Finite Group Databasebeta

← C67×#18434 #30697685

Subgroups — C67×#18434 #30697685

Order 17152.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3560C211yesmaximal, characteristic, complemented
2C67×#3213C211yesmaximal, characteristic, complemented
3C67×#3211C211yesmaximal, characteristic, complemented
4C67×#2662C211yesmaximal, characteristic, complemented
5C67×#1606C211yesmaximal, characteristic, complemented
6C67×#1604C211yesmaximal, characteristic, complemented
7C67×#1603C211yesmaximal, characteristic, complemented
8C67×#1601C211yesmaximal, characteristic, complemented
9C67×#1600C211yesmaximal, characteristic, complemented
10C67×#1598C211yesmaximal, characteristic, complemented
11C67×#1597C211yesmaximal, characteristic, complemented
12C67×#1595C211yesmaximal, characteristic, complemented
13C67×#1509C211yesmaximal, characteristic, complemented
14C67×#1502C211yesmaximal, characteristic, complemented
15C67×#1473C211yesmaximal, characteristic, complemented
16#563×C67—21no—
17#560×C67—21no—
18#553×C67—21no—
19#553×C67—21no—
20#551×C67—21no—
21#547×C67—21no—
22#546×C67—21no—
23#546×C67—21no—
24#542×C67—21no—
25#539×C67—21no—
26#539×C67C2211yescharacteristic
27#538×C67—21no—
28#538×C67—21no—
29#538×C67C2211yescharacteristic
30#537×C67C2211yescharacteristic
31#534×C67C2211yescharacteristic
32#532×C67C2211yescharacteristic
33#529×C67C2211yescharacteristic
34C2×#126×C67C2211yescharacteristic
35C2×#124×C67C2211yescharacteristic, complemented
36#496×C67—21no—
37#495×C67—21no—
38#489×C67—21no—
39#488×C67—21no—
40#464×C67—21no—
41#463×C67—21no—
42#463×C67—21no—
43#463×C67—21no—
44#451×C67C2211yescharacteristic, complemented
45#450×C67C2211yescharacteristic, complemented
46#448×C67C2211yescharacteristic
47#448×C67C2211yescharacteristic
48#448×C67C2211yescharacteristic, complemented
49#447×C67C2211yescharacteristic
50#447×C67C2211yescharacteristic
51#447×C67C2211yescharacteristic, complemented
52#432×C67C2211yescharacteristic, complemented
53#431×C67C2211yescharacteristic, complemented
54#396×C67—21no—
55#395×C67C2211yescharacteristic, complemented
56#394×C67—21no—
57#394×C67C2211yescharacteristic, complemented
58#393×C67C2211yescharacteristic
59#392×C67C2211yescharacteristic
60#390×C67—21no—
61#388×C67—21no—
62C4×C4⋊C4×C67C2211yescharacteristic, complemented
63#328×C67C2211yescharacteristic, complemented
64#328×C67C2211yescharacteristic, complemented
65#327×C67C2211yescharacteristic
66#327×C67C2211yescharacteristic
67#327×C67C2211yescharacteristic
68#327×C67C2211yescharacteristic
69#327×C67C2211yescharacteristic, complemented
70#327×C67C2211yescharacteristic, complemented
71#324×C67C2211yescharacteristic, complemented
72#324×C67C2211yescharacteristic, complemented
73#323×C67C2211yescharacteristic
74#323×C67C2211yescharacteristic
75C2×#41×C67—21no—
76C2×#41×C67—21no—
77C22×Q8×C67C2311yescharacteristic
78C22×D4×C67—21no—
79C22×D4×C67—21no—
80C22×D4×C67C2311yescharacteristic
81C2×Q16×C67—21no—
82C2×SD16×C67—21no—
83C2×SD16×C67—21no—
84C2×SD16×C67—21no—
85C2×SD16×C67—21no—
86C2×D8×C67—21no—
87C2×D8×C67—21no—
88C2×D8×C67—21no—
89C4⋊Q8×C67—21no—
90C4⋊Q8×C67D411yescharacteristic, complemented
91#127×C67D411yescharacteristic, complemented
92#126×C67—21no—
93#126×C67—21no—
94#126×C67—21no—
95#126×C67—21no—
96#126×C67—21no—
97#126×C67—21no—
98#126×C67—21no—
99#126×C67—21no—
100#126×C67—21no—
101#125×C67—21no—
102#125×C67—21no—
103#125×C67D411yescharacteristic, complemented
104#124×C67—21no—
105#124×C67—21no—
106#124×C67—21no—
107#124×C67—21no—
108#124×C67—21no—
109#124×C67—21no—
110#124×C67—21no—
111#124×C67—21no—
112#124×C67D411yescharacteristic, complemented
113#123×C67—21no—
114#123×C67—21no—
115#123×C67—21no—
116#123×C67—21no—
117#123×C67—21no—
118#123×C67—21no—
119#123×C67—21no—
120#123×C67—21no—
121#123×C67—21no—
122#123×C67—21no—
123#123×C67—21no—
124#123×C67—21no—
125C22⋊Q8×C67—21no—
126C22⋊Q8×C67—21no—
127C22⋊Q8×C67—21no—
128C22⋊Q8×C67—21no—
129C22⋊Q8×C67—21no—
130C22⋊Q8×C67—21no—
131C22⋊Q8×C67—21no—
132C22⋊Q8×C67C2311yescharacteristic
133#121×C67—21no—
134#121×C67—21no—
135#121×C67—21no—
136#121×C67—21no—
137#121×C67—21no—
138#121×C67—21no—
139#121×C67—21no—
140#121×C67—21no—
141#121×C67—21no—
142#121×C67—21no—
143#121×C67—21no—
144#121×C67—21no—
145#121×C67C2311yescharacteristic
146#121×C67C2311yescharacteristic
147#121×C67C2311yescharacteristic
148#120×C67—21no—
149#120×C67—21no—
150#120×C67—21no—
151#120×C67—21no—
152#120×C67—21no—
153C4×Q8×C67D411yescharacteristic, complemented
154C4×D4×C67—21no—
155C4×D4×C67—21no—
156C4×D4×C67—21no—
157C4×D4×C67—21no—
158C4×D4×C67—21no—
159C4×D4×C67—21no—
160C4×D4×C67—21no—
161C4×D4×C67—21no—
162C4×D4×C67D411yescharacteristic, complemented
163C4×D4×C67D411yescharacteristic, complemented
164C4×D4×C67D411yescharacteristic, complemented
165#117×C67—21no—
166#117×C67—21no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67—21no—
169C2×C4⋊C4×C67—21no—
170C2×C4⋊C4×C67D411yescharacteristic
171C2×C4⋊C4×C67D411yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C22⋊C4×C67—21no—
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67—21no—
176C2×C22⋊C4×C67—21no—
177C2×C22⋊C4×C67—21no—
178C2×C22⋊C4×C67—21no—
179C2×C22⋊C4×C67—21no—
180C2×C22⋊C4×C67—21no—
181C2×C22⋊C4×C67D411yescharacteristic
182C2×C22⋊C4×C67D411yescharacteristic
183C2×C22⋊C4×C67C2311yescharacteristic
184C2×C42×C67—21no—
185C2×C42×C67C2311yescharacteristic
186C4⋊C8×C67—21no—
187C4⋊C8×C67—21no—
188#103×C67—21no—
189#103×C67—21no—
190#103×C67—21no—
191#103×C67—21no—
192#102×C67—21no—
193#102×C67—21no—
194#102×C67—21no—
195#102×C67—21no—
196C22⋊C8×C67C2311yescharacteristic
197C22⋊C8×C67C2311yescharacteristic
198C22⋊C8×C67C2311yescharacteristic
199C22⋊C8×C67C2311yescharacteristic
200#97×C67—21no—
201C4×C8×C67—21no—
202#95×C67—21no—
203#95×C67—21no—
204#95×C67C2311yescharacteristic
205#95×C67C2311yescharacteristic
206C24×C67—21no—
207C24×C67—21no—
208C24×C67C2×D411yescharacteristic
209#41×C67—81no—
210#41×C67—81no—
211#41×C67—81no—
212#41×C67—81no—
213C2×Q8×C67—21no—
214C2×Q8×C67—21no—
215C2×Q8×C67—21no—
216C2×Q8×C67—21no—
217C2×Q8×C67—81no—
218C2×Q8×C67C2×D411yescharacteristic
219C2×D4×C67—21no—
220C2×D4×C67—21no—
221C2×D4×C67—21no—
222C2×D4×C67—21no—
223C2×D4×C67—21no—
224C2×D4×C67—21no—
225C2×D4×C67—21no—
226C2×D4×C67—21no—
227C2×D4×C67—21no—
228C2×D4×C67—21no—
229C2×D4×C67—21no—
230C2×D4×C67—21no—
231C2×D4×C67—21no—
232C2×D4×C67—21no—
233C2×D4×C67—42no—
234C2×D4×C67—81no—
235C2×D4×C67—81no—
236C2×D4×C67—81no—
237C2×D4×C67—81no—
238C2×D4×C67—81no—
239C2×D4×C67C2×D411yescharacteristic
240C2×D4×C67C2×D411yescharacteristic
241C2×D4×C67C2×D411yescharacteristic
242C22×C4×C67—21no—
243C22×C4×C67—21no—
244C22×C4×C67—21no—
245C22×C4×C67—21no—
246C22×C4×C67—21no—
247C22×C4×C67—21no—
248C22×C4×C67—21no—
249C22×C4×C67—21no—
250C22×C4×C67—21no—
251C22×C4×C67—21no—
252C22×C4×C67—21no—
253C22×C4×C67C2×D411yescharacteristic
254C22×C4×C67C2×D411yescharacteristic
255C22×C4×C67C2×D411yescharacteristic
256C22×C4×C67C2×D411yescharacteristic
257C22×C4×C67C2×D411yescharacteristic
258C22×C4×C67C2411yescharacteristic
259Q16×C67—81no—
260SD16×C67—81no—
261SD16×C67—81no—
262SD16×C67—81no—
263SD16×C67—81no—
264D8×C67—81no—
265D8×C67—81no—
266D8×C67—81no—
267C2×C8×C67—21no—
268C2×C8×C67—21no—
269C2×C8×C67—21no—
270C2×C8×C67—21no—
271C4⋊C4×C67—21no—
272C4⋊C4×C67—21no—
273C4⋊C4×C67—21no—
274C4⋊C4×C67—21no—
275C4⋊C4×C67—21no—
276C4⋊C4×C67—21no—
277C4⋊C4×C67—21no—
278C4⋊C4×C67—21no—
279C4⋊C4×C67—21no—
280C4⋊C4×C67—21no—
281C4⋊C4×C67—21no—
282C4⋊C4×C67—21no—
283C4⋊C4×C67—21no—
284C4⋊C4×C67—21no—
285C4⋊C4×C67—21no—
286C4⋊C4×C67—21no—
287C4⋊C4×C67—21no—
288C4⋊C4×C67—42no—
289C4⋊C4×C67—81no—
290C4⋊C4×C67C2×D411yescharacteristic
291C4⋊C4×C67C2×D411yescharacteristic
292C4⋊C4×C67C2×D411yescharacteristic
293C4⋊C4×C67C2×D411yescharacteristic
294C22⋊C4×C67—21no—
295C22⋊C4×C67—21no—
296C22⋊C4×C67—21no—
297C22⋊C4×C67—21no—
298C22⋊C4×C67—21no—
299C22⋊C4×C67—21no—
300C22⋊C4×C67—21no—
301C22⋊C4×C67—21no—
302C22⋊C4×C67—21no—
303C22⋊C4×C67—21no—
304C22⋊C4×C67—21no—
305C22⋊C4×C67—21no—
306C22⋊C4×C67—21no—
307C22⋊C4×C67—21no—
308C22⋊C4×C67—21no—
309C22⋊C4×C67—21no—
310C22⋊C4×C67—21no—
311C22⋊C4×C67—21no—
312C22⋊C4×C67—21no—
313C22⋊C4×C67—21no—
314C22⋊C4×C67—21no—
315C22⋊C4×C67—21no—
316C22⋊C4×C67—21no—
317C22⋊C4×C67—21no—
318C22⋊C4×C67—21no—
319C22⋊C4×C67—42no—
320C22⋊C4×C67—41no—
321C22⋊C4×C67—41no—
322C22⋊C4×C67—41no—
323C22⋊C4×C67—41no—
324C22⋊C4×C67—81no—
325C22⋊C4×C67—81no—
326C22⋊C4×C67—81no—
327C42×C67—21no—
328C42×C67—21no—
329C42×C67—21no—
330C42×C67—81no—
331C42×C67C2×D411yescharacteristic
332C42×C67C2×D411yescharacteristic
333C42×C67C2×D411yescharacteristic
334C42×C67C2×D411yescharacteristic
335C23×C67—21no—
336C23×C67—21no—
337C23×C67—21no—
338C23×C67—21no—
339C23×C67—21no—
340C23×C67—21no—
341C23×C67—41no—
342C23×C67—41no—
343C23×C67—41no—
344C23×C67—41no—
345C23×C67—41no—
346C23×C67—41no—
347C23×C67—41no—
348C23×C67—41no—
349C23×C67—41no—
350C23×C67—81no—
351C23×C67—81no—
352C23×C67—81no—
353C23×C67C22×D411yescharacteristic
354Q8×C67—41no—
355Q8×C67—41no—
356Q8×C67—41no—
357Q8×C67—41no—
358Q8×C67—41no—
359Q8×C67—81no—
360Q8×C67—81no—
361D4×C67—41no—
362D4×C67—41no—
363D4×C67—41no—
364D4×C67—41no—
365D4×C67—41no—
366D4×C67—41no—
367D4×C67—41no—
368D4×C67—41no—
369D4×C67—41no—
370D4×C67—41no—
371D4×C67—41no—
372D4×C67—41no—
373D4×C67—41no—
374D4×C67—81no—
375D4×C67—81no—
376D4×C67—81no—
377D4×C67—81no—
378D4×C67—81no—
379D4×C67—81no—
380D4×C67—81no—
381D4×C67—81no—
382D4×C67—81no—
383D4×C67—84no—
384C2×C4×C67—21no—
385C2×C4×C67—21no—
386C2×C4×C67—22no—
387C2×C4×C67—21no—
388C2×C4×C67—21no—
389C2×C4×C67—21no—
390C2×C4×C67—21no—
391C2×C4×C67—21no—
392C2×C4×C67—21no—
393C2×C4×C67—21no—
394C2×C4×C67—21no—
395C2×C4×C67—21no—
396C2×C4×C67—21no—
397C2×C4×C67—41no—
398C2×C4×C67—41no—
399C2×C4×C67—41no—
400C2×C4×C67—41no—
401C2×C4×C67—41no—
402C2×C4×C67—41no—
403C2×C4×C67—41no—
404C2×C4×C67—41no—
405C2×C4×C67—41no—
406C2×C4×C67—41no—
407C2×C4×C67—41no—
408C2×C4×C67—41no—
409C2×C4×C67—81no—
410C2×C4×C67—81no—
411C2×C4×C67—81no—
412C2×C4×C67—81no—
413C2×C4×C67—81no—
414C2×C4×C67—81no—
415C2×C4×C67—81no—
416C2×C4×C67—81no—
417C2×C4×C67#12011yescharacteristic
418C2×C4×C67#12011yescharacteristic
419C2×C4×C67#12011yescharacteristic
420C2×C4×C67#12011yescharacteristic
421C2×C4×C67C22×D411yescharacteristic
422C2×C4×C67C22×D411yescharacteristic
423C8×C67—41no—
424C8×C67—41no—
425C8×C67—41no—
426C8×C67—41no—
427C22×C67—21no—
428C22×C67—21no—
429C22×C67—41no—
430C22×C67—41no—
431C22×C67—41no—
432C22×C67—41no—
433C22×C67—41no—
434C22×C67—41no—
435C22×C67—41no—
436C22×C67—41no—
437C22×C67—41no—
438C22×C67—41no—
439C22×C67—41no—
440C22×C67—41no—
441C22×C67—81no—
442C22×C67—81no—
443C22×C67—81no—
444C22×C67—81no—
445C22×C67—81no—
446C22×C67—81no—
447C22×C67—81no—
448C22×C67—81no—
449C22×C67—81no—
450C22×C67—162no—
451C22×C67C2×#12011yescharacteristic
452C22×C67#57611yescharacteristic
453C22×C67#57711yescharacteristic
454C4×C67—21no—
455C4×C67—21no—
456C4×C67—21no—
457C4×C67—21no—
458C4×C67—21no—
459C4×C67—21no—
460C4×C67—42no—
461C4×C67—41no—
462C4×C67—41no—
463C4×C67—41no—
464C4×C67—41no—
465C4×C67—41no—
466C4×C67—41no—
467C4×C67—41no—
468C4×C67—41no—
469C4×C67—81no—
470C4×C67—81no—
471#18434C6711yesmaximal, characteristic, direct product factor, Sylow
472C2×C67—21no—
473C2×C67—21no—
474C2×C67—81no—
475C2×C67—81no—
476C2×C67—81no—
477C2×C67—81no—
478C2×C67—161no—
479C2×C67#301211yescharacteristic
480C2×C67#301811yescharacteristic
481C2×C67#302711yescharacteristic
482#3560C2×C6711yescharacteristic, complemented
483#3213C2×C6711yescharacteristic, complemented
484#3211C2×C6711yescharacteristic, complemented
485#2662C2×C6711yescharacteristic, complemented
486#1606C2×C6711yescharacteristic, complemented
487#1604C2×C6711yescharacteristic, complemented
488#1603C2×C6711yescharacteristic, complemented
489#1601C2×C6711yescharacteristic, complemented
490#1600C2×C6711yescharacteristic, complemented
491#1598C2×C6711yescharacteristic, complemented
492#1597C2×C6711yescharacteristic, complemented
493#1595C2×C6711yescharacteristic, complemented
494#1509C2×C6711yescharacteristic, complemented
495#1502C2×C6711yescharacteristic, complemented
496#1473C2×C6711yescharacteristic, complemented
497C67#1843411yescharacteristic, direct product factor, Sylow
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C6711yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C6711yescharacteristic
512#537C22×C6711yescharacteristic
513#534C22×C6711yescharacteristic
514#532C22×C6711yescharacteristic
515#529C22×C6711yescharacteristic
516C2×#126C22×C6711yescharacteristic
517C2×#124C22×C6711yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C6711yescharacteristic, complemented
527#450C22×C6711yescharacteristic, complemented
528#448C22×C6711yescharacteristic
529#448C22×C6711yescharacteristic
530#448C22×C6711yescharacteristic, complemented
531#447C22×C6711yescharacteristic
532#447C22×C6711yescharacteristic
533#447C22×C6711yescharacteristic, complemented
534#432C22×C6711yescharacteristic, complemented
535#431C22×C6711yescharacteristic, complemented
536#396—21no—
537#395C22×C6711yescharacteristic, complemented
538#394—21no—
539#394C22×C6711yescharacteristic, complemented
540#393C22×C6711yescharacteristic
541#392C22×C6711yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C6711yescharacteristic, complemented
545#328C22×C6711yescharacteristic, complemented
546#328C22×C6711yescharacteristic, complemented
547#327C22×C6711yescharacteristic
548#327C22×C6711yescharacteristic
549#327C22×C6711yescharacteristic
550#327C22×C6711yescharacteristic
551#327C22×C6711yescharacteristic, complemented
552#327C22×C6711yescharacteristic, complemented
553#324C22×C6711yescharacteristic, complemented
554#324C22×C6711yescharacteristic, complemented
555#323C22×C6711yescharacteristic
556#323C22×C6711yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C6711yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C6711yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C6711yescharacteristic, complemented
573#127D4×C6711yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C6711yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C6711yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C6711yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C6711yescharacteristic
628#121C23×C6711yescharacteristic
629#121C23×C6711yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C6711yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C6711yescharacteristic, complemented
645C4×D4D4×C6711yescharacteristic, complemented
646C4×D4D4×C6711yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C6711yescharacteristic
653C2×C4⋊C4D4×C6711yescharacteristic
654C2×C4⋊C4C23×C6711yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C6711yescharacteristic
664C2×C22⋊C4D4×C6711yescharacteristic
665C2×C22⋊C4C23×C6711yescharacteristic
666C2×C42—21no—
667C2×C42C23×C6711yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C6711yescharacteristic
679C22⋊C8C23×C6711yescharacteristic
680C22⋊C8C23×C6711yescharacteristic
681C22⋊C8C23×C6711yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C6711yescharacteristic
687#95C23×C6711yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C6711yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C6711yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C6711yescharacteristic
722C2×D4C2×D4×C6711yescharacteristic
723C2×D4C2×D4×C6711yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C6711yescharacteristic
736C22×C4C2×D4×C6711yescharacteristic
737C22×C4C2×D4×C6711yescharacteristic
738C22×C4C2×D4×C6711yescharacteristic
739C22×C4C2×D4×C6711yescharacteristic
740C22×C4C24×C6711yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C6711yescharacteristic
773C4⋊C4C2×D4×C6711yescharacteristic
774C4⋊C4C2×D4×C6711yescharacteristic
775C4⋊C4C2×D4×C6711yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C6711yescharacteristic
814C42C2×D4×C6711yescharacteristic
815C42C2×D4×C6711yescharacteristic
816C42C2×D4×C6711yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C6711yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C6711yescharacteristic
900C2×C4#120×C6711yescharacteristic
901C2×C4#120×C6711yescharacteristic
902C2×C4#120×C6711yescharacteristic
903C2×C4C22×D4×C6711yescharacteristic
904C2×C4C22×D4×C6711yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C6711yescharacteristic
934C22#576×C6711yescharacteristic
935C22#577×C6711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C67×#301211yescharacteristic
961C2C67×#301811yescharacteristic
962C2C67×#302711yescharacteristic
subgroupG/H
center, socleC22×C67C2×#120
commutator, Frattini, cosocleC22×C4C24×C67
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C67×#3560C2semidirect
2. C67×#3213C2semidirect
3. C67×#3211C2semidirect
4. C67×#2662C2semidirect
5. C67×#1606C2semidirect
6. C67×#1604C2semidirect
7. C67×#1603C2semidirect
8. C67×#1601C2semidirect
9. C67×#1600C2semidirect
10. C67×#1598C2semidirect
11. C67×#1597C2semidirect
12. C67×#1595C2semidirect
13. C67×#1509C2semidirect
14. C67×#1502C2semidirect
15. C67×#1473C2semidirect
35. C2×#124×C67C22semidirect
44. #451×C67C22semidirect
45. #450×C67C22semidirect
48. #448×C67C22semidirect
51. #447×C67C22semidirect
52. #432×C67C22semidirect
53. #431×C67C22semidirect
55. #395×C67C22semidirect
57. #394×C67C22semidirect
62. C4×C4⋊C4×C67C22semidirect
63. #328×C67C22semidirect
64. #328×C67C22semidirect
69. #327×C67C22semidirect
70. #327×C67C22semidirect
71. #324×C67C22semidirect
72. #324×C67C22semidirect
90. C4⋊Q8×C67D4semidirect
91. #127×C67D4semidirect
103. #125×C67D4semidirect
112. #124×C67D4semidirect
153. C4×Q8×C67D4semidirect
162. C4×D4×C67D4semidirect
163. C4×D4×C67D4semidirect
164. C4×D4×C67D4semidirect
471. #18434C67direct (N × H)
482. #3560C2×C67semidirect
483. #3213C2×C67semidirect
484. #3211C2×C67semidirect
485. #2662C2×C67semidirect
486. #1606C2×C67semidirect
487. #1604C2×C67semidirect
488. #1603C2×C67semidirect
489. #1601C2×C67semidirect
490. #1600C2×C67semidirect
491. #1598C2×C67semidirect
492. #1597C2×C67semidirect
493. #1595C2×C67semidirect
494. #1509C2×C67semidirect
495. #1502C2×C67semidirect
496. #1473C2×C67semidirect
497. C67#18434direct (N × H)
517. C2×#124C22×C67semidirect
526. #451C22×C67semidirect
527. #450C22×C67semidirect
530. #448C22×C67semidirect
533. #447C22×C67semidirect
534. #432C22×C67semidirect
535. #431C22×C67semidirect
537. #395C22×C67semidirect
539. #394C22×C67semidirect
544. C4×C4⋊C4C22×C67semidirect
545. #328C22×C67semidirect
546. #328C22×C67semidirect
551. #327C22×C67semidirect
552. #327C22×C67semidirect
553. #324C22×C67semidirect
554. #324C22×C67semidirect
572. C4⋊Q8D4×C67semidirect
573. #127D4×C67semidirect
585. #125D4×C67semidirect
594. #124D4×C67semidirect
635. C4×Q8D4×C67semidirect
644. C4×D4D4×C67semidirect
645. C4×D4D4×C67semidirect
646. C4×D4D4×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#35602
C67×#32132
C67×#32112
C67×#26622
C67×#16062
C67×#16042
C67×#16032
C67×#16012
C67×#16002
C67×#15982
C67×#15972
C67×#15952
C67×#15092
C67×#15022
C67×#14732
#1843467