Finite Group Databasebeta

← C67×#24031 #30703282

Subgroups — C67×#24031 #30703282

Order 17152.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3488C211yesmaximal, characteristic
2C67×#3093C211yesmaximal, characteristic, complemented
3C67×#2896C211yesmaximal, characteristic, complemented
4C67×#2500C211yesmaximal, characteristic, complemented
5C67×#2040C211yesmaximal, characteristic, complemented
6C67×#2039C211yesmaximal, characteristic, complemented
7C67×#2037C211yesmaximal, characteristic, complemented
8C67×#2037C211yesmaximal, characteristic, complemented
9C67×#1900C211yesmaximal, characteristic, complemented
10C67×#1871C211yesmaximal, characteristic, complemented
11C67×#1860C211yesmaximal, characteristic, complemented
12C67×#1859C211yesmaximal, characteristic, complemented
13C67×#1792C211yesmaximal, characteristic, complemented
14C67×#1792C211yesmaximal, characteristic, complemented
15C67×#1789C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C67C2211yescharacteristic
17C22×#41×C67C2211yescharacteristic
18C22×M16×C67C2211yescharacteristic, complemented
19#550×C67—21no—
20#548×C67—21no—
21#546×C67—21no—
22#546×C67—22no—
23D42×C67—22no—
24D42×C67—21no—
25#537×C67—21no—
26#537×C67C2211yescharacteristic
27#535×C67—21no—
28#535×C67C2211yescharacteristic
29#525×C67—21no—
30#525×C67C2211yescharacteristic
31C2×#121×C67—21no—
32C2×#121×C67C2211yescharacteristic
33#520×C67C2211yescharacteristic
34C2×#117×C67C2211yescharacteristic, complemented
35#485×C67—21no—
36#485×C67—21no—
37#482×C67—21no—
38#482×C67—21no—
39#428×C67C2211yescharacteristic, complemented
40#428×C67C2211yescharacteristic, complemented
41C2×#104×C67C2211yescharacteristic
42C2×#104×C67C2211yescharacteristic
43C2×#104×C67C2211yescharacteristic, complemented
44C2×#104×C67C2211yescharacteristic, complemented
45C2×#104×C67C2211yescharacteristic, complemented
46C2×#104×C67C2211yescharacteristic, complemented
47#419×C67—21no—
48#418×C67—21no—
49#417×C67C2211yescharacteristic
50#417×C67C2211yescharacteristic
51#417×C67C2211yescharacteristic, complemented
52#417×C67C2211yescharacteristic, complemented
53#417×C67C2211yescharacteristic, complemented
54#417×C67C2211yescharacteristic, complemented
55#416×C67—21no—
56#416×C67—21no—
57C2×#100×C67C2211yescharacteristic, complemented
58C2×#100×C67C2211yescharacteristic, complemented
59#407×C67C2211yescharacteristic, complemented
60#394×C67—22no—
61#390×C67C2211yescharacteristic, complemented
62#390×C67C2211yescharacteristic, complemented
63#388×C67—22no—
64#384×C67C2211yescharacteristic, complemented
65#382×C67C2211yescharacteristic, complemented
66C4×C22⋊C4×C67C2211yescharacteristic, complemented
67#343×C67C2211yescharacteristic, complemented
68#343×C67C2211yescharacteristic, complemented
69#339×C67C2211yescharacteristic, complemented
70#339×C67C2211yescharacteristic, complemented
71H(5,𝔽2)×C67—22no—
72H(5,𝔽2)×C67—22no—
73H(5,𝔽2)×C67—41no—
74H(5,𝔽2)×C67—41no—
75C2×#41×C67—21no—
76C2×#41×C67—21no—
77C2×#41×C67—21no—
78C2×#41×C67—21no—
79C2×#41×C67—22no—
80C2×#41×C67—22no—
81C2×#41×C67—41no—
82C2×#41×C67—41no—
83C2×#41×C67D411yescharacteristic
84C2×#41×C67D411yescharacteristic
85C2×#41×C67C2311yescharacteristic
86C2×#41×C67C2311yescharacteristic
87C2×#41×C67C2311yescharacteristic
88C22×Q8×C67D411yescharacteristic
89C22×D4×C67—21no—
90C22×D4×C67—22no—
91C22×D4×C67—22no—
92C22×D4×C67—21no—
93C22×D4×C67—21no—
94C22×D4×C67D411yescharacteristic
95C22×D4×C67D412yes—
96C22×D4×C67C2311yescharacteristic
97C23×C4×C67—21no—
98C23×C4×C67C2311yescharacteristic
99C2×M16×C67—21no—
100C2×M16×C67—41no—
101C2×M16×C67—41no—
102C2×M16×C67C2311yescharacteristic
103C2×M16×C67C2311yescharacteristic
104C2×M16×C67C2311yescharacteristic
105C2×M16×C67C2311yescharacteristic
106C22×C8×C67—21no—
107#127×C67—22no—
108#127×C67—21no—
109#124×C67—22no—
110#124×C67—21no—
111#123×C67—22no—
112#123×C67—21no—
113C22⋊Q8×C67—22no—
114C22⋊Q8×C67—21no—
115C22⋊Q8×C67—21no—
116C22⋊Q8×C67D411yescharacteristic
117C22⋊Q8×C67D411yescharacteristic
118#121×C67—22no—
119#121×C67—22no—
120#121×C67—22no—
121#121×C67—22no—
122#121×C67—22no—
123#121×C67—21no—
124#121×C67—21no—
125#121×C67—21no—
126#121×C67—21no—
127#121×C67—21no—
128#121×C67—21no—
129#121×C67—22no—
130#121×C67—21no—
131#121×C67—21no—
132#121×C67D411yescharacteristic
133#121×C67D411yescharacteristic
134#120×C67—22no—
135#120×C67—22no—
136#120×C67—22no—
137#120×C67—21no—
138#120×C67—22no—
139C4×Q8×C67—21no—
140C4×D4×C67—22no—
141C4×D4×C67—22no—
142C4×D4×C67—21no—
143C4×D4×C67—22no—
144C4×D4×C67—21no—
145C4×D4×C67—21no—
146#117×C67—21no—
147#117×C67—21no—
148#117×C67—21no—
149#117×C67—21no—
150#117×C67—21no—
151#117×C67C2311yescharacteristic
152C2×C4⋊C4×C67—21no—
153C2×C4⋊C4×C67—22no—
154C2×C4⋊C4×C67C2311yescharacteristic
155C2×C4⋊C4×C67C2311yescharacteristic
156C2×C4⋊C4×C67C2311yescharacteristic
157C2×C22⋊C4×C67—22no—
158C2×C22⋊C4×C67—21no—
159C2×C22⋊C4×C67—21no—
160C2×C22⋊C4×C67—22no—
161C2×C22⋊C4×C67—22no—
162C2×C22⋊C4×C67D412yes—
163C2×C42×C67—21no—
164C2×C42×C67C2311yescharacteristic
165C2×C42×C67C2311yescharacteristic
166#107×C67—21no—
167#107×C67—21no—
168#106×C67—21no—
169#106×C67—21no—
170#104×C67—22no—
171#104×C67—22no—
172#104×C67—41no—
173#104×C67—41no—
174#104×C67—41no—
175#104×C67—41no—
176#103×C67—21no—
177#103×C67—21no—
178#103×C67—21no—
179#103×C67—21no—
180#103×C67—21no—
181#103×C67—21no—
182#102×C67—21no—
183#102×C67—21no—
184#102×C67—21no—
185#102×C67—21no—
186#102×C67—21no—
187#102×C67—21no—
188#100×C67—41no—
189#100×C67—41no—
190C22⋊C8×C67—21no—
191C22⋊C8×C67—21no—
192#95×C67—21no—
193#95×C67—22no—
194C24×C67—22no—
195C24×C67—21no—
196C24×C67C2×D412yes—
197C24×C67C2×D411yescharacteristic
198#41×C67—21no—
199#41×C67—21no—
200#41×C67—22no—
201#41×C67—22no—
202#41×C67—21no—
203#41×C67—21no—
204#41×C67—21no—
205#41×C67—21no—
206#41×C67—21no—
207#41×C67—21no—
208#41×C67—21no—
209#41×C67—21no—
210#41×C67—42no—
211#41×C67—42no—
212#41×C67—41no—
213#41×C67—41no—
214#41×C67—42no—
215#41×C67—42no—
216#41×C67—42no—
217#41×C67—42no—
218#41×C67—42no—
219#41×C67—42no—
220#41×C67#4112yes—
221#41×C67#4112yes—
222C2×Q8×C67—21no—
223C2×Q8×C67—22no—
224C2×Q8×C67—41no—
225C2×Q8×C67C2×D411yescharacteristic
226C2×Q8×C67C2×D411yescharacteristic
227C2×Q8×C67C2×D411yescharacteristic
228C2×D4×C67—21no—
229C2×D4×C67—22no—
230C2×D4×C67—22no—
231C2×D4×C67—22no—
232C2×D4×C67—22no—
233C2×D4×C67—21no—
234C2×D4×C67—21no—
235C2×D4×C67—21no—
236C2×D4×C67—21no—
237C2×D4×C67—21no—
238C2×D4×C67—22no—
239C2×D4×C67—22no—
240C2×D4×C67—22no—
241C2×D4×C67—21no—
242C2×D4×C67—22no—
243C2×D4×C67—21no—
244C2×D4×C67—21no—
245C2×D4×C67—21no—
246C2×D4×C67—21no—
247C2×D4×C67—21no—
248C2×D4×C67—21no—
249C2×D4×C67—21no—
250C2×D4×C67—41no—
251C2×D4×C67—42no—
252C2×D4×C67—42no—
253C2×D4×C67—42no—
254C2×D4×C67—42no—
255C2×D4×C67—44no—
256C2×D4×C67—44no—
257C2×D4×C67—42no—
258C2×D4×C67—42no—
259C2×D4×C67—82no—
260C2×D4×C67—84no—
261C2×D4×C67C2×D411yescharacteristic
262C2×D4×C67C2×D411yescharacteristic
263C2×D4×C67C2×D411yescharacteristic
264C22×C4×C67—21no—
265C22×C4×C67—21no—
266C22×C4×C67—21no—
267C22×C4×C67—21no—
268C22×C4×C67—21no—
269C22×C4×C67—22no—
270C22×C4×C67—21no—
271C22×C4×C67—21no—
272C22×C4×C67—22no—
273C22×C4×C67—21no—
274C22×C4×C67—21no—
275C22×C4×C67—21no—
276C22×C4×C67—21no—
277C22×C4×C67—21no—
278C22×C4×C67—21no—
279C22×C4×C67—21no—
280C22×C4×C67—42no—
281C22×C4×C67—42no—
282C22×C4×C67C2×D411yescharacteristic
283C22×C4×C67C2×D411yescharacteristic
284C22×C4×C67C2×D411yescharacteristic
285C22×C4×C67C2×D411yescharacteristic
286C22×C4×C67C2×D411yescharacteristic
287C22×C4×C67C2×D412yes—
288C22×C4×C67C2411yescharacteristic
289M16×C67—21no—
290M16×C67—21no—
291M16×C67—21no—
292M16×C67—21no—
293M16×C67—21no—
294M16×C67—21no—
295M16×C67—21no—
296M16×C67—21no—
297M16×C67—42no—
298C2×C8×C67—21no—
299C2×C8×C67—21no—
300C2×C8×C67—21no—
301C2×C8×C67—21no—
302C2×C8×C67—42no—
303C4⋊C4×C67—22no—
304C4⋊C4×C67—22no—
305C4⋊C4×C67—21no—
306C4⋊C4×C67—21no—
307C4⋊C4×C67—21no—
308C4⋊C4×C67—21no—
309C4⋊C4×C67—21no—
310C4⋊C4×C67—21no—
311C4⋊C4×C67—21no—
312C4⋊C4×C67—21no—
313C4⋊C4×C67—82no—
314C4⋊C4×C67C2×D411yescharacteristic
315C4⋊C4×C67C2×D411yescharacteristic
316C22⋊C4×C67—22no—
317C22⋊C4×C67—22no—
318C22⋊C4×C67—22no—
319C22⋊C4×C67—22no—
320C22⋊C4×C67—22no—
321C22⋊C4×C67—21no—
322C22⋊C4×C67—21no—
323C22⋊C4×C67—21no—
324C22⋊C4×C67—21no—
325C22⋊C4×C67—22no—
326C22⋊C4×C67—22no—
327C22⋊C4×C67—21no—
328C22⋊C4×C67—42no—
329C22⋊C4×C67—44no—
330C22⋊C4×C67—41no—
331C22⋊C4×C67—41no—
332C22⋊C4×C67—82no—
333C42×C67—22no—
334C42×C67—21no—
335C42×C67—21no—
336C42×C67—21no—
337C42×C67—21no—
338C42×C67—21no—
339C42×C67—41no—
340C42×C67—41no—
341C23×C67—21no—
342C23×C67—21no—
343C23×C67—21no—
344C23×C67—22no—
345C23×C67—21no—
346C23×C67—21no—
347C23×C67—22no—
348C23×C67—22no—
349C23×C67—41no—
350C23×C67—41no—
351C23×C67—42no—
352C23×C67—42no—
353C23×C67—44no—
354C23×C67—42no—
355C23×C67—42no—
356C23×C67—81no—
357C23×C67—82no—
358C23×C67—82no—
359C23×C67#12011yescharacteristic
360C23×C67#12011yescharacteristic
361C23×C67C22×D411yescharacteristic
362Q8×C67—21no—
363Q8×C67—21no—
364Q8×C67—21no—
365Q8×C67—21no—
366Q8×C67—21no—
367Q8×C67—42no—
368Q8×C67#12312yes—
369D4×C67—22no—
370D4×C67—22no—
371D4×C67—21no—
372D4×C67—21no—
373D4×C67—21no—
374D4×C67—21no—
375D4×C67—21no—
376D4×C67—42no—
377D4×C67—42no—
378D4×C67—44no—
379D4×C67—42no—
380D4×C67—44no—
381D4×C67—44no—
382D4×C67—42no—
383D4×C67—41no—
384D4×C67—41no—
385D4×C67—41no—
386D4×C67—41no—
387D4×C67—41no—
388D4×C67—41no—
389D4×C67—41no—
390D4×C67—41no—
391D4×C67—81no—
392D4×C67—82no—
393D4×C67—82no—
394D4×C67—82no—
395D4×C67—82no—
396D4×C67#12312yes—
397C2×C4×C67—21no—
398C2×C4×C67—21no—
399C2×C4×C67—21no—
400C2×C4×C67—21no—
401C2×C4×C67—21no—
402C2×C4×C67—21no—
403C2×C4×C67—21no—
404C2×C4×C67—21no—
405C2×C4×C67—21no—
406C2×C4×C67—21no—
407C2×C4×C67—21no—
408C2×C4×C67—22no—
409C2×C4×C67—22no—
410C2×C4×C67—22no—
411C2×C4×C67—21no—
412C2×C4×C67—22no—
413C2×C4×C67—21no—
414C2×C4×C67—21no—
415C2×C4×C67—21no—
416C2×C4×C67—42no—
417C2×C4×C67—42no—
418C2×C4×C67—42no—
419C2×C4×C67—44no—
420C2×C4×C67—41no—
421C2×C4×C67—41no—
422C2×C4×C67—41no—
423C2×C4×C67—41no—
424C2×C4×C67—41no—
425C2×C4×C67—41no—
426C2×C4×C67—42no—
427C2×C4×C67—41no—
428C2×C4×C67—42no—
429C2×C4×C67—41no—
430C2×C4×C67—42no—
431C2×C4×C67—41no—
432C2×C4×C67—41no—
433C2×C4×C67—41no—
434C2×C4×C67—82no—
435C2×C4×C67#12011yescharacteristic
436C2×C4×C67#12011yescharacteristic
437C2×C4×C67C22×D411yescharacteristic
438C2×C4×C67C22×D411yescharacteristic
439C2×C4×C67C2×#4111yescharacteristic
440C2×C4×C67C2×#4111yescharacteristic
441C2×C4×C67H(5,𝔽2)11yescharacteristic
442C2×C4×C67H(5,𝔽2)11yescharacteristic
443C8×C67—41no—
444C8×C67—41no—
445C8×C67—41no—
446C8×C67—41no—
447C22×C67—21no—
448C22×C67—21no—
449C22×C67—21no—
450C22×C67—21no—
451C22×C67—22no—
452C22×C67—21no—
453C22×C67—21no—
454C22×C67—21no—
455C22×C67—21no—
456C22×C67—41no—
457C22×C67—41no—
458C22×C67—41no—
459C22×C67—41no—
460C22×C67—42no—
461C22×C67—41no—
462C22×C67—42no—
463C22×C67—41no—
464C22×C67—42no—
465C22×C67—41no—
466C22×C67—41no—
467C22×C67—81no—
468C22×C67—81no—
469C22×C67—82no—
470C22×C67—82no—
471C22×C67—84no—
472C22×C67—164no—
473C22×C67C2×#12011yescharacteristic
474C22×C67#54611yescharacteristic
475C22×C67#54611yescharacteristic
476C4×C67—21no—
477C4×C67—21no—
478C4×C67—22no—
479C4×C67—42no—
480C4×C67—41no—
481C4×C67—41no—
482C4×C67—41no—
483C4×C67—42no—
484C4×C67—41no—
485C4×C67—81no—
486C4×C67—81no—
487C4×C67—81no—
488C4×C67C2×#12311yescharacteristic
489C4×C67#53411yescharacteristic
490C4×C67#54611yescharacteristic
491C4×C67#54611yescharacteristic
492#24031C6711yesmaximal, characteristic, direct product factor, Sylow
493C2×C67—21no—
494C2×C67—21no—
495C2×C67—41no—
496C2×C67—41no—
497C2×C67—42no—
498C2×C67—81no—
499C2×C67—82no—
500C2×C67—81no—
501C2×C67#240511yescharacteristic
502C2×C67#301811yescharacteristic
503C2×C67#301911yescharacteristic
504#3488C2×C6711yescharacteristic
505#3093C2×C6711yescharacteristic, complemented
506#2896C2×C6711yescharacteristic, complemented
507#2500C2×C6711yescharacteristic, complemented
508#2040C2×C6711yescharacteristic, complemented
509#2039C2×C6711yescharacteristic, complemented
510#2037C2×C6711yescharacteristic, complemented
511#2037C2×C6711yescharacteristic, complemented
512#1900C2×C6711yescharacteristic, complemented
513#1871C2×C6711yescharacteristic, complemented
514#1860C2×C6711yescharacteristic, complemented
515#1859C2×C6711yescharacteristic, complemented
516#1792C2×C6711yescharacteristic, complemented
517#1792C2×C6711yescharacteristic, complemented
518#1789C2×C6711yescharacteristic, complemented
519C67#2403111yescharacteristic, direct product factor, Sylow
520C2×H(5,𝔽2)C22×C6711yescharacteristic
521C22×#41C22×C6711yescharacteristic
522C22×M16C22×C6711yescharacteristic, complemented
523#550—21no—
524#548—21no—
525#546—21no—
526#546—22no—
527D42—22no—
528D42—21no—
529#537—21no—
530#537C22×C6711yescharacteristic
531#535—21no—
532#535C22×C6711yescharacteristic
533#525—21no—
534#525C22×C6711yescharacteristic
535C2×#121—21no—
536C2×#121C22×C6711yescharacteristic
537#520C22×C6711yescharacteristic
538C2×#117C22×C6711yescharacteristic, complemented
539#485—21no—
540#485—21no—
541#482—21no—
542#482—21no—
543#428C22×C6711yescharacteristic, complemented
544#428C22×C6711yescharacteristic, complemented
545C2×#104C22×C6711yescharacteristic
546C2×#104C22×C6711yescharacteristic
547C2×#104C22×C6711yescharacteristic, complemented
548C2×#104C22×C6711yescharacteristic, complemented
549C2×#104C22×C6711yescharacteristic, complemented
550C2×#104C22×C6711yescharacteristic, complemented
551#419—21no—
552#418—21no—
553#417C22×C6711yescharacteristic
554#417C22×C6711yescharacteristic
555#417C22×C6711yescharacteristic, complemented
556#417C22×C6711yescharacteristic, complemented
557#417C22×C6711yescharacteristic, complemented
558#417C22×C6711yescharacteristic, complemented
559#416—21no—
560#416—21no—
561C2×#100C22×C6711yescharacteristic, complemented
562C2×#100C22×C6711yescharacteristic, complemented
563#407C22×C6711yescharacteristic, complemented
564#394—22no—
565#390C22×C6711yescharacteristic, complemented
566#390C22×C6711yescharacteristic, complemented
567#388—22no—
568#384C22×C6711yescharacteristic, complemented
569#382C22×C6711yescharacteristic, complemented
570C4×C22⋊C4C22×C6711yescharacteristic, complemented
571#343C22×C6711yescharacteristic, complemented
572#343C22×C6711yescharacteristic, complemented
573#339C22×C6711yescharacteristic, complemented
574#339C22×C6711yescharacteristic, complemented
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41D4×C6711yescharacteristic
588C2×#41D4×C6711yescharacteristic
589C2×#41C23×C6711yescharacteristic
590C2×#41C23×C6711yescharacteristic
591C2×#41C23×C6711yescharacteristic
592C22×Q8D4×C6711yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4D4×C6711yescharacteristic
599C22×D4D4×C6712yes—
600C22×D4C23×C6711yescharacteristic
601C23×C4—21no—
602C23×C4C23×C6711yescharacteristic
603C2×M16—21no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C23×C6711yescharacteristic
607C2×M16C23×C6711yescharacteristic
608C2×M16C23×C6711yescharacteristic
609C2×M16C23×C6711yescharacteristic
610C22×C8—21no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8D4×C6711yescharacteristic
621C22⋊Q8D4×C6711yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121D4×C6711yescharacteristic
637#121D4×C6711yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117—21no—
655#117C23×C6711yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C23×C6711yescharacteristic
659C2×C4⋊C4C23×C6711yescharacteristic
660C2×C4⋊C4C23×C6711yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4D4×C6712yes—
667C2×C42—21no—
668C2×C42C23×C6711yescharacteristic
669C2×C42C23×C6711yescharacteristic
670#107—21no—
671#107—21no—
672#106—21no—
673#106—21no—
674#104—22no—
675#104—22no—
676#104—41no—
677#104—41no—
678#104—41no—
679#104—41no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#103—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#102—21no—
692#100—41no—
693#100—41no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696#95—21no—
697#95—22no—
698C24—22no—
699C24—21no—
700C24C2×D4×C6712yes—
701C24C2×D4×C6711yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C6712yes—
725#41#41×C6712yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C6711yescharacteristic
730C2×Q8C2×D4×C6711yescharacteristic
731C2×Q8C2×D4×C6711yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C6711yescharacteristic
766C2×D4C2×D4×C6711yescharacteristic
767C2×D4C2×D4×C6711yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C6711yescharacteristic
787C22×C4C2×D4×C6711yescharacteristic
788C22×C4C2×D4×C6711yescharacteristic
789C22×C4C2×D4×C6711yescharacteristic
790C22×C4C2×D4×C6711yescharacteristic
791C22×C4C2×D4×C6712yes—
792C22×C4C24×C6711yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C6711yescharacteristic
819C4⋊C4C2×D4×C6711yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#120×C6711yescharacteristic
864C23#120×C6711yescharacteristic
865C23C22×D4×C6711yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#123×C6712yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#123×C6712yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4#120×C6711yescharacteristic
940C2×C4#120×C6711yescharacteristic
941C2×C4C22×D4×C6711yescharacteristic
942C2×C4C22×D4×C6711yescharacteristic
943C2×C4C2×#41×C6711yescharacteristic
944C2×C4C2×#41×C6711yescharacteristic
945C2×C4H(5,𝔽2)×C6711yescharacteristic
946C2×C4H(5,𝔽2)×C6711yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—22no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—42no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—42no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#120×C6711yescharacteristic
978C22#546×C6711yescharacteristic
979C22#546×C6711yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—42no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×#123×C6711yescharacteristic
993C4#534×C6711yescharacteristic
994C4#546×C6711yescharacteristic
995C4#546×C6711yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C67×#240511yescharacteristic
1005C2C67×#301811yescharacteristic
1006C2C67×#301911yescharacteristic
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×#3093C2semidirect
3. C67×#2896C2semidirect
4. C67×#2500C2semidirect
5. C67×#2040C2semidirect
6. C67×#2039C2semidirect
7. C67×#2037C2semidirect
8. C67×#2037C2semidirect
9. C67×#1900C2semidirect
10. C67×#1871C2semidirect
11. C67×#1860C2semidirect
12. C67×#1859C2semidirect
13. C67×#1792C2semidirect
14. C67×#1792C2semidirect
15. C67×#1789C2semidirect
18. C22×M16×C67C22semidirect
34. C2×#117×C67C22semidirect
39. #428×C67C22semidirect
40. #428×C67C22semidirect
43. C2×#104×C67C22semidirect
44. C2×#104×C67C22semidirect
45. C2×#104×C67C22semidirect
46. C2×#104×C67C22semidirect
51. #417×C67C22semidirect
52. #417×C67C22semidirect
53. #417×C67C22semidirect
54. #417×C67C22semidirect
57. C2×#100×C67C22semidirect
58. C2×#100×C67C22semidirect
59. #407×C67C22semidirect
61. #390×C67C22semidirect
62. #390×C67C22semidirect
64. #384×C67C22semidirect
65. #382×C67C22semidirect
66. C4×C22⋊C4×C67C22semidirect
67. #343×C67C22semidirect
68. #343×C67C22semidirect
69. #339×C67C22semidirect
70. #339×C67C22semidirect
492. #24031C67direct (N × H)
505. #3093C2×C67semidirect
506. #2896C2×C67semidirect
507. #2500C2×C67semidirect
508. #2040C2×C67semidirect
509. #2039C2×C67semidirect
510. #2037C2×C67semidirect
511. #2037C2×C67semidirect
512. #1900C2×C67semidirect
513. #1871C2×C67semidirect
514. #1860C2×C67semidirect
515. #1859C2×C67semidirect
516. #1792C2×C67semidirect
517. #1792C2×C67semidirect
518. #1789C2×C67semidirect
519. C67#24031direct (N × H)
522. C22×M16C22×C67semidirect
538. C2×#117C22×C67semidirect
543. #428C22×C67semidirect
544. #428C22×C67semidirect
547. C2×#104C22×C67semidirect
548. C2×#104C22×C67semidirect
549. C2×#104C22×C67semidirect
550. C2×#104C22×C67semidirect
555. #417C22×C67semidirect
556. #417C22×C67semidirect
557. #417C22×C67semidirect
558. #417C22×C67semidirect
561. C2×#100C22×C67semidirect
562. C2×#100C22×C67semidirect
563. #407C22×C67semidirect
565. #390C22×C67semidirect
566. #390C22×C67semidirect
568. #384C22×C67semidirect
569. #382C22×C67semidirect
570. C4×C22⋊C4C22×C67semidirect
571. #343C22×C67semidirect
572. #343C22×C67semidirect
573. #339C22×C67semidirect
574. #339C22×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#34882
C67×#30932
C67×#28962
C67×#25002
C67×#20402
C67×#20392
C67×#20372
C67×#19002
C67×#18712
C67×#18602
C67×#18592
C67×#17922
C67×#17892
#2403167