Finite Group Databasebeta

← C67×#18447 #30697698

Subgroups — C67×#18447 #30697698

Order 17152.

982 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3534C211yesmaximal, characteristic
2C67×#3193C211yesmaximal, characteristic, complemented
3C67×#3190C211yesmaximal, characteristic, complemented
4C67×#2814C211yesmaximal, characteristic, complemented
5C67×#1612C211yesmaximal, characteristic, complemented
6C67×#1610C211yesmaximal, characteristic, complemented
7C67×#1609C211yesmaximal, characteristic, complemented
8C67×#1607C211yesmaximal, characteristic, complemented
9C67×#1606C211yesmaximal, characteristic, complemented
10C67×#1604C211yesmaximal, characteristic, complemented
11C67×#1603C211yesmaximal, characteristic, complemented
12C67×#1601C211yesmaximal, characteristic, complemented
13C67×#1519C211yesmaximal, characteristic, complemented
14C67×#1513C211yesmaximal, characteristic, complemented
15C67×#1468C211yesmaximal, characteristic, complemented
16#562×C67—21no—
17#560×C67—21no—
18#553×C67—21no—
19#551×C67—21no—
20#546×C67—21no—
21#546×C67—21no—
22#546×C67—21no—
23D42×C67—21no—
24#540×C67—21no—
25#539×C67—21no—
26#539×C67C2211yescharacteristic
27#538×C67—21no—
28#538×C67C2211yescharacteristic
29#537×C67C2211yescharacteristic
30#534×C67—21no—
31#534×C67C2211yescharacteristic
32#525×C67C2211yescharacteristic
33C2×#123×C67C2211yescharacteristic
34C2×C22⋊Q8×C67C2211yescharacteristic, complemented
35C2×#121×C67C2211yescharacteristic
36#485×C67—21no—
37#484×C67—21no—
38#483×C67C2211yescharacteristic, complemented
39#480×C67C2211yescharacteristic
40#480×C67C2211yescharacteristic, complemented
41#480×C67C2211yescharacteristic, complemented
42#468×C67—21no—
43#468×C67—21no—
44#467×C67—21no—
45#465×C67—21no—
46#452×C67—21no—
47#451×C67C2211yescharacteristic, complemented
48#450×C67—21no—
49#448×C67C2211yescharacteristic
50#448×C67C2211yescharacteristic, complemented
51#448×C67C2211yescharacteristic, complemented
52#407×C67C2211yescharacteristic, complemented
53C2×C22⋊C8×C67C2211yescharacteristic, complemented
54#398×C67—21no—
55#398×C67C2211yescharacteristic, complemented
56#397×C67—21no—
57#397×C67C2211yescharacteristic, complemented
58#396×C67—21no—
59#395×C67C2211yescharacteristic, complemented
60#394×C67—21no—
61#393×C67C2211yescharacteristic, complemented
62#380×C67C2211yescharacteristic, complemented
63#328×C67C2211yescharacteristic, complemented
64#328×C67C2211yescharacteristic, complemented
65#327×C67C2211yescharacteristic
66#327×C67C2211yescharacteristic
67#327×C67C2211yescharacteristic, complemented
68#327×C67C2211yescharacteristic, complemented
69#327×C67C2211yescharacteristic, complemented
70#327×C67C2211yescharacteristic, complemented
71#324×C67C2211yescharacteristic, complemented
72#324×C67C2211yescharacteristic, complemented
73#323×C67C2211yescharacteristic, complemented
74#323×C67C2211yescharacteristic, complemented
75C2×#41×C67—21no—
76C2×#41×C67D411yescharacteristic
77C22×Q8×C67C2311yescharacteristic
78C22×D4×C67—21no—
79C22×D4×C67—21no—
80C22×D4×C67—21no—
81C22×D4×C67D411yescharacteristic
82C22×D4×C67D411yescharacteristic
83C23×C4×C67C2311yescharacteristic
84C2×Q16×C67—21no—
85C2×SD16×C67—21no—
86C2×SD16×C67—21no—
87C2×SD16×C67—21no—
88C2×M16×C67—21no—
89C22×C8×C67—21no—
90#127×C67—21no—
91#126×C67—21no—
92#126×C67—21no—
93#126×C67—21no—
94#126×C67—21no—
95#125×C67—21no—
96#125×C67—21no—
97#124×C67—21no—
98#124×C67—21no—
99#124×C67—21no—
100#123×C67—21no—
101#123×C67—21no—
102#123×C67—21no—
103#123×C67—21no—
104#123×C67—21no—
105#123×C67—21no—
106#123×C67—21no—
107#123×C67—21no—
108#123×C67—21no—
109#123×C67—21no—
110#123×C67—21no—
111#123×C67—21no—
112#123×C67—21no—
113#123×C67—21no—
114C22⋊Q8×C67—21no—
115C22⋊Q8×C67—21no—
116C22⋊Q8×C67—21no—
117C22⋊Q8×C67—21no—
118C22⋊Q8×C67—21no—
119C22⋊Q8×C67—21no—
120C22⋊Q8×C67—21no—
121C22⋊Q8×C67—21no—
122C22⋊Q8×C67—21no—
123C22⋊Q8×C67D411yescharacteristic
124C22⋊Q8×C67C2311yescharacteristic
125#121×C67—21no—
126#121×C67—21no—
127#121×C67—21no—
128#121×C67—21no—
129#121×C67—21no—
130#121×C67—21no—
131#121×C67—21no—
132#121×C67—21no—
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×C67D411yescharacteristic
141#121×C67D411yescharacteristic
142#121×C67D411yescharacteristic
143#121×C67C2311yescharacteristic
144#121×C67C2311yescharacteristic
145#121×C67C2311yescharacteristic
146#120×C67—21no—
147#120×C67—21no—
148#120×C67—21no—
149#120×C67—21no—
150#120×C67—21no—
151#120×C67—21no—
152#120×C67—21no—
153#120×C67—21no—
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—
162#117×C67—21no—
163#117×C67D411yescharacteristic
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67D411yescharacteristic
169C2×C4⋊C4×C67D411yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C22⋊C4×C67—21no—
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×C67D411yescharacteristic
180C2×C22⋊C4×C67D411yescharacteristic
181C2×C22⋊C4×C67C2311yescharacteristic
182#107×C67—21no—
183#107×C67—21no—
184#107×C67—21no—
185#106×C67—21no—
186#103×C67—21no—
187#103×C67—21no—
188#103×C67—21no—
189#103×C67—21no—
190#103×C67—21no—
191#102×C67—21no—
192#102×C67—21no—
193#102×C67—21no—
194C22⋊C8×C67—21no—
195C22⋊C8×C67—21no—
196C22⋊C8×C67C2311yescharacteristic
197C22⋊C8×C67C2311yescharacteristic
198C22⋊C8×C67C2311yescharacteristic
199C22⋊C8×C67C2311yescharacteristic
200#95×C67—21no—
201#95×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
209C24×C67C2×D411yescharacteristic
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—81no—
217C2×Q8×C67C2×D411yescharacteristic
218C2×D4×C67—21no—
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—21no—
234C2×D4×C67—21no—
235C2×D4×C67—81no—
236C2×D4×C67—81no—
237C2×D4×C67—81no—
238C2×D4×C67—81no—
239C2×D4×C67—81no—
240C2×D4×C67—81no—
241C2×D4×C67—82no—
242C2×D4×C67C2×D411yescharacteristic
243C2×D4×C67C2×D411yescharacteristic
244C2×D4×C67C2×D411yescharacteristic
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×C67—21no—
254C22×C4×C67—21no—
255C22×C4×C67—21no—
256C22×C4×C67—81no—
257C22×C4×C67C2×D411yescharacteristic
258C22×C4×C67C2×D411yescharacteristic
259C22×C4×C67C2×D411yescharacteristic
260C22×C4×C67C2×D411yescharacteristic
261C22×C4×C67C2×D411yescharacteristic
262C22×C4×C67C2×D411yescharacteristic
263C22×C4×C67C2×D411yescharacteristic
264C22×C4×C67C2×D411yescharacteristic
265C22×C4×C67C2411yescharacteristic
266Q16×C67—81no—
267SD16×C67—81no—
268SD16×C67—81no—
269SD16×C67—81no—
270M16×C67—81no—
271C2×C8×C67—21no—
272C2×C8×C67—21no—
273C2×C8×C67—21no—
274C2×C8×C67—21no—
275C2×C8×C67—81no—
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—21no—
289C4⋊C4×C67—21no—
290C4⋊C4×C67—21no—
291C4⋊C4×C67—41no—
292C4⋊C4×C67—41no—
293C4⋊C4×C67—81no—
294C4⋊C4×C67—81no—
295C4⋊C4×C67—81no—
296C4⋊C4×C67C2×D411yescharacteristic
297C4⋊C4×C67C2×D411yescharacteristic
298C4⋊C4×C67C2×D411yescharacteristic
299C4⋊C4×C67C2×D411yescharacteristic
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—21no—
320C22⋊C4×C67—21no—
321C22⋊C4×C67—21no—
322C22⋊C4×C67—21no—
323C22⋊C4×C67—21no—
324C22⋊C4×C67—21no—
325C22⋊C4×C67—41no—
326C22⋊C4×C67—41no—
327C22⋊C4×C67—81no—
328C22⋊C4×C67—81no—
329C22⋊C4×C67—81no—
330C42×C67—21no—
331C42×C67—21no—
332C42×C67—21no—
333C23×C67—21no—
334C23×C67—21no—
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—42no—
344C23×C67—41no—
345C23×C67—41no—
346C23×C67—81no—
347C23×C67—81no—
348C23×C67—81no—
349C23×C67—81no—
350C23×C67—81no—
351C23×C67#12011yescharacteristic
352C23×C67#12011yescharacteristic
353C23×C67C22×D411yescharacteristic
354Q8×C67—41no—
355Q8×C67—41no—
356Q8×C67—41no—
357Q8×C67—41no—
358Q8×C67—41no—
359Q8×C67—81no—
360D4×C67—41no—
361D4×C67—41no—
362D4×C67—41no—
363D4×C67—42no—
364D4×C67—42no—
365D4×C67—41no—
366D4×C67—41no—
367D4×C67—41no—
368D4×C67—41no—
369D4×C67—41no—
370D4×C67—41no—
371D4×C67—81no—
372D4×C67—81no—
373D4×C67—81no—
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—
383C2×C4×C67—21no—
384C2×C4×C67—21no—
385C2×C4×C67—21no—
386C2×C4×C67—21no—
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—41no—
394C2×C4×C67—41no—
395C2×C4×C67—41no—
396C2×C4×C67—41no—
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—41no—
410C2×C4×C67—41no—
411C2×C4×C67—41no—
412C2×C4×C67—41no—
413C2×C4×C67—81no—
414C2×C4×C67—81no—
415C2×C4×C67—81no—
416C2×C4×C67—81no—
417C2×C4×C67—81no—
418C2×C4×C67—81no—
419C2×C4×C67—81no—
420C2×C4×C67#12011yescharacteristic
421C2×C4×C67#12011yescharacteristic
422C2×C4×C67C22×D411yescharacteristic
423C2×C4×C67C22×D411yescharacteristic
424C8×C67—41no—
425C8×C67—41no—
426C8×C67—41no—
427C8×C67—41no—
428C22×C67—21no—
429C22×C67—21no—
430C22×C67—21no—
431C22×C67—21no—
432C22×C67—21no—
433C22×C67—21no—
434C22×C67—21no—
435C22×C67—21no—
436C22×C67—41no—
437C22×C67—41no—
438C22×C67—41no—
439C22×C67—41no—
440C22×C67—41no—
441C22×C67—41no—
442C22×C67—41no—
443C22×C67—41no—
444C22×C67—41no—
445C22×C67—41no—
446C22×C67—41no—
447C22×C67—41no—
448C22×C67—81no—
449C22×C67—81no—
450C22×C67—81no—
451C22×C67—81no—
452C22×C67—162no—
453C22×C67—162no—
454C22×C67C2×#12011yescharacteristic
455C22×C67#57611yescharacteristic
456C22×C67#57711yescharacteristic
457C4×C67—21no—
458C4×C67—21no—
459C4×C67—21no—
460C4×C67—21no—
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—
471C4×C67—81no—
472C4×C67—81no—
473#18447C6711yesmaximal, characteristic, direct product factor, Sylow
474C2×C67—21no—
475C2×C67—21no—
476C2×C67—41no—
477C2×C67—41no—
478C2×C67—81no—
479C2×C67—81no—
480C2×C67—81no—
481C2×C67—81no—
482C2×C67#301211yescharacteristic
483C2×C67#302211yescharacteristic
484C2×C67#302611yescharacteristic
485#3534C2×C6711yescharacteristic
486#3193C2×C6711yescharacteristic, complemented
487#3190C2×C6711yescharacteristic, complemented
488#2814C2×C6711yescharacteristic, complemented
489#1612C2×C6711yescharacteristic, complemented
490#1610C2×C6711yescharacteristic, complemented
491#1609C2×C6711yescharacteristic, complemented
492#1607C2×C6711yescharacteristic, complemented
493#1606C2×C6711yescharacteristic, complemented
494#1604C2×C6711yescharacteristic, complemented
495#1603C2×C6711yescharacteristic, complemented
496#1601C2×C6711yescharacteristic, complemented
497#1519C2×C6711yescharacteristic, complemented
498#1513C2×C6711yescharacteristic, complemented
499#1468C2×C6711yescharacteristic, complemented
500C67#1844711yescharacteristic, direct product factor, Sylow
501#562—21no—
502#560—21no—
503#553—21no—
504#551—21no—
505#546—21no—
506#546—21no—
507#546—21no—
508D42—21no—
509#540—21no—
510#539—21no—
511#539C22×C6711yescharacteristic
512#538—21no—
513#538C22×C6711yescharacteristic
514#537C22×C6711yescharacteristic
515#534—21no—
516#534C22×C6711yescharacteristic
517#525C22×C6711yescharacteristic
518C2×#123C22×C6711yescharacteristic
519C2×C22⋊Q8C22×C6711yescharacteristic, complemented
520C2×#121C22×C6711yescharacteristic
521#485—21no—
522#484—21no—
523#483C22×C6711yescharacteristic, complemented
524#480C22×C6711yescharacteristic
525#480C22×C6711yescharacteristic, complemented
526#480C22×C6711yescharacteristic, complemented
527#468—21no—
528#468—21no—
529#467—21no—
530#465—21no—
531#452—21no—
532#451C22×C6711yescharacteristic, complemented
533#450—21no—
534#448C22×C6711yescharacteristic
535#448C22×C6711yescharacteristic, complemented
536#448C22×C6711yescharacteristic, complemented
537#407C22×C6711yescharacteristic, complemented
538C2×C22⋊C8C22×C6711yescharacteristic, complemented
539#398—21no—
540#398C22×C6711yescharacteristic, complemented
541#397—21no—
542#397C22×C6711yescharacteristic, complemented
543#396—21no—
544#395C22×C6711yescharacteristic, complemented
545#394—21no—
546#393C22×C6711yescharacteristic, complemented
547#380C22×C6711yescharacteristic, complemented
548#328C22×C6711yescharacteristic, complemented
549#328C22×C6711yescharacteristic, complemented
550#327C22×C6711yescharacteristic
551#327C22×C6711yescharacteristic
552#327C22×C6711yescharacteristic, complemented
553#327C22×C6711yescharacteristic, complemented
554#327C22×C6711yescharacteristic, complemented
555#327C22×C6711yescharacteristic, complemented
556#324C22×C6711yescharacteristic, complemented
557#324C22×C6711yescharacteristic, complemented
558#323C22×C6711yescharacteristic, complemented
559#323C22×C6711yescharacteristic, complemented
560C2×#41—21no—
561C2×#41D4×C6711yescharacteristic
562C22×Q8C23×C6711yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C6711yescharacteristic
567C22×D4D4×C6711yescharacteristic
568C23×C4C23×C6711yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C6711yescharacteristic
609C22⋊Q8C23×C6711yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
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#121D4×C6711yescharacteristic
626#121D4×C6711yescharacteristic
627#121D4×C6711yescharacteristic
628#121C23×C6711yescharacteristic
629#121C23×C6711yescharacteristic
630#121C23×C6711yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C6711yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4D4×C6711yescharacteristic
654C2×C4⋊C4D4×C6711yescharacteristic
655C2×C4⋊C4C23×C6711yescharacteristic
656C2×C4⋊C4C23×C6711yescharacteristic
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⋊C4—21no—
664C2×C22⋊C4D4×C6711yescharacteristic
665C2×C22⋊C4D4×C6711yescharacteristic
666C2×C22⋊C4C23×C6711yescharacteristic
667#107—21no—
668#107—21no—
669#107—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C6711yescharacteristic
682C22⋊C8C23×C6711yescharacteristic
683C22⋊C8C23×C6711yescharacteristic
684C22⋊C8C23×C6711yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C6711yescharacteristic
690#95C23×C6711yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C6711yescharacteristic
694C24C2×D4×C6711yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C6711yescharacteristic
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—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C6711yescharacteristic
728C2×D4C2×D4×C6711yescharacteristic
729C2×D4C2×D4×C6711yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C6711yescharacteristic
743C22×C4C2×D4×C6711yescharacteristic
744C22×C4C2×D4×C6711yescharacteristic
745C22×C4C2×D4×C6711yescharacteristic
746C22×C4C2×D4×C6711yescharacteristic
747C22×C4C2×D4×C6711yescharacteristic
748C22×C4C2×D4×C6711yescharacteristic
749C22×C4C2×D4×C6711yescharacteristic
750C22×C4C24×C6711yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
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—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—81no—
779C4⋊C4—81no—
780C4⋊C4—81no—
781C4⋊C4C2×D4×C6711yescharacteristic
782C4⋊C4C2×D4×C6711yescharacteristic
783C4⋊C4C2×D4×C6711yescharacteristic
784C4⋊C4C2×D4×C6711yescharacteristic
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—21no—
802C22⋊C4—21no—
803C22⋊C4—21no—
804C22⋊C4—21no—
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—41no—
811C22⋊C4—41no—
812C22⋊C4—81no—
813C22⋊C4—81no—
814C22⋊C4—81no—
815C42—21no—
816C42—21no—
817C42—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C6711yescharacteristic
837C23#120×C6711yescharacteristic
838C23C22×D4×C6711yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
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—81no—
866D4—81no—
867D4—81no—
868C2×C4—21no—
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—41no—
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—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C6711yescharacteristic
906C2×C4#120×C6711yescharacteristic
907C2×C4C22×D4×C6711yescharacteristic
908C2×C4C22×D4×C6711yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C6711yescharacteristic
940C22#576×C6711yescharacteristic
941C22#577×C6711yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2C67×#301211yescharacteristic
967C2C67×#302211yescharacteristic
968C2C67×#302611yescharacteristic
subgroupG/H
center, socleC22×C67C2×#120
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC67×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
2. C67×#3193C2semidirect
3. C67×#3190C2semidirect
4. C67×#2814C2semidirect
5. C67×#1612C2semidirect
6. C67×#1610C2semidirect
7. C67×#1609C2semidirect
8. C67×#1607C2semidirect
9. C67×#1606C2semidirect
10. C67×#1604C2semidirect
11. C67×#1603C2semidirect
12. C67×#1601C2semidirect
13. C67×#1519C2semidirect
14. C67×#1513C2semidirect
15. C67×#1468C2semidirect
34. C2×C22⋊Q8×C67C22semidirect
38. #483×C67C22semidirect
40. #480×C67C22semidirect
41. #480×C67C22semidirect
47. #451×C67C22semidirect
50. #448×C67C22semidirect
51. #448×C67C22semidirect
52. #407×C67C22semidirect
53. C2×C22⋊C8×C67C22semidirect
55. #398×C67C22semidirect
57. #397×C67C22semidirect
59. #395×C67C22semidirect
61. #393×C67C22semidirect
62. #380×C67C22semidirect
63. #328×C67C22semidirect
64. #328×C67C22semidirect
67. #327×C67C22semidirect
68. #327×C67C22semidirect
69. #327×C67C22semidirect
70. #327×C67C22semidirect
71. #324×C67C22semidirect
72. #324×C67C22semidirect
73. #323×C67C22semidirect
74. #323×C67C22semidirect
473. #18447C67direct (N × H)
486. #3193C2×C67semidirect
487. #3190C2×C67semidirect
488. #2814C2×C67semidirect
489. #1612C2×C67semidirect
490. #1610C2×C67semidirect
491. #1609C2×C67semidirect
492. #1607C2×C67semidirect
493. #1606C2×C67semidirect
494. #1604C2×C67semidirect
495. #1603C2×C67semidirect
496. #1601C2×C67semidirect
497. #1519C2×C67semidirect
498. #1513C2×C67semidirect
499. #1468C2×C67semidirect
500. C67#18447direct (N × H)
519. C2×C22⋊Q8C22×C67semidirect
523. #483C22×C67semidirect
525. #480C22×C67semidirect
526. #480C22×C67semidirect
532. #451C22×C67semidirect
535. #448C22×C67semidirect
536. #448C22×C67semidirect
537. #407C22×C67semidirect
538. C2×C22⋊C8C22×C67semidirect
540. #398C22×C67semidirect
542. #397C22×C67semidirect
544. #395C22×C67semidirect
546. #393C22×C67semidirect
547. #380C22×C67semidirect
548. #328C22×C67semidirect
549. #328C22×C67semidirect
552. #327C22×C67semidirect
553. #327C22×C67semidirect
554. #327C22×C67semidirect
555. #327C22×C67semidirect
556. #324C22×C67semidirect
557. #324C22×C67semidirect
558. #323C22×C67semidirect
559. #323C22×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#35342
C67×#31932
C67×#31902
C67×#28142
C67×#16122
C67×#16102
C67×#16092
C67×#16072
C67×#16062
C67×#16042
C67×#16032
C67×#16012
C67×#15192
C67×#15132
C67×#14682
#1844767