—21no—
201#100×C67—22no—
202#100×C67—41no—
203C22⋊C8×C67—21no—
204C22⋊C8×C67—21no—
205#95×C67—22no—
206C24×C67—22no—
207C24×C67—21no—
208C24×C67C2×D412yes—
209C24×C67C2×D411yescharacteristic
210#41×C67—21no—
211#41×C67—21no—
212#41×C67—22no—
213#41×C67—22no—
214#41×C67—21no—
215#41×C67—21no—
216#41×C67—21no—
217#41×C67—21no—
218#41×C67—21no—
219#41×C67—21no—
220#41×C67—21no—
221#41×C67—21no—
222#41×C67—42no—
223#41×C67—42no—
224#41×C67—41no—
225#41×C67—41no—
226#41×C67—42no—
227#41×C67—42no—
228#41×C67—42no—
229#41×C67—42no—
230#41×C67—42no—
231#41×C67—42no—
232#41×C67C2×D412yes—
233#41×C67#4112yes—
234C2×Q8×C67—21no—
235C2×Q8×C67—22no—
236C2×Q8×C67—21no—
237C2×Q8×C67—21no—
238C2×Q8×C67—21no—
239C2×Q8×C67—21no—
240C2×Q8×C67—21no—
241C2×Q8×C67—21no—
242C2×Q8×C67—41no—
243C2×Q8×C67C2×D411yescharacteristic
244C2×Q8×C67C2×D411yescharacteristic
245C2×Q8×C67C2×D411yescharacteristic
246C2×D4×C67—21no—
247C2×D4×C67—22no—
248C2×D4×C67—22no—
249C2×D4×C67—22no—
250C2×D4×C67—22no—
251C2×D4×C67—21no—
252C2×D4×C67—21no—
253C2×D4×C67—21no—
254C2×D4×C67—21no—
255C2×D4×C67—21no—
256C2×D4×C67—22no—
257C2×D4×C67—22no—
258C2×D4×C67—22no—
259C2×D4×C67—21no—
260C2×D4×C67—22no—
261C2×D4×C67—21no—
262C2×D4×C67—21no—
263C2×D4×C67—21no—
264C2×D4×C67—21no—
265C2×D4×C67—21no—
266C2×D4×C67—21no—
267C2×D4×C67—21no—
268C2×D4×C67—41no—
269C2×D4×C67—42no—
270C2×D4×C67—42no—
271C2×D4×C67—42no—
272C2×D4×C67—42no—
273C2×D4×C67—44no—
274C2×D4×C67—44no—
275C2×D4×C67—42no—
276C2×D4×C67—42no—
277C2×D4×C67—82no—
278C2×D4×C67—84no—
279C2×D4×C67C2×D411yescharacteristic
280C2×D4×C67C2×D411yescharacteristic
281C2×D4×C67C2×D411yescharacteristic
282C22×C4×C67—21no—
283C22×C4×C67—21no—
284C22×C4×C67—21no—
285C22×C4×C67—21no—
286C22×C4×C67—21no—
287C22×C4×C67—22no—
288C22×C4×C67—21no—
289C22×C4×C67—21no—
290C22×C4×C67—22no—
291C22×C4×C67—21no—
292C22×C4×C67—21no—
293C22×C4×C67—21no—
294C22×C4×C67—21no—
295C22×C4×C67—21no—
296C22×C4×C67—21no—
297C22×C4×C67—21no—
298C22×C4×C67—42no—
299C22×C4×C67—42no—
300C22×C4×C67C2×D411yescharacteristic
301C22×C4×C67C2×D411yescharacteristic
302C22×C4×C67C2×D411yescharacteristic
303C22×C4×C67C2×D411yescharacteristic
304C22×C4×C67C2×D411yescharacteristic
305C22×C4×C67C2×D412yes—
306C22×C4×C67C2411yescharacteristic
307Q16×C67—42no—
308Q16×C67—42no—
309Q16×C67—42no—
310SD16×C67—42no—
311SD16×C67—42no—
312SD16×C67—42no—
313M16×C67—21no—
314M16×C67—21no—
315M16×C67—21no—
316M16×C67—21no—
317M16×C67—21no—
318M16×C67—21no—
319M16×C67—21no—
320M16×C67—42no—
321M16×C67C2×D412yescomplemented
322C2×C8×C67—21no—
323C2×C8×C67—21no—
324C2×C8×C67—21no—
325C2×C8×C67—21no—
326C2×C8×C67—42no—
327C4⋊C4×C67—22no—
328C4⋊C4×C67—22no—
329C4⋊C4×C67—21no—
330C4⋊C4×C67—21no—
331C4⋊C4×C67—21no—
332C4⋊C4×C67—21no—
333C4⋊C4×C67—21no—
334C4⋊C4×C67—21no—
335C4⋊C4×C67—42no—
336C4⋊C4×C67—41no—
337C4⋊C4×C67—41no—
338C4⋊C4×C67—82no—
339C4⋊C4×C67C2×D411yescharacteristic
340C4⋊C4×C67C2×D411yescharacteristic
341C22⋊C4×C67—22no—
342C22⋊C4×C67—22no—
343C22⋊C4×C67—22no—
344C22⋊C4×C67—22no—
345C22⋊C4×C67—22no—
346C22⋊C4×C67—21no—
347C22⋊C4×C67—21no—
348C22⋊C4×C67—21no—
349C22⋊C4×C67—21no—
350C22⋊C4×C67—22no—
351C22⋊C4×C67—22no—
352C22⋊C4×C67—21no—
353C22⋊C4×C67—42no—
354C22⋊C4×C67—44no—
355C22⋊C4×C67—41no—
356C22⋊C4×C67—41no—
357C22⋊C4×C67—82no—
358C42×C67—22no—
359C42×C67—21no—
360C42×C67—21no—
361C42×C67—21no—
362C42×C67—21no—
363C42×C67C2×D412yescomplemented
364C23×C67—21no—
365C23×C67—21no—
366C23×C67—21no—
367C23×C67—22no—
368C23×C67—21no—
369C23×C67—21no—
370C23×C67—22no—
371C23×C67—22no—
372C23×C67—41no—
373C23×C67—41no—
374C23×C67—42no—
375C23×C67—42no—
376C23×C67—44no—
377C23×C67—42no—
378C23×C67—42no—
379C23×C67—81no—
380C23×C67—82no—
381C23×C67—82no—
382C23×C67#12011yescharacteristic
383C23×C67#12011yescharacteristic
384C23×C67C22×D411yescharacteristic
385Q8×C67—21no—
386Q8×C67—21no—
387Q8×C67—21no—
388Q8×C67—21no—
389Q8×C67—21no—
390Q8×C67—42no—
391Q8×C67—41no—
392Q8×C67—41no—
393Q8×C67—41no—
394Q8×C67—41no—
395Q8×C67#12112yes—
396D4×C67—22no—
397D4×C67—22no—
398D4×C67—21no—
399D4×C67—21no—
400D4×C67—21no—
401D4×C67—21no—
402D4×C67—21no—
403D4×C67—42no—
404D4×C67—42no—
405D4×C67—44no—
406D4×C67—42no—
407D4×C67—44no—
408D4×C67—44no—
409D4×C67—42no—
410D4×C67—41no—
411D4×C67—41no—
412D4×C67—41no—
413D4×C67—41no—
414D4×C67—41no—
415D4×C67—41no—
416D4×C67—41no—
417D4×C67—41no—
418D4×C67—81no—
419D4×C67—82no—
420D4×C67—82no—
421D4×C67—82no—
422D4×C67—82no—
423D4×C67#12112yes—
424C2×C4×C67—21no—
425C2×C4×C67—21no—
426C2×C4×C67—21no—
427C2×C4×C67—21no—
428C2×C4×C67—21no—
429C2×C4×C67—21no—
430C2×C4×C67—21no—
431C2×C4×C67—21no—
432C2×C4×C67—21no—
433C2×C4×C67—22no—
434C2×C4×C67—21no—
435C2×C4×C67—21no—
436C2×C4×C67—22no—
437C2×C4×C67—21no—
438C2×C4×C67—22no—
439C2×C4×C67—21no—
440C2×C4×C67—21no—
441C2×C4×C67—21no—
442C2×C4×C67—22no—
443C2×C4×C67—42no—
444C2×C4×C67—42no—
445C2×C4×C67—42no—
446C2×C4×C67—44no—
447C2×C4×C67—41no—
448C2×C4×C67—41no—
449C2×C4×C67—41no—
450C2×C4×C67—41no—
451C2×C4×C67—41no—
452C2×C4×C67—41no—
453C2×C4×C67—42no—
454C2×C4×C67—41no—
455C2×C4×C67—42no—
456C2×C4×C67—41no—
457C2×C4×C67—41no—
458C2×C4×C67—41no—
459C2×C4×C67—41no—
460C2×C4×C67—41no—
461C2×C4×C67—41no—
462C2×C4×C67—82no—
463C2×C4×C67#12011yescharacteristic
464C2×C4×C67#12011yescharacteristic
465C2×C4×C67C22×D411yescharacteristic
466C2×C4×C67C22×D411yescharacteristic
467C2×C4×C67C22×D411yescharacteristic
468C2×C4×C67C2×#4111yescharacteristic
469C2×C4×C67H(5,𝔽2)11yescharacteristic
470C2×C4×C67H(5,𝔽2)11yescharacteristic
471C8×C67—22no—
472C8×C67—41no—
473C8×C67—41no—
474C8×C67—41no—
475C22×C67—21no—
476C22×C67—21no—
477C22×C67—21no—
478C22×C67—21no—
479C22×C67—22no—
480C22×C67—21no—
481C22×C67—21no—
482C22×C67—21no—
483C22×C67—21no—
484C22×C67—41no—
485C22×C67—41no—
486C22×C67—41no—
487C22×C67—41no—
488C22×C67—42no—
489C22×C67—42no—
490C22×C67—41no—
491C22×C67—41no—
492C22×C67—41no—
493C22×C67—42no—
494C22×C67—41no—
495C22×C67—81no—
496C22×C67—81no—
497C22×C67—82no—
498C22×C67—82no—
499C22×C67—84no—
500C22×C67—164no—
501C22×C67C2×#12011yescharacteristic
502C22×C67D4211yescharacteristic
503C22×C67#54611yescharacteristic
504C4×C67—21no—
505C4×C67—21no—
506C4×C67—22no—
507C4×C67—42no—
508C4×C67—41no—
509C4×C67—41no—
510C4×C67—42no—
511C4×C67—41no—
512C4×C67—41no—
513C4×C67—81no—
514C4×C67—81no—
515C4×C67—81no—
516C4×C67C2×#12111yescharacteristic
517C4×C67#53411yescharacteristic
518C4×C67D4211yescharacteristic
519C4×C67#54611yescharacteristic
520#24471C6711yesmaximal, characteristic, direct product factor, Sylow
521C2×C67—21no—
522C2×C67—21no—
523C2×C67—41no—
524C2×C67—41no—
525C2×C67—42no—
526C2×C67—81no—
527C2×C67—82no—
528C2×C67—81no—
529C2×C67#241011yescharacteristic
530C2×C67#301911yescharacteristic
531C2×C67#302211yescharacteristic
532#3488C2×C6711yescharacteristic
533#3056C2×C6711yescharacteristic, complemented
534C2×#455C2×C6711yescharacteristic, complemented
535#3007C2×C6711yescharacteristic, complemented
536C2×#421C2×C6711yescharacteristic, complemented
537#2620C2×C6711yescharacteristic, complemented
538#2039C2×C6711yescharacteristic, complemented
539#2037C2×C6711yescharacteristic, complemented
540#2007C2×C6711yescharacteristic, complemented
541#2004C2×C6711yescharacteristic, complemented
542#1900C2×C6711yescharacteristic, complemented
543#1897C2×C6711yescharacteristic, complemented
544#1882C2×C6711yescharacteristic, complemented
545#1859C2×C6711yescharacteristic, complemented
546#1792C2×C6711yescharacteristic, complemented
547C67#2447111yescharacteristic, direct product factor, Sylow
548C2×H(5,𝔽2)C22×C6711yescharacteristic
549C22×#41C22×C6711yescharacteristic
550C2×#137C22×C6711yescharacteristic
551C2×#137C22×C6711yescharacteristic, complemented
552C2×#137C22×C6711yescharacteristic, complemented
553C22×M16C22×C6711yescharacteristic, complemented
554#550—21no—
555#548—21no—
556#546—21no—
557#546—22no—
558D42—22no—
559D42—21no—
560#537—21no—
561#537C22×C6711yescharacteristic
562#535—21no—
563#535C22×C6711yescharacteristic
564C2×#124C22×C6711yescharacteristic, complemented
565#525—21no—
566#525C22×C6711yescharacteristic
567C2×C22⋊Q8C22×C6711yescharacteristic, complemented
568C2×#121—21no—
569C2×#121C22×C6711yescharacteristic
570#520C22×C6711yescharacteristic
571C2×#117C22×C6711yescharacteristic, complemented
572#470—21no—
573#468—21no—
574#467—21no—
575#465—21no—
576#455—24no—
577#452—21no—
578#452—21no—
579#451—21no—
580#450—21no—
581#428C22×C6711yescharacteristic, complemented
582#421—24no—
583C2×#104C22×C6711yescharacteristic
584C2×#104C22×C6711yescharacteristic
585C2×#104C22×C6711yescharacteristic, complemented
586C2×#104C22×C6711yescharacteristic, complemented
587C2×#104C22×C6711yescharacteristic, complemented
588C2×#104C22×C6711yescharacteristic, complemented
589#419C22×C6711yescharacteristic, complemented
590#417C22×C6711yescharacteristic
591#417C22×C6711yescharacteristic, complemented
592#417C22×C6711yescharacteristic, complemented
593C2×#100C22×C6711yescharacteristic, complemented
594C2×#100C22×C6711yescharacteristic, complemented
595#407C22×C6711yescharacteristic, complemented
596#396—22no—
597#394—22no—
598#391C22×C6711yescharacteristic, complemented
599#390C22×C6711yescharacteristic, complemented
600#384C22×C6711yescharacteristic, complemented
601#343C22×C6711yescharacteristic, complemented
602#343C22×C6711yescharacteristic, complemented
603#339C22×C6711yescharacteristic, complemented
604#339C22×C6711yescharacteristic, complemented
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41D4×C6711yescharacteristic
618C2×#41D4×C6711yescharacteristic
619C2×#41C23×C6711yescharacteristic
620C2×#41C23×C6711yescharacteristic
621C2×#41C23×C6711yescharacteristic
622C22×Q8D4×C6711yescharacteristic
623C22×Q8C23×C6711yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4D4×C6711yescharacteristic
630C22×D4D4×C6712yes—
631C22×D4C23×C6711yescharacteristic
632C23×C4—21no—
633C23×C4C23×C6711yescharacteristic
634#137—22no—
635#137—22no—
636#137—22no—
637#137—41no—
638#137—41no—
639#137—41no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×Q16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×SD16—21no—
646C2×M16—21no—
647C2×M16—22no—
648C2×M16—41no—
649C2×M16C23×C6711yescharacteristic
650C2×M16C23×C6711yescharacteristic
651C2×M16C23×C6711yescharacteristic
652C2×M16C23×C6711yescharacteristic
653C22×C8—21no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—22no—
659#124—41no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C6711yescharacteristic
670C22⋊Q8D4×C6711yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121D4×C6711yescharacteristic
686#121D4×C6711yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—22no—
701#117—41no—
702#117C23×C6711yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4C23×C6711yescharacteristic
708C2×C4⋊C4C23×C6711yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4D4×C6712yes—
715C2×C42C23×C6711yescharacteristic
716C2×C42C23×C6711yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C6714yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738C24—22no—
739C24—21no—
740C24C2×D4×C6712yes—
741C24C2×D4×C6711yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C6712yes—
765#41#41×C6712yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C6711yescharacteristic
776C2×Q8C2×D4×C6711yescharacteristic
777C2×Q8C2×D4×C6711yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C6711yescharacteristic
812C2×D4C2×D4×C6711yescharacteristic
813C2×D4C2×D4×C6711yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C6711yescharacteristic
833C22×C4C2×D4×C6711yescharacteristic
834C22×C4C2×D4×C6711yescharacteristic
835C22×C4C2×D4×C6711yescharacteristic
836C22×C4C2×D4×C6711yescharacteristic
837C22×C4C2×D4×C6712yes—
838C22×C4C24×C6711yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C6712yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C6711yescharacteristic
872C4⋊C4C2×D4×C6711yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C6712yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#120×C6711yescharacteristic
915C23#120×C6711yescharacteristic
916C23C22×D4×C6711yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8#121×C6712yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#121×C6712yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4#120×C6711yescharacteristic
996C2×C4#120×C6711yescharacteristic
997C2×C4C22×D4×C6711yescharacteristic
998C2×C4C22×D4×C6711yescharacteristic
999C2×C4C22×D4×C6711yescharacteristic
1000C2×C4C2×#41×C6711yescharacteristic
1001C2×C4H(5,𝔽2)×C6711yescharacteristic
1002C2×C4H(5,𝔽2)×C6711yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—22no—
1016C22—41no—
1017C22—41no—
1018C22—42no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—42no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—42no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#120×C6711yescharacteristic
1034C22D42×C6711yescharacteristic
1035C22#546×C6711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×#121×C6711yescharacteristic
1049C4#534×C6711yescharacteristic
1050C4D42×C6711yescharacteristic
1051C4#546×C6711yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C67×#241011yescharacteristic
1061C2C67×#301911yescharacteristic
1062C2C67×#302211yescharacteristic
subgroupG/H
center, socleC22×C67C2×#120
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC67×#3488C2
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
2. C67×#3056C2semidirect
3. C2×#455×C67C2semidirect
4. C67×#3007C2semidirect
5. C2×#421×C67C2semidirect
6. C67×#2620C2semidirect
7. C67×#2039C2semidirect
8. C67×#2037C2semidirect
9. C67×#2007C2semidirect
10. C67×#2004C2semidirect
11. C67×#1900C2semidirect
12. C67×#1897C2semidirect
13. C67×#1882C2semidirect
14. C67×#1859C2semidirect
15. C67×#1792C2semidirect
19. C2×#137×C67C22semidirect
20. C2×#137×C67C22semidirect
21. C22×M16×C67C22semidirect
32. C2×#124×C67C22semidirect
35. C2×C22⋊Q8×C67C22semidirect
39. C2×#117×C67C22semidirect
49. #428×C67C22semidirect
53. C2×#104×C67C22semidirect
54. C2×#104×C67C22semidirect
55. C2×#104×C67C22semidirect
56. C2×#104×C67C22semidirect
57. #419×C67C22semidirect
59. #417×C67C22semidirect
60. #417×C67C22semidirect
61. C2×#100×C67C22semidirect
62. C2×#100×C67C22semidirect
63. #407×C67C22semidirect
66. #391×C67C22semidirect
67. #390×C67C22semidirect
68. #384×C67C22semidirect
69. #343×C67C22semidirect
70. #343×C67C22semidirect
71. #339×C67C22semidirect
72. #339×C67C22semidirect
192. #104×C67D4semidirect
321. M16×C67C2×D4semidirect
363. C42×C67C2×D4semidirect
520. #24471C67direct (N × H)
533. #3056C2×C67semidirect
534. C2×#455C2×C67semidirect
535. #3007C2×C67semidirect
536. C2×#421C2×C67semidirect
537. #2620C2×C67semidirect
538. #2039C2×C67semidirect
539. #2037C2×C67semidirect
540. #2007C2×C67semidirect
541. #2004C2×C67semidirect
542. #1900C2×C67semidirect
543. #1897C2×C67semidirect
544. #1882C2×C67semidirect
545. #1859C2×C67semidirect
546. #1792C2×C67semidirect
547. C67#24471direct (N × H)
551. C2×#137C22×C67semidirect
552. C2×#137C22×C67semidirect
553. C22×M16C22×C67semidirect
564. C2×#124C22×C67semidirect
567. C2×C22⋊Q8C22×C67semidirect
571. C2×#117C22×C67semidirect
581. #428C22×C67semidirect
585. C2×#104C22×C67semidirect
586. C2×#104C22×C67semidirect
587. C2×#104C22×C67semidirect
588. C2×#104C22×C67semidirect
589. #419C22×C67semidirect
591. #417C22×C67semidirect
592. #417C22×C67semidirect
593. C2×#100C22×C67semidirect
594. C2×#100C22×C67semidirect
595. #407C22×C67semidirect
598. #391C22×C67semidirect
599. #390C22×C67semidirect
600. #384C22×C67semidirect
601. #343C22×C67semidirect
602. #343C22×C67semidirect
603. #339C22×C67semidirect
604. #339C22×C67semidirect
724. #104D4×C67semidirect
853. M16C2×D4×C67semidirect
895. C42C2×D4×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#34882
C67×#30562
C2×#455×C672
C67×#30072
C2×#421×C672
C67×#26202
C67×#20392
C67×#20372
C67×#20072
C67×#20042
C67×#19002
C67×#18972
C67×#18822
C67×#18592
C67×#17922
#2447167